SPIN-DEPENDENT UNITARY-GROUP APPROACH .2. DERIVATION OF MATRIX-ELEMENTS FOR SPIN-DEPENDENT OPERATORS

This paper is concerned with matrix elements of spin-dependent operato rs. We present a detailed derivation of the matrix elements of the ope rators DELTA(n)ij and DELTA(n + 1)ij shown in the article by Gould and Paldus [J. Chem. Phys. 92, 7394 (1990)] to lead to the matrix element s of all spin-dependent operators within the Gel'fand spin-adapted bas is; as required for spin-dependent CI and the calculation of relativis tic energy level shifts. Besides being useful for spin-dependent CI ca lculations, involving the incorporation of spin-orbit and spin-spin ty pe electronic interactions, our results can be used for the calculatio n of spin-dependent properties coming from a wave function with well d efined spin. Such wave functions can now be routinely computed using a ny one of numerous unitary group based program systems, hence the usef ulness of our formalism for chemical properties. In particular we give an application of this formalism to the calculation of the spin densi ty of a molecule using a spin-adapted wave function. In a future publi cation we will show how our formalism involving the DELTA(n) operator leads to compact formulas for the shifts in the electronic energy spec trum of a molecule due to relativistic effects. We briefly describe ou r numerical implementation of these new matrix elements as used for th e calculation of the spin density of a molecule.