Brian J. Duke

Utilization of Transferability in Molecular Orbital Theory

Publisher Summary This chapter discusses the utilization of transferability in molecular orbital theory. The chapter elaborates on the ways in which transferability can be utilized in the construction of wavefunctions for large systems. The chapter explores those methods that use such transferability to mimic ab initio calculations on large molecules, and the role played by transference in improving the numerical convergence of self-consistent field (SCF) cycling procedures. Within the molecular orbital theory, the transference of matrix elements from one molecule to another and their possible use in the construction of wavefunctions for large systems forms a natural alternative to the transferability of the parts of a wavefunction, such as localized orbitals. The chapter discusses various methods involving the transfer of matrix elements that includes the Non EmpiricaI Molecular Orbital (NEMO) scheme, and Simulated Ab initio Molecular Orbital (SAMO) scheme. The chapter presents the transference methods involving the use of localized orbitals, and finally considers the use of both transferred matrix elements and transferred localized orbitals in improving the efficiency of SCF cycling procedures.

The Iterative Extended Hckel Method (IEHM)

The iterative extended Hückel method for σ-electrons, analogous to the ω-technique for π-electrons, is used to calculate wave functions for BH4−, NH4+, CH4, C2H6, B2H6, C2H4 and C6H6. Results are compared with the simple extended Hückel method and with published selfconsistent field molecular orbital wave functions. It is found that iterating the extended Hückel method does not always lead to improvements in the wave function but that some improvements are found particular for ionic molecules. It is suggested that the reason for the failure of the iterated method is the neglect of terms due to charges on adjacent atoms.ZusammenfassungDie Wellenfunktionen von BH4−, NH4+, CH4, C2H6, B2H6, C2H4 und C6H6 werden mittels des erweiterten Hückelverfahrens mit Iteration, analog der ω-Methode für π-Elektronen, berechnet und die Resultate mit denen des analogen Verfahrens ohne Iteration verglichen. Dabei zeigt sich, daß die iterative Methode nur im Fall von Ionen zu wesentlichen Verbesserungen führt. Dies dürfte daran liegen, daß bei ihr die Terme, die von Ladungen an Nachbaratomen herrühren, vernachlässigt werden.RésuméLa méthode de Hückel étendue itérative pour les électrons σ, analogue à la technique ω utilisée pour les électrons π, est utilisée pour calculer les fonctions donde de BH4−, NH4+, CH4, C2H6, B2H6, C2H4 et C6H6. Les résultats sont comparés avec ceux de la méthode de Hückel étendue simple et ceux de la méthode des orbitales moléculaires S.C.F. Litération en méthode de Hückel étendue naméliore pas toujours les fonctions donde mais certaines améliorations sont particulières pour les molécules ioniques. La raison de cet échec de la méthode avec itérations semble dûe à la négligence des termes correspondant aux charges sur les atomes adjacents.

The simulated ab initio molecular orbital method for polymers polyglycine

Abstract The simulated ab initio molecular orbital (SAMO) method is here applied to polyglycine — the simplest polymer of biochemical interest. Results are compared with semi-empirical methods and experiment.

A theoretical investigation of the structure of some small nitrogen–sulphur molecules

The structure of the nitrogen–sutphur compounds NSF, HSN, N2S, N2S2, and H3NS has been investigated using the L.C.A.O.M.O. ab initio method and a moderately large basis set. The compound NSF is found to be more stable than SNF in agreement with experiment, HNS is predicted to be more stable than HSN, NNS (linear) is more stable than NSN, and the order of stability of the isomers of H3NS is predicted to be H2SNH < H3SN < HSNH2 < SNH3. The compound N2S2 is shown to be square planar in agreement with recent experimental evidence.

The role of d-orbitals in predicting accurate geometries Using ab initio molecular orbital methods

Abstract The crucial role of including d-orbital in predicting geometries of molecules containing second row atoms in the usual atom-centered LCAO MO ab initio method is critically discussed. Examples are taken from the literature and from calculations on H2S1 MeSH and FSN employing a variety of basis sets.

A theoretical investigation of nitramine structures

Abstract The molecules nitramine and dimethylnitramine have been studied using ab initio and semi-empirical molecular orbital methods. Nitramine is found to be non-planar at the amine group and dimethylnitramine is found to be planar, both in agreement with the experimental results. The N—N bonds in the two molecules are found to be very similar, in disagreement with the experimental results. The planarity of dimethylnitramine appears to be due to increased π bonding in the N—N bond. Calculated dipole moment values are in reasonable agreement with the experimental result. The barrier to inversion of the amine group in nitramine is likely to be less than the ab initio prediction of 7.9 kJ mol −1 .

The electronic structure of the B2H 5 + ion

The B2H5+ ion has been studied using theab initio SCF method employing a basis set of Gaussian orbitals and various semi-empirical methods. The most stable structure appears to be a planar structure with two vacantp orbitals rather than a triply bridged structure suggested by analogy with acetylene with which it is isoelectronic. The semi-empirical results reinforce earlier conclusions that inclusion of charges from neighbouring atoms in iterative Extended Hückel methods is necessary to satisfactorily treat ionic molecules.ZusammenfassungDas B2H5+-Ion ist mit Hilfe derab initio SCF-Methode unter Benutzung eines Basissatzes von Gaußorbitalen und mit verschiedenen semiempirischen Methoden untersucht worden. Die stabilste Struktur scheint eine planare Struktur mit zwei leerenp-Orbitalen und nicht eine dreifach verbrückte Struktur zu sein, wie sie durch Analogiebetrachtungen am Acetylen nahegelegt wird. Durch die semiempirischen Resultate werden die bereits früher erhaltenen Ergebnisse bestätigt, daß zur zufriedenstellenden Behandlung von Molekülionen mit iterativen erweiterten Hückel-Methoden die Berücksichtigung der Ladungen benachbarter Atome nötig ist.

The simulated ab initio molecular orbital (SAMO) method. VII. Extended basis sets for molecules and polymers

The simulated ab initio molecular orbital SAMO method has been extended to study the use of basis sets larger than minimum basis sets for hydrocarbon molecules and polymers. Inclusion of polarization functions leads to no new features but the diffuse nature of double zeta basis sets requires, for the simulation of molecular properties, larger pattern molecules than was previously the case. For polymers, the approximations made within the ab initio crystal orbital method are comparable to those made in the SAMO method and the results are correspondingly closely similar. The problem of near linear dependence in the basis set for polymers is thoroughly discussed. This study opens up the SAMO method to the utilization of a wider range of extended basis function.

Avoiding the use of integral lists in the ab initio LCAO SCF MO method

Abstract The suggestion is made that the storage of long lists of two-electron repulsion integrals in the LCAO SCF MO method could be avoided if such integrals were evaluated at each SCF cycle and an initial set of eigenvectors were available to lead to rapid convergence. Results are presented showing that the simulated ab initio molecular orbital (SAMO) technique provides an excellent set of initial eigenvectors for the SCF procedure.

On the transferability of Fock matrix elements

The transferability of Fock matrix elements in the linear combination of atomic orbitals molecular orbital scheme is analysed using localized orbitals. It is shown that this transferability is dependent on the transferability of these localized orbitals and the neglect of long-range contributions from partially cancelling Coulomb nuclear attraction and electron repulsion terms. A theoretical basis is thus provided for the simulated ab initio molecular orbital and related methods. Various corrections previously introduced in an ad hoc manner are shown to be justified. Transferability in both the closed shell and open shell schemes is analysed.