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A relativistic study of spectroscopic properties of the endohedral fullerenes Ng@C 60 q (where Ng = He, Ne and q=0,±1,±2 are the charges) associated with the C 60 molecule has been done using the equation of motion coupled cluster (EOM-CC) methodology. Specific properties estimated are the transition energies, dipole oscillator strengths, and transition probabilities for the low-lying excitations 1s 2 ( 1 S 0 ) → 1snp ( 1 P 1 ) (n = 2, 3, 4) for He@C 60 q and 1s 2 2s 2 2p 6 ( 1 S 0 ) → 1s 2 2s 2 2p 5 ns∕nd ( 1 P 1 ) (n = 3, 4) for Ne@C 60 q , which have been compared with those for the isolated atom to depict the confinement effect of the host molecule on the encapsulated atom. This is accomplished by introducing an effective potential to the atomic Hamiltonian induced by the fullerene moiety and its charge. The EOM-CC results have been compared with those estimated with the random phase approximation (and configuration interaction singles) to understand the effect of electron correlation under such confinement. The systematic and interesting behavior of the properties is highlighted indicating the effect of fullerene cage potential on the redistribution of electron density of the guest atom.

We propose a phenomenological model to describe the tricritical behavior of the nematic to smectic-A (N-SmA) phase transition in liquid crystal mixture. To describe the mesophase transitions in binary mixture, nematic and smectic order parameters have been coupled with the concentration. We show that a tricritical point on the N-SmA phase transition line can be achieved under certain conditions. The predictive capability of the present model for determining the tricritical point of a binary mixture displaying the N-SmA transition has been demonstrated by testing with reported phase diagrams sharing both phases.

A phenomenological model is developed to describe the isotropic-smectic-C phase transition in liquid-crystalline side-chain elastomers. We analyze the influence of external mechanical stress on the isotropic-smectic-C phase transition. While this phase transition is first order in low-molecular-weight materials, we show here that the order of this transition does not change in liquid-crystalline elastomers. The temperature dependence of the heat capacity and the nonlinear dielectric effect in the isotropic phase above the isotropic-smectic-C phase transition in liquid crystalline elastomers are calculated. The theoretical results are found to be in good agreement with experiment.

A phenomenological theory is presented, which describes the tricritical behavior of the R(I)-R(V) rotator phase transition in the mixture of alkanes with nanoparticles. The influence of the nanoparticles on the R(I)-R(V) transition in alkanes is discussed by varying the coupling between the order parameters of the rotator phases and nanoparticle. When nanoparticle solutes are added to pure alkanes, the R(I)-R(V) transition temperature is increased. It was observed from the theoretical calculations that for a particular value of the concentration of the nanoparticles, the first order R(I)-R(V) transition becomes second order at a tricritical point. Calculations based on this model agree qualitatively with experiment., (© 2011 American Institute of Physics)

A model for coupled tilt angle and lattice distortion parameter is proposed to describe the R(I)-R(V) transition in n-alkane. The model is treated in the framework of a Landau mean-field theory and renormalization-group theory. The influence of gauche conformations and molecular flexibility on the R(I)-R(V) transition is discussed within the mean-field theory. The fluctuations on the R(I)-R(V) transition are discussed by the renormalization-group theory. Renormalization-group theory predicts that the R(I)-R(V) transition can be driven first order by fluctuations and becomes second order at a tricritical point. Available experimental data are consistent with our model.

We present a mean-field description of the phase transitions, which are obtained when cooling from the isotropic liquid to the first liquid crystalline phase in compounds composed of achiral banana-shaped molecules. We put special emphasis on the isotropic to antiferroelectric B(2) phase transition. The free energy is written in terms of the coupled order parameters including the antiferroelectric polarization. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a direct isotropic to antiferroelectric B(2) phase transition is possible when compared with other phase transitions. The theoretical results are found to be in qualitative agreement with all published experimental results.

A phenomenological Landau-like theory is presented, which describes the tricritical behavior of the smectic-A to smectic-C(*) transition in a liquid crystal mixture. The influence of the concentration on this transition is discussed by varying the coupling between the concentration variable and the order parameters. It was observed from the theoretical calculations that for a particular value of the concentration, the first order smectic-A to smectic-C(*) transition becomes second order at a tricritical point. Calculations based on this model agree qualitatively with experiment.

We examine the effect of pressure on the rotator-II (R(II)) to rotator-I (R(I)) (R(II)-R(I)) transition within Landau phenomenological theory. The influence of pressure on the R(II)-R(I) transition is discussed by varying the coupling between the lattice distortion and the area/molecule. The pressure dependence of the area/molecule and the lattice distortion are calculated near the R(II)-R(I) transition. The R(II)-R(I) transition is found to be first order even at elevated pressure. The Landau coefficients are calculated from the experimental data. The theoretical results are in good agreement with available experimental results.

We describe new topologies in the phase diagrams involving biaxial nematic liquid crystals. We find that a direct isotropic-biaxial nematic phase transition is possible. Our results show that three different biaxial nematic phases can occur. We outline how the novel phase diagrams could be detected experimentally.

