An equation of motion approach for the vibrational transition energies in the effective harmonic oscillator formalism: the Random phase approximation

A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expanded in the harmonic oscillator ladder operators making a Hamiltonian a bosonic Hamiltonian. The excitation operator is expanded to include at most two creations and two annihilation operators making it equivalent to the random phase approximation. The method is applied for the calculation of vibrational spectral properties of two molecules. The results are found to be satisfactory, making this approach a viable option for large molecular systems. A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expressed in bosonic representation. The excitation operator is expanded to include at most two creation and annihilation operators.