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 work presents a low-cost, relativistic ADC(3) framework for ionization, attachment, and excitation energies in heavy-element systems, combining Cholesky decomposition (CD), frozen natural spinors (FNS), and the X2CAMF Hamiltonian. The theory rests on the ISR formulation of ADC with a mix of two- and three-body contributions and is extended by a state-specific FNS approach to accurately describe excited states, including perturbative corrections and Davidson root-homing. Benchmark results demonstrate close agreement with canonical four-component ADC(3) results across IP, EA, and EE for heavy elements, while achieving substantial computational savings (factors up to 6–15) and enabling large systems (e.g., >2600 basis functions). The method shows strong performance on spin–orbit coupled properties, with reliable IP/EA/EE predictions and competitive transition properties, highlighting its practical impact for high-level relativistic electronic structure in challenging, large-scale systems.

Abstract

We present an efficient relativistic implementation of the algebraic diagrammatic construction (ADC) theory up to third order, incorporating Cholesky decomposition (CD) and frozen natural spinor (FNS) techniques to address electronic ionization, attachment, and excitation problems in heavy-element systems. The exact two-component atomic mean-field (X2CAMF) Hamiltonian has been employed to balance accuracy with computational efficiency, and a state-specific frozen natural spinor (SS-FNS) extension has been developed to improve excited-state descriptions. The present implementation accurately reproduces canonical four-component third-order ADC results while significantly lowering computational demands. The efficiency and performance of the present implementation are demonstrated through calculations on larger systems, with the largest system successfully treated comprising more than 2600 basis functions.

Figures (7)

• Figure 1: The schematic flowchart of CD based FNS-IP-ADC(3), SS-FNS-EE-ADC(3) and SS-FNS-EA-ADC(3).
• Figure 2: The comparison of absolute error in IP (in eV) for FNS truncation scheme of CD-based X2CAMF version of IP-ADC(3) with respect to the canonical result for IBr molecule using dyall.v2z basis set.
• Figure 3: Histogram of errors with respect to experimental value for IP of molecules in SOC-81 dataset with standard FNS-CD-IP-ADC(3) (top) and semiemperically scaled FNS-CD-IP-smADC[(2)+x(3)] (bottom) where $x=0.5$.
• Figure 4: The comparison of absolute error in excitation energies (in eV) for FNS and SS-FNS truncation schemes of CD-based X2CAMF version of EE-ADC(3) with respect to the canonical result for AuH molecule (0$^{+}$(II) state) in singly augmented dyall.v2z basis set for Au and uncontracted aug-cc-pVDZ basis set for H at different truncation thresholds.
• Figure 5: The comparison of absolute error in EA (in eV) for SS-FNS and FNS truncation schemes of CD-based X2CAMF version of EA-ADC(3) with respect to the canonical result for IBr molecule using s-aug-dyall.v2z at different truncation thresholds.