Lecture 14 Chemistry 362 M. Darensbourg 2017 Spring term Molecular orbitals for diatomicsSlide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Orbitals of same symmetry, either on same atom or on adjacent atoms can mix. Thus sigma MO’s from s + s overlap or from pz + pz overlap can mix and affect each other if sufficiently close in energy. How do we know if they are?Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Electron Configurations: Assign electrons to energy levels but put in horizontal scheme:Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Lecture 14 Chemistry 362 M. Darensbourg 2017 Spring term Molecular orbitals for diatomicsSimplest example - H2: two H atoms HA and HBOnly two a.o.'s (1sA, 1sB) to form linear combinations.General rule: n a.o.'s n m.o.'sSo we can only construct 2 m.o.'s for H2 - and these are:ψb = 1sA + 1sB and ψa = 1sA - 1sBi.e. the sum (ψb) and the difference (ψa) of the constituent a.o.'s.Consider the electron distribution in each of these:Molecular Orbital Theory of the Chemical BondConsider in each case the INTERNUCLEAR REGIONProbability of finding electron there is: ψb > 1sA, 1sB > ψaElectron in this region attracted to BOTH nuclei, therefore most favourable position. Hence, electron in ψb will be at lower energy than in non-interacting a.o.'s, and electron in ψa will be at higher energy still.Thus an electron in ψb will hold the nuclei together, one in ψa will push them apart.ψb is a BONDING m.o., ψa is an ANTI-BONDING m.o.HA + HB 1s atomic orbitals either reinforce or cancel each otherThus we can draw ENERGY LEVEL DIAGRAM for m.o.'s of H2 :1sA1sBψbψaHA H2 HBBy aufbau & Pauli principles - the 2 electrons go into ψb - with paired spins.A AA22s2sσ2sσ*2sRemember: 1s orbitals effectively non-bonding,M.O.Energy Level Diagram for A2 (A = Li, Be)Li2Only two valence electrons, i.e. σs2σ*s0.Bond order = 1. DiamagneticLi2 exists in gas phase over metallic lithium."Be2"σs2σ*s2Bond order = 0 - no net bonding energy, so molecule does not exist.Beryllium in gas phase is monatomic.Use Aufbau, Pauli, Hund - just as in filling atomic orbitals+++––––pz/pzσ2pz. .pz + pz overlap everywhere positive→ BONDING M.O.+ +++–––σ*2pz..–pz – pz overlap everywhere negative→ ANTI-BONDING M.O.p orbitals: pz + pz overlap => sigma orbitals, bonding and anti-bonding in same area as sigma derived from s-orbital overlap.++++––––π*2px or π*2py. .+++–––px/pxorpy/pyπ2px or π2py. .p orbitals: px + px overlap => orbitals with one unit of angular momentum; 1 angular Node; or π orbitals, bonding and anti-bonding; py + py overlap identical giving π MOOrbitals of same symmetry, either on same atom or on adjacent atoms can mix. Thus sigma MO’s from s + s overlap or from pz + pz overlap can mix and affect each other if sufficiently close in energy. How do we know if they are? A complexity: Nodes, (not Toads): Angular => Sigma and Pi and Delta Angular Defined by change of sign when rotated around The bond axis. If no change: Angular Momentum of electrons in that orbital is zero: a Sigma, σ MO If one change in sign, a Pi, π MO If 2 changes in sign, a delta, δ MOMixing of s and p orbitals No mixing of s and p orbitalsConsequence of no mixing on energy level diagram: Homonuclear Diatomics No mixing of sigma orbitals Derived from 2s and 2pz Core (closed shell) electrons; little effect.Copyright © 2014 Pearson Education, Inc. Homonuclear Diatomics No mixing vs. mixing of sigma orbitals Derived from 2s and 2pz No mixing (O2 and F2) Mixing (B2, C2, N2)A AA22p2s2p2sσ2sσ*2sσ2pzπ2px,π2pyπ*2px,π*2pyσ*2pzM.O.Energy Level Diagram for A2 (A = O )O2Electronic configuration: σs2σ*s2σpz2πpx2πpy2π*px1π*py1Note Hund's rule again! Bond order = (8 - 4)/2 = 2(double bond) and PARAMAGNETIC.V.B. theory could not explain paramagnetism.Electron Configurations: Assign electrons to energy levels but put in horizontal scheme: [KK] < σ2s < σ*2s<s2pz<(π2px, π2py) < (π*2px, π*2py) < σ*2pz [KK] < σ2s < σ*2s< (π2px, π2py) <σ2pz < (π*2px, π*2py) < σ*2pz For no mixing: O2, F2, Ne2 Assign electrons and determine bond order, magnetism, and Term Symbols! B.O. = (# bonding electrons - # anti-bonding electrons)/2 For mixing: B2, C2, N2 But what about heteronuclear diatomics: CN-, NO, CO?HETERONUCLEAR DIATOMIC MOLECULESSimplest would be HHe. Differs from H2 in two ways:(1) A.O. energies for H, He different. He - greater nuclear charge, electrons more tightly bound.(2) Now three electrons to feed into m.o.'s.Energy level diagram is now:1sH1sHeψbψaaverage energyof a.o.'sH HHe HeFor heteronuclear diatomics, m.o.'s formed symmetrically above and below AVERAGE energy of constituent a.o.'sΨb = c1(1sH) + c2 (1sHe) where c2 > c1 Ψa= c1(1sH) - c2 (1sHe) where c1 > c2For HHe, bond order = (2 - 1)/2 = 1/2 i.e. v. wk. "1/2" bond - not formed under normal conditions - v. unstable.Unpaired electron, PARAMAGNETIC.Note for "He2" - extra electron in antibonding m.o. - therefore bond order = 0. Molecule does not exist - no force to hold atoms together.He is monatomic gas.More Dramatic for HF: Must use H1s + F 2pzs/pz gives bonding and anti-bonding pair.+++++++––––s/pzσspzσ*spz. ...s/px or py and pz/px or py all non-bonding (positive and negative overlaps cancel. No overlap at all for px/py.++–s/pxors/pynon-bonding++–pz/pxorpz/pynon-bonding–Before moving on to show the energy level diagram for A2 molecules - we need to be clear about the labels for m.o.’sMO Energy Level Diagrams for HF and CO from Shriver, 2.21Carbon Monoxide VSIE O2s = 32.3 eV O2p = 15.8 eV C2s = 19.4 eV C2pz = 10.6 eVCarbon Monoxide Consequence: CO binds to metals, such as iron, Through Carbon rather than Oxygen. Can produce dative bond by donating Electron density from the 3σ to empty orbital On metal, and will accept electron density From the metal via π-backbonding.Molecular Orbitals in Polyatomic Molecules In the vast majority of cases, bonds can be described as LOCALISED between pairs of nuclei - therefore can use VB approach. At this stage we only