Molecular Properties

While the energy is undoubtedly the fundamental quantity, chemists usually characterize molecules by other properties, for example, the dipole moment or the molecular structure. The ability to accurately calculate these properties is one of the major strengths of modern electronic structure theory. These calculations are made possible by the fact that the properties are responses of the molecule to external parameters such as the nuclear coordinates, applied electric and magnetic fields, etc. These parameters become variables on which a potential energy surface is mapped out. Therefore analytic derivatives of the energy with respect to these variables yield the familiar molecular properties.

The derivatives with respect to nuclear positions give the nuclear forces, which allows rapid minimization of the energy with respect to nuclear coordinates, providing the molecular structure. Second derivatives with respect to nuclear position reveal the force constants, allowing harmonic frequencies to be calculated. These derivatives also allow the classification of stationary points, greatly facilitating the location of transition structures (which will be first order saddle points).

The various derivatives with respect to electric field, magnetic field and nuclear spin allow determination of a range of properties, including: electric polarizability, infrared intensities, magnetic susceptibility, chemical shielding, spin-spin coupling, Raman intensities and hyperpolarizabilities. However they are beyond the scope of this thesis, and these properties will not be discussed here. What is important is that they all result from derivatives of the energy, and thus fast evaluation of the molecular energy is highly desired.