Charge and bond order matrix

D is the charge and bond order matrix 4>v(r) and r) are the basis functions... 

The approximate polarizabilities calculated by the steepest descent method are useful mainly because they are easily calculated from the charge-and-bond-order matrix of the imperturbed molecule but their... 

A recent re-examination of the perturbation problem (McWeeny, 1961 Diercksen and McWeeny, 1965), leads to a method of determining, to any prescribed order, the perturbation of an electronic system due to any applied field. This method involves the direct calculation of the first-, second-, third-order corrections to the charge-and-bond-order matrix... 

The new charge-and-bond-order matrix may be used as a basis for discussion of the reactivity of the heterocyclic system. 

The coefficients dpq form a matrix in the conventional sense, and y is completely determined if one indicates the basis functions yv and the matrix elements dpg. In practice, y is mostly given in this way, that is to say, as a matrix sensu stricto. In many applications, the atomic orbital basis can be supposed to be orthonormal and the matrix D with elements dpq can be identified with the charge and bond order matrix 7 8>. 

Form the charge and bond-order matrix R from the matrix of MO coefficients, the number of basis functions (m) and the number of electrons (2n). 

The R matrix subroutine scfR. The charge and bond-order matrix R is defined in terms of the (real) MO coefficient matrix by... 

R Input contains the charge and bond order matrix on input, unchanged on output... 

R The charge and bond order matrix generated is stored in R by columns (m x m)... 

R Workspace for the density (charge and bond order) matrix and contains this matrix on exit... 

Various totally or partially decoupled forms of these equations are also of interest [33-36]. In the next section we consider the normal representation of the independent collective population displacement modes. Each new representation is associated with a particular orthogonal transformation, O, of the population variables, v(0) = NO. The diagonal elements of the associated "charge-and-bond-order matrix, P(0) = O NO, where Njj = NjSij, Prr(O) s p,(0), can be identified as the occupations of the new collective populational modes, which preserve the global number of electrons in the system ... 

The MO-resolution [44,46,48,51] is based upon the MO occupation numbers, n, representing the diagonal elements of the charge-and-bond-order matrix of the canonical MO, >= />C. In the standard closed-shell LCAO MO formalism. 

Within the standard closed-shell HF theory the occupied canonieal MO constitute a very good approximation of the strongly occupied NO. The charge-and-bond-order matrix is diagonal, with the MO occupations, n — A , ... 

The simplest measure of MO bond order is the Coul-son charge and bond-order matrix, which is essentially the Fock-Dirac density matrix for the minimal basis of occupied valence AOs. When the first-order density matrix is expressed in terms of its NAOs (keyword DMNAO), one obtains a generalization of Coulson s charge and bond-order matrix that exhibits many parallels to the expected Hiickel-like patterns, but can be evaluated for an arbitrarily high ab initio treatment (HF, DFT, or Cl)... 

Since the charge and bond order matrix P for nonorthogonal orbitals and for symmetrically orthogonalized orbitals A. is ... 

These are the eigenfunctions of the charge and bond order matrix P. This formalism was introduced for double excitations and for single and double excitations on the Cl level in SlNDOl. 

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