Dynamic properties polarizability

Choosing a non-zero value for uj corresponds to a time-dependent field with a frequency u, i.e. the ((r r)) propagator determines the frequency-dependent polarizability corresponding to an electric field described by the perturbation operator QW = r cos (cut). Propagator methods are therefore well suited for calculating dynamical properties, and by suitable choices for the P and Q operators, a whole variety of properties may be calculated. " ... 

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

Keywords Excited state properties, Polarizable Continuum Model, Solvation dynamics, Time-... 

In the liquid phase, calculations of the pair correlation functions, dielectric constant, and diffusion constant have generated the most attention. There exist nonpolarizable and polarizable models that can reproduce each quantity individually it is considerably more difficult to reproduce all quantities (together with the pressure and energy) simultaneously. In general, polarizable models have no distinct advantage in reproducing the structural and energetic properties of liquid water, but they allow for better treatment of dynamic properties. 

Dynamic properties, such as the self-diffusion constant, are likewise strongly correlated with the dipole moment. This coupling between the translational motion and the dipole moment is indicated in the dielectric spectrum. Models that are overpolarized tend to undergo dynamics that are significantly slower than the real physical system. The inclusion of polarization can substantially affect the dynamics of a model, although the direction of the effect can vary. When a nonpolarizable model is reparameterized to include polarizability, the new model often exhibits faster dynamics, as with polarizable versions of TIP4P, ° Reimers-Watts-Klein and reduced... 

We present how to treat the polarization effect on the static and dynamic properties in molten lithium iodide (Lil). Iodide anion has the biggest polarizability among all the halogen anions and lithium cation has the smallest polarizability among all the alkaline metal cations. The mass ratio of I to Li is 18.3 and the ion size ratio is 3.6, so we expect the most drastic characteristic motion of ions is observed. The softness of the iodide ion was examined by modifying the repulsive term in the Born-Mayer-Huggins type potential function in the previous workL In the present work we consider the polarizability of iodide ion with the dipole rod method in which the dipole rod is put at the center of mass and we solve the Euler-Lagrange equation. This method is one type of Car-Parrinello method. 

Because charge defects will polarize other ions in the lattice, ionic polarizability must be incorporated into the potential model. The shell modeP provides a simple description of such effects and has proven to be effective in simulating the dielectric and lattice dynamical properties of ceramic oxides. It should be stressed, as argued previously, that employing such a potential model does not necessarily mean that the electron distribution corresponds to a fully ionic system, and that the general validity of the model is assessed primarily by its ability to reproduce observed crystal properties. In practice, it is found that potential models based on formal charges work well even for some scmi-covalent compounds such as silicates and zeolites. 

F. Barocchi and M. Zoppi. Experimental Determination of Two-Body Spectrum and Pair Polarizability of Argon. In J. van Kranendonk, (ed.), Intermolecular Spectroscopy and Dynamical Properties of Dense Systems—Proceedings of the International School of Physics "Enrico Fermi," Course LXXV, North-Holland, Amsterdam, 1980, pp. 237-262. 

The molecular response tensors are characterized by peculiar properties and satisfy a series of very general quantum-mechanical relations. First we observe that the dynamic properties can be rewritten as a sum of the corresponding static property and a function multiplying the square of the angular frequency. Thus, for instance, in the case of dipole electric polarizability, using Eqn. (117),... 

Molecular electric properties give the response of a molecule to the presence of an applied field E. Dynamic properties are defined for time-oscillating fields, whereas static properties are obtained if the electric field is time-independent. The electronic contribution to the response properties can be calculated using finite field calculations , which are based upon the expansion of the energy in a Taylor series in powers of the field strength. If the molecular properties are defined from Taylor series of the dipole moment /x, the linear response is given by the polarizability a, and the nonlinear terms of the series are given by the nth-order hyperpolarizabilities ()6 and y). 

Electron correlation plays a role in electrical response properties and where nondynamical correlation is important for the potential surface, it is likely to be important for electrical properties. It is also the case that correlation tends to be more important for higher-order derivatives. However, a deficient basis can exaggerate the correlation effect. For small, fight molecules that are covalently bonded and near their equilibrium structure, correlation tends to have an effect of 1 5% on the first derivative properties (electrical moments) [92] and around 5 15% on the second derivative properties (polarizabilities) [93 99]. A still greater correlation effect is possible, if not typical, for third derivative properties (hyperpolarizabilities). Ionic bonding can exhibit a sizable correlation effect on hyperpolarizabilities. For instance, the dipole hyperpolarizability p of LiH at equilibrium is about half its size with the neglect of correlation effects [100]. For the many cases in which dynamical correlation is not significant, the nondynamical correlation effect on properties is fairly well determined with MP2. For example, in five small covalent molecules chosen as a test set, the mean deviation of a elements obtained with MP2 from those obtained with a coupled cluster level of treatment was 2% [101]. 

Veldhuizen and de Leeuw (1996) used the OPLS parameters for methanol and both a nonpolarizable and a polarizable model for carbon tetrachloride for MD simulations over a wide range of compositions. The polarization contribution was found to be very important for the proper description of mixture properties, such as the heat of mixing. A recent study by Gonzalez et at (1999) of ethanol with MD simulations using the OPLS potential concluded that a nonpolarizable model for ethanol is sufficient to describe most static and dynamic properties of liquid ethanol. They also suggested that polarizabilities be introduced as atomic properties instead of the commonly approach of using a single molecular polarizability. 

