A theory of frequency, intensity and band-width changes due to solvents in infra-red spectroscopy
The Hamiltonian H , leading to the vibrational energy levels of a gaseous diatomic molecule, is normally written in the form (see Buckingham 1958) H = H 0 + H a (1·1) = - hcB c d 2 /dξ 2 + hcω c 2 /4 B c {ξ 2 + A / ω c ξ 3 + B / ω c ξ 4 + ...}, (1·2) where H 0 = - hcB c d 2 /dξ 2 + hcω c 2 /4 B c ξ 2 is the harmonic oscillator Hamiltonian, and hcω c 2 /2 B c r c 2 is the force-constant; ξ = ( r — r e )/ r e is a dimensionless parameter proportional to the displacement from the equilibrium inter-nuclear distance r e ; A / ω e , B/ω e ,..., are anharmonic coefficients. The constants r e , ω e , B e , 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 H a as a small perturbation to H 0 (see Herzberg 1950).