Pair polarizabilities computations

The influence of Van der Waals interactions on the polarizability of interacting molecules manifests itself in deviations from the Clausius-Mosotti equation in the Kerr effect and in collision induced li t scattering Ahhougji measurements of these effects are all performed on bulk systems in thermodynamical equilibrium and not on Van der Waals molecules per se, we will nevertheless say a few words about pair polarizabilities, because, just as in the case of the collision induced IR absorption, much can be learned about Van der Waals interactions from the comparison of experimental and computational results. 

Previous Reviews. A general survey of the effects of molecular interactions on the optical properties of matter was recently given by Buckingham [435]. The work concerning ab initio and approximate computations of pair polarizabilities has recently been reviewed by Hunt [80] a careful comparison of the data available from various measurements reveals a high degree of consistency with the fundamental theory. Hunt has also reviewed the utility of the DID model and its limitations [79]. The results of measurements of the polarizability invariants of rare-gas pairs have been reviewed by one of the authors [271]. Substantial discussions of induced polarizabilities can be found in a number of review articles on CILS and dielectric properties [11,27, 143, 274, 343, 376]. 

Computations. Efforts to compute pair polarizabilities from first principles, using perturbation techniques or modern quantum chemical methods, have been known for many years and are reviewed by Hunt [80] in the desirable detail. Amos s review of ab initio methods applied to the computation of molecular properties considers supermolecular properties, too [2]. 

Theory. If the invariants of the pair polarizability are known, along with a refined model of the intermolecular interaction potential, the lineshapes of binary spectra can be computed quite rigorously [227, 231, 271], Lineshape computations based on exact or approximate classical trajectories are known [196, 264, 276, 316, 337]. Such computations generate spectral functions that are symmetric, g — co) = g((o). For massive pairs at high enough temperatures, such classical profiles are often sufficient at frequency shifts much smaller than the average thermal energy, ha> < kT, albeit special precaution is necessary when the system forms van der Waals dimers [302]. 

It would be relatively easy to extend here our computer symbolic calculations to the hyperpolarizability part of the pair polarizability [see Eqs. (5) and (7)]. However, from all our numerical computations done for N2, C02, and CF4, it results that nonlinear part of the pair polarizability has a weak influence on the resulting spectrum (for details, see Refs. 8, 13, and 15-18). Bearing in mind these results in this review, we restrict our discussion to multipolar light scattering mechanisms. Formula (22) allows us to write the following simple symbolic program in Mathematica calculating the analytical form of the autocorrelation function (16) for a selected dipole-arbitrary order multipole induction operator ... 

Harder E, Anisimov VM, Vorobyov IV, Lopes PEM, Noskov SY, MacKerell AD, Roux B (2006) Atomic level anisotropy in the electrostatic modeling of lone pairs for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 2(6) 1587-1597... 

We have approached these multi-faceted systems by looking in particular at two local molecular properties the electrostatic potential, P(r) and Vs(r). and the local ionization energy, /s(r). In terms of these, we have addressed hydrogen bonding, lone pair-lone pair repulsion, conformer and isomer stability, acidity/basicity and local polarizability. We have sought to show how theoretical and computational analyses can complement experimental studies in characterizing and predicting molecular behavior. ... 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

It is interesting to compare the extent of proton transfer determined for complexes in inert matrices with those observed in the gas phase and predicted by ab initio computations. Consistent with the latter, H N-HF is found to be a neutral pair in Ar matrix , but the complex is somewhat more polar than it is in the gas phase. In fact, the frequency shift of the HF stretch rises quite noticeably as the polarizability of the matrix increases from Ar to N2. One can hence expect the matrix results to typically indicate greater proton transfer character than observed in the gas phase. Nonetheless, HF does not appear to form an ion pair with even stronger bases such as trimethylamine in Ar ", nor with In fact, HF... 