Let us return to the problem of solving the response of the quantum mechanical system to an external electric field. The zeroth-order wave function of the quantum mechanical system is obtained by use of any of the standard approximate methods in quantum chemistry and the coupling to the field is described by the electtic dipole operator. There exist a number of ways to determine the response functions, some of which differ in formulation only, whereas others will be inherently different. We will give a short review of the characteristics of tire most common formulations used for the calculation of molecular polarizabilities and hyperpolarizabilities. The survey begins with the assumption that the external perturbing fields arc non-oscillatory, in which case we may determine molecular properties at zero frequencies, and then continues with the general situation of time-dependent fields and dynamic properties. 

Calculations of analytic excited state properties for correlated methods have been reported by several groups [107-118]. Excited state dynamic properties from cubic response theory were first obtained by Norman et al. at the SCF level [55] and by Jonsson et al. at the MCSCF [56] level, and in a subsequent study a polarizable continuum model was applied to account for solvation effects [119]. Hattlg et al. presented a general theory for excited state response functions at the CC level using a quasi-energy formulation [120] which was subsequently implemented and applied at the CCSD level [121, 122]. The first ID DFT calculation of dynamic excited state polarizabilities, which we will shortly review here, was presented in [58] for pyrimidine and -tetrazine utilizing the double residue of the cubic response function derived in Section 2.7.3. 

Weakly bound complexes display unusual structural and dynamical properties resulting from the shape of their intermolecular potential energy surfaces. They show large amplitude internal motions, and do not conform to the dynamics and selection rules based on the harmonic oscillator/rigid rotor models (4). Consequently, conventional models used in the analysis of the spectroscopic data fail, and the knowledge of the full intermolecular potential and dipole/polarizability surfaces is essential to determine the assignments of the observed transitions. 

In addition to the above mentioned purely geometrical aspects, there is also a dynamic property of the ion which has a considerable influence on its crystallo-chemical behavior its polarizability, or, according to Fajans, its deformability. If a negative ion with readily movable electrons (e.g. iodine) enters the field of a small positive ion, the charge cloud of the former will attract the positive ion, the nucleus will repel it and the deformed ion will be characterized, not only by its charge, but also by an induced dipole moment. While formerly the interaction of the two... 

If the ions are treated explicitly, the ion-electron interaction is described by pseudopotentials. This allows us to eliminate all core electrons from the actual calculation and to deal only with the valence electrons. There exists a wide variety of pseudopotentials. The most elaborate of them are nonlocal operators because they project out of the occupied core electron states, see e.g. [18]. Separable approximations to projection can simplify the handling [19]. The simplest to use are, of course, local pseudopotentials, as e.g. the old empty-core potential of [20] or the more recent and extensive adjustment of [21]. It is a welcome feature that most simple metals, except for Li, can be treated fairly well with local pseudopotentials [22]. It is to be remarked that all these choices have been optimized with respect to structural properties. The performance concerning dynamical features has not yet been explored systematically. In fact, nSost of the available pseudopotentials tend to produce a blue-shifted plasmon position. An optimization of pseudopotentials for simple metals with simultaneous adjustment of static and dynamic properties is presently under way [23]. For noble metals, it is known that pseudopotentials alone (even when nonlocal) cannot reproduce the proper plasmon position. One needs to explicitly take into account the considerable polarizability of the ionic core, in particular of the rather soft last d shell [24]. 

Structural and dynamic properties of pure water in contact with uncharged realistic metal surfaces are obtained by molecular dynamics simulations. The influences of adsorption energy, surface corrugation, electronic polarizability and surface inhomogeneity are investigated. The adsorption energy of water on the metal surface is found to be the most important parameter. 

Using the complete form of the LR-CCSD (linear response CC formalism with single and double excitations) theory in combination with the ZPolC perturbation-tailored basis set Kowalski et have provided accurate estimates for the static and dynamic electronic polarizabilities of Ceo and have showed that the T2-dependent terms not included in CC2 play in important role in estimating these properties since they lead to a reduction of the polarizability by 12 13%. In the static limit, their estimate amounts to 82.23 in comparison with the 76.5 8 measured value. Note also that in the static limit the vibrational contribution is not necessary negligible. For a wavelength of 1064 nm, their estimate amounts to 83.62 A in comparison with the experimental value of 79 4 A. ... 

A third, less obvious limitation of sampling methods is that, due to the heavy computational burden involved, simpler interatomic potential models are more prevalent in Monte Carlo and molecular dynamics simulations. For example, polarizability may be an important factor in some polymer crystals. Nevertheless, a model such as the shell model is difficult and time-consuming to implement in Monte Carlo or molecular dynamics simulations and is rarely used. United atom models are quite popular in simulations of amorphous phases due to the reduction in computational requirements for a simulation of a given size. However, united atom models must be used with caution in crystal phase simulations, as the neglect of structural detail in the model may be sufficient to alter completely the symmetry of the crystal phase itself. United atom polyethylene, for example, exhibits a hexagonal unit cell over all temperatures, rather than the experimentally observed orthorhombic unit cell [58,63] such a change of structure could be reflected in the dynamical properties as well. 

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