Explicit Polarization Theory

Yingjie Wang, Michael J. M. Mazack, Donald G. Truhlar, and Jiali Gao  

University of Minnesota, Minneapolis, MN 55455, USA Theoretical Chemistry Institute, 

Jilin University, Changchun, Jilin Province 130023, P. R. China jiali jialigao.org 

Molecular mechanical force fields (MMFFs) were first proposed in the 1940s to study steric effects of organic molecules and were extended to model biomolecular systems by Lifson and coworkers in the 1960s.Since that time, significant progress has been made, and a number of force fields have been developed that can be used to provide excellent quantitative interpretation of experimental observations.  

Although the widely used force fields differ in their details (for example, some of them include coupling between internal coordinates), the functional forms used in MMFFs have remained essentially unchanged over the past half century and the functional form depicted in Eq. 2.1 captures the essence of a typical MMFF potential energy function  

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Isegawa, M., Gao, J., and Truhlar, D. G. (2011). Incorporation of charge transfer into the explicit polarization fragment method by grand canonical density functional theory, J. Chem. Phys. 135,084107. 

What is obviously needed is a generally accepted recipe for how atomic states should be dealt with in approximate density functional theory and, indeed, a few empirical rules have been established in the past. Most importantly, due to the many ways atomic energies can be obtained, one should always explicitly specify how the calculations were performed to ensure reproducibility. From a technical point of view (after considerable discussions in the past among physicists) there is now a general consensus that open-shell atomic calculations should employ spin polarized densities, i. e. densities where not necessarily... 

In spectroscopy we may distinguish two types of process, adiabatic and vertical. Adiabatic excitation energies are by definition thermodynamic ones, and they are usually further defined to refer to at 0° K. In practice, at least for electronic spectroscopy, one is more likely to observe vertical processes, because of the Franck-Condon principle. The simplest principle for understandings solvation effects on vertical electronic transitions is the two-response-time model in which the solvent is assumed to have a fast response time associated with electronic polarization and a slow response time associated with translational, librational, and vibrational motions of the nuclei.92 One assumes that electronic excitation is slow compared with electronic response but fast compared with nuclear response. The latter assumption is quite reasonable, but the former is questionable since the time scale of electronic excitation is quite comparable to solvent electronic polarization (consider, e.g., the excitation of a 4.5 eV n — n carbonyl transition in a solvent whose frequency response is centered at 10 eV the corresponding time scales are 10 15 s and 2 x 10 15 s respectively). A theory that takes account of the similarity of these time scales would be very difficult, involving explicit electron correlation between the solute and the macroscopic solvent. One can, however, treat the limit where the solvent electronic response is fast compared to solute electronic transitions this is called the direct reaction field (DRF). 49,93 The accurate answer must lie somewhere between the SCRF and DRF limits 94 nevertheless one can obtain very useful results with a two-time-scale version of the more manageable SCRF limit, as illustrated by a very successful recent treatment... 

The existence of the nonlinear polarization field does not ensure the generation of significant signal fields. With the exception of phenomena based on an intensity-dependent refractive index, the generation of the nonlinearly produced signal waves at frequency cos can be treated in the slowly varying amplitude approximation with well-known guided wave coupled mode theory (1). As already explicitly assumed in Equation 1, the amplitudes of the waves are allowed to vary slowly with... 

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