Vibrational—rotational dependence of molecular properties. Electric field gradients for HCl,LiCl, NaCl and KCl

The vibrational—rotational dependence of the nuclear quadrupole coupling constant (NQCC) for the isotopes ²H, ⁷Li, ²³Na, ³⁹K, and ³⁵Cl is analysed in detail for the diatomic Group 1 chlorides HCl, LiCl, NaCl and KCl. The potential energy curves were calculated pointwise by using coupled cluster techniques. The electric field gradients (EFGs) and dipole moments were obtained analytically from a QCISD procedure using the Z vector method. Generally the calculated spectroscopic properties are in very good agreement with experimental data. Relativistic effects taken into account by a coupled cluster Douglas—Kroll procedure can safely be neglected for the electric field gradients up to potassium. The Inglis model which explains the trend and magnitudes of EFGs within an ionic model of weakly polarized atoms is analysed. According to this model the derivatives of the EFG, ? ⁿ q(R)/?R ⁿ, with respect to the internuclear distance R should show alternating sign behaviour with increasing power n. Hence, the mechanical anharmonicity (deviation from Hooke's law potential) and the electrical anharmonicity (curvature of q(R)) are of different sign, and we expect partial cancellation of anharmonicity effects in the vibrational dependence of the NQCCs. Nevertheless, a perturbative vibrational—rotational analysis reveals a strong dependence of the chlorine and Group 1 element NQCCs on the vibrational level due to dominating mechanical anharmonicity.     

Molecular statistical model for adsorbed membrane particles

Indirect membrane-mediated forces influence aggregation, segregation and freezing processes of large particles inserted into a membrane or adsorbed to its surface. Colloidal particles, polymers, peptides and proteins are the source of deformations of the lipid double layer. These perturbations cause membrane-mediated attractive or repulsive forces between the particles. A molecular statistical treatment is useful for investigating the lateral organization of peripheral and trans-membrane peptides. To describe aggregation and freezing phenomena a density functional, which includes conventional short-range forces and membrane-mediated effects, is proposed. The method is applied to an ensemble of adsorbed peptides. It is investigated how the elastic splay-distortion modulus, the surface tension, the compression-expansion modulus of the bilayer and the cross-section of adsorbed particles influence aggregation and freezing. Assuming conventional values for the material parameters, membrane-mediated attractive forces are found to be sufficiently strong to enforce aggregation.     

The use of combinatorics in key management

We consider the key management problem in a large network wherecommunicating nodes use symmetric-key cryptography to provideend-to-end encryption. A number of interesting mathematicalapplications arise, and we concentrate on the use of combinatoricsto facilitate a number of important key management issues. Motivatedby a recent PhD thesis (Quinn 1991), we describe a combinatorialstructure, known as a key distribution pattern. This structureuses subkeys both to reduce storage requirements at the nodesand to allow direct secure communication between nodes withoutfurther recourse to the key distribution centre. The competinginterests of reduced storage and good security pose problemswhich find solutions in the use of certain combinatorial incidencestructures, geometrical configurations, and orthogonal arrays.     

PLANNING MARINE PROTECTED AREAS: A MULTIPLE USE GAME

Abstract The EU Marine Strategy Directive (MSD) has a regional focus in its implementation. The directive obliges countries to take multiple uses and the marine strategies of neighboring countries into account when formulating marine strategies and when designating marine protected areas (MPAs). We use game theoretical analysis both to find the optimal size of MPAs with multiple uses by multiple countries and to investigate the influences of multiple uses on cooperation. To this end, we develop a model in which two specific uses, fisheries and nature conservation, by multiple countries are considered in a strategic framework. The results of the paper suggest that EU marine policy such as the MSD and the coming Maritime Policy may help to secure the highest possible benefits from these MPAs if these policies induce cooperation among countries, but only if policies force countries to consider all possible benefits of MPAs. In fact cooperation on a single issue may give a worse outcome than the noncooperative equilibrium. The results also indicate that cooperation may be hard to achieve because of defector incentives, and therefore policy measures should be strict in enforcing cooperation on all possible uses of MPAs.     

Some semilinear elliptic equations with nonlinear boundary conditions: Radial solutions and simple symmetry-breaking

The subject of nonnegative solutions for semilinear equationshas received considerable attention in recent years. A significantomission is the consideration of nonlinear boundary conditions,and their impact upon the structure of solutions. In this papersome such problems defined on spherically symmetric domainsare presented. The author considers the existence of radiallysymmetric solutions as a function of domain size, and also showsthat infinitesimal symmetry-breaking bifurcations may occurin the simplest eigenmode. This is precluded in the case ofhomogeneous Neumann or Dirichlet problems for similar sourceterms. Given the importance of robust simple symmetry-breaking(in cell division for example), this result suggests attentionshould be further focused upon modelling nonlinear boundaryconditions.     

Application of the Truhlar basis set extrapolation procedure to ab initio calculations on van der Waals complexes

The simple basis set extrapolation procedure recently proposed by Truhlar [1998, Chem. Phys. Lett., 294, 45] has been applied to ab initio calculations on van der Waals clusters. Six test species, Ne₂, NeAr, Ar₂, ArH, ArFH and ArHF, were investigated. In general good agreement has been found with complete basis estimates of the van der Waals bond lengths and dissociation energies providing (i) the cc-pVDZ and cc-pVTZ basis sets originally employed by Truhlar are augmented by a single set of standard diffuse functions, and (ii) the counterpoise correction is used. Only ArHF yields disappointing results, presumably due to the substantial contribution of induction forces to the binding in this cluster. However, even in this case the calculated dissociation energy is within 15% of the complete basis set limit.     

An efficient parallel algorithm for non-equilibrium molecular dynamics simulations of very large systems in planar Couette flow

In this paper we present an efficient parallel domain decomposition algorithm for non-equilibrium molecular dynamics (NEMD) simulations of large systems under planar Couette flow. We propose a modified deforming cell method that permits NEMD simulations with negligible penalties due to the Lees-Edwards periodic boundary conditions. The algorithm was used to study large systems of the Weeks-Chandler-Andersen fluid in order to obtain better viscosity results at the low shear rate regimes where the signal-to-noise ratio is very small.     

Hydrophobic hydration at the level of primitive models. II: Large solutes and water restructuring

Details of structural changes that take place in water near an apolar solute have been studied by Monte Carlo simulations for hard sphere solutes of increasing size, including the limiting case of water at a hard structureless wall. Water has been modelled by two different types of extended primitive model, the four-site EPM4 model and five-site EPM5 model. Two different patterns of the orientational ordering of the water molecules around the solute as a function of its size have been found. For the EPM5 model, the structure of water and the orientation of its molecules near an apolar solute of finite diameter do not seem to be sensitive to the size of the solute, and only become more pronounced when the solute becomes a hard wall. On the other hand, the orientation ordering of the EPM4 molecules gradually changes with increasing size of the solute, and for solutes larger than approximately five times the size of the water molecule it is opposite to that near a small solute. A novel method to evaluate the excess chemical potential of large solutes has been implemented, and some thermodynamic quantities for water (distribution of hydrogen bonds and the excess chemical potential) have been computed as a function of the distance from the solute.