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1.
2.
The average interelectronic is the expectation value of the angle thetaij (0 < or = thetaij < or = pi) subtended by the position vectors ri and rj of a pair of electrons i and j. In the Hartree-Fock theory of atoms, we point out that the angle and its subshell-pair components nl,n'l' are bounded from above and below, where n and l are the principal and azimuthal quantum numbers. The upper bounds for nl,n'l' with 0 < or = l, l' < or = 3 are 9pi/16 (=101.25 degrees), 135pi/256 (approximately 94.922 degrees), 265pi/512 (approximately 93.164 degrees), and 129pi/256 (approximately 90.703 degrees) for sp, pd, df, and sf pairs, respectively, while they are pi/2 (=90 degrees ) for the other ll' pairs, independent of n and n'. A weighted sum of these subshell-pair bounds gives an upper bound to . The lower bounds are pi/2 in all the cases. 相似文献
3.
Toshikatsu Koga Shinichi Morishita 《Zeitschrift für Physik D Atoms, Molecules and Clusters》1995,34(2):71-74
An extensive optimization has been performed for the composition ofN terms, as well as the exponent and the mixing coefficients, of Kinoshita wave functions for heliumlike atoms with atomic numberZ. The optimalN-term Kinoshita functions have been constructed forN=1–10, 20, 30, 40, 50, 100 andZ=1(H–)–10(Ne8+). The present results demonstrate that the optimal term selection dramatically improves the accuracy of the Kinoshita function: In the case of He, for example, the optimal 100-term Kinoshita function gives – 2.903 724 376 95 hartrees, which is only 8×10–11 hartrees higher than the most accurate literature value. 相似文献
4.
The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus. 相似文献
5.
Toshikatsu Koga 《International journal of quantum chemistry》1984,25(2):347-354
The recently proposed method of using momentum densities for interatomic interactions is applied to the long-range force between the ground-state hydrogen atom and the proton, and the results are compared with those from using the position density based on the electrostatic Hellmann–Feynaman theorem. A new physical interpretation of the long-range force is obtained, which is complementary to that in position space. It is found that some perturbative changes in the position density do not accompany changes in the momentum density. 相似文献
6.
For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion)
<u
k
>
nl
and extracule (center-of-mass motion) <R
k
>
nl
subshell moments in position space are examined as well as their counterparts <v
k
>
nl
and <P
k
>
nl
in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule
and extracule moments the “2
k
-rule” is strictly valid, which means <u
k
>
nl
= 2
k
<R
k
>
nl
and <v
k
>
nl
= 2
k
<P
k
>
nl
for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u
2>
nl
= (N
nl
−1)<r
2>
nl
and <v
2>
nl
= (N
nl
−1)<p
2>
nl
hold exactly, where N
nl
(≥2) is the number of electrons in the subshell nl, and <r
k
>
nl
and <p
k
>
nl
are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes
a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through
the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear
relations between <u
k
>
nl
and <r
k
>
nl
and between <v
k
>
nl
and <p
k
>
nl
, in which the proportionality constant in each space depends on n,l, and k.
Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998 相似文献
7.
Toshio Takido Sachiko Tamura Kenji Sato Haruo Kamijo Toshikatsu Nakazawa Manabu Seno Tadashi Hata 《Journal of heterocyclic chemistry》1998,35(2):437-443
The synthesis of hexahydrooxoepithiopyridinedicarboxyimide (5: X2 = N-Ph) by the reaction of thioamides 1 with N-substituted maleimide ( 2a ) was examined. The reaction of primary thioamides, such as thiobenzamide and p-toluthioamide with N-phenylmaleimide gives compounds 5 together with corresponding 4-hydroxy-1,3-thiazoles 4 . However, a similar reaction of secondary thioamides, such as N-methylthioacetamide, thiobenzanilide, with N-phenylmaleimide did not provide compounds 5 without addition of acid. The reaction pathway and the configuration of 5 were also investigated. 相似文献
8.
Toshikatsu Takanami 《Tetrahedron letters》2005,46(16):2893-2896
The catalytic Z-selective Claisen rearrangement of simple aliphatic allyl vinyl ethers can be achieved using a chromium(III) porphyrin complex, Cr(TPP)Cl, as a catalyst: Cr(TPP)Cl significantly enhances reversal of E-Z selectivity in the thermal Claisen rearrangement of allyl vinyl ethers, especially, 4,5- and 4,6-disubstituted derivatives, at low catalyst loading. 相似文献
9.
Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the2
P states of Li and Na, and the3
P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size. 相似文献
10.
Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y
0,z
0) and the two-dimensional cut (x, y, z
0) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions
x
(x) and
xy
(x, y) and their difference functions
x
(x) and
xy
(x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H2 system. 相似文献