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 with experiment.

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

A summary and critical review of available information on molecular quadrupole and higher moments is presented. A theorem is also proved which shows that only one independent scalar quantity is required to determine a molecular electric multipole tensor of rank p for molecules with an n-fold axis of symmetry where p < n.

Molecular multipole moments

Temperature‐dependence measurements have been made on the chemical shift of the proton of a water molecule in the liquid state and in the gas state at varying pressure. The problem of relating these experimental data to the intermolecular forces leading to cohesion and to hydrogen‐bond formation between water molecules is considered in detail. It is shown that a consistent treatment of the chemical shift, thermal, and dielectric data for water can be given based on a two‐state model involving an equilibrium between a hydrogen‐bonded ``icelike'' fraction and a ``monomer'' fraction whose interaction with the lattice arises entirely from London dispersion forces.Using semiempirically derived values of the chemical shift and energy associated with the condensation of water vapor to ``monomer,'' the magnitude of the shift associated with the transformation to ice is calculated. It is then shown that, on the assumption that the hydrogen bond is electrostatic in character, the ``polar'' contribution to this shif...

Proton Resonance Shift of Water in the Gas and Liquid States

Methods of efficiently optimizing the orbitals of generalized valence bond (GVB) wavefunctions are discussed and applied to LiH, BH, H_3, H_(2)O, C_(2)H_6, and O_2. The strong orthogonality and perfect pairing restrictions are tested for the X^(1)Σ^+ state of LiH, the X 1Σ+, a^(3)π, and A^(1)π states of BH, and the H_(2)+D⇄H+HD exchange reaction. The orbitals of H_(2)O and C_(2)H_6 naturally localize into OH, CH, and CC bonding pairs. The nonbonding orbitals of H_(2_O are approximately tetrahedral but this description is only 2 kcal lower than the optimum description in terms of σ and π lone‐pair functions. The calculated rotational barrier for C_(2)H_6 is 3.1 kcal, in good agreement with the experimental value (2.9 kcal). The description of the O2 molecule in the GVB approach is presented and the results of carrying out CI calculations using the GVB orbitals are discussed. The GVB orbitals are found to be a good basis set for configuration interaction calculations. The general features of GVB orbitals in other molecules are summarized.

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Self‐Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H3, BH, H2O, C2H6, and O2

With the increasing availability of powerful computers, attempts to calculate the electronic structure and properties of molecules by the direct ab initio solution of a many-body Schrodinger equation have received a great stimulus. The authors review the mainstream developments in quantum chemistry and give a straightforward account of some of the many-body techniques borrowed, with appropriate modifications, from other areas of physics-field theory, nuclear theory and solid-state theory. After a historical introduction, the traditional approach based on the self-consistent field and the method of configuration interaction is developed in detail. This is followed by the introduction of the cluster expansion, various types of correlated electron-pair theory, and diagrammatic perturbation methods. Finally, propagator and Green function techniques are reviewed, not only as a means of calculating transition energies but also as an alternative approach to the determination of the electronic ground state.

http://iopscience.iop.org/article/10.1088/0034-4885/43/9/001/pdf

Quantum theory of molecular electronic structure

Non-empirical calculations of the electronic structure of the water molecule (treated as a full ten-electron system) are carried out for various types of wave function. These include a ‘bond orbital’ function, a ‘modified electron-pair’ function, and various Roothaan-type self-consistent field (s. c. f.) functions. These approximations are refined by admitting interaction with up to twelve configurational functions of ground-state symmetry. Three bond angles are considered. The results show that the modified electron pair function, which has not hitherto been used in non-empirical calculations, provides the most satisfactory first approximation. This function is constructed from orthonormalized hybrid orbitals in order to overcome non-orthogonality difficulties; and the inclusion of configuration interaction in this particular basis is found to be simple, effective and physically meaningful. The concept of a ‘core’, comprising the oxygen inner shell and lone pairs and providing an effective field for the bond pairs, is found to be remarkably satisfactory. Provided the effective field is properly defined, it is then possible to treat the molecule formally as a four-electron system and to obtain, nevertheless, a total energy 0⋅3 eV better than that given by the best of the s. c. f. calculations. This suggests that the ‘core approximation’ is not a real obstacle to progress. The one-electron density matrices are calculated from the various wave functions and the corresponding dipole moments are evaluated.

R. McWeeny

Papers

A Quantum-Mechanical Study of the Water Molecule