ЖУРНАЛ ФИЗИЧЕСКОЙ ХИМИИ, 2008, том 82, № 1, с. 99-103
СТРОЕНИЕ ВЕЩЕСТВА ^^^^^^^^^^^^ И КВАНТОВАЯ ХИМИЯ
Ordering in Higher Homologous Series of ^-и-Alkylbenzoic Acids Having Eight Alkyl Chain Carbon Atoms - A Computational Analysis © 2008 N. Ajeetha, G. Srinivas, D. P. Ojha
Liquid Crystal Research Laboratory, Postgraduate Department of Physics, Andhra Loyola College, Vijayawada-520 008, A.P., India E-mail: firstname.lastname@example.org Received November 01, 2006
Abstract—A computational analysis of ordering in higher homologous series of p-n-alkylbenzoic acids (nBAC), having 8(8BAC) carbon atoms in the alkyl chain, has been carried out based on quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic centre has been carried out through an all-valence electron (CNDO/2) method. The modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions while a '6-exp' potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations were used as input for calculating the probability of each configuration in a non-interacting and non-mesogenic solvent (i.e. benzene) at room temperature (300 K) using the Maxwell-Boltzmann formula. A comparative picture of molecular parameters, such as the total energy, binding energy, and total dipole moment of 8BAC with 7BAC and 9BAC has been given. The present article offers a theoretical support for the experimental findings.
In recent years, liquid crystal research has gained much prominence in multidirectional aspects with exciting practical applications . Liquid crystals are also at the centre of enormous advances in our understanding of fundamental science of condensed systems . The phase transitions in liquid crystals are often accompanied by interesting changes in their properties. The several techniques/methods are employed to investigate the phase transitions, depending on the nature of liquid crystals and properties of interest [3, 4]. Such studies are not only of an academic value in understanding the structural and mechanistic aspects of phase transitions, but can also be of technological importance. The proper understanding of liquid crystalline behaviour requires an adequate theoretical background as a precursor to application of developments and accounts abnormal properties of the materials .
It has been recognized for several years that an exclusively theoretical approach frequently yields ambiguous results. The majority of mesogenic molecules are composed of an aromatic core to which attached one or two alkyl chains. The primary role of the alkyl chain is to enhance the liquid crystal order by lowering the melting point. The liquid crystal properties, such as the nem-atic-isotropic transition temperature and the entropy of transitions, are influenced by the presence of the alkyl chain . The liquid crystalline phases are viscoelastic in nature, with long-range orientational order and varying degrees of positional order. The efforts have been made to understand the relationship between the liquid crystallinity and chemical constitution of the materials using various techniques resulting in a number of models [6-8]. The potential energy of interaction of two mole-
cules is considered as a prime requirement in the theoretical investigation on molecular interactions. This interaction determines the positional and orientational order of the mesomorphic compounds .
The role of molecular interactions in mesomorphic compounds attracted the attention of several workers [10-12] considered them on the basis of the Rayleigh-Schrodinger perturbation method. These studies aimed for establishing the anisotropic nature of the pair potential and subsequently finding out the minimum energy configuration of a pair of liquid crystalline molecules. Thus the main emphasis was laid on finding out the minimum energy with observed crystal structure. It was observed that the interaction energies for a pair of me-sogens indicate the preference of a particular configuration over the other depending on their energy values. These values, however, did not reflect the actual relative preference, which could be only obtained through their probabilities corresponding to each configuration.
Further, it is difficult to have direct correlation between pair energy and liquid crystallinity. It is not straightforward even if one takes the relative probabilities into account. It is, therefore, necessary to identify the characteristic features of liquid crystallinity in terms of the pair energy or configurational probabilities. Since mesogenic properties are related to molecular aggregation in a specific manner, the probability calculations based on energy distribution results can provide valuable information in this respect. The relative probabilities of observed configurations provide a tool for understanding the molecular tendency of alignment, layer
The relative probability of different minimum energy configurations obtained for stacking, in-plane and terminal interactions in vacuum and dielectric medium at 300 K
Interaction Configuration -Ev -Ed Pv Pd
Stacking x(0°) y(0°) 12.71 5.65 47.7 39.3
Stacking y(0°) z(180°) 12.22 5.43 20.9 27.3
Stacking y(0°)z(0°) 12.46 5.54 31.3 32.6
In-plane y(0°) 6.87 3.05 0.0 0.5
In-plane y(180°) 6.29 2.80 0.0 0.3
Terminal y(0°) 2.32 1.03 0.0 0.0
Notes: The average dielectric constant of benzene is taken as 2.25; Ev and are the energies in vacuum and in dielectric medium respectively, kcal/mole; Pv and Pd are the probabilities, %.
