Determination of molecular properties by the method of moments

The method of moments and the method of least squares is applied to electron scattering on a simple model potential. Some general problems connected with treatment of scattering problems by the method of moments and the method of least squares are discussed. The calculations give an example of the random sampling type error estimates discussed in previous papers of the series, and present a possible way of optimizing nonlinear parameters in the framework of the method of moments and the method of least squares.

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Zusammenfassung Die Momentenmethode und die Methode der kleinsten Quadrate wird auf die Elektronenstreuung an einem einfachen Modellpotential angewandt. Einige allgemeine Probleme bei der Anwendung dieser beiden Methoden auf Streuprobleme wurden diskutiert. Die Berechnungen geben ein Beispiel der Fehlerabschätzung vom Stichproben-Typ, der in vorhergehenden Artikeln dieser Serie untersucht wurde; sie stellen eine Möglichkeit der Optimierung nicht-linearer Parameter bei den genannten zwei Methoden dar.

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Résumé La méthode des moments et la méthode des moindres carrés sont appliquées à l'étude de la diffusion électronique sur un potentiel modèle simple. Discussion de certains problèmes généraux liés à l'emploi de ces méthodes à l'étude de la diffusion. Les calculs donnet un exemple de l'estimation d'erreur par échantillonage discutée dans les articles précédents, et présentent une méthode pour optimiser des paramètres non linéaires dans le cadre des méthodes des moments et des moindres carrés.

     

Determination of molecular properties by the method of moments

Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

Riemannian three dimensional molecular spaces

A simple manipulation of the first order density function permits to define a curved 3D Riemannian coordinate set, which can substitute the usual flat 3D Cartesian space, where atoms and molecules are supposed to exist. Several simple models are discussed. Gaussian type orbitals generate a space division with positive and negative curvatures, the later one being near the centre of the functions; contrarily Slater type orbitals provide a positive curvature everywhere.     

Determination of molecular properties by the method of moments. I

The method of moments appears to have some significant advantages over other variational methods of quantum chemistry if complicated molecular systems are investigated and elaborate variational wave functions are applied. The main advantages are (a) the possibility of avoiding the worst difficulties of integration or reducing the number of integrals (b) the possibility of improving the accuracy of the wave function in physically important regions of the configurational space and (c) the possibility of obtaining some random sampling type error estimates. The aim of the series of papers starting with the present one is to collect experience in applying the method of moments to problems of quantum chemistry.

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Zusammenfassung Die Methode der Momente scheint gegenüber den üblichen Variationsmethoden in der Quantenchemie einige bedeutende Vorteile zu besitzen, besonders wenn es sich um Untersuchungen komplizierter molekularer Systeme handelt, die nur mit umfangreichen Variationswellenfunktionen behandelt werden können. Die Hauptvorteile der neuen Methode sind: (a) Die bei der Integration auftretenden großen Schwierigkeiten bzw. die Anzahl der zu berechnenden Integrale können erheblich herabgesetzt werden. (b) In den physikalisch besonders wichtigen Bereichen des Konfigurationsraumes besteht die Möglichkeit, die Wellenfunktionen beträchtlich zu verbessern. (c) Es können Fehlerabschätzungen gemacht werden. Ziel dieser Arbeit ist es, erste Erfahrungen in der Anwendung der neuen Rechenmethode auf quantenchemische Probleme zu sammeln.

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Résumé La méthode des moments parait posséder des avantages nets sur les autres méthodes variationnelles de la chimie quantique si l'on étudie des systèmes moléculaires complexes et si l'on utilise des fonctions d'onde variationnelles perfectionnées. Les avantages principaux sont a) la possibilité d'éviter les difficultés les plus gênantes de l'intégration et de réduire le nombre d'intégrales; b) la possibilité d'améliorer la précision de la fonction d'onde dans les régions de l'espace de configuration les plus importantes pour une observable, et c) la possibilité d'obtenir des évaluations du type «échantillonnage au hasard» des erreurs commises. Le but de la série d'articles qu'inaugure celui-ci est de présenter une information sur l'application de la méthode des moments aux problèmes de la chimie quantique.

     

Determination of molecular properties by the method of moments. II

The wave functions and energies of a number of diatomic molecules have been determined for different nuclear separations by both the method of energy variation and the method of moments. The results obtained by the two methods are compared and indicate definite advantages of the method of moments over the method of energy variation.

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Zusammenfassung Für eine Reihe zweiatomiger Moleküle werden für verschiedene Kernabstände die Wellenfunktionen und Energien nach der Methode der Energievariation und nach der neueren Momentenmethode bestimmt. Der Vergleich der Ergebnisse zeigt, daß die Momentenmethode erhebliche Vorteile besitzt gegenüber der üblichen Methode der Energievariation.

