Large CI Calculations Research Articles

The half projected Hartree-Fock function for determining singlet excited states. Application to cyclobutanone and 3-cyclopenten-1-one

The Half-Projected-Hartree-Fock procedure (HPHF) for determining singlet ground states is briefly described and extended to the direct determination of singlet excited states. The procedure is applied, using a [7s,3p/2s,1p] basis set, to determine the optimal geometry of two relatively large molecules, to which large CI calculations cannot be easily applied. These two molecules are cyclobutanone and 3-cyclopenten-1-one in their lowest singlet ( n → π) excited state. Both molecules are found to exhibit in their excited state a pyramidal structure with the carbonyl oxygen atom pointing outward from the molecular plane. RHF calculations for the singlet ground state were also performed for comparison. The theoretical geometrical parameters compare well with the experimental data.

Molecular dipole moments calculated with density functional theory

Molecular dipole moments (MDM) of 32 molecules calculated with density functional (DFT) and Hartree-Fock (HF) methods are compared and analyzed. We found that calculations with DFT using a DZVPD (double-zeta plus polarization in valence orbitals and diffuse d functions on heavy atoms) basis set currently provide the best theoretical values of the vacuum MDM closest to the experimental values and to available results from large CI calculations. MDM from DFT using DZVPD basis set (DFT/DZVPD), DFT/DZVP2 and HF/6-31G* calculations lead to mean unsigned errors of 0.06, 0.18 and 0.30 D, respectively, relative to the experimental values. A use of triple zeta basis sets did not lead to further improvements in the computed MDM.

Valence bond calculations of the potential energy surface for CH4→CH3+H

A valence bond study of the potential energy surface for methane CH4→CH3+H is performed at the 6–31G level using (i) a valence bond self-constituent field (VB-SCF) method; (ii) a valence bond configuration interaction (VBCI) method; and (iii) an antisymmetrized product of strong-orthogonal geminals (APSG) method (also in VB form). The calculations show that, although the energies are somewhat inferior (on an absolute scale) to those obtained in very large CI calculations, the VB reduced potential energy surfaces behave better, in the intermediate range 2–3 Å, than those obtained using (i) the Mo/ller–Plesset fourth-order perturbation (MP4) approximation, (ii) configuration interaction with all singles and doubles (CISD), and (iii) coupled clusters with all singles and doubles (CCSD). The results are in very good agreement with those obtained from multi-reference configuration interaction (MR-CISD) calculations. The lower absolute energies obtained in the very extensive CI calculations indicate a better description of electron correlation, both in the molecule and in its dissociation products, but evidently they do not imply a better overall description of the PE surface. The remarkable fact is that a single VB structure, with carefully optimized orbitals, provides an excellent description of the whole dissociation process.

A CASSCF description of the nπ * singlet and triplet electronic excited states of the trans-glyoxal molecule

A CASSCF study is presented for the 1,3(n→π *) transitions of the trans-glyoxal molecule, based on a localized excitation model suggested by Iwata. It is shown that with a proper choice of the active space and the correct balance between intra- and intermoiety excitations, simple wavefunctions can produce results comparable to the ones obtained by large CI calculations, and in good agreement with experiment.

A statistical approach to the configuration interaction problem

A new statistical approach to the configuration interaction problem is proposed. It will potentially reduce the size of CI vectors significantly and thus alleviate one of the main hindrances to doing very large CI calculations. This method will also provide us with statistical confidence limits on lower and upper bounds. These confidence bounds are qualitative different from mathematically more rigorous lower bounds discussed elsewhere. The approach is discussed and possible algorithms presented.

Electronic structure calculations for the molecules Si2 and Ge2 using all electron ab initio HF‐CI methods

AbstractMolecular orbitals for Si2 and Ge2 have been optimized in hyper‐HF calculations and utilized in valenxe CI treatments to describe the low‐lying states of the molecules. The calculational results reveal pronounced similarities between the electronic structures of Si2 and Ge2. Thus, for both molecules the two lowest‐lying electronic states, 3Σ(σΠu3) and 3πu(∑g1πu3), have crossing potential energy curves, and the two lowestlying states of 1∑g+ symmetry exhibit crossing of configurations. The Sequence of the low‐lying electronic states can be rationalized on basis of a simple molecular‐orbital picture in which the σg and the πu valence orbitals are almost degenerate. The spectroscopic constants derived from the present work compare favorably with the results of more elaborate calculations. It appears that transition energies derived in valence CI calculations between states of identical configurations are improved in large CI calculations, whereas this is not the case for transition energies between states of different configurations. The valence CI calculations based on the molecular orbitals optimized in hyper‐HF calculations appear to effer reliable descriptions of the chemical bonds as well as of the electronic structures of the molecules Si2 and Ge2.

Nonorthonormal CI for molecular excited states. I. The sudden polarization effect in 90° twisted ethylene

The accurate and efficient calculation of properties of excited states, especially those involved in near-degeneracies and valence-Rydberg mixings, may depend crucially on the zeroth order orbitals employed for the description of a few important configurations. When self-consistent field orbitals specific for the states of interest are employed, one becomes involved with nonorthonormal basis sets, which circumstance has conceptual as well as computational implications. In this work, we have developed a nonorthonormal configuration interaction (NONCI) method and have applied it to the calculation of the ‘‘sudden polarization’’ effect in the zwitterionic excited states of ethylene, in the spirit of a state-specific theory. A very small NONCI, (6×6), yields similar results to those from previous large CI calculations. In particular, the sudden rise of the dipole moment as a function of the pyramidalization angle of the CH2 group of the 90° twisted Z state is predicted while it is shown that the inclusion of NON at 0° angle (D2d symmetry) is sufficient to recover the correct electronic charge distribution (zero dipole moment).