Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part I. Partial free energy coefficients

Derivations are given for the thermodynamic relations that are needed to compare experimental thermodynamic excess functions of various kinds with the corresponding functions obtained from models for the solutions by calculations made in the framework of the McMillan-Mayer theory. This contribution extends earlier results. The new results are used to elucidate the behavior of the McMillan-Mayer thermodynamic excess functions of solutions which are very nearly ideal on the mole-fraction scale, for example, isotope mixtures. The study of these ideal systems leads to the conclusion that liquid-structure effects associated with the packing of molecules contribute a negative term to the potential of the force between solute particles in the solvent.     

Automated identification and plotting of the function y = f(x)

A series of programs has been edited for automated identification and plotting of the function y=f(x). The QN-AU series contains thousands of models, which consists of various functions and their combinations. After input of data, the package selects automatically the most suitable model within a given range and produces a graphic display. The package can be run on various personal computers such as the IBM-PC or Apple II.     

XYZ,a program for modeling,validation, prediction and graphic display of data

A program for modeling, validation, prediction and graphic display of data is reported. The package is useful for dealing with responses that area function of a reduced number of variables. Implementation of user-defined models is easy and several very general equations can be selected. The structure of the program is shown and the use of the different modules is explained. Two typical, applications based on distinct mathematical models are shown.     

An evaluation of orthogonal signal correction methods for the characterisation of arabica and robusta coffee varieties by NIRS

Two orthogonal signal correction methods (OSC and DOSC) were applied on a set of 83 roasted coffee NIR spectra from varied origins and varieties in order to remove information unrelated to a specific chemical response (caffeine), which was selected due to its high discriminant ability to differentiate between arabica and robusta coffee varieties. These corrected NIR spectra, as well as raw NIR spectra and three chemical quantities (caffeine, chlorogenic acids and total acidity), were used to develop separate classification models accordingly using the potential functions method as a class-modelling technique in order to evaluate their respective capacities to discriminate between coffee varieties and the influence of these pre-processing methods on the classification of the coffee samples into their corresponding variety class. The transformation of roasted coffee NIR spectra by means of an orthogonal signal correction method, taking into account in this correction a chemical response closely related to the sample origin, prompted a notable improvement in the specificity of the constructed classification models.     

Multiparametric curve fitting XIV. Modus operandi of the least-squares algorithm MINOPT

Hybrid least-squares algorithm MINOPT for a nonlinear regression is introduced. MINOPT from CHEMSTAT package combines fast convergence of the Gauss-Newton method in a vicinity of minimum with good convergence of gradient methods for location far from a minimum. Quality of minimization and an accuracy of parameter estimates for six selected models are examined and compared with different derivative least-squares methods of five commercial regression packages.     

XMVB: a program for ab initio nonorthogonal valence bond computations

An ab initio nonorthogonal valence bond program, called XMVB, is described in this article. The XMVB package uses Heitler-London-Slater-Pauling (HLSP) functions as state functions, and calculations can be performed with either all independent state functions for a molecule or preferably a few selected important state functions. Both our proposed paired-permanent-determinant approach and conventional Slater determinant expansion algorithm are implemented for the evaluation of the Hamiltonian and overlap matrix elements among VB functions. XMVB contains the capabilities of valence bond self-consistent field (VBSCF), breathing orbital valence bond (BOVB), and valence bond configuration interaction (VBCI) computations. The VB orbitals, used to construct VB functions, can be defined flexibly in the calculations depending on particular applications and focused problems, and they may be strictly localized, delocalized, or bonded-distorted (semidelocalized). The parallel version of XMVB based on MPI (Message Passing Interface) is also available.     

Nonorthogonal ultralocalized functions and fitted Wannier functions for local electron correlation methods for solids

Despite the formal exponential decay behavior of Wannier functions (WFs), their spatial extent, which is a key parameter determining the computational cost of local correlation calculations for solids, is still rather large. The problems with the localization of the WFs can partly be attributed to their mutual orthogonality. Possibilities of reduction of the spatial extent of the WFs without losing the accuracy of the calculations are investigated. A method for generation of nonorthogonal ultralocalized functions based on maximization of their Löwdin populations is developed. A scheme for fitting of the WFs and nonorthogonal localized functions with a limited support is proposed. The calculations show that by combining both techniques one can obtain quite compact linearly independent localized functions, which may significantly decrease the computational cost in post-HF calculations.     

Exact finite series for the few-body auxiliary functions

The so-called few-body auxiliary functions play a very important role in bound-state calculations for nonrelativistic few-body systems. In particular, the functions of the first, second, and third orders are used in four-body calculations. By means of an original approach developed for the first time in the present study, we have found exact finite-series representations for the auxiliary functions A_n (n ≤ 3). It is shown that the auxiliary functions A_n are closely related to the Gaussian hypergeometric function ₂F₁. A few simple finite-series expansions are also presented, which seem to be very convenient for numerical computations. This work opens a new avenue in the study of auxiliary functions and their properties. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 269–278, 1997     

Contracted polarization functions for the atoms helium through neon

Contracted Gaussian-type function sets are proposed for polarization functions of the atoms helium through neon, with the exception of lithium. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the difference from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size. Received: 16 April 1997 / Accepted: 26 June 1997     

Evaluation of classification results with the disjoint classification program SOLOMON

Practical application of pattern recognition techniques is often limited because of the way in which variables are selected and the need for supplementation of missing data. The software package comprising the MICA transformation technique and the SOLOMON classification program is extended to include an algorithm for estimating and supplementing missing data. The performance of this package is compared with that of known classification techniques on simulated data sets. The supplementation algorithm is tested with a data set for hyperlipoproteinemia patients.     