In general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

Computational quantum mechanics continues to be a rapidly developing field, and its range of application, and especially the size of the molecules that can be studied, progresses with improvements in computer hardware. At present, ideal gas properties can be computed quite well, even for moderately sized molecules. Complete two-body force fields can also be developed from quantum mechanics, although generally only for small molecules, and this requires the study of pairs of molecules in a large number of separations and orientations. Once developed, such a force field can be used to compute the second virial coefficient, which can be used as a test of its accuracy, and in simulation to compute phase behavior, perhaps with corrections for multibody effects. However, this requires major computational effort and expert advice. At present, a much easier, more approximate method of obtaining condensed phase thermodynamic properties from quantum mechanics is by the use of polarizable continuum models based on COSMO calculations. 

Computations of minimum-energy configurations for some off-centre systems were first carried out on the basis of polarizable rigid-ion models, mainly devoted to KChLi" " [95,167-169]. Van Winsum et al. [170] computed potential wells using a polarizable point-ion model and a simple shell model. Catlow et al. used a shell model with newly derived interionic potentials [171-174]. Hess used a deformation-dipole model with single-ion parameters [175]. At the best of our knowledge, only very limited ab initio calculations (mainly Hartree-Fock or pair potential) have been performed on these systems [176,177]. 

Atom-Atom Interactions. - The methods applied, usually to interactions in the inert gases, are a natural extension of diatomic molecule calculations. From the interaction potentials observable quantities, especially the virial coefficients can be calculated. Maroulis et al.31 have applied the ab initio finite field method to calculate the interaction polarizability of two xenon atoms. A sequence of new basis sets for Xe, especially designed for interaction studies have been employed. It has been verified that values obtained from a standard DFT method are qualitatively correct in describing the interaction polarizability curves. Haskopoulos et al.32 have applied similar methods to calculate the interaction polarizability of the Kr-Xe pair. The second virial coefficients of neon gas have been computed by Hattig et al.,33 using an accurate CCSD(T) potential for the Ne-Ne van der Waals potential and interaction-induced electric dipole polarizabilities and hyperpolarizabilities also obtained by CCSD calculations. The refractivity, electric-field induced SHG coefficients and the virial coefficients were evaluated. The authors claim that the results are expected to be more reliable than current experimental data. 

The above conclusions have resulted from an analysis of computer simulation data carried out on pure liquids and supercritical fluids, and on liquids in equilibrium with their vapor. One immediate question one should ask concerns thus a more general validity of the reached conclusions. Particularly important problem is to what extent they may remain valid for mixtures. Due to polarizability and other possible effects brought about by electrostatic interactions between unlike species, the pair interaction, and hence the local and, particularly, orientational arrangement may be changed considerably. With respect to a wide variety of mixtures this problem will require rather an extensive investigation. The most difficult mixtures will evidently be solutions of charged objects as e.g. electrolytes. 

Computational studies investigate reaction mechanisms and pathways by constructing potential energy profiles. This involves exploring reaction thermodynamics and kinetics, by examining reactants and products as well as the transition states geometries and activation energy barriers. Like those seen in structure prediction, most current studies implement effective core potentials and density functional theory to perform calculations.However, ECPs can be paired with MP2 to account for electron correlation thus far, this approach has only been used for smaller chemical systems. " Eurthermore, solvation methods such as the polarizable continuum model can be employed to examine... 

The combination of a chosen pair potential and the polarization term provides a better interaction energy model, and one that incorporates multi-body/nonadditive effects that generally lower the total energy of the system (that is, it makes the energy more attractive). However, adding the polarizable contribution comes at the expense of a substantial increase in computation time. Simulation times increase by a factor of 3 to 10 times using... 

Figure 12 shows polymer concentration cP dependence of the anisotropy of the electrical polarizability Aa of a 64/128 base-pair DNA fragment. Aa increases on dilution of polymer concentration. Experimentally, Aa is determined via measurement of the Kerr constant of the polyelectrolyte solutions, and in the case of rodlike polyelectrolytes both quantities are proportional to each other. It has been observed that the Kerr constant of polyelectrolytes in salt-free aqueous solutions increases on dilution [46,47], This behavior of the Kerr constant is one of the characteristic properties of polyelectrolytes in salt-free aqueous solutions whose reproduction we have succeeded in by computer simulation. The figure also indicates that Aa is... 

---