Multi-reference algebraic diagrammatic construction theory for excited states: General formulation and first-order implementation

Abstract

We present a multi-reference generalization of the algebraic diagrammatic construction theory (ADC) [J. Schirmer, Phys. Rev. A 26, 2395] for excited electronic states. The resulting multi-reference ADC approach (MR-ADC) can be efficiently and reliably applied to systems, which exhibit strong electron correlation in the ground or excited electronic states. In contrast to conventional multi-reference perturbation theories, MR-ADC describes electronic transitions involving all orbitals (core, active, and external) and enables efficient computation of spectroscopic properties, such as transition amplitudes and spectral densities. Our derivation of MR-ADC is based on the effective Liouvillean formalism of Mukherjee and Kutzelnigg [D. Mukherjee, W. Kutzelnigg, in Many-Body Methods in Quantum Chemistry (1989), pp. 257-274], which we generalize to multi-determinant reference states. We discuss a general formulation of MR-ADC, perform its perturbative analysis, and present an implementation of the first-order MR-ADC approximation, termed MR-ADC(1), as a first step in defining the MR-ADC hierarchy of methods. We show results of MR-ADC(1) for the excitation energies of the Be atom, an avoided crossing in LiF, doubly excited states in C 2 , and outline directions for our future developments.

Second-Order Multireference Algebraic Diagrammatic Construction Theory for Photoelectron Spectra of Strongly Correlated Systems

“…(9). Following the effective Liouvillean approach, 60,72 we express the nth-order MR-ADC matrices as:…”

“…To determine the ionization operators h (k) † µ (k = 0, 1), we use the fact that these operators must satisfy two requirements: 60,72 (i) at the kth order, the particle-hole rank of h µ |Ψ 0 = 0, which ensures decoupling of the forward and backward components of the propagator in Eq. (1).…”

“…(1). 60,72 To obtain h (0) † µ , we recall that q (0) µ = a p , where the annihilation operator can be of three different types: a i , a x , or a a (core, active, or external). Out of these three classes, only the core operator a i satisfies VAC with respect to |Ψ 0 (a † i |Ψ 0 = 0) and, thus, can be added to h (0) † µ .…”

“…We have recently proposed a multi-reference formulation of algebraic diagrammatic construction theory (MR-ADC) for simulating spectroscopic properties of strongly correlated systems. 60 MR-ADC is a generalization of the conventional (single-reference) ADC theory proposed by Schirmer in 1982. 61 Rather than computing energies and wavefunctions of individual electronic states, in MR-ADC excitation energies and transition intensities are directly obtained from poles and residues of a retarded propagator approximated using multireference perturbation theory.…”

Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation

“…Another important direction is to improve accuracy of EA-/IP-ADC for systems with unpaired electrons and moderate or strong electron correlation, for example, by developing multi-reference formulations of these methods. 45,50 Work along these directions is ongoing in our group.…”