Transition Probabilities and Optical Properties

Relatively modest modifications are required to extend a static linear polarizability Hartree-Fock computer code to dynamic or frequency-depen-dent polarizabilities. And if the code already handles magnetic moment operators, then the conversion to optical rotatory dispersion (ORD) or circular dichroism (CD) is also straightforward. At the third derivative level, e.g., hyperpolarizabilities, modifications are more complicated. 

Molecular spectroscopy of every sort involves a response to applied radiation. Transition probabilities are the first manifestation. Given the wave-functions and energies of the states involved, these quantities may be directly evaluated. Of course, approximations simplify the evaluation and the doubly 

An interesting alternative approach is the direct calculation by polarization propagator, or linear response, methods.The poles of the propagator yield the transition frequencies, the residues yield the corresponding transition moments, and the propagator itself determines linear response properties such as the frequency-dependent (or dynamic) polarizability. 

In this chapter we have explored the fundamental theories and the cal-culational techniques for the properties of individual molecules. Generally, properties represent some behavior of the molecule or a response of a molecule to perturbations. Formally, these are all derivatives of the molecular energy. Solving for such derivatives is a natural generalization of the process of solving for state energies via the Schrodinger equation. Techniques exist today for the 

One of us (C.E.D.) wishes to acknowledge the support provided by the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of work discussed here relating to the direct calculation of molecular properties. 

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