formation, and extent of freedom corresponding to rotation, translation, etc.
The present work deals with the computation of pair energy and configurational probabilities between a molecular pair of p-n-alkylbenzoic acids having eight alkyl chain carbon atoms (8BAC) in a dielectric medium (i.e., benzene, the average dielectric constant of which has been taken to be 2.25) at an intermediate distance of 6 A for stacking and 8 A in-plane interactions. Similarly, a distance 22 A has been kept for terminal interactions. The choice of distance has been made to eliminate the possibility of the van der Waals contacts completely and to keep the molecules within the range of short- and medium-range interaction. Further, instead of finding the exact minimum energy configuration, a step has been put forward to elucidate the general behaviour of the molecules surrounding a fixed molecule in a particular frame of reference. The thermodynamic parameters reveal that 8BAC molecule shows nematic to iso-tropic transition temperature at 385.5 K .
SIMPLIFIED FORMULA AND
The molecular geometry of 8BAC has been constructed on the basis of the published crystallographic data with the standard values of bond lengths and bond angles . Depending on the property of interest, a number of following different methodologies have been employed in this work.
Evaluation of charge and atomic dipole distribution. The simplified formula for interaction energy calculations requires the evaluation of atomic charges and dipole moment components at each atomic centre through an all valence electron method. In the present computation, the CNDO/2 method  has been employed to compute the net atomic charge and dipole moment at each atomic centre of the molecule. A revised version QCPE № 142 of program, which is an extension of the original program 4 QCPE No. 141 for the third row elements of periodic table has been used.
Computation of interaction energy at various configurations. A detailed computational scheme based on
simplified formula provided by Claverie  for the evaluation of interaction energy between a molecular pair has been used to calculate the energy for fixed configuration. The computer program INTER, originally developed by Claverie and later on modified at Chemical Physics Group, Tata Institute of Fundamental Research, Bombay, India by Govil and associates has been used for this purpose with further modifications. According to the second order perturbation theory as modified for intermediate range interactions , the total pair interaction energy of molecules (Upair) is represented as sum of various terms:
Upair _ Uel + Upol + Udisp + Urep,
where Uel, Upol, Udisp and Urep are the electrostatic, polarization, dispersion and repulsion energy terms respectively.
Again, electrostatic term is expressed as
Uel = UQQ + UQMI + U
where Uqq, Uqmi, and UMIMI are monopole-monopole, monopole-dipole and dipole-dipole terms respectively. In fact, the inclusion of higher order multipoles does not affect significantly the electrostatic interaction energy and the calculation only up to dipole-dipole term gives satisfactory result . The computation of electrostatic term has, therefore, been restricted only up to dipole-dipole energy term.
In the present computation the dispersion and short-range repulsion terms are considered together because several semiempirical approaches, viz. the Lennard-Jones or Buckingham type approach, actually proceed in this way. Kitaygorodskii introduced  a Buckingham formula whose parameters were later modified by Kitay-gorodskii and Mirskaya for hydrocarbon and several other molecules and finally gave the expression :
U disp + U rep H U (X,v),
U(X, v) = KXKv(-A/Z6 + Be-*2),
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where Z = RXJR°Xv; R°Xv = [(2 RW )(2 R^! )]1/2; RW and
Rv are the van der Waals radii of atoms X and v respectively. The parameters A, B and у do not depend on the atomic species. But R0Xv and factor KX Kv allow the energy minimum to have different values according to the atomic species involved. The necessary formulae may be found elsewhere .
Computation of configurational probabilities
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