Nonadditive Potential Research Articles

Nonadditive intermolecular potential and thermodynamic properties of ethane

New intermolecular potential models incorporating nonadditive interactions are proposed for the ethane molecule. Three functional forms for the pair potentials were tested. Each was based on an initial fit to ab initio calculations of the pair interaction energy, followed by a first refinement fit to second virial coefficients. A nonadditive three-body contribution was then included, leading to a density-dependent effective pair potential. Finally, the resulting models were optimized against experimental thermodynamic data in the compressed gas region. In the interest of computational efficiency, thermodynamic properties were calculated from the intermolecular potentials using the molecular integral-equation theory with a recent approximation for the bridge function. The accuracy of the closure was verified by Monte Carlo simulations. The intermolecular potentials are able to reproduce the p(ρ,T) surface of ethane with an overall standard deviation of 0.2% up to the saturation line, or at densities up to the critical density, over a wide range of temperatures.

Entropic collapse transition of a polymer in a solvent with a nonadditive potential.

We use molecular dynamics simulations to study an entropy-driven collapse transition of a flexible polymer in a solvent. Monomers and solvent particles interact with a steeply repulsive soft-sphere potential. We consider a nonadditive potential system in which the effective diameter describing the solvent-monomer interaction is greater than or equal to the diameters corresponding to the solvent-solvent and monomer-monomer interactions, which are set equal. We examine the effects of nonadditivity of the solvent-monomer potential and solvent density on the collapse transition. We find that a small degree of nonadditivity will drive the transition at sufficiently high solvent density. Increasing the density leads to a collapse transition at lower values of nonadditivity.

Dressed zero-point field correlations and the non-additive three-body van der Waals potential

A method previously introduced to evaluate the far zone part (Casimir - Polder) of the non-additive van der Waals interaction between three ground-state isotropic non-overlapping atoms or molecules is extended to arbitrary separation of the sources. The results obtained are valid for arbitrary geometrical configurations of the three sources. In this method the non-additive van der Waals potential is obtained as the classical interaction energy between the dipole moments of two of the three atoms; these dipole moments are induced and correlated by the spatially correlated zero-point vacuum fluctuations, `dressed' by the presence of the third atom. This method, in addition, yields a new physical interpretation of the three-body forces, which throws light on the role of dressed vacuum field correlations.

The solvation of sodium ions in water clusters: intermolecular potentials for Na+-H2O and H2O-H2O

New model potentials are constructed for Na+-H2O and H2O-H2O, using quantum mechanical calculations of the monomer wavefunctions. One parameter in each model potential is fitted to experimental dimer properties. The resulting Na+-H2O potential is consistent with published thermodynamic and ab initio data, and the H2O-H2O potential reproduces the structure and energy of the water dimer at equilibrium, and the second virial coefficient of steam, within experimental uncertainties. The donor-acceptor interchange tunnelling pathway on the water dimer potential energy surface has a lower energy barrier than the acceptor-acceptor interchange, in agreement with recent spectroscopic studies. When a simple non-additive induction potential is included, calculated thermodynamic properties of solvated sodium ions are in agreement with experimental data. For small clusters in the gas phase, the first solvation shell of the sodium ion is predicted to contain four water molecules.

The energy and structure of Bjerrum defects in ice Ih determined with an additive and a nonadditive potential

The energy and the structure of the Bjerrum D defect have been determined with both an additive and a nonadditive potential and those of the L defect with the additive potential. The results showed that: the relaxations of the two molecules joined formally by the defect bond and their other six nearest neighbors were energetically and structurally significant for both D and L defects; the interactions of the sites permitted to relax with their surrounding neighbors should be included explicitly, since these interactions determine the orientations and positions of the former; the nonadditive component significantly altered both the energy and structure of the D defect.

The nonadditive intermolecular potential for water revised

The results of an improved version of a nonadditive intermolecular model for water that explicitly includes the nonadditive polarization energy are reported. The original polarizable water potential model (POL1), upon which the improved version is based, was developed by Caldwell, Dang, and Kollman [J. Am. Soc. Chem. 112, 9144 (1990)]. To improve the POL1 model, we developed a new set of atomic polarizabilities that reproduce the experimental molecular polarizability for water using the atom–dipole interaction model (Applequist, Carl, and Fung [J. Am. Soc. Chem. 94, 2952 (1972)]). Using the new atomic polarizabilities, we optimized the Lennard-Jones parameters for O–O interactions to improve the model. As expected, the new model has improved the radial distribution functions and the average potential energy for liquid water as well as the density and the average total dipole moment. The model is then used to compute the binding energies of Cs+–water clusters. Without the need for three-body forces (ion–water–water interaction), the agreement between the results of molecular-dynamics simulations and experimental energies of cluster formation is very good.

