Optical properties static field combinations

There are three main factors to consider in deciding on the best method to compute vibrational NLO properties i) the frequency of the optical fields, ii) the size of the chemical system, and iii) the anharmonicity of the (static) field-dependent PES. When the frequencies of the optical fields are comparable to vibrational frequencies, the only option is the BK procedure presented in Section 1. Nevertheless, the computational cost of such calculations can be radically reduced by combining BK expressions with frequency-dependent field-induced coordinates (see Section 3). 

The (monochromatic) electric fields are characterized by Cartesian directions indicated by the Greek letters and by circular optical frequencies, coi, a>2, and The induced dipole moment oscillates at a> = EjO,. and are such that the jS and y values associated with different NLO processes converge towards the same static value. The 0 superscript indicates that the properties are evaluated at zero electric fields. Eqn (2) is not the unique phenomenological expression defining the (hyper)polarizabilities. Another widely-applied expression is the analogous power series expansion where the 1/2 and 1/6 factors in front of the second- and third-order terms are absent. The static and dynamic linear responses, o(0 0) and a(—correspond to the so-called static and dynamic polarizabilities, respectively. At second order in the fields, the responses are named first hyperpolarizabilities whereas second hyperpolarizabilities correspond to the third-order responses. Different phenomena can be distinguished as a function of the combination of optical frequencies. So, (0 0,0), a>,a>)... 

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