A Perturbative Super-CI Approach for orbital optimization in Two-Component relativistic CASSCF

Abstract

In this work, we develop a new orbital optimization approach, perturbative Super-CI (Super-CIPT), for the two-component complete active space self-consistent field (2C-CASSCF) method. By variationally optimizing spinor orbitals and consistently incorporating spin--orbit coupling (SOC) at the orbital level, the 2C-CASSCF method enables a simultaneous treatment of relativistic effects and static correlation. The Super-CIPT approach demonstrates robust convergence behavior and is applicable to systems under strong SOC. The inclusion of Gaunt or Breit term via the atomic mean field approximation yields the most accurate results, with errors dropping below 2% for halogens. We systematically assess the performance of 2C-CASSCF on spin-orbit splittings (SOSs) of selected p-block elements. Results show that 2C-CASSCF outperforms conventional one-component (1C) CASSCF. This work establishes 2C-CASSCF with Super-CIPT as a reliable and efficient approach for multireference relativistic quantum chemistry.

Figures (6)

• Figure 1: Convergence patterns of 1C- and 2C-CAS(7,4) calculations of Br, I, and At.
• Figure 2: The relative errors of SOSs of $^2P$ configuration of Cl, Br, I, and At computed by 1C- and 2C-CASSCF with four different active spaces.
• Figure 3: The relative errors of SOSs of $^2P$ configuration of Al, Ga, In, and Tl computed by 1C- and 2C-CASSCF with four different active spaces.
• Figure 4: The $^3P_1$--$^3P_0$ gaps (cm$^{-1}$) of S, Se, Te, and Po computed by 2C-CASSCF with four different active spaces.
• Figure 5: The mean unsigned relative errors of SOSs of $p$-block elements from 4$^{th}$ to 6$^{th}$ row computed by 1C- and 2C-CASSCF. The experimental values are used as reference. The number of active electrons, X = [1, 5] for group 13 to 17.