EFFICIENT USE OF JACOBI ROTATIONS FOR ORBITAL OPTIMIZATION AND LOCALIZATION

Quantum chemical orbital optimizations can be accomplished by Newton-t ype iterations, where all orbitals are improved at each step; or by a succession of Jacobi rotations, where only two orbitals are improved a t any one step. In both schemes, the iterative updating of the four-in dex two-electron integrals requires a large computational effort. We s how that the four-index transformation due to a Jacobi rotation can be simplified to such a degree that the successive execution of the four -index transformations of N(N - 1)/2 different Jacobi rotations requir es no greater computational effort than that required by the one full orthogonal transformation which is the product of all N(N - 1)/2 Jacob i rotations. The four-index updating has therefore no bearing on the r elative merit of the Newton approach versus the Jacobi approach. The J acobi approach has, however, an advantage if the optimization of each Jacobi rotation angle is simple and if the effectiveness of the indivi dual Jacobi rotations can be assessed without the execution of four-in dex transformations. For, in that case, all ineffectual rotations are easily deleted from the iterative sequence. Whether convergence can be guaranteed for one or the other approach is also relevant. Our conclu sions are illustrated by application to the problem of intrinsic orbit al localization where the succession of Jacobi rotations is the more e ffective strategy.