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Contemporary design of new organic non-linear optical (NLO) materials relies to a large extent on the understanding of molecular and electronic structure–property relationships revealed during the years by available computational approaches. The progress in theory—hand-in-hand with experiment—has enabled us to identify and analyze various physical aspects affecting the NLO responses, such as the environmental effects, molecular vibrations, frequency dispersion, and system dynamics. Although it is nowadays possible to reliably address these effects separately, the studies analyzing their mutual interplay are still very limited. Here, we employ density functional theory (DFT) methods in combination with an implicit solvent model to examine the solvent effects on the electronic and harmonic as well as anharmonic vibrational contributions to the static first hyperpolarizability of a series of push–pull α , ω -diphenylpolyene oligomers, which were experimentally shown to exhibit notable second-order NLO responses. We demonstrate that the magnitudes of both vibrational and electronic contributions being comparable in the gas phase significantly increase in solvents, and the enhancement can be, in some cases, as large as three- or even four-fold. The electrical and mechanical anharmonic contributions are not negligible but cancel each other out to a large extent. The computed dynamic solute NLO properties of the studied systems are shown to be in a fair agreement with those derived from experimentally measured electric-field-induced second-harmonic generation (EFISHG) signals. Our results substantiate the necessity to consider concomitantly both solvation and vibrational effects in modeling static NLO properties of solvated systems. [ABSTRACT FROM AUTHOR]

Contemporary design of new organic non-linear optical (NLO) materials relies to a large extent on the understanding of molecular and electronic structure–property relationships revealed during the years by available computational approaches. The progress in theory—hand-in-hand with experiment—has enabled us to identify and analyze various physical aspects affecting the NLO responses, such as the environmental effects, molecular vibrations, frequency dispersion, and system dynamics. Although it is nowadays possible to reliably address these effects separately, the studies analyzing their mutual interplay are still very limited. Here, we employ density functional theory (DFT) methods in combination with an implicit solvent model to examine the solvent effects on the electronic and harmonic as well as anharmonic vibrational contributions to the static first hyperpolarizability of a series of push–pull α,ω-diphenylpolyene oligomers, which were experimentally shown to exhibit notable second-order NLO responses. We demonstrate that the magnitudes of both vibrational and electronic contributions being comparable in the gas phase significantly increase in solvents, and the enhancement can be, in some cases, as large as three- or even four-fold. The electrical and mechanical anharmonic contributions are not negligible but cancel each other out to a large extent. The computed dynamic solute NLO properties of the studied systems are shown to be in a fair agreement with those derived from experimentally measured electric-field-induced second-harmonic generation (EFISHG) signals. Our results substantiate the necessity to consider concomitantly both solvation and vibrational effects in modeling static NLO properties of solvated systems.

Equations for the intramolecular surfaces of the3JHHcoupling constants in ethane, ethylene, and acetylene are formulated, and the corresponding coefficients are estimated from calculations at the DFT/B3LYP level. The chosen variables are changes in bond lengths, in the torsion angle φ between the coupled protonsHaandHb, in bond angles, and in dihedral angles. The3JHHsurface of ethane is formulated as an extended Karplus equation with the coefficients of a truncated Fourier series on the torsion angle φ expanded as second-order Taylor series in the chosen variables taking into account the invariance of3JHHunder reflections and rotations of nuclear coordinates. Partial vibrational contributions from linear and square terms corresponding to changes in the geometry of theHa−Ca−Cb−Hbfragment are important while those from cross terms are small with a few exceptions. The3JHHsurface of ethane is useful to predict contributions to3JHHfrom changes in local geometry of derivatives but vibrational contributions are predicted less satisfactorily. The predicted values at the B3LYP/BS2 level of the3JHHcouplings (vibrational contributions at 300 K) from equilibrium geometries are 9.79 (−0.17) for acetylene, and 17.08 (1.93) and 10.73(0.93) for thetransandciscouplings of ethylene. [ABSTRACT FROM AUTHOR]

