Chemical Physics

A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic energy containing force constants between {\em all}monomer-pairs as variational parameters. By a judicious choice of representation and the use of incremental matrix inversion, an efficient and fast-convergent iterative algorithm is constructed, that optimizes the free energy. The computational demand scales as N 3 rather than N 4 as expected in a more naive approach. The method has the additional advantage that in contrast to Monte Carlo calculations the entropy is easily computed. An analysis of the high and low temperature limits is given. Also, the variational formulation is shown to respect the appropriate virial identities.The accuracy of the approximations introduced are tested against Monte Carlo simulations for problem sizes ranging from N=20 to 1024. Very good accuracy is obtained for chains with unscreened Coulomb interactions. The addition of salt is described through a screened Coulomb interaction, for which the accuracy in a certain parameter range turns out to be inferior to the unscreened case. The reason is that the harmonic variational Ansatz becomes less efficient with shorter range interactions. As a by-product a very efficient Monte Carlo algorithm was developed for comparisons, providing high statistics data for very large sizes -- 2048 monomers. The Monte Carlo results are also used to examine scaling properties, based on low- T approximations to end-end and monomer-monomer separations. It is argued that the former increases faster than linearly with the number of bonds.

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of D 3h -triatomic molecules.

A new method to obtain a local parameterization for the exchange term in the many--body electronic problem is presented. The approach amounts to the introduction of a coordinate dependent electron effective mass. Numerical results for metallic clusters in the jellium model are compared with other standard methods.

The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm −1 (and a r.m.s. deviation of 1.16 cm −1 ).

In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a linear scaling multigrid algorithm.This work is done in the context of minimizing the Kohn-Sham energy functionaldirectly in real space with a multiscale approach. The efficacy of the approximation is illustrated bylocating the ground state density of simple one electron atoms and moleculesand more complicated multiorbital systems.

Density functional theory(DFT) and Hartree-Fock(HF) calculations are reported for the family of transition metal fluorides ScF 3 , TiF 4 , VF 5 , and CrF 6 . Both HF and the local-density-aproximation (LDA) yield excellent agreement with experimental bond lengths, while the B-LYP gradient-corrected density functional gives bond lengths 0.04−0.05 Å too long. An investigation of various combinations of exchange and correlation functionals shows that, for this series, the origin of this behavior lies in the Becke exchange functional. Much improved bond distances are found using the hybrid HF/DFT functional advocated by Becke. This approximation also leads to much improved thermochemistries. The LDA overestimates average bond energies in this series by 30−40 kcal/mol, whereas the B-LYP functional overbinds by only ∼8−12 kcal/mol, and the hybrid HF/DFT method overbinds by only ∼2 kcal/mol. The hybrid method predicts the octahedral isomer of CrF 6 to be more stable than the trigonal prismatic form by 14 kcal/mol. Comparison of theoretical vibrational frequencies with experiment supports the assignment of an octahedral geometry.

Using the optimized effective potential method in conjunction with the semi-analytical approximation due to Krieger, Li and Iafrate, we have performed fully self-consistent exact exchange-only density-functional calculations for diatomic molecules with a fully numerical basis-set-free molecular code. The results are very similar to the ones obtained with the Hartree Fock approach. Furthermore we present results for ground states of positive atomic ions including correlation contributions in the approximation of Colle and Salvetti. It is found that the scheme performs significantly better than conventional Kohn-Sham calculations.

A classical microscopic theory of rovibrational motion at high angular momenta in symmetrical non-linear molecules AB 2 is derived within the framework of small oscillations near the stationary states of a rotating molecule. The full-dimensional analysis including stretching vibrations has confirmed the existence of the bifurcation predicted previously by means of the rigid-bender model. The formation of fourfold energy clusters has already been experimentally verified for H 2 Se and it has been demonstrated in fully-dimensional quantum mechanical calculations using the MORBID computer program. We show in the present work that apart from the level clustering, the bifurcation produces physically important effects including molecular symmetry-breaking and a transition from the normal mode to the local mode limit for the stretching vibrations due to rovibrational interaction. The application of the present theory with realistic molecular potentials to the H 2 Te, H 2 Se and H 2 S hydrides results in predictions of the bifurcation points very close to those calculated previously. However for the lighter H 2 O molecule we find that the bifurcation occurs at higher values of the total angular momentum than obtained in previous estimations. The present work shows it to be very unlikely that the bifurcation in H 2 O will lead to clustering of energy levels. This result is in agreement with recent variational calculations.

We develop a simple optimization procedure for assigning binary values to the amino acids. The binary values are determined by a maximization of the degree of pattern conservation in groups of closely related protein sequences. The maximization is carried out at fixed composition. For compositions approximately corresponding to an equipartition of the residues, the optimal encoding is found to be strongly correlated with hydrophobicity. The stability of the procedure is demonstrated. Our calculations are based upon sequences in the SWISS-PROT database.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid crystalline phase digram: a higher-density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction; and a lower-density cholesteric region with fluid-like positional order. X-rays scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a six-fold azimuthal modulation of the first order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order that had been expected from the change in optical birefringence patterns and that is consistent with a rapid onset of molecular positional disorder. This change in motion was previously inferred from intermolecular force measurements and is now confirmed by 31 P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between ∼120 mg/ml to ∼600 mg/ml, allows measurement of the free energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.