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Calcium Phosphate Prenucleation Complexes in Water by Means of ab Initio Molecular Dynamics Simulations
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† Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
‡ School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff, CF10 3XQ, United Kingdom
*E-mail: [email protected]
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Crystal Growth & Design

Cite this: Cryst. Growth Des. 2016, 16, 6, 3353–3358
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https://doi.org/10.1021/acs.cgd.6b00327
Published April 13, 2016

Copyright © 2016 American Chemical Society. This publication is licensed under CC-BY.

Abstract

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The nucleation of calcium phosphates, the main inorganic component of bone and tooth tissues, is thought to proceed by aggregation of prenucleation clusters recently identified as calcium triphosphate complexes. We have performed ab initio molecular dynamics simulations to elucidate their structures and stabilities in aqueous solution. We find the calcium to be seven-coordinated by two water molecules, two bidentate phosphates, and one monodentate phosphate. Free energy results obtained using umbrella sampling simulations show that the complex with a Ca/P ratio of 1:3 is the most energetically favored and more thermodynamically stable than the free ions.

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Synopsis

Calcium phosphates nucleate by aggregating calcium triphosphate entities. Our molecular dynamics simulations, together with the umbrella sampling technique, show that the structure of these complexes is Ca(η2-HPO42−)2(η1-HPO42−)(H2O)2, and they are more thermodynamically stable than the free ions.

Introduction

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Calcium phosphate (CaP) is the major inorganic component of biological hard tissues, (e.g., bone and teeth), where it is mainly present in the form of hydroxyapatite (nominally, Ca10(OH)2(PO4)6). However, CaP is also responsible for pathological crystallization, leading to several common diseases including atherosclerosis, dental caries, osteoporosis, and kidney stones. (1) Hydroxyapatite (2) originates from an amorphous calcium phosphate (ACP) precursor in a process of dissolution and reprecipitation. (3) In the 1970s, Posner and Betts proposed that structural units of the form Ca9(PO4)6 would aggregate randomly, with the intercluster space filled with water, into larger spherical particles of ACP. (4) More recently, a cluster-growth model for the formation of ACP was proposed, (5) and aggregating clusters were found to be present in body fluids even before nucleation. (6) XANES and XRD experiments of the early stages of CaP crystallization have suggested that an idealized cluster with the formula Ca9(PO4)6(H2O)30 may act as the structural unit of ACP, (7) whereas the most abundant clusters detected in solution at the early stage of nucleation have been reported to be of the form Ca(η2–PO43–)2L2 (L = H2O or η1–PO43–, where η1 and η2 stand for monodentate and bidentate binding of the phosphate groups). (8) Habraken et al. (9) showed that the prenucleation complexes (PNCs), aggregating in solution to form polymeric structures, have the formula [Ca(η2–HPO4)3]4–. Interestingly, a Posner’s cluster can be seen as two deprotonated PNCs in which all negative charges are compensated by complexing calcium ions. To explain the formation of ACP at the supersaturations used in their experiment, the PNCs were proposed to have an excess free energy over that of free ions, which dramatically reduces the nucleation barrier. (10)
Despite the CaP PNCs representing a key factor for understanding ACP formation, because of the difficulties in accessing experimental data at such small scale, there is no general consensus about their structures. Here, we therefore present a theoretical investigation based on ab initio molecular dynamics (MD) simulations, which suggests that the resulting PNC geometry differs from the existing models in the literature. In addition, we provide an estimate for the free energy cost required to decompose a PNC into isolated free ions, from which we deduce that calcium triphosphate PNCs are more stable entities than other Ca-to-P ratios.

Theoretical Methods

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The simulations have been carried out using the QUICKSTEP program of CP2K, (11-16) which solves the Kohn–Sham equations of density functional theory (DFT) by combining a Gaussian basis set for the wave functions with an auxiliary plane wave basis set for the density. We have used Goedecker–Teter–Hutter (GTH)-type pseudopotentials (17-19) together with the PBE functional. (20)
It is known that gradient-based functionals give an overstructured water system with a lower diffusivity compared to those of experiments. (21, 22) Although hybrid functionals can improve the structural and dynamic properties of water, (23) their application in this already highly compute-intensive work would make the simulations beyond reasonable high performance computing capabilities. We note that the adoption of higher simulation temperatures or the inclusion of empirical van der Waals corrections to PBE can lead to a softening of the structure and to higher mobilities. (21, 24) However, because it is not clear how they would affect the free energy barriers investigated, we have not pursued these routes in this work.
The [Ca(HPO4)3]4– PNC was optimized in the gas phase before the resulting structure was solvated with 93 water molecules using the Visual Molecular Dynamics (VMD) solvation tool (25) in a cell of ∼15 × 15 × 15 Å3. Two calcium ions were added to neutralize the −4 charge of the complex. The system was first equilibrated in an NPT ensemble for 57.5 ps at a constant temperature of 300 K and 1 bar of pressure to regulate the density of water and then for a further 60 ps in an NVT ensemble (T = 300 K). The time step was set to 0.5 fs.
The stability of the calcium triphosphate complex in water has been evaluated through the analysis of free energy profiles obtained with the umbrella sampling (US) technique. (26, 27) In this method, a bias potential is introduced to ensure efficient sampling along reaction coordinate ξ. A series of MD simulations is performed. In each, the system is restrained at a specific value of the reaction coordinate (“target”) with the help of the bias potential. The value of the reaction coordinate oscillates around the target, producing a Gaussian-like distribution called the US window. The US windows, centered at increasing values of the target, are then combined with the weighted histogram analysis method (WHAM). (28-31) The potential used in this work was harmonic with strength k(1)where ξiref is the target of each window i. The system was equilibrated at each target value for 7.5 ps, and only the last 5 ps were considered for the WHAM analysis. In some cases, more than 2.5 ps were required for equilibrating the system at the new target. A value of 100 kcal mol–1 Å–2 was chosen for k in most of the US windows. Around the minima, lower values of k were sufficient to keep the reaction coordinate oscillating around the target, whereas in the steepest regions of free energy, k was increased up to 150 kcal mol–1 Å–2.

Results and Discussion

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Prenucleation Complex in Water

Figure 1(I) shows the structure obtained after the gas phase optimization. Three bidentate phosphate groups are present, giving a calcium coordination number of six. A similar structure with three bidentate phosphate groups, and ligating one water molecule, has been found by both ab initio calculations with a number of explicit water molecules (9) and classical MD simulations in water. (32) However, during our NVT dynamics starting from the PNC depicted in Figure 1(I), two water molecules entered the first coordination sphere and during the simulation never exchanged with other water molecules. For almost 90% of the simulation time, the PNC remained in a Ca (η2–HPO42–)2(η1–HPO42–)(H2O)2 distorted pentagonal bipyramidal geometry (Figure 1(II)). A similar arrangement of the calcium ligands has been found during classical MD for several types of calcium–phosphate ion pairs. (32) Here, two η2– HPO42– groups and one water molecule occupy the equatorial positions, whereas the η1–HPO42– oxygen and a second water molecule occupy the axial sites. As the two equatorial groups could undergo a (η2–HPO42–) to (η1–HPO42–) transition, we observed a calcium coordination of six for approximately 10% of the simulation time (Figure 1(III)). The relative appearances of the two complexes are described by the time evolution of the six Ca–Oph distances during the simulation (Figure 2).

Figure 1

Figure 1. Structures obtained in the gas phase (I) and in water (II, III, IV). The dotted lines represent hydrogen bonds. Color key: Ca–cyan, P–green, O–red, H–white.

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Figure 2

Figure 2. Time evolution of the Ca–Oph distances during the NVT run. The red lines refer to the oxygen atoms of the phosphate group at the axial site, and the black and blue lines refer to those of the two groups at the equatorial sites. The dashed horizontal line highlights the bond distance cutoff of 3.35 Å corresponding to the minimum in the Ca–Oph radial distribution function. One attempt to form an eight-coordinated structure is evidenced by the black arrow.

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We show in Figure 3 the radial distribution functions g(r) obtained during the entire 60 ps of NVT trajectory for the pairings Ca–O, Ca–P, P–O, O–O, and P–P. The first maxima (corresponding to the first coordination sphere of Ca2+) of the Ca–Oph and Ca–Owat pairings are located at 2.45 and 2.55 Å, respectively. This result is in line with the findings of Almora-Barrios and de Leeuw for the nucleation of hydroxyapatite at a collagen template by means of classical MD. (32) They reported Ca–Oph and Ca–Owat distances for various calcium phosphate complexes in water of 2.2–2.6 and 2.4 Å, respectively. Slightly shorter Ca–O distances (Ca–Owat, 2.35 Å; Ca–Obicarb, 2.36 Å; and Ca–Ocarb, 2.38 Å) have been predicted by Car–Parrinello simulations of the calcium ion, calcium bicarbonate, and calcium carbonate complexes in water, (33) which could be attributed to the lower coordination of calcium (six) or to the less pronounced steric effect of the (bi)carbonate ligand. The Ca–P g(r) shows two maxima signaling bidentate and monodentate phosphate ligands, whose Ca–P distances are 3.15 and 3.65 Å, respectively. The contributions to the first coordination sphere of the phosphorus atom are given by the four oxygens directly ligated, whereas the water oxygens are relegated to the second coordination sphere, as shown by the P–O g(r). The Ca–O, P–O, and P–P distances are in good agreement with the ab initio calculations of the structure proposed by Habraken et al., whereas the Ca–P and O–O ones are approximately 0.1 Å larger than their upper limits. (9) In general, the computational data tend to overestimate the distances for Ca–O, P–O, and P–P with respect to the experiments on ACP, (4) but the latter were obtained in the solid phase without solvent effects. Our results are summarized in Table S1 of the Supporting Information, where the coordination numbers, obtained by integrating g(r) between the relevant minima, are consistent with the distorted pentagonal bipyramidal geometry described above.

