<P> In his publications, Walsh showed through multiple examples that the geometry adopted by a molecule in its ground state primarily depends on the number of its valence electrons . He himself acknowledged that this general concept was not novel, but explained that the new data available to him allowed the previous generalizations to be expanded upon and honed . He also noted that Mulliken had previously attempted to construct a correlation diagram for the possible orbitals of a polyatomic molecule in two different nuclear configurations, and had even tried to use this diagram to explain shapes and spectra of molecules in their ground and excited states . However, Mulliken was unable to explain the reasons for the rises and falls of certain curves with increases in angle, thus Walsh claimed "his diagram was either empirical or based upon unpublished computations ." </P> <P> Walsh originally constructed his diagrams by plotting what he described as "orbital binding energies" versus bond angles . What Walsh was actually describing by this term is unclear; some believe he was in fact referring to ionization potentials, however this remains a topic of debate . At any rate, the general concept he put forth was that the total energy of a molecule is equal to the sum of all of the "orbital binding energies" in that molecule . Hence, from knowledge of the stabilization or destabilization of each of the orbitals by an alteration of the molecular bond angle, the equilibrium bond angle for a particular state of the molecule can be predicted . Orbitals which interact to stabilize one configuration (ex . Linear) may or may not overlap in another configuration (ex . Bent), thus one geometry will be calculably more stable than the other . </P> <P> Typically, core orbitals (1s for B, C, N, O, F, and Ne) are excluded from Walsh diagrams because they are so low in energy that they do not experience a significant change by variations in bond angle . Only valence orbitals are considered . However, one should keep in mind that some of the valence orbitals are often unoccupied . </P> <P> In preparing a Walsh diagram, the geometry of a molecule must first be optimized for example using the Hartree--Fock (HF) method for approximating the ground - state wave function and ground - state energy of a quantum many - body system . Next, single - point energies are performed for a series of geometries displaced from the above - determined equilibrium geometry . Single - point energies (SPEs) are calculations of potential energy surfaces of a molecule for a specific arrangement of the atoms in that molecule . In conducting these calculations, bond lengths remain constant (at equilibrium values) and only the bond angle should be altered from its equilibrium value . The single - point computation for each geometry can then be plotted versus bond angle to produce the representative Walsh diagram . </P>

Walsh diagram for tri and penta atomic molecules