Hyperpolarizability pure vibrational

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

The techniques and approximations involved in obtaining computationally tractable schemes for the calculation of the linear and nonlinear opAcal properties differ for the three contributions given in Eq. (86), and the different strategies will be presented and reviewed in the different chapters of this book. In the next section, we will briefly describe a few of the approximate methods used to calculate hyperpolarizabilities. Most of these methods will be directed toward the electronic contributions, but some of the approaches will also be able to extract Information about the pure vibrational contributions. 

We shall review the electronic and the pure vibrational contributions to the hyperpolarizabilities of pyrrole [50]. The original article involved also dipole moment and polarizabilities. The molecule is placed on the yz plane (Fig. 5.2). The computations have been performed at the Hartree-Fock level, employing the Pol basis set [45]. 

Table 5.16 Analysis of the pure vibrational contribution to the first hyperpolarizability components (a.u.) of pyrrole ...

We note that the evaluation of CARS requires largely the same quantity as is needed for conventional Raman spectroscopy as well as ROA, namely the polarizability gradient. If the nonresonant contributions are also wanted, then the electronic second hyperpolarizability is also needed, as well as the off-resonant pure vibrational contributions [292]. Ab initio studies of CARS have to date been very limited [292, 293]. 

Apart from purely electronic effects, an asymmetric nuclear relaxation in the electric field can also contribute to the first hyperpolarizability in processes that are partly induced by a static field, such as the Pockels effect [55, 56], and much attention is currently devoted to the study of the vibrational hyperpolarizability, can be deduced from experimental data in two different ways [57, 58], and a review of the theoretical calculations of p, is given in Refs. [59] and [60]. The numerical value of the static P is often similar to that of static electronic hyperpolarizabilities, and this was rationalized with a two-state valence-bond charge transfer model. Recent ab-initio computational tests have shown, however, that this model is not always adequate and that a direct correlation between static electronic and vibrational hyperpolarizabilities does not exist [61]. 

For N, there is a sizeable triples contribution to the lowest dipole allowed excitation energy of about 0.07 eV or 0.7%. As a consequence of tliis (unrelaxed) CCSD underestimates the absolute value of the isotropic hyperpolarizability and its dispersion. Tire electronic contribution to the static limit y - has been calculated at the CCSD/t-aug-cc-pVTZ level [32] to be 903.0 a.u. However, as indicated above, the triple- level is often too low for the calculation of second hyperpolarizabilities and the yj obtained at the CCSD/t-aug-cc-pVTZ level turned out to be about 40 a.u. above the CCSD basis-set limit result. Tlie latter has been calculated to be 863.3 3.3 a.u. [35]. Before comparing this result to tlie value extrapolated from experimental results, it has to be corrected for the ZPV contribution, which has been obtained in [32] to 12.0 a.u., thereby yielding 875.3 3.3 a.u. as tlie best estimate for the electronic contribution to y at the CCSD level. Shelton [6] obtained an experimental value of yj , 917 9 a.u., from the extrapolation of tlie results in [2] corrected for the pure rotational and vibrational contributions. Tire discrepancy between this experimental value and the CCSD best estimate is as large as 42 a.u. and makes very clear the importance of tire triples contribution. 

Rotational reorientation of frans-stilbene in alkane solution at room temperature occurs in the 10 to 30-ps time domain [347]. Rare-gas complexes with trons-stilbene were studied by purely rotational coherence spectroscopy [51,364]. Moreover, the decay kinetics of excited trans-stil-bene-cyclodextrin complexes were examined [366], It is worth mentioning that great progress has also been made in high-resolution spectroscopy [52, 369-372], Resonance coherent Raman spectroscopy showed a large enhancement of the electronic hyperpolarizability of t with respect to ground state trons-stilbene [374]. Vibrational motions were observed with ps transient Raman spectroscopy [375]. 

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