SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian With Size-Intensive Picture Change

Abstract

We present a simple relativistic exact 2-component (X2C) Hamiltonian that models two-electron picture-change effects using Lehtola's superposition of atomic potentials (SAP) [S. Lehtola, J. Chem. Theory Comput. 15, 1593-1604 (2019)]. The SAP-X2C approach keeps the low-cost and technical simplicity of the popular 1-electron X2C (1eX2C) predecessor, but is significantly more accurate and has a well-defined thermodynamic limit, making it applicable to extended systems (such as large molecules and periodic crystals). The assessment of the SAP-X2C-based Hartree-Fock total and spinor energies, spin-orbit splittings, equilibrium bond distances, and harmonic vibrational frequencies suggests that SAP-X2C is similar to the more complex atomic mean-field (AMF) X2C counterparts in its ability to approximate the 4-component Dirac-Hartree-Fock reference.

Figures (3)

• Figure 1: Errors of $Z$-adjusted X2C-HF energies with respect to 4C-DCHF. $\Delta_{\mathrm{X2C-HF}} = (E_{\mathrm{X2C-HF}} - E_{\mathrm{4C-DCHF}})/ \sum_A Z_A^2$, where $\sum_A Z_A^2$ is sum of squares of atomic numbers of all atoms in the system.
• Figure 2: Aligned potential energy surfaces (PESs) of coinage dimers (\ref{['fig:pes_Cu2']},\ref{['fig:pes_Ag2']},\ref{['fig:pes_Au2']}) and halogen dimers (\ref{['fig:pes_Br2']},\ref{['fig:pes_I2']},\ref{['fig:pes_At2']}) with 4C-DCHF and X2C-HF methods. $\Delta E \equiv E(R) - E(R_\text{eq})$.
• Figure 3: Difference between the X2C energies of the central Xe atom embedded in a $n$-atom crystal fragment ($E_{n}$) and an isolated Xe atom ($E_{1}$). Note the logarithmic scale of the horizontal axis.