1、,Section 3.4 & 3.5 Homo- and Hetero-nuclear Diatomic Molecules Construction and Classification of Molecular Orbitals Energy Sequence of Molecular Orbitals Electron Configuration Energy Level Correlation Diagram Failure of Simple Molecular Orbital Theory,Construction and Classification of Molecular O

2、rbitals,Construction of Molecular Orbitals,1sA,1sB,H2+ At Equilibrium Bond Length( 2.5 a0 ),0.465a.u.,0.191a.u.,Recall of the Chemical Bonding in H2+,Another picture,1sA,1sB,0.065a.u.,0.591a.u.,A,B,1s,2s,1s,2s,z,Molecular Orbitals in Homo-Nuclear Diatomic Molecules,A,B,A,B,2p,2p,z,Molecular Orbitals

3、 in Homo-Nuclear Diatomic Molecules,Classification of Molecular Orbitals,Symmetry in the Atomic Orbitals,Symmetry of force field,Spherical,Coordination system,Spherical polar coordination (r,q,j),Wave function (Angular),Spherical harmonic function Ylm(q,j),Quantization of Angular Moment,l = 0 , 1, 2

4、 s p d,m = 0,m = -1,m = 1,Two good quantum numbers:,l & m,s,p,Coordination System in Diatomic Molecules,Symmetry of force field,Elliptical,Coordination system,Elliptical coordination (,),A,B,rA,rB,R,Z,P,Molecular Orbitals: Angular Wavefunctions,Examplified by the chemical bonding between two Y11 ato

5、mic orbitals along the z-axis (Shoulder to Shoulder),Picture of Chemical Bonding Using Real Atomic Orbital Functions,Bonding Orbital,Anti-Bonding Orbital,Node (j = 0) around the z-axis,m is a Good Quantum Number,Symmetry of Ylm(q,j)=Qlm (q) Fm (j) is lost except in the part of Fm (j),is no longer a

6、good quantum number.,l,However,m,remains to be a good one !,with a different notation,l,but Denoted with a Different Symbol l,A,B,rA,rB,R,Z,P,Quantization of the z-component of angular moment,s, p, d, .,Notation of Molecular Orbitals:,Symmetry in Molecular Orbitals,Complex Wave function ( z-componen

7、t):,Node number in Real functions:,l 0,0 = 0,Degeneracy of Energy Levels:,2 0,1 = 0,Real Wave function ( z-component):,s,p, d, .,s,p, d, .,Classification of MOs,s s pz pz dz2 dz2 p ( px - px) ( py - py) (dxz - dxz) (dyz - dyz) d (dxy - dxy) (dx2-y2 - dx2-y2 ),Symmetry of Inversion in MOs,Inversion a

8、bout the molecular center,“g”,“u”,Only valid for molecules with inversion symmetry,“u”,“g”,Energy Level Sequence of Molecular Orbitals Electron Configuration Energy Level Correlation Diagram,Energy Level Sequences for Long Bond Diatomic Molecules,A,B,1s,2s,2p,1s,2s,2p,1sg,1su,2sg,2su,3sg,3su,1pu,1pg

9、,O2, F2,Energy Level Sequences for Short Bond Diatomic Molecules,2s,2p,2s,2p,2sg,2su,3sg,3su,1pu,1pg,B2, C2, N2,A,B,1s,1s,1sg,1su,Experimental Evidence: Photo-electronic Spectra of N2,Explanation I,Shorter Chemical bond make it easy for the orbital overlap between 2s and 2p atomic orbitals, which sh

10、ould have been less effective overlaped in long bond molecules.,Explanation I,However, in failure of getting support from experimental observation of Equilibrium Bond lengths,Bond length (pm) B2 159.0 C2 124.25 N2 109.4 O2 120.75 F2 140.9,AO B C N O F,Explanation II,E2p-E2s(eV) 4.6 5.3 5.8 14.9 20.4

11、,The 2s and 2p orbitals of B, C, N are energetically closer compare to O and F. So the 2s and 2pz may also have large overlaps, which results in the energy level sequence changes in B, C, N diatomic molecules,1pu,1pg,Energy Level Correlation Diagram,Rules: 1. The principle of the lowest energy: The

12、energy levels are correlated in the order of increasing energy. 2. The Non-Crossing Rule Two correlating lines characterized by the same quantum number l and equal parity should never cross each other.,Energy Level Correlation Diagram,Ground State Electron Configurations,Neutral Molecules,H2 (1sg)2