Figure 3

Figure 3. Radial distribution functions for the Ca–O, Ca–P, P–O, O–O, and P–P pairings.

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Stability of Secondary Configurations

To better evaluate the stability of the six-coordinated PNC (Figure 1(III)) present during approximately 10% of the MD trajectory, we have calculated the free energy profile for the Ca(η2–HPO42–)2(η1–HPO42–) to Ca(η2–HPO42–)(η1–HPO42–)2 transition. We show it in the upper panel of Figure 4, where the reaction coordinate is given by the distance between the calcium and a phosphorus from an equatorial group. The minimum of the six-coordinated structure (Figure 1(III)) is only 1.9 kcal/mol higher in energy than that of the seven-coordinated structure (Figure 1(II)). An additional 5 ps simulation with the reaction coordinate restrained at the target, corresponding to the six-coordinated minimum, revealed no significant coordination changes, confirming that a Ca(η2–HPO42–)(η1–HPO42–)2 PNC can exist in aqueous solution.

Figure 4

Figure 4. Free energy profiles obtained when moving away one of the bidentate groups from calcium (upper panel) and pulling the monodentate group (lower panel) toward calcium. The minima are labeled consistently with the structures in Figure 1. Color key: Ca-cyan, P-green, O-red, H-white.

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During the entire 60 ps NVT run, two water molecules were tightly ligated to the PNC, whereas we observed a number of attempts by the three phosphate groups to bind simultaneously to calcium in a bidentate mode (Figure 2). To shed light on the possibility of formation of a Ca(η2–HPO42–)3 PNC, we have studied the free energy profile corresponding to the monodentate-bidentate transition of the central phosphate group. We present it in the lower panel of Figure 4, where the reaction coordinate is the distance between the central calcium and the phosphorus of the monodentate phosphate. We observe that the structure found after equilibration (Figure 1(II)) is slightly more stable than the structure at shorter Ca–P distances (Figure 1(IV)) in which the central phosphate group is bidentate. However, during the US, we observed the η2–HPO42– to η1–HPO42– transition of an equatorial phosphate, which prevented the formation of a Ca(η2–HPO42–)3 PNC and led to the formation of a Ca(η2–HPO42–)2(η1–HPO42–) cluster. This behavior can be explained by considering the bridging between the phosphate groups: in both minima, the central phosphate is linked to an equatorial phosphate via a direct hydrogen bond and a bridging water and to the other equatorial group via a second bridging water (types (g) and (h), respectively, in Figure S1). For retaining the bridging structures, the lateral bidentate phosphate in the structure in Figure 1(II) had to become monodentate in the structure in Figure 1(IV).
Other than water bridging between phosphate groups, the constant presence of one monodentate ligand can be explained in terms of charge transfer: when the 2+ cation is surrounded by three 2– anions, its partial positive charge is decreased, and therefore, there is a loss of charge–charge interaction with the ligands. (34) The weakening of metal–phosphate interactions increases the importance of other factors, such as the effect of hydrogen bonds with water, which favors the monodentate binding mode, as it maximizes the interaction with the first solvation sphere.
The Ca(η2–HPO42–)2(η1–HPO42–)(H2O)2 geometry emerging from our MD simulations differs from that suggested by Habraken et al. (9) in the substitution of a (η2–HPO42–) with (η1–HPO42–)H2O. Zhang et al. have been able to detect the presence of CaP PNCs at the early stage of ACP formation in solution. (8) On the basis of calcium K-edge XANES spectrum features, they have speculated the presence of Ca(η2–HPO42–)2L2 PNCs, where L is either a η1–HPO42– or a water molecule with calcium in a coordination of six. However, we note that a seven-coordinated calcium remains consistent with these experimental findings, as coordinations of six and seven give similar XANES edge positions. (35)

Estimation of the Stability of the Complex in Water

Next, we have evaluated the stability of the PNC by deriving the free energy profile for the dissociation of the η1–HPO42– from the central calcium ion(2)We set the reaction coordinate to be the distance between the central calcium ion and the phosphorus atom of the η1–HPO42– detaching group. Starting from the equilibrated structure (Figure 1(II)), a series of US simulations were performed with increasing target distances up to the complete removal of the phosphate from the Ca2+ first coordination sphere. The free energy profile depicted in the upper panel of Figure 5 confirms that the PNC is very stable in water, as the energetic cost for moving the η1–HPO42– to the second coordination sphere of calcium is approximately 22 kcal/mol. The calcium biphosphate complex in Figure 6(V) appears to be in a shallow minimum located at a distance of 6.4 Å. Because of a third water molecule replacing the η1–HPO42–, the calcium coordination is still seven, and the complex is in a Ca(η2–HPO42–)2(H2O)3 arrangement. The detached HPO42– group interacts with the calcium biphosphate via two bridging water molecules (type (g) in Figure S1) and a direct hydrogen-bond, as shown in Figure 6 (V).

Figure 5

Figure 5. Free energy profiles for the breakdown of the PNC into free ions. Each graph corresponds to the detachment of a phosphate group. The minima are labeled consistently with the structures in Figures 1 and 6. Color key: Ca–cyan, P–green, O–red, H–white.

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Figure 6

Figure 6. Metastable structures obtained during the dissociation of the PNC into free ions. Color key: Ca–cyan, P–green, O–red, H–white. The dotted lines represent hydrogen bonds.

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The significant increase in free energy for the dissociation process described above suggests that the PNC is stable with respect to the isolated free ions. To verify this hypothesis, we continued the fragmentation process, removing a second phosphate group from the calcium according to the reaction(3)We have plotted the corresponding free energy profile in the middle panel of Figure 5. Here, it is possible to observe three minima: the first, at a Ca–P distance of 3.2 Å, corresponds to the starting Ca(η2–HPO42–)2; the second at ∼3.6 Å is Ca(η2–HPO42–)(η1–HPO42–), and the third corresponds to Ca(η2–HPO42–) with (η1–HPO42–) not in the first coordination sphere of calcium. The free energy barrier is ∼9 kcal/mol, and the free energy difference between the Ca(η2–HPO42–)(η1–HPO42–) and Ca(η2–HPO42–)2 is 2.6 kcal/mol, a value slightly higher than that of the transition in the central phosphate (see Figure 4, lower panel). Furthermore, the position of the minimum for the dissociated structure (5.1 Å) is lower than that in the upper panel of Figure 5 (6.4 Å), where two bulky ligands form hydrogen bonds and water bridges with the leaving group. These interactions oppose the separation of the leaving ion and are reflected in the shape of the free energy curve. Only after breaking the bridges with one of the equatorial phosphates does the curve smooth down to a shallow minimum. The structure with the calcium ion coordinating one bidentate phosphate and five water molecules (Figure 6(VI)) has already been found during classical molecular dynamics simulations of calcium phosphate complexes. (32) The authors reported a similar arrangement of the ligands and distances Ca–Oph of 2.5 Å. We found that, for Ca(η2–HPO42–)(H2O)5, the Ca–Oph distances oscillate between 2.45 and 2.55 Å, with the distance between the calcium and the oxygen atom carrying the proton shifted toward the upper value of the range.
Finally, starting from the minimum in Figure 6(VI), we have detached the last phosphate group, obtaining the isolated ions in solution shown in Figure 6 (VIIa and VIIb)(4)The corresponding free energy profile is illustrated in the lower panel of Figure 5. Similar to the profile in the middle panel of Figure 5, its main features are a minimum at ∼3.2 Å (bidentate binding mode), a flattening at ∼3.6 Å (monodentate binding mode), and a third depression corresponding to the egress of the phosphate group from the first coordination sphere of the calcium. The free energy barrier is ∼10 kcal/mol, whereas the free energy difference between the monodentate and bidentate binding modes is 2.7 kcal/mol. We note that all the positions and energy differences of the minima involved in reactions 3 and 4 are very similar. The isolated calcium ion shown in Figure 6(VIIa) is six-coordinated, and the structure is a distorted octahedron. Di Tommaso and de Leeuw reported an equivalent structure during Car–Parrinello molecular dynamics simulations of calcium carbonates in water. (33) Despite the similarity, we found a Ca–Owat average distance of 2.45 Å, 0.1 Å longer than theirs, which presumably is due to the different choice of pseudopotentials.
Taking into account the three free energy profiles in Figure 5, we can deduce that each process of a phosphate leaving the calcium coordination shell has an important energetic cost (≥9 kcal/mol) and that the complex is more stable than the free ions. It is worth noting that the energetic expense of the detachment of the first phosphate group was approximately two times more costly than the subsequent detachments, suggesting that calcium triphosphate complexes are more stable entities than other Ca/P ratios, in agreement with experimental data. (9)

Conclusions

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We have studied the structures and stabilities of [Ca(HPO4)3]4– prenucleation complexes in water by means of ab initio molecular dynamics simulations and umbrella sampling techniques. We have found that, in the most stable configuration, one phosphate group ligated to the calcium is monodentate, whereas two are bidentate and placed at opposite sides of the calcium. In addition, two water molecules also bind the calcium ion, which prefers to stay in a (η2–HPO42–)2(η1–HPO42–)(H2O)2 arrangement. The calcium triphosphate PNC is more stable than the isolated ions, as evidenced by the free energy profiles simulating the dissociation process. Moreover, our data suggest that a Ca/P ratio of 1:3 is thermodynamically favored over other ratios, supporting the experimental findings in the literature. (9)
Because nucleation processes take place on a molecular scale, a future theoretical investigation of the aggregation of the clusters would be useful to further support experimental findings, and the interaction of the PNCs with positive counterions (Na+ or Ca2+) may improve our understanding of the aggregation of these negatively charged entities. We intend to examine these issues in future work.

