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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) Å, RNH =1.079(1.063) Å, 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.

The principles and structure of an LCAO-MO ab-initio computer program which recalculates all twoelectron integrals needed in each SCF iteration are formulated and discussed. This approach-termed "direct SCF"-is found to be particularly efficient for calculations on very large systems, and also for calculations on small and medium-sized molecules with modern minicomputers. The time requirements for a number of sample calculations are listed, and the distribution of two-electron integrals according to magnitude is investigated for model systems.easily accessible at low cost. At present, the price/performance ratio for CPU and memory appears to decrease much faster than that for 1/0 operations and use of peripheral devices. It has sometimes been pointed out4 that a favorable I/O-to-cPU price ratio would make i t more economical to recompute integrals in every iteration than to store and retrieve these.

A general contraction scheme for Gaussian basis sets is presented. The contraction coefficients are defined by the natural orbitals obtained from an atomic configuration-interaction calculation. Such atomic natural orbitals provide an excellent basis for molecular electronic structure calculations. Large primitive sets can be contracted to only a few functions without significant loss in either the SCF or correlation energy. Polarization functions can be included using the same approach.

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We discuss how the computational obstacles related to energy denominators in various schemes for electron-correlation calculations can be circumvented by a Laplace transform technique. The method is applicable to a wide variety of electronic structure calculations. We discuss in detail an algorithm for the contribution of triple excitations in fourth-order Mq,ller-Plesset perturbation theory, which grows only with the sixth power of the siz~ of the system, as compared to conventional N7 algorithms. Special consideration is given to efficient schemes for numerical quadrature of the integrals occurring in the Laplace transformations.

Ab initio calculations including geometry optimization at the Hartree-Fock, MP2, and LDF levels have been carried out for free-base porphyrin and for the tautomers of free-base chlorin, using polarized basis sets. TheHartree-Fock approximation artificially favors frozen resonance structures with alternating single and double bonds for these compounds. This incorrect behavior is completely reversed when correlation effects are accounted for. Correct, delocalized structures of tetrapyrroles are obtained with the MP2 and LDF levels of approximation.