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Pair Density (pair + density)

Distribution by Scientific Domains

Chemistry	75%

Kinds of Pair Density

electron pair density

Selected Abstracts

Necessary conditions for the N -representability of pair distribution functions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2006
Paul W. Ayers
Abstract A necessary condition for the N -representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N -representability conditions for the second-order density matrix. The extension to spin-resolved electron pair densities is considered, as is the extension to higher-order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N -representability constraints are considered. For reference, constraints for the N -representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

The 2-matrix of the spin-polarized electron gas: contraction sum rules and spectral resolutions

ANNALEN DER PHYSIK, Issue 3 2004
P. Ziesche
Abstract The spin-polarized homogeneous electron gas with densities ,, and ,, for electrons with spin ,up' (,) and spin ,down' (,), respectively, is systematically analyzed with respect to its lowest-order reduced densities and density matrices and their mutual relations. The three 2-body reduced density matrices ,,,, ,,,, ,a are 4-point functions for electron pairs with spins ,,, ,,, and antiparallel, respectively. From them, three functions G,,(x,y), G,,(x,y), Ga(x,y), depending on only two variables, are derived. These functions contain not only the pair densities according to g,,(r) = G,uarr;(0,r), g,,(r) = G,,(0,r), ga(r) = Ga(0,r) with r = |r1 - r2|, but also the 1-body reduced density matrices ,, and ,, being 2-point functions according to ,s = ,sfs and fs(r) = Gss(r, ,) with s = ,,, and r = |r1 - r,1|. The contraction properties of the 2-body reduced density matrices lead to three sum rules to be obeyed by the three key functions Gss, Ga. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions n,(k) and n,(k), following from f,(r) and f,(r) by Fourier transform, are correctly normalized through fs(0) = 1. In addition to the non-negativity conditions ns(k),gss(r),ga(r) , 0 [these quantities are probabilities], it holds ns(k) , 1 and gss(0) = 0 due to the Pauli principle and ga(0) , 1 due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin-polarized case and (ii) to the 2-body reduced density matrix giving thus its spectral resolutions. [source]

Resonance Structures of the Amide Bond: The Advantages of Planarity

CHEMISTRY - A EUROPEAN JOURNAL, Issue 27 2006
Jon I. Mujika
Abstract Delocalization indexes based on magnitudes derived from electron-pair densities are demonstrated to be useful indicators of electron resonance in amides. These indexes, based on the integration of the two-electron density matrix over the atomic basins defined through the zero-flux condition, have been calculated for a series of amides at the B3LYP/6-31+G* level of theory. These quantities, which can be viewed as a measure of the sharing of electrons between atoms, behave in concordance with the traditional resonance model, even though they are integrated in Bader atomic basins. Thus, the use of these quantities overcomes contradictory results from analyses of atomic charges, yet keeps the theoretical appeal of using nonarbitrary atomic partitions and unambiguously defined functions such as densities and pair densities. Moreover, for a large data set consisting of 24 amides plus their corresponding rotational transition states, a linear relation was found between the rotational barrier for the amide and the delocalization index between the nitrogen and oxygen atoms, indicating that this parameter can be used as an ideal physical-chemical indicator of the electron resonance in amides. [source]

Inequivalent electron densities derived from an approximate correlated ground-state wave function using the Hiller,Sucher,Feinberg identity: Comparisons with quantum Monte Carlo densities for He and Ne atoms

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2009
Claudio Amovilli
Abstract The Hiller,Sucher,Feinberg (HSF) identity is combined with the three-parameter correlated wave function of Chandrasekhar in order to generate an alternative electron density ,(r) for the He atom. This and the conventional "local" operator form of ,(r) are then compared with a diffusion quantum Monte Carlo density. An exact limiting relation is also presented, via HSF identity, between the one-particle density matrix and the pair density in a many-electron atom, which transcends its Hartree,Fock counterpart and has no N -representability difficulties. For the Ne atom, the accuracy of the semiempirical correlated electron density recently obtained by Cordero et al. (Phys. Rev. A 2007, 75, 052502) using fine-tuning of Hartree,Fock theory was assessed by appealing to the ground-state density from diffusion quantum Monte Carlo. The high accuracy of the Cordero et al. density was thereby confirmed. A HSF calculation on neon, with a correlated many-body wave function as starting point, is a worthwhile future aim. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

Necessary conditions for the N -representability of pair distribution functions

Electron localizability indicators ELI and ELIA: The case of highly correlated wavefunctions for the argon atom

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2008
Viktor Bezugly
Abstract Electron localizability indicators based on the same-spin electron pair density and the opposite-spin electron pair density are studied for correlated wavefunctions of the argon atom. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations aiming at the understanding of the effect of local electron correlation when approaching the exact wavefunction. The populations of the three atomic shells of Ar atom in real space are calculated for each case. © 2007 Wiley Periodicals, Inc. J Comput Chem 29: 1198,1207, 2008 [source]

Chemical bonding: From Lewis to atoms in molecules

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 1 2007
R. F. W. Bader
Abstract The Lewis electron pair concept and its role in bonding are recovered in the properties of the electron pair density and in the topology of the Laplacian of the electron density. These properties provide a bridge with the quantum mechanical description of bonding determined by the Feynman, Ehrenfest, and virial theorems, bonding being a consequence of the electrostatic forces acting within a molecular system. © 2006 Wiley Periodicals, Inc. J Comput Chem, 2007 [source]

Wave functions derived from experiment.

