Chemistry Reference
In-Depth Information
interaction raises the energy of the out-of-plane
p
orbital relative to the in-plane
p
orbital. As a result, the coefficient for the doubly occupied in-plane
p
orbital
determinant in the
1
A
1
irreducible representation is computed to be significantly
larger (0.84) than the doubly occupied out-of-plane
p
orbital determinant on nitrogen
(0.41) at the complete active space self-consistent field CASSCF(8,8)/cc-pVTZ level
of theory.
12
This configuration thus represents a hybrid state: it is neither fully closed-
shell nor fully open-shell. For an open-shell singlet state, one expects an occupation of
approximately one electron in each
p
orbital; in a closed-shell state, one expects an
occupation of two and zero electrons. In this
1
A
1
state of phenylnitrene, the occupation
of the orthogonal
p
orbitals is 1.58 and 0.45 electrons—an intermediate value. While
the singlet-triplet energy gap is reduced relative to methylnitrene, the triplet state of
phenylnitrene remains the lower energy state (Scheme 2.1).
At the other end of this continuum, aminonitrenes show an even stronger breaking
of the degeneracy between the
p
orbitals through a powerful anisotropic interaction
of the amino lone pair with the nitrene out-of-plane
p
orbital.
13-15
This interaction
increases the gap in the frontier orbitals sufficiently to make the singlet state the
ground state of this nitrene. Furthermore, the singlet ground state can be well-
described by a single reference closed-shell wavefunction, with very little contribu-
tion from the other higher-energy doubly occupied determinant. Thus, this state is
reasonably labeled closed-shell because of an essentially negligible contribution
of the second determinant; the frontier orbitals have occupations of nearly 2 and
0 electrons.
2.2.4 Singlet-Triplet Gap of Nitrenes
The relative energies of the singlet and triplet electronic states of nitrenes can
be explained in qualitative terms as dependent on two factors—the magnitude of the
exchange integral between the two unpaired electrons of the triplet state, and
the energy gap between the nitrene's frontier orbitals. In general, when the exchange
integral between the two unpaired electrons in the triplet state exceeds the magnitude
of the frontier orbital energy gap, the ground state of the nitrene is the triplet state.
Thus, nitrenes with small frontier orbital gaps have triplet ground states. When the
frontier orbitals are degenerate, the triplet state must be the ground state following
Hund's rule (since the exchange energy is finite and the frontier orbital gap is zero).
In nitrenes with singlet ground states, the energy gap between the frontier
p
orbitals is
sufficiently large that the cost of promoting an electron into the higher-energy orbital
is not fully compensated by the favorable exchange energy that derives from
unpairing the electrons in the triplet state.
The practical consequence of these theoretical considerations is that nitrenes
substituted with strong electron donors (e.g., amines, oxygen substituents, acyl
groups
12-16
) have significantly decreased singlet-triplet gaps (
E
ST
) relative to the
parent nitrene species (NH). With very powerful donor substituents (or with other
type of substituents that strongly break the degeneracy of the frontier
p
orbitals), it is
even possible to have nitrenes with singlet ground states. Because the magnitude of
this degeneracy breaking between the frontier orbitals correlates roughly with the
D
