Density scaling and relaxation of the Pauli principle

The relaxation of the Pauli principle associated with density scaling is examined. Scaling the density has been investigated in the development of density functional computational methods with higher accuracy. Scaling the density by rho(r)(zeta)=rho(r)zeta reduces the number of electrons to M=Nzeta when zeta>1. The minimum kinetic energy of the scaled density, T(s)[rhozeta], can be scaled back to the N-electron system by multiplying the M-electron Kohn-Sham-type occupation numbers by zeta to produce T(zeta)[rho]. This relaxes the Pauli principle when the orbital occupation numbers are greater than 1 in the N-electron system. The effects of antisymmetry on solutions to the Kohn-Sham equations are examined for Ne and the Be isoelectronic series. The changes in T(zeta)[rho] and the exchange energy E(xzeta)[rho] when zeta is varied show that these two quantities are inextricably linked.     

The forces of symmetry and the physical meaning of the Pauli exclusion principle

Russian Chemical Bulletin - A mathematically strict analysis of the consequences of the requirement of wave function antisymmetry is presented. It is shown that the probability density for...     

Is the Pauli exclusive principle an independent quantum mechanical postulate?

Foundation of the Pauli exclusive principle is discussed. It is demonstrated that the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusive principle. The heuristic arguments are given in favor that the existence in nature of only the nondegenerate permutation representations (symmetrical and antisymmetrical) is not occasional. As follows from our analysis of possible scenarios, the permission of degenerate permutation representations leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of degenerate permutation states by the Pauli exclusive principle follows from the general physical assumptions inside quantum theory, but the problem of spin–statistics connection is still open. It is pointed out that the Pauli exclusive principle and the Jahn–Teller effect have some similar features. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

An interpretation of Hund's rule

An interpretation of Hund's rule is presented. The Pauli principle, the variational principle and the virial theorem are shown to be essentially sufficient to account for the roles of the various energetic components in establishing the inter-multiplet separation.

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Zusammenfassung Es wird eine Interpretation der Hundschen Regel gegeben. Das Pauliprinzip, das Variationsprinzip und das Virialtheorem sind im wesentlichen ausreichend, um die Rollen der verschiedenen energetischen Komponenten beim Zustandekommen der Inter-Multiplett-Separation zu erklärenwie hier gezeigt wird.

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Based on a section of a thesis to be submitted to the senate of the Technion — Israel Institute of Technology, in partial fulfilment of the requirements for the D. Sc. degree.     

Examination of the Hund rule in closed-shell systems: Investigation of spin correlation effects

The validity of the Hund rule in atomic orbitals (AO s) of the carbon atoms inside closed-shell molecules, such as acetylene, ethylene, and ethane, is examined. Electron-pair populations and contributions of the two-electron covalent structures with parallel (?) and antiparallel (↑↓) spins are calculated by multielectron population analysis of MO + CI wave functions. Such an analysis, which allows the visualization of various cooperative electronic effects in some target AO s, is extended on the basis of (strictly orthogonal) hybrid orbitals. Although the HF level shows, incorrectly, that the Hund rule is not satisfied, the CI clearly shows a preference for (?) spins to those of (↑↓): This holds for both the electron-pair populations [those of (↑↓) spins diminish with the CI more drastically than those of (?) spins], as well as for contributions of the two-electron covalent structures [those of (?) spins increase with the CI more drastically than do those of (?) spins]. The calculation of the correlation functions (or dependent functions) in AO space allows the comparison of repulsive or “attractive” behaviour of (?) and (↑↓) spins in various AO couples. Mutual dependence of the two electrons inside the sigma system increases in the series ethane < ethylene < acetylene. Also found is that parallel spins in (pure) AO s of sigma systems are preferred to the antiparallel spins when going from ethane to acetylene. The preference parallel–antiparallel spins in AO s belonging to two different atoms, including hydrogens, is also examined. © 1993 John Wiley & Sons, Inc.     

Decomposition and interpretation of the SCF interaction and deformation energies by the modified Pauli Blockade method

The SCF interaction energy in He … Li⁺, (H₂O) … HOH, and OC … BH₃ complexes is decomposed, using the original and modified-by-the-author Pauli Blockade (PB ) method of Gutowski and Piela. The changes of the dipole moment of the deformed constituents are similarly decomposed and discussed as some indices of the deformation. The deformation is due mainly to the electrostatic interaction, but in some cases, the valence repulsion deformation effects are dominant. The comparison of the PB technique with some other decompositions is discussed. The PB methods seem to be more widely applicable, e.g., they are applicable for small intermolecular distances and large basis sets. The modified PB method is less-time consuming than is the original one. © 1993 John Wiley & Sons, Inc.     

A study of the interpretation of Hund's rule

Energy differences between atomic terms belonging to the same configuration are analysed into their components, kinetic energy, nuclear attraction and interelectronic repulsion. The results are discussed from the point of view of the interpretation of Hund's rule. The main conclusion is that the energy differences between terms are essentialy determined by nuclear attraction differences, an obvious contradiction to the traditional interpretation of Hund's rule.

