BUILDING MOLECULES OUT OF MOLECULAR ORBITALS

Transcription

1 Leture #34 page 1 BUILDING MLECULES UT F MLECULAR RBITALS HETERNUCLEAR DIATMICS If the atoms are similar, e.g. in moleules N and C, onsiderations are similar Same Ms and energ ordering an be used C isoeletroni with N - has similar triple bond onfiguration N has one additional eletron in a π p x, antibonding orbital Bond order.5 Unpaired eletron - paramagneti L= 1, M =± 1, S = 1, M =± 1 L Π "doublet pi" state S Generall Ms for heteronulear diatomis must be formed from As of unequal energies E A B E A A E HAA E HAB SE = 0 H SE H E AB Note H AA H To a first approximation, neglet overlap between the orbitals (S = 0). Then E = ( ) 1 4 ( ) AA ± AA AB AA H H H H H H H 1 H AB measures interation between As entered on different atoms Small when energies are ver different In the limit H << ( H H ), E = H or H AB AA AA

2 Leture #34 page Don't need to onsider Ms onstruted from As of ver different energies 1 AB AA AB AA AB AA If H << ( H H ), then 1 4H ( H H ) 1 H ( H H ) H E H E H AB AB 1 AA HAA H HAA H H As before, desribe moleular wavefuntion through VB or M approah M approah far more ommonl used Construt 1-eletron Ms out of the As ψ = A A 1 1A A 1B B Bonding M If A energ is lower ( H < H ), then > A AA 1A 1B ψ = A A A A B B Antibonding M If A energ is lower ( H < H ), then < A AA 1A 1B Simplest M treatment: put eletrons in lower M ( 1, ) = 1() 1 1( ) = 1 A () 1 1 A ( 1) 1 A ( ) 1 A ( ) () 1 ( ) () 1 ( ) () 1 ( ) () 1 ( ) ψ ψ ψ el A A B B A A B B = 1AAA AA 1A1B AA AB AB AA 1BAB AB "ioni" ovalent "ioni" Configuration interation: inlude ontribution from higher M ( 1, ) = ( 1) ( ) ( 1) ( ) CI ψ 1ψ1 ψ1 ψ ψ el C C Man more Ms ould be inluded in CI ψ el Instead of using As to onstrut the Ms, ould use other funtions e.g. Gaussians whih might approximate the As. Variational optimization of the Gaussian or other funtions, and the oeffiients C i in ψ CI el

3 Leture #34 page 3 e.g. diatomi moleule AB, with B more eletronegative than A Atom A Moleule AB σ p Atom B p A π p σ p p B π p σ s s A σ s s B σ 1s 1s A σ 1s 1s B e.g. C triple bond Eletron onfiguration KK ( sσ ) ( sσ *) ( pπ) 4 ( pσ )

4 Leture #34 page 4 Note no parit designations no enter of smmetr for inversion ften Ms have ontributions from various As (not just one A on eah atom) In this ase Ms an't be labeled b speifi As Ms an't be labeled as stritl "bonding" or "antibonding" But σ, π smmetries still hold, so σ and π Ms are just numbered in order of inreasing energ 4 Eletron onfiguration ( 1σ ) ( σ) ( 3σ) ( 4σ) ( 1π) ( 5σ ) Hartree-Fok self-onsistent field (SCF) alulations of Ms based on LCAs As are desribed b H-like orbitals, or one or a sum of gaussians n1 ξr l N r e Y θ, φ or Slater-tpe orbitals (STs) of form ( ) e.g. C p z orbital involved in σ bonding desribed as sum of 3 STs labeled pσ, pσ', pσ'' Initial level of M desription: eah 1-eletron M is a linear ombination of As, one from eah atom Sine As are written as sums of Slater-tpe orbitals, the Ms are also nl m Higher level of M desription: Eah 1-eletron M is written as a linear ombination of more than As, more than one from eah atom Table below: shows results of SCF LCA M alulation for C From W.M. Huo, J. Chem. Phs. 43, 64 (1965) Eah M is a sum of man orbitals all the oeffiients > 0.1 are given This defines the moleular wavefuntion, whih puts eletrons into eah M (Eah M energ in a.u. is given above the M designation.)

