Overlap charge density

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). 

These integrals are clearly of the exchange type because they involve the coulombic interaction of the 2s 2px y or z overlap charge density with itself. 

The excellent agreement between the MM, QM/MM and QM PES results directly from the consistent and consequent screening of the interactions for overlapping charge densities. Therefore, as was already shown previously [74,137], our model gives static and response potentials that are as good as SCF calculations (and better if the dispersion is accounted for) which let us separate the total system into different subsystems. 

In the CNDO/2 approach, only valence electrons are treated explicitly by choosing a minimum set of basis functions (atomic orbitals) for the molecule in its ground state. The main approximations are (1) Basis functions n are treated as an orthonormal set i.e., the overlap integrals are put to zero unless < u =r, in which case they are unity. (2) All two electron integrals which involve overlapping charge densities between... 

This is fairly obvious from a simple schematic drawing showing the overlapping charge densities of two interacting j3-orbitals ... 

Note that overiap-forbidden transitions also tend to have small singlet-triplet splitting. This is given in the first approximation by IK, that is, by twice the self-repulsion of the overlap charge density If the overlap charge density is small everywhere, its self-repulsion can hardly be large. 

Two-center (overlap) charge densities were partitioned into one-center (atomic) charges by means of MuUiken population analysis [16] with the self-consistent charge (SCC) method [17] which is used to approximate the self-... 

Overlap charge density. 26. 33 Overlap density. 14. 79. 125. 150. 209. 485 Overlap integral. 237. 362 Overlap selection rule, 32-33 Oxabicyclobuianc, 433 Oxacarbene, 386... 

The DHFB Hamiltonian (95) writes electron-electron interaction integrals in the traditional Slater notation (i,k G R) j,l) in which the orbitals i,k of the bra are assigned respectively the coordinates Xj,X2 and a similar assignment is made to the orbitals j,l of the ket. In the matrix formulation, it is more convenient to write integrals in terms of the overlap charge density at each of the points, so that in the case of the Coulomb interaction, this would be written... 

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