Supporting Information

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00327.

  • Hydrogen bonding between phosphate groups and water molecules observed during the molecular dynamics and coordination numbers and distances for the first coordination sphere of Ca–O, Ca–P, P–O, O–O, and P–P (PDF)

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Author Information

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  • Corresponding Author
    • Nora H. de Leeuw - School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff, CF10 3XQ, United Kingdom;  Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom;  Email: [email protected]
  • Authors
    • Giulia Mancardi - Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
    • Umberto Terranova - School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff, CF10 3XQ, United Kingdom;  Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom
  • Notes
    The authors declare no competing financial interest.

Acknowledgment

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We thank EPSRC for funding of a studentship. This work has used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk) via our membership with the UK’s HEC Materials Chemistry Consortium, which is funded by EPSRC (EP/L000202), and the computational facilities of the Advanced Research Computing @ Cardiff (ARCCA) Division, Cardiff University.

References

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    Amorphous Ca phosphate often forms as a precursor phase in a soln. at sufficiently high supersatn. and pH, and then transforms to the thermodynamically stable hydroxyapatite. The chem. compn., structure, and property of the amorphous phase are dependent on the structure of its composing clusters. Based on the results from the measurements of in situ Ca K-edge x-ray near-edge structure and ex situ X-ray diffraction, as well as the concomitant pH change in the reaction process, here the authors propose an improved model for the structure of Posner's cluster and identify the three types of reactions that give amorphous Ca phosphate and its subsequent transition to cryst. hydroxyapatite.
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    Zhang, Q.; Jiang, Y.; Gou, B. D.; Huang, J.; Gao, Y. X.; Zhao, J. T.; Zheng, L.; Zhao, Y. D.; Zhang, T. L.; Wang, K. In Situ Detection of Calcium Phosphate Clusters in Solution and Wet Amorphous Phase by Synchrotron X-ray Absorption Near-Edge Spectroscopy at Calcium K-Edge Cryst. Growth Des. 2015, 15, 2204– 2210 DOI: 10.1021/cg5018505
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    8
    In Situ Detection of Calcium Phosphate Clusters in Solution and Wet Amorphous Phase by Synchrotron X-ray Absorption Near-Edge Spectroscopy at Calcium K-Edge
    Zhang, Qun; Jiang, Yun; Gou, Bao-Di; Huang, Jian; Gao, Yu-Xi; Zhao, Jia-Ting; Zheng, Lei; Zhao, Yi-Dong; Zhang, Tian-Lan; Wang, Kui
    Crystal Growth & Design (2015), 15 (5), 2204-2210CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
    Ca phosphate clusters are present in both aq. solns. and an amorphous phase during crystn. It is a challenging task to acquire the structural information on such clusters, owing to their small size, chem. lability, and inaccessibility to most detection techniques. The authors demonstrate the feasibility of detecting such clusters in situ by synchrotron x-ray absorption near-edge spectroscopy at Ca K-edge, a technique that is sensitive to the short-range order in Ca coordination sphere. At the initial stage of crystn., the most abundant clusters are detected to be Ca(η2-PO43-)2L2 (L = H2O or η1-PO43-) in soln. More reactive clusters engage in the development of an amorphous phase via growing and fusing. The amorphous phase exhibits a dual character in its short-range order: Some of its clusters are similar to hydrated Ca ions, and some others to those in cryst. hydroxyapatite. When the amorphous dissolves, the detected unit is mainly Ca(η2-PO43-)(H2O)4 in the released soln. clusters. While these findings provide a basis for a better understanding and rational control of Ca phosphate crystn. at mol. level, the exptl. technique in assessing wet samples adopted in this work might be applicable to the crystn. studies of other materials as well.
  9. 9
    Habraken, W. J. E. M.; Tao, J.; Brylka, L. J.; Friedrich, H.; Bertinetti, L.; Schenk, A. S.; Verch, A.; Dmitrovic, V.; Bomans, P. H. H.; Frederik, P. M.; Laven, J.; van der Schoot, P.; Aichmayer, B.; de With, G.; DeYoreo, J. J.; Sommerdijk, N. a. J. M. Ion-association complexes unite classical and non-classical theories for the biomimetic nucleation of calcium phosphate Nat. Commun. 2013, 4, 1507 DOI: 10.1038/ncomms2490
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    9
    Ion-association complexes unite classical and non-classical theories for the biomimetic nucleation of calcium phosphate
    Habraken Wouter J E M; Tao Jinhui; Brylka Laura J; Friedrich Heiner; Bertinetti Luca; Schenk Anna S; Verch Andreas; Dmitrovic Vladimir; Bomans Paul H H; Frederik Peter M; Laven Jozua; van der Schoot Paul; Aichmayer Barbara; de With Gijsbertus; DeYoreo James J; Sommerdijk Nico A J M
    Nature communications (2013), 4 (), 1507 ISSN:.
    Despite its importance in many industrial, geological and biological processes, the mechanism of crystallization from supersaturated solutions remains a matter of debate. Recent discoveries show that in many solution systems nanometre-sized structural units are already present before nucleation. Still little is known about the structure and role of these so-called pre-nucleation clusters. Here we present a combination of in situ investigations, which show that for the crystallization of calcium phosphate these nanometre-sized units are in fact calcium triphosphate complexes. Under conditions in which apatite forms from an amorphous calcium phosphate precursor, these complexes aggregate and take up an extra calcium ion to form amorphous calcium phosphate, which is a fractal of Ca(2)(HPO(4))(3)(2-) clusters. The calcium triphosphate complex also forms the basis of the crystal structure of octacalcium phosphate and apatite. Finally, we demonstrate how the existence of these complexes lowers the energy barrier to nucleation and unites classical and non-classical nucleation theories.
  10. 10
    Hu, Q.; Nielsen, M. H.; Freeman, C. L.; Hamm, L. M.; Tao, J.; Lee, J. R. I.; Han, T. Y. J.; Becker, U.; Harding, J. H.; Dove, P. M.; De Yoreo, J. J. The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways Faraday Discuss. 2012, 159, 509 DOI: 10.1039/c2fd20124k
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    10
    The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways
    Hu, Q.; Nielsen, M. H.; Freeman, C. L.; Hamm, L. M.; Tao, J.; Lee, J. R. I.; Han, T. Y. J.; Becker, U.; Harding, J. H.; Dove, P. M.; De Yoreo, J. J.
    Faraday Discussions (2012), 159 (), 509-523CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
    Nucleation in the natural world often occurs in the presence of org. interfaces. In mineralized tissues, a range of macromol. matrixes are found in contact with inorg. phases and are believed to direct mineral formation. In geochem. settings, mineral surfaces, which are often covered with org. or biol. films, surround the vol. within which nucleation occurs. In the classical picture of nucleation, the presence of such interfaces is expected to have a profound effect on nucleation rates, simply because they can reduce the interfacial free energy, which controls the height of the thermodn. barrier to nucleation of the solid phase. However, the recent discovery of a nearly monodisperse population of calcium carbonate clusters-so called pre-nucleation clusters-and the many observations of amorphous precursor phases have called into question the applicability of classical descriptions. Here we use in situ observations of nucleation on organothiol self-assembled monolayers (SAMs) to explore the energetics and pathways of calcite nucleation at org. interfaces. We find that carboxyl SAM-directed nucleation is described well in purely classical terms through a redn. in the thermodn. barrier due to decreased interfacial free energy. Moreover, the differences in nucleation kinetics on odd and even chain-length carboxyl SAMs are attributable to relative differences in these energies. These differences arise from varying degrees of SAM order related to oxygen-oxygen interactions between SAM headgroups. In addn., amorphous particles formed prior to or during crystal nucleation do not grow and are not obsd. to act as precursors to the cryst. phase. Instead, calcite appears to nucleate independently. These results imply that the recently proposed model of calcite formation as a non-classical process, one which proceeds via aggregation of stable pre-nucleation clusters that form an amorphous precursor from which the cryst. phase emerges, is not applicable to template-directed nucleation on carboxyl SAMs and does not provide a universal description of calcite formation.
  11. 11
    Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. cp2k: atomistic simulations of condensed matter systems Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4, 15– 25 DOI: 10.1002/wcms.1159
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    11
    cp2k: atomistic simulations of condensed matter systems
    Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
    Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
    A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
  12. 12
    Borštnik, U.; Vandevondele, J.; Weber, V.; Hutter, J. Sparse matrix multiplication: The distributed block-compressed sparse row library Parallel Comput. 2014, 40, 47– 58 DOI: 10.1016/j.parco.2014.03.012
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  13. 13
    Vandevondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach Comput. Phys. Commun. 2005, 167, 103– 128 DOI: 10.1016/j.cpc.2004.12.014
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    13
    QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
    VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
    Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
  14. 14
    Frigo, M.; Johnson, S. G. The design and implementation of FFTW3 Proc. IEEE 2005, 93, 216– 231 DOI: 10.1109/JPROC.2004.840301
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    VandeVondele, J.; Hutter, J. An efficient orbital transformation method for electronic structure calculations J. Chem. Phys. 2003, 118, 4365– 4369 DOI: 10.1063/1.1543154
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    15
    An efficient orbital transformation method for electronic structure calculations
    VandeVondele, Joost; Hutter, Jurg
    Journal of Chemical Physics (2003), 118 (10), 4365-4369CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    An efficient method for optimizing single-determinant wave functions of medium and large systems is presented. It is based on a minimization of the energy functional using a new set of variables to perform orbital transformations. With this method convergence of the wave function is guaranteed. Preconditioners with different computational cost and efficiency have been constructed. Depending on the preconditioner, the method needs a no. of iterations that is very similar to the established diagonalization-DIIS approach, in cases where the latter converges well. Diagonalization of the Kohn-Sham matrix can be avoided and the sparsity of the overlap and Kohn-Sham matrix can be exploited. If sparsity is taken into account, the method scales as O(MN2), where M is the total no. of basis functions and N is the no. of occupied orbitals. The relative performance of the method is optimal for large systems that are described with high quality basis sets, and for which the d. matrixes are not yet sparse. We present a benchmark calcn. on a DNA crystal contg. 2×12 base pairs, solvent and counter ions (2388 atoms), using a TZV(2d,2p) basis (38688 basis functions) and conclude that the electronic structure of systems of this size can now be studied routinely.
  16. 16
    Lippert, G.; Hutter, J.; Parrinello, M. A hybrid Gaussian and plane wave density functional scheme Mol. Phys. 1997, 92, 477– 488 DOI: 10.1080/00268979709482119
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    A hybrid Gaussian and plane wave density functional scheme
    Lippert, Gerald; Hutter, Juerg; Parrinello, Michele
    Molecular Physics (1997), 92 (3), 477-487CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis)
    A d.-functional theory-based algorithm for periodic and nonperiodic ab initio calcns. is presented. This scheme uses pseudopotentials in order to integrate out the core electrons from the problem. The valence pseudo wave functions are expanded in Gaussian-type orbitals and the d. is represented in a plane wave auxiliary basis. The Gaussian basis functions make it possible to use the efficient anal. integration schemes and screening algorithms of quantum chem. Novel recursion relations are developed for the calcn. of the matrix elements of the d.-dependent Kohn-Sham self-consistent potential. At the same time the use of a plane wave basis for the electron d. permits efficient calcn. of the Hartree energy using fast Fourier transforms, thus circumventing one of the major bottlenecks of std. Gaussian based calcns. Furthermore, this algorithm avoids the fitting procedures that go along with intermediate basis sets for the charge d. The performance and accuracy of this new scheme are discussed and selected examples are given.
  17. 17
    Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1703– 1710 DOI: 10.1103/PhysRevB.54.1703
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    Separable dual-space Gaussian pseudopotentials
    Goedecker, S.; Teter, M.; Hutter, J.
    Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
  18. 18
    Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 3641 DOI: 10.1103/PhysRevB.58.3641
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    Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
    Hartwigsen, C.; Goedecker, S.; Hutter, J.
    Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.
  19. 19
    Krack, M. Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals Theor. Chem. Acc. 2005, 114, 145– 152 DOI: 10.1007/s00214-005-0655-y
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    Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals
    Krack, M.
    Theoretical Chemistry Accounts (2005), 114 (1-3), 145-152CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)
    Pseudopotential parameter sets for the elements from H to Kr using the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotentials of Goedecker, Teter, and Hutter (GTH) are presented as optimized for the gradient-cor. exchange-correlation functionals of Becke, Lee, Yang, and Parr (BLYP), Becke and Perdew (BP), and Perdew, Burke, and Ernzerhof (PBE). The accuracy and reliability of the GTH pseudopotentials is shown by calcns. for a series of small mols.
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    Perdew, J. P.; Burke, K.; Ernzerhof, M. of Physics, D.; Quantum Theory Group Tulane University, N. O. L. . J. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868 DOI: 10.1103/PhysRevLett.77.3865
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    Fernández-Serra, M. V.; Artacho, E. Network equilibration and first-principles liquid water J. Chem. Phys. 2004, 121, 11136– 11144 DOI: 10.1063/1.1813431
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    Network equilibration and first-principles liquid water
    Fernandez-Serra, M. V.; Artacho, Emilio
    Journal of Chemical Physics (2004), 121 (22), 11136-11144CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    Motivated by the very low diffusivity recently found in ab initio simulations of liq. water, we have studied its dependence with temp., system size, and duration of the simulations. We use ab initio mol. dynamics (AIMD), following the Born-Oppenheimer forces obtained from d.-functional theory (DFT). The linear-scaling capability of our method allows the consideration of larger system sizes (up to 128 mols. in this study), even if the main emphasis of this work is in the time scale. We obtain diffusivities that are substantially lower than the exptl. values, in agreement with recent findings using similar methods. A fairly good agreement with D(T) expts. is obtained if the simulation temp. is scaled down by ≈20%. It is still an open question whether the deviation is due to the limited accuracy of present d. functionals or to quantum fluctuations, but neither tech. approxns. (basis set, localization for linear scaling) nor the system size (down to 32 mols.) deteriorate the DFT description in an appreciable way. We find that the need for long equilibration times is consequence of the slow process of rearranging the H-bond network (at least 20 ps at AIMDs room temp.). The diffusivity is obsd. to be very directly linked to network imperfection. This link does not appear an artifact of the simulations, but a genuine property of liq. water.
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    Grossman, J. C.; Schwegler, E.; Draeger, E. W.; Gygi, F.; Galli, G. Towards an assessment of the accuracy of density functional theory for first principles simulations of water J. Chem. Phys. 2004, 120, 300– 11 DOI: 10.1063/1.1630560
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    Towards an assessment of the accuracy of density functional theory for first principles simulations of water
    Grossman, Jeffrey C.; Schwegler, Eric; Draeger, Erik W.; Gygi, Francois; Galli, Giulia
    Journal of Chemical Physics (2004), 120 (1), 300-311CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
    A series of Car-Parrinello (CP) mol. dynamics simulations of water are presented, aimed at assessing the accuracy of d. functional theory in describing the structural and dynamical properties of water at ambient conditions. We found negligible differences in structural properties obtained using the Perdew-Burke-Ernzerhof or the Becke-Lee-Yang-Parr exchange and correlation energy functionals; we also found that size effects, although not fully negligible when using 32 mol. cells, are rather small. In addn., we identified a wide range of values of the fictitious electronic mass (μ) entering the CP Lagrangian for which the electronic ground state is accurately described, yielding trajectories and av. properties that are independent of the value chosen. However, care must be exercised not to carry out simulations outside this range, where structural properties may artificially depend on μ. In the case of an accurate description of the electronic ground state, and in the absence of proton quantum effects, we obtained an oxygen-oxygen correlation function that is overstructured compared to expt., and a diffusion coeff. which is approx. ten times smaller.
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    Todorova, T.; Seitsonen, A. P.; Hutter, J.; Kuo, I.-F. W.; Mundy, C. J. Molecular dynamics simulation of liquid water: hybrid density functionals J. Phys. Chem. B 2006, 110, 3685– 91 DOI: 10.1021/jp055127v
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    Molecular Dynamics Simulation of Liquid Water: Hybrid Density Functionals
    Todorova, Teodora; Seitsonen, Ari P.; Hutter, Juerg; Kuo, I-Feng W.; Mundy, Christopher J.
    Journal of Physical Chemistry B (2006), 110 (8), 3685-3691CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    The structure, dynamical, and electronic properties of liq. water utilizing different hybrid d. functionals were tested within the plane wave framework of first-principles mol. dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calcns. of the structural and bonding properties of the water dimer and cyclic water trimer. Liq. water simulations were performed at the state point of 350 K at the exptl. d. Simulations included three different hybrid functionals, a meta-functional, four gradient-cor. functionals, and the local d. and Hartree-Fock approxns. The hybrid functionals are superior in reproducing the exptl. structure and dynamical properties as measured by the radial distribution function and self-diffusion const. when compared to the pure d. functionals. The local d. and Hartree-Fock approxns. show strongly over- and understructured liqs., resp. Hydrogen bond anal. shows that the hybrid functionals give slightly smaller av. nos. of hydrogen bonds than pure d. functionals but similar hydrogen bond populations. The av. mol. dipole moments in the liq. from the three hybrid functionals are lower than those of the corresponding pure d. functionals.
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    Lin, I.; Seitsonen, A. P.; Coutinho-Neto, M. D.; Tavernelli, I.; Rothlisberger, U. Importance of van der Waals Interactions in Liquid Water J. Phys. Chem. B 2009, 113, 1127– 1131 DOI: 10.1021/jp806376e
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    Importance of van der Waals Interactions in Liquid Water
    Lin, I.-Chun; Seitsonen, Ari P.; Coutinho-Neto, Mauricio D.; Tavernelli, Ivano; Rothlisberger, Ursula
    Journal of Physical Chemistry B (2009), 113 (4), 1127-1131CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    We present ab initio mol. dynamics studies on liq. water using d. functional theory in conjunction with either dispersion-cor. atom-centered potentials or empirical van der Waals corrections. Our results show that improving the description of van der Waals interactions in DFT-GGA leads to a softening of liq. water's structure with higher mobility. The results obtained with dispersion-cor. atom-centered potentials are esp. encouraging. In particular, the radial distribution functions are in better agreement with expt., and the self-diffusion coeff. increases by more than three-fold compared with the one predicted by the BLYP functional. This work demonstrates that van der Waals interactions are essential in fine-tuning both structural and dynamical properties of liq. water.
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    Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics J. Mol. Graphics 1996, 14, 33– 38 DOI: 10.1016/0263-7855(96)00018-5
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    VDM: visual molecular dynamics
    Humphrey, William; Dalke, Andrew; Schulten, Klaus
    Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
    VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
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    Torrie, G.; Valleau, J. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling J. Comput. Phys. 1977, 23, 187– 199 DOI: 10.1016/0021-9991(77)90121-8
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    Kästner, J. Umbrella sampling Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1, 932– 942 DOI: 10.1002/wcms.66
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    Grossfield, A. WHAM: the weighted histogram analysis method, version 2.0.9. http://membrane.urmc.rochester.edu/content/wham.
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    Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method J. Comput. Chem. 1992, 13, 1011– 1021 DOI: 10.1002/jcc.540130812
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    The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
    Kumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.
    Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.
    The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.
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    Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. Multidimensional Free - Energy Calculations Using the Weighted Histogram Analysis Method J. Comput. Chem. 1995, 16, 1339– 1350 DOI: 10.1002/jcc.540161104
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    The calculation of the potential of mean force using computer simulations
    Roux, Benoit
    Computer Physics Communications (1995), 91 (1-3), 275-82CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
    The problem of unbiasing and combining the results of umbrella sampling calcns. is reviewed. The weighted histogram anal. method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with mol. dynamics simulations of the alanine dipeptide for one- and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.
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    Almora-Barrios, N.; de Leeuw, N. H. Molecular dynamics simulation of the early stages of nucleation of hydroxyapatite at a collagen template Cryst. Growth Des. 2012, 12, 756– 763 DOI: 10.1021/cg201092s
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    Molecular dynamics simulation of the early stages of nucleation of hydroxyapatite at a collagen template
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    Crystal Growth & Design (2012), 12 (2), 756-763CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
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    Monodentate versus Bidentate Carboxylate Binding in Magnesium and Calcium Proteins: What Are the Basic Principles?
    Dudev, Todor; Lim, Carmay
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    Aspartate and glutamate side chains are unique among the 20 amino acids in terms of their side-chain carboxylate groups that can bind metal cations in either a monodentate (via one of the carboxylate O atoms) or bidentate (via both carboxylate O atoms) fashion. In this work, we elucidate the phys. principles that det. the carboxylate-binding mode in metalloproteins by surveying the Protein Data Bank (PDB) and performing d. functional and continuum dielec. calcns. The metal and its first-shell ligands are explicitly modeled and treated quantum mech., whereas the second-shell effects and the metal-binding site environment are implicitly taken into account. We systematically investigate the effect on the carboxylate denticity of (i) its immediate surroundings, (ii) the metal type and coordination no., (iii) the total charge of the metal complex, and (iv) the relative solvent exposure of the metal-binding site. The results suggest that the carboxylate-binding mode is detd. by competition between the metal cation and nonacidic neighboring ligands from the metal inner or outer coordination sphere for the second O atom of the COO- moiety. When the pos. charge of the metal is reduced by coordination to neg. charged ligands, first- or second-shell ligand-carboxylate (as opposed to direct metal-carboxylate) interactions dictate the carboxylate-binding mode. In such cases, water mols. have a crucial role in stabilizing the monodentate carboxylate-binding mode of water-rich Mg complexes, whereas the peptide backbone has a role in destabilizing the monodentate carboxylate-binding mode of the "drier" and bulkier Ca complexes. Thus, by fine-tuning the resp. interactions, the protein can adopt an appropriate binding-site configuration.
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    Systematic empirical analysis of calcium-oxygen coordination environment by calcium K-edge XANES
    Sowrey, F. E.; Skipper, L. J.; Pickup, D. M.; Drake, K. O.; Lin, Z.; Smith, M. E.; Newport, R. J.
    Physical Chemistry Chemical Physics (2004), 6 (1), 188-192CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The x-ray absorption near edge structure (XANES) at the Ca K-edge is rich in information, but complex and difficult to interpret fully. A systematic study is presented of a range of Ca/O contg. compds. and minerals, and the XANES may be used to obtain qual. information on the Ca coordination environment.

