Quantum polarizable models

A number of quantum polarizable models have been developed. " " These treatments of polarizability represent a step toward full ab initio methods. The models can be characterized by a small number of electronic states or potential energy surfaces, which are coupled to each other. For the purposes of this tutorial, our description is of the method of In his method,... 

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... 

Classical anharmonic spring models with or without damping [9], and the corresponding quantum oscillator models seem well removed from the molecular problems of interest here. The quantum systems are frequently described in terms of coulombic or muffin tin potentials that are intrinsically anharmonic. We will demonstrate their correspondence after first discussing the quantum approach to the nonlinear polarizability problem. Since we are calculating the polarization of electrons in molecules in the presence of an external electric field, we will determine the polarized molecular wave functions expanded in the basis set of unperturbed molecular orbitals and, from them, the nonlinear polarizability. At the heart of this strategy is the assumption that perturbation theory is appropriate for treating these small effects (see below). This is appropriate if the polarized states differ in minor ways from the unpolarized states. The electric dipole operator defines the interaction between the electric field and the molecule. Because the polarization operator (eq lc) is proportional to the dipole operator, there is a direct link between perturbation theory corrections (stark effects) and electronic polarizability [6,11,12]. 

Recent sequential molecular dynamics/quantum mechanics (MD/QM) calculations of the water dipole moment [51] using a polarizable model for water [52] indicate that the average dipole moment in the liquid is not dependent on the number... 

Future directions in the development of polarizable models and simulation algorithms are sure to include the combination of classical or semiempir-ical polarizable models with fully quantum mechanical simulations, and with empirical reactive potentials. The increasingly frequent application of Car-Parrinello ab initio simulations methods " may also influence the development of potential models by providing additional data for the validation of models, perhaps most importantly in terms of the importance of various interactions (e.g., polarizability, charge transfer, partially covalent hydrogen bonds, lone-pair-type interactions). It is also likely that we will see continued work toward better coupling of charge-transfer models (i.e., EE and semiem-pirical models) with purely local models of polarization (polarizable dipole and shell models). 

In their approach, Yamamoto and Kato let Fext(> be determined through a non-polarizable model for the solvent so that Fext(>0 can be written as a superposition of Coulomb potentials from point charges representing the solvent. They showed, subsequently, how electron-transfer processes could be treated within their approach, even in the case when quantum effects of light nuclei (most notably, protons) need to be included. Finally, they presented results for a specific electron-transfer process. 

Since pNA and most of the chromophores of interest have large dipole moments an important feature of the continuum models is the introduction of the reaction field. The pNA molecule at the centre of the cavity in the continuum induces a polarization on the surface of the cavity, which produces the reaction field acting on the central molecule. This reaction field changes the dipole moment of the pNA molecule via the linear polarizability. A self consistent procedure is required in which the effects of the reaction field and also the effects of the applied macroscopic fields modified by the internal field factors are included in a self-consistent determination of the molecular response within a specified quantum mechanical model. 

Nevertheless, these methods are mostly applied with fixed charges (even if these are chosen in a sophisticated way) and with pairwise additivity approximation as well as with the neglect of nuclear quantum effects. Suggestions for polarizable models appeared in literature mainly for water [23], The quality of potential parameterization varies from system to system and from quantity to quantity, raising the question of transferability. Spontaneous events like reactions cannot appear in simulations unless the event is included in the parameterization. Despite these problems, it is possible to reproduce important quantities as structural, thermodynamic and transport properties with traditional MD (MC) mainly due to the condition of the nanosecond time scale and the large system size in which the simulation takes place [24],... 

This observation paves the way to the work by Tsiper and Soos that proposed a mean-field approximation for the calculation of the linear polarizability of molecular crystals and films [25, 62, 63, 64]. The approach is based again on the neglect of intermolecular overlap. A quantum chemical model is adopted for each molecular... 

Figure 19. PI-QTST activation free-energy curves for a model A-H-A proton transfer system which demonstrate the effect of solvent electronic polarizability (see Ref. 77). The solid line depicts the classical free-energy curve for the solute in isolation with a rigid A-A distance. The short-dashed line is for the rigid solute in an electronically nonpolarizable solvent. The long-dashed line depicts the quantum free-energy curve for the rigid solute solvated in a quantum polarizable solvent, while the dot-dashed line depicts the quantum free energy for the same solute but in a classically polarizable solvent.

Linear Free-Energy and Related Mathematical Models (2) Polarizability Models and, (3) Quantum Chemical Models. These methods differ in the level of theoretical sophistication needed to obtain a working relationship, but all presently rely heavily on the use of multiple regression techniques in relating observed biological activities to a given mathematical model. 

Mata et al have determined the dynamic polarizability and Cauchy moments of liquid water by using a sequential molecular dynamics(MD)/ quantum mechanical (QM) approach. The MD simulations are based on a polarizable model of liquid water while the QM calculations on the TDDFT and EOM-CCSD methods. For the water molecule alone, the SOS/TDDFT method using the BHandHLYP functional closely reproduces the experimental value of a(ffl), provided a vibrational correction is assumed. Then, when considering one water molecule embedded in 100 water molecules represented by point charges, a(co) decreases by about 4%. This decrease is slightly reduced when the QM part contains 2 water molecules but no further effects are observed when enlarging the QM part to 3 or 4 water molecules. These molecular properties have then been employed to simulate the real and imaginary parts of the dielectric constant of liquid water. 

A general description of quantum-chemical models based on a representation of the solvent as an infinite polarizable dielectric medium (dielectric continuum) is given below. All of these models are derived from the direct solution of the Poisson equations [21] defining the total electrostatic potential as... 

The electronic response x in Eq. (13) is a static susceptibility involving even-parity singlets of polymers with centrosymmetric backbones. The p in Eq. (1) indicate to be a bond-order/bond-order polarizability [20]. Since the excited states F> in the sum depend on V R), different s are found in Hubbard or PPP models. The large NLO responses of conjugated polymers are also due to V electrons. The dipole operator in the ZDO approximation of quantum cell models is [12]... 

Z. Y. Lu and Y. K. Zhang,/. Chem. Theory Comput., 4(8), 1237-1248 (2008). Interfacing Ab Initio Quantum Mechanical Method with Classical Drude Oscillator Polarizable Model for Molecular Dynamics Simulation of Chemical Reactions. 

Calculated spectral characteristics for propyne obtained by transferring bond polarizability parameters are compared with those evaluated by RHF/6-3 lG(d,p) ab initio MO calculations [311] in Table 9.10 and Fig. 9.4. It is seen that the predicted spectrum obtained in applying the bond polarizability model is in better agreement with experiment than the ab initio estimated spectrum. More advanced quantum mechanical computations are, evidently, needed to satisfactorily calculate the Raman intensities of propyne. The computations employing transferable sets of polarizability derivatives are simple and give good results. 

It is evident from the previous analysis that flexible, polarizable models in conjimction with quantum (path integral) simulations are truly transferable models, which can be used to simiflate the properties of different environments that are associated with dissimilar inter- and intra-molecular zero-point energies and magnitude of cooperative effects. 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

When an atom or molecule approaches a surface, the electrons in the particle - due to quantum fluctuations - set up a dipole, which induces an image dipole in the polarizable solid. Since this image dipole has the opposite sign and is correlated with fluctuations in the particle, the resulting force is attractive. In the following we construct a simple model to elucidate the phenomenon. 

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