Bruno Linder

Effect of Dispersion Interaction on Nuclear Magnetic Resonance Shifts

The continuum model treatment of long‐range intermolecular forces is applied to the effect of dispersion interaction on NMR shifts. The theory is applied to infinitely dilute solutions of nonpolar molecules in nonelectrolytes and to pure gaseous substances. Calculated shifts are in semiquantitative agreement with the experimental values; the general trends are accurately predicted. Polar solvents show no unusual behavior. Several empirical relations, previously proposed, are derived and discussed.

Unified Treatment of van der Waals Forces between Two Molecules of Arbitrary Sizes and Electron Delocalizations

Publisher Summary This chapter presents a unified treatment for the interaction between two non-overlapping molecular systems of arbitrary sizes and electron delocalizations. The theory is formulated on the basis of a generalization of the reaction-field technique developed earlier and results are expressed in terms of spatially dependent susceptibilities. The present approach is an infinite-order perturbative method which, in the absence of resonance interaction, yields an expression for the interaction (free) energy in terms of the properties of the noninteracting system. A rigorous expression is derived for the second-order free energy at finite temperatures and an approximate closed-form expression is obtained for the perturbation series by invoking the decorrelation approximation which neglects correlations between virtual excitations within each molecule. Special forms are derived for the dipolar approximation and the results are found to agree with previously derived results obtained by other methods. The connection between the reaction-field approach and those formulations based on collective behavior is discussed.

Continuum‐Model Treatment of Long‐Range Intermolecular Forces. I. Pure Substances

A theory is presented whereby the long‐range intermolecular forces, including the London dispersion forces, of pure nonelectrolytes may be calculated from optical and dielectric data. The method is based on the continuum‐model approach, where one molecule is treated explicitly while the others are replaced by a medium of uniform dielectric. The classical and quantum‐mechanical oscillators are used as working models and expressions are derived for computing the cohesive energy appropriate for both types of oscillators. The potential energy based on the quantum‐mechanical oscillator is calculated for a number of liquids and is shown to be in fair agreement with the experimental energy of vaporization.

Generalized Form for Dispersion Interaction

A general treatment of dispersion interaction, based on the continuum model, is presented. Expressions are derived which relate the dispersion free energy of a molecule to the complex dielectric constant. Approximate relations are given for calculating the free energy from the static dielectric constant and mean absorption frequencies. The theory applies to homogeneous dielectrics, irrespective of composition or phase.

Polarizability and Second Dielectric Virial Coefficient of Interacting He Atoms

The polarizability α of the pair of interacting He atoms has been calculated by Hartree–Fock perturbation theory, both coupled and uncoupled. A basis of 16 Gaussians was used, eight centered on each atom. Good convergence was obtained in the region of overlap between one and six atomic units internuclear separation, R. Values of α for large separations were obtained by extrapolation using an R−6 dependence as predicted by previous long‐range calculations. The effect of the interatomic interaction on the second dielectric virial coefficient was then calculated using the radial distribution function based on empirical Lennard‐Jones parameters. The results show that the effect of overlap and exchange do not sufficiently counteract the positive deviation caused by the van der Waals interaction to produce the substantial negative value as measured by Orcutt and Cole.

Many‐Body Aspects of Physical Adsorption

A theory is presented for determining the effect of many‐body interactions on the dispersion energy of a pair of gas molecules adsorbed on a crystalline solid. The formalism is based on a reaction field technique and includes potential nonadditivity to fourth order. Model calculations are carried out for the change in the interaction energy between a pair of Ne atoms, a pair of Ar atoms, and a pair of Kr atoms adsorbed on solid Xe by summing over the Xe lattice. The results are analyzed and compared with calculations based on a model which treats the solid as a continuous dielectric.

van der Waals induced dipoles

Expressions are derived for calculating the induced dipole moment of an arbitrary molecule A interacting with an arbitrary system B through first‐ and second‐order Coulomb interaction. The theory is formulated in terms of linear and quadratic charge‐density susceptibilities and takes account of charge penetration but not exchange between the systems. The theory is specialized to the interaction of two nonoverlapping molecules and to a molecule interacting with a nonferroelectric solid, metallic, or crystalline. In the case of two interacting molecules, the induced moment is developed in inverse powers of R, the distance between the centers of the molecules, up to and including R−7; the coefficients of the series are given in terms of the total charges, permanent moments, polarizabilities, and hyperpolarizabilities. In the case of the solid, the results are given in terms of the molecule–solid distance z0, the dielectric function of the solid, and the permanent moments, polarizabilities, and hyperpolarizab...

Van der Waals Interaction Potential between Polar Molecules. Pair Potential and (Nonadditive) Triple Potential

A unified treatment, based on the method of the fluctuating reaction field, is presented for the van der Waals potential between polar molecules. Only dipolar interactions exclusive of retardation effects are considered. The general formulation is given in terms of frequency‐dependent molecular susceptibilities and holds for any finite temperature. It is shown that, under certain restrictive conditions, the generalized potential can be decomposed into three parts representing the three constituents of the van der Waals attraction: dispersion, orientation, and induction. The general formalism is applied to the attraction between two bodies and between three bodies. The dispersive, orientative, and inductive parts of the pair potential are compared with the corresponding potentials of London, Keesom, and Falkenhagen and the (nonadditive) triple dispersive potential with the potential of Axilrod and Teller. Explicit expressions are also given for the (nonadditive) triple orientation and induction potentials. The significance of the results is discussed.

Interaction Between Two Rotating Dipolar Systems and a Generalization to the Rotational Double‐Temperature Potential

A field‐theoretic approach is used to derive general expressions for the adiabatic interaction between two rotating dipolar systems. The treatment applies to systems having the same temperature as well as to systems having different temperatures. The results, which are expressed in terms of the dipole moments, moments of inertia, and temperatures of the two systems are valid, in second‐order approximation, over the whole range of temperatures including the region where quantum effects are important. The classical limit reduces to the Keesom potential for equal temperatures. When the temperatures are different the classical potential can take on positive (repulsive) values as well as negative (attractive) values, depending on the temperature difference and ratio of temperature to moment of inertia of the two systems for large temperature differences the potential is always repulsive. The general equations are analyzed and the quantum‐statistical implication underlying the theory is discussed.

Many—Body Aspects of Intermolecular Forces

The many‐body aspects of intermolecular forces are examined for the model based on a fluctuating reaction field. This is accomplished by expanding the reaction field in a series involving optical and translational parameters, and an expression is obtained for the cohesive free energy in terms of frequency‐dependent polarizabilities and dipole‐coupling tensors. When applied to a system of fixed translational parameters a series expansion is obtained for the configurational total potential energy, the leading term of which arises from pair interactions, the next higher term from triple interactions, etc. It is shown that the pair and triple potentials reduce to forms identical with the ones obtained by ordinary quantum‐mechanical second‐ and third‐order perturbation theory. The significance of the results is discussed.