Monte Carlo simulation studies have demonstrated the possibility of the first order isotropic to smectic-B phase transition. We present a mean-field description of the direct isotropic to hexatic-B phase transition. We analyze the question under which conditions a direct isotropic to hexatic-B phase transition is possible when compared to other phase transitions. Within this model the direct isotropic to hexatic-B phase transition is found to be always strongly first order than the isotropic to nematic and isotropic to smectic-A phase transitions. The presented analysis is in good agreement with Monte Carlo simulation studies.

A phenomenological theory is presented to describe the pressure effect on the cholesteric to smectic-A phase transition. The problem of first or second order character of the cholesteric to smectic-A phase transition is explored by means of the variation of the pressure. The possibility of the tricritical point at the cholesteric to smectic-A transition line is discussed in a phenomenological way. It is shown that with a particular value of the pressure, the first order cholesteric to smectic-A transition becomes second order at a pressure induced tricritical point. The obtained topologies of the pressure-temperature phase diagram qualitatively agree with experimental results.

Simple Landau-type free energy function is presented to describe the R(IV)-R(III)-R(V) rotator phase sequence and the transitions between them. The order parameters necessary to describe the above rotator phase transitions are identified. Varying the coupling between the order parameters, the R(IV)-R(III) and R(III)-R(V) transitions occur. Available experimental results are consistent with our model.

A phenomenological approach to the description of the smectic-A to smectic-C phase transition in a liquid crystal mixture is proposed. The problem of the first or second order transition is explored by means of the variation of the concentration. The influence of the concentration on this transition is discussed by varying the coupling between the concentration variable and the order parameters. We show that a tricritical point on the smectic-A to smectic-C phase transition line can be achieved under certain conditions. The theoretical prediction is found to be in good qualitative agreement with experimental results.

In this work we present a method based on the perturbation theoretic approach of Bishop and co-workers [J. Chem. Phys. 95, 2646 (1991); 97, 5255 (1992); 108, 10013 (1998)] to calculate the effect of torsional motion on the polarizability and hyperpolarizabilities of hydrogen peroxide. The frequency dependence has been evaluated using the time-dependent Hartree-Fock method. The results obtained show that the zero-point vibrational averaging contributions are small compared to the corresponding electronic contributions. In the static limit the pure vibrational contributions are very large, specially for beta and gamma. These contributions are significant for the hyperpolarizabilities even in the visible region, except for the second harmonic generation and third harmonic generation processes.

A phenomenological approach to the description of the rotator phases and transitions among them in mixtures of normal alkanes is proposed. The mixture exhibits crystal and three different rotator phases R(II), R(I), and R(V). The two phase regions are formed where the crystal+rotator and rotator+rotator phases coexist. The reason of these two phase regions is discussed by means of the Landau formalism. The influence of the concentration on these transitions and the transition temperatures are discussed by varying the coupling between the concentration variable and the order parameters. The theoretical predictions are found to be in good qualitative agreement with the experimental results.

The pentacosane undergoes a series of structural phase transitions in addition to the melting transition according to an x-ray scattering study. A phenomenological theory is developed to describe the structural phase transitions between different phases observed in pentacosane. We present a detailed analysis of the different phases and analyze the temperature anomalies of the elastic constants and heat capacity. The thermodynamic anomalies on the different phase transitions are described by the coupling between the order parameters and the elastic strains. The theoretical predictions are found to be in good qualitative agreement with experimental results.

A phenomenological theory is presented to describe the nematic to lamellar phase transition in lyotropic liquid crystals. The problem of the first or second order transition is explored by means of the variation of the surfactant concentration. The possibility of the tricritical point at the nematic to lamellar phase transition is discussed in a phenomenological way. The influence of the electrolyte on this transition is also discussed by varying the coupling between the electrolyte concentration variables and the order parameters. The theoretical prediction is found to be in good qualitative agreement with experimental results.

Variational calculations using Hylleraas coordinates have been performed for the first time for estimating the energies of 3dnf((1,3)D(o)) state of helium for n=4,5,6. We predict absorption peaks at 12.219, 12.647, and 12.857 eV for the (3)D(o) series converging to N=3 ionization threshold of He(+) which can be expected to be observed in the experiment of single photon double excitation of lowest (3)P(e) state of helium placed in synchrotron radiation.

Nonrelativistic energy of the (2p(2))(3)P(e) state of Be(2+) has been calculated using Ritz-variational method. The trial wave function is of Hylleraas type. The upper-bound energy E=-3.382 712 420 77 a.u. calculated by us is the lowest yet obtained.

An orientational order parameter is proposed for the isotropic to smectic C*A phase transition in antiferroelectric liquid crystals. A phenomenological theory is developed to describe the direct isotropic to smectic-C*A phase transition on the basis of a free energy expansion. The free energy is written in terms of the coupled order parameters including the antipolar correlations. We present a detailed analysis of the different phases that can occur and analyze the question: under which conditions a direct isotropic to smectic-C*A phase transition is possible when compared to other phase transitions? The theoretical results are compared with experimental results., ((c) 2004 American Institute of Physics)