MCSCF Calculations Research Articles

Correlation effects in the nitrogen 1s photoelectron spectrum of nitric oxide

An interpretation of the anomalous intensity ratio of the two peaks arising from nitrogen 1s ionization of nitric oxide is presented. It is found that correlation effects in both the ground state of NO, and the ionic states ( 3Π, 1Π) of NO + contribute to deviations of this intensity ratio from the “frozen orbital” value of 3 to the experimental value of 3.43. MC SCF calculations are described which result in an excellent prediction of this intensity ratio. THe satellite peaks associated with core ionization from NO are briefly discussed.

Molecular MC SCF calculations by direct minimization

Calculations on the H2CO ground state and excited states at the equilibrium planar geometry, using the single excitation MC SCF method, are described for two basis sets. The results obtained by a full calculation including all the electrons are compared with those obtained by a pseudopotential version of the method including only the valence electrons. The results agree quite well both with each other and with the observed values.

The optimization of MCSCF functions by application of the generalized brillouin theorem: The LiH2 potential energy surface

The generalized Brillouin theorem is used to construct an optimization procedure for MCSCF functions by iterative contracted CI calculations. Special attention is paid to the MO transformation step in each iteration. In this method the MCSCF calculation may easily be augmented by a restricted CI calculation involving a configuration set which is uniquely determined by the trial function. An application to the calculation of the potential energy surface for linear LiH2 in the reaction LiH + H⇆Li + H2 leads to the conclusion that this restricted CI is necessary, in order to obtain satisfactory results for the potential energy barrier in this reaction.

Molecular MCSCF calculations by direct minimization

Molecular MCSCF calculations by direct minimization

A computational method of performing MC SCF calculations using bonded functions

A computational method for carrying out MC SCF calculations using as basis configuration the bonded functions of Boys et al. is described. These functions are commonly used in large scale CI calculations, and the method described here utilizes many of the techniques used in such calculations, particularly the use of a list symbolic matrix elements. The method is shown to have good convergence properties.

A b i n i t i o calculations of the 3Σg+ and 3Σu+ states of singly excited Ar2

CI calculations were performed for the 3Σg+ and 3Σu+ excimer states of Ar2 using molecular orbitals determined by MCSCF calculations. The 3Σg+ state has a small barrier and shallow well, as expected from analogy with other rare gas dimers. The deeply bound 3Σu+ potential curve has a well depth of 0.68 eV at an internuclear separation of 4.59 ao. Elastic scattering on these curves was calculated and compared with experimental data. The primary rainbow from the 3Σu+ state is found to be in excellent agreement with observation.

Molecular MCSCF calculations by direct minimization

Molecular MCSCF calculations by direct minimization

Molecular MCSCF calculations by direct minimization

An MCSCF method using single excitations is described. The wave-function is obtained by direct minimization. An illustrative calculation on LiH indicates that the method is appropriate for the calculation of one-electron properties, especially in bond-breaking geometries.

Frozen core approximation, a pseudopotential method tested on six states of NaH

A pseudopotential formulation, more appropriately called the frozen core approximation (FCA), is presented in detail. This FCA is tested by performing MCSCF calculations on the six low lying states, X1Σ+, A1Σ+, a3Σ+, c3Σ+, B1Π, and b3Π of NaH. The results obtained are compared with those of an analogous previous MCSCF calculation on these states without the use of FCA, i.e., with all orbitals optimized. It is found that energies are obtained rather accurately with FCA; however, calculated molecular properties are affected more strongly and the shapes of the potential curves appear to be distorted somewhat by FCA. It is argued that no pseudo- or model-potential calculation can give errors less than FCA unless the potential is made valence shell dependent. This, however, would be analogous to a full calculation, and the savings due to a pseudopotential approximation would be lost.

MCSCF calculations for six states of NaH

A b initio multiconfiguration self-consisting-field calculations are reported for the energies, electronic wavefunctions, and one-electron properties of the X1Σ+, A1Σ+, B1Π, a3Σ+, b3Π, and c3Σ+ states of NaH over a wide range of internuclear distances. In these calculations, only the two valence electrons are correlated. Three states (X1Σ+, A1Σ+, and b3Π) were found to be bound, with the following dissociation energies and internuclear separations (with known experimental values in parentheses): De (X1Σ+) = 1.878 (2.12±0.20) eV, Rmin (X1Σ+) = 3.609 (3.566) bohr; De (A1Σ+) = 1.203 (1.41±0.20) eV, Rmin (A1Σ+) = 6.186 (6.062) bohr; and De (b3Π) = 0.109 eV, Rmin (b3Π) = 4.458 bohr.

Theoretical study of curve crossing: ab initio calculations on the four lowest 1Σ+ states of LiF

The potential curves of the four lowest 1Σ+ states of LiF have been studied by ab initio configuration interaction methods, using a contracted Gaussian basis set of better than double-ζ quality, augmented with diffuse basis functions on the fluorine atom. The choice of orbitals and selection of configurations were carried out with the objective of obtaining a balanced treatment of the four states and of the different regions of the potential curves. ``Generalized valence-bond'' orbitals, obtained from ground-state MCSCF calculations, together with ``improved virtual orbitals,'' were found suitable for the construction of the configuration functions. The latter were energy selected from all single and double excitations relative to a set of 12 ``reference configurations,'' chosen to include all contributions found important for any of the four states at any internuclear distance. The expected avoided crossing between the lowest covalent and ionic structures is found at an internuclear distance of about 11 bohr, compared to the experimentally deduced value of 14 bohr, due to the considerable difficulty in obtaining a balanced description of the electron correlation of the separated species, particularly the F− ion. A set of diabatic potential curves was generated from the two lowest adiabatic curves by a novel procedure based on the Rittner model of the ionic state. A set of adjusted adiabatic potentials was obtained from the diabatic curves after shifting the ionic diabatic curve downward by 0.42 eV to correct for the error in the computed electron affinity of the fluorine atom, resulting in a shift of the avoided crossing to the correct internuclear distance of 14 bohr. The dipole moments of the four states were computed as a function of internuclear distance and were interpreted in terms of the electronic structure.

MC SCF calculations on the lowest triplet state of H 2O

Recent electron impact work on H 2O has shown a broad absorption peak near 4.5 eV which has generally been attributed to the lowest triplet ( 3B 1) state of H 2O. However, the results of SCF and multi-configuration SCF (MC SCF) calculations reported here indicate that the 3B 1 state is unbound with respect to the dissociative asymptotes H( 2S) + OH ( 2Π) and O( 3P) + H 2( 1Σ + g, in disagreement with experimental interpretation.

Multiconfiguration self-consistent wavefunctions for CH 4, C 2H 4 and C 2H 6

The results of several MC SCF calculations on CH 4, C 2H 4 and C 2H 6 with minimun bases of Slater type AO's are reported. The computing method is a quadratically convergent process. Better final energies are obtained if localized MO's are used.

An MC SCF calculation for the ammonia molecule

A multi-configuration self-consistent field wavefunction is reported for ammonia. The correlation energy associated with a 51 configurations wavefunction is 0.071au and is analyzed in terms of various contributions. Electron-density maps are illustrative of angular and left—right correlation.

Multi-configuration SCF calculations

In multi-configuration self-consistent field (MC SCF) calculations a many-configuration approximation to the wave function is optimized by variation of the orbitals. The equations satisfied by the optimum orbitals are formulated, along with a practicable method of numerical solution. Incidental problems arising in the computer implementation of MC SCF calculations are also discussed.