# 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.

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 =

Free Ion Term or Atomic State are very important in the interpretation of spectra of coordination compounds.

Free Ion Term or Atomic State for d

The value of 'L' = 2 + 1 = 3

and spin multiplicity (2S + 1) = 2(2/2) + 1 = 3

so, Free Ion Term or Atomic State =

According to

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- d

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.

Term symbol for a particular atomic state or free ion term is written as-

Where-

2S + 1 = Spin multilicity and J = total angular momentum

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

Examples-

p

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 =

Angular momentum (J) = |L + S| to |L − S|

J = 1 + 1 to 1 − 1

J = 2, 1, 0

since p

Ground state term symbol =

### Q. Calculate the spectroscopic term symbol for d

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 =

Angular momentum (J) = |L + S| to |L − S|

J = 3 + 1 to 3 − 1

J = 4, 3, 2

since d

Ground state term symbol =

### Q. The term symbol not possible for the nd

Answer: D.

### Q. The term symbol for the ground state of

Answer: A. [Kr]4d

### Q. Calculate the spectroscopic term symbol for the electronic configuration 2p

First take 2p

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 2p

Now each of six states can couple with 3d

For

L = 2 and S = 1

and for 3d

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

Similarly we can calculate others too.

2. Calculate spin multiplicity (2S + 1)

3. Calculate the maximum possible value of 'L'

Example-

### Q. Calculate the ground state term symbol for [Cr(CN)

Its a high spin d

so, L = 4 + 1 + 0 = 5

Spectroscopic symbol = H

Spin multiplicity (2S + 1) = (2 X 1) + 1 = 3

J = L − S as d

J = 5 − 1 = 4

so, the Ground state term symbol of [Cr(CN)

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+1}LFree Ion Term or Atomic State are very important in the interpretation of spectra of coordination compounds.

Free Ion Term or Atomic State for d

^{2}system-+2 | +1 | 0 | −1 | −2 |
---|---|---|---|---|

↑ | ↑ |

and spin multiplicity (2S + 1) = 2(2/2) + 1 = 3

so, Free Ion Term or Atomic State =

^{3}F [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- d

^{2}system has^{1}G,^{3F},^{3}P,^{1}D,^{1}S freee ion terms. According to Hund's rule,^{3}F 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 d**^{n}Configuration-Configuration | Ground State Term | Other Terms |
---|---|---|

d^{1}, d^{9} | ^{2}D | - |

d^{2}, d^{8} | ^{3}F | ^{3}P, ^{1}G, ^{1}D, ^{1}S |

d^{3}, d^{7} | ^{4}F | ^{4}P,^{2}P, ^{2}D, ^{2}F, ^{2}G,^{2}H |

d^{4}, d^{6} | ^{5}F | ^{3}P,^{3}D,^{3}F,^{3}G,^{3}H,^{1}S,^{1}D,^{1}F,^{1}G,^{1}F |

d^{5} | ^{6}S | ^{4}P,^{4}D,^{4}F,^{4}G,^{2}S,^{2}P,^{2}D,^{2}F,^{2}G,^{2}H,^{2}I |

d^{10} | ^{1}S | - |

## 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 configuration2. 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-

p

^{2}Configuration-+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 =

^{3}PAngular momentum (J) = |L + S| to |L − S|

J = 1 + 1 to 1 − 1

J = 2, 1, 0

since p

^{2}is less than half filled so J = 0Ground state term symbol =

^{3}P_{0}**MPSET 2019**### Q. Calculate the spectroscopic term symbol for d^{8} Configuration-

L = 4 + 2 + 0 −1 −2 = 3Spectroscopic symbol = F

S = 0 + 0 + 0 + 1/2 + 1/2 = 1

Spin multiplicity (2S + 1) = (2 x 1) + 1 = 3

so, Ground state term =

^{3}FAngular momentum (J) = |L + S| to |L − S|

J = 3 + 1 to 3 − 1

J = 4, 3, 2

since d

^{8}is more than half filled so J = 4Ground state term symbol =

^{3}F_{4}### Q. The term symbol not possible for the nd^{2} electronic configration is-

A. ^{3}F

B. ^{1}D

C. ^{1}G

D. ^{1}F

Answer: D. ^{1}F### Q. The term symbol for the ground state of _{45}Rh is ^{4}F. The electronic configuration for this term symbol is-

A. [Kr]4d^{7}5s^{2}

B. [Kr]4d^{9}5s^{0}

C. [Kr]4d^{8}5s^{1}

D. [Kr]4d^{7}5s^{1}5p^{1}

Answer: A. [Kr]4d^{7}5s^{2}**TIFR 2013**### Q. Calculate the spectroscopic term symbol for the electronic configuration 2p^{1}3p^{1}3d^{1}

First take 2p^{1}and 3p^{1}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 2p

^{1}and 3p^{1}are-^{3}D,^{3}P,^{3}S,^{1}D,^{1}P, and^{1}S.Now each of six states can couple with 3d

^{1}electron to give the resultant L and S-For

^{3}D-L = 2 and S = 1

and for 3d

^{1}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

^{3}D 3d^{1}are-^{4}G,^{4}F,^{4}D,^{4}P,^{4}S,^{2}G,^{2}F,^{2}D,^{2}P and^{2}S.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 d^{4}systemso, L = 4 + 1 + 0 = 5

Spectroscopic symbol = H

Spin multiplicity (2S + 1) = (2 X 1) + 1 = 3

J = L − S as d

^{4}is less than half filled configurationJ = 5 − 1 = 4

so, the Ground state term symbol of [Cr(CN)

_{6}]^{−4}=^{3}H_{4}