Use of Nonlinear Frequency Response for Discriminating Adsorption Kinetics Mechanisms Resulting with Bimodal Characteristic Functions

One of the characteristic examples of the inability of the classical linear frequency response (FR) method to identify the correct kinetic mechanism is adsorption of some substances (p-xylene, 2-butane, propane or n-hexane) on silicalite-1. The linear FR resulted with bimodal FR characteristic functions, which fitted equally well to three different kinetic models: nonisothermal micropore diffusion, two independent isothermal diffusion processes, and an isothermal diffusion-rearrangement process. We show that the second order frequency response functions (FRFs), obtained from the nonlinear FR, can be used for discrimination among these three mechanisms. Starting from the nonlinear models, we derive the theoretical expressions for the first and second order FRFs corresponding to these three mechanisms and show that different shapes of the second order FRFs are obtained for each mechanism. This would enable identification of the real mechanism from nonlinear FR data.     

Structural correlations and motifs in liquid water at selected temperatures: ab initio and empirical model predictions

To gain further insight into liquid water's structure and explore the role of different physical forces underlying the interaction between water molecules, the radial and angular structure of water is probed as a function of temperature for a carefully selected set of theoretical models. Simulations are performed with empirical rigid, empirical polarizable, empirical flexible with classical and quantum nuclei, and ab initio models with classical nuclei at 300 and 353 K and quantum nuclei at 300 K. The predicted radial distribution functions, spatial maps, and angular distributions of the neighboring water molecules are consistent with a model of liquid water in which water molecules are tetrahedrally coordinated. In addition, three-dimensional joint distribution functions are introduced and analyzed. By comparison of the functions obtained for hexagonal ice to those of liquid water, several thermally disordered, ice-like cluster structures are identified in the fluid.     

Spherical hybrids

A general solution is presented to the problem of finding hybrid functions which point from the center toward the vertices of a regular solid. Results are given for the examples of 6, 8, 12, and 24 vertices. By taking linear combinations with suitable alias functions, the hybrids have been given nodes passing through all vertices except their own. This allows them to be used for interpolation and quadrature. The various functions required are defined as solid harmonics and group theoretical methods of generating these are discussed fully. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 197–214, 1997     

Influenza virus neuraminidase inhibitors: generation and comparison of structure-based and common feature pharmacophore hypotheses and their application in virtual screening

X-ray crystallographic data of the influenza virus neuraminidase in complex with different inhibitors were used to generate chemical feature-based pharmacophore models of the binding site of this enzyme. The models were built using the software package Catalyst. Pharmacophore hypotheses derived from the 3-D structure of ligands cocrystallized with the enzyme were then compared with automatically generated common feature pharmacophore hypotheses for neuraminidase inhibitors. The latter models were found to contain fewer features and exhibited lower selectivity in virtual screening experiments. Some functions of the inhibitors obviously participate in more than one mode of interaction with the enzyme (charge-charge interaction and hydrogen bond) or form hydrogen bonds to several amino acids. Since such multiple interactions of one chemical function cannot be included into the Catalyst data format, strategies are presented to overcome these limitations. Finally, the results of 3-D database searching experiments using these hypotheses are described.     

Parameters of models and conditional sensitivity coefficients of radial distribution functions for water calculated by molecular dynamics data

The influence of parameters of rigid models of the 12-6-1 type on the properties calculated in computer experiments, viz., radial distribution functions and internal energy, was studied by the method of step-by-step transform of the water models supplemented by calculations of conditional sensitivity coefficients.     

Atom and Bond Fukui Functions and Matrices: A Hirshfeld‐I Atoms‐in‐Molecule Approach

The Fukui function is often used in its atom‐condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms‐in‐molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld‐I atoms‐in‐molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld‐I approach to obtain atom‐ and bond‐condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms‐in‐molecule approach shows low correlation between the two partitioning schemes.     

Contracted polarization functions for the atoms Ca, Ga–Kr, Sr, and In–Xe

 Contracted Gaussian-type function sets are proposed for polarization functions of the atoms Ga–Kr and In–Xe. We also report polarization functions for Ca and Sr. A segmented contraction scheme is used for its compactness and computational efficiency. The contraction coefficients and orbital exponents are fully optimized to minimize the deviation from accurate atomic natural orbitals. The present polarization functions yield more than 99% of atomic correlation energies predicted by accurate natural orbitals of the same size. Received: 23 February 2001 / Accepted: 19 April 2001 / Published online: 13 June 2001