Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

Abstract

Restricted Hartree-Fock 6-31G calculations of electrical and mechanical anharmonicity contributions to the longitudinal vibrational second hyperpolarizability have been carried out for eight homologous series of conjugated oligomers-polyacetylene, polyyne, polydiacetylene, polybutatriene, polycumulene, polysilane, polymethineimine, and polypyrrole. To draw conclusions about the limiting infinite polymer behavior, chains containing up to 12 heavy atoms along the conjugated backbone were considered. In general, the vibrational hyperpolarizabilities are substantial in comparison with their static electronic counterparts for the dc-Kerr and degenerate four-wave mixing processes ͑as well as for static fields͒ but not for electric field-induced second harmonic generation or third harmonic generation. Anharmonicity terms due to nuclear relaxation are important for the dc-Kerr effect ͑and for the static hyperpolarizability͒ in the -conjugated polymer, polysilane, as well as the nonplanar systems polymethineimine and polypyrrole. Restricting polypyrrole to be planar, as it is in the crystal phase, causes these anharmonic terms to become negligible. When the same restriction is applied to polymethineimine the effect is reduced but remains quantitatively significant due to the first-order contribution. We conclude that anharmonicity associated with nuclear relaxation can be ignored, for semiquantitative purposes, in planar -conjugated polymers. The role of zero-point vibrational averaging remains to be evaluated.

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

“…23 Many of the lower-order derivatives required for our treatment were obtained analytically using the GAUSSIAN 98 suite of programs. 34 These include a 20 , a 01 , a 11 , a 02 , a 12 , and a 03 at the HF level and all but the last two of this list at the MP2 level. All vibrational derivatives are computed with respect to atomic Cartesian coordinates.…”

“…18 From a computational viewpoint NR ͑hyper͒polarizabilities can be evaluated either by means of analytical formulas 19 as they are in the BK method, or by numerical finite field ͑FF͒ techniques. 15,20,21 The FF treatment is computationally advantageous especially when used in conjunction with highly correlated electronic structure methods and/or when applied to large systems. 22 The remaining higher-order square bracket terms ͑de-noted below by C-ZPVA͒, in combination with the zeropoint vibrational averaging ͑ZPVA͒ term, collectively give rise to what has been referred to as the curvature ͑C͒ contribution 23 to the property P, i.e., P c ϭ P zpva ϩ P c-zpva .…”

Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections

“…5,6 It has been shown that in many circumstances the corrections arising from the molecular vibrations are of similar magnitude, or even larger, than the electronic counterparts. [7][8][9][10][11][12][13][14][15][16] For systems on condensed phase the influence of the medium must also be considered, being the description of solvated systems usually made through simulation methods ͑molecular dynamics or Monte Carlo͒ or continuum models. [17][18][19][20][21][22][23] Methanol has been the subject of a number of recent theoretical and experimental investigations.…”

Variational calculation of vibrational linear and nonlinear optical properties

“…Even for some ordinary -conjugated NLO molecules, such as 1-formyl-6-hydroxyhexa-1,3,5-triene, the perturbation series for the ab initio static vibrational hyperpolarizabilities is ͑at least͒ initially divergent. 13,20,21 Assuming that all vibrational frequencies are small compared to optical frequencies, i.e., within the infinite ͑optical͒ frequency approximation, there exists an alternative to the perturbation approach for calculating vibrational contributions [22][23][24][25] to the most important NLO processes. In this alternative finite field ͑FF͒ procedure, the total vibrational hyperpolarizability is expressed as the sum of a nuclear relaxation ͑P nr ͒ and a curvature ͑P c ͒ term.…”