Polarizability models schemes

Almost all the formalism and the approximation schemes of Sections II and III have a natural extension to systems of polarizable dipolar particles, but the precise details of the extension depend on the way polarizability is introduced into the Hamiltonian. We refer to the two quite distinct Hamiltonian models that have been most thoroughly developed in this context as the constant-polarizability model and the fluctuating-polarizability model. The dielectric behavior of the former was first systematically investigated from a statistical mechanical viewpoint by Kirkwood and by Yvon, who considered the model almost exclusively in the absence of permanent dipole moments. (Kirkwood S subsequently pioneered an exact formulation of the statistical mechanics of polar molecules, but largely as a separate enterprise that did not attempt to treat the polarizability exactly.) The general case of polar-polarizable particles remained only very partially developed ... 

Polarizable potential schemes are evolving rapidly, as are the techniques involved in using them in calculations. Polarizable potentials allow self-consistent determinations of the induced moments. The series of models examined next are rather similar in their structure, but they vary widely in their ability to provide an adequate representation of liquid water. 

The dipole polarizability model is not the only way in which polarization effects can be included in an MM force field. An alternative, although less widely used, scheme is based upon the concept of electronegativity equalization [38, 39]. In the most common version of the method it is supposed that the electrostatic energy of a MM system, Ee ec, can be written as ... 

The induced dipole formulation is an example of the so-called polarizable embedding but it is not the only possible choice. There are in fact various alternatives schemes to simulate the polarization of the MM subsystem, such as the fluctuating charges [24, 25], the classical Drude oscillators [26], or the Electronic Response of the Surroundings (ESR) [27] which mixes a non-polarizable MM scheme with a polarizable continuum model characterized by a dielectric constant extrapolated at infinite frequency. 

We have presented a necessarily shortened and simplified overview of hybrid QM/MM methods by focusing on the aspects which are more specific for their applications to photoinduced processes in biosystems. We have tried to show that the QM/MM strategy can be effectively used to describe both specific and bulk effects of the environment as well as to account for dynamic effects which are required to simulate reactive processes involving different electronic states. We have also shown that some important problems are still open and further developments of the model are necessary in order to obtain accurate simulations of photoinduced processes. In the near future, we may expect improvements in the efiiciency and applicability of QM/MM dynamics as well an expansion in the applicability of polarizable MM schemes. 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

Polarizability Effects. The next model demonstrates that an additivity scheme can be combined with other forms of mathematical relations to extract the fundamental parameters of a model from primary information. And furthermore, it shows than an additivity scheme useful for the estimation of a global molecular proparty can be modified to obtain a local, site specific property. 

In contrast, EET has been historically modelled in terms of two main schemes the Forster transfer [15], a resonant dipole-dipole interaction, and the Dexter transfer [16], based on wavefunction overlap. The effects of the environment where early recognized by Forster in its unified theory of EET, where the Coulomb interaction between donor and acceptor transition dipoles is screened by the presence of the environment (represented as a dielectric) through a screening factor l/n2, where n is the solvent refractive index. This description is clearly an approximation of the global effects induced by a polarizable environment on EET. In fact, the presence of a dielectric environment not only screens the Coulomb interactions as formulated by Forster but also affects all the electronic properties of the interacting donor and acceptor [17],... 

Addressing large molecular systems is the aim of Chapter 3, which reviews a recently developed model based on the combined use of quantum mechanics and molecular mechanics (QM/MM). This approach uses a fully self-consistent polarizable embedding (PE) scheme described in the paper. The PE model is generally compatible with any quantum chemical method, but this review is focused on its combination with density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The PE method is based on the use of an electrostatic embedding potential resulting from the permanent charge distribution of the classically treated part of... 

At the same time, the formally independent particle nature of DFT allows the application of standard interpretative tools developed for the HF approach. This is true not only for the standard MuUiken population analysis, but also for more sophisticated schemes, like the Natural Bond Orbital (NBO) analysis [9], the Atomic Polarizable Tensor population [10], or the Atom in Molecule (AIM) approach [11]. These tools allow the use of familiar and well known models to analyze the molecular wave function and to rationalize it in terms of classical chemical concepts. In short, DFT is providing very effective quantum... 

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