Dimensional scaling in H sub 2 sup + and H sub 2

Miscellaneous · Sun Jan 01 00:00:00 EST 1989

OSTI ID:5132262

Frantz, D D

Dimensional scaling methods, characterized by their use of spatial dimension D as a variable, are extended to the simplest molecules, H{sub 2}{sup +} and H{sub 2}. As in atomic systems, a scaling transformation shrinks the wavefunction densities to delta functions in the limit D {yields} {infinity}, thus reducing the electronic structure to a classic electrostatic form with the electrons in a fixed geometrical configuration relative to the nuclei, akin to the traditional Lewis electron-dot structure. In D-dimensional cylindrical coordinates, the electronic energy reduces simply to the global minimum of effective potential surfaces that are parametrically dependent upon the internuclear distance R. These surfaces change form as R is varied, exhibiting local minima corresponding to different Lewis structures for each valence configuration. When the nuclear repulsion is added to the ground state energy, the net interaction is repulsive and both H{sub 2}{sup +} and H{sub 2} are unbound at large D. Since the D {yields} {infinity} limit corresponds to the zeroth-order term in a 1/D expansion, the higher order terms in 1/D then are solely responsible for chemical bonding at finite D. For H{sub 2}{sup +}, an interdimensional degeneracy linking D and the orbital angular momentum projection {vert bar}m{vert bar} gives all D-dimensional eigenstates by simple correspondence with suitably scaled D = 3 states. The wave equation for fixed nuclei is separable in D-dimensional spheroidal coordinates, resulting in generalized two-center differential equations. By incorporating {vert bar}m{vert bar} into D, the resulting eigenstates can be classified by two dimension independent quantum numbers corresponding to the number of ellipsoidal and hyperboloidal nodal surfaces in the wavefunction, denoted in united atom notation by k and l {minus} {vert bar}m{vert bar}, respectively.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• OSTI ID: 5132262
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
HYDROGEN
ELECTRONIC STRUCTURE
HYDROGEN IONS
MOLECULES
CALCULATION METHODS
CHEMICAL BONDS
COORDINATES
DELTA FUNCTION
EIGENSTATES
GROUND STATES
MOLECULAR IONS
NUMERICAL ANALYSIS
QUANTUM NUMBERS
SCALING LAWS
TRANSFORMATIONS
WAVE FUNCTIONS
CHARGED PARTICLES
ELEMENTS
ENERGY LEVELS
FUNCTIONS
IONS
MATHEMATICS
NONMETALS
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory