Spectroscopic Term | Term Symbol | Atomic Term Symbol

Spectroscopic Term | Term Symbol

The interaction of orbital angular momentum (l) of different electrons gives total orbital angular momentum(L) of the system. The value of 'L' ranges from +L to −L and the value of 'L' gives spectroscopic symbol.

Value of L	Term
0	S
1	P
2	D
3	F
4	G
5	H
6	I
7	K

We know that spin multiplicity is 2S+1 and orbital multiplicity is 2L+1. When spin multiplicity is shown with the symbol of 'L', Free Ion Term or Atomic State is indicated.
Free Ion Term or Atomic State = ^2S+1L
Free Ion Term or Atomic State are very important in the interpretation of spectra of coordination compounds.
Free Ion Term or Atomic State for d² system-

+2	+1	0	−1	−2
↑	↑

The value of 'L' = 2 + 1 = 3
and spin multiplicity (2S + 1) = 2(2/2) + 1 = 3
so, Free Ion Term or Atomic State = ³F     [Triplet F]
According to Hund's Rule, if a system has several free ion terms of different spin multiplicity then-
1. Free ion term having highest spin multiplicity has the lowest energy and the term is ground free ion term.
2. If there are more than one free ion terms of same spin multiplicity, then the term having highest value of 'L' has lowest energy.
Example- d² system has ¹G, ^3F, ³P, ¹D, ¹S freee ion terms. According to Hund's rule, ³F has the lowest energy as its 'L' value is highest.

3. If spin multiplicities are same and the values of 'L' are also same for two atomic states, then the state having lowest 'J' value will be of lowest energy if the sub shell is less than half filled and the state having highest value of 'J' will be of lowest energy if the subshell is more than half filled.
4. If subshell is exactly half filled, it has only one value of 'J'. This is applicable when spin-orbit coupling is taken into account.

Terms of dⁿ Configuration-

Configuration	Ground State Term	Other Terms
d1, d9	2D	-
d2, d8	3F	3P, 1G, 1D, 1S
d3, d7	4F	4P,2P, 2D, 2F, 2G,2H
d4, d6	5F	3P,3D,3F,3G,3H, 1S,1D,1F,1G,1F
d5	6S	4P,4D,4F,4G,2S, 2P,2D,2F,2G,2H,2I
d10	1S	-

Term symbol

A term symbol is a unique 'nickname' for an electronic state. Term symbol is an abbreviated description of the total angular momentum quantum numbers in a multi-electron atom. However, even a single electron can also be described by a term symbol. Each energy level of an atom with a given electron configuration is described by not only the electron configuration but also its own term symbol, as the energy level also depends on the total angular momentum including spin. The usual atomic term symbols assume L-S coupling (also known as Russell–Saunders coupling or spin-orbit coupling). The ground state term symbol is predicted by Hund's rules.
Term symbol for a particular atomic state or free ion term is written as-
^{2S + 1}L_J
Where-
2S + 1 = Spin multilicity and J = total angular momentum

Atomic Term Symbol

How to Find Ground State Term or Ground State Term Symbol

1. First write the electronic configuration
2. Now consider only the valence electron
3. Calculate the total orbital angular momentum 'L' value
4. Calculate the total spin quantum number 'S' value
5. Calculate the spin multiplicity (2S+1) value
6. Calculate the total angular momentum'J' value
7. For ground state term
J = (L-S) if subshell is less than half filled
J= (L+S) if subshell is more than half filled
J = S if subshell is half filled or fulfilled
8. Now write the term symbol in this format ^(2S+1)L_J


Examples-
p² Configuration-

+1	0	−1
↑	↑

L = 1 + 0 = 1
Spectroscopic symbol = P
S = 1/2 + 1/2 = 1
Spin multiplicity (2S + 1) = (2 x 1) + 1 = 3
so, Ground state term = ³P
Angular momentum (J) = |L + S| to |L − S|
J = 1 + 1 to 1 − 1
J = 2, 1, 0
since p² is less than half filled so J = 0
Ground state term symbol = ³P₀


MPSET 2019  

Q. Calculate the spectroscopic term symbol for d⁸ Configuration-

L = 4 + 2 + 0 −1 −2 = 3
Spectroscopic symbol = F
S = 0 + 0 + 0 + 1/2 + 1/2 = 1
Spin multiplicity (2S + 1) = (2 x 1) + 1 = 3
so, Ground state term = ³F
Angular momentum (J) = |L + S| to |L − S|
J = 3 + 1 to 3 − 1
J = 4, 3, 2
since d⁸ is more than half filled so J = 4
Ground state term symbol = ³F₄

Q. The term symbol not possible for the nd² electronic configration is-
A. ³F
B. ¹D
C. ¹G
D. ¹F

Answer: D. ¹F

Q. The term symbol for the ground state of ₄₅Rh is ⁴F. The electronic configuration for this term symbol is-
A. [Kr]4d⁷5s²
B. [Kr]4d⁹5s⁰
C. [Kr]4d⁸5s¹
D. [Kr]4d⁷5s¹5p¹

Answer: A. [Kr]4d⁷5s²


TIFR 2013  

Q. Calculate the spectroscopic term symbol for the electronic configuration 2p¹3p¹3d¹

First take 2p¹ and 3p¹
L = 1 for both configuration
Spectroscopic symbol =
L = 1 + 1 = 2 --- D
L = 1 + 1 − 1 = 1 --- P
L = 1 − 1 = 0 --- S
S = 1/2 + 1/2 = 1
SO, spin multiplicity (2S + 1) = 3
and S = 1/2 − 1/2 = 0
SO, spin multiplicity (2S + 1) = 1
Thus, the term symbol due to coupling of 2p¹ and 3p¹ are-
³D, ³P, ³S, ¹D, ¹P, and ¹S.

Now each of six states can couple with 3d¹ electron to give the resultant L and S-
For ³D-
L = 2 and S = 1
and for 3d¹
L = 2 and S = 1/2
So, Spectroscopic symbol =
L = 2 + 2 = 4 --- G
L = 2 + 2 − 1 = 3 --- F
L = 2 + 2 − 2 = 2 --- D
L = 2 + 2 − 3 = 1 --- P
L = 2 − 2 = 0 --- S
S = 1 + 1/2 = 3/2
and S = 1 − 1 /2 = 1/2
SO, spin multiplicity (2S + 1) = (2 x 3/2 + 1) = 4
and spin multiplicity (2S + 1) = (2 x 1/2 + 1) = 2
Thus, term symbol due to coupling of ³D 3d¹ are-
⁴G, ⁴F, ⁴D, ⁴P, ⁴S, ²G, ²F, ²D, ²P and ²S.
Similarly we can calculate others too.

How to Find Ground State Term or Ground State Term Symbol in Octahedral Complexes

1. Draw the energy level (t_2g and e_g)diagram showing d-electrons with maximum value of M_s
2. Calculate spin multiplicity (2S + 1)
3. Calculate the maximum possible value of 'L'
Example-
GATE 2017  

Q. Calculate the ground state term symbol for [Cr(CN)₆]⁻⁴

Its a high spin d⁴ system


so, L = 4 + 1 + 0 = 5
Spectroscopic symbol = H
Spin multiplicity (2S + 1) = (2 X 1) + 1 = 3
J = L − S as d⁴ is less than half filled configuration
J = 5 − 1 = 4
so, the Ground state term symbol of [Cr(CN)₆]⁻⁴ = ³H₄

Molecular Term Symbol