Nematic Behaviour of a Compound EBBA – A Compuational Analysis

EBBAA computational analysis has been carried out to determine the configurational preferences of a pair of p-ethoxybenzylidine-p-n-butylaniline () molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. The configurational energy has been computed using the Rayleigh-Schrödinger perturbation method. The interaction energies obtained through these computations were used to calculate the probability of each configuration at 300 K. The energy of a molecular pair during stacking, in-plane, and terminal interaction has been calculated. The results are discussed in the light of other experimental and theoretical results.

Role of Dielectric Medium on a Nematogen. A Statistical Approach Based on Quantum Mechanics and Computer Aided Modelling

ECCPA statistical analysis has been carried out to determine the configurational preferences of a pair of 5-(4-ethylcyclohexyl)-2-(4-cyanophenyl) pyrimidine () molecules. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. The configurational energy has been computed using the Rayleigh-Schrödinger perturbation theory. The total interaction energies obtained by these computations were used to calculate the probability of each configuration in vacuum and in a dielectric medium (benzene) at the phase transition temperature using the Maxwell-Boltzmann formula. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pair have been considered. An attempt has been made to explain the nematogenic behavior of liquid crystals and thereby develop a molecular model for liquid crystallinity.

Smectogenic Behaviour of 7O.6 at it's Phase Transition Temperature: A Computational Analysis Reprint request to

A computational analysis has been carried out to determine the configurational preference of a pair of Ar-(4-n-heptyloxybenzylidine)-4-hexylaniline (70.6) molecules with respect to translatory and orien­ tational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atom ic dipole components at each atomic centre of the molecule. The configurational energy has been com­ puted using the modified Rayleigh-Schrödinger perturbation method. The obtained energies were used to calculate the probability of each configuration at phase transition temperature, using Maxwell-Boltz-mann's formula. The flexibility of various configurations has been studied in terms of variations of the probability due to small departures from the most probable configuration. The results are discussed in the light of experimental as well as other theoretical observations. The smectogenic character of the molecule has been correlated with the parameters introduced in this paper.

Molecular Organization in a Nematogen: PBPCN -A Computational Analysis Based on Quantum Mechanics

A computational analysis has been carried out to determine the configurational preference of a pair of 4'-n-pentyloxy-4-biphenylcarbonitrile (PBPCN) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Modified Rayleigh-Schrödinger 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. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of molecular pair have been considered. It has been observed that the molecule has a strong preference for stacking through a particular face, while the other configurations, such as stacking through the other face, in-plane and terminal interactions show, in general, an aligned structure along molecular axis. The results are discussed in the light of experimental as well as other theoretical observations.

Nematogenic Behaviour of a Cyano-Compound Using Quantum Mechanics and Computer Simulations

Using quantum mechanics and intermolecular forces, the molecular ordering of a nematogenic cya-no-compound, 5-(frans-4-ethylcyclohexyl)-2-(4-cyanophenyl)-pyrimidine (ECCPP), has been exam­ ined. The CNDO/2 method has been employed to evaluate the net atomic charge and the dipole mo­ ment components at each atomic centre of the molecule. The configuration energy has been computed using the modified Rayleigh-Schrödinger perturbation method at intervals of 1Ä in translation and 10P in rotations, and corresponding probabilities have been calculated using Maxwell-Boltzmann statistics. The flexibility of various configurations has been studied in terms of the variation of the probability due to small departures from the most probable configuration. All possible geometrical arrangements between a molecular pair have been considered during stacking, in-plane and terminal interactions, and the most favourable configuration of pairing has been obtained. An attempt has been made to under­ stand the behaviour of the molecules in terms of their relative order. The results have been compared with those obtained for other nematogens like DPAB [4,4'-di-n-propoxy-azoxybenzene] and EMBAC [ethyl 4-(4'-methoxybenzylidene amino) cinnamate].

Towards a Direct Numerical Solution of Schrödinger’s Equation for (e, 2e) Reactions

The finite-difference method for electron{hydrogen scattering is presented in a simple, easily understood form for a model collision problem in which all angular momentum is neglected. The model Schrödinger equation is integrated outwards from the atomic centre on a grid of fixed spacing h. The number of difference equations is reduced each step outwards using an algorithm due to Poet, resulting in a propagating solution of the partial-differential equation. By imposing correct asymptotic boundary conditions on this general, propagating solution, the particular solution that physically corresponds to scattering is obtained along with the scattering amplitudes. Previous works using finite differences (and finite elements) have extracted scattering amplitudes only for low-level transitions (elastic scattering and n = 2 excitation). If we are to eventually extract ionisation amplitudes, however, the numerical method must remain stable for higher-level transitions. Here we report converged cross sections for transitions up to n = 8, as a first step towards obtaining ionisation (e; 2e) results.

ELECTRONIC SPIN STATES IN CHROMIUM

The electronic spin density and its spatial and temporal variation in Cr and its alloys are still not fully understood. The suggestion that Cr is an example of a spin-split metal is not supported by the evidence. Instead, it appears that three rather different types of magnetic moment are required to describe the electronic spin density in Cr: (1) static spin-density-wave moments and associated low-energy spin fluctuations that collapse at high temperatures; (2) higher-energy paramagnetic fluctuations that increase with temperature; and (3) 3d atomic moments formed due to intra-atomic exchange within 1 Å of the atomic centre showing almost no temperature dependence. We suggest further experiments to clarify this picture.

Lie Group Calculation of the Green Function of Disordered Systems

ABSTRACTWithin the framework of the muffin-tin multiple-scattering theory, the scattering path operators are given by the inverse of a matrix consisting of atomic t-matrices and a structural matrix. The influence of the displacement of an atomic centre on the structural matrix can be described analytically using Lie group techniques. From this analytical expression and the standard perturbation expansion of the Lippmann-Schwinger equation, it is possible to write the Green function of a disordered system as a series of terms whichare averages over configurations. These averages can be calculated analytically from themoments of the interatomic distances. Special terms of this series are then summed up toinfinity using Dyson equation. This formalism is computationally very effective to calculate electronic properties of systems with thermal or structural disorder. In this paper, the theoretical basis of this approach is briefly described and the convergence properties of the expansions are investigated.