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  • Abstract

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    Figure 1

    Figure 1. Structures obtained in the gas phase (I) and in water (II, III, IV). The dotted lines represent hydrogen bonds. Color key: Ca–cyan, P–green, O–red, H–white.

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    Figure 2

    Figure 2. Time evolution of the Ca–Oph distances during the NVT run. The red lines refer to the oxygen atoms of the phosphate group at the axial site, and the black and blue lines refer to those of the two groups at the equatorial sites. The dashed horizontal line highlights the bond distance cutoff of 3.35 Å corresponding to the minimum in the Ca–Oph radial distribution function. One attempt to form an eight-coordinated structure is evidenced by the black arrow.

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    Figure 3

    Figure 3. Radial distribution functions for the Ca–O, Ca–P, P–O, O–O, and P–P pairings.

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    Figure 4

    Figure 4. Free energy profiles obtained when moving away one of the bidentate groups from calcium (upper panel) and pulling the monodentate group (lower panel) toward calcium. The minima are labeled consistently with the structures in Figure 1. Color key: Ca-cyan, P-green, O-red, H-white.

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    Figure 5

    Figure 5. Free energy profiles for the breakdown of the PNC into free ions. Each graph corresponds to the detachment of a phosphate group. The minima are labeled consistently with the structures in Figures 1 and 6. Color key: Ca–cyan, P–green, O–red, H–white.

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    Figure 6

    Figure 6. Metastable structures obtained during the dissociation of the PNC into free ions. Color key: Ca–cyan, P–green, O–red, H–white. The dotted lines represent hydrogen bonds.

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  • References

    This article references 35 other publications.

