Michael C. Zerner

Triplet states via intermediate neglect of differential overlap: Benzene, pyridine and the diazines

The intermediate neglect of differential overlap technique is modified and applied to the calculation of excited triplet states. The resulting method generally reproduces the transition energies of the better-classified observations within a rms error of 1000 cm−1. Trends are well reproduced, and the calculated orders ofn-π* and π-π* triplet states are in good accord with the experimental information to date.The method is applied to benzene and the azines. The lowest four triplet states of benzene are calculated in good accord with experiment. Pyridine is calculated to have an-π* triplet nearly degenerate with the lowest lying π-π* triplet, corroborating suggestions of Japar and Ramsay based on experimental information. A detailed analysis is made of the diazines, and assignments are suggested for the higher lying triplet states not yet classified or not yet observed.

The linked singles and doubles model: An approximate theory of electron correlation based on the coupled‐cluster ansatz

From the diagrammatic construction of the full coupled‐cluster theory of all single and double excitations, a linearized theory, a direct configuration interaction theory (CISD), a CEPA‐like theory, and a linked singles and doubles (LSD) theory are separated. These theories are then compared with one another, with the results from full fourth‐order perturbation theory, and with exact results when available. The LSD model, corresponding to the removal of unlinked terms of the CISD, and its spin adapted version, appear most accurate in Pariser–Parr–Pople studies where the exact numbers are known. Examples within the localized bond model are given indicating that this model is also the most successful of those examined in generating not only the basis set correlation, but the necessary delocalization and polarization required to correct for the zeroth‐order local description.

Removal of core orbitals in ‘valence orbital only’ calculations

Examination is made of inner (core) and outer-shell (valence) separation in molecular orbital calculations. Assuming a set of simple Slater type functions, pseudo-potentials are examined which approximate the formation of a valence set of basis functions which are orthogonal and non-interacting with the core, and which simulate the core in ‘valence-orbital only’ calculations. The simplest form of this potential is , where Δαi is the overlap between valence orbital i and core orbital α and F αα, the diagonal element of the Fock matrix for core orbital α, is estimated from atomic X-ray terms or fitted empirically from model diatomic calculations. Errors introduced by dropping explicit consideration of core orbitals in the formation of the Fock matrix elements for valence orbitals are not small, but can be compensated for in adjustments of F αα in approximate formulations. The total energy is examined and it is found that the ‘valence-orbital only’ energy gives a rather accurate description of the system ene...

The calculated spectra of the azanaphthalenes

Abstract A modified INDO (intermediate neglect of differential overlap) method is used to calculate the electronic spectra of naphthalene and some mono-, di-, and tetraazanaphthalenes. The technique is capable of reproducing the better classified bands of this series within a rms error of ∼1000 cm−1. The four lowest π-π ∗ bands of naphthalene are well represented; a fifth band reported at ∼52,600 cm−1, and generally assigned 1 B 2u (π-π ∗ ) , may be 1 B 3g (π-π ∗ ) borrowing intensity. The lowest excited singlet state calculated for quinoline is n → π ∗ , estimated nearly degenerate with the lowest π-π ∗ , while that for isoquinoline is calculated π-π ∗ ; experimental evidence supports the π-π ∗ assignment in both cases, but the corresponding absorption in quinoline appears complex. Of the diazanaphthalenes examined (with two nitrogens in one benzenoid ring) all are calculated to have one n-π ∗ transition before the first π-π ∗ except phthalazine, in which two n-π ∗ transitions are calculated to be the lowest lying. This is in accord with experimental evidence to date, although the nature of the observation in phthalazine is reinterpreted as one 1B2(n-π). 1,4,5,8-tetrazanaphthalene is predicted to have a group theoretically forbidden n-π ∗ excited state as low as 21,000 cm−1, and should prove interesting experimentally. Even though n-π ∗ excited states are often calculated to be the lowest lying, none of these compounds are predicted to have an “n” orbital as homo. Further interpretations of the spectra of the azanaphthalenes are made in view of the calculations. Theoretical limitations of the method employed for this study are discussed.

