Liquid crystals quantum computing

The maintenance of a connection to experiment is essential in that reliability is only measurable against experimental results. However, in practice, the computational cost of the most reliable conventional quantum chemical methods has tended to preclude their application to the large, low-symmetry molecules which form liquid crystals. There have however, been several recent steps forward in this area and here we will review some of these newest developments in predictive computer simulation of intramolecular properties of liquid crystals. In the next section we begin with a brief overview of important molecular properties which are the focus of much current computational effort and highlight some specific examples of cases where the molecular electronic origin of macroscopic properties is well established. 

The model of a dipole in a spherical cavity can only provide qualitative insights into the behaviour of real molecules moreover, it cannot explain the effect of electrostatic interactions in the case of apolar molecules. More accurate predictions require a more detailed representation of the molecular charge distribution and of the cavity shape this is enabled by the theoretical and computational tools nowadays available. In the following, the application of these tools to anisotropic liquids will be presented. First, the theoretical background will be briefly recalled, stressing those issues which are peculiar to anisotropic fluids. Since most of the developments for liquid crystals have been worked out in the classical context, explicit reference to classical methods will be made however, translation into the quantum mechanical framework can easily be performed. Then, the main results obtained for nematics will be summarized, with some illustrative... 

With the aim of quantitatively predicting the orientational order of rigid solutes of small dimensions dissolved in the nematic liquid crystal solvent, 4-n-pentyl-4 cyanobiphenyl (5CB), an atomistic molecular dynamics (MD) computer simulation has been applied. It is found that for the cases examined the alignment mechanism is dominated by steric and van der Waals dispersive forces. A computer simulation of the deuterium NMR spectra of molecules in a thin nematic cell has been carried out and the director distribution in the cell has been studied. An experiment for the direct estimation of an element of the order matrix from H NMR spectra of strongly dipolar coupled spins that is based on the multiple quantum spin state selected detection of single quantum transitions has been proposed. The experiment also enables obtaining nearly accurate starting dipolar... 

Such processes are obviously dependent on the optical frequency and the resonant frequencies of the liquid crystal constituent molecules. They are also understandably extremely complicated, owing to the complex electronic and energy level stracture of liquid crystal molecules. Even calculating such basic quantities as the Hamiltonian, the starting point for quantum mechanical calcnlations of the electronic wave function and energy levels and linear optical properties, requires very powerful numerical computational techniques. 

Though the above argument can leave no doubt that in the jellium model there will be a localized assembly of electrons, i.e. a Wigner crystal, in the extremely low density limit, the actual analytic calculation of when the electron liquid, at absolute zero of temperature, freezes as the density is lowered has proved very delicate [20]. Eventually, this matter was settled using quantum Monte Carlo computer simulation by Ceperley and Alder [38], They found in this way that the crystallization first occurred at rs = 100. Herman and March [39] subsequently pointed out that, for the Wigner crystal phase, the theoretical expression [40,41]... 

For molecules in the gas phase these are questions for which quantum chemical ab initio methods provide answers with about the same accuracy as experiments. For crystals like zeolites with up to hundreds of atoms in the unit cell, the same type of question is a real challenge for computational chemistry in general and ab initio quantum chemistry in particular. Compared to other very large systems such as liquids, molecules in solution, or biomolecules, zeolites have the advantage of a regular and well-defined structure yet with a broad variety. Hence, the methods developed for zeolite catalysts and the experience gained when applying them can be exploited in studies on other, even more complex, systems, for example enzymes. 

There are a number of many-body systems which exhibit quantum effects on a macroscopic scale. These include liquid and crystal states of both He-3 and He-4, the electron gas, and neutron matter which probably constitutes the interior of pulsors. In addition, "nuclear matter" - a hypothetical extensive system of nucleons has been studied for the insight one may gain into the nature of finite nuclei. The theoretical studies of these systems have by now a long history, but are by no means concluded. In the last few years, significant advances have been made. This has come in part from the maturity of and gradual unification of many-body theory, in part from the development and application of powerful new expansion procedures, especially varieties of hypernetted-chain equations (3 ) and finally to the growing power of computer simulation methods for quantum systems. This article is intended as a review of some recent development in computational methods for extensive quantum systems, and of the relation between results so obtained to the evolution of other theoretical work. 

In this brief review we have chosen to concentrate upon the character of some new methods for the Monte Carlo modelling of quantum systems. In so doing we have emphasized certain deficiencies of the older method which rests upon the product trial function in a variational expression. It is necessary to remark that this latter technique remains useful it is a reasonable guide to the phenomena in quantum systems and for soft-core systems gives results for the equation of state of liquids and crystals which are adequate for most purposes. The extension of the Monte Carlo variational method to include three-body correlations is straightforward but computationally slow it should be done to provide reliable checks on the theoretical work on such effects in He-4. The study of inhomogeneous systems and mixtures remains largely unexplored. 

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