Extended Second-Order Multireference Algebraic Diagrammatic Construction Theory for Charged Excitations

Abstract

We report a new implementation of multireference algebraic diagrammatic construction theory (MR-ADC) for simulations of electron attachment and ionization in strongly correlated molecular systems (EA/IP-MR-ADC). Following our recent work on IP-MR-ADC [J. Chem. Theory Comput. 2019, 15, 5908], we present the first implementation of the second-order MR-ADC method for electron attachment (EA-MR-ADC(2)) and two extended second-order approximations (EA- and IP-MR-ADC(2)-X) that incorporate a partial treatment of third-order electron correlation effects. Introducing a small approximation for the second-order amplitudes of the effective Hamiltonian, our implementation of EA- and IP-MR-ADC(2)-X has a low computational scaling with the basis set size M. Additionally, we describe an efficient algorithm for solving the first-order amplitude equations in MR-ADC and partially contracted second-order N-electron valence perturbation theory (NEVPT2) which completely avoids computation of the four-particle reduced density matrices without introducing any approximations or imaginary-time propagation. For a benchmark set of eight small molecules, a carbon dimer, and a twisted ethylene, we demonstrate that EA- and IP-MR-ADC(2)-X achieve an accuracy similar to that of strongly contracted NEVPT2 while having a lower computational scaling with the active space size and providing efficient access to transition properties.

Simulating X-ray photoelectron spectra with strong electron correlation using multireference algebraic diagrammatic construction theory

“…For more details, we refer the readers to our previous publications. [67][68][69][70] Ionization of a many-electron system irradiated with light of frequency o is described by the backward component of the one-particle Green's function, 92,93 G pq (o):…”

“…[73][74][75][76][77][78] In this work, we use two MR-ADC methods: the strict secondorder approximation (MR-ADC(2)) and its extended version (MR-ADC(2)-X). 68,69 Fig. 1 shows the perturbative structure of the effective Hamiltonian matrix M for both methods where each matrix element corresponds to a pair of excitations.…”

“…The higher-order treatment of the hC (1) m |-|C (1) m i block in MR-ADC(2)-X significantly improves the description of orbital relaxation effects for singly-ionized states and provides a better description of the satellite transitions, which involve an ionization and a one-electron excitation simultaneously. In addition, the MR-ADC(2)-X method incorporates higher-order contributions to the effective transition moments matrix T. 68,69 2.2 MR-ADC with core-valence separation for X-ray photoelectron spectra An important feature of MR-ADC is the ability to simulate electronic excitations involving all electrons and molecular orbitals of the system, in contrast to conventional multireference methods that can only simulate excitations in active orbitals. This feature is particularly useful for simulating the electronic transitions in X-ray absorption or photoelectron spectra, which originate from doubly occupied core orbitals that are not strongly correlated and should not be included in the active space.…”

“…We combined the CVS approximation with the second-order MR-ADC(2) and extended second-order MR-ADC(2)-X methods for electron ionization. 68,69 The resulting CVS-MR-ADC(2) and CVS-MR-ADC(2)-X methods were implemented in Prism, a standalone Python program for spectroscopic simulations of multireference systems. To obtain the one-and two-electron integrals and the reference CASSCF wavefunctions, Prism was interfaced with the Pyscf software package.…”

“…In this work, we present a new approach for the XPS simulations of strongly correlated systems that combines multireference algebraic diagrammatic construction theory (MR-ADC) [67][68][69][70] with a core-valence separation technique (CVS). 71,72 The MR-ADC approach is naturally suited for the simulations of core-level excitations combining several attractive features: (i) low computational cost (similar to that of multireference perturbation theories), [73][74][75][76][77][78] (ii) Hermitian equations, and (iii) the ability to calculate excitations from all molecular orbitals, including inner-shell and core.…”