bution is cylindrically symmetrical about the internu-
clear axis.)
See alsoSIGMA, PI.
sigma (σ) constant Specifically, the substituent con-
stant for meta- and for para-substituents in benzene
derivatives as defined by Hammett on the basis of the
ionization constant of a substituted benzoic acid in
water at 25°C, i.e., lg(Ka/Kao), where Kais the ioniza-
tion constant of an m- or p-substituted benzoic acid
and Kaois that of benzoic acid itself.
The term is also used as a collective description for
related electronic substituent constants based on other
standard reaction series, of which σ+, σ–, and σoare
typical; it is also used for constants that represent dis-
sected electronic effects, such as σI and σR. For this
purpose it might be better always to spell out the term
in full, i.e., as “Hammett sigma constant,” and restrict
σ-constants to the scale of substituent constants, based
on benzoic acid.
A large positive σ-value implies high electron-with-
drawing power by inductive and/or resonance effect
relative to H; a large negative σ-value implies high elec-
tron-releasing power relative to H.
See also HAMMETT EQUATION; RHO (ρ) VALUE;
TAFT EQUATION.
sigma (σ) orbital Molecular orbital bonding with
cylindrical symmetry about the internuclear axis.
See alsoSIGMA, PI.
sigmatropic rearrangement A MOLECULAR REAR-
RANGEMENTthat involves both the creation of a new
sigma bond between atoms previously not directly
linked and the breaking of an existing sigma bond.
There is normally a concurrent relocation of pi bonds
in the molecule concerned, but the total number of pi
and sigma bonds does not change. The term was origi-
nally restricted to INTRAMOLECULAR PERICYCLIC REAC-
TIONs, and many authors use it with this connotation.
It is, however, also applied in a more general, purely
structural, sense.
If such reactions are INTRAMOLECULAR, their
TRANSITION STATEmay be visualized as an ASSOCIA-
TIONof two fragments connected at their termini by
two partial sigma bonds, one being broken and the
other being formed as, for example, the two allyl frag-
ments in (a′). Considering only atoms within the (real
or hypothetical) cyclic array undergoing reorganiza-
tion, if the numbers of these in the two fragments are
designated i and j, then the rearrangement is said to
be a sigmatropic change of order [i,j] (conventionally
[i] ≤[j]). Thus the rearrangement (a) is of order [3,3],
while reaction (b) is a [1,5]sigmatropic shift of hydro-
gen. (Note that by convention, the square brackets
[...] here refer to numbers of atoms, in contrast with
current usage in the context of cycloaddition.)The descriptors a and s (ANTARAFACIAL and
SUPRAFACIAL) may also be annexed to the numbers i
and j; (b) is then described as a [1s,5s] sigmatropic
rearrangement, since it is suprafacial with respect
both to the hydrogen atom and to the pentadienyl
system:The prefix homo(meaning one extra atom, inter-
rupting CONJUGATION, cf. HOMOAROMATICITY) has fre-
quently been applied to sigmatropic rearrangements,
but it is misleading.
See alsoCYCLOADDITION; TAUTOMERISM.signal peptide A sequence of amino acids that deter-
mines the location of a protein in a eukaryotic cell.
See alsoEUKARYOTE.246 sigma (σ) constant