Vibrational second hyperpolarizability of CH4−nFn molecules with n=0–4

Abstract

The frequency-dependent vibrational second hyperpolarizability of CH4−nFn molecules with n=0–4 has been computed for the most common nonlinear optical (NLO) processes by adopting the perturbation approach due to Bishop and Kirtman [J. Chem. Phys. 95, 2646 (1991)]. These calculations have been performed by using the Sadlej atomic basis set with the Hartree-Fock technique as well as with the Mo/ller-Plesset second order perturbation theory (MP2) procedure. The inclusion of electron correlation and of the first-order mechanical and electrical anharmonicities turn out to be of quantitative importance for most quantities. In particular, it permits us to improve the agreement with the experimental data for the difference between the anisotropic dc-Kerr and mean electric-field-induced second harmonic generation (ESHG) vibrational second hyperpolarizability of CF4. With the exception of the small ESHG vibrational second hyperpolarizability the infinite optical frequency method turns out to be a satisfactory approximation for evaluating the vibrational NLO responses.

Simple finite field nuclear relaxation method for calculating vibrational contribution to degenerate four-wave mixing

“…The latter approximation leads to vibrational NLO contributions through second order in BK-PT. In comparison, to evaluate the same properties ͑through second order͒ using the BK-PT method, it is necessary to calculate a 20 ii ͑0 , 0͒, a 30 ijk ͑0 , 0͒, a 12 i,aa ͑0 , 0͒, a 40 iijk ͑0 , 0͒, a 22 ij,aa ͑0 , 0͒, a 13 i,aaa ͑0 , 0͒, a 32 iij,aa ͑0 , 0͒, a 23 ii,aaa ͑0 , 0͒, a 14 i,aaaa ͑0 , 0͒, and a 24 ii,aaaa ͑0 , 0͒. The cost of calculating high-order normal coordinate derivatives, such as a 32 iij,aa ͑0 , 0͒ and a 40 iijk ͑0 , 0͒, increases dramatically with the number of atoms.…”

“…20,21 Experimental measurements are often carried out at optical frequencies much larger than the frequencies of the relevant vibrational excitations. In that event, one may invoke the infinite optical frequency approximation [22][23][24] ͑IOFA͒ in calculating vibrational NLO properties. Although not strictly required, 25 usually the FF-NR treatment is applied in conjunction with the IOFA.…”

Linear response functions for a vibrational configuration interaction state

“…From Table V we observe, as expected, that the PV polarizability is significant in the static or low frequency ͑IR͒ region but tends to zero for optical frequencies. [47][48][49] Thus, already around a frequency equal to 0.0428 a.u. ͑1064 nm͒ the PV contribution is very small and essentially negligible.…”

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

“…However, the treatment of small molecules indicates that electrical and mechanical anharmonicity effects can sometimes [23][24][25][26][27][28][29][30][31][32][33] be important and that is the subject of the present paper. In particular, we will examine the second hyperpolarizability of eight different homologous series of conjugated oligomers.…”

“…The merits of the infinite optical frequency approximation, as applied to that term, have been demonstrated by Bishop and Dalskov 28 and, subsequently, by Quinet and Champagne. 33 A successful implementation of the BHK method, including careful treatment of the Eckart conditions, has very recently been published. 41 As in previous studies we characterize increasingly large oligomers in order to access the properties of long ''polymeric'' chains.…”