High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

In this paper we investigate a variationally stable procedure for multipolar dynamic polarizabilities calculation as well as the two- and three-body van der Waals coefficients of the hydrogen atom. This approach provides precise, fast convergent values for real and imaginary frequency-dependent 2 ^L -pole dynamic polarizabilities. Highly accurate two- and three-body van der Waals dispersion coefficients are calculated from dynamic polarizabilities at imaginary photon frequencies. The present approach is also precise for higher interaction orders. The results are compared with previous calculations found in the literature.     

Van der Waals attraction between cylinders,rods or fibers

In a first step, we calculate the van der Waals energy between two cylinders by pairwise integration of unscreenedr ⁻⁶ interactions between any two molecules. It turns out proportional tod ^−3/2 at small separations and proportional tod ⁻⁵ at large separationsd of the cylinders. In a second step, we use an integration method for multiplet interactions, which relates the latter to screening and represents the van der Waals energy by macroscopic reaction fields. We expand these reaction fields in terms of modified Bessel functions. The van der Waals energy evolves from a sum over the numberl of field reflections, from a frequency integral over the dielectric constants involved, and from a wave number integral over the radii and the separation of the cylinders. The lowest order term verifies the results found by integration of pair interactions, yet replaces the unscreened polarizabilities of the atoms by the screened dielectric constants of the media. The higher order reflection termsl≧2 likewise turn out to be proportional tod ^−3/2 at small separationsd, but decrease in weight more rapidly than 1/l ³. Their contribution at large separation is proportional tod ^−(4l+1). From a comparison of our results with those obtained for spheres and half-spaces, we conclude that retardation entails ad ^−5/2 and ad ⁻⁶ law at small and large separations, respectively. This suggestion is confirmed by preliminary calculations based on the Helmholtz equation.     

Estimate of P-and P,T-odd effects in diatomic van der Waals molecules

The magnitudes of the possible P-and P, T-odd effects in diatomic van der Waals molecules are estimated. The estimates fall between the values corresponding to atoms and molecules/radicals. Arguments are presented showing that the loss of approximately two orders of magnitude in the strength of the effect for van der Waals molecules with an unpaired electron, such as CsXe, as compared with molecules/radicals can be partially compensated by a number of experimental advantages of working with van der Waals molecules. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 659–663 (25 November 1996)     

Improved van der Waals potentials for alkali halide crystals

Improved values of the van der Waals energy coefficients are presented for 16 alkali halides using more recent electronic polarizabilities and, for each ion, three alternative values of the effective number of electrons. The statistical method of calculating interionic potentials is used to obtain the correlation energy at small interionic separations and the values are scaled to fit the van der Waals energy at large separation. The resultant correlation energy as a function of interionic separation is fitted to both a cubic polynomial and a cr^?6 analytic form. The extent to which the van der Waals interactions are quenched by ionic overlap is derived and contrasted with Catlow et al. work on this effect.     

On the damping of multiquantum coherences with an increase in their order. An asymptotic behavior

Expressions describing the asymptotic (as a function of the order n) damping of multispin multiquantum coherences in systems with an infinite-range interaction (van der Waals model) have been obtained. The results coincide with the results of the numerical experiment for nanocavities.     

Static van der Waals interactions in electrolytes

Using a field-theoretic formalism, we calculate the static contribution to the van der Waals interaction between two dielectric semi-infinite half-spaces in the presence of mobile salt ions. The ions can be located in the slab, in one, or in both half-spaces. We include an excess polarizability of the salt ions, i.e., each (spherical) ion has a dielectric constant which in general is different from the surrounding medium. This leads to a modification of the effective dielectric constant of the medium hosting the ions. This shift can be large for high salt concentrations and therefore influences the Hamaker constant decisively. Salt ions in the slab screen the static van der Waals interaction, as was shown by Davies and Ninham. The salt-modified van der Waals interaction also contains salt-confinement and salt-correlation effects. This is clearly demonstrated by the fact that the interaction is non-zero even in the case when the dielectric constant is homogeneous throughout the system, in which case salt correlations are solely responsible for the interaction. If the salt ions are in one or both of the two half-spaces (and no ions in the slab), the van der Waals interaction is not screened but the effective Hamaker constant approaches a universal value for large slab thickness which is different from the value in the absence of salt ions and which is independent of the salt concentration and of the effective electrolyte dielectric constant. If both half-spaces contain salt, the asymptotic value of the Hamaker constant for large separation between the half-spaces is the one obtained for the interaction between two metallic half-spaces through an arbitrary dielectric medium, which is given by A≃ - 1.20. As is explicitly demonstrated, ion enrichment or depletion at the interfaces due to image-charge effects is already included on the one-loop level and therefore does not lead to a change of the screened van der Waals interaction as given by Davies and Ninham. For positive and negative ions with different valencies or different excess polarizabilities, we obtain different adsorbed surface excesses of positive and negative ions, leading to a non-vanishing surface potential, which is computed explicitly. All of these results are obtained on the linear one-loop level. For a special case we extend the calculation of the dispersion interaction to the two-loop level. We find the corrections to the one-loop results to be quite large for high salt concentrations or multivalent ions. Received 17 February 2000     

