Vibrations in small Mg clusters

The equilibrium geometries, binding energies, and harmonic frequencies of Mg₃ and Mg₄ have been determined using large atomic natural orbital basis sets in conjunction with high levels of electron correlation. The correlation treatments comprise multireference configuration interaction (MRCI), singles and doubles coupled-cluster (CCSD) theory and the CCSD(T) extension that includes a perturbational estimate of connected triple excitations. As with our previous studies of small Be clusters, the CCSD(T) method is found to reproduce the MRCI results with a remarkable degree of accuracy and at a fraction of the computational cost. Using the CCSD(T) method, full quartic force fields for Mg₃ and Mg₄ have been determined and anharmonic analyses have been performed using second-order perturbation theory. Vibration-rotation interaction constants and centrifugal distortion constants have also been determined. The fundamental vibrational frequencies are predicted to occur at ν₁ (a₁′) = 96 and ν₂ (e′) = 104 cm^-1 for Mg₃, and ν₁ (a₁) = 184, ν₂ (e) = 143, and ν₃ (t₂) = 167 cm^-1 for Mg₄. Infrared (IR) intensities, evaluated for the IR active modes via the double harmonic approximation, are 0.2 and 2.4 km/mol for the e′ (Mg₃) and t₂ (Mg₄) modes, respectively.