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 complete Intermediate Neglect of Differential Overlap model suitable for the examination of transition metal complexes is described. The model is characterized by the inclusion of all the one-center exchange terms necessary for rotational invariance and accurate spectroscopic predictions, as well as an accurate description of integrals involving 3d atomic orbitals. The model is within the unrestricted Hartree-Fock formalism, and a method for spin purification is described. Problems with convergence of the self-consistent field are discussed, and a method that has been found successful in aiding the convergence is outlined. The model has been applied to many transition metal systems. In this article the results of calculations on the chlorides of Fe, Co and Cu are described. The results of these calculations are compared with experiment, and with the results of calculations by other methods.

An intermediate neglect of differential overlap theory for transition metal complexes: Fe, Co and Cu chlorides

Theory of Orientation and Stereoselection

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.

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

Starting from a general quantum-mechanical perturbation theory on the nonlinear optical (NLO) effect in crystals, this review gives a systematic presentation of the basic concepts and calculation methods of the ‘anionic group theory for the NLO effect of crystals’ and a brief discussion of the approximations involved. Calculations have been made for the second harmonic generation (SHG) coefficients of a few typical NLO crystals. Comparisions between these theoretical values and the experimental values made both on powdered crystals and on single crystals suffice to show the feasibility of the theoretical treatment and calculation methods. On this basis, borate ions of various structure types are classified and systematic calculations are carried out for the NLO susceptibilities of some typical borate crystals with good prospects of applications in opto-electronics. Through these calculations, a series of structural criteria serving as useful guidelines for searching and developing new NLO crystal...

The anionic group theory of the non-linear optical effect and its applications in the development of new high-quality NLO crystals in the borate series

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser‐Parr‐Pople method, and by the introduction of a new empirical parameter κ to differentiate resonance integrals between σ orbitals from those between π orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyridazine, pyrimidine, and pyrazine. The results obtained were refined by a limited CI calculation and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both n→π* and π→π* singlet‐singlet transitions. The relative energies of the pi and lone‐pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the “lone pairs” in these compounds is discussed.

Use of the CNDO Method in Spectroscopy. I. Benzene, Pyridine, and the Diazines

The modified CNDO method previously reported has been used to calculate the electronic spectra of cyclopentadiene, the cyclopentadienide ion, pyrrole, furan, pyrazole, imidazole, 2‐pyrrolecarboxaldehyde, and furfural. In general, the results obtained agree quite well with experimental data. Because the CNDO method treats explicitly all σ and π valence electrons of a molecule, the results of the calculations are used to discuss some of the σ–π interactions which previously could not be treated. The calculations are successful in reflecting changes in the electronic spectra of compounds as a result of extending conjugation or addition of a substituent.

Use of the CNDO Method in Spectroscopy. II. Five‐Membered Rings

The modified CNDO method previously reported has been applied to the calculation of a series of monosubstituted benzenes and pyridines, namely, aniline, anilinium ion, benzonitrile, nitrosobenzene, phenol, phenoxide ion, toluene, pyridinium ion, pyridine‐N‐oxide, 1‐hydroxy‐pyridinium ion, the aminopyridines, and the cyanopyridines. The calculated values of the transition energies and corresponding oscillator strengths are in good agreement with available experimental data on the electronic spectra of these compounds. An analysis of the lower‐energy excited states by means of the calculated results suggests that there is an astonishingly small amount of charge‐transfer character associated with the observed ultraviolet bands. The calculations indicate that the changes in charge densities in going from the ground state to the lowest energy π → π* excited state can be related to the Hammett σ's for the substituents.

Use of the CNDO Method in Spectroscopy. III. Monosubstituted Benzenes and Pyridines

The modified CNDO method has been applied to the study of the electronic‐absroption spectra of several small molecules; namely, formaldehyde, formic acid, formamide, allene, ketene, and diazomethane, with quite satisfactory results. The lowest energy excited state of the last three compounds has been assigned as the state which arises from a π → π′* transition. A study has also been made of the calculation of ground‐state properties from the spectroscopic parameterization. It has been concluded that although this method can give reasonable estimates of these properties, it is most reliable when used to evaluate ground‐state properties which depend upon calculated eigenvalues.

H. H. Jaffé

Papers

Use of the CNDO Method in Spectroscopy. I. Benzene, Pyridine, and the Diazines

Use of the CNDO Method in Spectroscopy. II. Five‐Membered Rings

Use of the CNDO Method in Spectroscopy. III. Monosubstituted Benzenes and Pyridines

Use of the CNDO Method in Spectroscopy. IV. Small Molecules: Spectra and Ground‐State Properties

Comments on “Lowest Ionization Potentials of Some Nitrogen Heterocyclics”