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Zusammenfassung Die Energieunterschiede zwischen Atomtermen mit derselben Konfiguration werden mit Hilfe der Zerlegung in kinetische Energie, Kernanziehung und Elektronenabstoßung untersucht. Die Ergebnisse werden im Hinblick auf die Interpretation der Hundschen Regel diskutiert. Das Hauptergebnis ist, daß die Energiedifferenzen zwischen Termen im wesentlichen durch die Differenzen in der Kernanziehung bestimmt sind; dies stellt einen offensichtlichen Widerspruch zur traditionellen Interpretation der Hundschen Regel dar.

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Résumé Analyse des différences d'énergie entre termes atomiques appartenant à la même configuration selon leurs composantes: énergie cinétique, attraction nucléaire et répulsion interélectronique. Les résultats sont discutés du point de vue de l'interprétation de la règle de Hund. La conclusion principale est que les différences d'énergie entre les termes sont essentiellement déterminées par les différences d'attraction nucléaire, ce qui est en contradiction évidente avec l'interprétation traditionnelle de la règle de Hund.

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Based on a part of a thesis to be submitted to the senate of the Technion-Israel Institute of Technology, in partial fulfilment of the requirements for the D. Sc. degree.     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

The principle and basic theory of the quotient calorimeter

Summary A novel method for dynamic determination of caloric properties is described. The measurement result is directly obtained as the ratio of the heat capacity of the sample under test to that of an inert reference sample. To a first approximation, the result is not affected by non-linear heating or cooling, temperature dependent heat conductance, and construction tolerances. The second order errors introduced by these effects are discussed; typically, they are below 1%.

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Zusammenfassung Ein neuartiges Verfahren zur dynamischen Bestimmung kalorischer Größen wird beschrieben, bei dem das Meßresultat direkt aus dem Verhältnis der Wärmekapazität der Meßprobe zu der einer inerten Vergleichsprobe gebildet wird. Das Meßergebnis wird in erster Näherung nicht durch nichtlineare Aufheizung oder Abkühlung, temperaturabhängige Wärmeübertragung und Herstellungstoleranzen beeinflußt. Die Fehler zweiter Ordnung, die durch diese Effekte entstehen, werden diskutiert; sie liegen i. a. unterhalb 1%.

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With 4 figures and 1 table     

Electron-electron cusp condition and asymptotic behavior for the Pauli potential in pair density functional theory

In the ground state, the pair density n can be determined by solving a single auxiliary equation of a two-particle problem. Electron-electron cusp condition and asymptotic behavior for the Pauli potential of the effective potential of the two-particle equation are presented.     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.     

Experimental test of the possible violation of the Pauli exclusion principle by photo-activation analysis of carbon content in pure boron

Experiments which search for chemically boron-like carbon nuclei in samples of pure boron were carried out by a photo-activation technique. Use was made of the ¹²C(γn)¹¹C reaction with irradiation by bremsstrahlung photons of below 30 MeV. The resulting positron active isotope carbon-11 has a half-life of 20 min, and there are no radioactive nuclides formed by boron. These features of carbon-11 allow use of the rather sensitive and selective γ-γ coincidence technique to detect carbon nuclei. Special radiochemical procedures were developed for purification of the samples from initial carbon and metal impurities in the samples. Experimental results provided an estimate of the lifetime of atomic electrons relative to the Pauli exclusion principle of T > 10²¹ yr.     

Graph theory and molecular orbitals. The loop rule

Graph theory is applied to the study of the dependence of total π-electron energy, π-electron charge distribution and free valency indices of conjugated hydrocarbons on molecular topology. It is shown that the number of loops in the molecular graph determines these quantities.     

原子和分子片的洪特多重度规则的量子化学解释

以7种原子和5种分子片物种为例，采用UHF／6—311＋＋G（3df，2p）方法，优化了它们的电子在垂直和绝热跃迁过程中的构型，计算了相同电子组态，不同低自旋态和高自旋态物种的最低单点能量（ES，ET）；比较了它们的最高占据轨道能量（低态能εS-HOMO，高态能εT-HOMO）．结果发现，无论是绝热还是垂直变化过程，也不论键距长短，总会存在如下关系：△εHOMO=εS-HOMO—εT-HOMO〉0，△ES-T≈△εHOMO〉0．最后证明了这些关系式．     

Information theory applied to feature selection of binary-coded infrared spectra for automated interpretation by retrieval of reference data

A method is described for feature selection from infrared spectra, intended for identification of organic compounds by computer-aided retrieval of reference data contained in small files. Complete discrimination of the binary-coded spectra is achieved by selecting a minimum number of spectral features; the information content is used as the selection criterion. The selection procedure is applied to five data sets (saturated and unsaturated hydrocarbons, alcohols, ethers and aldehydes/ketones) involving some 400 spectra. Each spectrum is uniquely coded by using about 10% of the 140 spectral features (binary-coded peak positions) available originally. For the intensity, a threshold of 50% appears to be applicable in some cases. For coding the frequency or wavelength parameter, wavenumbers (cm^-1) are preferred to wavelengths (mm). The method takes into account the a priori probabilities of spectral features and their correlations. Results of a retrieval program for a few “unknown” spectra are given.