Spin-free approach for evaluation of electronic matrix elements using character operators of ℒN

A spin-free method is presented for evaluating electronic matrix elements over a spin-independent many-electron Hamiltonian. The spin-adapted basis of configuration state functions is obtained using a nonorthogonal spin basis consisting of projected spin eigenfunctions. The general expressions for the matrix elements are given explicitly, and it is demonstrated how the matrix elements may be obtained simply from the knowledge of the irreducible characters of the permutation group ℒ_N. The presented formulas are very general and may be applied in connection with both spin-coupled valence bond studies and in conventional configuration interaction (CI) methods based on an orthonormal orbital basis. © 1996 John Wiley & Sons, Inc.     

On R(4) symmetries in atomic structure

By defining a new rotation group in four dimensions we show that previous phase discrepancies can be accounted for. Furthermore we demonstrate that the new R(4) group is the one to be used in the study of atomic correlation.     

A programmable spin-free method for configuration interaction

In this note a method is presented for quick implementation of configuration interaction (CI) calculations in molecules. A spin-free Hamiltonian for anN electron system in a spin stateS, expressed in terms of the generators for the unitary group algebra, is diagonalized over orbital configurations forming a basis for the irreducible representation [2^1/2N-S 1^2S ] of the permutation group S _N . It has been found that the basic algebraic expressions necessary for the CI calculation involve a limited category of permutations. These have been displayed explicitly. On leave from the Indian Institute of Technology, Bombay, India.     

Representations of the symmetric group generated by projected spin functions: A graphical approach

The representation matrices generated by the projected spin functions have some very interesting properties. All the matrix elements are integers and they are quite sparse. A very efficient algorithm is presented for the calculation of these representation matrices based on a graphical approach and a new indexing scheme for representation of primitive spin functions is introduced. Test calculations show that the method is very fast and suited for calculations on vector computers. © 1996 John Wiley & Sons, Inc.     

Spin-coupled calculations based on projected spin eigenfunctions

It is outlined how the utilization of a basis of projected spin eigenfunctions can lead to increased computational efficiency in the evaluation of matrix elements and density matrices in spin-coupled valence bond calculations. Received: 17 September 1997 / Accepted: 23 October 1997     

Ab initio calculations of electrostatic potentials and deformation densities for a series of choline ester model systems

Ab initio LCAO-MO-SCF calculations using a double zeta basis set have been performed for the methyl esters of acetic acid, carbamic acid, methylcarbonic acid, and trifluoracetic acid, in order to model the corresponding choline esters. The systems have been compared by means of population analyses, electron density differences, electrostatic potentials and potential differences. The significance of the electrostatic potential in connection with crystal structure and packing has been studied. The differences in the proton affinity of the compounds have been correlated to differences in the potentials.     

Normalization of projected spin eigenfunctions

We find the normalization integral for projected spin eigenfunctions, defined by means of character projection operators of the symmetric group. We also obtain a reduced expression for these spin eigenfunctions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Configuration interaction studies using biorthogonal approach to VB basis

In the present article, we have attempted a systematic procedure for use of biorthogonal techniques to the configuration interaction studies in molecules using nonorthogonal valence bond (VB ) orbitals. The procedure developed is integral-driven and a program based on this has been developed. Test runs of the program have been carried out in case of full and truncated configuration spaces. © 1995 John Wiley & Sons, Inc.     

Molecular point group adaptation of spin–free configurations

Symmetry adaptation of spin–free multishell electron configurations in molecules to general non-Abelian point groups has been carried out. Using the basis spanning the irreducible representation [2^N/2?S, 1^2S, 0^n?N/2?S] of the unitary group U(n) as primitives, the Wigner operators for point groups were applied to generate the required basis. In the process it was found that the segments of the Weyl tableaux could be handled individually. Using this and the matric algebra of permutation group a viable procedure has been developed for point groups adaptation. A program based on the procedure has been generated and implemented.     

A graphical scheme for representing many‐electron spin‐free configurations

The present approach is a graphical technique for representing and generating primitive configurations of space orbitals for electronic systems. The graph is developed as a tree whose paths define the allowed space configurations of electrons admitting at most double occupancy for each orbital. The emphasis in the graph is on the nodes representing occupied orbitals rather than on the arcs compared with previous graphical procedures used in graphical unitary and symmetric group approaches. This leads to a compact representation of the orbital configurations and provides a computationally very efficient indexing scheme. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001