Excited States from State-Specific Orbital-Optimized Pair Coupled Cluster

Abstract

The pair coupled cluster doubles (pCCD) method (where the excitation manifold is restricted to electron pairs) has a series of interesting features. Among others, it provides ground-state energies very close to what is obtained with doubly occupied configuration interaction (DOCI), but with a polynomial cost (compared with the exponential cost of the latter). Here, we address whether this similarity holds for excited states by exploring the symmetric dissociation of the linear H 4 molecule. When ground-state Hartree−Fock (HF) orbitals are employed, pCCD and DOCI excited-state energies do not match, a feature that is assigned to the poor HF reference. In contrast, by optimizing the orbitals at the pCCD level (oo-pCCD) specifically for each excited state, the discrepancies between pCCD and DOCI decrease by 1 or 2 orders of magnitude. Therefore, the pCCD and DOCI methodologies still provide comparable energies for excited states, but only if suitable, state-specific orbitals are adopted. We also assessed whether a pCCD approach could be used to directly target doubly excited states, without having to resort to the equation-of-motion (EOM) formalism. In our Δoo-pCCD model, excitation energies are extracted from the energy difference between separate oo-pCCD calculations for the ground state and the targeted excited state. For a set comprising the doubly excited states of CH + , BH, nitroxyl, nitrosomethane, and formaldehyde, we found that Δoo-pCCD provides quite accurate excitation energies, with root-mean-square deviations (with respect to full configuration interaction results) lower than those of CC3 and comparable to those of EOM-CCSDT, two methods with a much higher computational cost.

Reduced density matrix functional theory from an ab initio seniority-zero wave function: Exact and approximate formulations along adiabatic connection paths

“…Finally, the computational burden of performing DOCI calculations within our seniority-zero reformulation of RDMFT can be bypassed by considering recent advances in practical DOCI calculations, such as variational 2RDM-based approximations [97,[130][131][132], CIPSI [68], FCIQMC solvers [133], a proper choice of Richardson-Gaudin states [134], the pair parametric two-electron reduced density matrix approach [73], or even using quantum computers [135]. Turning to the second term on the left-hand side of Eq.…”

“…Even though seniority-zero wave functions can describe accurately strong (static) correlation effects, their evaluation is computationally demanding and a proper description of dynamical correlation effects requires taking into account higher seniorities [67] or mixing excitation degrees and seniority numbers [68]. Other promising approaches that retain the computational cost of a mean-field and are adequate for the treatment of strong correlation have been proposed, like the so-called antisymmetric product of one-reference-orbital geminals (AP1roG) [62,69,70] equivalent to the pair-coupled cluster theory (p-CCD) [71,72], or more recently the pair parametric two-electron reduced density matrix approach [73].…”

“…Orbital optimization is essential in these approaches for the accurate description of both ground [71,74,75] and excited states [68,76]. Despite promising results, AP1roG and related geminal-based wave functions are not adequate to capture dynamical correlation [77].…”

Supporting Notebook for "Energy Landscape of State-Specific Electronic Structure Theory"

“…This philosophy relies on the existence of additional higher-energy mathematical solutions, which have been found in Hartree-Fock (HF), 22, density functional theory (DFT), [49][50][51][52] multiconfigurational self-consistent field (MC-SCF), [53][54][55][56][57][58][59][60][61] and coupled a) Electronic mail: hugh.burton@chem.ox.ac.uk cluster (CC) theory. [62][63][64][65][66] These multiple solutions correspond to higher-energy stationary points of a parametrised approximate energy function, including local energy minima, saddle points, or maxima. It has long been known that the exact k-th excited state forms a saddle point of the energy with k negative Hessian eigenvalues (where k = 0 is the ground state).…”

Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation

“…N P ×N P G N P ×(N orb −N P ) G † (N orb −N P )×N P I (N orb −N P )×(N orb −N P ), so variational optimization of the AP1roG wavefunction has factorial scaling. It has however shown promise when targeting states specifically 89,90. …”