Fotoquimica

4421

Organic and Biological Chemistry
Quantum Organic Photochemistry. I. Intramolecular
Potential Energy Surfaces for the Lowest 37r7r* State of Polyenes’
N . Colin Baird” and Richard M. West
Contribution f r o m the Department of C hemistry, University of Western Ontario,
London, Ontario, Canada, Received November 5 , 1970
Abstract: The potential energy surfaces for the lowest3nn*states of polyenes are investigated by ab initio (ethylene
only), semiempirical SCF-CI, and perturbation molecular orbital theories. The calculated positions of the
A,
and 0-0 band positions are in good agreement with available experimental data. The configuration interaction results predict that twisting of one “essentially double” carbon-carbon bond is favorable i n polyenes, and
indicate apreference for inner, rather than terminal, bond twisting. The barriers to planarity and shapes of the
potential curves are rationalized using first-order perturbation theory and the relative stabilities of the biradicals
involved.

U

ntil recently, the majority of theoretical calculations
r eported for the excited states of conjugated
molecules have been concerned with the prediction of
band position in singlet-singlet absorption
the A,
spectra. Thus such calculations deal with the energy
difference between the lowest vibrational level of the
ground state and an upper vibrational level of the
excited state. In contrast, we are concerned in this
series of papers with the energetics of the lowest
vibrational level of electronically excited states (particularly triplets), sinceonly with such information can
intermolecular photochemical reactions in solution be
rationalized and predicted.
T o this end, molecular orbital calculations at three
levels of sophistication-all-electron a b initio theory,
semiempirical K electron theory with configuration
interaction, and independent-electron perturbation techniques-are used to predict the equilibrium bond angles,
bondlengths, and bonding energies in low-lying excited
states. In the present report, these methods are employed to study the intramolecular energy surface
for the lowest 3 7r7* state of ethylene and conjugated
polyenes.

Theoretical Methods
(1) A b initio Calculations. T he optimum carboncarbon bond distances in the planar and twisted con~
formations of ethylene in its 3 ~ state * were evaluatedb y all-electron, nonempirical SCF-LCAO-MO calculations using a minimal Slater orbital basis set ( I s
o rbitals on H ; Is, 2s, 2p orbitals on C ) . T he closedshell Hartree-Fock-Roothaan method2 was used to
determine optimum eigenvectors for the ground state,
from which the triplet energy was computed by Pople’s
formula3
AE

= E ,*

-

E,

- J,,*

( I ) (a) Publication N o. 22from the photochemistry unit; (b) research supported by the National Research Council of Canada; (c) presented, in p art, a t the ACSICIC Joint Conference, May 24-29, 1970, in
Toronto, Canada, and at the 3rd IUPAC Conference o n P hotochemistry, July 12-17, 1970, in S t. Moritz, Suitzerland.
( 2 ) C . C . J . R oothaan, R ei. M od. P hJ,s., 2 3, 69 (1951).
(3) J . A . Pople, Proc. Phys. S oc.. A68, 8 1 (1955).

Here E, a nd E,* represent eigenvalues for the 7 a nd T*
molecular orbitals, and J,,* is the Coulomb repulsion
integral between these MOs. All the energy integrals
required were evaluated by simulating each Slater-type
orbital (STO) as a linear combination of two Gaussiantype orbitals (GTOs) using the STO-2G expansion
coefficients and GTO exponents of Hehre, et aL4
T heSTO exponents employed were those found to be
optimum for the ground state at the STO-3G level;4
i .e., 1.23 for lsH, 5.67 for Isc, and 1.70 for 2sc and 2pc
orbitals. Previous experience with such basis sets
suggests that accurate bond lengths can be obtained in
this manner.5
T he optimum bond distance R e for each conformation
was determined by calculating the triplet energy for
four R...