Hyperpolarizability associated molecular properties

The ab initio calculation of NLO properties has been a topic of research for about three decades. In particular, response theory has been used in combination with a number of electronic structure methods to derive so-called response functions [41 8], The latter describe the response of a molecular system for the specific perturbation operators and associated frequencies that characterize a particular experiment. For example, molecular hyperpolarizabilities can be calculated from the quadratic and cubic response functions using electric dipole operators. From the frequency-dependent response functions one can also determine expressions for various transition properties (e.g. for multi-photon absorption processes) and properties of excited states [42]. 

Bartkowiak reviewed the connection between the NLO response and solva-tochromlc behavior of donor-acceptor Tr-conjugated molecules. The marked NLO properties of these molecules are associated with an intra-molecular charge-transfer excited state. This author points out that the environmental interactions may have a very significant effect on the hyperpolarizabilities (they may even lead to a change of sign). Bartkowiak shows that a simple two-state model combined with the solvatochromic methods may allow the prediction of changes of in molecular hyperpolarizabilities as a function of the solvent polarity. 

A few further general remarks are in order at this stage. One is to note the fact that the sum over intermediate molecular states, as in Eqs. (76) and (79), in principle applies not only to electronic but also to vibrational levels. Although this issue initially received most attention in connection with molecular hyperpolarizabilities [44], it applies equally to other optical response tensors. The vibrational contributions, which were previously largely overlooked, have now been extensively studied and shown to be important in many applications [45,46]. Second, the polarizabilities associated with nonlinear parametric processes may in most circumstances be regarded as properties of the ground-state molecule, since it is the molecular ground state that usually constitutes the... 

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