Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School



Heptacovalent bonding, in which seven atoms are bonded to a central atom, is known for substances whose structures conform to three different symmetry types. The IF_7 molecule has pentagonal bypyramidal symmetry; the ZrF_7^(--) ion has the structure of a distorted octahedron; NbF_7^(--) and TaF_7^(--) both have distorted trigonal prism symmetry. An investigation of NbF_7^(--) is reported here; the theory of direct-valence bonding is used to determine the approximate bond strengths and bond angles for the ion. The direct valence method is one of two widely used methods of studying chemical structures, the other being the molecular orbital method. These methods both involve approximate solution of an n-body problem which is incapable of exact quantum-mechanical solution because of its complexity. Both are perturbation calculations starting from an assumed set of wave functions describing the behavior of the electrons in the system. The principle difference lies in the original set of wave functions chosen. In the directed valence method the hydrogen-like atomic orbitals of the constituent atoms are considered, and bond orbitals for each atom are written as linear combinations of the available atomic orbitals of the atom. Covalent bonds are then formed by overlapping bond orbitals of the atoms. Molecular orbital theory treats the electrons as extending over the entire molecule; n one-electron wave functions represent the n electrons of the system. The directed valence method is the more useful in dealing with bonding between atoms, and is therefore applied to the bonding problem of NbF_7^(--). The molecular orbital method will not be further discussed. The theory section contains a brief discussion of directed valence theory as it pertains to the problem. Group theory is introduced as a means of analyzing and discussing symmetry properties of the structure and the relation of symmetry to calculation of the bond orbitals. The remaining sections contain a calculation of the bond orbitals of NbF_7^(--) and a discussion of the results.

Library of Congress Subject Headings

Valence (Theoretical chemistry


Includes bibliographical references



Number of Pages



South Dakota State University