Polarizable models

In the first example of applications of the theory in this chapter, we made a point with respect to the polarizability of molecules and showed how the problem could have been handled by the RISM-SCF/MCSCF theory. However, the current level of our method has a serious limitation in this respect. The method can handle the polarizability of molecules in neat liquids or that of a single molecule in solution in a reasonable manner. But in order to be able to treat the polarizability of both solute and solvent molecules in solution, considerable generalization of the RISM side of the theory is required. When solvent molecules are situated within the influence of solute molecules, the solvent molecules are polarized differently depending on the distance from the solute molecules, and the solvent can no longer be neat. Therefore, the polarizable model developed for neat liquids is not valid. In such a case, solvent-solvent PCF should be treated under the solute... 

Raman intensities of the molecular vibrations as well as of their crystal components have been calculated by means of a bond polarizibility model based on two different intramolecular force fields ([87], the UBFF after Scott et al. [78] and the GVFF after Eysel [83]). Vibrational spectra have also been calculated using velocity autocorrelation functions in MD simulations with respect to the symmetry of intramolecular vibrations [82]. 

Interesting properties of the induced dipole polarizable model can be derived by simple mathematical manipulation. A particularly important one relates the minimum of the energy with converged values of the induced dipole. By combining Eqs. (9-9) and (9-10), the induction energy can be rewritten as... 

For a given a the force constant ko can be chosen in a way that the displacement d of the Drude particle remains much smaller than the interatomic distance. This guarantees that the resulting induced dipole jl, is almost equivalent to a point dipole. In the Drude polarizable model the only relevant parameter is the combination q /ko which defines the atomic polarizability, a. It is... 

Results of parameter optimization and MD simulations of small model compounds have been published, including alcohols [63], alkanes [63], aromatic [64] and heteroaromatic [209] compounds and liquid amides [65], Studies of ions in aqueous solution were also performed [61, 88] and results from an MD simulation on a DPPC lipid monolayer have been reported (Harder, MacKerell, Roux, submitted). Notable from the monolayer study was the reproduction of the dipole potential across the monolayer, a value that cannot be reproduced using non-polarizable models. This exciting, unforeseen observation points to the types of results that may be obtained from polarizable macromolecular force fields that are not accessible to the present additive models. 

Lamoureux G, MacKerell AD, Roux B (2003) A simple polarizable model of water based on classical Drude oscillators. J Chem Phys 119(10) 5185—5197... 

Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD (2006) A polarizable model of water for molecular dynamics simulations of biomolecules. Chem Phys Lett 418(l-3) 245-249... 

Yu HB, Hansson T, van Gunsteren WF (2003) Development of a simple, self-consistent polarizable model for liquid water. J Chem Phys 118(1) 221—234... 

Yu HB, Geerke DP, Liu HY, van Gunsteren WE (2006) Molecular dynamics simulations of liquid methanol and methanol-water mixtures with polarizable models. J Comput Chem 27(13) 1494-1504... 

Lu ZY, Zhang YK (2008) Interfacing ab initio quantum mechanical method with classical Drude os-illator polarizable model for molecular dynamics simulation of chemical reactions. J Chem Theory Comput 4(8) 1237-1248... 

Sprik M, Klein ML (1988) A polarizable model for water using distributed charge sites. J Chem Phys 89(12) 7556-7560... 

Chelli R, Barducci A, Bellucci L, Schettino V, Procacci P (2005) Behavior of polarizable models in presence of strong electric fields. I. Origin of nonlinear effects in water point-charge systems. J Chem Phys 123(19) 194109... 

Chialvo AA, Cummings PT (1996) Engineering a simple polarizable model for the molecular simulation of water applicable over wide ranges of state conditions. J Chem Phys 105(18) ... 

Mahoney MW, Jorgensen WL (2001) Rapid estimation of electronic degrees of freedom in Monte Carlo calculations for polarizable models of liquid water. J Chem Phys 114(21) 9337-9349... 

A multitude of semiempirical and semiclassical theories have been developed to calculate electron impact ionization cross sections of atoms and atomic ions, with relatively few for the more complicated case of molecular electron impact ionization cross sections. One of the earlier treatments of molecular targets was that of Jain and Khare.38 Two of the more successful recent approaches are the method proposed by Deutsch and Mark and coworkers12-14 and the binary-encounter Bethe method developed by Kim and Rudd.15,16 The observation of a strong correlation between the maximum in the ionization efficiency curve and the polarizability of the target resulted in the semiempirical polarizability model which depends only on the polarizability, ionization potential, and maximum electron impact ionization cross section of the target molecule.39,40 These and other methods will be considered in detail below. 

A critical comparison between experiment and theory is hindered by the range of experimental values reported in the literature for each molecule. This reflects the difficulty in the measurement of absolute ionization cross sections and justifies attempts to develop reliable semiempirical methods, such as the polarizability equation, for estimating the molecular ionization cross sections which have not been measured or for which only single values have been reported. The polarizability model predicts a linear relationship between the ionization cross section and the square root of the ratio of the volume polarizability to the ionization potential. Plots of this function against experimental values for ionization cross sections for atoms are shown in Figure 7 and for molecules in Figure 8. The equations determined... 

Interpretation of the v(CO) Raman intensities of a variety of carbonyls using a bond polarizability model... 

The Raman line shape is calculated with the bond polarizability model as described above. The unpolarized Raman line shape computed from the sum of the VV and VH line shapes is shown in Fig. 3. One again sees fair agreement between theory and experiment, with excellent peak position and evidence of a... 

A related, relatively unexplored topic is the importance of many-body forces in the simulations of interfacial systems. The development of water-polarizable models has reached some level of maturity, but one needs to explore how these models must be modified to take into account the interactions with the metal surface atoms and the polarizable nature of the metal itself... 

Polarized Raman spectra from the alkali fluorides LiF, NaF and CsF habe been observed with argon laser excitations by Evans and Fitchen 09). These spectra are of interest as an extreme test of lattice dynamics theories and polarizability models. 

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