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      A review and discussion. The inorg. part of hard tissues (bones and teeth) of mammals consists of calcium phosphate, mainly of apatitic structure. Similarly, most undesired calcifications (i.e. those appearing as a result of various diseases) of mammals also contain calcium phosphate. For example, atherosclerosis results in blood vessel blockage caused by a solid composite of cholesterol with calcium phosphate. Dental caries result in a replacement of less sol. and hard apatite by more sol. and softer calcium hydrogen phosphates. Osteoporosis is a demineralization of bone. Therefore, from a chem. point of view, processes of normal (bone and teeth formation and growth) and pathol. (atherosclerosis and dental calculus) calcifications are just an in vivo crystn. of calcium phosphate. Similarly, dental caries and osteoporosis can be considered to be in vivo dissoln. of calcium phosphates. On the other hand, because of the chem. similarity with biol. calcified tissues, all calcium phosphates are remarkably biocompatible. This property is widely used in medicine for biomaterials that are either entirely made of or coated with calcium phosphate. For example, self-setting bone cements made of calcium phosphates are helpful in bone repair and titanium substitutes covered with a surface layer of calcium phosphates are used for hip joint endoprostheses and tooth substitutes, to facilitate the growth of bone and thereby raise the mech. stability. Calcium phosphates have a great biol. and medical significance and in this review the authors give an overview of the current knowledge in this subject.
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      A series of amorphous Ca phosphate and hydroxylapatite samples synthesized under different preparative conditions were studied by the x-ray radial distribution method. The results indicate that amorphous Ca phosphate has a reproducible structure independent of a wide variety of prepn. conditions. Detail in the radial distribution function of amorphous Ca phosphate diminishes rapidly for at. sepns. greater than 9.5 Å, suggesting ordered domains or clusters of about this size. It is proposed that amorphous Ca phosphate is an amorphous cluster or micro-crystallite material rather than a random network structure. Small-angle x-ray scattering and dehydration studies indicate that the amorphous Ca phosphate water of constitution is interstitial to the domains. Finally, hydroxylapatite prepd. at 25° has lower perfection of at. order than material prepd. at 100°.
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      An intensity-enhanced dynamic light scattering technique revealed Ca phosphate clusters from 0.7 to 1.0 nm in size in a simulated body fluid. The clusters were also present in fluids undersatd. with respect to octacalcium and amorphous Ca phosphates and supersatd. with respect only to hydroxyapatite. These clusters are the growth unit of hydroxyapatite judging from the fact that hydroxyapatite grows by step flow 0.8 or 1.6 nm in height and that the probability of incorporation of the growth unit into the crystal is extremely low, as revealed previously. The authors propose a cluster growth model where hydroxyapatite grows by selective hexagonal packing of left- and right-handed chiral Ca9(PO4)6 clusters 0.8 nm in size. Theor., stacking faults of clusters create a reflection-twin crystal, edge dislocations with a Burgers vector of C/2 and screw dislocations. An example of the reflection-twin is the merohedry twin which is frequently found in Cd chlorapatite. An at. image corresponding to the edge dislocations with a Burgers vector of C/2 was actually obtained on the surface of synthetic single-crystal hydroxyapatite.
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      Dey, A.; Bomans, P. H. H.; Müller, F. a.; Will, J.; Frederik, P. M.; de With, G.; Sommerdijk, N. a. J. M. The role of prenucleation clusters in surface-induced calcium phosphate crystallization Nat. Mater. 2010, 9, 1010– 1014 DOI: 10.1038/nmat2900
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      The role of prenucleation clusters in surface-induced calcium phosphate crystallization
      Dey, Archan; Bomans, Paul H. H.; Mueller, Frank A.; Will, Julia; Frederik, Peter M.; de With, Gijsbertus; Sommerdijk, Nico A. J. M.
      Nature Materials (2010), 9 (12), 1010-1014CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Unravelling the processes of formation is important in our understanding of both bone and tooth formation, and also of pathol. mineralization, for example in cardiovascular disease. Serum is a metastable soln. from which ppts. in the presence of calcifiable templates such as collagen, elastin and cell debris. A pathol. deficiency of inhibitors leads to the uncontrolled deposition of calcium phosphate. In bone and teeth the formation of apatite crystals is preceded by an amorphous (ACP) precursor phase. ACP formation is thought to proceed through prenucleation clusters-stable clusters that are present in soln. already before nucleation-as was recently demonstrated for (refs ). However, the role of such nanometer-sized clusters as building blocks for ACP has been debated for many years. Here we demonstrate that the surface-induced formation of apatite from simulated body fluid starts with the aggregation of prenucleation clusters leading to the nucleation of ACP before the development of oriented apatite crystals.
    7. 7
      Du, L.-W.; Bian, S.; Gou, B.-D.; Jiang, Y.; Huang, J.; Gao, Y.-X.; Zhao, Y.-D.; Wen, W.; Zhang, T.-L.; Wang, K. Structure of Clusters and Formation of Amorphous Calcium Phosphate and Hydroxyapatite: From the Perspective of Coordination Chemistry Cryst. Growth Des. 2013, 13, 3103– 3109 DOI: 10.1021/cg400498j
      7
      Structure of Clusters and Formation of Amorphous Calcium Phosphate and Hydroxyapatite: From the Perspective of Coordination Chemistry
      Du, Lin-Wei; Bian, Sha; Gou, Bao-Di; Jiang, Yun; Huang, Jian; Gao, Yu-Xi; Zhao, Yi-Dong; Wen, Wen; Zhang, Tian-Lan; Wang, Kui
      Crystal Growth & Design (2013), 13 (7), 3103-3109CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
      Amorphous Ca phosphate often forms as a precursor phase in a soln. at sufficiently high supersatn. and pH, and then transforms to the thermodynamically stable hydroxyapatite. The chem. compn., structure, and property of the amorphous phase are dependent on the structure of its composing clusters. Based on the results from the measurements of in situ Ca K-edge x-ray near-edge structure and ex situ X-ray diffraction, as well as the concomitant pH change in the reaction process, here the authors propose an improved model for the structure of Posner's cluster and identify the three types of reactions that give amorphous Ca phosphate and its subsequent transition to cryst. hydroxyapatite.
    8. 8
      Zhang, Q.; Jiang, Y.; Gou, B. D.; Huang, J.; Gao, Y. X.; Zhao, J. T.; Zheng, L.; Zhao, Y. D.; Zhang, T. L.; Wang, K. In Situ Detection of Calcium Phosphate Clusters in Solution and Wet Amorphous Phase by Synchrotron X-ray Absorption Near-Edge Spectroscopy at Calcium K-Edge Cryst. Growth Des. 2015, 15, 2204– 2210 DOI: 10.1021/cg5018505
      8
      In Situ Detection of Calcium Phosphate Clusters in Solution and Wet Amorphous Phase by Synchrotron X-ray Absorption Near-Edge Spectroscopy at Calcium K-Edge
      Zhang, Qun; Jiang, Yun; Gou, Bao-Di; Huang, Jian; Gao, Yu-Xi; Zhao, Jia-Ting; Zheng, Lei; Zhao, Yi-Dong; Zhang, Tian-Lan; Wang, Kui
      Crystal Growth & Design (2015), 15 (5), 2204-2210CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
      Ca phosphate clusters are present in both aq. solns. and an amorphous phase during crystn. It is a challenging task to acquire the structural information on such clusters, owing to their small size, chem. lability, and inaccessibility to most detection techniques. The authors demonstrate the feasibility of detecting such clusters in situ by synchrotron x-ray absorption near-edge spectroscopy at Ca K-edge, a technique that is sensitive to the short-range order in Ca coordination sphere. At the initial stage of crystn., the most abundant clusters are detected to be Ca(η2-PO43-)2L2 (L = H2O or η1-PO43-) in soln. More reactive clusters engage in the development of an amorphous phase via growing and fusing. The amorphous phase exhibits a dual character in its short-range order: Some of its clusters are similar to hydrated Ca ions, and some others to those in cryst. hydroxyapatite. When the amorphous dissolves, the detected unit is mainly Ca(η2-PO43-)(H2O)4 in the released soln. clusters. While these findings provide a basis for a better understanding and rational control of Ca phosphate crystn. at mol. level, the exptl. technique in assessing wet samples adopted in this work might be applicable to the crystn. studies of other materials as well.
    9. 9
      Habraken, W. J. E. M.; Tao, J.; Brylka, L. J.; Friedrich, H.; Bertinetti, L.; Schenk, A. S.; Verch, A.; Dmitrovic, V.; Bomans, P. H. H.; Frederik, P. M.; Laven, J.; van der Schoot, P.; Aichmayer, B.; de With, G.; DeYoreo, J. J.; Sommerdijk, N. a. J. M. Ion-association complexes unite classical and non-classical theories for the biomimetic nucleation of calcium phosphate Nat. Commun. 2013, 4, 1507 DOI: 10.1038/ncomms2490
      9
      Ion-association complexes unite classical and non-classical theories for the biomimetic nucleation of calcium phosphate
      Habraken Wouter J E M; Tao Jinhui; Brylka Laura J; Friedrich Heiner; Bertinetti Luca; Schenk Anna S; Verch Andreas; Dmitrovic Vladimir; Bomans Paul H H; Frederik Peter M; Laven Jozua; van der Schoot Paul; Aichmayer Barbara; de With Gijsbertus; DeYoreo James J; Sommerdijk Nico A J M
      Nature communications (2013), 4 (), 1507 ISSN:.
      Despite its importance in many industrial, geological and biological processes, the mechanism of crystallization from supersaturated solutions remains a matter of debate. Recent discoveries show that in many solution systems nanometre-sized structural units are already present before nucleation. Still little is known about the structure and role of these so-called pre-nucleation clusters. Here we present a combination of in situ investigations, which show that for the crystallization of calcium phosphate these nanometre-sized units are in fact calcium triphosphate complexes. Under conditions in which apatite forms from an amorphous calcium phosphate precursor, these complexes aggregate and take up an extra calcium ion to form amorphous calcium phosphate, which is a fractal of Ca(2)(HPO(4))(3)(2-) clusters. The calcium triphosphate complex also forms the basis of the crystal structure of octacalcium phosphate and apatite. Finally, we demonstrate how the existence of these complexes lowers the energy barrier to nucleation and unites classical and non-classical nucleation theories.
    10. 10
      Hu, Q.; Nielsen, M. H.; Freeman, C. L.; Hamm, L. M.; Tao, J.; Lee, J. R. I.; Han, T. Y. J.; Becker, U.; Harding, J. H.; Dove, P. M.; De Yoreo, J. J. The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways Faraday Discuss. 2012, 159, 509 DOI: 10.1039/c2fd20124k
      10
      The thermodynamics of calcite nucleation at organic interfaces: Classical vs. non-classical pathways
      Hu, Q.; Nielsen, M. H.; Freeman, C. L.; Hamm, L. M.; Tao, J.; Lee, J. R. I.; Han, T. Y. J.; Becker, U.; Harding, J. H.; Dove, P. M.; De Yoreo, J. J.
      Faraday Discussions (2012), 159 (), 509-523CODEN: FDISE6; ISSN:1359-6640. (Royal Society of Chemistry)
      Nucleation in the natural world often occurs in the presence of org. interfaces. In mineralized tissues, a range of macromol. matrixes are found in contact with inorg. phases and are believed to direct mineral formation. In geochem. settings, mineral surfaces, which are often covered with org. or biol. films, surround the vol. within which nucleation occurs. In the classical picture of nucleation, the presence of such interfaces is expected to have a profound effect on nucleation rates, simply because they can reduce the interfacial free energy, which controls the height of the thermodn. barrier to nucleation of the solid phase. However, the recent discovery of a nearly monodisperse population of calcium carbonate clusters-so called pre-nucleation clusters-and the many observations of amorphous precursor phases have called into question the applicability of classical descriptions. Here we use in situ observations of nucleation on organothiol self-assembled monolayers (SAMs) to explore the energetics and pathways of calcite nucleation at org. interfaces. We find that carboxyl SAM-directed nucleation is described well in purely classical terms through a redn. in the thermodn. barrier due to decreased interfacial free energy. Moreover, the differences in nucleation kinetics on odd and even chain-length carboxyl SAMs are attributable to relative differences in these energies. These differences arise from varying degrees of SAM order related to oxygen-oxygen interactions between SAM headgroups. In addn., amorphous particles formed prior to or during crystal nucleation do not grow and are not obsd. to act as precursors to the cryst. phase. Instead, calcite appears to nucleate independently. These results imply that the recently proposed model of calcite formation as a non-classical process, one which proceeds via aggregation of stable pre-nucleation clusters that form an amorphous precursor from which the cryst. phase emerges, is not applicable to template-directed nucleation on carboxyl SAMs and does not provide a universal description of calcite formation.
