Multi-state Multireference Rayleigh–Schrödinger Perturbation Theory for Mixed Electronic States: Second and Third Order

The formalism for multi-state multireference configuration-based Rayleigh-Schrödinger perturbation theory and procedures for its implementation for the second-order and third-order energy within a multireference configuration interaction computer program are reviewed. This formalism is designed for calculations on electronic states that involve strong mixing between different zero-order contributions, such as avoided crossings or mixed valence-Rydberg states. Such mixed states typically display very large differences in reference-configuration mixing coefficients between the reference MCSCF wave function and an accurate correlated wave function, differences that cannot be reflected in state-specific (diagonalize-then-perturb) multireference perturbation theory through third order. A procedure described in detail applies quasidegenerate perturbation theory based on a model space of a few state-averaged MCSCF functions for the states expected to participate strongly in the mixing, and can be characterized as a “diagonalize-then-perturb-thendiagonalize†approach. It is similar in various respects to several published methods, including an implementation by Finley, Malmqvist, Roos, and Serrano-Andrés [Chem. Phys. Lett. 1998, 288, 299–306]

Multi-state Multireference Rayleigh–Schrödinger Perturbation Theory for Mixed Electronic States: Second and Third Order

Abstract: The formalism for multi-state multireference configuration-based Rayleigh-Schrödinger perturbation theory and procedures for its implementation for the second-order and third-order energy within a multireference configuration interaction computer program are reviewed. This formalism is designed for calculations on electronic states that involve strong mixing between different zero-order contributions, such as avoided crossings or mixed valence-Rydberg states. Such mixed states typically display very large differences in reference-configuration mixing coefficients between the reference MCSCF wave function and an accurate correlated wave function, differences that cannot be reflected in state-specific (diagonalize-then-perturb) multireference perturbation theory through third order. A procedure described in detail applies quasidegenerate perturbation theory based on a model space of a few state-averaged MCSCF functions for the states expected to participate strongly in the mixing, and can be characterized as a “diagonalize-then-perturb-thendiagonalize” approach. It is similar in various respects to several published methods, including an implementation by Finley, Malmqvist, Roos, and Serrano-Andrés [Chem. Phys

CYCLOPROPENYL CATION: A PROTOTYPE AROMATIC SYSTEM

Author Institution: Battelle Columbus LaboratoriesThe cyclopropenyl cation is the simplest member of the $(4n \ + \ 2) \Pi -$electron H\""{u}ckel aromatic series. Therefore, it provides an economical case on which to test computational procedures that might be applied to cyclic $\Pi$-electron systems. Self-consistent field and configuration interaction wavefunctions are used to calculate the ground state and some lowlying excited state energies of the $C_{3}H_{3} ^{+}$ system. The effects of polarization end diffuse basis functions in conjunction with various prescriptions for defining the CI wavefunctions are studied. A comparison among these prescriptions can provide a means to judge the approximations necessary to treat larger aroamatic systems

AVERAGE AND DIRECTIONAL COMPTON PROFILES OF H2OH_{2}O FROM SCF AND CI WAVEFUNCTIONS.

Author Institution: Department of Chemistry, The Ohio State UniversityThe expressions necessary for calculating the spherically averaged and directional Compton profiles using Caussian and Slater basis sets have been derived and applied to calculations on the water molecule. The Spherically averaged profile and profiles along the principal axes and several other directions in the molecular plane have been calculated from high-quality wavefunctions at both the SCF and CI levels. Calculations were carried out at 36 points on the molecular potential surface and the results were vibrationally averaged. The anisotropy of the Compton profile, the electron correlation effects, and the vibrational corrections are described

ELECTRONIC STRUCTURE OF HCCO RADICAL

Author Institution: Department of Chemistry, The Ohio State UniversitySeveral electronic states of the HCCO radical have been studied by ab initio SCF, MCSCF, CI, and UMP2 calculations. Geometry optimizations have been carried out with a TZP basis set at the UMP2 level for the lower two states and at the SDCl level for the upper two states. Generally-contracted Dunning correlation-consistent pVDZ and pVTZ basis sets have been used for the accurate energy determination. The two lowest states form a Renner-Teller pair, degenerate ($^{2}\Pi$) at the linear geometry and split into a bent $1^{2}A^{\prime\prime}$ ground state and a linear $1^{2}\Pi$ excited state which becomes $^{2}A^{\prime}$ upon bending.Davidson-corrected 56-reference SDCI with a Dunning generally-contracted [431/31] basis set gives an energy difference of 981 $cm^{-1}$ for the lower Renner-Teller pair. Two higher states, $2^{2}A^{\prime}$ and $2^{2}\Pi$, also form a Renner-Teller pair with a barrier to the linearity of 311 $cm^{-1}$. The same level of calculation places these states about 32316 $cm^{-1}$ above the ground state minimum. The bonding is mostly $H-C=C=O$ in the two lowest states, and is H-C$\equiv$ C- \.{O} in the upper pair of states. The equilibrium geometries of the various states are given in the following table. [FIGURE] Optimized at the UMP2 and SDCl levels with a Dunning TZP segmented -contraction basis set. The bent structures are in trans conformation."