Influence of complexation and solid environment on the vibrational coherence of DCl

The vibrational dynamics of DCl molecules embedded in different cryogenic matrices is studied by time resolved infrared Degenerate Four Wave Mixing experiments using the infrared free electron laser CLIO. The coherence behaviour of the D-Cl stretch in pure argon as well as in mixed argon/nitrogen van der Waals solids is investigated. Different interactions between the excited molecules and their environment are probed: the van der Waals interaction between the trapped molecules and the solid lattice and the interaction binding complexes trapped in the matrix (either the vdW interaction between DCl and nitrogen or weak H bonds in (DCl)_n clusters). The dependence of the dephasing time on the solid and on specific interactions is clearly observed.     

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C ₆, C ₈, and C ₁₀ of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.     

Proton magnetic resonance of ethane in the liquid and gaseous states

The proton chemical shift of ethane is reported, covering for gaseous ethane the density range 0 to 0·5 g cm^-3 and the temperature range 0 to 110°C, and for liquid ethane from the critical temperature down to -55°C. The results are discussed in terms of the van der Waals interaction term σ _w , using a virial expansion including both binary and ternary collisions. A parallel is drawn between the medium shifts and the equation of state for non-ideal gases. Some comments are made regarding (i) the uniqueness of the parameter B for protons in a C-H bond in non-polar molecules, (ii) the neighbour anisotropy contribution σ _a in molecules such as ethane and ethylene, and (iii) the van der Waals gas-to-liquid medium shift, and its temperature dependence, in larger molecules.     

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.     

The macroscopic theory of van der Waals attraction

The van der Waals energy between two films is calculated from the average quantum energy of the electromagnetic radiation field. All branch points and different Riemann surfaces appearing in earlier treatments vanish by applying finite boundary conditions. The final frequency integration runs over the full imaginary axis.     

Acceleration of canonical molecular dynamics simulations using macroscopic expansion of the fast multipole method combined with the multiple timestep integrator algorithm

A canonical molecular dynamics (MD) simulation was accelerated by using an efficient implementation of the multiple timestep integrator algorithm combined with the periodic fast multiple method (MEFMM) for both Coulombic and van der Waals interactions. Although a significant reduction in computational cost has been obtained previously by using the integrated method, in which the MEFMM was used only to calculate Coulombic interactions (Kawata, M., and Mikami, M., 2000, 98, J. Comput. Chem., in press), the extension of this method to include van der Waals interactions yielded further acceleration of the overall MD calculation by a factor of about two. Compared with conventional methods, such as the velocity-Verlet algorithm combined with the Ewald method (timestep of 0.25 fs), the speedup by using the extended integrated method amounted to a factor of 500 for a 100 ps simulation. Therefore, the extended method reduces substantially the computational effort of large scale MD simulations.     

Analysis of crystal binding of ammonium halides

Electronic polarizabilities and sizes of ions in NH₄Cl, NH₄Br and NH₄I crystals are calculated using Ruffa's theory and an empirical relation between polarizability and radius. Using the electronic polarizabilities we have estimated the van der Waals dipole-dipole and dipole-quadrupole potentials following the Slater-Kirkwood varitional method. These potentials and ionic radii are then used to calculate the cohesive energies of ammonium halides. The results are discussed and compared with those of other investigators.     

Interaction of water‐soluble triphenylphosphines with β‐cyclodextrin: a quantum chemistry study

The interaction of β‐cyclodextrin (β‐CD) with meta‐trisulfonated triphenylphosphine derivatives bearing one or two methyl (or methoxy) groups on the aromatic rings has been investigated by PM3 calculations. The results show that phosphine molecules interact with β‐CD having either an unsubstituted sulfophenyl group or a substituted sulfophenyl group at the para and/or meta‐position. The presence of one methyl or methoxy group in the ortho‐position on each aromatic ring prevents the formation of an inclusion complex between meta‐trisulfonated triphenylphosphine derivatives and β‐CD. The deeply included phosphines in the β‐CD cavity show significant van der Waals interactions with β‐CD. These interactions are at the origin of the high association constants between these molecules and β‐CD. Phosphines exhibiting small association constants interact with β‐CD by forming H‐bonds and weak (or null) van der Waals interactions. Copyright © 2011 John Wiley & Sons, Ltd.     

