Quantum chemical calculations of X-ray emission spectroscopy

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time dependent density functional theory (TDDFT) and resolution of the identity single excitation configuration interaction with second order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s or- bitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment, however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range cor- rected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B66LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, ace- tone, dimethyl sulfoxide and CF3Cl in good agreement with experiment

Exploring copper(I)-based dye-sensitized solar cells : a complementary experimental and TD-DFT investigation

The structures and properties of the homoleptic copper(I) complexes [Cu(1)(2)][PF6] and [Cu(2)(2)][PF6] (1 = 6,6`-dimethyl-2,2`-bipyridine, 2 = 6,6`-bis2-[4-(N,N`-diphenylamino)phenyl]ethenyl-2,2`-bipyridine) are compared, and a strategy of ligand exchange in solution has been used to prepare eight TiO2 surface-bound heteroleptic complexes incorporating ligands with bpy metal-binding domains and carboxylate or phosphonate anchoring groups. The presence of the extended pi-system in 2 significantly improves dye performance, and the most efficient sensitizers are those with phosphonate or phenyl-4-carboxylate anchoring units; a combination of [Cu(2)(2)](+) with the phosphonate anchoring ligand gives a very promising performance (eta = 2.35% compared to 7.29% for standard dye N719 under the same conditions). The high-energy bands in the electronic absorption spectrum of [Cu(2)(2)](+) which arise from ligand-based transitions dominate the spectrum, whereas that of [Cu(1)(2)](+) exhibits both MLCT and ligand pi* >- pi bands. Both [Cu(1)(2)][PF6] and [Cu(2)(2)][PF6] are redox active; while the former exhibits both copper-centred and ligand-based processes, [Cu(2)(2)][PF6] shows only ligand-based reductions. Results of TD-DFT calculations support these experimental data. They predict an electronic absorption spectrum for [Cu(1)(2)](+) with an MLCT band and high-energy ligand-based transitions, and a spectrum for [Cu(2)(2)](+) comprising transitions involving mainly contributions from orbitals with ligand 2 character. We have assessed the effects of the atomic orbital basis set on the calculated absorption spectrum of [Cu(1)(2)](+) and show that a realistic spectrum is obtained by using a 6-311++G** basis set on all atoms, or 6-311++G** on copper and 6-31G* basis set on all other atoms; a smaller basis set on copper leads to unsatisfactory results. Electronic absorption spectra of six heteroleptic complexes have been predicted using TD-DFT calculations, and the transitions making up the dominant bands analysed in terms of the character of the HOMO-LUMO manifold. The calculational data reveal dominant phosphonate ligand character in the LUMO for the dye found to function most efficiently in practice, and also reveal that the orbital character in the HOMOs of the two most efficient dyes is dominated by the non-anchoring ligand 2, suggesting that ligand 2 enhances the performance of the sensitizer by minimizing back-migration of an electron from the semiconductor to the dye