Jan Almlöf

TL;DR: A combination of variable-metric second-order update schemes and the DIIS method for both geometry and Hartree-Fock wave function optimization is described and a recursive procedure for updating large Hessians is presented.

TL;DR: In this paper, a general contraction scheme for Gaussian basis sets is presented, where the contraction coefficients are defined by the natural orbitals obtained from an atomic configuration interaction calculation, which provides an excellent basis for molecular electronic structure calculations, and large primitive sets can be contracted to only a few functions without significant loss in either the SCF or correlation energy.

Abstract: The complete active space (CAS) SCF method is presented in detail with special emphasis on computational aspects. The CASSCF wave function is formed from a complete distribution of a number of active electrons in a set of active orbitals, which in general constitute a subset of the total occupied space. In contrast to other MCSCF schemes, a CASSCF calculation involves no selection of individual configurations, and the wave function therefore typically consists of a large number of terms. The largest case treated here includes 10 416 spin and space adapted configurations. To be able to treat such large CI expansions, a density‐matrix oriented formalism is used. The Newton–Raphson scheme is applied to calculate the orbital rotations, and the secular problem is solved with recent developments of CI techniques. The applicability of the method is demonstrated in calculations on the HNO molecule in ground and excited states, using a triple‐zeta basis and different sizes of the active space. With a reasonable choice of active space, the calculations converge in 6–10 iterations. This is true also for states which are not the lowest state of the symmetry in question. The equilibrium geometry for the ground state is RNO=1.215(1.212) A, RNH =1.079(1.063) A, ϑHNO=108.8(108.6) °, the experimental values given in parenthesis for comparison. The best estimates for the transition energies to the lowest 3A″ and 1A″ states are 0.67(0.85) eV and 1.52(1.63) eV, respectively. The results obtained indicate that the choice of active space may be crucial for the convergence properties of CASSCF calculations.

TL;DR: In this article, a method for obtaining electron-repulsion integrals over a molecular-orbital basis without any explicit four-index transformation involving input/output is proposed, which allows for calculations that would otherwise be prohibited by storage limitations with conventional techniques.

TL;DR: In this article, the principles and structure of an LCAO-MO ab-initio computer program which recalculates all two-electron integrals needed in each SCF iteration are formulated and discussed.