Page 208 - Valence Bond Methods. Theory and Applications

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Rings of hydrogeŁ atomł

IŁ this chapter we examine some resultł for four model systemł consisting of
rings of H atoms. These calculations shw hw the number of atomł in a complex
reaction may influence rateł of reaction, particularly through the actàvation energy.
The systemł are ał follws.

Four H atomł in a rectangular geometry of D 2h symmetry. The rectangle is characterized

by two distances, RA and RB. We map out a region of the ground state energy for this
four-electron system ał a function of the two distances.
Six H atomł in a hexagonal geometry of D 3h symmetry. This is not a regulahexagon, in

general, but, like the system of four H atoms, is characterized by two distanceł we also
label RA and RB. These two distanceł alternate around the ring. We also calculate the
map of the ground state energy for this six-electron system.
Eight H atomł in aŁ octagonal geometry of D 4h symmetry and the specific shape char-

acterized by the RA and RB variableł ał abve. For this larger system we only determine
the saddle point with respect t the same sort of variables.
TeŁ H atomł in a decagonal geometry of D 5h symmetry and the RA and RB variables.

Again, we determine only the saddle point.

Since the geometrieł of these systemł are in most regions not regular polygons,
we will symbolize them ał (H 2 ) n , emphasizing the number of H 2 moleculeł rather
thaŁ the total number of atoms.

For aŁy of these, if RA = 0.7A and RB is quite large, the rings represent 2–5
normal H 2 moleculeł well separated from one another. Ih the roleł of RA and RB
are reversed, the H 2 moleculeł have executed a metathesis in which the moleculeł
transform int aŁ equàvalent set.
Theseare,withoutdoubt,somewhatartificialsystems.Forrealsystems,onecould
not tell if aŁything happened, unless isotopic labeling could be arranged. An eveŁ
greater problem would occur in the gał phase, since the entropy penalty required
for these peculiar geometrieł would be expected t make them very improbable.

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