A theory of frequency, intensity and band-width changes due to solvents in infra-red spectroscopy

Abstract

Abstract The Hamiltonian H, leading to the vibrational energy levels of a gaseous diatomic molecule, is normally written in the form (see Buckingham 1958) H = H0 + Ha (1·1) = -hcBcd2/dξ2 + hcωc2/4Bc{ξ2 + A/ωcξ3 + B/ωcξ4 + ...}, (1·2) where H0 = -hcBcd2/dξ2 + hcωc2/4Bcξ2 is the harmonic oscillator Hamiltonian, and hcωc2/2Bcrc2 is the force-constant; ξ = (r — re)/re is a dimensionless parameter proportional to the displacement from the equilibrium inter-nuclear distance re; A/ωe, B/ωe,..., are anharmonic coefficients. The constants re, ωe, Be, A, B, ..., can be obtained from the vibration-rotation spectrum of the gas by comparing the observed energies with those obtained by treating the anharmonic Hamiltonian Ha as a small perturbation to H0 (see Herzberg 1950).