474 research outputs found
A Systematic Study of Symmetry Properties of Graphs I. Petersen Graph
Recently (Chem. Phys. Lett. 42 283 (1976) a simple procedure
for deriving symmetry properties of graphs has been suggested. It
is based on a canonical numbering of the vertices of a graph, and
consists in searching for all the acceptable numberings which have
a unique adjacency matrix. In the series of papers initiated here we
will apply the above procedure and derive all symmetry operations
for graphs of interest to chemistry. We start with the Petersen
graph which is of interest in discussions of isomerizations of
trigonal bipyramidal structures
Hybridization in Planar XY 4 Molecules
Maximum overlap hybriid orbitals for planar XY4 molecules
are described assuming various orbitals for ligand and central
atoms. Distribution of s and d character in square snp2d2-n hybridization
as a tunction of ilnteratomilc distances, and for different
relamive effective charges iof bonded atoms .is g.iven. Maximum
overlap hybdds, when compared with those based on Pauling\u27s
criterion of hybrid 1strength, show a generally smaller contribuition
of d z2 orbdtal in the hybnidizati\u27on, especially evident
for ~ligand< μm etal, when in SOlffie cases they _ reduce to simple
dsp2 hybrids . Calculait:i.ons are based <on tabulated overlap integrals
data for Slaiter functions
Hybridization in 1,5,9-Tridehydro(l2)Annulene
The hybridization \u27in l,5,9-tridehydro(12)annulene has been
calculated by the method of maximum overlap. The results show
that the hybrids describing CC double bonds and CC triple
bonds have more s-character than the hybrids of the same carbon
atoms involved in single CC bonds. Consequently, CC double and
CC triple bonds are strengthened not only by the additional n-type
overlap, but also by an increase of cr-type overlap, which accompanies
the rise of the s-content. By using available empirical
correlations a comparison between calculated and experimental
NMR data (spin-spin coupling constant J (C13- H) and chemical
shift i;) is made
Hybridization in Highly Strained Small Ring Hydrocarbons. II. Methylene Biscyclopropylidene and Dimethylene Biscyclopropylidenes
The hybridization in methylene biscyclopropylidene, 1,1\u27-dimethylene
biscyclopropylidene, and 1,2-dimethylene biscyclopropylidene
is considered by applying the method of maximum
overlap. The results show variations in hybrids describing exocyclic
double bonds: for ring carbons from sp~.ss to sp2-85, and
for off-ring carbons from sp1-10 to sp1-41, depending on the immediate
surounding. Bond overlaps for C=C consequently vary
somewhat, the largest bond overlap being of the central C=C
bond connecting two three membered rings. The results of the
maximum overlap calculations are compared with available
experimental data
Hybridization in 1,3,5-Cycloheptatriene and Some Related Molecules by the Method of Maximum Overlap
The hybridization in 1,3,5-cycloheptatriene, 1,3,5,7-cyclooctatetraene,
1,3-cyclohexadiene, and 1,4-cyclohexadiene has been calculated
by the method of maximum overlap. The results show that
if the molecules are assumed to be planar, hybrids describing the
molecular skeleton deviate from the line joining the neighbouring
carbon atoms and are directed towards the ins.ide of the ring. The
deviation angles for the above molecules vary between 1.25° and
7 .5°. For non-planar structures the deviation angles are decreased
or are equal to zero. The puckering of the molecular skeleton
thus considerably reduces the strain
Reduction of Hybrid Electron-repulsion Integrals to Overlap Integrals
It is shown how two-center electron-repulsion integrals of
hybrid type can be reduced to linear combinations of overlap
integrals. In certain cases the overlap integrals involve orbitals
whose principal quantum numbers are less than their azimuthal
quantum numbers. Explicit formulas are presented for the reduction
of all hybrid integrals containing only orbitals of principal
quantum numbers 1 or 2
Graph-theoretical Search for Benzenoid Polymers with Zero Energy Gap
Recently structural features which characterize the energy
gap in polymeric conjugated hydrocarbons within the framework
of the simple Hiickel MO theory have been specified using graphtheoretical
methods. It has been shown that molecules of interest
as potential units in polymers with zero energy gap have to satisfy
certain structural conditions which relate the number of selected
»excited« valence structures to that of the Kekule structures for
the system. As in the previous work we consider units separated by
essentially single bonds.
Here we elaborate on the search for benzenoid systems which
can satisfy the requirement. A necessary condition that a system
may have zero energy gap is that the repeating benzenoid unit
has a non-prime number (K) of Kekule valence structures. Then
K could be factored: K1 • K2 ... Km. (Generally, there are more
factorizations of K and our procedure needs to be carried out over
all of them). Fragments Fi that have the number of Kekule structures
given by K; are recognized, and we try to superimpose
all of them over the skeleton of monomer unit. (Our procedure
needs to be carried out for all possible fragmentations corresponding
to a given factorization) . If it is possible to cover the monomer
unit with all the fragments leaving at least two positions available
for linking the units in polymer form, then the energy gap of such a
polymer is zero.
In a number of examples it is illustrated how the actual search
is performed. A list of benzenoid systems of interest as units in a
polymer with zero energy gap is given. The search is quite efficient
and speedy
Hybridization in Several Polycyclic Alkanes by the Method of Maximum Overlap
The hybridization · in spiropentane, nortricyclene, cu bane, tricyclo(
l.1.0.02,4)butane, bicyclo(l.1.l)pentane, and tetracyclo(3,3.l 2, 8.04,6)
nonane has been determined by the method of maximum
overlap. For the atomic functions Clementi Orbitals (ref. 1) have
been assumed. A comparison between these results and those,
obtained previously, by assuming Slater orbitals indicates the improvements that can be achieved by using more exact wave functions. The overlaps for CC bonds fall into the groups: (1) S 0.64. They are characteristic of highly
strained three-membered rings, (6 ~ 20°), of four membered rings,
(b ~ 10°), and of normal or very slightly bent bonds, (6 < 5°),
respectively
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