Transcript l value 0 1 2 3

ATOMIC/MOLECULAR SPECTROSCOPY
Various spectroscopic techniques are used
to elucidate molecular structures (eg. NMR),
to study molecular vibrations (IR and Raman
spectra – often associated with force field
calculations), to study molecular rotational
energies (usually microwave spectra but also
high resolution gas phase IR, Raman and UV
spectra).
ELECTRONIC SPECTRA:
Electronic spectra, even of closed shell
molecules, can be complex since electronic
energies, vibrational energies and rotational
energies can all change simultaneously.
Rotational energy patterns can be extremely
complex for “heavy” molecules or for
asymmetric rotors. Additional complications
exist when there are unpaired electrons.
ELECTRONIC SPECTRA
Electronic spectra of atoms/monatomic ions
provide details of atomic structure. Such
spectra find practical applications in
analytical chemistry (eg. atomic absorption
spectroscopy). Atomic emission “spectra”
are used in light emitting devices such as
sodium vapor lamps and in more complex
devices such as the helium neon laser.
COMPLEX SPECTRA
Rich spectra are a reflection of complex
atomic or molecular atomic energy level
patterns (complexity increasing with growing
numbers of atoms/electrons and loss of
symmetry). Temperature is also a factor. An
increase in temperature pushes molecules
into higher energy states and allows more
spectral lines/transitions to be observed.
SPECTRA FOR ONE ELECTRON SPECIES
The simplest electronic spectra, not
surprisingly, are due to the one electron (and
monatomic) species H, He+, Li2+, etc. For
these species familiar energy degeneracies
are seen.
Aside: For the one electron species H2+
energy level patterns are much more
complex. Why?
HYDROGEN ATOM ENERGY LEVELS
H ATOM DEGENERACIES

H ATOM ANGULAR MOMENTA

QUANTUM NUMBERS – H ATOM
For one electron species we employ lower
case letters to designate both quantum
numbers and operators. We associate
specific l values with subshells.
l value
0
Subshell
s
1
2
p
d
3
f
MANY ELECTRON ATOMS
For many electron atoms life is more
complicated (not surprisingly?). The energy
degeneracies seen for H, He+, Li2+ etc. are
removed/lifted due to electron-electron
interactions.
MULTI-ELECTRON ATOM ENERGY LEVELS
MULTI-ELECTRON ATOMS
For multi-electron atoms life is also more
complex since angular momenta can
“couple” (vector addition). This is most
important when there are unpaired
electrons. As a final complication, the H
atom quantum numbers (n, l…) are not good
quantum numbers for multi-electron atoms
or multi-electron monatomic ions.
MULTI-ELECTRON ATOMS/IONS

MULTI-ELECTRON ATOMS/IONS
However, the z-components of orbital
angular momentum and of spin angular
momentum add as scalar quantities and,
correspondingly, we have the sums ML and
MS which enable us to define the quantum
numbers L and S.
ML = ∑ lzi = ∑ ml(i) and MS = ∑ szi = ∑ ms(i)
TOTAL ANGULAR MOMENTUM

RUSSELL-SAUNDERS COUPLING
In earlier courses we wrote electron
configurations for both ground and excited
state atoms/ions
 He atom ground state - 1s2
He atom first excited state - 1s12s1
In fact, the electron configuration written
above represents two excited states. Why?
RUSSELL SAUNDERS COUPLING
We will write so-called term symbols to
specify different atomic states. Here only J is
strictly a good quantum number. We write
the term symbols as (2S+1)LJ where J is the
total angular momentum, L is the total
orbital angular momentum and S is the total
spin angular momentum. 2S+1 is the spin
multiplicity.
RUSSELL SAUNDERS COUPLING
For the H atom the permitted values of
orbital angular momentum (due to the lone
electron) are specified using either
numerical l = 0,1,2,3.. values or lower case
letters s, p, d, f….. For multi-electron
atoms/ions the possible L values are
specified using upper case letters S, P, D F….
1,
TERM SYMBOLS
Class examples will illustrate the use/writing
of term symbols for atoms and monatomic
ions.