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Lecture 15 Molecular Bonding Theories 1) Molecular Orbital Theory. Considers all electrons in the field of all atoms constituting a polyatomic species, so that all molecular orbitals (MO’s) are multicenter .
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Lecture 15 Molecular Bonding Theories 1) Molecular Orbital Theory • Considers all electrons in the field of all atoms constituting a polyatomic species, so that all molecular orbitals (MO’s) are multicenter. • The most common way to build MO’s, yMO,j, is by using a linear combination of all available atomic orbitals yAO, i (LCAO): • Consider dihydrogen molecule ion H2+ as an example. We can form two molecular orbitals from two hydrogen’s atomic orbitals yA and yB : • The probability to find an electron on the yg orbital is then where S is the overlap integral for atomic orbitals yA and yBand N is normalizing constant. S > 0 corresponds to a bonding (yg) and S < 0 (yu) – to antibonding situations.
2) Molecular Orbital Theory. Dihydrogen molecule • In dihydrogen molecule we have 2 electrons, 1 and 2. Assuming that 1 and 2 are independent one from another (one-electron approximation), we can get: • The first term corresponds to ionic contribution and the second one – to covalent contribution to the bonding (compare with VB theory).
3) Atomic orbital overlap and covalent bonding • Interaction between atomic orbitals leads to formation of bonds only if the orbitals: • 1) are of the same molecular symmetry; • 2) can overlap well (see explanation of the overlap integral below); • 3) are of similar energy (less than 20 eV energy gap). • Any two orbitals yA and yB can be characterized by the overlap integral, • Depending on the symmetry and the distance between two orbitals, their overlap integral S may be positive (bonding), negative (antibonding) or zero (non-bonding interaction).
4) Simplified MO diagram for homonuclear diatomic molecules (second period) • Combination of 1s, 2s, 2px, 2py and 2pz atomic orbitals of two atoms A of second row elements leads to ten molecular orbitals. 10) s*2p = y2pA – y2pB (3su) 9) p*2py = y2pyA – y2pyB (pg) 8) p*2px = y2pxA – y2pxB (pg) 7) p2py = y2pyA + y2pyB (pu) 6) p2px = y2pxA + y2pxB (pu) 5) s2p = y2pA + y2pB (3sg) 4) s*2s = y2sA – y2sB (2su) 3) s2s = y2sA + y2sB (2sg) 2) s*1s = y1sA – y1sB (1su) 1) s1s = y1sA + y1sB (1sg)
5) Orbital mixing and level inversion in homonuclear diatomic molecules • Orbitals belonging to the same atom mix if all of the following is true: 1) they are of the same symmetry; 2) they are of similar energy (less than 20 eV difference). • Note that there is no p-orbitals of the same symmetry in diatomic homonuclear molecules (pg and pu only). So, they energy levels will remain unaffected by mixing.
6) MO diagrams of homonuclear diatomic molecules • Filling the resulting MO’s of homonuclear diatomic molecules with electrons leads to the following results: Bond order = ½ (#Bonding e’s - #Antibonding e’s) Li2 1 0 1.1 Be2 0 0 - B2 2 3.0 1 C2 2 0 6.4 N2 3 9.9 0 2 O2 2 5.2 F2 1 0 1.4 Ne2 0 0 -
7) Molecular Orbital Theory. Energy levels in N2 molecule • Photoelectron spectroscopy of simple molecules is an invaluable source of the information about their electronic structure. • The He-I photoelectron spectrum of gaseous N2 below proves that there is the s-p level inversion in this molecule. It also allows identify bonding (peaks with fine vibronic structure) and non-bonding MO (simple peaks) in it.
