Bonding Analysis of Ab Initio Electronic Wave Functions in Molecules

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Klaus Ruedenberg and Mark Gordon of Iowa State University are supported by an award from the Chemical Theory, Models and Computational Methods Program in the Chemistry Division to continue the development of a rigorous and widely applicable method for understanding the chemical bonding that occurs in molecules and molecular systems. This bonding analysis quantitatively identifies and sorts out the different types of physical interactions that act together in creating bonds between atoms in molecules. As yet, a rigorous understanding does not exist for this fundamental phenomenon in chemistry. While the discovery of 'bonds' goes back two hundred years, it was only a hundred years later that that the simplest chemical bond, in the hydrogen molecule, could be quantitatively calculated on the basis of quantum mechanics. As a result of the recent development of computers, energies of many molecules can now be calculated quite accurately. However, the physical origins of the vast diversity of chemical bonds are still elusive. For instance, only speculations exist on why the carbon monoxide molecule has a stronger bond than the nitrogen molecule even though these simple molecules have very similar electronic structures. In the present analysis, a rigorous quantitative understanding of bond energies in terms of relevant and familiar physical interactions is developed by extracting this information from theoretical calculations. The analysis provides a more reliable guide for intuitive use by practicing chemists in understanding and anticipating bonding patterns than current qualitative rationalizations. The analysis is also provides sound material for teaching the physical origin of chemical binding based on a solid theoretical basis. The goal of the project is to enhance the impact of rigorous quantum mechanical calculations on practical chemistry. The bonding analysis is included in the freely available and widely used GAMESS (General Atomic and Molecular Electronic Structure System) program suite.From the molecular electronic ab initio wave function, orbitals are deduced that have very large overlap with atomic orbitals of the free atoms and, at the same time, are adapted to the bonding pattern in the molecule. The wave function is expressed in terms of these quasi-atomic orbitals and it, thereby, becomes a sum of three terms. The first term embodies the juxtaposed atoms in their valence states without electron migration between them and, hence, without covalent bonding interactions. The second term embodies electron sharing, and hence, covalent bonding between the neutral atoms. The third term embodies charge transfers between the atoms. From this resolution of the wave function, a decomposition of the energy is obtained in terms of five additive contributions that represent the following interactions: formation of the atomic valence states, quasi-classical Coulombic interactions, interference interactions, sharing-penetration interactions, and charge transfer interactions. These interactions are furthermore resolved into contributions of the various orbitals. On the basis of these resolutions, the bonds that link various atoms in specific molecules are characterized and compared.