Charge density function

Elstner M, Porezag D, Jungnickel G, Eisner J, Flaugk M, Frauenheim Th, Suhai S and Seifert G 1998 Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties Phys. Rev. B 58 7260... 

Figure 1.7 Plots of (a) the radial wave function (b) the radial probability distribution function and (c) the radial charge density function 4nr Rl( against p...

MULTI-SCALE QM/MM METHODS WITH SELF-CONSISTENT-CHARGE DENSITY-FUNCTIONAL-TIGHT-BINDING (SCC-DFTB)... 

Keywords Self-consistent-charge density-functional-tight-binding, Generalized solvent boundary... 

G. Seifert, Phys. Rev. B, 58, 7260 (1998). Self-consistent-charge Density-Functional Tight-binding Method for Simulations of Complex Materials Properties. 

The normalization expression (3.26) is appropriate for wave functions. For a charge density function, a different normalization must be used, because the charge is given by the integral over the first power of the function. The density functions in general use are labeled d,mp, and are defined by the normalization... 

The calculation thus consists of three steps (1) calculating the scattering factors of the analytical charge density functions (see appendix G for closed-form expressions), (2) Fourier transformation of the electrostatic operator, and (3) back transformation of the product of two Fourier transforms. 

The effective potential in Eq. (4.33) is then calculated from this charge-density function as a sum of the classical Coulomb energy and the exchange-... 

Frauenherm, T.. Seifert, G., Elstner, M., Hajnal, Z., Jungnickel. G.. Porezag. D.. Suhai. S.. and Scholz. R. 2000. A Self-consistent Charge Density-functional Based Tight-binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology , Phys. Stat. Sol. B. 217. 41. 

Not only is hybridization an artificial simulation without scientific foundation, but even the assumed "orbital shapes" that it relies upon, are gross distortions of actual electron density distributions. The density plot shown above, like all textbook caricatures of atomic orbitals, is a misrepresentation of the spherical surface harmonics that describe normal excitation modes of atomic charge distributions. These functions are defined in the surface of the charge-density function, as in Fig. 2.13, and not at r = 0, as shown in Figure 2.16. 

Kalinowski JA, Lesyng B, Thompson JD, Cramer CJ, Truhlar DG (2004) Class IV Charge Model for the Self-Consistent Charge Density-Functional Tight-Binding Method. J. Phys. Chem A, 108 2545-2549... 

Cui Q, M Elstner, E Kaxiras, T Frauenheim, M Karplus (2001) A QM/MM implementation of the self-consistent charge density functional tight binding (SCC-DFTB) method. J. Phys. Chem. B 105 (2) 569-585... 

Using Slater s rules the radius Rm of the maximum is a spherical charge density function which can be calculated using the formula... 

The discrete set of the nuclear point distribution is generalized to more general three-dimensional objects, for example, to the continuous molecular charge density functions p(r). 

In the special case of selecting the three-dimensional object as a molecular charge density function p(r), the analogies between point symmetry and symmorphy are rather clear. By analogy with the point symmetry of nuclear arrangements, the molecular charge density function pit) can provide a criterion for selecting the symmorphy transformations of p(r) from the infinite family G, of homeomorphisms of the three-dimensional space. A homeomorphism 5 is a symmorphy transformation... 

For the molecular charge density function p(r), all those homeomor-phisms S of family Ghom are symmorphy transformations for which... 

However, real molecules are quantum mechanical objects and they do not have a finite body defined in precise geometrical terms and a finite boundary surface that contains all the electron density of the molecule. The peripheral regions of a molecule can be better represented by a continuous, 3D electronic charge density function that approaches zero value at large distances from the nuclei of the molecule. This density function changes rapidly with distance within a certain range, but the change is continuous. The fuzzy, cloud-like electronic distribution of a molecule is very different from a macroscopic body [251], and no precise, finite distance can be specified that could indicate where the molecule ends. No true molecular surface exists in the classical, macroscopic sense. 

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