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Energy Levels and Molecular Orbitals in Homonuclear Diatomic Molecules, Study notes of Physics

Nyack College Physics

The concepts of energy levels and molecular orbitals in homonuclear diatomic molecules and their ions. It covers the determination of paramagnetic or diamagnetic properties, bond order calculation, and the correlation between bond order and bond length/strength. The document also explains the principles of atomic orbital interaction and the formation of bonding and antibonding molecular orbitals. Relevant questions about the energy ordering schemes for diatomic molecules and the impact of 2s-2p mixing on energy level diagrams are addressed.

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2021/2022

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ENERGYLEVELSFORHOMONUCLEARDIATOMICMOLECULES



WhatdoIhavetoknow?

Youwillberesponsibleforbeingabletowriteoridentifygroundandexcitedstate

configurationsforhomonucleardiatomicmoleculesandtheirionsandbeableto:

I. Determinewhetherthemoleculeisparamagneticordiamagnetic

II. Calculatethebondorder

III. Fromthebondorderdeterminetheirrelativebondlengthandbondstrength

Todothisyouwillneedtoremembertheenergyorderingschemesfordiatomicmolecules.

Forthelighter(B2,C2,N2)andheavier(O2,F2,Ne2)therearetwodifferentenergyorderingsfor

themolecularorbitalsarisingfromthebonding(constructiveinterference)andantibonding

(destructiveinterference)combinationsof2patomicorbitals:



AppliestoB2,C2,N2AppliestoO2,F2,Ne2



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ENERGY LEVELS FOR HOMONUCLEAR DIATOMIC MOLECULES

What do I have to know? You will be responsible for being able to write or identify ground and excited state configurations for homonuclear diatomic molecules and their ions and be able to: I. Determine whether the molecule is paramagnetic or diamagnetic II. Calculate the bond order III. From the bond order determine their relative bond length and bond strength To do this you will need to remember the energy ordering schemes for diatomic molecules. For the lighter (B 2 , C 2 , N 2 ) and heavier (O 2 , F 2 , Ne 2 ) there are two different energy orderings for the molecular orbitals arising from the bonding (constructive interference) and antibonding (destructive interference) combinations of 2p atomic orbitals: Applies to B 2 , C 2 , N 2 Applies to O 2 , F 2 , Ne (^2)

Remember the two principles that determine whether a.o.’s on two atoms will interact to form bonding and antibonding m.o.’s: A. The a.o.’s must have similar energies B. The two a.o.’s must ‘overlap’ and interact to have net constructive and destructive interference. The degree of stabilization by constructive interference (and destabilization by destructive) is determined by the extent of this interaction. We can ask the following relevant questions:

1. Why are there a pair of degenerate levels for each of the p2p and p2p m.o.’s?*

the two side ‐ on interactions (2p y )A ï (2p y )A’ and (2p z )A ï (2p z )A’ are equivalent with the

only difference being their directions in space; constructive interference leads to two p 2p

m.o.’s of equal (lower) energy and destructive interference leads to two p 2p* of equal

(higher) energy.

2. Why in the “expected” is the energy of the s 2p is lower than that of the p 2p in the ‘simple’ energy level scheme (Fig 14.38)? the end ‐ on interactions of the (2p (^) x)A ñ(2p (^) x)A’ are stronger than the side ‐ on interactions of (2p (^) y )A ñ(2p (^) y )A’ or (2p (^) z )A ñ(2p (^) z )A’ (principle B).

What is meaning of 2s‐2p mixing and why is it more important for B 2 , C 2 , N 2 than for O 2 , F 2 , Ne 2? A 2s orbital on atom A will have net interference (‘overlap’) with a 2p (^) x on atom A’. yes for 2s ‐ 2p (^) x we can have net constructive or destructive interference 2s on A 2px on A’ and thus they could contribute to the same m.o. (principle B) if they had similar energies (principle A). In O 2 , F 2 , Ne 2 the larger Z (nuclear charge) makes the energy of the 2s atomic orbital much lower than the 2p atomic orbital and thus the 2s and 2p on A and A’ DO NOT mix when forming m.o.’s (simple scheme no 2s ‐ 2p mixing). However in B 2 , C 2 , N 2 the energies of the 2s and 2p atomic orbitals are much closer and thus the s2s and s2s* m.o.’s contain some contribution from 2p (^) x a.o.s and the s2p and s 2p* m.o.’s contain some contribution from 2s a.o.’s.; i.e. THERE IS 2s ‐ 2p mixing for B 2 , C 2 , N 2