Abstract
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.
Highlights
The characterisation of molecules in excited electronic states remains a challenge, both for experimental and theoretical chemistry
Benchmark studies,[12,13,14,15] found that EOM-CCSD ground and excited state harmonic frequencies agree with values derived from experiment with a root mean squared deviation (RMSD) of 20–30 cmÀ1
The molecule para-difluorobenzene has been the focus of a considerable number of spectroscopic explorations to determine its ground and excited state structure and dynamics[43,44,45,46,47,48] including the intramolecular vibrational redistribution pathways in the excited state, which are mediated by rotational coupling and through Fermi resonance.[49,50]
Summary
The characterisation of molecules in excited electronic states remains a challenge, both for experimental and theoretical chemistry. Second-order electronic response properties for ground and excited states and ground state nuclear Hessians as analytic second derivatives of the energy have been implemented.[25,26,27] To preserve both the high computational efficiency and the low storage demands for second derivatives the RI approximation is combined with a numerical Laplace transformation of orbital energy denominators[28] for the contribution of double excitation amplitudes to first derivatives of the density matrices. Recently has a similar route has been pursued for TDDFT.[29,30] With the implementation of analytic Hessians for CC2 and ADC(2) it becomes possible to compute anharmonic vibrational spectra of polyatomic molecules with a correlated ab initio wavefunction method. We demonstrate the applicability of our implementation by computing harmonic and anharmonic excited state frequencies for medium sized molecules, which we compare to experimentally observed band centres
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