Electronic Contributions to Hyper Polarizabilities

In this section, we shall discuss the electronic contributions to a, (3 and 7. In particular, two following aspects will be considered in detail the assessment of reliability of results obtained using various exchange-correlation functionals and the relation between the structure of investigated systems and their non-linear optical properties. Before we proceed to analysis of NLO properties of investigated systems, it is inter- 

N refers to nitrogen atom located in carbazole moiety. Distances are given in Aand angles in degrees 

In Table3.5, the results of calculations of fix, a.xx and xxx for several model systems are presented. The systems have been selected according to the electron donating character of substitutes. Two functionals were selected for comparison, namely CAM-B3LYP and LB94. The former provides the value of xxx for 1 close 

3 Nonlinear Optictil Properties of Fullerene Derivatives first- (a), second- (yS) and third-order polarizability 

The results of calculations of electrooptic properties for 1,2 and 3 are presented in Table3.6. Due to the computational limitations, MP2 results are presented only for single component (x) of /x, a, / and 7. Since rotationally invariant hyperpolarizabilities are more suitable for structure-property relationships analysis, one have to select reliable level of theory for calculations of a, (3 and 7. The values of axx, (3xxx and Yxxxx calculated at the MP2 level of theory may serve as a reference data. Based on the results presented in Tables 3.3 and 3.6 the following ordering of axx values can be observed a It is worth noticing, that PM6 model 

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Relativistic effects on the pure electronic contributions to (hyper)polarizabilities of coinage metal hydrides (CuH, AgH, AuH) have been studied extensively [31-34]. However, the vibrational contributions on the L NLO properties have been mainly studied for systems involving light nuclei [35]. In systems composed of heavy nuclei one may expect significant differences between relativistic and nonrelativistic vibrational contributions. Thus the objective of this study was to find out the effect of the relativistic contribution on the vibrational contributions. The present study considered only the parallel components of the (hyper jpolarizabilities. 

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