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\begin{document}

\title{New Implementation of Spin-orbit Coupling Calculation on
Multi-configuration Electron Correlation Theory}



\author[1]{Qianlong Zhou}%
\author[1]{Bingbing Suo}%
\affil[1]{Northwest University}%


\vspace{-1em}



  
  \date{May 28, 2024}


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\begin{abstract}
For treating both relativistic effect and electron correlation, the
spin-free exact two-component and spin-dependent first-order
Douglas-Kroll-Hess (sf-X2C-so-DKH1) Hamiltonian and the
state-interaction (SI) method are combined to calculate the spin-orbit
coupling (SOC) on multi-configuration electron correlation theory. Here,
SOC is evaluated via SI among the spin-free states from the complete
active space self-consistent field (CASSCF) calculation, and the dynamic
electron correlation could be reckoned via the high-level
multi-reference electron correlation method. Work equations to evaluate
SOC matrix elements over spin-adapted Gelfand states in the framework of
the graphic unitary group approach (GUGA) are presented. Benchmark
calculations have verified the validity of the present implementation.
As a pilot application, the internally contracted MRCI (icMRCI) with the
inclusion of SOC calculation produces the reasonable equilibrium bond
length and the harmonic vibrational frequency of the ground state of
AuO, as well as the transition energy of
\$X\^{}2\textbackslash{}Pi\_\{3/2\} \textbackslash{}leftarrow
\^{}2\textbackslash{}Pi\_\{1/2\}\$.%
\end{abstract}%



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\textbf{Hosted file}

\verb`soc-guga-bsuo.tex`  available at \url{https://authorea.com/users/412190/articles/520957-new-implementation-of-spin-orbit-coupling-calculation-on-multi-configuration-electron-correlation-theory}

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