Coupled cluster study of the $X̃ 2Π$ and $Ã 2Σ+$ electronic states of the HCGe radical: Renner–Teller splitting and the effects of relativistic corrections

The $X̃ 2Π$ and $Ã 2Σ+$ states of the germanium methylidyne radical (HCGe) have been investigated at the SCF, CISD, CCSD, and CCSD(T) levels of theory. The total energies, equilibrium geometries, dipole moments, harmonic vibrational frequencies, infrared intensities, and Renner–Teller splitting are reported. The relativistic one-electron Darwin and mass-velocity terms are calculated using first-order perturbation theory and the effects of these corrections on energetics, harmonic vibrational frequencies, and Renner–Teller splitting are discussed. At our highest level of theory [CCSD(T)/cc-pVQZ], the ground electronic state $(X̃ 2Π)$ has a linear geometry with $re(CH)=1.079 Å$ and $re(CGe)=1.769 Å,$ in good agreement with the experimental values of $r0(CH)=1.067 Å$ and $r0(CGe)=1.776 Å.$ In the electronically excited $Ã 2Σ+$ state, HCGe is also found to have a linear geometry with $re(CH)=1.074 Å$ and a much shorter $re(CGe)=1.669 Å$ at the [CCSD(T)/cc-pVQZ] level, in agreement with experimental values of $r0(CH)=1.059 Å,$ $r0(CGe)=1.674 Å,$ and the observation of a C–Ge triple bond character. The $Ã 2Σ+$ state C–Ge stretching vibrational frequency is determined to be $ω3=990.2 cm−1$ at the CCSD(T)/cc-pVTZ level with the inclusion of relativistic effects, which is in essentially perfect agreement with the experimental value of $ν3=990 cm−1.$ With the same method, the $X̃ 2Π$ state harmonic vibrational frequencies are predicted to be 846 cm⁻¹ for the C–Ge stretching, 443 and 506 cm⁻¹ for the two nondegenerate bending Renner–Teller components, and 3249 cm⁻¹ for the C–H stretching modes for which experimental values are not available. The quantum mechanical splitting $(T0$ value) was determined to be 38.0 kcal/mol at the nonrelativistic $CCSD(T)/TZ3P(2 f,2d)+2diff$ level, while it is found to be 39.9 kcal/mol with the inclusion of relativity, in very good agreement with the experimental value of 39.8 kcal/mol. The Renner parameter (ε) is determined to be −0.1386, and the effects of relativity were seen to produce a smaller Renner parameter of −0.1329.