Accurate relativistic adapted Gaussian basis sets for hydrogen through xenon without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) from H (Z = 1) through Xe (Z = 54) without variational prolapse have been developed by employing a polynomial version of the Generator Coordinate Dirac‐Fock (p‐GCDF) method. Two nuclear models have been used in this work: (1) the finite nucleus of uniform proton‐charge distribution, and (2) the finite nucleus with a Gaussian proton–charge distribution. The largest errors observed are only 1.5 mHartree (silver and cadmium) and the RAGBS sizes are much smaller than previous accurate relativistic Gaussian basis sets that were shown to be free of variational prolapse. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 61–71, 2006     

Accurate relativistic adapted Gaussian basis sets for Cesium through Radon without variational prolapse and to be used with both uniform sphere and Gaussian nucleus models

Accurate relativistic adapted Gaussian basis sets (RAGBSs) from Cs (Z = 55) through Rn (Z = 86) without variational prolapse were developed by using the polynomial version of the Generator Coordinate Dirac-Fock method. The RAGBSs presented here can be used with any of two popular finite nucleus models, the uniform sphere and the Gaussian models. The largest RAGBS error is 4.5 mHartree for Radon with a size of 30s27p17d11f.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

The general Gaussian product theorem

The Gaussian Product Theorem between two 1s Gaussian Type Orbitals (GTOs) is extended to an arbitrary number of s-type functions, giving a compact formula which permits to express the condensed GTO result. Then, this new formulation is combined with the product of arbitrary GTO Cartesian angular parts, obtaining a finite expansion expressing this product as a multilinear combination of such functions sharing a common center. The combination of both results constitutes the General Gaussian Product Theorem (GGPT), a final compact expression for the product of an arbitrary number of Cartesian GTOs. The notation provides an easy way to express algebraically any general multicenter GTO product expression. It is also shown how by means of Nested Summation Symbols the computational implementation can be easily and elegantly achieved. Computational parallelizable schemes of the GGPT are provided.     

Relativistic Gaussian basis sets for molecular calculations: Fully optimized single‐family exponent basis sets for H?Hg

Relativistic single‐family exponent Gaussian basis sets for molecular calculations are presented for the 80 atoms ₁H through ₈₀Hg. The exponent parameters shared by Gaussian basis functions of all symmetry species are fully optimized. Two nucleus models of uniformly charged sphere and Gaussian charge distribution are considered and two kinds of basis sets are generated accordingly. The total energy errors are less than 2 mhartree in any atoms. Some of the present basis sets include small variational collapse (or prolapse), but test calculations show that they could be reliably applied to molecular calculations. © 2005 Wiley Periodicals, Inc. J Comput Chem 27: 48–52, 2006     

Estimation of Flat‐topped Gaussian distribution with application in system identification

Uniformly distributed uncertainty exists in industrial process; additive error introduced by quantization is an example. To be able to handle additive uniform and Gaussian measurement uncertainty simultaneously in system identification, the Flat‐topped Gaussian distribution is considered in this paper as an alternative to the Gaussian distribution. To incorporate this type of uncertainty in the maximum likelihood estimation framework, the explicit form of its density function is of necessity. This work proposes an approach for obtaining both the functional structure and corresponding parameter estimation of Flat‐topped Gaussian distribution by a moment fitting strategy. The performance of the proposed approximation function is verified by comparison to the Flat‐topped Gaussian distributed random variable with different Gaussian and uniform components. Results of numerical simulations and industrial applications in system identification are presented to verify the effectiveness of the Flat‐topped Gaussian distribution for noise distribution in handling additional uniform uncertainty.     

Quantification of AES depth profiling data of polycrystalline Al films with Gaussian and non‐Gaussian surface height distributions

Sputtering‐induced roughness is the main distortional factor on the depth resolution of measured depth profiles, in particular, for sputtering of polycrystalline metals. Frequently, the surface height distribution of the sputtering‐induced roughness exhibits an asymmetrical feature. In such a case, a non‐Gaussian height distribution function (HDF) has to be applied for the quantification of a measured depth profile. By replacing the usually applied Gaussian HDF with that of an asymmetrical triangle in the Mixing‐Roughness‐Information depth model, measured Auger electron spectroscopy depth profiling data of the interface of polycrystalline Al films on Si are perfectly fitted. The asymmetric triangle height distributions obtained from the best fit are a reasonable approximation of the height distributions measured by atomic force microscopy. Copyright © 2013 John Wiley & Sons, Ltd.     

