A systematic and feasible method for computing nuclear contributions to electrical properties of polyatomic molecules

Abstract

An analytic method to evaluate nuclear contributions to electrical properties of polyatomic molecules is presented. Such contributions control changes induced by an electric field on equilibrium geometry ͑nuclear relaxation contribution͒ and vibrational motion ͑vibrational contribution͒ of a molecular system. Expressions to compute the nuclear contributions have been derived from a power series expansion of the potential energy. These contributions to the electrical properties are given in terms of energy derivatives with respect to normal coordinates, electric field intensity or both. Only one calculation of such derivatives at the field-free equilibrium geometry is required. To show the useful efficiency of the analytical evaluation of electrical properties ͑the so-called AEEP method͒, results for calculations on water and pyridine at the SCF/TZ2P and the MP2/TZ2P levels of theory are reported. The results obtained are compared with previous theoretical calculations and with experimental values.

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

“…We are, therefore, obliged to save that contribution for the future, leaving us with the NR term. 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.…”

“…That is to say, if (n,m) denotes the order in electrical ͑n͒ and mechanical ͑m͒ anharmonicity, I denotes the sum ͑0,1͒ϩ͑1,0͒ while IIϭ͑0,2͒ϩ͑2,0͒ϩ͑1,1͒. Equations ͑8͒-͑10͒ have also been derived by the property expansion method of Luis et al [28][29][30] For the static ␥ v(r) ͓cf. Eq.…”

“…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.…”

Linear response functions for a vibrational configuration interaction state

“…[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.…”

“…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.…”