Accurate calculation of Franck-Condon factors for molecules with strongly anharmonic potentials
Physical Chemistry of Molecules, Liquids and Interfaces, Biophysical Chemistry
Final Report Abstract
Two programs for calculating photoelectron spectra have been implemented into the M OLPRO suite of ab initio programs, which make use of correlated anharmonic vibrational wavefunctions of molecules of arbitrary size. These programs are based on the Watson Hamiltonian and thus rely on normal coordinates. Both of them fully account for Duschinsky effects and can treat correlation spaces including several million of configurations (Hartree products). The first approach depends on state-specific configuration-selective VCI calculations, which have been accelerated by 2-3 orders of magnitude. These calculations rely on simple VSCF modals or on wavefunctions obtained from a new implementation of configuration average VSCF theory (CA-VSCF), which showed much better convergence properties than state-average VMCSCF calculations. This approach, which fully accounts for vibrational angular momentum terms, allows for the efficient calculations of photoelectron spectra as long as the contributing vibrational states show leading VCI coefficients larger than about 0.5. This has been demonstrated for the photoelectron spectrum of ketene and its deuterated analog. Excellent agreement in comparison to an experimental spectrum has been achieved from Franck-Condon factors relying on multi-dimensional potential energy surfaces obtained from explicitly correlated coupled-cluster theory. However, this approach fails once the spectrum is dominated by states, which are not dominated by a single configuration (leading VCI coefficients less than 0.5). In such cases an approach based on time-independent Raman wavefunction (RWF) theory was found to perform much better. It’s strength arises from bypassing the individual calculation of vibrational states and their proper assignment. The inhomogeneous Schrodinger equation (ISE) offers a convenient ansatz for the eigenstate-free determination of the RWF. Moreover, in dependence on the required resolution, RWF calculations can be much faster than sum-over-states Franck-Condon calculations. Based on high-level (U)CCSD(T)-F12a/cc-pVTZ-F12 calculations for the potential energy surfaces of difluoromethane and its radical cation, we have computed the X˜2B2 ←− X˜1A1 photoelectron spectrum. Again, in comparison to experimental results excellent agreement has been achieved from RWF calculations, while the state-specific VCI approach failed in this extreme case. Consequently, a pool of methods for calculating anharmonic photoelectron spectra of increasing complexity has been provided, which has been benchmarked on selected molecules.
Publications
- Transformation of potential energy surfaces for estimating isotopic shifts in anharmonic vibrational frequency calculations. J. Chem. Phys. 2014, 140, 184111
P. Meier, D. Oschetzki, R. Berger and G. Rauhut
(See online at https://doi.org/10.1063/1.4874849) - Anharmonic Franck-Condon factors for the X˜2B2 ←− X˜1A1 photoionization of ketene. J. Phys. Chem. A 2015, 119, 10264
G. Rauhut
(See online at https://doi.org/10.1021/acs.jpca.5b06922) - Comparison of methods for calculating Franck-Condon factors beyond the harmonic approximation: how important are Duschinsky rotations? Mol. Phys. 2015, 113, 3859
P. Meier and G. Rauhut
(See online at https://doi.org/10.1080/00268976.2015.1074740) - Time-independent eigenstate-free calculation of vibronic spectra beyond the harmonic approximation. J. Chem. Phys. 2015, 143, 234106
T. Petrenko and G. Rauhut
(See online at https://doi.org/10.1063/1.4937380) - Towards an automated and efficient calculation of resonating vibrational states based on state-averaged multiconfigurational approaches. J. Chem. Phys. 2015, 143, 244111
P. Meier, D. Oschetzki, F. Pfeiffer and G. Rauhut
(See online at https://doi.org/10.1063/1.4938280) - A new efficient method for the calculation of interior eigenpairs and its application to vibrational structure problems. J. Chem. Phys. 2017, 146, 124101
T. Petrenko and G. Rauhut
(See online at https://doi.org/10.1063/1.4978581)