Reply to: ‘‘Comment on ‘Water–water and water–ion potential functions including terms for many-body effects,’ T. P. Lybrand and P. Kollman, J. Chem. Phys. 8 3, 2923 (1985) and on ‘Calculation of free energy changes in ion–water clusters using nonadditive potential and the Monte Carlo methods,’ P. Cieplak, T. P. Lybrand, and P. Kollman, J. Chem. Phys. 8 6, 6393 (1987)’’

Reply to: ‘‘Comment on ‘Water–water and water–ion potential functions including terms for many-body effects,’ T. P. Lybrand and P. Kollman, J. Chem. Phys. <b>8</b> <b>3</b>, 2923 (1985) and on ‘Calculation of free energy changes in ion–water clusters using nonadditive potential and the Monte Carlo methods,’ P. Cieplak, T. P. Lybrand, and P. Kollman, J. Chem. Phys. <b>8</b> <b>6</b>, 6393 (1987)’’

Geometries, energies, and electrostatic properties of nonadditively optimized small water clusters

Several local energy minima have been determined for small water clusters, (H2O)n, of n=3, 4, and 6 molecules. Their geometries were optimized with the nonadditive potential of Campbell and Mezei. For n=6, the inclusion of the nonadditive component of the potential altered the order of the energies of the local minima on the energy surface. Whereas the additive approximation (pairwise energy sum) favored a nearly planar ring, the nonadditive energy preferred a staggered hexagon, as found in ice Ih. It has been shown that the nonadditive component—and even the energy contribution from the cooperative reinforcement of the induced dipole fields—are larger than the energy differences between different ice forms with their very different orientations. When both nonadditive and dispersion energy contributions were included, the equilibrium oxygen–oxygen distance for (H2O)6 was reduced from the optimal dimer distance to the range of vibrationally averaged oxygen–oxygen distances in condensed phases. Electric fields and substantially enhanced molecular dipole vectors have been calculated. The molecular dipole moments in the clusters are substantially larger than the isolated molecule moment.

Calculation of free energy changes in ion–water clusters using nonadditive potentials and the Monte Carlo method

A thermodynamic perturbation method, using a Monte Carlo procedure, has been applied to the calculation of the free energy differences between ion–water clusters containing a given number of water molecules (n=1,...,6) and different monovalent ions, i.e., Li+, Na+, K+, F−, and Cl−. To our knowledge, this is the first application of the free energy perturbation approach with a nonadditive intermolecular potential. The results confirm the usefulness of the method and yield free energy differences of hydration which are in generally very good agreement with experiment. Our calculations have also revealed some structural changes which take place within the first hydration shell when one ion is replaced by another in the hexahydrate clusters. For Li+ one obtains a well defined 4+2 mean structure, whereas for a larger ion such as K+ the solvation structure is closer to a 5+1 type. For anions, this tendency is reversed, i.e., for F− one finds a well defined four coordinate structure for a cluster with four water molecules, but for the larger anion Cl− the cluser tends to be a 3+1 structure. In addition, favorable water–water interactions are apparent in anion–water clusters, but not in cation–water clusters.

The non-additive dispersion energies for N molecules: a quantum electrodynamical theory

With the aid of the Heisenberg operators for the electromagnetic field in the neighbourhood of several molecules, the many-body interaction potentials are calculated by finding the energy of a test molecule in this field. In the first instance the calculation is made for the case where the intermolecular separations are very large. In this far-zone range, the energies depend on the molecules through their static polarizabilities. The three-body non-additive dispersion energy is calculated for an arbitrary configuration and the dependence on the geometry is investigated. The four-body non-additive potential is found for the regular tetrahedral configuration. The theory is extended to cover all separations outside regions of overlap. It is shown that the interaction energy in this case depends on the dynamic polarizabilities. The full Casimir-Polder potential follows directly from the general expression. The near-zone limit of the complete formula tends to the form obtained by using electrostatic couplings only: as with, for example, the Axilrod-Teller potential for N = 3. The work described here presents an alternative viewpoint to the conventional perturbation theory and lends further insight into the nature of intermolecular forces.

