The ethylene 1 1B1u V state revisited

Abstract

We describe a general procedure to resolve the problem of artifical valence/Rydberg mixing encountered in ab initio CI calculations on the V (1 1B1u) state of ethylene. Davidson and McMurchie realized that the key to this problem are orbitals which adequately represent the V state. A two-step procedure is proposed, in which the first step focuses on generating appropriate molecular orbitals and the second step aims to describe the electron correlation quantitatively. A series of the currently most extensive MCSCF, MR-CISD, and MR-AQCC calculations for basis sets up to quadruple zeta quality and up to 80 million configurations are presented. Size extensivity corrections turn out to be crucial for highly accurate excitation energies. Our best estimate for the N–V state excitation energy of 7.7 eV lies between the experimental absorption maximum of 7.66 eV and a vibrationally corrected value of 7.8 eV. Hence, we do not find it necessary to refer to nonadiabatic effects in order to achieve agreement with the experimental data. The V state is characterized by its spatial extent, measured through the expectation value 〈x2〉, where x is the out-of-plane direction. With 16.5–17.0a02 it has a strong valence character, as compared to ≈90a02 for the 2 1B1u Rydberg state and 11.7a02 for the ground state.

Photoinduced dynamics of ethene in the N, V, and Z valence states: A six-dimensional nonadiabatic quantum dynamics investigation

“…19 The accuracy of the CASPT2 data also should be checked in critical regions of the PE surface by more accurate MRCI calculations. 8 Finally, nonadiabatic couplings with low-lying Rydbergs states, especially the 3s Rydberg state, may play a role for the radiationless decay dynamics of the V state ͑the Rydberg states have also been omitted, however, in the recent directdynamics simulations 30,32 ͒. Clearly, more comprehensive and more accurate electronic-structure and dynamics calculations are required for a complete understanding of the photochemistry of the carbon-carbon double bond.…”

Theoretical characterization of the lowest-energy absorption band of pyrrole

“…The MRMP 9 and CC 12 results can therefore be explained in the same context. Müller et al 45 recently showed that a complete removal of the valence-Rydberg mixing problems was not possible even for the most accurate correlation methods such as MS-CASPT2, multireference-singles and doubles configuration interaction ͑MR-SDCI͒, multireference quadratic coupled-cluster ͑MR-AQCC͒, or equation of motion-coupled-cluster ͑EOM-CC͒ in ethene unless the reference wave function is corrected including dynamical correlation effects. We find that MS-CASPT2 can remove most of the mixing 25 and provide good excitation energies, but in severe valence-Rydberg situations the PMCAS-CI properties can be largely perturbed by the mixing.…”

Role of Rydberg States in the Photochemical Dynamics of Ethylene

“…27 The exponent of this orbital was set to 0.0208 (in atomic units), which was determined by fitting the energy of the π-3s Rydberg [Ryd(3s) in Mulliken notation] state at the FranckÀCondon (FC) and Ryd(3s)/ππ* intersection geometries to previous computational and experimental results. 18,20,24,43,44 Details of the fitting procedure are provided in Supporting Information. The CASSCF active space consisted of three orbitals (π, π*, and 3s) with two electrons.…”