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by this definition, but it is often concep- chirality The components ψ , ψ R of a
L
tually convenient to use the term also for Dirac spinor ψ → e iβγ 5 ψ are called chiral com-
changes involving single molecular entities (i.e., ponents or Weyl components.
“microscopic chemical events”).

chemical species An ensemble of chem- cholesteric phase See liquid-crystal transi-
ically identical molecular entities that can tions.
explore the same set of molecular energy lev-
els on the time scale of the experiment. The term
Christoffel symbols on a (pseudo)-
is applied equally to a set of chemically identi-
Riemannian manifold (M, g), the coefficients of
cal atomic or molecular structural units in a solid µ
the Levi-Civita connection.If g = g (x) dx
µν
array. ⊗ dx ν is the local expression of the metric
For example, two conformational isomers
tensor, its Christoffel symbols are given by:
may be interconverted sufficiently slowly to be
detectable by separate NMR spectra and hence α 1 α"
} = g
{ βµ g −∂ g + ∂ g + ∂ g
" βµ
µ "β
β µ"
to be considered to be separate chemical species 2
on a time scale governed by the radiofrequency α"
where g denotes the covariant inverse metric,
of the spectrometer used. On the other hand, in a
and ∂ denotes the partial derivative with respect
slow chemical reaction the same mixture of con- µ µ
formers may behave as a single chemical species, to x . µ
i.e., there is virtually complete equilibrium popu- µ Under changes of local coordinates x =
lation of the total set of molecular energy levels x (x), Christoffel symbols transform as:
belonging to the two conformers. Except where
α α γ ¯ ¯ ν ¯ γ
δ
} J J + J
} = J
the context requires otherwise, the term is taken { βµ g γ { δν g β µ βµ
to refer to a set of molecular entities containing α
α
isotopes in their natural abundance. The word- where J = ∂x γ is the jacobian of the coordinate
γ
∂x
γ
ing of the definition given in the first paragraph is transformation, J ¯ γ = ∂x α is the inverse Jaco-
α
∂x
intended to embrace both cases such as graphite, γ ∂ x
2 γ
bian, and we set J ¯ βµ = β µ .If ∇ denotes the
sodium chloride, or a surface oxide, where the ∂x ∂x
covariant derivative operator associated to the
basic structural units may not be capable of iso-
Levi-Civita connection, then one has:
lated existence, as well as those cases where they
are. λ
} ∂ .
∇ ∂ ={ µν g λ
∂ µ ν
In common chemical usage generic and spe-
cific chemical names (such as radical or hydrox-
ide ion) or chemical formulae refer either to a chromatic number The minimum number
chemical species or to a molecular entity. of colors needed to color the nodes of a graph,
such that no two adjacent nodes have the same
Chern classes See characteristic classes.
color. Denoted χ(G).
chiral group In QCD (quantum chromo
dynamics) the group SU × SU . See chromo- chromodynamics, quantum (QCD) The
3
3
dynamics, quantum. quantum field theory describing the strong inter-
actions of quarks and gluons.
chiral transformation The transformation
of a Dirac spinor ψ → e iβγ 5 ψ is called chiral
transformation, or chiral symmetry, where β is chromophore The part (atom or group of
0
1
3
2
a constant and γ = iγ γ γ γ with the 4 × 4 atoms) of a molecular entity in which the elec-
5
gamma matrices defined by the Pauli matrices tronic transition responsible for a given spectral

01 0 −i 10 band is approximately localized. The term arose
1 2 3
σ = , σ = , σ =
10 i 0 0 −1 in the dyestuff industry, referring originally to the
i
0 −σ groupings in the moleculaer that are responsible
i
by γ = i .
σ 0 for the dye’s color.
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC