A MCSCF method for ground and excited states based on full optimizations of successive Jacobi rotations

Abstract

A new multiconfigurational self-consistent field (MCSCF) method based on successive optimizations of Jacobi rotation angles is presented. For given one- and two-particle density matrices and an initial set of corresponding integrals, a technique is developed for the determination of a Jacobi angle for the mixing of two orbitals, such that the exact energy, written as a function of the angle, is fully minimized. Determination of the energy-minimizing orbitals for given density matrices is accomplished by successive optimization and updating of Jacobi angles and integrals. The total MCSCF energy is minimized by alternating between CI and orbital optimization steps. Efficiency is realized by optimizing CI and orbital vectors quasi-simultaneously by not fully optimizing each in each improvement step. On the basis of the Jacobi-rotation based approach, a novel MCSCF procedure is formulated for excited states, which avoids certain shortcomings of traditional excited-state MCSCF methods. Applications to specific systems show the practicability of the developed methods.

Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources

“…In the classical literature it is common to use the second order approximation of u u = e t ≈ I + t + 1 2 t 2 (12) to minimize energy in a Newton-Raphson style [44][45][46][47]. A well known alternative to parameterizing the unitary as an exponentiated antihermitian matrix is the use of Givens rotations [48,49]. This parameterization uses a set of angles {θ} associated with the set of non-redundant orbital rotation generators.…”

“…The optimal rotation of a single angle with respect to the input 2-RDM, one-, and two-electron integrals has been derived [49] along with a sweep procedure to find an energy minimizing U . This algorithm was used for developing 2-RDM MCSCF methods [50] and the first orbital-optimized coupled-cluster doubles methods [51].…”

Quantum mechanical/molecular mechanical/continuum style solvation model: Time-dependent density functional theory

“…One is for the conductorlike polarizable continuum model (CPCM, 69, 70 a variant of COSMO 71 ) and the EFP 9, 10, 58, 59 method (code already released for public use in Aug 2011), the other is for the FixSol 72 solvation model (similar to COSMO 71 and CPCM 69, 70 but with modified short-range surface charge interactions) and general induced dipole polarizable force field methods in the quantum chemistry polarizable force field (QuanPol) 73 program, which is designed for general MM and QM/MM calculations. In QuanPol calculations, the QM methods can be HF, generalized valence bond theory (GVB), 74 multiconfiguration selfconsistent-field (MCSCF, [75][76][77][78] including state-average MC-SCF, or SA-MCSCF 79-81 ), DFT, 82 TDDFT, 16,17 and second order Møller-Plesset perturbation theory (MP2) 83 methods. The QuanPol program is integrated in and distributed with the GAMESS package.…”

Mean field QM/MM method: Average position approximation

“…The QM methods can be Hartree-Fock (HF), generalized valence bond theory (GVB 7 ), multiconfiguration self-consistent-field (MCSCF [8][9][10][11] ), density functional theory (DFT 12 ), time-dependent density functional theory (TDDFT 13,14 ), and second order Møller-Plesset perturbation theory (MP2 15 ) methods. The QuanPol package is integrated in and distributed with the General Atomic and Molecular Electronic Structure System (GAMESS 16,17 ) package.…”