Two extended basis sets (termed 5–31G and 6–31G) consisting of atomic orbitals expressed as fixed linear combinations of Gaussian functions are presented for the first row atoms carbon to fluorine. These basis functions are similar to the 4–31G set [J. Chem. Phys. 54, 724 (1971)] in that each valence shell is split into inner and outer parts described by three and one Gaussian function, respectively. Inner shells are represented by a single basis function taken as a sum of five (5–31G) or six (6–31G) Gaussians. Studies with a number of polyatomic molecules indicate a substantial lowering of calculated total energies over the 4–31G set. Calculated relative energies and equilibrium geometries do not appear to be altered significantly.

Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules

An LCAO-MO-SCF-CI model along the lines introduced by Del Bene and Jaffe is developed that is capable of reproducing the better identified observed spectra of nitrogen heterocycles with a rms error of ∼ 1000 cm−1. The model is applied to the spectra of pyrrole, benzene, pyridine, the diazines, symmetric triazine and symmetric tetrazine. The benzene and pyridine spectra are reproduced nearly exactly. The band observed in pyrrole at ∼ 6.5 eV is calculated as two bands at ∼ 6.5 eV, but they are assigned π→σ
* and not π→π. No evidence is found for the low lying 1
B
2g
 in pyrazine, reported at ∼ 30400 cm−1 in pure crystals. The lowest excited singlet of sym. triazine is calculated as 1
E″ (n→π
*), not 1
A″2 (n→π), in agreement with a recent interpretation of Fischer and Small. Several bands are reassigned, and the electronic nature of the transitions discussed. Naphthalene and quinoxaline are examined to insure that no large drift of results are met with molecules of other sizes. Comparison of eigenvalues with molecular ionization potentials is made. Here the numerical agreement appears satisfactory for the first few ionization potentials only.

An intermediate neglect of differential overlap technique for spectroscopy: Pyrrole and the azines

A configuration selection method for CI calculations is discussed and applied in which the energy lowering produced in a secular equation by the addition of a given test species to a series of dominant configurations is used as an ordering parameter. Configurations with energy lowerings below a given energy cut-off value are not included in the final secular equations but instead a method of estimating the combined effect of the neglected species on the corresponding non-selected CI results is developed. The influence of the choice of main configurations used in the selection process is given close examination as well as the importance of the MO basis employed in the treatment as a whole; in the latter case a non-iterative procedure for obtaining approximate natural orbitals for such calculations is suggested. The resulting configuration selection procedure is equally applicable to all types of electronic states in any nuclear geometry and the results of the associated CI calculations are seen to be essentially equivalent to a complete treatment in which all single- and double-excitation species with respect to aseries of dominant configurations in a given state are included.

Individualized configuration selection in CI calculations with subsequent energy extrapolation

Publisher Summary This chapter discusses a model that relies on the knowledge of the molecular electrostatic potential, which is derived from a molecular wavefunction by using the usual methods for calculating the mean expectation value of an operator. In its basic premises the model employs quantum mechanics, with only the approximations necessary in molecular quantal calculations. The model is also discussed regarding its relationships with the Hellmann–Feynman theorem. The electrostatic potential V itself is examined in order to show how the electrostatic potential reflects the characteristics of the electronic distribution of a molecule and then the reliability of V is discussed as a reactivity index. The shape of the electrostatic potential and its relationship to the electronic molecular structure is discussed with the aid of various examples. One of them includes the glycine tautomers and the corresponding anion example. The chapter also discusses the electrostatic molecular potential in terms of local group contributions.

Electronic Molecular Structure, Reactivity and Intermolecular Forces: An Euristic Interpretation by Means of Electrostatic Molecular Potentials

Implementation of a multi-reference double-excitation CI (MRD-CI) method is discussed and its results are compared with those of related techniques. This approach employs a configuration selection procedure to order the various generated species according to their energy-lowering capability and then uses an energy extrapolation procedure based on perturbation theory to obtain suitably accurate estimates of the eigenvalues of the entire MRD-CI space. By employing this selection procedure it is possible to test from 2000 to 4000 symmetry-adapted functions (SAF's) per second of CPU time on an IBM 370–168 system, thereby allowing one to apply the energy extrapolation quite conveniently to CI spaces consisting of several hundred thousand species. By systematically increasing the number of reference configurations in the MRD-CI it is clear that the limit of a full CI can be approached and as a result such a computational procedure appears to be generally valid for any type of electronic state and for any nuclea...

Applicability of the multi-reference double-excitation CI (MRD-CI) method to the calculation of electronic wavefunctions and comparison with related techniques

A configuration interaction (CI) procedure which is designed to produce energies and wavefunctions from relatively large scale computations on ground and excited molecular states is presented based on an orthonormal set of molecular orbitals. The method of generating configurations is referenced to the particular state of interest and involves a two‐pass procedure: First, the generation of configurations by single and double excitations from selected important configurations (parents), subject to a threshold criterion, followed by diagonalization of the energy to obtain an initial approximation to the wavefunctions of interest; second, the use of these wavefunctions as parents and a repeat of the generation and diagonalization steps to produce the final CI wavefunction. CI studies of the 1,3A2 (n→π*), 1,3A1 (π→π*, n→3p), 1B1 (σ→π*, π→3s), and 1B2 (n→3s) states of formaldehyde are reported for several large Gaussian basis sets of near atomic Hartree–Fock quality based on molecular orbitals determined from ...

Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules. I. The CI Formulation and Studies of Formaldehyde

Ab initio SCF and CI treatments of the ground state and n → π* and π → π* excited states of pyrazine, C4H4N2, are reported for the molecule in its ground state equilibrium geometry. In the case of n → π* transitions, the two symmetry combinations of nitrogen lone pair orbitals n1 and n2 are found to correspond to the description n+ ≈ n1 + n2 + λσ and n− ≈ n1 − n2 in which the n+ orbital has the higher orbital energy and is significantly more delocalized than n− by interaction with the pyrazine ring sigma system. This result leads to a significant splitting at the CI level of description of 1.4 eV between the B3u and B2g excited states which are derived from the orbital promotions n+ → π* and n− → π*, respectively. Calculated transition energies to the lowest n → π* excited states 3B3u and 1B3u of 3.56 and 4.22 eV, respectively, are in good agreement with experimental values. A low‐lying 3B1u(π → π*) state for which there exists indirect experimental evidence is found to occur between the 3B3u and 1B3u sta...

Melvyn Hackmeyer

Papers

Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules. I. The CI Formulation and Studies of Formaldehyde

Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules II. The Electronic States and Spectrum of Pyrazine