J. A. Pople

Approximate Self‐Consistent Molecular Orbital Theory. III. CNDO Results for AB2 and AB3 Systems

The approximate self‐consistent molecular orbital theory with complete neglect of differential overlap (CNDO) presented in earlier papers has been modified in two ways. (a) Atomic matrix elements are chosen empirically using data on both atomic ionization potentials and electron affinities. (b) Certain penetration‐type terms, which led to excess bonding between formally nonbonded atoms in the previous treatment, have been omitted. The new method (denoted by CNDO/2) has been applied to symmetrical triatomic (AB2) and tetratomic (AB3) molecules, for a range of bond angles. The theory leads to calculated equilibrium angles, dipole moments, and bending force constants which are in reasonable agreement with experimental values in most cases.

Approximate Self‐Consistent Molecular Orbital Theory. I. Invariant Procedures

A general discussion of approximate methods for obtaining self‐consistent molecular orbitals for all valence electrons of large molecules is presented. It is shown that the procedure of neglecting differential overlap in electron‐interaction integrals (familiar in π‐electron theory) without further adjustment may lead to results which are not invariant to simple transformations of the atomic orbital basis set such as rotation of axes or replacement of s, p orbitals by hybrids. The behavior of approximate methods in this context is examined in detail and two schemes are found which are invariant to transformations among atomic orbitals on a given atom. One of these (the simpler but more approximate) involves the complete neglect of differential overlap (CNDO) in all basis sets connected by such transformations. The other involves the neglect of diatomic differential overlap (NDDO) only, that is only products of orbitals on different atoms being neglected in the electron‐repulsion integrals.

Approximate Self‐Consistent Molecular Orbital Theory. II. Calculations with Complete Neglect of Differential Overlap

The approximate self‐consistent molecular orbital method with complete neglect of differential overlap (CNDO), described in Paper I, is used to calculate molecular orbitals for the valence electrons of diatomic and small polyatomic molecules. A small number of bonding parameters (β‐resonance integrals) are chosen semiempirically so that the results are comparable to previous accurate LCAO—SCF wavefunctions for diatomic hydrides using a similar basis set. With this calibration, it is found that calculations on other diatomics and polyatomics lead to molecular orbitals and electron distributions in reasonable agreement with the full calculations where available. Although the new method is not yet successful in predicting bond lengths and dissociation energies, it does lead to the correct geometry, reasonable bond angles and bending force constants for the polyatomic molecules considered. It also gives calculated barriers to internal rotation for ethane, methylamine, and methanol which are in fair agreement ...

Molecular‐Orbital Theory of Diamagnetism. I. An Approximate LCAO Scheme

An independent‐electron molecular‐orbital theory is developed for the diamagnetic behavior of electrons in the presence of an applied magnetic field. The molecular orbitals are written as linear combinations of gauge‐invariant atomic orbitals, the dependence of the (complex) coefficients on the magnetic field being studied by perturbation theory. By making a systematic set of approximations involving the neglect of some interatomic terms, a general expression is derived for the diamagnetic susceptibility tensor as a sum of atomic contributions. Each atomic contribution is made up of two parts, the first being a diamagnetic (Langevin‐type) term and the second being a paramagnetic contribution involving the details of the electronic excited states. At a lower level of approximation, this second term can be expressed in terms of atomic charge densities and bond orders together with a mean electronic excitation energy.It is pointed out that the theory provides a convenient basis for detailed interpretation of...

Nuclear Spin Coupling Between Geminal Hydrogen Atoms

A molecular orbital theory of nuclear spin coupling between geminal hydrogen atoms is developed and found to give a satisfactory interpretation of substituent effects evident in experimental data. The theory suggests that the value of geminal coupling constants provides a means of distinguishing between inductive and hyperconjugative electron transfer. A number of geometrical rules are also proposed which should make these constants valuable in studies of molecular conformation.

Molecular‐Orbital Theory of Diamagnetism. II. Calculation of Pascal Constants for Some Noncyclic Molecules

The general formulas for atomic contributions to diamagnetic susceptibilities derived in part I are used to calculate Pascal‐type constants for some simple molecules containing hydrogen, carbon, nitrogen, oxygen, and fluorine. For noncyclic saturated molecules, the theory reproduces the relative values of empirical atomic contributions fairly satisfactorily, although absolute numerical agreement is poor. For unsaturated groups, the theory provides an interpretation of the constitutive corrections required in the Pascal scheme. Considerable positive corrections are calculated for the carbon—carbon double bond and the carbonyl group, but not for the carbon—carbon triple bond. This is in agreement with the empirical rules. The theory also makes a number of predictions about diamagnetic anisotropies.

Molecular Orbital Theory of Diamagnetism. V. Anisotropies of Some Aromatic Hydrocarbon Molecules

Molecular orbital theory is used to calculate the diamagnetic susceptibility contributions of local intraatomic currents in a series of polycyclic aromatic hydrocarbons. It is found that a considerable part of the excess diamagnetism perpendicular to the molecular plane is due to the anisotropy of these local terms so that the contribution of interatomic ring currents is less than has been believed previously. The theory also reproduces the trend for the in‐plane susceptibility to be (numerically) greatest along the long axis of the molecule.

Molecular Orbital Theory of Diamagnetic Polarization. III. Anisotropic Properties of the Carbonate and Nitrate Ions

Many conjugated molecules have anisotropic diamagnetic susceptibilities (with the axis of high diamagnetism perpendicular to the molecular plane) which cannot be explained in terms of interatomic ring currents as for aromatic hydrocarbons. The carbonate and nitrate ions are well‐known examples. In this paper, the approximate molecular orbital theory developed in Part I is applied to these systems and predicts considerable anisotropy of the correct sign for both, mainly on the central atom. A corresponding calculation of the C13 chemical shift of CO32— provides an interpretation of the NMR anisotropy observed by Lauterbur [Phys. Rev. Letters 1, 343 (1958)].