Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

Abstract

We have calculated state-averaged complete-active-space self-consistent-field (SA-CASSCF), multiconfiguration pair-density functional theory (MC-PDFT), hybrid MC-PDFT (HMC-PDFT), and n-electron valence state second-order perturbation theory (NEVPT2) excitation energies with the approximate pair coefficient (APC) automated active-space selection scheme for the QUESTDB benchmark database of 542 vertical excitation energies. We eliminated poor active spaces (20–40% of calculations) by applying a threshold to the SA-CASSCF absolute error. With the remaining calculations, we find that NEVPT2 performance is significantly impacted by the size of the basis set the wave functions are converged in, regardless of the quality of their description, which is a problem absent in MC-PDFT. Additionally, we find that HMC-PDFT is a significant improvement over MC-PDFT with the translated PBE (tPBE) density functional and that it performs about as well as NEVPT2 and second-order coupled cluster on a set of 373 excitations in the QUESTDB database. We optimized the percentage of SA-CASSCF energy to include in HMC-PDFT when using the tPBE on-top functional, and we find the 25% value used in tPBE0 to be optimal. This work is by far the largest benchmarking of MC-PDFT and HMC-PDFT to date, and the data produced in this work are useful as a validation of HMC-PDFT and of the APC active-space selection scheme. We have made all the wave functions produced in this work (orbitals and CI vectors) available to the public and encourage the community to utilize this data as a tool in the development of further multireference model chemistries.

The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

“…255,272−277 Benchmark tests on a diverse set of excitation energies suggest that for the tPBE on-top functional, the optimal hybridization parameter is λ = 0.25, the same as in the "PBE0" exchange−correlation functional 278,279 of Kohn− Sham density functional theory; this hybrid on-top functional is referred to as "tPBE0". 255,272 The LAMBDA keyword is used in the MC-PDFT program to control the hybridization. The recommended tPBE0 functional, for instance, can be specified by LAMBDA = 0.…”

Linearized Pair-Density Functional Theory

“…13 Multiconfiguration pair-density functional theory 14 (MC-PDFT) is a post-SCF method that that has been shown to be a computationally efficient method for computing potential energy surfaces (PESs) of excited states. 15,16 Starting from a multiconfigurational wave function, such as that provided by the complete active space SCF (CASSCF) method, MC-PDFT computes a corrected energy through a nonvariational energy expression which is a functional of the electron density (ρ) and on-top pair density (Π). Consequently, the MC-PDFT energies are not eigenvalues of any particular Hamiltonian or quantum operator, and the energy of each state is computed independently of the other states involved in the calculation.…”

“…16 with λ equal to 0.25 and the tPBE functional in the MC-PDFT term as an HMC-PDFT calculation with the hybrid functional tPBE0. Because it has been found that hybrid functionals, such as tPBE0, are more accurate than non-hybrid ones for certain systems, 16 we also construct a hybrid linearized PDFT (HL-PDFT) Hamiltonian.…”

Orthogonally Constrained Orbital Optimization: Assessing Changes of Optimal Orbitals for Orthogonal Multireference States

“…As an alternative for systems based on large active spaces, Density-Matrix-Renormalization-Group techniques have been also employed in the context of ensemble calculation with orbital optimization 11,12 benchmarking multireference excitation energies using stateaverage methods and the active space selection issue. 14 In this letter, our objective is to emphasize that stateaveraged methods may not be necessarily the best starting points to quantitatively evaluate vertical transition. A hereproposed alternative is the application of the variational method restricted to a subspace orthogonal to the ground state.…”

“…As an alternative for systems based on large active spaces, Density-Matrix-Renormalization-Group techniques have been also employed in the context of ensemble calculation with orbital optimization , (e.g., see ref for an application to photochromic systems). Tremendous efforts are still put into benchmarking multireference excitation energies using state-average methods and the active space selection issue …”