Efficiency of perturbation-selection and its orbital dependence in the SAC-CI calculations for valence excitations of medium-size molecules

Abstract

The efficiency and accuracy of the perturbation-selection used in the symmetry-adapted cluster-configuration interaction (SAC-CI) calculations are investigated for several low-lying valence excited states of 21 medium-size molecules, including typical chromophores with heterocyclic macrocycles (free-base porphine, coumarin, indole, and BODIPY), nucleobases, amino acids (tyrosine and tryptophan), polycyclic aromatic hydrocarbons, and organometallics (ferrocene and Re(bpy)(CO)4+1). Benchmark SAC-CI calculations with up to 110 million operators are performed. The efficiency of the perturbation-selection depends on the molecular orbitals (MOs); therefore, the canonical MO and localized MO (LMO) obtained by Pipek-Mezey's method are examined. Except for the highly symmetric molecules, using LMOs improves the efficiency and accuracy of the perturbation-selection. With using LMOs and perturbation-selection, sufficiently reliable results can be obtained in less than 10% of the computational costs required for the full-dimensional calculations. The perturbation-selection with LMOs is suggested to be a promising method for excited states in larger molecular systems.

Projected CAP/SAC‐CI method with smooth Voronoi potential for calculating resonance states

“…To reduce the computational cost, we used the perturbation selection of both R and S operators . Recently, we have performed the benchmark calculations with respect to the energy thresholds of operator selection using the reference functions of canonical and localized molecular orbitals (MOs) . The LevelFour accuracy with the energy thresholds of and was adopted in the present calculations.…”

Theoretical prediction of valence and Rydberg excited states: Minnesota exchange‐correlation functionals vs symmetry adapted cluster‐configuration interaction

“…Pragmatically, for the SAC‐CI calculations we have utilized the SAC‐CI SD‐ R framework where the linked operators consist of the single (S) and double (D) excitation operators. In addition, following previous suggestions on the levels of the perturbation selection of linked operators in the SAC‐CI calculations, the LevelThree accuracy (the energy thresholds (au) of λ g = 1.0 × 10 −6 and λ e = 1.0 × 10 −7 for the ground and excited states, respectively) which provides reasonably accurate results in most cases was adopted …”

Comparing the performance of TD‐DFT and SAC‐CI methods in the description of excited states potential energy surfaces: An excited state proton transfer reaction as case study

“…The benchmark calculations comparing SAC‐CI and TD‐DFT were also recently done for vertical and adiabatic transition energies as well as CT index . Typical error of the SAC‐CI transition energy is below 0.3 eV observed in the recent benchmarks, while the accuracy for the relative energy and barrier is nearly the same as CCSD whose error is usually less than few kcal/mol in the ground state reaction. The partial optimization was performed by SAC‐CI/6‐31G(d) followed by single point calculations with 6‐31 + G(d,p) basis set.…”

“…The partial optimization was performed by SAC‐CI/6‐31G(d) followed by single point calculations with 6‐31 + G(d,p) basis set. The Pipek‐Mezey localized MOs were used for reducing the error from perturbation selection of operators . Here, accurate calculations with very tight thresholds, 1.0 10 −9 and 1.0 10 −10 for 6‐31G(d) and 0.5 10 −9 and 0.5 10 −10 for 6‐31 + G(d,p) were carried out for ground and ESs, respectively.…”