inorganic chemistry

Franck–Condon factor with an exponential factor with the form
of the WKB approximation for tunneling through intersecting
parabolas. This is intrinsically a multidimensional problem,
and a generalized bond-length displacement coordinate was
introduced to make it tractable. In the process of reducing the
coordinates, a measure of the relative number of identical
oscillators (samemando) was included in the exponential factor,
, and the tunneling rate was expressed as( 50 )

k¼wnexp

ffiffiffiffiffiffi

2 m

p

ℏ

ffiffiffiffiffiffiffiffiffi

DE{

p Dx

2 



(12)

wheren¼o/(2p),wis a nonadiabatic factor (w<<1 for nonadia-
batic transitions such as intersystems crossing), andDxis the
width of the tunneling barrier. The application ofEq. (12) to
radiationless transitions provides a simple method to separate
electronic and nuclear factors that contribute to the rates of such
transitions.

FIG. 6. Generalized bond-length displacement in radiationless tran-
sition in large molecules.

206 LUIS G. ARNAUT