Use of a non-pair-additive intermolecular potential function to fit quantum-mechanical data on water molecule interactions

Permanent and induced multipole, repulsion, and dispersion terms are proposed as a model for the nonadditive potential of water molecules. 229 quantum-mechanical dimer energies of near Hartree–Fock accuracy which have been published by Popkie, Kistenmacher, and Clementi and by Kistenmacher, Lee, Popkie, and Clementi have been fit to an approximation to this model. The standard deviation 0.0019 of calculated dimerization energies for one simple form of the present model compares with a standard deviation 0.0023 given by an additive analytical fit developed by the above group. Nonadditive contributions calculated for the present model are compared with those given by the HF calculations of Hankins, Moskowitz, and Stillinger and by Kistenmacher, Lee, Popkie, and Clementi. The proposed model is compared with other models, and results to aid in the choice of multipole expansion orders in applications are given.

Extended time dependent Hartree theory of van der Waals interaction: Inclusion of electric quadrupoles

Expressions are derived for the van der Waals interaction free energy, to infinite order, which include dipole and quadrupole interactions. The treatment is an extension of the time-dependent Hartree approximation developed previously for dipolar interactions. The results are obtained via linear response theory. Just as in the dipolar case, the results are expressed in terms of the eigen frequencies of a normal mode matrix. In the present formulation, however, the normal modes are determined not only by electric dipolar coupling but also by coupling of electric quadrupoles with each other and with dipoles. The method is also useful in generating the perturbation terms of the free energy shift. It is found that the second order term, when applied to isotropic oscillators at zero degrees, reduces to the result derived earlier by Margenau. The nonadditive three-body potential, derived here, reduces to the Axilrod–Teller triple dipole potential in the absence of quadrupoles. Numerical results are given for the interaction between two and between three isotropic oscillators.

Linear Polarizability Contribution to the Nonadditive Three-Molecule Potential

In its diagrammatic form the perturbation expansion for the dispersion interaction can be rearranged to an expansion in the degree of hyperpolarizability considered. The total contribution of the linear dipole polarizabilities is given explicitly.

Pairwise Nonadditive Dispersion Potential for Asymmetric Molecules

The form of the pairwise nonadditive three-body dispersion potential for asymmetric molecules is derived. It is found that molecular asymmetry can have a large influence on interactions of this type. An example indicating the possible use of these results in understanding cohesive energies in crystals is given.

Shock Compression of Argon. II. Nonadditive Repulsive Potential

By means of the Monte Carlo method the shock Hugoniots of argon have been analyzed for an effective pair potential. This effective pair potential for the low-density Hugoniots closely agrees with the potential derived from molecular beams indicating the high accuracy of the pair-wise additivity approximation besides confirming the consistency of two complex experiments. For the high-density Hugoniot, however, the effective pair potential is considerably stiffer than the pair-wise potential at high compression. For liquid argon compressed twofold, the nonadditivity effect in the potential is about 30%. The theoretically derived pair-wise potential is only a few percent softer than this nonadditive potential. This theory might be improved further by allowing for distortions of the outer electron shell in a direction away from the contact region of the interacting pair of atoms. At high density the surrounding medium inhibits this distortion which leads to the observed stiffening and to the close agreement with the theory of spherical atoms.

Physical-Cluster Theory for a Reactive Gas

Physical-cluster expansions are given for the thermodynamic properties and equation of state of a reactive fluid. This provides a statistical-mechanical characterization of the fluid in terms of the stable atomic aggregates or molecules which actually are present rather than in terms of the more familiar, but less intuitive, Ursell—Mayer cluster integrals. Here, the Ursell—Mayer cluster development is applied only to the molecular interactions and not to the stronger ``chemical'' forces which are responsible for the stability of these aggregates. Detailed attention is given to a system composed exclusively of monomers and dimers. Formulas are derived for all of the coefficients needed to determine the first-order density corrections to the equation of state and composition of the fluid. Numerical results are reported for the special case of a square-well atom—atom interaction and a nonadditive three-body potential which is rigid and repulsive. Finally, we present a more general, quantum-mechanical version of the theory.