Computational Design of Rhenium(I) Carbonyl Complexes for Anticancer Photodynamic Therapy

New Re(I) carbonyl complexes are proposed as candidates for photodynamic therapy after investigating the effects of the pyridocarbazole-type ligand conjugation, addition of substituents to this ligand, and replacement of one CO by phosphines in [Re(pyridocarbazole)(CO)3(pyridine)] complexes by means of the density functional theory (DFT) and time-dependent DFT. We have found, first, that increasing the conjugation in the bidentate ligand reduces the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gap of the complex, so its absorption wavelength red-shifts. When the enlargement of this ligand is carried out by merging the electron-withdrawing 1H-pyrrole-2,5-dione heterocycle, it enhances even more the stabilization of the LUMO due to its electron-acceptor character. Second, the analysis of the shape and composition of the orbitals involved in the band of interest indicates which substituents of the bidentate ligand and which positions are optimal for reducing the HOMO–LUMO energy gap. The introduction of electron-withdrawing substituents into the pyridine ring of the pyridocarbazole ligand mainly stabilizes the LUMO, whereas the HOMO energy increases primarily when electron-donating substituents are introduced into its indole moiety. Each type of substituents results in a bathochromic shift of the lowest-lying absorption band, which is even larger if they are combined in the same complex. Finally, the removal of the π-backbonding interaction between Re and the CO trans to the monodentate pyridine when it is replaced by phosphines PMe3, 1,4-diacetyl-1,3,7-triaza-5-phosphabicyclo[3.3.1]nonane (DAPTA), and 1,4,7-triaza-9-phosphatricyclo[5.3.2.1]tridecane (CAP) causes another extra bathochromic shift due to the destabilization of the HOMO, which is low with DAPTA, moderate with PMe3, but especially large with CAP. Through the combination of the PMe3 or CAP ligands with adequate electron-withdrawing and/or electron-donating substituents at the pyridocarbazole ligand, we have found several complexes with significant absorption at the therapeutic window. In addition, according to our results on the singlet–triplet energy gap, all of them should be able to produce cytotoxic singlet oxygen.

S2 Discussion 1. Validating the computational protocol for geometry optimizations. S4
S9 Figure S1. Two comparative views for the X-ray and B3LYP-D3/6-31+G(d)-LANL2DZ structures of the Re(I) complex 1 ref . S10 Table S2. X-Ray and B3LYP-D3/6-31+G(d)-LANL2DZ bond distances of the Re(I) complex 1 ref along with absolute difference and square of the absolute difference of these distances. S11 Table S3. X-Ray and B3LYP-D3/6-31+G(d)-LANL2DZ bond angles of the Re(I) complex 1 ref together with absolute difference and square of the absolute difference of these angles. S13 Table S4. Excitation energies and oscillator strengths of the first ten lowest-lying singlet-singlet electron transitions calculated for complex 1. Table S5. Excitation energies and oscillator strengths of the first ten lowest-lying singlet-singlet electron transitions calculated for complex 2. Table S6. Excitation energies and oscillator strengths of the first ten lowest-lying singlet-singlet electron transitions calculated for complex 3. S17 Figure S2. Electronic spectra computed for complex 1. S18 Figure S3. Electronic spectra computed for complex 2. S20 Figure S4. Electronic spectra computed for complex 3. S22 Table S7. Excitation energy of the most red-shifted absorption band found for complexes 1-3 along with the difference in absolute value between the computed excitation energies and the experimental value and the total error obtained.

