Electrostatic fields, density functional

For a quantum mechanical calculation, the single point calculation leads to a wave function for the molecular system and considerably more information than just the energy and gradient are available. In principle, any expectation value might be computed. You can get plots of the individual orbitals, the total (or spin) electron density and the electrostatic field around the molecule. You can see the orbital energies in the status line when you plot an orbital. Finally, the log file contains additional information including the dipole moment of the molecule. The level of detail may be controlled by the PrintLevel entry in the chem.ini file. 

Theoretical considerations leading to a density functional theory (DFT) formulation of the reaction field (RF) approach to solvent effects are discussed. The first model is based upon isolelectronic processes that take place at the nucleus of the host system. The energy variations are derived from the nuclear transition state (ZTS) model. The solvation energy is expressed in terms of the electrostatic potential at the nucleus of a pseudo atom having a fractional nuclear charge. This procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy, since all integrations involved are performed over [O.ooJ The quality of the approximations made are discussed within the frame of the Kohn-Sham formulation of density functional theory. 

In chapter 2, Profs. Contreras, Perez and Aizman present the density functional (DF) theory in the framework of the reaction field (RF) approach to solvent effects. In spite of the fact that the electrostatic potentials for cations and anions display quite a different functional dependence with the radial variable, they show that it is possible in both cases to build up an unified procedure consistent with the Bom model of ion solvation. The proposed procedure avoids the introduction of arbitrary ionic radii in the calculation of insertion energy. Especially interesting is the introduction of local indices in the solvation energy expression, the effect of the polarizable medium is directly expressed in terms of the natural reactivity indices of DF theory. The paper provides the theoretical basis for the treatment of chemical reactivity in solution. 

Almost all the parameters yielded by the various types of radiofrequency spectroscopy arise from the interaction of nuclear magnetic or electrostatic moments with the magnetic or electrostatic fields produced by the surrounding electrons. A consideration of the way these interactions arise shows that they fall into two groups one of the groups contains terms proportional to the electron density at the nucleus, N, itself, Vn(0), and consequently reflects only the s-character of the wave-function centered on N, v>n while the other is proportional to the value for all or some of the electrons surroimding the nucleus N (Table 1). This latter term vanishes for s-type orbitals and for p, d, f orbitals of the same principal quantum number has values in the order p > > d > > f. In practice this means that in a first approximation, only p-electrons contribute to and that the direct effect of the d-orbitals is only... 

Example 7.2 Consider a dust-laden gas passing through an electrostatic precipitator. Assume that all particles have the same charge-to-mass ratio, q/m, and the electric field is uniform. Use the Deutsch equation to estimate the overall collection efficiency if the particle size distribution based on weight percentage (wt%) can be expressed by the mass density function, /M, as... 

Other flexible molecular models of nitromethane were developed by Politzer et al. [131,132]. In these, parameters for classical force fields that describe intramolecular and intermolecular motion are adjusted at intervals during a condensed phase molecular dynamics simulation until experimental properties are reproduced. In their first study, these authors used quantum-mechanically calculated force constants for an isolated nitromethane molecule for the intramolecular interaction terms. Coulombic interactions were treated using partial charges centered on the nuclei of the atoms, and determined from fitting to the quantum mechanical electrostatic potential surrounding the molecule. After an equilibration trajectory in which the final temperature had been scaled to the desired value (300 K), a cluster of nine molecules was selected for a density function calculation from which... 

To improve upon a double- basis, one generally adds polarization functions whose / values correspond to orbitals unoccupied in the free atoms. For example, to expand upon a double- basis for HjO, one would add 2p functions on H and 3d functions on O. Such functions are called polarization functions since they describe the polarization of atomic electron density arising from molecule formation. For example, if a H atom is placed in the electrostatic field of an O atom, its electron density will be polarized along the 0-H bond direction, a change that can be described by the mixing of H 2p character into the His wave function. 

For the case of a purely electrostatic external potential, P = (F , 0), the complete proof of the relativistic HK-theorem can be repeated using just the zeroth component f (x) of the four current (in the following often denoted by the more familiar n x)), i.e. the structure of the external potential determines the minimum set of basic variables for a DFT approach. As a consequence the ground state and all observables, in this case, can be understood as unique functionals of the density n only. This does, however, not imply that the spatial components of the current vanish, but rather that j(jc) = < o[w]liWI oM) has to be interpreted as a functional of n(x). Thus for standard electronic structure problems one can choose between a four current DFT description and a formulation solely in terms of n x), although one might expect the former approach to be more useful in applications to systems with j x) 0 as soon as approximations are involved. This situation is similar to the nonrelativistic case where for a spin-polarised system not subject to an external magnetic field B both the 0 limit of spin-density functional theory as well as the original pure density functional theory can be used. While the former leads in practice to more accurate results for actual spin-polarised systems (as one additional symmetry of the system is take into account explicitly), both approaches coincide for unpolarized systems. 

Tel. 412-279-6700, fax 412-279-2118, e-mail info gaussian.com Gaussian 92 for ab initio molecular orbital calculations (Hartree-Fock, direct HF, Moller-Plesset, Cl, reaction field theory, electrostatic-potential-derived charges, vibrational frequencies, etc.). Gaussian 92/DFT for density functional theory calculations. Browse for archival storage of computed results. Processing on parallel machines. NEWZMAT to interconvert molfile formats. Inter-... 

A field is a function that describes a physical property at points in space. In a scalar field, this physical property is completely described by a single value for each point (e.g. temperature, density, electrostatic potential). For vector fields, both a direction and a magnitude are required for each point (e.g. gravitation, electrostatic field intensity). 

This integral (aside from the factor Ze2/32ir2ao) represents the mutual electrostatic energy of two spherically symmetrical distributions of electricity, with density functions e", i and respectively. It can be evaluated by calculating the potential due to the first distribution, by integrating over dri, and then evaluating the energy of the second distribution in the field of the first. 

As mentioned above, the nuclei are assumed to be fixed and are thus nothing more than sources of an external electrostatic potential in which the electrons move. If there is no magnetic field external to the molecule under consideration, and if external electric fields are time-independent, we arrive at the so-called electrostatic limit of relativistic density functional theory. Note that most molecular systems fall within this regime. In this case, one can prove the relativistic Hohen-berg-Kohn theorem using the charge density, p(r) = J f), only. This leads to a definition of an exchange-correlation functional -Exc[p( )]... 

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