Coulomb, integrals

When n is odd, the first ASF in both A) and B) is positive, while the second is negative. The two resulting Coulomb integrals are equal contributing together 2Q-... 

In fact, the Coulomb integrals discussed in Section IV.C are available in contemporary quantum chemistry packages. We do not really need to develop our own method to calculate them. However, it is necessary to master the algebra so that we can calculate the matrix elements of the derivatives of the Coulomb potential. In the following, we shall demonstrate the evaluation of these matrix elements. 

ZlNDO/S is differen t from ZINDO/1 because th ey use differen t algorithms in computing the Coulomb integrals. Hence the two et uation s used in th e rn ixed m odel in ZINDO/1 are also employed... 

One convention (Dickson. 1968) for oxygen heterocycles sets the coulomb integral at z 2f) and the resonance integral at Eor the oxirane moiety,... 

Coulomb integrals Jij describe the coulombic interaction of one charge density (( )i2 above) with another charge density (c )j2 above) exchange integrals Kij describe the interaction of an overlap charge density (i.e., a density of the form ( )i( )j) with itself ((l)i(l)j with ( )i( )j in the above). 

The off-diagonal coulomb integrals ia,b are commonly approximated either by the Mataga-Nishimoto formula ... 

The problem of electrophilic substitution into the anilinium ion has been examined by the methods of m.o. theory. Attempts to simulate the --inductive effect in Hiickel M.o. theory by varying the Coulomb integral of C(j) (the carbon atom to which the NH3+ group is attached) remove 7r-electrons from the o- and -positions and add them to the... 

All non-zero integrals over atomic orbitals on the two centers are set equal, as in CNDO/INDO, to an averaged y. Thus, (s sj s s ) = (s s I PbPb) = (PaPa I PbPb) = The two-center Coulomb integrals, rather than being calculated from first principles using s orbitals as in CNDO/INDO, are approximated by an Ohno-Klop-man [K.Ohno, Theor. Chim. Acta, 2, 219 (1964) G. Klopman,... 

The sum A is over all the atoms in the quantum region and B is over all the atoms in the classical region. The two-electron and two-center Coulomb integral, Y b, is computed in MINDO/3 by... 

Hi2 is the resonance integral, usually symbolized by p. In a homonuclear diatomic molecule Hi I = H22 = a, which is known as the Coulomb integral, and the secular determinant becomes... 

When m = n the Coulomb integral is assumed to be the same for each atom and is given the symbol a ... 

For unsubstituted aromatic hydrocarbons all the carbon atoms are assigned the same Coulomb integral (a) and all C—C bonds are assigned the same resonance Integral (/3). 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

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