A set of exchange-correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM-B3LYP, LC-BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all- trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller-Plesset second-order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM-B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity-dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro-optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field-induced second harmonic generation all of them, as well as the Hartree-Fock approximation, yield the wrong sign. We have also found that the Pople 6-31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The vibrational (hyper)polarizabilities of some selected Xe derivatives are studied in the context of Bishop-Kirtman perturbation theory (BKPT) and numerical finite field methodology. It was found that for this set of rare gas compounds, the static vibrational properties are quite large, in comparison to the corresponding electronic ones, especially those of the second hyperpolarizability. This also holds for the dc-Pockels β(−ω;ω,0), Kerr γ(−ω;ω,0,0) and electric field second harmonic generation γ (−2ω;ω,ω,0) effects, although the computed nuclear relaxation (nr) vibrational contributions are smaller in magnitude than the static ones. HXeOXeH was used to study the effects of electron correlation, basis set, and geometry. Geometry effects were found to lead to noticeable changes of the vibrational and electronic second hyperpolarizability. A limited study of the effect of Xe insertion to the nr vibrational properties is also reported. Assessment of the results revealed that Xe insertion has a remarkable effect on the nr (hyper)polarizabilities. In terms of the BKPT, this is associated with a remarkable increase of the electrical and mechanical anharmonicity terms. The latter is consistent with the anharmonic character of several vibrational modes reported for rare gas compounds. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Vibrational contributions to the [image omitted] couplings of six mono- and five 1,1-di-substituted ethanes, three mono-substituted cyclohexanes, three norbornane-type molecules, and 11 three-membered rings have been calculated at the DFT/B3LYP level for the Fermi contact term using a moderate sized basis set. When, for a data set of 70 couplings, the sums of the values for the equilibrium configurations Je and the respective vibrational contributions [image omitted] at 300 K are multiplied by a factor of 0.8485, the corresponding predicted couplings [image omitted] are in good agreement with the experimental couplings [image omitted] with a standard deviation σ of 0.18 Hz. The same σ results when [image omitted] values are obtained by multiplying the Je values by 0.9016. However, the vibrational contributions must be taken into account, together with the Je values, in order to achieve a procedure for a reliable and accurate prediction of [image omitted] couplings since, globally, [image omitted] contributions amount to about 7% of the Je values and the correlation coefficient between [image omitted] and Je is only 0.68 with a σ deviation of 0.20. The first and diagonal second derivatives of J with respect to each normal coordinate Qk, required to estimate the vibrational contributions, have been obtained from six Jk values computed for molecular geometries positively [image omitted] and negatively [image omitted] displaced from the equilibrium geometry along the normal coordinate Qk and using for δ the values 0.01, 0.05 and 0.10. The computational precision of the results obtained when using one, two and three δ values is analysed. [ABSTRACT FROM AUTHOR]

Abstract: In the present study, we report on the results of computations of the electronic and the vibrational contributions to the static first hyperpolarizability of meta-dinitrobenzene molecule. It turned out that the electron correlation effects are much more important for reliable prediction of the electronic counterpart than for determining vibrational corrections: value is increased by about 500% passing from the HF to the CCSD(T) level of theory. The preliminary assessment of density functional theory in determination of hyperpolarizabilities shows that harmonic contributions to , contrary to the purely electronic contributions, are substantially underestimated in comparison with the wave function theory results. Another important finding of this study is that long-range corrected functionals tend to improve upon traditional functionals both in determining electronic as well as vibrational hyperpolarizabilities. It is also demonstrated that the vibrations of the nitro groups have a predominant influence on the vibrational contributions to . The mechanical and electrical anharmonicity correction terms to the vibrational hyperpolarizability were found to be substantially larger than the lowest-order harmonic term. [Copyright &y& Elsevier]

The importance of vibrational contributions to the static linear and nonlinear optical coefficients is investigated. We apply the exact sum-over-state (SOS) formulas for polarizabilities and hyperpolarizabilities expressed in terms of vibronic states to a two-level system with a single vibrational mode. The Herzberg–Teller expansion is applied to the SOS formulas including vibrational energy levels without employing the Placzek’s approximation within both the Born–Oppenheimer approximation and electrical and mechanical harmonicities. The results include not only the vibrational contribution from the lattice relaxation expression but also the contribution arising from the higher-order correction terms. Model calculations on a diatomic system with two electronic states show that the contribution of these correction terms is small. Moreover, most of these higher-order terms are negligible in the solid-state limit. In polyacetylene, the contribution of the lattice relaxation expression is much larger than that in the diatomic case. Within the tight-binding approximation, the contribution of the lattice relaxation expression is 44% of the pure electronic contribution for the second hyperpolarizability. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the relationship between static vibrational and electronic hyperpolarizabilities of a series of push–pull molecules within the two-state valence-bond charge-transfer model are reinvestigated computationally at the Møller–Plesset level of theory. Although the level of theory employed here gives significantly different results for electronic and vibrational counterparts than those obtained by Bishop et al. [D. Bishop, B. Champagne, B. Kirtman, J. Chem. Phys. 109 (1998) 9987] at the RHF level, the overall conclusions remain unchanged: The comparison of ab initio computations with the predictions of the VB–CT model gives a little confidence in the latter. [Copyright &y& Elsevier]

Abstract: Static and dynamic vibrational contributions to the linear polarizability and the first and second nonlinear hyperpolarizabilities of methanol, ethanol and propanol have been calculated. Both the pure vibrational contribution and the zero-point vibrational averaging contribution have been determined by adopting the perturbation treatment of Bishop and Kirtman at the Hartree–Fock level. The pure vibrational contribution is quite important at the static limit, while in the optical region it varies for different nonlinear optical processes. The zero-point vibrational averaging contribution is a quite large correction to the electronic nonlinear optical (NLO) properties, especially for the second hyperpolarizability at finite fundamental frequencies. Vibrational analysis shows that the swinging modes at around 300cm-1 and the C–H stretching modes at around 3160cm-1 often give large contributions. [Copyright &y& Elsevier]