13、1Sg+ 1 4.748 74.12 He2 (1sg)2 (1su)2 1Sg+ 0 Li2 KK(2sg)2 1Sg+ 1 1.140.3 267.25 Be2 KK (2sg)2 (2su)2 1Sg+ 0 B2 KK (2sg)2 (2su)2 (1pu)2 3Sg- 1 0.30.2 159.0 C2 KK (2sg)2 (2su)2 (1pu)4 1Sg+ 2 6.240.22 124.25 N2 KK (2sg)2 (2su)2 (1pu)4 (3sg)2 1Sg+ 3 9.760.00 109.4 O2 KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)2

14、 3Sg- 2 5.1160.004 120.75 F2 KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)4 1Sg+ 1 1.6040.1 140.9 Ne2 KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)4 (3su)2 1Sg+ 0,Molecule Electronic configuration Term Bond order De/eV Re/pm,Ground State Electron Configurations,Ions,O2+ KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)1 2Pg- 2.5

15、6.662 111.7 O2 KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)2 3Sg- 2 5.116 120.8 O2- KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)3 2Pg- 1.5 4.07 133 O22- KK (2sg)2 (2su)2 (3sg)2 (1pu)4 (1pg)4 1Sg+ 1 149,Molecule Electronic configuration Term Bond order De/eV Re/pm,Bond order :,NB-NA,2,NB: Number of electrons in Bond

16、ing Orbitals NA: Number of electrons in Anti-Bonding Orbitals,Properties of Homo-Nuclear Diatomic Molecules,He2 does not exist, but He2+ was detected, Dissociate energy 2.5eV (241 kJ/mol) Compared to H2+ 2.65eV(255 kJ/mol) H2 4.75eV (458 kJ/mol) Li2 Bond Order : 1 D.E. is small (1.14eV),Properties o

17、f Homo-Nuclear Diatomic Molecules,C2 Bond Order : 2 D.E. is large (6.24eV) However, only exists in flames or overheated vapors B2 Bond Order : 1 D.E. is small (0.3eV) Only exists in high temperature vapors O2 Bond Order : 2 D.E. is large (5.116eV) However, it is very active It is paramagnetic, it is

18、 a free radical,Hetero-Nuclear Diatomic Molecules,Comparison with Homo-Nuclear Diatomic Molecules,Symmetry in molecules and orbitals,Origin of Polarity,Origin of polarity in heteronuclear diatomic molecules,h,h,aA- aB,aA,aB,E+= aA-h,If aB aA,E-= aB+h,A,B,0 k 1,E+,E-,More contribution from B,More con

19、tribution from A,3.5 Heteronuclear Diatomic Molecules,When forming chemical bond, AOs from more electronegative atoms (e.g. O, F, Cl, etc.) usually act as the lower energy orbital(ja), so that they have larger percent of composition in bonding orbitals. Since most of the anti-bonding orbitals are va

20、cant, actually, summation of the electron density near these atoms will be larger than less electronegative atoms. This is the origin of the polarity,Case Study: HF,HF,F,1s,2s,2p,H,1s,2s,3s,4s,1p,1s,Ground State: Term 1S+ Re 91.7 pm De 6.11 eV m 1.82 Debye,Case Study: CO,CO,Ground State: Term 1S+ Re

21、 112.8 pm De 11.09 eV m 0.112 Debye,C,O,1s,2s,2p,1s,2s,2p,1s,2s,3s,4s,5s,6s,1p,2p,C O,d-,d +,1 1 C 1S 0.00005 0.99281 -0.11555 0.13533 0.00000 0.00000 -0.14607 0.00000 0.00000 0.03371 2 2S 0.00030 0.04861 0.22352 -0.30076 0.00000 0.00000 0.27414 0.00000 0.00000 0.07762 3 2PX 0.00000 0.00000 0.00000

22、0.00000 0.31545 0.00000 0.00000 0.55245 0.00000 0.00000 4 2PY 0.00000 0.00000 0.00000 0.00000 0.00000 0.31545 0.00000 0.00000 0.55245 0.00000 5 2PZ -0.00042 0.00411 0.21699 -0.11007 0.00000 0.00000 -0.44417 0.00000 0.00000 -0.16174 6 2 O 1S 0.99277 -0.00039 -0.20165 -0.11653 0.00000O 0.00000 0.01098

23、 0.00000 0.00000 -0.10928 7 2S 0.02595 0.00034 0.44558 0.26109 0.00000 0.00000 -0.03931 0.00000 0.00000 0.14454 8 2PX 0.00000 0.00000 0.00000 0.00000 0.56457 0.00000 0.00000 -0.40923 0.00000 0.00000 9 2PY 0.00000 0.00000 0.00000 0.00000 0.00000 0.56457 0.00000 0.00000 -0.40923 0.00000 10 2PZ -0.00130 0.00030 -0.17829 0.48994 0.00000 0.00000 0.28357 0.00000 0.00000 -0.11469,Looking for t