In order to predict the vibrational absorption spectrum and the VCD spectrum of a molecule, we need to know the wavefunctions and energies of the states of the molecule, predicted by the Schrödinger equation:
H Ei i iΨ Ψ= (3.1)
The molecular Hamiltonian, H, is
H V V V T Tee en nn e n= + + + + (3.2)
where Vee is the potential energy of electron-electron repulsion, Ven is the potential energy of electron-nucleus attraction, Vnn is the potential energy of nucleus-nucleus repulsion, Te is the electronic kinetic energy, and Tn is the nuclear kinetic energy. Ei and Ψi are the energy and wavefunction of the ith state. The wavefunctions are functions of the electronic coordinates, r, and nuclear coordinates, R.