Excitation energies from extended random phase approximation employed with approximate one- and two-electron reduced density matrices

Abstract

Starting from Rowe's equation of motion we derive extended random phase approximation (ERPA) equations for excitation energies. The ERPA matrix elements are expressed in terms of the correlated ground state one- and two-electron reduced density matrices, 1- and 2-RDM, respectively. Three ways of obtaining approximate 2-RDM are considered: linearization of the ERPA equations, obtaining 2-RDM from density matrix functionals, and employing 2-RDM corresponding to an antisymmetrized product of strongly orthogonal geminals (APSG) ansatz. Applying the ERPA equations with the exact 2-RDM to a hydrogen molecule reveals that the resulting (1)Σ(g)(+) excitation energies are not exact. A correction to the ERPA excitation operator involving some double excitations is proposed leading to the ERPA2 approach, which employs the APSG one- and two-electron reduced density matrices. For two-electron systems ERPA2 satisfies a consistency condition and yields exact singlet excitations. It is shown that 2-RDM corresponding to the APSG theory employed in the ERPA2 equations yields excellent singlet excitation energies for Be and LiH systems, and for the N(2) molecule the quality of the potential energy curves is at the coupled cluster singles and doubles level. ERPA2 nearly satisfies the consistency condition for small molecules that partially explains its good performance.

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

“…10 We briefly summarize two approaches, called ERPA and ERPA2, proposed in Ref. 10. They are based on the equations of motion of Rowe.…”

“…Only recently some initial results have been presented. 10 We briefly summarize two approaches, called ERPA and ERPA2, proposed in Ref. 10.…”

“…It has been shown that in case of singlet two-electron systems the ERPA excitation operator does not yield exact singlet excited states. 10 The problem is cured by including the diagonal double excitations in the operator that leads to the ERPA2 approximation…”

“…Only recently, first examples of excitation energies obtained by employing APSG density matrices in the extended random phase approximation equations (ERPA and ERPA2) have been presented. 10 The proposed ERPA2 approach has been shown to be exact for singlet excitation energies of two-electron systems and to provide very accurate single and double excitations of beryllium atom and LiH molecule.…”

Perspective on natural orbital functional theory

“…[58] A way around the adiabatic approximation is the recently proposed extended random phase approximation (ERPA) method. [59] Both methods provide a practical route for obtaining excitation energies in the NOFT as it is highly difficult to impose the N-representability conditions on these states. The ERPA method looks quite promising as have already demonstrated the calculations of the excitation energies within the APSG framework.…”