Geometry optimization inab initio SCF calculations

The floating orbital geometry optimization (FOGO) described previously [1, 2] for atoms without polarized inner-shell electrons, is extended to the general case. Instead of the Hellmann-Feynman force a special gradient is calculated analytically and utilized in a variable metric procedure simultaneously with the ordinary energy gradient. Test calculations on a sample of 12 molecules were performed to check the efficiency of the method. The geometries obtained are better than those obtained with the corresponding double-zeta basis set. The most striking results, however, are excellent dipole moments.     

Accelerated convergence in SCF calculations and the level shifting technique

The possibility of improving the convergence rate in SCF calculations by exploiting the essential arbitrariness of the diagonal matrix elements of the Fock operator formed in the MO basis is studied. It is shown that it is possible to accelerate convergence in many cases by adopting a different form of level shifting technique (called the reverse level shifting technique by us).     

Geometry optimization in ab initio SCF calculations. VII. Proton affinities and ion structures calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate absolute proton affinities of the molecules H₂, HF, NH₃, H₂O, CH₃OH, C₂H₅OH, H₂O₂, CH₂O, CO, and CH₂CO. Comparison with experimental values demonstrates that the geometrical and energetical data resulting from this type of ab initio calculation are of chemical accuracy. Predictive data for higher energy isomers, such as hydroxymethylene and ethynol are given as possible aid for the identification of these species.     

Density matrix methods in orbital optimization for MCSCF calculations

The problem considered is that of selecting the finite orbital basis which will minimize the energy in a given size CI calculation. (1) A one-body operator is defined which has as eigenfunctions the desired optimal basis. The operator is defined in terms of the basis which leads to a self-consistency problem of Hartree-Fock type. (2) A method of successive orbital rotations is defined which is shown to have desirable convergence properties.     

Geometry optimization in ab initio SCF calculations: Part IV. Energy barriers and dipole moments obtained with floating orbital geometry optimization (FOGO)

The floating orbital geometry optimization (FOGO) described previously is applied to H₂O₂, NH₃, HNC, HNO, HNCO, and CH₃OH. In the FOGO method we apply two analytically calculated energy gradients in a variable metric method. Some orbitals are no longer fixed on the corresponding nuclei, but their position is optimized simultaneously with the nuclear coordinates. It is shown that relative energies (e.g. rotational barriers) are obtained with similar accuracy to basis sets including polarization functions. Further, it is confirmed that FOGO yields excellent dipole moments. The FOGO method involves a considerable time saving compared to conventional calculations with DZ + P basis sets.     

The constrained space orbital variation analysis for periodic ab initio calculations

The constrained space orbital variation (CSOV) method for the analysis of the interaction energy has been implemented in the periodic ab initio CRYSTAL03 code. The method allows for the partition of the energy of two interacting chemical entities, represented in turn by periodic models, into contributions which account for electrostatic effects, mutual polarization and charge transfer. The implementation permits one to carry out the analysis both at the Hartree-Fock and density functional theory levels, where in the latter the most popular exchange-correlation functionals can be used. As an illustrating example, the analysis of the interaction between CO and the MgO (001) surface has been considered. As expected by the almost fully ionic character of the support, our periodic CSOV results, in general agree with those previously obtained using the embedded cluster approach, showing the reliability of the present implementation.     

Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions

A quasi-Newton method involving a diagonal guess orbital hessian with iterative updates has been proposed recently by Almlof for the optimization of closed shell self-consistent field (SCF) wavefunctions. The technique is extended in the present work to more general wavefunctions, ranging from open shell SCF through multiconfigurational SCF. A number of examples are presented to show that convergence for closed and open shell SCF rivals conventional direct inversion in the iterative subspace (DIIS). For multiconfigurational SCF wavefunctions, the method presented here requires more iterations than an exact second order program, but since each iteration is substantially faster, leads to a more efficient overall program. Received: 15 August 1996 / Accepted: 22 January 1997     

Use of molecular symmetry in SCF calculations

A method is described whereby molecular symmetry properties may be used to reduce the numbers of one- and two-electron integrals that need to be calculated and stored in the course of a molecular SCF calculation. The method is a generalization of a previously reported procedure, extending the earlier work to cover those molecules belonging to point groups which have complex representations. The practical application of the method is discussed and an illustrative example given. The quite extensive tables of molecular symmetry properties which the method uses may be computer generated in a straightforward manner. A procedure for doing this using a minimum amount of input data is presented.     

SCF Dirac-Hartree-Fock calculations in the periodic system

Binding energies calculated by DHF method were compared with modified DFS method calculations and experimental values. First ionization potentials of all elements from Z=1 to Z=120 (excluding the lanthanide and actinide series) were obtained from DHF values. These calculated values were compared with spectroscopically determined first ionization potentials for the region Z=1 to Z=88. The obtained ratios of DHF calculated and experimental values in the Z88 region (correlation ratios) were extrapolated for 104–120 elements and used in correcting calculated DHF eigenvalues to obtain expected values for the first ionization potential in this region.     

