Unknown Symbol in Molecular Term Symbols

In summary: X is used by convention as the designation for the ground state. A, B, C, etc. denote electronic states with the same multiplicity as the ground state.
  • #1
luke
25
0
Hello,

I am interested in the electronic states of the N2 molecule. Now it is a homonuclear diatomic molecule and http://en.wikipedia.org/wiki/Molecular_term_symbol" ) but I do not understand what the Latin letters before the molecular term symbols mean. Here are some of the states

[tex]X^{1} \Sigma_{g}^{+}[/tex]
[tex]A^{3} \Sigma_{u}^{+}[/tex]
[tex]B^{3} \Pi_{g}}[/tex]
[tex]W^3 \Delta_u[/tex]
[tex]B'^3 \Sigma_u^{-}[/tex]
[tex]C^3 \Pi_u [/tex]

What do the X, A, B, W, B', and C stand for? I understand the rest of the symbols. Any pointers would be helpful.
 
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  • #2
luke said:
Hello,

I am interested in the electronic states of the N2 molecule. Now it is a homonuclear diatomic molecule and http://en.wikipedia.org/wiki/Molecular_term_symbol" ) but I do not understand what the Latin letters before the molecular term symbols mean. Here are some of the states

[tex]X^{1} \Sigma_{g}^{+}[/tex]
[tex]A^{3} \Sigma_{u}^{+}[/tex]
[tex]B^{3} \Pi_{g}}[/tex]
[tex]W^3 \Delta_u[/tex]
[tex]B'^3 \Sigma_u^{-}[/tex]
[tex]C^3 \Pi_u [/tex]

What do the X, A, B, W, B', and C stand for? I understand the rest of the symbols. Any pointers would be helpful.

The letter X refers to the ground state, while A, B, C, etc. refer to higher electronic states of the same multiplicity. If lowercase, a, b, c, etc. then the electronic states have different multiplicity.
 
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  • #3
Thank you gabriels for the fast reply. I have a few follow up questions. If you could recommend a reference that uses this notation that might be easier then answering my questions. Either way is fine by me.


From what I have read it makes sense that the X would denote the ground state but it seem that you would be able to recognize the ground state without the X. Is the X just there to make it explicit which state is the ground state?

A, B, C denote electronic states with the same multiplicity as what? Do you mean that all states with an A in front have the same multiplicity? It seems like there should be some other hidden meaning to the letters since why would the paper I am reading choose to use X,A,B,W,B',C,E,D?
 
  • #4
luke said:
From what I have read it makes sense that the X would denote the ground state but it seem that you would be able to recognize the ground state without the X. Is the X just there to make it explicit which state is the ground state?

A, B, C denote electronic states with the same multiplicity as what? Do you mean that all states with an A in front have the same multiplicity? It seems like there should be some other hidden meaning to the letters since why would the paper I am reading choose to use X,A,B,W,B',C,E,D?

a) My guess is that X is used by convention as you suggested, because the gorund state might not be apparent when filling N2 and O2, for example.

b) A,B,C,D etc. have the same multiplicity (2S+1) as the ground state, while a,b,c,d, etc. have a different multiplicity than the ground state. I have not seen the prime notation, however.
 
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  • #5
Thank you for your help. I found a reference that give essentially the same information but might be helpful to someone else who stumbles upon this.

Molecular Spectra and Molecular Structure, Vol I by Herzberg. The appendix has a list of electronic structures and provides an explanation of notation. N2 seems to be a special case. The appendix says,

"The only exception to this rule is N2 where the custom of designating the excited singlet states a, b, ... and the excited triplet states A, B, ... appeared too well established to make a change. The order a, b, c, ... A, B, C, ... is usually the order of increasing energy. But in some cases, particularly H2 He2, exceptions were made in order to be in agreement with earlier designations."
 

Related to Unknown Symbol in Molecular Term Symbols

1. What is an unknown symbol in molecular term symbols?

An unknown symbol in molecular term symbols is a placeholder used to represent a quantum number that has not been determined. Molecular term symbols are used to describe the electronic states of molecules, and each symbol contains a series of letters and numbers that represent different quantum numbers.

2. How are unknown symbols determined in molecular term symbols?

Unknown symbols in molecular term symbols are typically determined through spectroscopic experiments and calculations. These experiments involve measuring the energy levels of molecules and using mathematical equations to determine the values of the unknown quantum numbers.

3. What do the letters and numbers in molecular term symbols represent?

The letters in molecular term symbols represent the total orbital angular momentum (L), the total spin angular momentum (S), and the total electronic angular momentum (Λ). The numbers represent the values of these quantum numbers, with L ranging from 0 to n-1, S equaling 0 or 1, and Λ ranging from |L-S| to L+S.

4. Can unknown symbols in molecular term symbols be negative?

Yes, unknown symbols in molecular term symbols can be negative. This is because the quantum numbers they represent can take on negative values. For example, the quantum number Λ can be negative if the molecule has an odd number of electrons.

5. Why are molecular term symbols important in chemistry?

Molecular term symbols are important in chemistry because they provide a way to describe the electronic states of molecules and predict their properties. They are also used to understand and interpret the spectra of molecules, which is crucial in identifying and characterizing different chemical compounds.

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