Theoretical Thermodynamics for Large Molecules: Walking the Thin Line between Accuracy and Computational Cost

Tobias Schwabe studied chemistry at the university of Münster. In his advanced courses, he focused on theoretical chemistry. He received his diploma degree for his thesis about the X2-PLYP density functionals. Now he is continuing his research in DFT development and application for a Ph.D. under the supervision of Stefan Grimme.

Stefan Grimme studied Chemistry at the TU Braunschweig and finished his Ph.D. in 1991 in Physical Chemistry on a topic in laser spectroscopy. He then moved to Bonn where did his Habilitation in Theoretical Chemistry in the group of Sigrid Peyerimoff. In 2000, he got the C4 chair for Theoretical Organic Chemistry at the University of Münster. His research interests are the development of quantum chemical methods for large systems, density functional theory, electronic spectroscopy/excited states and the properties of chiral systems.

The thermodynamic properties of molecules are of fundamental interest in physics, chemistry, and biology. This Account deals with the developments that we have made in the about last five years to find quantum chemical electronic structure methods that have the prospect of being applicable to larger molecules. The typical target accuracy is about 0.5–1 kcal mol⁻¹ for chemical reaction and 0.1 kcal mol⁻¹ for conformational energies. These goals can be achieved when a few physically motivated corrections to first-principles methods are introduced to standard quantum chemical techniques. These do not lead to a significantly increased computational expense, and thus our methods have the computer hardware requirements of the corresponding standard treatments. Together with the use of density-fitting (RI) integral approximations, routine computations on systems with about 100 non-hydrogen atoms (2000–4000 basis functions) can be performed on modern PCs.

Our improvements regarding accuracy are basically due to the use of modified second-order perturbation theory to account for many-particle (electron correlation) effects. Such nonlocal correlations are responsible for important parts of the interaction in and between atoms and molecules. A common example is the long-range dispersion interaction that lead to van der Waals complexes, but as shown here also the conventional thermodynamics of large molecules is significantly influenced by intramolecular dispersion effects.

We first present the basic theoretical ideas behind our approaches, which are the spin-component-scaled Møller–Plesset perturbation theory (SCS-MP2) and double-hybrid density functionals (DHDF). Furthermore, the effect of the independently developed empirical dispersion correction (DFT-D) is discussed. Together with the use of large atomic orbital basis sets (of at least triple- or quadruple-ζ quality), the accuracy of the new methods is even competitive with computationally very expensive coupled-cluster methods, but they still remain routinely applicable for day-to-day chemical problems. This is demonstrated for the G3/99 benchmark set of heats of formation, 34 organic isomerization energies, and barriers for a number of pericyclic reactions. As an electronically complicated example, the relative energies of three isomeric Au₈ clusters are considered.

In general, we recommend the very robust B2PLYP-D density functional approach for heat of formation calculations and for electronically complicated situations like transition metal complexes or open-shell species. With B2PLYP-D, an unprecedented low mean absolute deviation for the G3/99 test set with a DFT approach of 1.7 kcal mol⁻¹ has been achieved. For closed-shell main-group molecules and many relative energies, SCS-MP2 is the method of choice, because it completely avoids the self-interaction error problem that still plagues current DFT. In critical cases, it is recommended to apply SCS-MP2 and B2PLYP-D simultaneously, where also the comparison with standard MP2 and density functionals like B3LYP may lead to additional insight.