Anharmonic excited state frequencies of para-difluorobenzene, toluene and catechol using analytic RI-CC2 second derivatives.

Analytic second nuclear derivatives for excited electronic state energies have been implemented for the resolution-of-the-identity accelerated CC2, CIS(D∞) and ADC(2) models. Our efficient implementation with O(N2) memory demands enables the treatment of medium sized molecules with large basis sets and high numerical precision and thereby paves the way for semi-numerical evaluation of the higher-order derivatives required for anharmonic corrections to excited state vibrational frequencies. We compare CC2 harmonic and anharmonic excited state frequencies with experimental values for para-difluorobenzene, toluene and catechol. Basis set problems occur for out-of-plane bending vibrations due to intramolecular basis set superposition error. For non-planar molecules and in plane modes of planar molecules, the agreement between theory and experiment is better than 30 cm-1 on average and we reassign a number of experimental bands on the basis of the ab initio predictions.

Excited state polarizabilities for CC2 using the resolution-of-the-identity approximation.

We report an implementation of static and frequency-dependent excited state polarizabilities for the approximate coupled cluster single and doubles model CC2 as analytic second derivatives of an excited state quasienergy Lagrangian. By including appropriate conditions for the normalization and the phase of the eigenvectors, divergent secular terms are avoided. This leads to response equations in a subspace orthogonal to the unperturbed eigenvectors. It is shown how these projected equations can be solved without storage of the double excitation part of the eigenvectors. By exploiting the resolution-of-the-identity approximation and a numerical Laplace transformation, the quadratic scaling of the main memory demands of RI-CC2 with the system size could be preserved. This enables calculations of excited state polarizabilities for large molecules, e.g., linear polyacenes up to decacene with almost 2500 basis functions on a single compute node within a few days. For a test set of molecules where measurements are available as reference data, we compare the orbital-relaxed and unrelaxed CC2 approaches with experiment to validate its accuracy. The approach can be easily extended to other response methods, in particular CIS(D∞). The latter gives results which, in the orbital-relaxed case, are within a few percent of the CC2 values, while coupled cluster singles results deviate typically by about 20% from orbital-relaxed CC2 and experimental reference data.

Benchmarks for 0-0 transitions of aromatic organic molecules: DFT/B3LYP, ADC(2), CC2, SOS-CC2 and SCS-CC2 compared to high-resolution gas-phase data.

In the present study a benchmark set of medium-sized and large aromatic organic molecules with 10-78 atoms is presented. For this test set 0-0 transition energies measured in supersonic jets are compared to those calculated with DFT and the B3LYP functional, ADC(2), CC2 and the spin-scaled CC2 variants SOS-CC2 and SCS-CC2. Geometries of the ground and excited states have been optimized with these methods in polarized triple zeta basis sets. Zero-point vibrational corrections have been calculated with the same methods and basis sets. In addition the energies have been corrected by single point calculations with a triple zeta basis augmented with diffuse functions, aug-cc-pVTZ. The deviations of the theoretical results from experimental electronic origins, which have all been measured in the gas phase with high-resolution techniques, were evaluated. The accuracy of SOS-CC2 is comparable to that of unscaled CC2, whereas ADC(2) has slightly larger errors. The lowest errors were found for SCS-CC2. All correlated wave function methods provide significantly better results than DFT with the B3LYP functional. The effects of the energy corrections from the augmented basis set and the method-consistent calculation of the zero-point vibrational corrections are small. With this benchmark set reliable reference data for 0-0 transition energies for larger organic chromophores are available that can be used to benchmark the accuracy of other quantum chemical methods such as new DFT functionals or semi-empirical methods for excitation energies and structures and thereby augments available benchmark sets augments present benchmark sets which include mainly smaller molecules.