Tosinobu Anno

Semiempirical calculation on the electronic structure of the nitrogen-containing heterocyclic molecules. I. General theory

A semiempirical theory for n — π and π — π spectra of nitrogen heterocycles is proposed. The theory is an extension of the semiempirical molecular‐orbital method of Pariser and Parr, and the nonbonding electrons localized at the nitrogen atoms as well as π electrons are considered explicitly into the interaction term in the Hamiltonian. The orbitals in which nonbonding electrons are contained may be any 2s—2p hybrids. The differential overlap between atomic orbitals are formally neglected. One‐center electronic‐interaction integrals are obtained from atomic spectral data and two‐center integrals at moderate internuclear distances are extrapolated, using corresponding one‐center integrals obtained from atomic spectral data together with the theoretical value of the two‐center integrals at larger internuclear distances. On account of the hybrid nature of the nonbonding AOs (AOs from which nonbonding MOs are constructed), various kinds of two‐center integrals as well as one‐center ones appear. The method ...

Systematic Determination of the Slater Parameters for the First Transition Elements

Slaters parameter Fk and Gk with k ≠O have been determined systematically from the experimental atomic energy levels for the neutral atoms and singly through triply positive ions of the first transition elements in their 3dn, 3dn−14s, 3dn−14p, 3dn−24s4p, and 3dn−24s2. configurations, by a least‐squares procedure. A procedure of obtaining the semiempirical values of F0s, which have never been obtained from the data of atomic spectra, is given along the line suggested by Anno [J. Chem. Phys. 47, 5335 (1967)] involving the consideration of appropriate “electron‐transfer reactions.” Data on ΔE, the energy change in the course of the electron‐transfer reaction, are also given, which may be combined with Fks and/or Gks (k ≠ 0) to obtain F0s. Ideal correlation lines, which correlate a particular kind of Fk, Gk (k ≠ 0), or ΔE with the atomic number Z and/or electron configuration in ideal situations where no anomaly due such as to CI or misassignment were present, are discussed and are given in such a way th...

Analysis of the Near Ultraviolet Absorption Spectra of ortho‐ and para‐Dichlorobenzene Vapors

The absorption spectra of o‐ and p‐dichlorobenzene vapors appearing in the region 2900—2400 A and 2950—2400 A, respectively, were photographed and measured. For the ortho‐spectrum the band at 36 232 cm—1 is assigned as the 0—0 band. The progression with frequency intervals of 1089 cm—1 starts from the stronger bands. For the para‐spectrum, the band at 35 750 cm—1 is taken to be the 0—0 band. The only progression‐forming frequency is 1051 cm—1. In both the spectra, most of the prominent bands are assigned to progressions or combinations of the possible fundamental frequencies. The fundamental frequencies are compared with the Raman values. From the vibrational analysis it is concluded that both molecules in the excited electronic states retain all their elements of symmetry in the ground states. For the para‐compound the molecular structure in the upper state is discussed in some detail.

Electronic States of p‐Benzoquinone. VI. Molecular Geometry in the Excited Electronic State of the 4500‐A Absorption System as Derived from the Franck‐Condon Principle

The method used for evaluating the Condon overlap integral associated with any vibronic band of an electronic absorption system of an XY2 molecule, as developed by J. B. Coon and his co‐workers, is applied to more complex molecules. Thus, some information about the geometry of the excited electronic state of a complex molecule may be determined if the geometry in the ground state, the intensities of vibronic bands of the associated electronic absorption system, and normal coordinates and frequencies in both electronic states are known. The method is applied to the 4500‐A absorption system of p‐benzoquinone. Since the normal coordinate treatment for this molecule is only qualitatively valid, especially in its excited state, the results are expected to be more or less qualitative. If we take the resulting change of bond angles into account, the ring‐bending frequency of species Au in the excited electronic state is calculated to be 438 cm—1 by the method described in Part III of this series [T. Anno and A. ...

