Electronic spectroscopy Flashcards
Selection rules for an atom
ΔS = 0
ΔL = 0, +/- 1
ΔJ = 0, +/- 1
L = 0 <-> L = 0 forbidden
J = 0 <-> J = 0 forbidden
Δn = anything consistent with Δl
n quantum number
The principal quantum number describes the electron shell of an electron. The value of n ranges from 1 to the shell containing the outermost electron of that atom
n = 1, 2, 3, …
s quantum number
Spin quantum number (s) because electrons behave as if they were spinning in either a clockwise or counterclockwise fashion. One of the electrons in an orbital is arbitrarily assigned an s quantum number of +1/2, the other is assigned an s quantum number of -1/2.
S total spin
Clebsh gordan series
S = s1 + s2, s1 + s2 -1, …, s1 - s2
Magnitude of total spin angular momentum, S
{S(S+1)} 1/2 h
l quantum number
orbital angular momentum = quantum number describes the shape of a given orbital. Its value is equal to the total number of angular nodes in the orbital. The value of l can indicate either an s, p, d, or f subshell which vary in shape
ℓ = 0 is s orbital, ℓ = 1, p orbital, ℓ = 2, d orbital, and ℓ = 3, f orbital.
Total orbital angular momentum, L
Is the result of coupling the individual orbital angular momenta of unpaired electrons
L = l1 + l2, l1 + l2 - 1, …, l1 - l2.
Magnitude of total orbital angular momentum, L
{L(L+1)}1/2 h
Magnetic moment quantum number ML
specifies the z-component of the orbital angular momentum
quantum number j
Total angular momenta
j = l+s, l+s-1, …, |l-s|
How to calculate J with weak spin orbit coupling (Russell Saunders coupling)
1) individual orbital angular momenta, l, couple to give total L
2) individual spin angular momenta, s, couple to give total S
3) Only at this stage do S and L couple to give J
J = L + S, L + S - 1, …, L - S
How to calculate J with strong spin orbit coupling (jj-coupling) (when atoms heavy with large Z)
1) Individual orbital and spin angular momenta, l and s, couple to give individual j
2) The individual total angular momenta, j and j couple to give J
ml
The magnetic quantum number describes the specific orbital within the subshell, and yields the projection of the orbital angular momentum along a specified axis
Values of mℓ range from −ℓ to ℓ, with integer intervals
ms
The spin magnetic quantum number describes the intrinsic spin angular momentum of the electron within each orbital and gives the projection of the spin angular momentum S along the specified axis
Values of ms range from −s to s, where s is the spin quantum number
mj
2j +1 values of mj
mj = j, j-1, j-2, …, -j
Microconfiguration
specified one of the possible combinations of ml and ms in a configuration. Each microconfig defines an L, S, J and MJ state
Term
Commonly applied to describe what arises from an approximate treatment of the electronic configuration in which just L and S are accounted for i.e. ignoring spin-orbit interactions
Level
used to describe what arises when spin orbit coupling has been taken into account. i.e. where L, S and J are accounted for
State
Takes account of not only L, S and J but also MJ. Number of states is therefore the same as number of microconfigurations. In absence of external field all states within particular level have same energy with degeneracy of 2J + 1
Multiplicity
Is the number of levels in a term for S<L the multiplicity equals 2S +1 for S>L multiplicity equals 2L +1
Spin orbit interaction energy, E
E = 1/2 hcA {j(j+1) -l(l+1) -s(s+1)
Why do paired electron have overall spin of zero?
the 2 electrons have their spin angular momentum vectors oriented spin that the resultant spin is 0
How to find the lowest energy microconfiguration of electron config?
Microconfiguration that maximises both Ml and Ms
Overall L and S for filled/closed shell
L=0 and S=0
For a single electron outside a closed shell values of S and L are the same as s and l for that electron
In absence of external field what degeneracy does each J level have?
2J + 1 degeneracy arising from 2J + 1 MJ states
What multiplicity lies lowest in energy?
Term of greatest multiplicity lies lowest in energy (Triplet lower than Singlet)
Is a result of spin correlation and the tendency of electrons with parallel spin to stay apart
What value of L lies lowest in energy?
The term with the highest value of L lies lowest in energy
For atoms with less than half filled subshell which level lies lowest in energy?
Lowest J value will lie lowest in energy - normal multiplet
For atoms with more than half filled subshell which level lies lowest in energy?
Highest J value will lie lowest in energy - inverted multiplet
How to triplet and singlet states occur
The spins of 2 electrons may be aligned or paired with aligned spins corresponding to s=1 (triplet) or s=0 (singlet)
Zeeman Effect
In presence of magnetic field
J precesses round field direction and becomes poorly defined. System is instead defined by MJ. Each MJ value splits into a different energy level
Degeneracy is completely lifted
Stark effect
In presence of electric field J precesses round field direction and becomes poorly defined. System is instead defined by MJ. Only partial lifting of degeneracy as +/- MJ have same energy
Orbital angular momentum, Why is l no longer a good quantum number?
In a diatomic molecule, the electron experiences an axially symmetric electric field generated by the 2 nuclei.
l couples so strongly to electric field that use ml as still well defined.
Classify MOs according to 𝛌 = ml = 0, +/- 1, +/- 2, +/- 3. etc
For a filled orbital/ closed shell what is the value of 𝛬
𝛬 = 0, either because both electrons have 𝛌 = 0 or bc there are equal number of electrons with 𝛌 = 1 and 𝛌= -1
Therefore filled shell will have term symbol Σ
What is inversion symmetry of diatomics
orbitals labelled with g or u depending on whether the change sign upon inversion
Overall parity in multielectron homonuclear diatomic found by multiplying parity of each occupied orbital
g x g = g
u x u = g
u x g = u
Symmetry under reflection in a plane, term symbol post superscript
All linear molecules possess a mirror plane containing the internuclear axis
Overall symmetry with respect to reflection is found by assigning +1 to each electron in symmetric orbital and -1 to antisymmetric then multiply
Total angular momentum along internuclear axis in linear molecule, Ω
Ω = 𝛬 + Σ
Where 𝛬 = equiv to term symbol
Where Σ = S, S-1, S-2, …, -S
Selection rules concerned with a linear molecule
Δ𝛬 = 0, +/- 1
ΔS = 0
ΔΣ = 0
ΔΩ = 0, +/- 1
Symmetry requirements for transition for linear molecule
+ > - forbidden
- > - allowed
+ > + allowed
g > g forbidden
u > u forbidden
g > u allowed