5 Leture #34 page au au -1.5 au au au Carbon ξ 1σ σ 3σ 4σ 5σ 1s s s s pσ pσ pσ 5.8 xgen 1s s s s pσ pσ pσ au Carbon ξ 1π pπ pπ 3.34 xgen pπ pπ pπ 5.78 Results: 1sσ eletrons mostl on oxgen Non-bonding orbital 1sσ = 1s 1s 1 1σ C C >> 1σ 1σ C σ eletrons mostl on arbon Non-bonding orbital 1s s σ σ σ = C C 1 >> σ σ C

6 Leture #34 page 6 3σ eletrons mostl on oxgen Lone pair (nonbonding) orbital 3 s s 3σ 3σ σ = C C >> 3σ 3σ C 4σ eletrons on both C and 4 σ 4 σ ( 4 σ 4 σ 4 σ 4σ = CssC s s C3s3sC CppC pp) Bonding orbital ( eletrons) 4σ 4σ C 1π eletrons on both C and Bonding orbital (4 eletrons) 1π 1π 1 C C π = p p 1π 1π C 5σ eletrons mostl on arbon Non-bonding orbital 5σ 5σ 5 C C σ = p p << 5σ 5σ C Similar treatment for LiH or other simple hdrides From B.J. Ransil, Rev. Mod. Phs. 3, 45 (1960) au au Lithium ξ 1σ σ 1s s pσ Hdrogen 1s PLYATMIC MLECULES Usuall similar to diatomis beause most bonding eletrons are loalized around atoms That's wh e.g. C-H bond energies and bond lengths and vibrational frequenies are similar even in ver different moleules e.g. H S triatomi water-like

7 Leture #34 page 7 H (1 s) S 6 4 (1s s p 3s 3 p ) n S atom, put eletrons in 3p z orbital, one eletron on eah of 3p x and 3p S atom an make bonds with half-filled p orbitals p orbitals are at 90 so the H-S-H bond angle should be 90 Experimental angle: 9 e.g. PH 3 ammonia-like H (1 s) P 6 3 (1s s p 3s 3 p ) P atom an make 3 bonds with half-filled p orbitals H-P-H bond angles should be 90 Experimental angle 93 S P 1-eletron Ms and moleular wavefuntions For H S, label the two H nulei H x, H Form Ms from S 3p x orbital and H x 1s orbital, S 3p orbital and H 1s orbital

8 Leture #34 page 8 1-eletron Ms: φ = a1s b3 p φ = a1s b3 p a b = 1 (normalization) x Hx xs H S Moleular eletroni onfiguration: 1s s p 3s 3p φ φ 6 S S zs S zs x Note that this shows whih orbitals are oupied, but it is not the wavefuntion itself. The wavefuntion is the properl antismmetrized ombination. For H it would be: ψ (1,,...,10) = () () () () () () () () () () ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) φβ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) φα( 10) φ β( 10) 1s α 1 1s β 1 s α 1 s β 1 p α 1 p β 1 φ α 1 φ β 1 φ α 1 φ β 1 x x x x α α 3 3 1s α 4 4 α 5 5 α 6 6 α 7 7 α 8 8 α 9 9 1s α 10 1s β 10 s α 10 s β 10 p α 10 p β 10 φ α 10 φ β 10 x x x x PH 3 is similar H (1 s) P 6 3 (1s s p 3s 3 p ) Form Ms from P 3p x orbital and H x 1s orbital, P 3p orbital and H 1s orbital, P 3p z orbital and H z 1s orbital 1-eletron Ms: φ = a1s b3 p φ = a1s b3 p φ = a1s b3 p a b = 1 (normalization) x Hx xp H P z Hz zp 6 Moleular eletroni onfiguration: 1s s p 3s φ φφ P P P P x z