Walsh Diagrams Research Articles

Walsh's rules for AH4 systems derived from united atom molecular orbitals

Walsh's rules for AH4 systems derived from united atom molecular orbitals

Geometry of Molecules. I. Wavefunctions for Some Six- and Eight-Electron Polyhydrides

Potential surfaces have been investigated for BH2+, BH2−, NH2+, BeH2, BH3, CH3+, and BeH3− by means of LC (Hartree—Fock) AO MO SCF wavefunctions. One-electron-energy-versus-angle diagrams were determined for these AH2 and AH3 molecules, and comparison with the widely used empirical diagrams of Walsh demonstrates a quantitative similarity between them. In addition, mathematical inequalities are derived relating changes in the sum of one-electron energies with angle to changes in the total energy with angle. Aided by these expressions, we are able to make direct connection between Walsh's qualitative rules and the physically well-defined ab initio solutions.

Note on the significance of Walsh's rules

The success of Walsh's method is due to the fact that several large errors cancel out approximately. The ordinate of the correlation diagrams corresponds to the eigenvalues of the self-consistant hamiltonian.

Nature of the one electron energies of the independent electron molecular orbital theory and of the Walsh diagrams

It is suggested that the “one electron energy” or “binding energy” of the independent electron molecular orbital theory is the change in the ionization energy of the molecular orbital on molecule formation. This interpretation is discussed in the context of the Walsh diagram for the water molecule. The general method is to reduce the self-consistent field molecular orbital theory to the independent electron theory by systematic approximations and by appeal to physical arguments. Broadly speaking, the results support Walsh's method of constructing his diagrams but they also show that it is important to distinguish clearly between ionization energies and binding energies and also between the different types of delocalized molecular orbital. If these distinctions are not made, one may emerge with a diagram which is a mixture of several different but related diagrams. Walsh's original diagrams seem to be based on an unusual type of delocalized molecular orbital. The work also gives a clear definition of the terms bonding, non-bonding and antibonding molecular orbitals.

Die WALSHsche Regel im Rahmen der MO-LCAO-Näherung III (AB2-Moleküle)

In order to find an explanation for the WALSH rules on a more theoretical basis for molecules of type AB2 (non hydrides) a simple MO-LCAO calculation with SLATER-Functions of the L-shell was carried out. The results are presented as tables and graphs, which give the dependence of the one-electron energies on the valence angle. In accordance with WALSH’S rules the apex angle decreases with the number of electrons in the range of 16 to 20 valency electrons, molecules with not more than 16 valency electrons being linear. However according to the present calculation the reason for this is that with increasing number of electrons more orbitals are occupied which are lower in energy for the bent species, rather than WALSH’S explanation which lies in the increasing s-character of the πU non-bonding orbital.

Die Walshsche Regel im Rahmen der MO-LCAO-Näherung II (AH3-Moleküle)

In order to find an explanation for the WALSH rules on a more theoretical basis the molecules of type AH3 were treated for atoms A of the first period by a simple MO—LCAO method with SLATER-Functions. The dependence of the one-electron energies on the valence angle was found more similar to that obtained by accurate SCF—LCAO calculations than to the WALSH energy curves. But the WALSH rules were generally reproduced very well, except perhaps for the 7 electron case, where in agreement with experiment a more planar structure is preferred. The results are presented as tables and graphs.