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Lecture 26: Homonuclear Diatomic Molecules-I The material in this lecture covers the following in Atkins. 14 Molecular structure Molecular Orbital Theory 14.5 The structure of diatomic molecules (b) bond order (c) Period 2 diatomic molecules (d) p-orbitals (e) The overlap integral Lecture on-line Homonuclear diatomic molecules (PowerPoint) Homonuclear diatomic molecules (PDF) Handout for this lecture Audio-visuals on-line Shape of molecular orbitals in homonuclear diatomic molecules (PowerPoint)(From the Wilson Group,***) Shape of molecular orbitals in homonuclear diatomic molecules (PDF)(From the Wilson Group,***) Composition of orbitals in homonuclear molecules (6 MB MBQuick-Time with music) (A must from the Wilson Group,*****) The Occupation of homonuclear diatomic orbitals (PowerPoint)(From the Wilson Group,***) The Occupation of homonuclear diatomic orbitals(PDF) (From the Wilson Group,***) Molecular Orbital Theory Diatomics We used the orbitals of the one - electron hydrogen to build up wavefunctions for many- electron atoms We shall use the orbitals of the one - electron H+ molecule 2 to describe diatomic molecules The molecular orbitals are written as linear combinations of atomic orbitals The atomic orbitals are in general those centered on the atoms of our molecule Molecular Orbital Theory Diatomics H2 For H2 we have one 1sH orbital on each hydrogen : 1sA (1) = A(1); and 1sB (1) = B(1) : From these we can form two different molecular orbitals 1 1 (1) [A(1) B(1)] (1) [A(1) B(1)] 2(1 S) 2(1 S) J+K e2 1 With energies : E E1sH (1+ S) 4o R J-K e2 1 ;E E1sH (1- S) 4o R E1sH Molecular Orbital Theory Diatomics H2 E1sH The H2 molecule has two electrons. They will be in the bonding 1 orbital Molecular Orbital Theory Diatomics He 2 The ground electronic configuration of the hypothetical four-electron molecule He2 has two bonding electrons and two antibonding electrons. It has a higher energy than the separated atoms, and so is unstable. The bond order is: The He2 molecule has four 1 electrons. They will be in the b = (n n* ) 2 bonding 1 orbital and in the n occupied bonding orb anti - bonding 2 * orbital: 2 2 n* occupied anti - bonding orb 1 (2*) Molecular Orbital Theory Diatomics Second row In second row elements we have both 2s and 2p S A Bdv orbitals The 2s orbitals can form strong overlaps 2p 2p with each other We also have two p 2s 2s orbitals pointing along the A - B bond vector They can overlap with And with 2s each other These are the - orbitals, they do not change sign with rotation around A- B vector Molecular Orbital Theory Diatomics We finally have two sets of p - orbitals S A Bdv perpendicular to the A - B bond 2p 2p vector They can overlap with each other in pairs 2s 2s and These are the - orbitals, they change sign with rotation of 180 around A- B vector Molecular Orbital Theory Diatomics The - and - orbitals do not overlap S0 2p 2p S0 2s 2s S0 negative S0 S A Bdv In all cases positive positive and negative contributions cancel Molecular Orbital Theory Diatomics (a) When two orbitals are on atoms that are far apart, the wavefunctions are small where they overlap, so S is small. (b) When the atoms are closer, both orbitals have significant amplitudes where they overlap, and S may approach 1. Note that S will decrease again as the two atoms approach more closely than shown here, because the region of negative amplitude of the p orbital starts to overlap the positive overlap of the s orbital. When the centres of the atoms coincide, S = 0. Molecular Orbital Theory Diatomics Overlap is 1 when functions Data 1 coinside 1 0.8 0.6 Zero at infinite 0.4 separation 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 The overlap integral, S, between two H1s orbitals as a function of their separation R. Molecular Orbital TheoryDiatomics J-K e2 1 E o Consider two orbitals A (1- SAB ) 4o R and A on nuclei A and B 1 [A B ] of the same energy o : 2(SAB 1) They will interact to form a bonding orbital + of energy E+ o o A B And the anti- bonding orbital - of energy E- The interaction intergral K 1 will be proportional to S . AB [A B ] 2(SAB 1) K ~ SAB A Bdv J+K e2 1 E o (1+ SAB ) 4o R Molecular Orbital Theory Diatomics 2p 2p 2s 2s According to molecular orbital theory, orbitals are built from all orbitals that have the appropriate symmetry. In homonuclear diatomic molecules of Period 2, that means that two 2s and two 2pz orbitals should be used. From these four orbitals, four molecular orbitals can be built. Molecular Orbital Theory Diatomics From two 2s orbitals and two 2p orbitals we can form 4 molecular orbitals: 1 c1 2sA c1 2sB 2sA 2sB 4 c1 A 2pA c1 B 2pB 2P 2P 2 c2 2sA c2 2sB 2sA 2sB 2p 2p 3 c2 A 2pA 2P c2 B 2pB 2P 2 3 c3 2sA 2sA c3 2sB 2sB 2s 2s c3 A 2pA c3 B 2pB 2P 2P 4 c2sA 2sA c4 2sB 4 2sB 1 c4 A 2pA c4 B 2pB 2P 2P Molecular Orbital Theory Diatomics To a first approximation 2s and 2p are separated sufficiently in energy so that: We can form two orbitals made up of 2s 4 1 c1 2sA c1 2sB 2sA 2sB 2p 2p 3 2 c2 2sA 2sA c2 2sB 2sB and two orbitals 2 made up of 2p 3 c3 A 2pA c3 B 2pB 2P 2P 2s 2s 4 c2PA 2p A c4 B 2pB 4 2P 1 Molecular Orbital Theory Diatomics A representation of the composition of bonding 4 and antibonding orbitals built from the overlap of p 2p 2p orbitals. These illustrations 3 are schematic. 3 c3 A 2pA c3 B 2pB 2P 2P 4 c2PA 2p A c4 B 2pB 4 2P Or from symmetry Or from symmetry 1 1 3 [2pA 2p B ] 4 [2pA 2p B ] 2(1 S) 2(1 S) bonding anti bonding Molecular Orbital Theory Diatomics We also have two p- orbitals perpendicular to the bond- vector They will form the - orbitals : 1 1 1y [2pyA 2pyB ] 1x [2p xA 2p xB ] 2(S 1) 2(S 1) 1 2 x * 1 [2p xA 2p xB ] 2 y * [2pyA 2pyB ] 2(S 1) 2(S 1) 2y 2x 2py 2py 2px 2px 1x 1y Molecular Orbital Theory Diatomics orbitals do not change sign on rotation arounf A- B bond vector A schematic representation of the structure of bonding and antibonding molecular orbitals. orbitals change sign once on rotation around A- B bond vector Molecular Orbital Theory Diatomics For oxygen and flourine where 2p and 2s are well separated we get the orbital diagram What you must learn from this lecture 1. Understand the difference between bonding and anti- bonding orbitals in diatomic molecules 2. Understand the difference between constructive interferrence (in bonding orbitals) and destructive interferrence in (anti - bonding) orbitals 3. Understand the difference between - orbitals with complete rotational symmetry around bond vector and - orbitals that change sign on 180 rotation. 4. Be able to construct qualitatively the molecular orbitals of the homonuclear diatomic molecules as a linear combination of atomic orbitals 5. Be able to deduce the bond order for a diatomic molecule from its electronic configuration