Index of multi-determinantal and multi-reference character in coupled-cluster theory.

A full configuration interaction calculation (FCI) ultimately defines the innate molecular orbital description of a molecule. Its density matrix and the natural orbitals obtained from it quantify the difference between having N-dominantly occupied orbitals in a reference determinant for a wavefunction to describe N-correlated electrons and how many of those N-electrons are left to the remaining virtual orbitals. The latter provides a measure of the multi-determinantal character (MDC) required to be in a wavefunction. MDC is further split into a weak correlation part and a part that indicates stronger correlation often called multi-reference character (MRC). If several virtual orbitals have high occupation numbers, then one might argue that these additional orbitals should be allowed to have a larger role in the calculation, as in MR methods, such as MCSCF, MR-CI, or MR-coupled-cluster (MR-CC), to provide adequate approximations toward the FCI. However, there are problems with any of these MR methods that complicate the calculations compared to the uniformity and ease of application of single-reference CC calculations (SR-CC) and their operationally single-reference equation-of-motion (EOM-CC) extensions. As SR-CC theory is used in most of today's "predictive" calculations, an assessment of the accuracy of SR-CC at some truncation of the cluster operator would help to quantify how large an issue MRC actually is in a calculation, and how it might be alleviated while retaining the convenient SR computational character of CC/EOM-CC. This paper defines indices that identify MRC situations and help assess how reliable a given calculation is.

Relaxed active space: fixing tailored-CC with high order coupled cluster. II.

Due to the steep increase in computational cost with the inclusion of higher-connected cluster operators in coupled-cluster applications, it is usually not practical to use such methods for larger systems or basis sets without an active space partitioning. This study generates an active space subject to unambiguous statistical criteria to define a space whose size permits treatment at the CCSDT level. The automated scheme makes it unnecessary for the user to judge whether a chosen active space is sufficient to correctly solve the problem. Two demanding applications are presented: twisted ethylene and the transition states for the bicyclo[1,1,0]butane isomerization. As bi-radicals both systems require at least a CCSDT level of theory for quantitative results, for the geometries and energies.

The HOOH UV spectrum: importance of the transition dipole moment and torsional motion from semiclassical calculations on an ab initio potential energy surface.

The absorption cross section of HOOH, a starting point for larger ROOH, was calculated using the "Wigner method." Calculations use the Wigner transform of ground state wave functions and classical approximations for excited state wave functions. Potential energy and transition dipole moment surfaces were calculated using the equation-of-motion coupled-cluster singles and doubles method over an extended Franck-Condon region. The first two O-O stretches and the first five HOOH torsional levels are included. This study also addresses two fundamental questions about ROOH photodissociation. The long wavelength A(1)A:B(1)B excited state preference has been measured from dynamics experiments, but a Franck-Condon overlap explanation has not been directly verified. A moderate barrier to HOOH torsional motion and excited state dynamics affect the temperature dependence in the UV spectrum. Based on these initial findings for HOOH, photodissociation of large ROOH cannot be eliminated as an important factor for ozone and particulate matter production seen in both ambient and laboratory studies.