Computational insight into relations between electronic and vibrational polarizabilities within the two-state valence-bond charge-transfer model

doi:10.1016/j.chemphys.2007.06.031

Chemical Physics

Volume 337, Issues 1–3, 16 August 2007, Pages 77-80

https://doi.org/10.1016/j.chemphys.2007.06.031 Get rights and content

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.

Introduction

Nonlinear optical (NLO) properties of molecules are the subject of growing interest of many research groups because of the potential applications of NLO materials in many areas of modern technology. Computational methods in electronic structure theory of molecules carry out their own difficulties: The inability to solve efficiently vibronic Schrödinger equation for complex polyatomic molecules leads to separation of electronic and vibrational motions. Although such a procedure seems to be physically justified in most cases, in particular it results in splitting of NLO response into vibrational and electronic parts [1], [2], [3], [4]. Usually, several further approximations are required for evaluation of vibrational counterpart of the response, as being much more computationally demanding at the given level of theory [2], [5]. Thus, the ability to predict the relationship between both contributions (vibrational and electronic) to the total NLO response is of great importance for rational design of new molecular systems of desired NLO properties.

Although enormous progress in computational methods as well as computational resources has been achieved in recent years, theoretical models are still of great importance due to their simplicity and ability to formulate structure–property relationships.

Being conceptually simple, the valence-bond charge-transfer (VB–CT) model and its extensions are still very fruitful in the description of NLO properties [6], [7], [8], [9], [10]. It was originally proposed by Mulliken [11] and used in numerous studies [12], [13], [14]. Moreover, the VB–CT model has been the basis for the establishment of mutual relations between electronic and vibrational contributions to NLO response [15], [16], [17], [18]. It was the paper of Bishop et al. that brought the question about the reliability of results obtained using the VB–CT model [15]. Most of the computational investigations of vibrational NLO properties have been done at the RHF level of theory with relatively small basis sets [19], [20], [21], [22], [23], [24], [25], [26]. However, recent studies of Kirtman et al. revealed that the inclusion of electron correlation combined with the choice of appropriate basis set is necessary for reliable prediction of vibrational contributions to NLO properties [27], [28], [29].

Usually, the impact of the level of theory on NLO properties is different for electronic and vibrational corrections. Moreover, the dependence of α, β and γ on inclusion of electron correlation is different. It is the goal of the present paper to assess whether the inclusion of electron correlation and the use of medium size basis set will improve the predictions of the VB–CT model with respect to mutual relationship between electronic and vibrational hyperpolarizabilities.

Section snippets

Computational aspects

The idea how to verify the VB–CT model was presented by Bishop et al. [15]. Below, we present two relations used in the present work to verify the validity of predictions of the VB–CT model: $\frac{(β^{v} / α^{v})}{(β^{e} / α^{e})} = 3,$ $\frac{([α^{2}]^{0, 0} / α^{v})}{(β^{e} / α^{e})^{2}} = 3,$ where $α^{v} = \sum_{i = 1}^{3 N - 6} \frac{1}{ω_{i}^{2}} {(\frac{\partial μ_{z}^{e}}{\partial Q_{i}})}^{2},$ $β^{v} = 3 \sum_{i = 1}^{3 N - 6} \frac{1}{ω_{i}^{2}} (\frac{\partial μ_{z}^{e}}{\partial Q_{i}}) (\frac{\partial α_{zz}^{e}}{\partial Q_{i}}),$ $[α^{2}]^{0, 0} = 3 \sum_{i = 1}^{3 N - 6} \frac{1}{ω_{i}^{2}} {(\frac{\partial α_{zz}^{e}}{\partial Q_{i}})}^{2} .$ In Eqs. (1), (2), α^e and β^e denote purely electronic contributions to polarizability and first–order hyperpolarizability, respectively. α^v, β^v and [α²]^0,0, given by Eqs. (3), (4)

Results and conclusions

The key concept of the VB–CT model is mixing of two resonant forms of a molecule, namely valence-bond and charge-transfer. The parameter that is a measure of the degree of mixing of the two will be further denoted as θ. Within the VB–CT model, the dependence of purely electronic contributions to α, β and γ on the parameter θ is given by [15]: $α^{e} \sim (\sin 2 θ)^{2},$ $β^{e} \sim (\sin 2 θ)^{2} \cos 2 θ,$ $γ^{e} \sim (\sin 2 θ)^{2} (5 \cos^{2} 2 θ - 1) .$ This parameter is proportional to the bond-length alternation (BLA) and bond-order alternation (BOA).

Acknowledgements

Calculations have been carried out in ACK Cyfronet and Wroclaw Centre for Networking and Supercomputing. This research was supported by the Grant 3 T08E 08430 from the Polish Committee for Scientific Research and by the Cooperation grant CZ25 (Czech-Polish cooperation) from the Polish Committee foe Scientific Research and the Ministry of Education, Youth, and Sports of the Czech Republic as well as the ONR Grant N00014-03-1-0498 and the NSF Grant HRD-0401730.

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Computational insight into relations between electronic and vibrational polarizabilities within the two-state valence-bond charge-transfer model

Abstract

Introduction

Section snippets

Computational aspects

Results and conclusions

Acknowledgements

Chem. Phys. Lett.

Chem. Phys. Lett.

Chem. Phys.

Chem. Phys. Lett.

Chem. Phys.

Chem. Phys.

Chem. Phys. Lett.

Chem. Phys. Lett.

Rev. Mod. Phys.

Adv. Chem. Phys.

Calculations of dynamic hyperpolarizabilities for small and medium sized molecules

Theoretical approach to the design of organic molecular and polymeric nonlinear optical materials

J. Chem. Phys.

J. Opt. Soc. Am. B

J. Phys. Chem. A

J. Phys. Chem. A

J. Phys. B

J. Am. Chem. Soc.

J. Am. Chem. Soc.

J. Am. Chem. Soc.

J. Chem. Phys.

J. Chem. Phys.

J. Chem. Phys.