    11. 11
      Hutter, J.; Iannuzzi, M.; Schiffmann, F.; VandeVondele, J. cp2k: atomistic simulations of condensed matter systems Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4, 15– 25 DOI: 10.1002/wcms.1159
      11
      cp2k: atomistic simulations of condensed matter systems
      Hutter, Juerg; Iannuzzi, Marcella; Schiffmann, Florian; VandeVondele, Joost
      Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (1), 15-25CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
      A review. Cp2k has become a versatile open-source tool for the simulation of complex systems on the nanometer scale. It allows for sampling and exploring potential energy surfaces that can be computed using a variety of empirical and first principles models. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern and massively parallel hardware. This review briefly summarizes the main capabilities and illustrates with recent applications the science cp2k has enabled in the field of atomistic simulation. WIREs Comput Mol Sci 2014, 4:15-25. doi: 10.1002/wcms.1159 The authors have declared no conflicts of interest in relation to this article. For further resources related to this article, please visit the WIREs website.
    12. 12
      Borštnik, U.; Vandevondele, J.; Weber, V.; Hutter, J. Sparse matrix multiplication: The distributed block-compressed sparse row library Parallel Comput. 2014, 40, 47– 58 DOI: 10.1016/j.parco.2014.03.012
      There is no corresponding record for this reference.
    13. 13
      Vandevondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach Comput. Phys. Commun. 2005, 167, 103– 128 DOI: 10.1016/j.cpc.2004.12.014
      13
      QUICKSTEP: fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
      VandeVondele, Joost; Krack, Matthias; Mohamed, Fawzi; Parrinello, Michele; Chassaing, Thomas; Hutter, Juerg
      Computer Physics Communications (2005), 167 (2), 103-128CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      We present the Gaussian and plane waves (GPW) method and its implementation in which is part of the freely available program package CP2K. The GPW method allows for accurate d. functional calcns. in gas and condensed phases and can be effectively used for mol. dynamics simulations. We show how derivs. of the GPW energy functional, namely ionic forces and the Kohn-Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn-Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calcns. for single mols. and plane wave based calcns. in the condensed phase is excellent. Wave function optimization with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born-Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the d. matrix. We illustrate these findings with calcns. using commodity PCs as well as supercomputers.
    14. 14
      Frigo, M.; Johnson, S. G. The design and implementation of FFTW3 Proc. IEEE 2005, 93, 216– 231 DOI: 10.1109/JPROC.2004.840301
      There is no corresponding record for this reference.
    15. 15
      VandeVondele, J.; Hutter, J. An efficient orbital transformation method for electronic structure calculations J. Chem. Phys. 2003, 118, 4365– 4369 DOI: 10.1063/1.1543154
      15
      An efficient orbital transformation method for electronic structure calculations
      VandeVondele, Joost; Hutter, Jurg
      Journal of Chemical Physics (2003), 118 (10), 4365-4369CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      An efficient method for optimizing single-determinant wave functions of medium and large systems is presented. It is based on a minimization of the energy functional using a new set of variables to perform orbital transformations. With this method convergence of the wave function is guaranteed. Preconditioners with different computational cost and efficiency have been constructed. Depending on the preconditioner, the method needs a no. of iterations that is very similar to the established diagonalization-DIIS approach, in cases where the latter converges well. Diagonalization of the Kohn-Sham matrix can be avoided and the sparsity of the overlap and Kohn-Sham matrix can be exploited. If sparsity is taken into account, the method scales as O(MN2), where M is the total no. of basis functions and N is the no. of occupied orbitals. The relative performance of the method is optimal for large systems that are described with high quality basis sets, and for which the d. matrixes are not yet sparse. We present a benchmark calcn. on a DNA crystal contg. 2×12 base pairs, solvent and counter ions (2388 atoms), using a TZV(2d,2p) basis (38688 basis functions) and conclude that the electronic structure of systems of this size can now be studied routinely.
    16. 16
      Lippert, G.; Hutter, J.; Parrinello, M. A hybrid Gaussian and plane wave density functional scheme Mol. Phys. 1997, 92, 477– 488 DOI: 10.1080/00268979709482119
      16
      A hybrid Gaussian and plane wave density functional scheme
      Lippert, Gerald; Hutter, Juerg; Parrinello, Michele
      Molecular Physics (1997), 92 (3), 477-487CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis)
      A d.-functional theory-based algorithm for periodic and nonperiodic ab initio calcns. is presented. This scheme uses pseudopotentials in order to integrate out the core electrons from the problem. The valence pseudo wave functions are expanded in Gaussian-type orbitals and the d. is represented in a plane wave auxiliary basis. The Gaussian basis functions make it possible to use the efficient anal. integration schemes and screening algorithms of quantum chem. Novel recursion relations are developed for the calcn. of the matrix elements of the d.-dependent Kohn-Sham self-consistent potential. At the same time the use of a plane wave basis for the electron d. permits efficient calcn. of the Hartree energy using fast Fourier transforms, thus circumventing one of the major bottlenecks of std. Gaussian based calcns. Furthermore, this algorithm avoids the fitting procedures that go along with intermediate basis sets for the charge d. The performance and accuracy of this new scheme are discussed and selected examples are given.
    17. 17
      Goedecker, S.; Teter, M.; Hutter, J. Separable dual-space Gaussian pseudopotentials Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1703– 1710 DOI: 10.1103/PhysRevB.54.1703
      17
      Separable dual-space Gaussian pseudopotentials
      Goedecker, S.; Teter, M.; Hutter, J.
      Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
    18. 18
      Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 3641 DOI: 10.1103/PhysRevB.58.3641
      18
      Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
      Hartwigsen, C.; Goedecker, S.; Hutter, J.
      Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.
    19. 19
      Krack, M. Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals Theor. Chem. Acc. 2005, 114, 145– 152 DOI: 10.1007/s00214-005-0655-y
      19
      Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals
      Krack, M.
      Theoretical Chemistry Accounts (2005), 114 (1-3), 145-152CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)
      Pseudopotential parameter sets for the elements from H to Kr using the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotentials of Goedecker, Teter, and Hutter (GTH) are presented as optimized for the gradient-cor. exchange-correlation functionals of Becke, Lee, Yang, and Parr (BLYP), Becke and Perdew (BP), and Perdew, Burke, and Ernzerhof (PBE). The accuracy and reliability of the GTH pseudopotentials is shown by calcns. for a series of small mols.
    20. 20
      Perdew, J. P.; Burke, K.; Ernzerhof, M. of Physics, D.; Quantum Theory Group Tulane University, N. O. L. . J. Generalized Gradient Approximation Made Simple Phys. Rev. Lett. 1996, 77, 3865– 3868 DOI: 10.1103/PhysRevLett.77.3865
      There is no corresponding record for this reference.
    21. 21
      Fernández-Serra, M. V.; Artacho, E. Network equilibration and first-principles liquid water J. Chem. Phys. 2004, 121, 11136– 11144 DOI: 10.1063/1.1813431
      21
      Network equilibration and first-principles liquid water
      Fernandez-Serra, M. V.; Artacho, Emilio
      Journal of Chemical Physics (2004), 121 (22), 11136-11144CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      Motivated by the very low diffusivity recently found in ab initio simulations of liq. water, we have studied its dependence with temp., system size, and duration of the simulations. We use ab initio mol. dynamics (AIMD), following the Born-Oppenheimer forces obtained from d.-functional theory (DFT). The linear-scaling capability of our method allows the consideration of larger system sizes (up to 128 mols. in this study), even if the main emphasis of this work is in the time scale. We obtain diffusivities that are substantially lower than the exptl. values, in agreement with recent findings using similar methods. A fairly good agreement with D(T) expts. is obtained if the simulation temp. is scaled down by ≈20%. It is still an open question whether the deviation is due to the limited accuracy of present d. functionals or to quantum fluctuations, but neither tech. approxns. (basis set, localization for linear scaling) nor the system size (down to 32 mols.) deteriorate the DFT description in an appreciable way. We find that the need for long equilibration times is consequence of the slow process of rearranging the H-bond network (at least 20 ps at AIMDs room temp.). The diffusivity is obsd. to be very directly linked to network imperfection. This link does not appear an artifact of the simulations, but a genuine property of liq. water.
    22. 22
      Grossman, J. C.; Schwegler, E.; Draeger, E. W.; Gygi, F.; Galli, G. Towards an assessment of the accuracy of density functional theory for first principles simulations of water J. Chem. Phys. 2004, 120, 300– 11 DOI: 10.1063/1.1630560
      22
      Towards an assessment of the accuracy of density functional theory for first principles simulations of water
      Grossman, Jeffrey C.; Schwegler, Eric; Draeger, Erik W.; Gygi, Francois; Galli, Giulia
      Journal of Chemical Physics (2004), 120 (1), 300-311CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      A series of Car-Parrinello (CP) mol. dynamics simulations of water are presented, aimed at assessing the accuracy of d. functional theory in describing the structural and dynamical properties of water at ambient conditions. We found negligible differences in structural properties obtained using the Perdew-Burke-Ernzerhof or the Becke-Lee-Yang-Parr exchange and correlation energy functionals; we also found that size effects, although not fully negligible when using 32 mol. cells, are rather small. In addn., we identified a wide range of values of the fictitious electronic mass (μ) entering the CP Lagrangian for which the electronic ground state is accurately described, yielding trajectories and av. properties that are independent of the value chosen. However, care must be exercised not to carry out simulations outside this range, where structural properties may artificially depend on μ. In the case of an accurate description of the electronic ground state, and in the absence of proton quantum effects, we obtained an oxygen-oxygen correlation function that is overstructured compared to expt., and a diffusion coeff. which is approx. ten times smaller.
    23. 23
      Todorova, T.; Seitsonen, A. P.; Hutter, J.; Kuo, I.-F. W.; Mundy, C. J. Molecular dynamics simulation of liquid water: hybrid density functionals J. Phys. Chem. B 2006, 110, 3685– 91 DOI: 10.1021/jp055127v