A constant denominator perturbation theory for molecular energy

A “constant denominator” perturbation theory is developed based on a zeroth order Hamiltonian characterized by degenerate subsets of orbitals. Such a formulation allows for a decoupling of the numerators of the perturbation sequence, allowing for much more rapid evaluation of the resultant sums. For example, the full fourth order theory can be evaluated as an N6 step rather than N7, where N is proportional to the basis set.Although the theory is general, a constant denominator is chosen for this study as the difference between the average occupied and average virtual orbital energies scaled so that the first order wavefunction yields the lowest possible variational bound. The third order correction then appears naturally as a scaled Langhoff-Davidson correction. The full fourth order with this partitioning is developed. Results are presented within the localized bond model utilizing both the Pariser-Parr-Pople and CNDO/2 model Hamiltonians. The second order theory presents a useful bound, usually containing a good deal of the basis set correlation. In all cases examined the fourth order theory shows remarkable stability, even in those cases in which the Nesbet-Epstein partitioning seems poorly convergent, and the Moller-Plesset theory uncertain.

On the excited states ofp-quinones and an interpretation of the photocycloaddition ofp-quinones to alkenes

A theoretical investigation is made of the electronic states ofp-benzoquinone (PBQ), methyl substituted PBQs and 1,4-naphthoquinone (NQ). In accord with experiment, the lowest triplet state of PBQ is calculated to be3B1g (n, π*), while that for duroquinone (DQ) is3B3g (π, π*). The electron densities of these states are consistent with the hypothesis that3n, π* states lead to oxetan formation and3π, π* states to cyclobutanes. It is predicted that trimethyl PBQ might form both adducts, as the two states are calculated to be nearly degenerate.The photochemistry of NQ is more complex. The lowest excited triplet state is calculated to be ofn, π* symmetry, in accord with experiment; however, several other states are predicted near in energy, and the photochemistry cannot be rationalized unambiguously.

An approximate molecular orbital method

An approximate molecular orbital method is developed for hydrogen and first row elements at the minimum basis set level. Although the basis set consists of only valence orbitals, the explicitly ignored inner shell is accommodated through pseudopotentials. The one center one electron terms are evaluated from atomic spectra. The two and three center one electron terms are exactly calculated. The two electron Coulomb matrix is evaluated rapidly in a mixed representation using a simple projection overlap. The two electron exchange matrix is estimated in a symmetrically orthogonalized set, with simple empirical corrections. The resulting method executes approximately as rapidly as does the popular INDO method. The model is applied to molecules up to the size of adenine, C5N5H5. Where comparison can be made with minimum basis set STO calculations, the method reproduces occupied molecular orbital eigenvalues, electron densities, and calculated bond distances to within a rms error of 0.03 a.u. The virtual molecul...

Calculated spectra of benzaldehyde and benzoic acid

Abstract A modified Intermediate Neglect of Differential Overlap technique is used to examine the absorption and emission spectra of benzaldehyde and the benzoic acid monomer and cyclic dimer. The lowest energy singlet and triplet of benzaldehyde are found to be of n-π ∗ type. The strong spin-orbit interaction 3 (n-π ∗ ) ⇝ 1 (π-π ∗ ) is held responsible for the observed weak fluorescence-strong phosphorescence. A lowest 1 (n-π ∗ ) has been calculated for the monomer of benzoic acid. The presence of this transition accounts for the non-fluorescent-strongly phosphorescent nature of the monomer via the coupling 3 (π-π ∗ ) ⇝ 1 (n-π ∗ ) . The calculations suggest that the 1 ( n -π ∗ ) will lie above the 1 (π-π ∗ ) in the dimer and thus provide an explanation for the observed dimer fluorescence.

An approximate variational perturbation method

Abstract The Goldhammer—Feenberg variational procedure is applied to the perturbation treatment of the configuration interaction matrix of Diner, Malrieu and Claverie (PCILO) to yield a scheme (PVCILO) that appears more accurate for the small systems investigated. In addition, PVCILO shows promise as executing as an N2 method, where N is the number of basis bonds.

APPROXIMATE QUANTUM MECHANICAL METHODS FOR LARGE MOLECULES

I discussed two approximate quantum mechanical methods that are particularly useful in examining the electronic structure of large molecular systems. The first method mentioned was the Zero Differential Overlap theory, which has been developed and used quite successfully in describing electronic spectroscopy and the properties of excited states. Most recently, this theory has been extended to include elements of the first transition series. I discussed some details of the system that suggest that all one‐centered integrals must be included for accurate predictions. Results for ferrocene and for a model oxyheme complex demonstrate that the balance between charge transfer, d‐d, and ligand‐ligand excitations, so difficult to obtain in ab initio work, is easily reached by this theory.