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  • 1
    ISSN: 1432-2234
    Keywords: Key words: Two-electron intracule density ; Electron-pair distance ; Atomic subshell radius ; Position space ; Momentum space
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. For the 53 neutral atoms from He to Xe in their ground states, the average distances 〈 u〉 n l , n ′ l ′ in position space and 〈 v〉 n l , n ′ l ′ in momentum space between an electron in a subshell nl and another electron in a subshell n ′ l ′ are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances 〈 u〉 n l , n ′ l ′ in position space have an empirical but very accurate linear correlation with a one-electron quantity U n l , n ′ l ′≡L r +S r 2/(3L r ), where L r and S r are the larger and smaller of subshell radii 〈 r〉 n l and 〈 r〉 n ′ l ′, respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances 〈 〉 n l , n ′ l ′ have an accurate linear correlation with a one-electron momentum quantity V n l , n ′ l ′≡L p +S p 2/(3L p ), where L p and S p are the larger and smaller of average subshell momenta 〈 p〉 n l and 〈 p〉 n ′ l ′, respectively. Trends in the proportionality constants between 〈 u〉 n l , n ′ l ′ and U n l , n ′ l ′ and between 〈 〉 n l , n ′ l ′ and V n l , n ′ l ′ are discussed based on a hydrogenic model for the subshell radial functions.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-2234
    Keywords: Key words: Contracted Gaussian-type basis sets ; Third-row atoms ; Cu2 molecule
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu2 molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2234
    Keywords: Key words: Hartree ; Fock wave functions ; Slater ; type functions ; Atoms Cs to Lr
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract.  Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-2234
    Keywords: Key words: Valence 4p basis functions – Gaussian-type functions – First-row transition atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. For the valence 4p orbitals of the first-row transition metal atoms Sc through Zn, Gaussian-type basis functions are developed referring to excited 3d  m 4s 14p 1 electronic configurations. Molecular tests of the present work 4p sets are performed for the Cu atom, the diatomic Cu2 molecule, and Cu9 and Cu13 clusters, and the results are compared with those from two literature sets.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 105 (2000), S. 96-99 
    ISSN: 1432-2234
    Keywords: Key words: Isomorphism – Electron-pair density – Intracule density – Extracule density – Atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. The spherically averaged electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are a couple of densities which characterize the motion of electron pairs in atomic systems. We study a generalized electron-pair density (q; a, b) that represents the probability density function for the magnitude of two-electron vector a r j +b r k of any pair of electrons j and k to be q, where a and b are nonzero real numbers. In particular, h(u)=g(u;1, −1) and d(R) = . It is shown that the scaling property of the Dirac delta function and the inversion symmetry of orbitals in atoms due to the central force field generate several isomorphic relations in the electron-pair density (q; a, b) with respect to the two parameters a and b. The approximate isomorphism d(R)≅8h(2R) known in the literature between the intracule and extracule densities is a special case of the present results.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1432-2234
    Keywords: Momentum electron density ; H 2 + System
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The method of momentum electron density for interatomic interactions has been applied to the two lowest σ states of the H 2 + system. For attractive (1sσg) and repulsive (2pσ u ) interactions, the behaviour of momentum density and its effect on the stabilization energy of the system are examined quantitatively. The concept of contraction and expansion of the momentum density is shown to form an important guiding principle in this approach. The origin of covalent bonding is discussed based on the energy partitioning proposed previously.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 59 (1981), S. 639-648 
    ISSN: 1432-2234
    Keywords: Momentum electron density ; Hellmann-Feynman theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The integrated Hellmann-Feynman theorem is used to derive a rigorous relation between the energy and the electron density in momentum space. Choosing the electron mass as a differential parameter, we obtain a formula corresponding to the Wilson-Frost formula in coordinate space. Analysing the mass-dependence of momentum density, we then show that the present formula is equivalent to one of the previous results deduced from the virial theorem. Use of the integral Hellmann-Feynman theorem is also discussed. Several illustrative examples are given for the calculation of energy from momentum density.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1432-2234
    Keywords: Nuclear charge effect ; Chemical bonding ; Hellmann-Feynman theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract For a one-electron homonuclear diatomic system with arbitrary nuclear charge Z, the change in the nature of diatomic interaction and its density origin are quantitatively examined as a function of Z by the method of binding/antibinding analyses based on the Hellmann-Feynman theorem. In the Isσg ground state, two energy extrema, potential barrier at a large internuclear distance and potential minimum at a smaller distance, appear for 1〈Z〈1.44. The binding part of the partitioned Hellmann-Feynman forces suffers little effect of Z, and these two extrema are attributed respectively to the increase in the nuclear repulsion and to the decrease in the antibinding part of the partitioned forces. In the “antibonding” 2pσu state, a stable molecule is formed for Z〈1. This appearance of the bonding nature is shown to have its origin in the binding part which is almost unchanged by the decrease of Z.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 64 (1984), S. 249-257 
    ISSN: 1432-2234
    Keywords: Compton profile ; Momentum density ; Characteristic function ; Moments of momentum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Methods of constructing approximate Compton profiles J(q) are proposed and compared, when only the energy E of a system is known. For the q-range of interest, the inferential Compton profiles are shown to be of the accuracy of the non-variational single STO (Slater-type orbital) description for atoms.
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  • 10
    ISSN: 1432-2234
    Keywords: Momentum density ; BH 2 − and BH 2 + ; geometries of ∼ ; virial theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Based on a special form of the molecular virial theorem, the recently proposed method of momentum density for interatomic interactions is here applied to the problem of molecular geometry. Two molecules BH 2 − and BH 2 + , which have the same nuclear framework but favor respectively bent and linear conformations, are comparatively studied. Using an approximate Hartree-Fock momentum density, the total molecular energy (including the nuclear repulsion) is partitioned into orbital components, and a geometry correlation diagram is derived. An atom-bond partitioning of the total energy is also examined based on the one- and two-center decomposition of the momentum density.
    Type of Medium: Electronic Resource
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