SCF Dirac-Hartree-Fock calculations in the periodic system

Using the Dirac-Hartree-Fock (DHF) program which includes the exchange terms for electrostatic interactions, the Dirac equation was solved numerically by UNIVAC computer for all elements with Z=1–120. A solution was performed for each element of the periodic system in several electronic configurations, to obtain the configuration with lowest total energy as the calculated ground state.

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Zusammenfassung Mit Hilfe des Dirac-Hartree-Fock-(DHF)-Programms, das die Austauschterme für elektrostatische Wechselwirkungen einschließt, wurde die Dirac-Gleichung für alle Elemente mit Z=1–120 numerisch (UNIVAC-Rechenanlage) gelöst. Die Rechnung wurde für jedes Element des Periodensystems in verschiedenen Elektronenkonfigurationen durchgeführt, um die Konfiguration mit der tiefsten Gesamtenergie für den Grundzustand zu erhalten.

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Résumé En utilisant un programme Dirac-Hartree-Fock (DHF) comportant les termes d'échange de l'interaction électrostatique, l'équation Dirac a été résolue numériquement avec un ordinateur UNIVAC, pour tous les éléments de Z=1 à 120. Les calculs ont été developpés pour plusieurs configurations électroniques de chacun des éléments de la classification périodique afin de déterminer celle dont l'énergie est la plus basse, qui correspond à l'état fondamental.

     

Tempered orbital energies in SCF MO calculations and their relation to the ordinate in Mulliken-Walsh correlation diagrams and extended Hückel orbital energies

An “average state” of a molecule is defined by distributing the electrons equally among the valence orbitals of a minimal basis set Hartree-Fock calculation. The resulting eigenvalues, called tempered orbital energies, behave much more like the Mulliken-Walsh diagram energies or extended Hückel eigenvalues than do the Hartree-Fock canonical orbital energies.     

Energy-conformation studies of HCN,HNC and CN−: A comparison of results from EH-SCC and SCF molecular orbital calculations

We have made an Extended Hückel Self Consistent Charge (EH-SCC) molecular orbital calculation for hydrogen cyanide, hydrogen isocyanide and cyanide ion. The main purpose of this calculation was to compare the EH-SCC and the more accurate SCF MO calculations for HCN in order to evaluate the method we used here for future use. Specifically, we have calculated and compared the following properties of HCN: total energy, binding energy, variation of ground state energy with geometric conformation, ionization potential and dipole moment. In addition, we have extended previous calculations of HCN by also considering its energy variation with bond angle for two excited state configurations and deducing some of the characteristics of its electronic spectra. Finally we have also made an MO calculation of the isocyanide isomer HNC and CN^– ion to compare with and add to the known characterization of the H, C, N, system.

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Zusammenfassung Rechnungen nach der erweiterten Hückeltheorie werden für HCN, HNC und CN^– durchgeführt und mit ab initio Resultaten verglichen. Im einzelnen wurden Gesamtenergie, Bindungsenergie in Abhängigkeit von der geometrischen Struktur, Ionisierungspotential und Dipolmoment von HCN berechnet und außerdem die Energie für zwei doppelt angeregte Konfigurationen in Abhängigkeit vom Bindungswinkel bestimmt. Darüber hinaus sind MO-Rechnungen für HNC und CN^– gemacht worden.

     

Multiple stationary point representations in MC SCF calculations

By using a complete second-order Newton-Raphson multiconfigurational self-consistent field (MC SCF) procedure combined with the Fletcher restricted step constraint algorithm and a modification of the surface walking procedure of Simons et al., an MC SCF energy hypersurface at fixed geometry has been examined in considerably more detail than had been done previously. By calculational example, it is shown that there may exist several MC SCF stationary points which fulfill all four structural criteria we require of a state for being a “good” representation of an exact state. The problem with the existence of several stationary point solutions may be reduced if care is taken in the selection of the MC SCF configuration space. Calculational examples also demonstrate that near-lying stationary points exist which fulfill some, but not all, of these four structural criteria. Hence, stationary points should be obtained with a global MC SCF method which automatically eliminates convergence to as many as possible of these unwanted stationary points. Upon convergence, structural criteria which are not automatically fulfilled should be examined in detail.     

Anab initio SCF molecular orbital study of acetylcholine

A standard ab initio (STO 3 G) study indicates, in distinction to theab initio molecular fragment results, that the preferred conformation of acetylcholin is gauche.     

Small,simultaneous adjustments of orbital exponents in LCAO–MO–SCF calculations using self-consistent perturbation theory

Self-consistent perturbation theory is introduced to facilitate making small, simultaneous variations in orbital exponents. This is accomplished by interpreting these variations as perturbations on the quantum mechanical system. The minimum-energy condition yields a set of linear equations for the desired exponential corrections.     

Ground-state dipole polarizability of lithium hydride. Accurate SCF and CAS SCF calculations

Accurate calculations of the dipole polarizability tensor of lithium hydride are performed using the finite-field perturbation approach in the SCF and CAS SCF method. The SCF results (α_? = 22.1, α_⊥ = 25.4 au) are expected to be very close to the HF values. The CAS SCF calculations predict a positive correlation contribution, giving α_? = 26.3 and α_⊥ = 29.3 au.