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In this paper benchmark results are presented on the calculation of vertical electronic excitation energies using a long-range second-order polarisation propagator approximation (SOPPA) description with a short-range density functional theory (srDFT) description based on the Perdew-Burke-Ernzerhof (PBE) functional. The excitation energies are investigated for 132 singlet states and 71 triplet states across 28 medium sized organic molecules. The results show that overall SOPPA-srPBE always performs better than PBE, and that SOPPA-srPBE performs better than SOPPA for singlet states, but slightly worse than SOPPA for triplet states when CC3 results are the reference values.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets, H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photo-induced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory using a truncated active-space version of the multi-configurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates dubbed ``proj LRSD'' and ``all-proj LRSD''.

In this study, the performance of the doubles-corrected higher random-phase approximation (HRPA(D)) has been investigated in calculations of NMR spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA), and is therefore computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore when calculating SSCCs it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a CCSD(T) or MP2 geometry optimization was optimal for a SOPPA and a HRPA(D) SSCCs calculation for 8 smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for the HRPA(D) SSCC calculations.

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wavefunction that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wavefunction and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarisation propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available i.e. CC3//CCSD(T) + CCSD//CCSD(T). CCSD//CCSD(T) statistics showed favourable statistics in comparison to experimental values, albeit at an unfavourably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basi

In this study, the performance of the doubles-corrected higher random-phase approximation (HRPA(D)) has been investigated in calculations of NMR spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA), and is therefore computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore when calculating SSCCs it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a CCSD(T) or MP2 geometry optimization was optimal for a SOPPA and a HRPA(D) SSCCs calculation for 8 smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for the HRPA(D) SSCC calculations.

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Op penheimer-derived electronic wavefunction that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wavefunction and adding this expectation value as a correction to an equilibrium property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, the second-order polarisation propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium values to form the highest-order vibrationally corrected values available i.e. CC3//CCSD(T) + CCSD//CCSD(T). CCSD//CCSD(T) statistics showed favourable statistics in comparison to experimental values, albeit at an unfavourably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis and/or lack of solvation effects for

The calculation of the origin-independent density of the dynamic electric dipole polarizability, previously presented for uncorrelated and density functional theory (DFT)-based methods, has been developed and implemented at the coupled cluster singles and doubles (CCSD) level of theory. A pointwise analysis of polarizability densities calculated for a number of molecules at Hartree–Fock (HF) and CCSD clearly shows that the electron correlation effect is much larger than one would argue considering the integrated dipole electric polarizability alone. Large error compensations occur during the integration process, which hide fairly large deviations mainly located in the internuclear regions. The same is observed when calculated CCSD and B3LYP polarizability densities are compared, with the remarkable feature that positive/negative deviations between CCSD and HF reverse sign, becoming negative/positive when comparing CCSD to B3LYP.

This presentation considers theoretical investigations of dye-sensitized solar cells (DSSC). Theoretical methods were applied to investigate the interactions between titanium dioxide nanoparticles and sensitizers. The ONIOM model was used to obtain the geometries of different conformers of dye molecules with TiO2 and their binding energies. TD-DFT calculations were carried out to obtain the absorption spectra and the relative orbital energy levels of sensitizers and TiO2. The electronic couplings between different sensitizers and TiO2 were calculated using the fragment charge difference method. The redox potentials of the sensitizers are calculated to complete the full working cycle of a DSSC. We observed that the -COOH group is not the only possible binding site, and the sensitizers are more likely to be adsorbed horizontally on the TiO2 surface instead of being perpendicular to the surface having the -COOH group as a linker. The TiO2 nanoparticle was found to have minor influence on the absorptions of the sensitizers with the spectra shift smaller than 0.2 eV. TiO2 has more influence on the absorptions of softer and larger molecules because the interactions between sensitizers and TiO2 twist the conjugated chromophore structures. Compared to the neutral form, the deprotonated anion conformers of the sensitizers have larger binding energy and lower LUMO level against conduction band of TiO2. The gap between the LUMO of sensitizers and conduction band edge of TiO2 might indicate the coupling strength between the sensitizers and TiO2. Several binding groups have shown promising properties for interacting with the TiO2 nanoparticle and generally deprotonated anion forms of the dyes were strongly bonded to the TiO2 nanoparticle. The model and associated calculated results provide close agreement with experimental data and give crucial atomistic information of the relevant processes in dye-sensitized solar cells.