Rydberg states in the condensed phase studied by fluorescence depletion spectroscopy

Higher Rydberg states of NO trapped in rare gas matrices have been studied by inducing Rydberg-Rydberg transitions from the lowest Rydberg state and detecting its fluorescence depletion. This technique unravels Rydberg states, which cannot be accessed by ground state absorption. However, no clear cut Rydberg series show up. The data show a compression of the n-(n + 1) splittings between Rydberg states, as well as of the splittings. The results are rationalised in terms of the quantum defect model and the lack of extended Rydberg series is due to the compression of high-n Rydberg states in a tiny energy region below the ionisation potential. Finally, fluorescence depletion data of NO trapped in amorphous sites (the so-called red sites) of solid Ar can be interpreted in terms of the gas phase NO-Ar van der Waals data. A general discussion on the fate of Rydberg states in van der Waals complexes, in liquids, and in solids is presented in an attempt to relate the data in these different media. Received 28 July 1999 and Received in final form 8 November 1999     

Character tables of n-dimensional hyperoctahedral groups and their applications*

We have shown that powerful matrix-type-based multinomial generators together with combinatorial techniques can be applied to derive the conjugacy classes, irreducible representations and the character tables of n-dimensional hyperoctahedral or hypercube groups of order n! × 2ⁿ, which are generalisations of non-rigid molecular theory formulated by Longuet-Higgins. The hyperoctahedral groups appear in the symmetry groups of non-rigid molecules, non-rigid water clusters, and other weakly bound van der Waals complexes that exhibit rapid tunnelling motion among various low-lying surmountable potential energy minima. These groups also have applications in quantum chromodynamics in the classification of states of quarks. The associated combinatorics has applications in enumerations, nuclear spin statistics and NMR spectroscopy. Finally, the groups enhance understanding of chirality in biosystems, that is, the functionality of intrinsically disordered proteins. We have derived the character tables of hyperoctahedral groups of sixth dimension, and techniques have been outlined to generalise for higher dimensions in the form of matrix generators.     

Hydrogenic Rydberg states of molecular van der Waals complexes: resolved Rydberg spectroscopy of DABCO-N2

The complementary threshold ionization techniques of MATI and ZEKE spectroscopy have been used to reveal well-resolved, long-lived (>10 micros) hydrogenic Rydberg series (50< or =n< or =98) in a van der Waals complex formed between a polyatomic molecule and a diatomic molecule for the first time. The series are observed within 50 cm(-1) of the adiabatic ionization threshold as well as two core-excited thresholds corresponding to excitation of up to two quanta in the van der Waals vibrational mode.     

Nuclear magnetic shielding and diamagnetic susceptibility of interacting hydrogen atoms

A quantum-mechanical study is made of the changes of the nuclear magnetic screening constant σ and the diamagnetic susceptibility X of two interacting hydrogen atoms due to van der Waals and overlap interatomic forces (effects of electron spin being neglected). At large distances the calculations show that van der Waals forces decrease the nuclear screening but increase the diamagnetic susceptibility (in magnitude). As the internuclear distance is reduced the first effect of overlap forces is to increase the screening in the repulsive (electronic triplet) state but this is followed by a further reduction. Attractive overlap forces (as in the ground state of H₂) ultimately lead to an increase in screening.     

Many-body theory for multipole polarizabilities and dispersion forces in helium-helium interactions

Linked cluster many-body perturbation theory has been developed for the calculation of the dynamic quadrupole polarizabilities of the helium atom in its ground state. The polarizabilities have been used to calculate the London dispersion force constants for He-He interactions. The results for the polarizabilities and the van der Waals constants compare very well with other standard values.     

Surface tension compressibility relation

The generalized van der Waals result for the surface tension of a simple liquid-vapour interface is shown to follow from the exact statistical mechanical expression with the approximation c(r, z ₁, z ₂) = c(r, n(z¯)). Using the statistical mechanical equation for the derivative of the density profile we derive the relation between the surface tension and the isothermal compressibility, to lowest order in T-T_c .