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Résumé Les fonctions d'onde et les énergies de plusieurs molécules diatomiques ont été déterminées à différentes distances internucléaires par la méthode de variation de l'énergie et par la méthode des moments. Les résultats comparés des deux méthodes indiquent de nets avantages de la méthode des moments sur la méthode de variation de l'énergie.

     

Determination of molecular properties by the method of moments. III

The wave functions of the water and the ammonia molecules have been determined for many nuclear configurations by both the method of moments and the method of energy variation. The accuracy of the results obtained by the two methods is similar although the method of moments requires considerably less integrational work. Some technical problems connected with the use of the method of moments are discussed.

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Zusammenfassung Die Wellenfunktionen des Wasser- und Ammoniakmoleküls wurden für mehrere molekulare Konfigurationen nach der Momentenmethode und der Methode der Energievariation bestimmt. Die Genauigkeit beider Methoden ist ungefähr gleich, obwohl bei der Momentenmethode weniger Aufwand an Integration benötigt wird. Einige technische Probleme bei der Verwendung der Momentenmethode werden diskutiert.

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Résumé Les fonctions d'onde de l'eau et de l'ammoniac ont été déterminées pour de nombreuses configurations nucléaires par la méthode des moments et la méthode variationnelle. Les précisions atteintes par les deux méthodes sont comparables quoique la méthode des moments nécessite un moindre effort sur le plan des intégrations. Discussion de certains problèmes techniques liés à l'emploi de la méthode des moments.

     

Solutions to the Quantum QSPR problem in molecular spaces

The molecular quantum similarity framework is used to present a new set of Quantum Quantitative Structure– Properties Relationship (QQSPR) procedures. The theoretical basis consists of the so-called fundamental QQSPR equation, deducible from quantum mechanical first principles, associated with the quantum mechanical expectation values computation. Approximate solutions of the fundamental QQSPR equation within direct and reciprocal spaces, containing molecular density functions, are studied in a common framework. Contribution to the Serafín Fraga Memorial Issue. This paper is dedicated to Serafín Fraga and Xavier Gironès, in memoriam. They have formed part of my life as a scientist: I had been an apprentice with the first and I tried to be a teacher with the second. I learned from both, though. They will be like stars in my mind, until we can walk together the endless path of nothingness.     

Anomaly of CH4 molecular assembly confined in single-wall carbon nanohorn spaces

Vibrational-rotational properties of CH(4) adsorbed on the nanopores of single-wall carbon nanohorns (SWCNHs) at 105-140 K were investigated using IR spectroscopy. The difference vibrational-rotational bands of the ν(3) and ν(4) modes below 130 K show suppression of the P and R branches, while the Q branches remain. The widths of the Q branches are much narrower than in the bulk gas phase due to suppression of the Doppler effect. These results indicate that the rotation of CH(4) confined in the nanospaces of SWCNHs is highly restricted, resulting in a rigid assembly structure, which is an anomaly in contrast to that in the bulk liquid phase.     

Calculations of molecular properties in hybrid coupled-cluster and molecular mechanics approach

We report benchmark calculations obtained with our new coupled-cluster singles and doubles (CCSD) code for calculating the first- and second-order molecular properties. This code can be easily incorporated into combined [Valiev, M.; Kowalski, K. J. Chem. Phys. 2006, 125, 211101] classical molecular mechanics (MM) and ab initio coupled-cluster (CC) calculations using NWChem, enabling us to study molecular properties in a realistic environment. To test this methodology, we discuss the results of calculations of dipole moments and static polarizabilities for the Cl2O system in the CCl4 solution using the CCSD (CC with singles and doubles) linear response approach. We also discuss the application of the asymptotic extrapolation scheme (AES) [Kowalski, K.; Valiev, M. J. Phys. Chem. A 2006, 110, 13106] in reducing the numerical cost of CCSD calculations.     

Determination of the molecular symmetry in crystalline germane

The symmetry of the germane molecule in the various crystalline phases of solid germane has been investigated using the IR spectrum of the isotopically dilute GeH₃D molecule. The observed spectra indicate that the cubic crystal symmetry of the higher-temperature phases is lost in phase III and possible site symmetries are proposed. Band broadening is found in phase I and is interpreted as arising from rapid molecular reorientation.     

分子荧光法测定水中的微量铁

基于Fe（Ⅱ）与邻菲口罗啉生成络合物使其荧光猝灭的特性,讨论了在室温下,pH 5.5的乙酸-乙酸铵的缓冲介质中,以λex=270 nm为激发波长,于eλm=365 nm波长处测定该络合物荧光强度。结果表明Fe（Ⅱ）质量浓度在0.8-120.0 ng/mL范围内与络合物的荧光强度具有良好的线性关系,相关系数0.9994,检出限0.50 ng/mL。对60 ng/mL的Fe RSD（n=9）为2.8%。Fe的回收率为98.03%-102.9%。方法已用于水中微量铁的测定。     

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.