Explicitly correlated Gaussian calculations of the (2)D Rydberg states of the boron atom

Accurate non-relativistic variational calculations are performed for the seven lowest members of the (2)D Rydberg series (1s(2)2s2p(2), and 1s(2)2s(2)nd, n = 3, [ellipsis (horizontal)], 8) of the boron atom. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian basis functions and the effect of the finite nuclear mass is directly included in the calculations allowing for determining the isotopic shifts of the energy levels. The Gaussian basis is optimized independently for each state with the aid of the analytic energy gradient with respect to the Gaussian parameters. The calculations represent the highest accuracy level currently achievable for the considered states. The computed energies are compared with the available experimental data.     

Using Gaussian model to improve biological sequence comparison

One of the major tasks in biological sequence analysis is to compare biological sequences, which could serve as evidence of structural and functional conservation, as well as of evolutionary relations among the sequences. Numerous efficient methods have been developed for sequence comparison, but challenges remain. In this article, we proposed a novel method to compare biological sequences based on Gaussian model. Instead of comparing the frequencies of k‐words in biological sequences directly, we considered the k‐word frequency distribution under Gaussian model which gives the different expression levels of k‐words. The proposed method was tested by similarity search, evaluation on functionally related genes, and phylogenetic analysis. The performance of our method was further compared with alignment‐based and alignment‐free methods. The results demonstrate that Gaussian model provides more information about k‐word frequencies and improves the efficiency of sequence comparison. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Free Energy of a Non‐Gaussian Polymer Brush

An analytical theory describing layers of polymer chains grafted to a planar surface (i.e. polymer brush) is developed. We consider a brush of chains with finite extensibility (or non‐Gaussian brush) within the framework of molecular field theory. An analytical solution for free energy of the brush and a few other brush characteristics are obtained and studied. Comparison with other known models of a brush is also made.

Chain extensibility E(x, y) for Gaussian model (dashed lines) and BCC model (solid lines) for a few chain end positions y (numbers near curves).     

A simplified representation of the potential produced by Gaussian charge distributions

A procedure is presented which allows a more economical representation of the potential produced by orbital charge distributions in which the orbitals are expanded in terms of a finite set of polynomial Gaussian functions. The basic idea is that the products of pairs of Gaussian basis functions, on which the charge distributions are expanded, are expressed in terms of a new basis set of optimally chosen single Gaussian functions. Such a procedure has been tested in a particular case and a few possible applications have been suggested.     

Gaussian expansion method for molecular integrals of molecular properties

The finite Gaussian Expansion method for molecular integrals proposed by Taketa, O-ohata and Huzinaga has been extended to the integrals of molecular properties. The integral formulas of so-called moment, field and field gradient integrals have been derived. It has been numerically shown that in order to evaluate the field and the field gradient integrals based on Slater type orbitals, eight- or ten-term Gaussian expansions are sufficient but this method fails to attain sufficient effective numbers for the moment integrals.     

Modified Chain Displacement Function for Gaussian Networks

The probability that a polymeric chain reaches from one crosslink junction to a second is given by the probability that the chain's end-to-end vector is equal in magnitude and direction to the junction-to-junction vector. In calculating this probability, conventional Gaussian theories assume independent probabilities in the three coordinate directions. This assumption of independent probabilities means that the conventional Gaussian chain displacement function cannot refer to a specified direction as is required. In this paper, the directional probability is re-introduced into the Gaussian chain displacement function which leads to a novel strain-energy function. This strain-energy function is shown to be in quantitative agreement with reversible deformation data in extension and in pure shear. No additional parameters are introduced into the new function which allows the independent determination of both the crosslink density and the “front factor” (the ratio of the mean-square end-to-end distances of free and crosslinked chains).     

