A new approximate self‐consistent‐field method for the determination of molecular orbitals for all valence electrons of a molecule is proposed. This method features neglect of differential overlap in all electron‐interaction integrals except those involving one center only. The parameters involved in the calculation are generally obtained semi‐empirically. The new method is known as the Intermediate Neglect of Differential Overlap (INDO) method, and may be regarded as an improvement over the CNDO method proposed in Part I, in that atomic term‐level splittings and unpaired spin distributions are better accommodated. Calculations on geometries of AB2 and AB3 molecules are reported to substantiate the proposed method, and calculated unpaired spin distributions for methyl and ethyl radicals are discussed.

Approximate Self‐Consistent Molecular‐Orbital Theory. V. Intermediate Neglect of Differential Overlap

An analysis of the electron spin resonance of x‐irradiated single crystals of β‐succinic acid shows that: (a) the principal long‐lived paramagnetic species produced by the radiation damage is (CO2H)CH2–ĊH(CO2H); (b) the radical is oriented in the crystal lattice in nearly the same way that the parent succinic acid molecule is oriented in the undamaged lattice; (c) the strongly anisotropic hyperfine interaction due to the σ proton is very nearly the same as that previously found for the σ proton in the malonic acid radical, (CO2H)ĊH(CO2H). In these molecules the σ proton is directly bonded to the carbon atom on which the odd electron is largely localized. The two methylene protons in the radical are not equivalent, and their hyperfine interactions are nearly isotropic, and in the range 80–100 Mc.

Radiation Damage in Organic Crystals. II. Electron Spin Resonance of (CO2H)CH2CH(CO2H) in β-Succinic Acid

In a radical the single determinant wave function which gives the lowest electronic energy is one where electrons of opposite spins occupy different sets of molecular orbitals and thereby lower the ‘exchange’ part of the energy. The unpaired spin density may be negative in a wave function of this type and is easily found by perturbation theory if certain exchange integrals are small. We show that the spin density is then almost the same as one finds by combining the usual single determinant function (with one unpaired electron, and 2n paired ones in n orbitals) with its singly excited doublet configurations. In alternant hydrocarbons the Pariser and Parr theory leads to a simple formula for the spin density: ρr = cro 2 - λ Σ s πrscso 2, where cro is the Huckel coefficient of the odd orbital on atom r, πrs is the mutual polarizability of atoms r and s, and λ is a constant derived from the theory. The observed hyperfine structure in the electron resonance spectra of naphthalene, anthracene, perylene, diphen...

Self-consistent field theory of the electron spin distribution in π-electron radicals

A quantitative theory of the isotropic electron‐nuclear spin interactions of carbon 13 in pi‐electron radicals is presented and applied to the hyperfine splittings observed in the electron spin resonance spectra of these substances. The splittings arise from sigma‐pi interactions which polarize both the 1s and 2s electrons. The 1s‐orbital spin polarization is shown to contribute a term of negative sign with a magnitude comparable to that from the 2s electrons. For an sp2 hybridized carbon atom that is bonded to three atoms, Xi (i=1, 2, 3), the hyperfine constant aC has the form aC=(SC+ ∑ i=13QCXiC)ρπ+ ∑ i=13QXiCCρiπ, where ρπ and ρiπ(i=1,2,3) are the pi‐electron spin densities on atoms C and Xi, respectively. The contribution of the 1s electrons is determined by SC and that of the 2s electrons by the Q's, where QBCA is the sigma‐pi parameter for the nucleus of atom A resulting from the interaction between the bond BC and the pi‐electron spin density on atom B. Calculations for a planar CHC2 fragment model...

Theoretical Interpretation of Carbon‐13 Hyperfine Interactions in Electron Spin Resonance Spectra

THEORETICAL INTERPRETATION OF CARBON-13 HYPERFINE INTERACTIONS IN ELECTRON SPIN RESONANCE SPECTRA. Technical Note Report No. 9

An analysis of the electron magnetic resonance of single crystals of malonic acid that were subjected to x-ray damage indicates that: (a) the principal long-lived paramagnetic species produced by the x-ray darnage is gen atoms of this radical are oriented in the crystalline lattice in the same way as these atoms are arranged in the parent undamaged malonic acid molecule. (c) The z,x,y components of the diagonal (electron-spin) - (nuclear-spin) coupling dyadic for the proton attached to the alpha -carbon atom are found to be of the same relative sign and of magnitudes 29. 61, and 91 Mc, respectively. In this orthogonal axis system, z is the CH bond direction and x is perpendicular to the plane of the three carbon atoms. These results are in excellent agreement with theoretical values of the distributed dipole and contact hyperfine interactions and show that this molecule is a pi -electron radical, that the unpaired electron is concentrated almost entirely on the alpha -carbon and that the spin density on the in-plane sigma -proton is negative. The observed g-factors for this radical are g/sub x/ = 2.0026, g/sub y/ = 2.0035, and g/sub z/ = 2.0033 and are in good qualitative agreement withmore » previous theoretical estimates of these quantities. (auth)« less

Radiation Damage in Organic Crystals. I. CH(COOH)2 in Malonic Acid1

We have carried out a detailed analysis of the electron magnetic resonance spectra of single crystals of malonic acid that were subjected to 50-kv. X-ray damage at room temperature. A typical spectrum of an aged single crystal is shown in Figure 1. The positions and intensities of the principle signals (1-4 in Fig. 1) depend on the crystal orientation relative to the applied magnetic field (3,400 gauss). All of the observed spectra can be accounted for in terms of the following set of assumptions.

T. Cole

Papers

Radiation Damage in Organic Crystals. I. CH(COOH)2 in Malonic Acid1

Electron magnetic resonance of ch(cooh)(2).