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24 November 2000 Chemical Physics Letters 331 2000 83 88 www elsevier nl locate cplett Ab initio investigation of the sum frequency hyperpolarizability of small chiral molecules Beno t Champagne a Peer Fischer b A David Buckingham b a Laboratoire de Chimie Th eorique Appliqu ee Facult es Universitaires Notre Dame de la Paix rue de Bruxelles 61 Namur B 5000 Belgium b Department of Chemistry University of Cambridge Lens eld Road Cambridge CB2 1EW UK Received 21 July 2000 in nal form 2 October 2000 Abstract Using a sum over states procedure based on con guration interaction singles 6 311 G we have computed the sum frequency hyperpolarizability bijk 3x 2x x of two small chiral molecules R mono uoro oxirane and R propylene oxide Excitation energies were scaled to t experimental UV absorption data and checked with ab initio values from time dependent density functional theory The isotropic part of the computed hyperpolarizabilities b 3x 2x x is much smaller than that reported previously from sum frequency generation experiments on aqueous solutions of arabinose Comparison is made with a single centre chiral model 2000 Elsevier Science B V All rights reserved 1 Introduction In the electric dipole approximation coherent three wave mixing TWM processes in isotropic media are only symmetry allowed for sum and di erence frequency generation in chiral media 1 Indeed coherent second order nonlinear optical NLO processes appear either in non centrosymmetric media such as crystals and interfaces or in isotropic media provided they contain chiral molecules and are not racemic Chirality allowed sum frequency generation SFG in isotropic media was rst reported over 30 years ago for d and l arabinose solutions in water Corresponding author Fax 32 81 724567 E mail address benoit champagne fundp ac be B Champagne with a sum frequency susceptibility about onetenth that of quartz 2 3 In a recent joint theoretical experimental study 4 it has been shown that the SFG phenomenon in chiral liquids is much weaker than previously reported 2 3 5 Firstly a single centre chiral model and ab initio calculations on small chiral molecules indicate that the isotropic part of the SFG rst hyperpolariz is at least two orders of magnitude ability b smaller than that reported experimentally for arabinose Secondly three and four wave mixing experiments support the absence of a strong SFG response in simple chiral liquids In this Letter we describe the theoretical procedure we have adopted for computing the dynamic sum frequency hyperpolarizability and its isotropic part Two simple chiral molecules are considered propylene oxide C3 H6 O and mono uoro oxirane C2 H3 OF 0009 2614 00 see front matter 2000 Elsevier Science B V All rights reserved PII S 0 0 0 9 2 6 1 4 0 0 0 1 1 4 9 0 84 B Champagne et al Chemical Physics Letters 331 2000 83 88 2 Methodology and computational procedure The TWM in chiral liquids is related to the completely antisymmetric isotropic component of the second

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