Charge distribution matrix representation

Because of the implicit use of the first derivative of the coefficient functions, the Simpson-type discretization method may be problematic if piecewise-defined potential terms are present (for some finite-nucleus models such as the homogeneous charge distribution of Eq. (6.151)). For such special cases, it would be more advantageous to use a scheme which employs a diagonal matrix representation of the effective potential (cf. Ref. [492] for details). 

Segmental multipole moments contain extremely compact linearly scaling 0(N) representation of molecular charge distribution, which may otherwise occupy 0(N ) disk space in the form of electron density matrix. This feature should become more important in future, when advances in direct and linearly scaling algorithms will allow to produce routinely electron density matrices for very large molecular systems which could not be permanently stored. 

Now it is useful to introduce any representation of the charge distribution of the solute, which might be a set of partial charges, multipoles, densities on grid points, or the elements of the density matrix. Let us represent this charge distribution by an n-dimensional vector Q. Then the solute potential 4>soi can be written as... 

In this work we have used this version of the mutually consistent field method (MCF) (48) which has been developed to treat the interactions between polymer chains (69). Each subsystem is computed in the potential field of the partner system. The Coulomb potentials of the elementary cell of one chain, represented by a point charge distribution which are fitted to the Hartree-Fock Coulomb potential are included in the one-electron part of the Fock matrix of the other chain and vice versa (for more details see Section 2.4). The procedure of taking into account the effect of the mutually polarization is repeated until consistent solutions are obtained for the charge distributions. Computing finally the interaction between these point charge representations, one obtains the electrostatic and the polarization energy contribution together. 

The system electron density p(r) and hence the one-electron probability distribution p(r) = p(r)/N, that is, the density per electron or the shape factor of p, are determined by the first-order density matrix y in the AO representation, also called the charge and bond order (CBO) matrix,... 

For a cytosine stack model calculations have been performed to investigate the effect of water molecules on its electronic structure (16). In this first approach the water structure of a cytidine unit in aperiodic B-DNA obtained with the help of Monte Carlo computer experiments (17) has been used. This choice of the water structure, of course, does not give a realistic description for cytosine,but we get in a relatively simple model calculation an order of magnitude estimate of the effects. The bound water molecules act on the electronic system of the stacked nucleotide bases as an external field. By a proper representation of the electron distribution of the water molecules through point charges one can easily calculate the matrix elements of this perturbing field in terms of the Bloch functions of the finite polymer and include in this way its effect on the band structure. 

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