摘要:

Formulae are derived for matrix elements of the hamiltonian and spin density operators between wave functions written as antisymmetrized products of group functions. The wave functions may differ either in the multiplicity of the group functions or by a transfer of one electron between the groups. The derivation of the formulae is based on the general type ofN-electron wave function proposed by Kotani. In the case of matrix elements of the hamiltonian, simple formulae are obtained which depend on the multiplicity of the group functions and on spinless density matrices; for matrix elements of the spin density operator a summation over Clebsch-Gordan coefficients remains and could not be removed.

ISSN:0026-8976    

DOI:10.1080/00268977100100381

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

By application of the formulae derived in I, a general formula for proton-proton coupling constants is derived which is independent of the function used for the separated π and σ-electron systems. It is shown that in previous descriptions wave functions have been neglected which yield important contributions to the coupling constant.

ISSN:0026-8976    

DOI:10.1080/00268977100100391

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The splitting constants of protons of methyl substituents in π-electron radicals are calculated by use of a method in which the wave functions for the π-electron system and the methyl substituent are assumed to be calculated in the best possible way before the two systems are coupled together. From the results of I a formula is derived which, after substitution of suitable parameters, is in good agreement with experimental splitting constants. The formula also applies to methyl substituents bonded to atoms having a negative spin density. A comparison is made with the more usual hyperconjugation and pseudo-hetero-atom approximations.

ISSN:0026-8976    

DOI:10.1080/00268977100100401

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The resolvent formalism is used to derive equations for the singlet and doublet distribution functions for a classical dense fluid not in equilibrium. The selection of diagrams to be included in the analysis is based strictly on perturbation techniques and order of magnitude criteria. A new and generalized equation is obtained for the pair distribution (in § 7) and the analysis confirms the singlet equation derived earlier by Allen and Cole using a different method. The relation of the present analysis to certain other theories is indicated.

ISSN:0026-8976    

DOI:10.1080/00268977100100411

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The SCF finite perturbation theory of indirect spin-spin coupling constants was applied to2JHHand3JHHin a series of mono-substituted cyclopropanes, C3H5X. where X=Li, H, CN, CO2H, COCH3, NH2, OH and F. The calculated results are qualitatively consistent with the experimental patterns exhibited by2JHHand3JHH. Problems were encountered for substituents for whichthrough-spaceinteractions may be important, particularly if X is a -I-substitutent.

ISSN:0026-8976    

DOI:10.1080/00268977100100421

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

An equation of motion is derived for the reduced density matrix of a system of spins coupled to a second system of spins strongly relaxing on account of their coupling to a thermal reservoir. The symmetry and other general properties of this equation are discussed. The applications of the equation are considered in relation to the problem of calculating the high resolution nuclear magnetic resonance band shape of a group of spin - 1/2 nuclei scalar coupled to a group of nuclei of spin > 1/2 which are relaxing via the quadrupolar mechanism. Explicit formulae are derived for some simple examples of such spin systems.

ISSN:0026-8976    

DOI:10.1080/00268977100100431

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The general method for calculating the high resolution nuclear magnetic resonance band shape of the2A2B region of the2A2B3X system for all rates of X quadrupolar relaxation is given in the extreme narrowing approximation. Explicit expressions are derived for the line widths in the limit of rapid X relaxation. It is shown that the behaviour of this line shape is different from the corresponding behaviour of the2A3X system. An experimental variable temperature study of the spectrum of 2-bromothiazole is described; ratios of scalar proton-nitrogen coupling constants and activation energies for rotational diffusion are given. Spectra recorded at two different spectrometer frequencies verified the theoretical prediction that the AB line widths are field dependent.

ISSN:0026-8976    

DOI:10.1080/00268977100100441

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A tentatively complete set of independent and commuting symmetry operators is defined for point groups of symmetry elements. Eigenvalues of these operators are discussed and the relation of the eigenvalue description to the standard notation of irreducible representations is shown. A new useful type of symmetry projection operator is introduced.

ISSN:0026-8976    

DOI:10.1080/00268977100100451

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The Hartree-Fock perturbation method formulated in a previous paper [7] for approximate calculations of the magnetic susceptibilities of polyatomic molecules using CNDO/2 or INDO wavefunctions is reviewed. The method uses gauge-invariant atomic orbitals together with a set of approximations proposed in People's MO theory of diamagnetism. An expression is obtained for the susceptibility of a molecule involving three different parts which are referred to as intra-atomic, interatomic and cross contributions, respectively. All these contributions are used to calculate the susceptibilities of a series of hydrocarbons (CH4, C2H6, C2H4, C2H2, cyclopropane). The mean values are in good agreement with experiment (except C2H2). Surprisingly, the interatomic and cross terms make considerable contributions to the total susceptibility. It seems justified to include the cross terms in the other terms and to define new terms which can be referred to as local or non-local contributions to the susceptibility. The local part can be divided up into a sum of atomic contributions which are comparable with the empirical Pascal constants. The numerical results reproduce very well the empirical atomic contributions and the constitutive correction for the carbon-carbon double bond. The calculations cover also the principal components of the atomic contributions. The non-local contribution may be considered as a generalization of the formula of Hall and Hardisson to all valence electrons.

ISSN:0026-8976    

DOI:10.1080/00268977100100461

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

ISSN:0026-8976    

DOI:10.1080/00268977100100471

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor