Approximate relativistic coupled-cluster calculations on heavy alkali-metal diatomics: Application to the spin-orbit-coupled $A^1{\mathrm{\Sigma }}^{+}$ and $b^3\mathrm{\Pi }$ states of RbCs and ${\mathrm{Cs}}_2$

A simple approximate version of the Fock-space relativistic coupled-cluster method is developed and applied for modeling the spin-orbit-coupling effect in the $A^1{\mathrm{\Sigma }}_{\left(u\right)}^{+}$ and $b^3{\mathrm{\Pi }}_{\left(u\right)}$ states of the heavy alkali diatomics RbCs and ${\mathrm{Cs}}_2$. Numerical stability in a wide range of molecular geometries is achieved at the cost of a very moderate loss of accuracy for low-lying states and negligibly small deviations of the computational scheme from strict size consistency. The adiabatic potential energy curves computed for the $(2,3)0^{+}$ (RbCs) and $(1,2)0_u^{+}$ (${\mathrm{Cs}}_2$) states are converted into “quasidiabatic” potentials and effective spin-orbit-coupling functions via projection of the scalar relativistic states onto the subsets of fully relativistic states. A detailed comparison of the present ab initio results with their experimental and preceding theoretical counterparts is performed.

Figure 1

Relativistic PECs ${\mathcal{E}}_i\left(R\right)$ obtained by Eq. (12) for the adiabatic $\left(2\right)0^{+}$ and $\left(3\right)0^{+}$ states of the RbCs molecule in the framework of the present FSRCC approximation: 18 electrons correlated (filled circles); 28 electrons correlated (open circles). Solid lines: empirical adiabatic PECs evaluated by Eq. (13) from the deperturbed PECs of the $A{(}^1{\mathrm{\Sigma }}^{+})$ and $b0{(}^3{\mathrm{\Pi }}_0^{+})$ states and relevant spin-orbit-coupling function ${\xi }^{\mathrm{SO}}\left(R\right)$ borrowed from Ref. [29]. Dashed lines: “difference-based” ab initio PECs built from the configuration interaction data in Ref. [30].

Figure 2

Relativistic PECs ${\mathcal{E}}_i\left(R\right)$ obtained by Eq. (12) for two lowest $(1,2)0_u^{+}$ states of ${\mathrm{Cs}}_2$ in the framework of the present FSRCC approximation: 18 electrons correlated (filled circles); 38 electrons correlated (open circles). Solid lines: empirical adiabatic PECs evaluated by Eq. (13) from the empirically deperturbed PECs of the $A{(}^1{\mathrm{\Sigma }}_u^{+})$ and $b0{(}^3{\mathrm{\Pi }}_{0u}^{+})$ states and spin-orbit-coupling function ${\xi }^{\mathrm{SO}}\left(R\right)$ from Ref. [31]. Dashed lines denote the ab initio configuration interaction data [32].

Figure 3

Locally deperturbed PECs obtained directly for the quasidiabatic $A{(}^1{\mathrm{\Sigma }}^{+})$ and $b0{(}^3{\mathrm{\Pi }}_0^{+})$ states of the RbCs molecule within the present FSRCC approximation by Eq. (9) (filled circles) and estimated by Eq. (13) from the relevant relativistic PECs (open circles). Empirically deperturbed PECs (solid lines) of the $A\sim b$ complex are taken from Ref. [29].

Figure 4

Locally deperturbed PECs obtained directly for the quasidiabatic $A{(}^1{\mathrm{\Sigma }}_u^{+})$ and $b0{(}^3{\mathrm{\Pi }}_{0u}^{+})$ states of the ${\mathrm{Cs}}_2$ molecule within the present FSRCC approximation with 18 electrons correlated by Eq. (9) (filled circles) and estimated by Eq. (13) from the relevant relativistic FSRCC PECs calculated with 38 electrons correlated (open circles). Empirically deperturbed PECs of the $A\sim b$ complex (solid lines) were borrowed from Ref. [31], while the Rydberg-Klein-Rees potential of the regularly perturbed $b^3{\mathrm{\Pi }}_{0u}^{-}$ state (dotted black line) was constructed in Ref. [33].

Figure 5

Effective spin-orbit-coupling (SOC) matrix elements ${\xi }^{\mathrm{SO}}\left(R\right)$ between the $A$ and the $b0$ states of the RbCs and ${\mathrm{Cs}}_2$ molecules. Filled circles: the present FSRCC approximation, Eq. (9). Solid lines: empirical data taken from Ref. [29] (RbCs) and Ref. [31] (${\mathrm{Cs}}_2$). Dashed line: ab initio SOC function calculated by the multireference configuration interaction method between scalar singlet $A^1{\mathrm{\Sigma }}_{\left(u\right)}^{+}$ and scalar triplet $b^3{\mathrm{\Pi }}_{0\left(u\right)}^{+}$ states in Ref. [34]. Dotted line: ab initio results obtained in Ref. [35] by the relativistic configuration interaction valence-bond method. Dotted vertical lines mark the positions of the $A-b0$ crossing point.