Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules

Abstract

A novel efficient implementation of the non-Dyson algebraic diagrammatic construction (ADC) scheme of the (N − 1)-part of the electron propagator up to third order of perturbation theory is presented. Due to the underlying spin-orbital formulation, for the first time, the computation of ionization potentials of open-shell radicals is thus possible via non-Dyson ADC schemes. Thorough evaluation of the accuracy, applicability, and capabilities of the new method reveals a mean error of 0.15 eV for closed- as well as open-shell atoms and molecules.

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

“…(19) and (24)) with respect to the zeroth-order operators h (0) † ±µ (i.e., 1p-1p or 1h-1h block) are precomputed in the beginning of the Davidson procedure, stored in memory, and reused at every iteration. A similar approach has been recently taken by Dempwolff and co-workers 41 in the efficient implementation of IP-ADC(3). Once the Davidson diagonalization is complete, the eigenvalues and eigenvectors are used to compute the spectroscopic amplitudes X ± (Eq.…”

“…We have verified that our IP-ADC(n) (n = 2, 3) program reproduces results from IP-ADC(n) implemented in Q-Chem. 41,52 Our EA-and IP-ADC(n) implementation features two algorithms for computing energies and density of states, which we briefly outline below.…”

“…Since then, several implementations of the single-reference non-Dyson IP-ADC methods up to third order in perturbation theory (IP-ADC(n), n = 2, 3) have been developed and applied to closed-and open-shell systems. 37,41 For computations of IP of strongly correlated systems, a multi-reference formulation of IP-ADC (2) has been recently implemented in our group. 45 Two implementations 1 of the non-Dyson EA-ADC(n) (n = 2, 3) approximations have been reported, 46,47 although performance of these methods has not been documented thoroughly in the literature.…”

adcc: A versatile toolkit for rapid development of algebraic‐diagrammatic construction methods

“…In the future we plan to extend adcc to other ADC methods of similar mathematical structure, such as IP-ADC. [53][54][55][56] To reduce the current memory requirements we want to resort to factorization techniques for the electronrepulsion integral tensor [57][58][59] or extend our tensor interface to simplify batched operations 21 and disk-based algorithms. For this we expect our focus on python and open interfaces to accelerate developments.…”

Search for long lasting electronic coherence using on-the-fly ab initio semiclassical dynamics

“…To this end, several computational schemes, such as the outer-valence Green's function (OVGF) method, 47,50 two-particle-onehole Tamm-Dancoff approximation (2ph-TDA), 50 a socalled partial third-order (P3) 51 and its renormalized variants 52 schemes, as well as the algebraic diagrammatic construction (ADC) 53,54 and the equation-ofmotion coupled-cluster for ionization potential (EOM-CC-IP) [55][56][57] techniques, have been developed in last few decades. Among these methods, ADC and EOM-CC-IP have been proven to be both highly accurate and computationally efficient [58][59][60] which make them appropriate techniques for studying electronically excited states of ionized molecules.…”