Roy McWeeny

Quantum theory of molecular electronic structure

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.

A matrix partitioning approach to the calculation of intermolecular potentials. General theory and some examples

Abstract A general expression for the interaction energy of two molecules is obtained by using a matrix partitioning method. The wavefunction of the whole system is expanded in terms of antisymmetrized products of free-molecule functions and using a matrix perturbation scheme it is possible to describe the interaction energy in terms of free-molecule quantities (like frequency-dependent polarizabilities and density or spin density matrices) that, in principle, can be evaluated at any level of approximation. By way of example, the interaction potentials are calculated for (N 2 ) 2 and Ne 2 using wavefunctions of HF and TDHF form. The results are in substantial accord with those available in the literature. Application of these potentials to the calculation of macroscopic properties, however, leads to considerable errors. From the analysis of our results it appears that the dispersion energy is underestimated, probably on account of the neglect of intrasystem correlation energy in the TDHF approximation. The use of more sophisticated methods of evaluation of dynamic polarizabilities will not involve any extension of the approach presented in this work.

Shape and similarity: two aspects of molecular recognition

Abstract Two new procedures are presented for obtaining information on molecular shape and molecular similarity; both are non-empirical and involve the use of approximate molecular wavefunctions. Preliminary applications to small molecules and ions and to the hexane isomers give numerical results in general accord with intuitive expectations. Applications to much larger systems would present no great difficulty and could be of value in discussing problems of molecular recognition.

Valence bond calculations of the potential energy surface for CH4→CH3+H

A valence bond study of the potential energy surface for methane CH4→CH3+H is performed at the 6–31G level using (i) a valence bond self‐constituent field (VB‐SCF) method; (ii) a valence bond configuration interaction (VBCI) method; and (iii) an antisymmetrized product of strong‐orthogonal geminals (APSG) method (also in VB form). The calculations show that, although the energies are somewhat inferior (on an absolute scale) to those obtained in very large CI calculations, the VB reduced potential energy surfaces behave better, in the intermediate range 2–3 A, than those obtained using (i) the Mo/ller–Plesset fourth‐order perturbation (MP4) approximation, (ii) configuration interaction with all singles and doubles (CISD), and (iii) coupled clusters with all singles and doubles (CCSD). The results are in very good agreement with those obtained from multi‐reference configuration interaction (MR‐CISD) calculations. The lower absolute energies obtained in the very extensive CI calculations indicate a better de...

Classical structures in modern valence bond theory

The results of some recent ab initio valence bond calculations, in which both structure coefficients and orbital forms are optimized, are analysed. The origin of structures in which the optimum orbitals are no longer “atomic” in character but instead delocalized, is traced back to the presence of certain symmetries in the wavefunction. When such symmetries exist it is possible to choose alternative linear combinations of the delocalized orbitals and to rewrite the wavefunction in terms of VB structures of “classical” form. The advantages of the classical structures are discussed in the context of a simple example — a square planar conformation of four hydrogen atoms.

Perturbation calculations of molecular interaction energies: an example, HF....HF

Abstract An expression for the interaction energy of two molecules, obtained by expanding the wavefunction for the whole system in terms of antisymmetrized products of free-molecule functions and using a matrix perturbation scheme, is used in ab initio calculations on the HF dimer. The computed interaction energy is fitted with considerable accuracy by a simple analytical formula. The equilibrium geometry and hydrogen-bond energy are in satisfactory agreement with available experimental results.

Hybridization in valence bond theory: The water molecule

Abstract The hybridization concept is explored within the framework of ab initio valence bond (VB) theory, using the water molecule (in a minimal basis approximation) for illustrative purposes. With suitably optimized hybrids a few structures are capable of giving results close to those obtained at the full-CI limit, while even a single structure (the “perfect-pairing” approximation) easily surpasses in accuracy the results of a conventional SCF calculation.

Separability of Quantum Systems: A Density Matrix Approach

The idea of ‘separability’ is concerned with the quantum mechanical description of systems in which it is possible to recognize experimentally the presence of certain ‘structural units’, each with a ‘personal’ identity. This idea is formulated mathematically in terms of ‘group functions’, each referring explicitly only to the electrons of one group in the field of the others. The density matrices for the whole system are expressible in terms of those of the separate groups and global optimization of the wavefunction is reduced to an iterative optimization involving only one group at a time: this provides a basis for many experimental ‘additivity rules’. The feasibility of extending the approach to admit relativistic effects is also examined.

The electron affinity of H2 : a valence bond study

A valence bond study of the potential energy curve for H + H− shows the system to be stable, against dissociation into H2 and a free electron, only for internuclear distances greater than 3.12 a0. For shorter distances the energy curve shows a minimum at a bond length of about 1.5 a0, but this represents a metastable state embedded in the continuum of H2 plus a scattered electron. Electron impact experiments on hydrogen might be expected to reveal a Feshbach resonance at about 2.0 eV.

Electron density and response theory

Abstract The response of the electron density in a molecule to an arbitrary time-dependent perturbation is discussed using linear response theory. The response is characterized in terms of frequency-dependent polarizabilities (FDPs) of a particular kind, and these may be calculated by means of time-dependent Hartree—Fock (TDHF) theory. Two applications are presented, using a linear polyene (hexatriene) as a simple model system: (i) it is shown how the propagation of signals along the molecule may be discussed using time-correlation functions (Fourier transforms of the FDPs) and (ii) the (electron) dispersion energy between two such molecules has been calculated and found to be thermally significant, besides showing a remarkable geometry dependence.