Perturbation theory long-range forces

Dalgarno A, Lewis JT (1955) The exact calculation of long-range forces between atoms by perturbation theory. Proc Roy Soc (London) A 233 70-74... 

There are no electrostatic or induction forces between spherical molecules, such as argon, and yet there is clearly a long-range attractive force that causes the liquefaction of argon at low temperatures. This is the dispersion energy, the universal long-range force, which appears at second-order perturbation theory as ... 

F. Perturbation Theories—Long Range Forces as the Perturbation... 

Intermolecular Interactions by Perturbation Theory Molecular Dynamics and Hybrid Monte Carlo in Systems with Multiple Time Scales and Long-range Forces Reference System Propagator Algorithms Molecular Dynamics Simulations of Nucleic Acids Molecular Dynamics Studies of Lipid Bilayers Molecular Dynamics Techniques and Applications to Proteins Monte Carlo Simulations for Liquid Monte Carlo Simulations for Polymers. 

Interatomic Force Constants (IFCs) are the proportionality coefficients between the displacements of atoms from their equilibrium positions and the forces they induce on other atoms (or themselves). Their knowledge allows to build vibrational eigenfrequencies and eigenvectors of solids. This paper describes IFCs for different solids (SiC>2-quartz, SiC>2-stishovite, BaTiC>3, Si) obtained within the Local-Density Approximation to Density-Functional Theory. An efficient variation-perturbation approach has been used to extract the linear response of wavefunctions and density to atomic displacements. In mixed ionic-covalent solids, like SiC>2 or BaTiC>3, the careful treatment of the long-range IFCs is mandatory for a correct description of the eigenfrequencies. 

R..J. Drachman High Rydberg States of Two-Electron Atoms in Perturbation Theory , in Long-Range Casimir Forces Theory and Recent Experiments on Atomic Systems, ed. by F.S. Levin and D. Micha (Plenum Press, New York, 1993) pp. 219-272, and earlier references therein... 

The relation between the supermolecule coupled cluster approach and the perturbation theory of intermolecular forces in even less obvious than the case of the Mpller-Plesset theory, and no formal analysis has been reported in the literature thus far. Rode et al.68 analyzed the long-range behavior of the CCSD(T) method65, and showed that this method, although very popular and in principle accurate, may lead to wrong results for systems with the electrostatic term strongly depending on the electronic correlation, e.g. the CO dimer. 

Further extension of the internuclear separation reduces the diatomic interaction to the problem of long-range and van der Waals forces, where we can neglect the overlap of AOs on different atoms (i.e., there is no overlap density) and apply the perturbation theory with respect to R l (see, for example, Hirschfelder et al., 1964a). 

In the preceding sections, we have discussed nonspecific adsorption, where long-range electrostatic forces perturb the distribution of ions near the electrode surface, and specific adsorption, where a strong interaction between the adsorbate and the electrode material causes the formation of a layer (partial or complete) on the electrode surface. The difference between nonspecific and specific adsorption is analogous to the difference between the presence of an ion in the ionic atmosphere of another, oppositely charged, ion in solution (e.g., as modeled by the Debye-Huckel theory) and the formation of a bond between the two solution species (as in a complexation reaction). 

The properties of a fluid are determined largely by short-range repulsive forces. The long-range attractive forces can be considered to be perturbations. Using these concepts, a perturbation theory of fluids is developed. In addition, the relationship of empirical equations of state to the perturbation theory is examined. The major weakness of most empirical equations is the use of the van der Waals free-volume term, (V-Nb) 1, to represent the contributions of the repulsive forces. Replacement of this term by more satisfactory expressions results in better agreement with experiment. 

A second theoretical approach to understanding E- V transfer is based on the notion that long-range attractive forces might couple the electronic and vibrational degrees of freedom. Ewing has developed a theory for such coupling that is similar to the theory for V- V transfer proposed earlier by Sharma and Brau. First order perturbation theoiy is used in this approach to calculate the probability for the E->V transition ... 

Equation (2.109) has the standard form of the dispersion force. Obviously, Ec is able to reproduce the correct long-range behavior proportional to 1/i . However, the exact result for the coefficient Cq involves the full atomic polarizabilities, while the present DFT-variant of Cq is determined by the KS polarizabilities (as a consequence of second order perturbation theory). So, the next question is how close the KS coefficients come to the exact CqI First calculations [78] show that, for light atoms, (2.109) yields reasonably accurate coefficients They underestimate the full Ce by 10-20%. On the other hand, for heavier atoms higher order correlation becomes important, and (2.109) is substantially off. 

Angyan> J. G.> Gerber, I. C.> Savin, A., Toulouse, J. (2005). van der Waals forces in density functional theory Perturbational long-range electron-interaction corrections. Physical Review A, 72, 012510. 

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