In this work we present a systematic, theoretical investigation of the 13C NMR chemical shifts for several mono-, di- and trisaccharides in the solid state. The chemical shifts have been calculated using density functional theory (DFT) together with the gauge including the projector augmented wave (GIPAW) method as implemented in the CASTEP program. We studied the changes in the 13C NMR chemical shifts in particular due to the formation of one or two glycosidic linkages and due to crystal water. The largest changes, up to 14 ppm, are observed between the mono- and disaccharides and typically for the glycosidic linkage atoms, but not in all cases. An analysis of the bond angles at the glycosidic linkage and the observed changes in chemical shifts displays no direct correlation between them. Somewhat smaller changes in the range of 2 to 5 ppm are observed when single crystal water molecules are close to some of the atoms. Relating the changes in the chemical shifts of the carbon atoms closest to the crystal water to the distance between them does, however, not lead to a simple relation between them.

With this work we first test various DFT functionals against CCSD(T) for calculation of EFGs at the position of Cd(II) in a very small model system, Cd(SCH3)2. Moreover, the available basis sets in ADF are tested in terms of basis set convergence, and the effect of including relativistic effects using the scalar relativistic and spin orbit ZORA hamiltonians is explored. The results indicate that an error of up to around 10 % on the calculated EFG may be expected using spin-orbit ZORA and the BHandH functional with a locally dense basis set. Next, this method was applied to model systems of the CueR protein, aiming to interpret 111Ag-PAC spectroscopic data. Note that 111Ag decays to 111Cd on which the PAC data are recorded. Surprisingly, model systems truncated - as is often done - at the first C-C bond from the central Cd(II) are inadequate in size, and larger model systems must be employed to achieve reliable EFG calculations. The calculated EFGs agree well with experimental PAC data, and indicate that shortly after the nuclear decay the structure relaxes from linear two-coordinate AgS2 in the native protein, to a structure (or structures) where Cd(II) recruits additional ligands such as backbone carbonyl oxygens to achieve higher coordination number(s).

In this work, 242 NMR spin-spin coupling constants (SSCC) in 20 molecules have been calculated either with correlated wave-function methods, SOPPA and HRPA(D), or with density functional theory based on the B3LYP, BHandH, or PBE0 functionals. The calculations were carried out with and without treatment of solvation via a polarizable continuum model in both the geometry optimization step and/or the SSCC calculation, and thereby four series of calculations have been considered (the full-vacuum calculation, the full-solvent calculation, and the two cross combinations). The results were compared with the experimental results measured in a solvent. With the goal of reproducing experimental values, we find that the performance of the PBE0 and BHandH SSCCs improves upon including solvation effects. On the other hand, the quality of the B3LYP SSCCs worsens with the inclusion of solvation. The performance of the SOPPA and HRPA(D) calculations was almost not affected by whether solvation was included. We find the PBE0-based calculations of the spin-spin coupling constants to have the best agreement with the experimental data.

In this article, a modification of the second order polarization propagator approximation (SOPPA) method is introduced and illustrated for the calculation of the indirect nuclear spin-spin couplings. The standard SOPPA method, although cheaper in terms of computational cost, offers less accurate results than the ones obtained with coupled cluster methods. A new method, named SOPPA+A3-3, was therefore developed by adding the terms of the third order A matrix that rely on the second order double amplitudes. The performance of this third order contribution was studied using the CCSD method as a reference, calculating the spin-spin couplings of molecules of diverse sizes and compositions, and comparing them to the SOPPA method. The results show that inclusion of this third order contribution gives more accurate results than the standard SOPPA method with a level of accuracy close to that of the coupled cluster method with only small increase of computational cost of the response calculation that dominates the computational cost for small to medium sized molecules. The implementation of the first contributions to the third order polarization propagator approximation (TOPPA) in the Dalton program thus already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets, H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.