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881.
The electronic structure of the tetrahedral molecule VCL4 is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ4 = 1.10) and 4p(d 3 p 2) orbitals have been established, but V 3d(d n ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a 1, 2 e and 4t 2 molecular orbital (ground state electronic configurations2 A 1,2 E, and2 T 2, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,2 A 1,2 E, and2 T 2, are investigated as functions of the component 3d(d n ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant2 A 1 and2 T 2 calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the2 E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl4 of 4t 2 < 3a 1 < 2e < 5t 2 seems most consistent with the numerous calculations. This suggested ground state electronic configuration of2 T 2 introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl4. Experimental data pertinent to the electronic structure of VCl4 has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations. 相似文献
882.
Dr. Bernhard Reiser 《Theoretical chemistry accounts》1976,41(4):287-299
The success of perturbation calculations of second order for the NFE (“Nearly Free Electron”) metals and that of the two-parameter model of Pettifor for the transition elements show that the lattice-stability of the metals has simple physical reasons. Using the results of Harrison, Heine and Weaire, Deegan, and Pettifor, a model is developed which allows to explain the stability of the three metal lattices in terms of differences in the potentials. Only those potential differences are considered which are caused by the different packing of the lattices. With the aid of the virial theorem the band structure energy is connected with the potential bandstructure energy. The sequence of stability is predicted to be body centered cubic (bcc), hexagonal close packed (hcp), face centered cubic (fcc) with increasing valence electron concentration. The ranges of stability can be expressed in simple numbers. This simple model holds in principle for NFE as well as for transition metals because it contains no assumptions restricted to only one of these metal types. Deviations of the observed lattice stability from the model can be understood from the approximations involved. 相似文献
883.
Dr. J. Dembczyński W. Ertmer U. Johann P. Stinner 《Zeitschrift für Physik A Hadrons and Nuclei》1980,294(4):313-317
The hyperfine structure of the metastable atomic states (3d 74s)5 F 2,3,4,5 and (3d 7 4s)3 F 2,3,4 of57Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(5 F 2)=55.994(7) MHzA(5 F 3)=69.632(5) MHzA(5 F 4)=78.435(4) MHzA(5 F 5)=87.246(3) MHzA(3 F 2)=143.328(4) MHzA(3 F 3)=50.602(10) MHzA(3 F 4)=13.456(5) MHz 相似文献
884.
Prof. Dr. Edmund Hlawka 《Monatshefte für Mathematik》1980,89(1):19-44
A new proof of a theorem of W. Neiss is given that the rays of the Quadratwurzelschnecke are uniformly distributed mod 2 . The exact order of the discrepancy of the sequence is determined. Multidimensional generalizations of this sequence are also considered. It is shown that the Quadratwurzelschnecke is something like a roulette.
Mit 2 Abbildungen
Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet 相似文献
Mit 2 Abbildungen
Herrn Prof. R. M. Redheffer in Freundschaft zum 60. Geburtstag gewidmet 相似文献
885.
Dr. Lisa Hefendehl-Hebeker 《Monatshefte für Mathematik》1980,90(3):219-228
Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set
of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT
1. If the trivial algebra
is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF
*; forr3 the space is notT
1. The set of division algebras is open in. 相似文献
886.
Dr. Frank Piefke 《Monatshefte für Mathematik》1980,89(1):45-56
We continue our investigations started in a paper with the same title. The -length of a curve defined in this paper can be written as an integral along the curve. Furthermore, we determine necessary and sufficient conditions for the existence of a measure of orientated lines which generates a given non-symmetric pseudo-metric.
Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet 相似文献
Herrn Prof. Dr. H.-J. Kanold zum 65. Geburtstag gewidmet 相似文献
887.
Dr. Wolfgang Stadje 《Monatshefte für Mathematik》1980,89(4):315-322
It is proved that iff∈L 1(?),f'∈L 1(?) and ∫∣x∣ i ∣f(x)∣dx<∞ fori=1, ...,k?1 and ifA=(a ij ) is a (k×k)-matrix with non-vanishing determinant, for $$\tilde f_A (\zeta ): = \smallint \exp (i\zeta _1 \sum\limits_{j = 1}^k {a_{1j} x^j } + ... + i\zeta _k \sum\limits_{j = 1}^k {a_{kj} x^j } )f(x)dx$$ the following relation holds: $$\tilde f_A (\zeta ) = O(\left\| \zeta \right\|)^{ - b_k } with b_k : = (\sum\limits_{j = 1}^k {j!)^{ - 1} } for k \in \mathbb{N}$$ . 相似文献
888.
Dr. H. G. Kopetzky 《Monatshefte für Mathematik》1977,84(3):213-217
Arithmetic formulae and an asymptotic expression for the order of magnitude of the arithmetic function
ged (s, n) and of a generalisation of it are derived. 相似文献
889.
Dr. Hartmut Pecher 《manuscripta mathematica》1977,20(3):227-244
This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where denotes the Laplacian, a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain LP-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems. 相似文献
890.
Prof. Dr. Alexander Aigner 《Monatshefte für Mathematik》1977,83(2):89-91
It is shown by a simple induction that any square-free natural number is the square-free kernel of Euler's -function of infinitely many natural numbers. Furthermore every square-free natural number >1 is the square-free kernel of Euler's -function of infinitely many square-numbers. 相似文献