A simple method for determining approximate static and dynamic vibrational hyperpolarizabilities

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Ab initio Hartree-Fock and MP2 calculations of the longitudinal ͑hyper͒polarizability-including the static electronic, static zero-point vibrational average ͑ZPVA͒, and pure vibrational ͑static and dynamic͒ contributions-have been carried out on a set of seven typical medium size conjugated nonlinear optical ͑NLO͒ molecules. The ZPVA is obtained through first-order in mechanical plus electrical anharmonicity. Based on physical ''nuclear relaxation'' considerations the individual ͑square bracket͒ terms that contribute to the pure vibrational ͑hyper͒polarizability are then taken into account through third-, fourth-, or fifth-order depending upon the type of term. In order to carry out the correlated treatment, field-induced coordinates and a special finite field technique are utilized. Correlation leads to very substantial differences in the absolute and relative values of the various contributions. In comparison to the electronic term the ZPVA correction is usually small but in one case is over two-thirds as large. On the other hand, both static and dynamic pure vibrational contributions are commonly of a magnitude that is comparable to, or are larger than, the electronic term. The higher-order pure vibration terms are often large. For dynamic processes they can be almost as important as the lowest-order terms; for static ͑hyper͒polarizabilities they can be more important. Thus, for typical NLO molecules, the initial convergence behavior of the perturbation series in mechanical and electrical anharmonicity requires further investigation.

Section: Introductionmentioning

confidence: 99%

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

Torrent‐Sucarrat

Solà

Duran

et al. 2002

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“…The longitudinal electronic properties L e , ␣ L e , and ␤ L e are, then, evaluated at the field-dependent optimum geometry. If P L e (E,R E ) is the property value obtained in this manner and P L e (0,R 0 ) is the corresponding zero-field result, then it can be shown 39 that the difference between the two is given by…”

Section: Methodological and Computational Aspectsmentioning

confidence: 99%

“…By combining Eqs. ͑8͒-͑10͒ one can obtain an alternative expression 39 which is valid through the first-order of perturbation theory. However, we prefer to use the exact relation, i.e., Eq.…”

Section: ͑11͒mentioning

confidence: 99%

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

Champagne

Luis

Duran

et al. 2000

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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.

“…[26][27][28][29] The simplest of these, the so-called double-harmonic ͑DH͒ approximation, 25 which for ␣ is equivalent to the nuclear relaxation contribution to the polarizability ͑␣ nr ͒, 28 considers a harmonic potential and a linear ͑one-mode͒ property surface. Literature values for the PV polarizability of water obtained using these simpler approaches have also been included in Table III. Here we find for ␣ nr that the yy component compares well with the more elaborate results, whereas the zz component is underestimated leading to an overall underestimation of 7.8% for the isotropic polarizability.…”

Section: Convergence With Respect To Details Of the Potential And Promentioning

confidence: 99%

“…15,16,25 An alternative procedure based on field induced nuclear relaxation geometry optimizations can be used to calculate static or infinite frequency vibrational ͑hyper͒polarizabilities. [26][27][28][29] Variational methods have been more limited in use, and primarily restricted to calculation of zero-point vibrational averages, see for example Ref. 30 and references therein.…”

Section: Introductionmentioning

confidence: 99%

Linear response functions for a vibrational configuration interaction state

Christiansen¹,

Kongsted²,

Paterson

et al. 2006

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach.