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Infinite optical frequency approximation

Under the infinite optical frequency approximation, which corresponds to the limit w 00, the expression for the dynamic P" and also can be obtained from... [Pg.108]

For typical laser optical frequencies test calculations [31-33] confirm that the infinite optical frequency approximation is highly accurate, although this does not necessarily hold at lower frequencies [33],... [Pg.108]

The static NR contribution to axx" was with 11.78 au considerably smaller than the corresponding electronic value (501.3 au). For Pxxx, however, the NR contribution (-608.7 au) was much larger than the electronic one (-35.8 au). The vibrational contribution to the Pockels effect, computed in the infinite optical frequency approximation was found to be 42.9 au, approximately equal in magnitude to the electronic static value. In the same approximation, the vibrational contribution to the EFISH property, y(-2co co,a),0), was -40 au, thus much smaller than the electronic counterpart (40,201 au). [Pg.153]

Here, P" denotes the nuclear relaxation part of P, and the subscript oo -> oo invokes the infinite optical frequency approximation, which is generally considered to be good approximation to the frequency-dependent properties at the usual laser frequencies applied in experiments [75]. Due to the high computational cost of these calculations, in general the rather small 6-3IG basis was used. For some control calculations, the 6-31-fG basis set was used. [Pg.157]

Table 5.25 NR contribution to the dc-Pockels effect (P" (-oo m,0)(o- oo) of LiOCeo in the infinite optical frequency approximation... Table 5.25 NR contribution to the dc-Pockels effect (P" (-oo m,0)(o- oo) of LiOCeo in the infinite optical frequency approximation...
In addition to the static vibrational properties, the NR contributions to the dc-Pockels effect of Li C6o in the infinite optical frequency approximation were also reported in Ref [61] (Table 5.25). Compared with their electronic counterparts the values were small, but not negligible. [Pg.158]

Buckingham [4], these results are not really comparable because their calculations include the effect of temperature. In addition, they applied several strong approximations, such as assuming a spherical field-free potential inside the cage. On the other hand, our calculations do not include higher-order vibrational contributions omitted in the NR treatment. It would be worthwhile to add temperature-dependence to the NR approach as we plan to do in the future. Whereas the NR contribution to the static a is quite small for both endohedral fullerenes, it becomes quite large for the static hyperpolarizabilities. This contribution is reduced for the dynamic Pockels effect, computed in the infinite optical frequency approximation, but is still not negligible. [Pg.110]

The argument Rp implies structure relaxation in the field, and P" means the nuclear relaxation part of P, while the subscript oc oo invokes the so-called infinite optical frequency (lOF) approximation. In principle, this procedure allows one to obtain most of the major dynamic vibrational NR contributions in addition to the purely static ones of Eqs.4.5. 7. The linear term in the electric field expansion of Eq. (4) gives the dc-Pockels effect the quadratic term gives the optical Kerr Effect and the linear term in the expansion of beta yields dc-second harmonic generation (all in the lOF approximation). For laser frequencies in the optical region it has been demonstrated that the latter approximation is normally quite accurate [29-31]. In fact, this approximation is equivalent to neglecting terms of the order with respect to unity (coy is a vibrational frequency). In terms of Bishop and Kirt-man perturbation theory [32-34] all vibrational contributions through first-order in mechanical and/or electrical anharmonicity, and some of second-order, are included in the NR treatment [35]. [Pg.102]

From the results in the last section it is clear that for particular applied radiative frequencies or frequency multiples, close to resonance with particular molecular states, each molecular tensor will be dominated by certain terms in the summation of states as a result of their diminished denominators—a principle that also applies to all other multiphoton interactions. This invites the possibility of excluding, in the sum over molecular states, certain states that much less significantly contribute. Then it is expedient to replace the infinite sum over all molecular states by a sum over a finite set—this is the technique employed by computational molecular modelers, their results often producing excellent theoretical data. In the pursuit of analytical results for near-resonance behavior, it is often defensible to further limit the sum over states and consider just the ground and one electronically excited state. Indeed, the literature is replete with calculations based on two-level approximations to simplify the optical properties of complex molecular systems. On the other hand, the coherence features that arise through adoption of the celebrated Bloch equations are limited to exact two-level systems and are rarely applicable to the optical response of complex molecular media. [Pg.643]

As I have said, Sekino and Bartlett [31] were the first to show how to proceed to calculate frequency-dependent hyperpolarizabilities within the TDCPHF approximation. They developed an infinite-order recursive procedure, using density matrices, and, by solving the equations iteratively at each order, could, in principle, calculate any non-linear optical property. Their first application was to H2, FH (the work on FH was analysed in detail in another paper [38]), CH4 and the fluoromethanes. The processes SHG, OR, dc-SHG, dc-OR, IDRI and THG were considered but not all hyperpolarizability components were computed (the assumption of Kleinman symmetry was made). [Pg.19]


See other pages where Infinite optical frequency approximation is mentioned: [Pg.109]    [Pg.110]    [Pg.114]    [Pg.162]    [Pg.28]    [Pg.109]    [Pg.110]    [Pg.114]    [Pg.162]    [Pg.28]    [Pg.115]    [Pg.34]    [Pg.73]    [Pg.310]    [Pg.281]    [Pg.460]    [Pg.278]    [Pg.183]    [Pg.1159]    [Pg.420]   
See also in sourсe #XX -- [ Pg.108 , Pg.110 , Pg.114 ]




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