      23
      Molecular Dynamics Simulation of Liquid Water: Hybrid Density Functionals
      Todorova, Teodora; Seitsonen, Ari P.; Hutter, Juerg; Kuo, I-Feng W.; Mundy, Christopher J.
      Journal of Physical Chemistry B (2006), 110 (8), 3685-3691CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      The structure, dynamical, and electronic properties of liq. water utilizing different hybrid d. functionals were tested within the plane wave framework of first-principles mol. dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calcns. of the structural and bonding properties of the water dimer and cyclic water trimer. Liq. water simulations were performed at the state point of 350 K at the exptl. d. Simulations included three different hybrid functionals, a meta-functional, four gradient-cor. functionals, and the local d. and Hartree-Fock approxns. The hybrid functionals are superior in reproducing the exptl. structure and dynamical properties as measured by the radial distribution function and self-diffusion const. when compared to the pure d. functionals. The local d. and Hartree-Fock approxns. show strongly over- and understructured liqs., resp. Hydrogen bond anal. shows that the hybrid functionals give slightly smaller av. nos. of hydrogen bonds than pure d. functionals but similar hydrogen bond populations. The av. mol. dipole moments in the liq. from the three hybrid functionals are lower than those of the corresponding pure d. functionals.
    24. 24
      Lin, I.; Seitsonen, A. P.; Coutinho-Neto, M. D.; Tavernelli, I.; Rothlisberger, U. Importance of van der Waals Interactions in Liquid Water J. Phys. Chem. B 2009, 113, 1127– 1131 DOI: 10.1021/jp806376e
      24
      Importance of van der Waals Interactions in Liquid Water
      Lin, I.-Chun; Seitsonen, Ari P.; Coutinho-Neto, Mauricio D.; Tavernelli, Ivano; Rothlisberger, Ursula
      Journal of Physical Chemistry B (2009), 113 (4), 1127-1131CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      We present ab initio mol. dynamics studies on liq. water using d. functional theory in conjunction with either dispersion-cor. atom-centered potentials or empirical van der Waals corrections. Our results show that improving the description of van der Waals interactions in DFT-GGA leads to a softening of liq. water's structure with higher mobility. The results obtained with dispersion-cor. atom-centered potentials are esp. encouraging. In particular, the radial distribution functions are in better agreement with expt., and the self-diffusion coeff. increases by more than three-fold compared with the one predicted by the BLYP functional. This work demonstrates that van der Waals interactions are essential in fine-tuning both structural and dynamical properties of liq. water.
    25. 25
      Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual molecular dynamics J. Mol. Graphics 1996, 14, 33– 38 DOI: 10.1016/0263-7855(96)00018-5
      25
      VDM: visual molecular dynamics
      Humphrey, William; Dalke, Andrew; Schulten, Klaus
      Journal of Molecular Graphics (1996), 14 (1), 33-8, plates, 27-28CODEN: JMGRDV; ISSN:0263-7855. (Elsevier)
      VMD is a mol. graphics program designed for the display and anal. of mol. assemblies, in particular, biopolymers such as proteins and nucleic acids. VMD can simultaneously display any no. of structures using a wide variety of rendering styles and coloring methods. Mols. are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resoln. raster images of displayed mols. may be produced by generating input scripts for use by a no. of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate mol. dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biol., which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs, VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.
    26. 26
      Torrie, G.; Valleau, J. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling J. Comput. Phys. 1977, 23, 187– 199 DOI: 10.1016/0021-9991(77)90121-8
      There is no corresponding record for this reference.
    27. 27
      Kästner, J. Umbrella sampling Wiley Interdiscip. Rev. Comput. Mol. Sci. 2011, 1, 932– 942 DOI: 10.1002/wcms.66
      There is no corresponding record for this reference.
    28. 28
      Grossfield, A. WHAM: the weighted histogram analysis method, version 2.0.9. http://membrane.urmc.rochester.edu/content/wham.
      There is no corresponding record for this reference.
    29. 29
      Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. THE weighted histogram analysis method for free-energy calculations on biomolecules. I. The method J. Comput. Chem. 1992, 13, 1011– 1021 DOI: 10.1002/jcc.540130812
      29
      The weighted histogram analysis method for free-energy calculations on biomolecules. I. The method
      Kumar, Shankar; Bouzida, Djamal; Swendsen, Robert H.; Kollman, Peter A.; Rosenberg, John M.
      Journal of Computational Chemistry (1992), 13 (8), 1011-21CODEN: JCCHDD; ISSN:0192-8651.
      The Weighted Histogram Anal. Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomol. Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free-energy and Potential of Mean Force calcns. This algorithm possesses the following advantages over methods that are currently employed: (1) it provides a built-in est. of sampling errors thereby yielding objective ests. of the optimal location and length of addnl. simulations needed to achieve a desired level of precision; (2) it yields the "best" value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addn. to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better ests. of the free-energy differences. By recasting the Ferrenberg-Swendsen Multiple Histogram equations in a form suitable for mol. mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine.
    30. 30
      Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A. Multidimensional Free - Energy Calculations Using the Weighted Histogram Analysis Method J. Comput. Chem. 1995, 16, 1339– 1350 DOI: 10.1002/jcc.540161104
      There is no corresponding record for this reference.
    31. 31
      Roux, B. The calculation of the potential of mean force using computer simulations Comput. Phys. Commun. 1995, 91, 275– 282 DOI: 10.1016/0010-4655(95)00053-I
      31
      The calculation of the potential of mean force using computer simulations
      Roux, Benoit
      Computer Physics Communications (1995), 91 (1-3), 275-82CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
      The problem of unbiasing and combining the results of umbrella sampling calcns. is reviewed. The weighted histogram anal. method (WHAM) of S. Kumar et al. (J. Comp. Chem. 13 (1992) 1011) is described and compared with other approaches. The method is illustrated with mol. dynamics simulations of the alanine dipeptide for one- and two-dimensional free energy surfaces. The results show that the WHAM approach simplifies considerably the task of recombining the various windows in complex systems.
    32. 32
      Almora-Barrios, N.; de Leeuw, N. H. Molecular dynamics simulation of the early stages of nucleation of hydroxyapatite at a collagen template Cryst. Growth Des. 2012, 12, 756– 763 DOI: 10.1021/cg201092s
      32
      Molecular dynamics simulation of the early stages of nucleation of hydroxyapatite at a collagen template
      Almora-Barrios, Neyvis; De Leeuw, Nora H.
      Crystal Growth & Design (2012), 12 (2), 756-763CODEN: CGDEFU; ISSN:1528-7483. (American Chemical Society)
      The authors used mol. dynamics simulations to investigate the early processes in the nucleation of hydroxylapatite at a collagen template, by immersing a triple-helical collagen mol. in a stoichiometric soln. of Ca2+, PO43-, and OH- ions, where they obsd. the formation of Ca phosphate clusters at the collagen template. Electrostatic attractions were prevalent between Ca2+ ions and O atoms of the glycine and hydroxyproline residues, which were the starting point for the formation of the Ca phosphate clusters. Some phosphate ions formed H-bonds with the OH groups of hydroxyproline residues, whereas most of the OH- ions remained in soln., although some became attached to Ca phosphate clusters. The obsd. nucleation and clustering was too early in the hydroxylapatite formation process to show differentiation between distinct hydroxylapatite surfaces. However, calcns. of the interaction of a collagen peptide with the (0001) and (01‾10) surfaces of hydroxylapatite showed a clear energetic preference by the peptide for adsorption at the (01‾10) surface, which suggested that in the presence of the collagen matrix the hydroxylapatite crystal would grow more rapidly in the (0001) direction and express the (01‾10) surface in the particle shape, in agreement with the obsd. morphol. of biol. hydroxylapatite.
    33. 33
      Di Tommaso, D.; de Leeuw, N. H. The onset of calcium carbonate nucleation: A density functional theory molecular dynamics and hybrid microsolvation/continumn study J. Phys. Chem. B 2008, 112, 6965– 6975 DOI: 10.1021/jp801070b
      There is no corresponding record for this reference.
    34. 34
      Dudev, T.; Lim, C. Monodentate versus Bidentate Carboxylate Binding in Magnesium and Calcium Proteins: What Are the Basic Principles? J. Phys. Chem. B 2004, 108, 4546– 4557 DOI: 10.1021/jp0310347
      34
      Monodentate versus Bidentate Carboxylate Binding in Magnesium and Calcium Proteins: What Are the Basic Principles?
      Dudev, Todor; Lim, Carmay
      Journal of Physical Chemistry B (2004), 108 (14), 4546-4557CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      Aspartate and glutamate side chains are unique among the 20 amino acids in terms of their side-chain carboxylate groups that can bind metal cations in either a monodentate (via one of the carboxylate O atoms) or bidentate (via both carboxylate O atoms) fashion. In this work, we elucidate the phys. principles that det. the carboxylate-binding mode in metalloproteins by surveying the Protein Data Bank (PDB) and performing d. functional and continuum dielec. calcns. The metal and its first-shell ligands are explicitly modeled and treated quantum mech., whereas the second-shell effects and the metal-binding site environment are implicitly taken into account. We systematically investigate the effect on the carboxylate denticity of (i) its immediate surroundings, (ii) the metal type and coordination no., (iii) the total charge of the metal complex, and (iv) the relative solvent exposure of the metal-binding site. The results suggest that the carboxylate-binding mode is detd. by competition between the metal cation and nonacidic neighboring ligands from the metal inner or outer coordination sphere for the second O atom of the COO- moiety. When the pos. charge of the metal is reduced by coordination to neg. charged ligands, first- or second-shell ligand-carboxylate (as opposed to direct metal-carboxylate) interactions dictate the carboxylate-binding mode. In such cases, water mols. have a crucial role in stabilizing the monodentate carboxylate-binding mode of water-rich Mg complexes, whereas the peptide backbone has a role in destabilizing the monodentate carboxylate-binding mode of the "drier" and bulkier Ca complexes. Thus, by fine-tuning the resp. interactions, the protein can adopt an appropriate binding-site configuration.
    35. 35
      Sowrey, F.; Skipper, L.; Pickup, D.; Drake, K.; Lin, Z.; Smith, M.; Newport, R. Systematic empirical analysis of calcium-oxygen coordination environment by calcium K-edge XANES Phys. Chem. Chem. Phys. 2004, 6, 188– 192 DOI: 10.1039/B311715D
      35
      Systematic empirical analysis of calcium-oxygen coordination environment by calcium K-edge XANES
      Sowrey, F. E.; Skipper, L. J.; Pickup, D. M.; Drake, K. O.; Lin, Z.; Smith, M. E.; Newport, R. J.
      Physical Chemistry Chemical Physics (2004), 6 (1), 188-192CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The x-ray absorption near edge structure (XANES) at the Ca K-edge is rich in information, but complex and difficult to interpret fully. A systematic study is presented of a range of Ca/O contg. compds. and minerals, and the XANES may be used to obtain qual. information on the Ca coordination environment.

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    Supporting Information

    The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00327.

    • Hydrogen bonding between phosphate groups and water molecules observed during the molecular dynamics and coordination numbers and distances for the first coordination sphere of Ca–O, Ca–P, P–O, O–O, and P–P (PDF)


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