Gaussian density function

Mineva T, Russo N and Sicilia E 1998 Solvation effects on reaction profiles by the polarizable continuum model coupled with Gaussian density functional method J. Oomp. Ohem. 19 290-9... 

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

F, St-Amant A, I Papai and D R Salahub 1992. Gaussian Density Functional Calculations on Hydrogen-Bonded Systems, journal of the American Chemical Society 114 4391-4400. ter J C1974. Quantum Theory of Molecules and Solids Volume 4 The Self-Consistent Field for Molecules and Solids. New York, McGraw-Hill. 

Nanda, H. Lu, N. Kofke, D. A., Using non-Gaussian density functional fits to improve relative free energy calculations, J. Chem. Phys. 2005,122, 134110 1-8... 

The effect of the shape of the distribution can be taken into consideration, without loss of generality, if it is assumed that the shape of the distribution in question can be approximated with a weighted sum of gaussian density functions (16)... 

Sim F, St-Amant A, Papai I, Salahub DR (1992) Gaussian density functional calculations on hydrogen-bonded systems, J Am Chem Soc, 114 4391-4400... 

Mele F, Mineva T, Russo N, Toscano M (1995) Hydrogen-bonded and van-der-Waals complexes studied by a gaussian density-functional method - the case of (HF)2, ArHCl, Ar2HCl systems, Theor Chim Acta, 91 169-177... 

In this equation. Dose is the administered dose, F is fraction absorbed, MAT is the mean input time or mean absorption time, N A is the normalized variance of the Gaussian density function, and T is the modulus time following administration of a dose. 

D, dose F, bioavailability fr, fraction of dose undergoing first-order input in a dual absorption model K, zero-order input rate L and k, first-order absorption rate constants MAT, mean absorption time NV, normalized variance of Gaussian density function, t, nominal time ti g, duration of time-lag x, duration of rapid input in dual absorption model Ti f, duration of zero-order IV infusion T, modulus time. 

Then, applying a Fourier inversion directly leads to the Gaussian density function... 

Now, together with our series expansion of the pdf (3.8) we obtain a series expansion in terms of derivatives of the Gaussian density function given by... 

Gaussian Density Functional Calculations on Hydrogen-Bonded Systems. 

There are many different probability density functions encountered in statistical analysis. Of particular interest to regression analysis are the normal, and F distributions, which will be discussed in this section. The normal or Gaussian density function has the form ... 

---