A Low Cost Relativistic Algebraic Diagrammatic Construction Method Based on Cholesky Decomposition and Frozen Natural Spinors for Electronic Ionization, Attachment and Excitation Energy Problem

TL;DR

This paper introduces a computationally efficient relativistic ADC method for electronic ionization, attachment, and excitation energies in heavy-element systems, utilizing Cholesky decomposition and frozen natural spinors to reduce cost without losing accuracy.

Contribution

It develops a low-cost relativistic ADC(3) implementation combining Cholesky decomposition and frozen natural spinors, with a semi-empirical scaled variant for improved excited state description.

Findings

Achieves significant computational savings over canonical methods.

Accurately reproduces four-component ADC(3) results.

Demonstrates effectiveness on large molecular systems with over 2600 basis functions.

Abstract

We present an efficient relativistic implementation of algebraic diagrammatic construction (ADC) theory up to third order for the treatment of electronic ionization potentials (IP), electron affinities (EA), and excitation energies (EE) in heavy-element systems using an exact two-component atomic mean-field (X2CAMF) Hamiltonian. The approach combines Cholesky decomposition (CD) of two-electron integrals with frozen natural spinors (FNS) to significantly reduce the computational cost without compromising accuracy. To improve the description of excited states, we have implemented a state-specific frozen natural spinor (SS-FNS) framework and applied it to both electron affinity and excitation energy calculations. In addition to the standard relativistic ADC(3) method, we investigate a semi-empirically scaled variant in which the third-order contribution to the ADC secular matrix is multiplied by a scaling factor (x), denoted as FNS/SS-FNS-[ADC(2)+(x)(3)]. This [ADC(2)+(x)(3)] approach shows systematic improvements over conventional ADC(3) in a variety of cases. Substantial computational savings are achieved through the use of FNS and SS-FNS schemes when compared to canonical calculations, resulting in significant speedups for ionization, attachment, and excitation energy computations. The current implementation accurately reproduces the canonical four-component ADC(3) results while significantly reducing computational cost. The efficiency and robustness of the method are demonstrated through applications to medium and large-sized molecular systems, including systems with 70 atoms and over 2600 basis functions.