S4
Discussion 1. Validating the computational protocol for geometry optimizations.
The geometry of all the Re(I) carbonyl complexes investigated in this work was optimized in the gas phase at the B3LYP-D3/6-31+G(d)-LANL2DZ level of theory.
Although this computational level was chosen on the basis of numerous theoretical investigations on the photophysical and spectroscopic properties of Re(I) carbonyl complexes,  we checked its performance for geometry optimizations by comparing the X-ray structure of a N-benzylated derivative of the Re(I) tricarbonyl complex containing pyridyl and pyridocarbazol ligands (1 ref in Scheme S1) 40 with its B3LYP-D3/6-31+G(d)-LANL2DZ optimized structure. Complex 1 ref is closely related to the Re(I) carbonyl indolato complexes studied in the present investigation and furthermore its X-ray structure is available. 40 Cartesian coordinates of both structures are collected in Table S1.
Scheme S1. N-benzylated derivative of the Re(I) tricarbonyl complex containing a pyridine ligand and another pyrido [2,3-a]pyrrolo [3,4-c]carbazole-5,7(6H)-dione ligand considered in the validation calculations of the B3LYP-D3/6-31+G(d)-LANL2DZ level for geometry optimizations. Atom numbering of the non-hydrogen atoms, the most relevant ones, is included. Figure S1 shows that the main difference between X-ray (in blue colour) and B3LYP-D3/6-31+G(d)-LANL2DZ (in red colour) structures lies in the orientation of the benzyl S5 group attached to the nitrogen atom N32 of the pyridocarbazol ligand (Scheme S1), which can be ascribed to the crystal packing of 1 ref . Specifically, as collected in Table   S2, we note that the absolute difference between X-ray and B3LYP-D3 bond distances involving non-hydrogen atoms in 1 ref varies from 0.0002 Å (C27-C28 bond distance) to 0.048 Å (Re1-N8 bond distance). The mean absolute deviation (MAD) and the root mean square deviation (RMSD) between all those X-ray and B3LYP-D3 bond distances are 0.011 and 0.014 Å, respectively. When comparing X-ray and B3LYP-D3 bond angles involving non-hydrogen atoms in 1 ref (see Table S3), the absolute discrepancy between them ranges from 0.020º (Re1-N21-C20 bond angle) to 3.9º (C2-Re1-N8 bond angle). MAD of all the differences in those bond angles is 0.65º, whereas the RMSD value is about 1.0º. The relatively small RMSD value obtained for both bond distances (less than 0.02 Å) and bond angles (less than 2º) [41][42][43] confirms the adequacy of using the B3LYP-D3/6-31+G(d)-LANL2DZ optimized geometries to carry out Time-Dependent Density Functional Theory (TD-DFT) calculations.
As seen in Figure S2, B3LYP-D3, PBE, TPSS, and TPSSh provide UV/Vis absorbance spectra for 1 in Scheme S2 that differ greatly from the experimental one.
The B3LYP-D3 spectrum shows three absorption bands as in the experimental one, but the sequence of the first and third intensities is erroneously predicted. Specifically, the most red-shifted absorption band is more intense than the least one, while the reverse trend was found experimentally. For PBE, TPSS, and TPSSh, the simulated UV/Vis spectra do not clearly show the presence of three absorption bands, nor at least the two most intense ones. However, the general shape of the UV/Vis spectrum of 1 is respectively) and clearly larger than the previous functionals. The remaining DFT methods provide discrepancies larger than 0.25 eV, thus preventing their use to predict reliable UV/Vis spectra. In the case of 2 (seventh column in Table S7), we found that M06, PBE0, and M05 with absolute discrepancies of 0.003, 0.04, and 0.06 eV are the most adequate to fit the excitation energy of the experimental most red-shifted absorption band. We note, however, that M06 behaves better than PBE0 and M05. It S8 then follows B3LYP-D3 that only differs by 0.09 eV (in absolute value) from the experimental excitation energy. All the others functionals investigated present absolute errors larger than 0.23 eV. Concerning 3 (eighth column in Table S7) Table S7). M05 and PBE0 are the following functionals in level of accuracy with total absolute errors of 0.14 and 0.16 eV, respectively. By contrast, wB97xD and wB97x present the largest total absolute errors, 1.18 and 1.80 eV, respectively. In addition, M06 is also one of the best functionals in reproducing the general shape of the UV/Vis absorption spectrum for complexes 1-3. So, we conclude that M06 presents the best performance in order to investigate the spectroscopic properties of the Re(I) pyridocarbazole complexes investigated in the present work.  Figure S1. Two comparative views for the X-ray and B3LYP-D3/6-31+G(d)-LANL2DZ structures (blue and red colours, respectively) of the N-benzylated derivative of the Re(I) tricarbonyl complex containing pyridine and pyridocarbazole ligands (1 ref in Scheme S1). Table S2. X-Ray and B3LYP-D3/6-31+G(d)-LANL2DZ bond distances (r X-Ray and r B3LYP-D3 , respectively) of the Re(I) tricarbonyl complex 1 ref in Scheme S1. Absolute difference and square of the absolute difference of the X-Ray and B3LYP-D3/6-31+G(d)-LANL2DZ distances are also given for each bond. Only bond distances involving non-hydrogen atoms (the most relevant ones) are considered.     Table S10. B3LYP-D3/6-31+G(d)-LANL2DZ relevant optimized geometry data for Re(I) complexes 1-3 and 1a-1s in their triplet excited states. Bond distances, bond angles, and dihedral angles are given in Å, degrees, and degrees, respectively. The atom numbering used is collected for complex 1. a  Table S11. Energies in the singlet ground state and triplet excited state (< = > and < ? @ in hartree, respectively), difference between < ? @ and < = > (∆E ST  Species   S29   Table S12. Variations of some relevant bond distances (in Å), bond angles (in degrees), and dihedral angles (in degrees) when going from their singlet ground states to their corresponding triplet excited states of Re(I) complexes 1-3 and 1a-1s at the B3LYP-D3/6-31+G(d)-LANL2DZ level of theory. The atom numbering used is collected for complex 1. a   Table S14. Excitation energies in eV (E) and nm (λ), and oscillator strengths (f) of the first ten lowest-lying singlet-singlet electron transitions calculated at the PCM-TD-M06/6-31+G(d)-LANL2DZ//B3LYP-D3/6-31+G(d)-LANL2DZ level for Re(I) complexes 1a-1h. For comparison purposes, the data obtained for complex 1 are also included.