5.2 MO diagram for water. Now put the AOs(SOs) in the order of energyEt.Nowusethekeyprinciple:onlyAOs(SO)s withthesamesymmetrywill interacttoformMOs2p, B,B,1)O2p,(B) + the B, SO(9,)ofHls2p,BA,2p.A,(ci, C2 ~coefficients)y(B) = c)2px + C2 02→Two MOs with B, symmetry!(in-phase & out-of-phase)2)02s, 2p, (A,) + the A, SOy(A,) = d,2s + dp, + d,1(d,~d; ~coefficients)→Three MOs withA,symmetry!2sA,3) 02p, gives a non-bonding MO with B, symmetry !OxygenhydrogenMOs→Atotal of sixVMOs (valencemolecular orbitals)AOsAOs/SOs
5.2 MO diagram for water • Now put the AOs(SOs) in the order of energy. • Now use the key principle: only AOs(SO)s with the same symmetry will interact to form MOs. 1) O2px (B1 ) + the B1 SO(2 ) of H1s. 3) O2py gives a non-bonding MO with B2 symmetry！ 2) O2s, 2pz (A1 ) + the A1 SO. (B1 ) = c12px + c2 2 (A1 ) = d12s + d2pz + d31 (c1 , c2 ~coefficients) (d1~d3 ~coefficients) ? MOs with B1 symmetry! ? MOs with A1 symmetry! Two Three (in-phase & out-of-phase) Oxygen AOs MOs hydrogen AOs/SOs A1 B1 2s A1 2px B1 2py B2 2pz A1 E A total of six VMOs (valence molecular orbitals)
5.2 MO diagram for waterMolecular-orbital diagram of H,OLabelling the MOs(C2v)2b:The inner Olsgives the lowest-energy, non-40bonding MO of A, IR, therefore labelled la,: The O2p, gives a non-bonding MO of B, IR,2pyB2It-1b20labelled1b22px B,A2pz A,3aIt.TheO2p,interactswiththeB,SOtoformabonding MO 1b, and an anti-bonding MO 2b,11-1b,.The02p,and 2s interact withtheA,SOtogiveWeaklythree MOs, labelled 2aj, 3a, and 4ajbonding or.Computer calculation is needed todeterminethenonbondingposition of 3a, in relation to lb,and Ib22sA,.8VEsThe lowest four VMOs are occupied.t2a1hydrogenOxygenMOsAOsAOs/SOs·Electronicconfiguration:2a 1b,3a1b
5.2 MO diagram for water Labelling the MOs Molecular-orbital diagram of H2O (C2v) • The O2px interacts with the B1 SO to form a bonding MO 1b1 and an anti-bonding MO 2b1 . • The O2py gives a non-bonding MO of B2 IR, labelled 1b2 . 1b2 1b1 2b1 • The O2pz and 2s interact with the A1 SO to give three MOs, labelled 2a1 , 3a1 and 4a1 . 2a1 3a1 4a1 • 8 VEs • Computer calculation is needed to determine the position of 3a1 in relation to 1b1 and 1b2 . Weakly bonding or nonbonding • Electronic configuration: 2a1 21b1 23a1 21b2 2 The lowest four VMOs are occupied. • The inner O1s gives the lowest-energy, nonbonding MO of A1 IR, therefore labelled 1a1 . Oxygen AOs MOs hydrogen AOs/SOs A1 B1 2s A1 2px B1 2py B2 2pz A1
Form of the MOsConstruction of the MOs for H,O.B22py1b2Wecanalsomakesomeeducatedguessesabouttheform oftheMOs.B1. The 1b, MO is solely the 02py AO1b,in-phase2pxcombination:Theinteraction of theO2p,and ,SO of B,IRnodalleads totheformation ofa bondingMO,lb,andplane2b1(SA = SB)out-of-phasean anti-bonding MO, 2br.combination.TheinteractionoftheAOsandSOwithA1in-phasesymmetryA,gives three MOs:combination212s(mainly2s+SO)>TheA,MO,2a,arisesfromin-phasecombinationoftheO2s,O2p,(minor)andthe2p23a1e, sO.>The3a,MOarises fromout-of-phasecombinationofO2s(minor)andin-phaseout-of-phasecombinationcombinationofO2p,(major)withthe,SO(SA + Sg)4a(mainly2p,+SO)
Form of the MOs • We can also make some educated guesses about the form of the MOs. Construction of the MOs for H2O. • The 1b2 MO is solely the O2py AO. • The interaction of the O 2px and 2 SO of B1 IR leads to the formation of a bonding MO, 1b1 , and an anti-bonding MO, 2b1 . • The interaction of the AOs and SO with symmetry A1 gives three MOs: The A1 MO, 2a1 , arises from in-phase combination of the O2s, O2pz (minor) and the 1 SO. 2a1 3a1 4a1 The 3a1 MO arises from out-of-phase combination of O2s (minor) and in-phase combination of O2pz (major) with the 1 SO
Form of the MOs1b.:Thispicture shows plots ofthe occupied1b2MOs of H,Obased on a computercalculation using the Hyperchemprogram.The2ai,1b,and1b,MOsdoindeedmatch3a,up with our expectations based on thequalitative arguments given above1h: The 3a, MO is weakly bonding, asevidencedbythesmallamountofelectrondensitybetweentheOandHatoms2aContourplot3Disosurface
Form of the MOs • This picture shows plots of the occupied MOs of H2O based on a computer calculation using the Hyperchem program. • The 2a1 , 1b1 and 1b2 MOs do indeed match up with our expectations based on the qualitative arguments given above. • The 3a1 MO is weakly bonding, as evidenced by the small amount of electron density between the O and H atoms. Contour plot 3D isosurface 2a1 3a1 1b1 1b2
H,O的占据分子轨道&PESI.E. (eV)12.61b214.73a11b118.5C[Cu(H,O)]2+2a1(32.2)PES-chem.libretexts.org3D等值面等值线图
等值线图 3D 等值面 2a1 1b1 3a1 1b2 E H2O的占据分子轨道 & PES I.E. (eV) (32.2) 18.5 14.7 12.6 PES-chem.libretexts.org [Cu(H2O)6 ] 2+ Q: Which MO of H2O will be used when coordinating to a metal center?