Gaussian density

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. 

Fig. 77.—Gaussian density distribution of the chain displacement vec tors for chain molecules consisting of 10 freely jointed segments, each of length 1 = 2.5 A. The end-to-end length r is in Angstrom units and W(x, y, z) is expressed in A". ...

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 idea of mixture models is to consider the overall density function as a sum of the density functions of the single groups. Usually, the group density functions are modeled by Gaussian densities covariance matrix Xr leading to a model... 

Since the joint probability density of the complete set of positions and momenta is Gaussian, the distribution of any subset must also be Gaussian. But the characteristic function corresponding to a Gaussian density takes a simple form, and in the present case is... 

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)... 

The width rj 1 of the gaussian is chosen to be of the order of the lattice step, so that the two series, in the real and reciprocal spaces, converge rapidly. For the whole lattice, including the origin 0, and for a wave vector K, the dipole-moment gaussian density is... 

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... 

Most synthetic polymers in which the monomer units are connected via single bonds have rather flexible chains. The bond torsion energy is relatively small and the units can rotate around their bonds [14,30,31]. Each molecule can adopt a large number of energetically equivalent conformations and the resulting molecular geometry is that of a statistical coil, approximately described by a Gaussian density distribution. This coil conformation is the characteristic secondary structure of macromolecules in solution and in the melt. It is entropically favoured because of its... 

Figure 5. The amorphous structure of an organic matrix leads to a Gaussian density of states for the HOMO of the donor transport matrix. Some of the donors will have a relatively small oxidation potential (in the shaded region) and these sites are likely to experience a potential barrier inhibiting charge hopping to adjacent sites of higher oxidation potential. A hole may in this way become an immobilized cation.

J.E. Straub, J. Ma, P. Amara, Simulated annealing using coarse grained classical dynamics Smoluchowski dynamics in the Gaussian density approximation, J. Chem. Phys. 103 (1995), 1574. 

C. Tsoo, C.L. Brooks, Cluster structure determination using Gaussian density distribution global minimization methods, J. Chem. Phys. 101 (1994), 6405... 

Figure 14-10 DoD plot for comparison of two drug assays parametric analysis. A histogram shows the relative frequency of N = 65 differences with the estimated Gaussian density distribution. Parametrically estimated 2.5, and 97.5 percentiles are shown with 90% CIs.

In the case of electrochemical ET, the relevant overlap was between the gaussian density-of-states function of the reacting species in solution and the Fermi-Dirac distribution function of the charge carriers in the electrode (Fig. 4.21). Figure 4B. 1 shows the analogous density-of-states functions for a homogeneous ET reaction. The rate... 

X. Zhang, K. Nieforth, J. M. Lang, R. Rouzier-Panis, J. Reynes, A. Dorr, S. Kolis, M. R. Stiles, T. Kinchelow, and I. H. Patel, Pharmacokinetics of plasma enfuvirtide after subcutaneous administration to patients with human immunodeficiency virus inverse Gaussian density absorption and 2-compartment disposition. Clin Pharmacol Ther 72 10-19 (2002). 

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. 

---