Distributed basis sets of s-type Gaussian functions for molecular electronic structure calculations: Applications of the Gaussian cell model to one-electron polycentric linear molecular systems

A particular formulation of the distributed Gaussian basis-set approach, the extended Gaussian cell model, is applied to the simplest polycentric molecule, the linear H₃²⁺ ion. Calculations of the total energy using two extensions of the original Gaussian cell model are described and results are reported for the ground state and the first excited state. A comparison with recently reported finite element calculations is made for a number of nuclear geometries. © 1996 John Wiley & Sons, Inc.     

On the measure of non-gaussianity of a nearly Gaussian noise

A procedure for the determining of the measure of non-gaussianity of nearly Gaussian noise is suggested, which used trimmed interval of concentration. The procedure is based on the Parseval finite-interval theorem. The following notions have been introduced: the scalar measure of non-gaussianity, the vector measure of non-gaussianity, and multicomponent partial measure of non-gaussianity. The method allows decreasing the probability of the mistaking of a purely Gaussian noise for nearly Gaussian one. The procedure was validated using a mixed normal distribution. The testing showed the finite-interval analog of the Gram-Charlier expansion to have only a few main (meaningful) components. The procedure for the determining of the measure of non-gaussianity of nearly Gaussian noise can be used in the noise diagnostics of various electrochemical systems and for noise monitoring of objects and processes in the electrochemical power engineering.     

Gaussian 03 Workshop

Das Programmpaket „Gaussian”︁, eines der größten und am häufigsten genutzten quantenchemischen Rechenprogramme, ist Ende März in der neuen Version „Gaussian 03”︁ erschienen. Der weltweit erste Workshop zu diesem Programmpaket, „Introduction to Gaussian 03, Theory and Practice”︁, hat Anfang April an der Universität Ulm stattgefunden. Vorbereitet und organisiert wurde der Workshop in Ulm von Hans‐Ullrich Siehl, Abteilung Organische Chemie I und dem Center of Exellence (CoE) for Computational Chemistry der Universität Ulm ‐ eine Einrichtung des Kommunikations‐und Informationszentrums (KIZ) der Universität Ulm (Leiter: Hans Peter Großmann) ‐ in Zusammenarbeit mit Sun Microsystems und Gaussian.     

Notes on hydrogenic Gaussian lobe functions

The Gaussian lobe representation of 2p and 3d_xy functions of a one-electron atom has been reconsidered. Contrary to earlier results, it has been found that the minimum energy associated with the simplest case of these functions is reached when the expansion centers coincide with the nucleus. This also seems to be true for representations with larger expansion lengths. Under similar conditions, Whitten's octahedral representation of the 2p function gives a better energy value than Poshusta's tetrahedral one.     

Problem of Molecular Vibrations with the Gaussian Potential

The choice of the form of a potential function in calculating the characteristics of stationary states for atomic vibrations in a molecule is discussed. With regard to the features of the purely Coulomb potential and general considerations on the stable states of a bound nucleus set, and also a decrease in distances between the energy levels with increasing excitation energies, it is proposed to use a potential in the form of the “overturned” multidimensional Gaussian. It is demonstrated that this problem is solved by a variational procedure in the basis of products of one-dimensional functions forming a complete set.     

Effects of the Gaussian energy dispersion on the statistics of polarons and bipolarons in conducting polymers

We discuss the interpretation of usually broad oxidation peaks observed in electronically conducting polymers, in terms of the statistical distributions functions of polarons and bipolarons. The analysis is based on examining the chemical capacitance, that relates the change of concentration to a modification of the chemical potential of a given species, for different statistical models. We first review the standard models for single energy species that provide a nernstian dependence, and the limitations of these models are discussed. A new model that assumes a Gaussian distribution of energies related to molecular geometry fluctuations is suggested, and this model shows excellent agreement with the results of electrochemical oxidation of polypyrrole in quasiequilibrium conditions. From a fit of the data, it is found that the density of conjugated chain segments in polypyrrole, Ns approximately 10(21) cm(-3), shows a Gaussian distribution of half width sigma approximately 170 meV, tentatively attributed to bipolaron formation energies.