A generalized Gay-Berne intermolecular potential for biaxial particles, Chem.Phys.Lett. 236, 462 (1995)

A biaxial version of the Gay-Beme potential used to model uniaxial anisotropic molecules is developed. This novel biaxial potential can be used to deal with molecules with different attractive and repulsive contributions along their three axes. The Gay-Berne (GB) [l] potential can be regarded as an anisotropic and shifted version of the Lennard-Jones 6-12 (LJ) interaction suitable for uniaxial molecules, where the strength E and the range parameter (T depend on the orientations of the two particles and their intermolecular vector. An explicit expression for E and g has been obtained by Berne and Pechukas [ 21 by representing each molecule with a uniaxial ellipsoidal Gaussian and their interaction as related to their overlap integral. This integral can in turn be written down as a Gaussian whose preexponential and width are taken to be proportional to E and g. Gay and Berne [ l] then modified the Gaussian-overlap potential in order to introduce a parametric angular dependence on the well depth and width. In the case of uniaxial particles the analytic form of the potential can be written down explicitly [ I]. Other slightly different potentials based on the same E and cr have been put forward [ 31. The GB potential presents several useful features, in particular: (i) it uses less (albeit anisotropic) centres than atomic site models, e.g., one GB site with suitable parameters can model benzene with results similar to those of six united atom centres [ 31; (ii) its parameters can be interpreted and altered as the shape of the molecule changes; (iii) it can be easily differentiated analytically with respect to the positional variables avoiding the discontinuities of purely hard core models. More importantly, the Gay-Berne potential [ 1 ] has proved to be successful in modelling the various condensed phases resulting from a collection of prolate or oblate uniaxial particles. Various simulations [ 4-101 have now shown that a GB system exhibits the most important liquid crystalline phases, namely nematic, smectic A and B for prolate and, respectively, nematic and columnar for oblate particles. On the other hand the current version of the potential is only appropriate for uniaxial molecules, while the need to generalize the GB potential to biaxial particles is rather pressing because, for instance: (a) practically all mesogenic molecules are not uniaxial; (b) the effects of molecular biaxiality are essential for understanding the detailed temperature dependence of ordering in liquid crystals; (c) biaxial contributions to the potential will be essential for obtaining biaxial phases; (d) there is widespread interest in studying the behaviour of biaxial solutes. 0009-2614/95/$09.50 @ 1995 Elsevier Science B.V. All rights reserved SSDJ0009-2614(95)00212-X R. Berurdi et al./Chemical Physics Letters 236 (I 995) 462-468 463 The aim of this Letter is thus to propose a generalization of the Gay-Berne potential suitable for the description of the interaction of biaxial ellipsoids. We start with an overlap model for fully asymmetric ellipsoidal Gaussians and show how this can be used to obtain a generalized biaxial potential. We then parametrize this potential using the interaction of two rigid oligophenyls as a reference. A particle i at position ri and orientation w with respect to the laboratory frame is represented by a Gaussian function G, (wi, r) that, apart from a normalization factor, can be written as [ 11,121 Gi(wj,r) =exp[-i(r-ri)TMTS,‘Ml(r-ri)],