Aspects of quantum chemistry (1977)
AuthorsDoonan, I. J.show all
Theoretical models which do not use any experimental parameters other than molecular geometry are usually referred to as ab initio methods. One such ab initio molecular orbital method is used in this thesis to study the molecules nitrous acid (HONO), dinitrogen trioxide (N₂O₃) and germane (GeH₄). An ab initio valence bond study was done on dihydrogen sulfide (SH₂). All used a slater-type minimal basis set. Except for germane, integrals were calculated by using closed formulae, but some repulsion integrals were calculated numerically with a gaussian expansion technique. The integral program was enlarged to accommodate orbital types 3s through to 4p. Heavy, perhaps even excessive, reliance has been put in Mulliken's population analysis for interpreting the molecular orbital wavefunctions. This method has been criticized often and can be misleading, but it does offer a simple conceptual way of interpreting wavefunctions. Used in a comparative manner most of its difficulties are reduced. Chapter one outlines briefly the theory necessary for an understanding of the methods used, implementations of these methods, interpreting techniques and the extensions to the integral program. A discussion and comparison on length of gaussian expansion and extent of its use (the nG/S and STO-nG methods) in integral evaluation is given. Chapter Two discusses and reviews the bonding and structure of nitrous acid, [diagram here] HONO has two stable planar forms which are almost equal energetically. A high barrier separates them. The geometry of the cis form has longer N=O and O-H bonds, but a shorter N-O bond with respect to the trans. These features and the barrier have been discussed in the literature in terms of some weak hydrogen bonding in the cis and a partial N-O π bond or by the various lone pair interactions. Calculations at three HONO geometries were done; the experimental cis and trans geometries and a gauche form to represent the barrier top. The results were interpreted within the framework of perturbation theory with the unperturbed wavefunction being that, of trans. This represents a picture of the geometry differences between cis and trans as being due to the mixing in, under the increased N=O oxygen-hydrogen interaction, of the unoccupied 0-H* orbital by the HOMO to give a weaker O-H bond but a stronger N-O σ bond in cis. This stronger N-O σ skeleton allows greater π interaction (oxygen lone pair electrons delocalizing into the N=O n* orbital). The breaking of this partial N-O π bond is a major component of the barrier between the planar isomers. To date four other ab initio calculations have been made on HONO. Chapter Three presents the results of a calculation on N₂O₃ at its experimental geometry. For reference purposes calculations were done on NO and NO₂ using the N₂O₃ parameters. In reviewing N₂O₃; [diagram here] the molecules [diagram here] been included, as these three form a set with the common features of a very long N-N bond (and small ∆Hdiss) and yet are planar. The NO and NO₂ geometries in this set are very similar to those for free NO and NO₂. The bonding in the three molecules is thus intermediate between normal and Van der Waals bonding, and is in a similar position to hydrogen bonding. To the author's knowledge no other calculation has been published on N₂O₃. There are several ab initio calculations on N₂O₄ and N₂O₂. N₂O₄ has a long history of empirical attempts to explain its long N-N bond and planarity, such as: (i) a 'π-only' bond with no σ bond; (ii) a charge transfer configuration; and (iii) a weakening of the σ bond by delocalization of oxygen's lone pair electrons into the σ antibonding orbital. A similar case is stabilization of the odd electrons in NO₂ which is not available in N₂O₄. The barrier is explained by most as being due to a weak N-N π bond, but a few use a weak cis O … O bond. The two latest ab initio calculations' models are for either a delocalization of the oxygen lone pairs into the N-N σ* with the barrier due to the cis O … O bond making this interaction more favourable in the planar form, or for repulsion due to the occupied molecular orbitals of NO₂ with a stabilization from only the HOMO. This HOMO is a linear combination of NO₂'s HOMO which is delocalized over NO₂ and so gives a smaller N-N bond order. The barrier is then due to the balance of less repulsion in the skew form with greater cis O ... O bonding in the planar geometry. The results for N₂O₃ showed that it needs a multi-configurational wavefunction to describe it energetically. The localized molecular orbitals of N₂O₃ gave orbitals that are similar to the classical concepts of bonds, lone pairs and inner shells. They resemble those of the free NO and NO₂ for the two cis N-O bonds and that of NO₂- for the third N-O bond. There is a nitrogen bond but it is cancelled by the antibonding tails from the nitrogen and cis oxygen lone pairs. The N₂O₃ HOMO contains the net N-N bonding and is a linear combination of the NO and NO2 HOMO’s. There is also a weak cis O … O bond. Simple models for N₂O₃ bonding were explored and the rotation barrier studied by the semiempirical extended Hückel theory. Reasons for the long N-N bond were advanced. i.e. A 'normal' N-N bonded N₂O₃ is intrinsically unstable with respect to NO and NO₂ due to the loss of 'three electron bonding' in NO and NO₂. Perturbation theory shows that there is a stabilization from the interaction of the NO and NO₂ HOMO's as they are singly occupied. This can overcome the basic instability at the longer bond lengths. The interaction is weakened by the fact that the HOMO's are delocalized over NO and NO₂ and that the repulsions from the doubly occupied molecular orbitals will increase faster than the stabilization at shorter bond lengths. Planarity needed both the O … O bonding and the N-O 'three electron bonding'. Chapter four deals with the valence bond calculations on SH₂ done at three angles but with the same S-H distance. This is a continuation of similar calculations on H₂O, CH₂, BH₃ and BeH₂. Several molecular orbital calculations and one other valence bond calculation have been done. However some different aspects were looked at in this work. A frozen 'core' approximation was used resulting in only six electrons being considered directly (eight for the hybrid orbital configurations). Convergence was slow with respect to numbers of configurations after the first three to five. Use of hybrid orbital configurations is 2.5 times better in terms of number of determinants needed to reach a certain energy. Relative importance of configurations was explored but was found to be an imprecise concept which was dependent on the number and type of configurations present. In comparison with H₂O, CH₂, BH₃, and BeH₂, SH₂ converged more slowly to the molecular orbital energy. This was due to its larger core of 12 electrons compared with 6 valence electrons, as opposed to 10 and 6 for, say, H₂O. It was, however, the only one for which the calculated value of the angle θ between the bonding hybrids was close to the experimental. These five molecules all exhibited 'non-perfect following' of θ, i.e. as the bond angle was changed, the optimum value of θ for the lowest energy remained constant.