Semiempirical Calculation on the Lower Electronic States of the Benzene Molecule

Within the semiempirical ASP—LCAO—MO—CI framework proposed by Pariser and Parr, the lower excited levels of the benzene molecule are calculated by considering CI up to and including doubly excited configurations. This calculation has three purposes: (i) a check on the value of the core resonance integral βCC, (ii) the symmetry assignment of the controversial absorption system around 2000 A and (iii) the elucidation of the change of the ring‐breathing vibrational frequency due to electronic excitation. From the condition that the calculated value of the lowest 1 B2u−1 A1g transition energy agree with experiment, the core integral βCC is found to be −2.7217 eV, which is to be compared with −2.39 eV suggested originally by Pariser and Parr without considering CI. By using this new value of βCC, CI calculations for the lower singlet levels are carried out. The theoretical energy levels are compared with the experimental data as well as the calculated values with nonempirical and the other semiempirical method...

Electronic States of p‐Benzoquinone. V. Vibrational Analysis of the Vapor Absorption Spectrum around 4500‐A Region

The absorption spectrum of p‐benzoquinone vapor in the region between 4080 and 5100 A was photographed and measured. Although the theoretical calculation as well as the experimental crystal spectrum indicate that two singlet‐singlet electronic transitions exist in this region, prominent vibrational structure of the vapor spectrum can be interpreted as caused by a single forbidden electronic transition. If we assume that the hydrogen vibrations are not effective as perturbing vibrations which make the forbidden electronic transitions allowed through the vibrational‐electronic interaction, this fact suggests the following two sets of assignments for the symmetries of the forbidden transition and the perturbing allowed transition: (1) the spectrum is a superposition of 1Au, 1B2u←1Ag transitions perturbed by a 1B2u←1Ag transition, (2) the spectrum is caused by a single 1B1g←1Ag transition being allowed through vibrational‐electronic interaction with the allowed 1B1u←1Ag transition. Vibrational structure alone...

Semiempirical calculation on the electronic structure of the nitrogen-containing heterocyclic molecules. II. Electronic structure of pyrazine with particular reference to its n-π transition

The semiempirical theory of n—π and π—π spectra of nitrogen analogs of aromatic hydrocarbons proposed in Part I is applied to calculate the lower excited levels of the pyrazine molecule. The doubly excited configurations as well as singly excited configurations are considered in CI calculation. It is shown that the usual assumption of sp2 hybridization of the nonbonding orbital of the nitrogen atoms in the pyrazine molecule results in a considerably higher calculated value for the n—π transition energy as compared with experiment, even if the doubly excited configurations are considered. In order to bring the calculated values of the lowest 1Ag→1B1u,1B3g (n−π) transition energies in agreement with the observed values, the s character of the nonbonding orbital of the nitrogen atom should be taken as 0.103. Discussions which support the lower s character of the nonbonding orbitals of the nitrogen atoms in this molecule are presented.

Finer examination of Politzer’s improved approximate energy formula for molecules

Politzer’s relation1,2 connecting the total energy E of a molecule with the total electrostatic potential VO,A at the nucleus of A within the molecule is given by: E=ΣA kA ZA VO,A. It is argued that changes in KA due to change of the nuclear environmental of A should be taken into accounts to get an accurate value of E. (AIP)

Out‐of‐Plane Vibrations of a Conjugated Hydrocarbon : trans‐Butadiene

A method of obtaining some of the out‐of‐plane force constants in conjugated hydrocarbons from bond orders and of borrowing the other kinds of these constants from similar molecules is described. The method includes the assumptions that the force constant of torsion around the CC bond is proportional to the product of the π bond order and the overlap integral of the carbon 2pπ atomic orbital and that the interaction constant between wagging motion of a CH group and a torsion around a CC bond to which the CH group is attached is proportional to the diagonal constant of the torsion. The validity of these assumptions is discussed. As an application of the method the nonplanar frequencies of trans‐butadiene are calculated and compared with experimental values. The results are found to be encouraging.

Further Significance of the Pariser Method for Evaluation of the One‐Center Electron Repulsion Integral

There is a difference between the nonempirical and the semiempirical value of the one‐center electron repulsion integral, even if correct recognition is made of the atomic species for which the semiempirical value of the integral is determined with consideration of an electron‐transfer reaction according to Pariser. This difference has been analyzed for the integral which represents the average interaction of a pair of 2p electrons within an atom. It is shown that the main source of the difference is the failure of the usual nonempirical determination of the integral in considering properly the reorganization of the electrons occuring in the course of the electron‐transfer reaction. The correlation energy is shown to have only minor contribution to this difference.