Free‐Electron Model and Doublet Splitting in Aromatic Hydrocarbon Ions

Abstract: The emission spectrum of 1, 3, 5-C 6 F 3 D + 3 in the 4376–5435 A region has been photographed and vibronically analyzed. The transition is B 2 A″ 2 -X 2 E″. Vibrational frequencies were assigned using the isodynamic molecule method as previously done in analyzing the 1, 3, 5-C 6 F 3 H + 3 spectrum. Out-of-plane a″ 2 and e″ modes are active in even quanta only and are associated with sequence bands a′ 1 and e′ modes are active in both odd and even quanta. The e′ mode activity is shown to be due to dynamic Jahn—Teller effects in the X 2 E″ state. A brief review of the relevant theory leads to a discussion of criteria for identifying Jahn—Teller spectral effects. Two importants parameters enter into the linear coupling model calculations: D , the interaction constant, and ω, the deperturbed frequency of the Jahn—Teller active mode. These parameters are determined by fitting calculated band positions and intensities to experimental results. It is shown how to resolve possible ambiguities in these determinations, D and ω values were obtained for four e′ modes of 1, 3, 5-C 6 F 3 D + 3 and 1, 3, 5-C 6 F 3 + 3 , modes 6, 7, 8 and 9. The corresponding Jahn—Teller barrier heights for interconversion between the lowest energy asymmetric configurations were evaluated for the two ions.

Abstract: Using a free‐electron model for the π‐electron system in benzene the electronic quadrupole moment has been calculated to be 2629 × 10−26 esu which is in fair agreement with the experimental value of 3486 × 10−26 esu Considering the molecular interaction to be quadrupolar in origin for benzene crystal the sublimation energy was calculated to be 1064 kcal/mole which is in good agreement with the experimental value of 1067 kcal/mole

Abstract: Using the free electron wave function it has been shown that the propability of photoionization of a π-electron from aromatic hydrocarbons should be maximum if the incident photon has energy sufficient to ionize and to leave an additional momentum p=√5 Kħ2/2 to the escaping electron. This momentum further appears to be independent of the ring size.

Abstract: Using a free electron model for the π-electron system in aromatic hydrocarbons the π- electron susceptibility due to Langevin diamagnetism and Van Vleck High frequency para-magnetism (H. F.) have been calculated. The H. F. term has been found to increase rapidly with the ring size.

Abstract: The classification of π‐orbitals in a cata‐condensed aromatic system is like that of the orbitals of a free electron traveling in a one‐dimensional loop of constant potential around the perimeter. To take into account electron interaction, certain quantities corresponding to angular momenta may be added or subtracted. Introduction of the cross‐links in the molecule removes the degeneracy. The first excited configuration in such systems gives two low frequency singlet weak absorption bands and two higher singlet strong dipole absorption bands. Selection and polarization rules are given. The levels are identified from the spectra and some of their properties are determined. An explanation is given of the regularities found by Klevens and Platt. A systematic nomenclature is given. The results agree qualitatively with LCAO theory, can be applied easily to unsymmetrical molecules, and can possibly be extended to other types of ring systems.

Abstract: Values of the diamagnetic anisotropy of benzene and other aromatic hydrocarbon molecules are calculated on the basis of the assumption that the p_z electrons (one per aromatic carbon atom) are free to move from carbon atom to adjacent carbon atom under the influence of the impressed fields. When combined with the assumed values for the contributions of the other electrons (‐2.0×10^(‐6) for hydrogen, ‐4.5×10^(‐6) for aromatic carbon, ‐6.0×10^(‐6) for aliphatic carbon) these lead to principal diamagnetic susceptibilities of molecules in approximate agreement with the available experimental data. The diamagnetic anisotropy of graphite is also discussed.

Abstract: An approximate wave-equation (6) is set up which takes into account terms of the order ${(\frac{v}{c})}^{2}$ in the interaction of two electrons. This equation (6) is reduced to a form (48) which can be interpreted in terms of electronic spins. Disregarding the effect of retardation the two electrons are described by formula (10). This is reduced to a form (36) which can also be described in terms of spins. It is shown that the retarded equation (48) differs from the non-retarded (36) by terms which affect the fine structur of orthohelium and which have not been known so far.The derivation of the wave-equation (6) is made first in configuration space and later by the Heisenberg-Pauli theory of wave-fields. The latter method is used only to terms of the first order in the Coulomb interaction. It is shown from the consideration of (36) that it cannot be the correct equation and that the modifications due to retardation introduced in (6) and (48) are necessary. These modifications are appreciable only for spectra of elements with low atomic number.

Abstract: Transition probabilities and selection rules are calculated for the lower triplet‐singlet transitions of benzene. The relativistic spin‐orbit coupling term combines the triplet state with an intermediate singlet state, and then dipole transition to the ground state occurs. The selection rules are deduced group‐theoretically, and the transition probabilities are calculated using the LCAO one‐electron approximation. The effect of vibration is discussed. The theoretical results obtained agree with Shull's and McClure's experimental results.

Abstract: The proton resonance spectra of a number of alternant aromatic hydrocarbons are reported. With the exception of benzene and pyrene, two or more signals were obtained for each hydrocarbon. A probable assignment of the spectrum for each compound is given, and this was confirmed for anthracene and phenanthrene by deuteration. The spectrum of the non-alternant hydrocarbon azulene is also presented. The observed nuclear magnetic resonance spectra of the aromatic hydrocarbons cannot be interpreted on the basis of symmetry considerations or $\pi $-electron density, but are readily explained in terms of a simple model based on induced diamagnetic currents in the conjugated aromatic rings. The spectra calculated for each hydrocarbon on the basis of this model satisfactorily reproduce the main features of the observed spectra.