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 4 2003

Abstract The constrained Hartree,Fock method using experimental X-ray diffraction data is extended and applied to the case of noncentrosymmetric molecular crystals. A new way to estimate the errors in derived properties as a derivative with respect to added Gaussian noise is also described. Three molecular crystals are examined: ammonia [NH3], urea [CO(NH2)2], and alloxan [(CO)4(NH)2]. The energetic and electrical properties of these molecules in the crystalline state are presented. In all cases, an enhancement of the dipole moment is observed upon application of the experimental constraint. It is found that the phases of the structure factors are robustly determined by the constrained Hartree,Fock model, even in the presence of simulated noise. Plots of the electron density, electrostatic potential, and the electron localization function for the molecules in the crystal are displayed. In general, relative to the Hartree,Fock model, there is a depletion of charge around hydrogen atoms and lone pair regions, and a build-up of charge within the molecular framework near nuclei, directed along the bonds. The electron localization function plots reveal an increase in the pair density between vicinal hydrogen atoms. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 470,483, 2003 [source]

Use of Restored Small Wetlands by Breeding Waterfowl in Prince Edward Island, Canada

RESTORATION ECOLOGY, Issue 1 2003
C. E. Stevens
Abstract Since 1990 under the Eastern Habitat Joint Venture over 100 small wetlands have been restored in Prince Edward Island, Canada. Wetlands were restored by means of dredging accumulated sediment from erosion to emulate pre-disturbance conditions (i.e., open water and extended hydroperiod). In 1998 and 1999 we compared waterfowl pair and brood use on 22 restored and 24 reference wetlands. More pairs and broods of Ring-necked Ducks, Gadwall, Green-winged Teal, and American Black Ducks used restored versus reference wetlands. In restored wetlands waterfowl pair density and species richness were positively correlated with wetland/cattail area, percent cattail cover, and close proximity to freshwater rivers. In addition, a waterfowl reproductive index was positively correlated with percent cattail cover. Green-winged Teal pair occurrence in restored wetlands was positively correlated with greater amounts of open water and water depths. American Black Duck pairs occurred on most (86%) restored wetlands. Restored small wetlands likely served as stopover points for American Black Duck broods during overland or stream movements, whereas they likely served as a final brood-rearing destination for Green-winged Teal broods. We suggest that wetland restoration is a good management tool for increasing populations of Green-winged Teal and American Black Ducks in Prince Edward Island. [source]

The high-density electron gas: How momentum distribution n (k) and static structure factor S(q) are mutually related through the off-shell self-energy , (k, ,)

ANNALEN DER PHYSIK, Issue 10 2010
P. Ziesche
For the spin-unpolarized uniform electron gas, rigorous theorems are used (Migdal, Galitskii-Migdal, Hellmann-Feynman) which allow the calculation of the pair density, g(r), or equivalently its Fourier transform, the static structure factor, S(q), from the dynamical 1-body self-energy , (k, ,), supposing the self-energy is (approximately) known as a functional, depending on the kinetic energy of a single electron, t(k), and on the bare Coulomb repulsion between two electrons, v(q). With the momentum distribution, n(k), and with the kinetic (t) and potential (v) components of the total energy e = t + v, the respective steps are: (i) , (k, ,) , n(k) , t, (ii) , (k, ,) , v, (iii) t + v = e, S(q). How this general scheme works in detail is shown explicitly for the high-density limit (as an illustration). For this case the ring-diagram partial summation or random-phase approximation applies. In this way, the results of Macke (1950), Gell-Mann/Brueckner (1957), Daniel/Vosko (1960), Kulik (1961), and Kimball (1976) are summarized in a coherent manner. Besides, several identities were brought to the light, e.g. the Kimball function for S(q) proves to be identical with Macke's momentum transfer function I(q) for e. [source]

Charge-Shift Bonding,A Class of Electron-Pair Bonds That Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach

CHEMISTRY - A EUROPEAN JOURNAL, Issue 21 2005
Sason Shaik Prof.
Abstract This paper deals with a central paradigm of chemistry, the electron-pair bond. Valence bond (VB) theory and electron-localization function (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair density plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RECS, and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contributions to the bond energy. The paper defines the atomic propensity and territory for CS bonding: Atoms (fragments) that are prone to CS bonding are compact electronegative and/or lone-pair-rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and involves: a) homopolar bonds of heteroatoms with zero static ionicity, b) heteropolar , and , bonds of the electronegative and/or electron-pair-rich elements among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental manifestations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reactions as compared to hydrogen-transfers. [source]