An ab initio molecular orbital calculation of the addition compound of boron hydride and ammonia has been carried out. By expanding the molecular orbitals of the addition compound in terms of the molecular orbitals of boron hydride and of ammonia in a separated state, the origin of charge transfer and bond formation between these two species in the interaction has been studied. A configuration analysis of the wavefunction of the addition compound has been performed.

Molecular orbital calculations of the electronic structure of borazane

The seminal work of Nijboer and De Wette [Physica 23, 309 (1957)] enables the calculation of lattice sums of spherical harmonics, but has long been overlooked. In this article, their central result is recast in a simplified form suitable for modern multipole algorithms that employ the solid harmonics. This formulation makes possible the imposition of periodic boundary conditions within modern versions of the fast multipole method, and other fast N-body methods. The distinction between the extrinsic values obtained with the lattice sums M of the multipole interaction tensors, and the intrinsic values associated with Taylor’s expansion of the Ewald formulas, is made. The central constants, M, are computed to 32 digit accuracy using extended precision arithmetic. Timings and corresponding errors obtained with a periodic version of the fast multipole method are presented for particle numbers spanning [103,106], and a range of expansion orders. A qualitative comparison is made between the present implementatio...

Periodic boundary conditions and the fast multipole method

Configuration interaction calculations with a Gaussian basis were carried out on the lowest five states of each symmetry 1A′, 3A′, 1A″, and 3A″ for H3+. All geometries with bond lengths between 1.2 and 3.6 a.u. were examined. Other than the ground state, only the 1 3A′ surface contained a stable state. This is a linear symmetric 3Σu+ level with energy equal −1.11422 a.u. and bond lengths of 2.457 a.u. It is stable by only 6.47 kcal/mole with respect to dissociation to H2+ (X2Σg+)+H(1s). The state is computed to have vibrational frequencies of 1191 cm−1 (symmetric stretch), 683 cm−1 (asymmetric stretch), and 775 cm−1 (degenerate bend).

Gaussian basis configuration interaction calculations on twenty electronic states of H3+. A bound 3Σu+ excited level

Publisher Summary The word “polymer” embraces a large class of complex and diverse compounds among which the quantum theory at present considers only a rather restricted subset. The range of applications of this quantum theory is not at all restricted to such unusual materials. The main limitation comes obviously from the ability of the model to comprise the physics and chemistry of what is actually a “regular” polymer. For all these materials, and in the same way as for simpler molecules, quantum chemistry is now starting to provide powerful instruments for interpreting and predicting the physical and chemical properties (structure, bonding, reactivity, etc.) for which a rather detailed knowledge of the electronic structure is required. Another reason for developing quantum methods for polymers is the increasing use of refined techniques (XPS, IR, NMR, etc.) to solve fundamental polymer problems—for example,XPS (or ESCA-electron spectroscopy for chemical analysis) spectra obtained with monochromatic X-ray radiation turn out to be powerful tools with which to study the electronic structure of polymers, both by providing precise information on core level binding energies and line shapes and by allowing the recording of the distribution of the valence electronic levels that might constitute a real and unique “fingerprint” of the polymer. The main conclusion of this chapter is that quantum mechanical methods are now able to provide significant understanding and insight into the electronic properties of regular polymers.

Quantum Mechanical Methods for Regular Polymers

An ab initio self-consistent-field (SCF) algorithm taking into account all the features of the one-dimensional translational periodicity and the helical symmetry is presented. This algorithm includes the long-range correction to the Coulomb potential and is designed to calculate the band structure of periodic one-dimensional polymers (planar or helical). Its efficiency in terms of computing time and numerical accuracy is tested via applications on a (LiH)n chain, polyethylene, and four conformers of polypropylene.

Ab initio calculations of the electronic structure of helical polymers

Approximations, accurate to ± 1 × 10−8, have been developed for the functions Fm(z) which arise in molecular calculations using Gaussian basis functions. These are found to reduce integral computation time by about a factor of 5 over other methods. Approximations are listed for 0 ≤ m ≤ 16.

G. O. Morrell

Papers

Approximations for the Functions Fm(z) Occurring in Molecular Calculations with a Gaussian Basis