Chapter 5 Structures of Polyatomic Molecules ()IntroductionMolecular Orbital Theory vs.Valence Bond TheoryVB theory: focusing on the (localized) bonds formedbetweenvalence electrons/atomicorbitalsof neighboringatom(s),easiertovisualize/imagineVB modelofamolecule, i.e.,“of chemical intuition!".e.g., CH4Mo theory: more powerful and more sophisticated thanVB theory in many aspects, e.g., description of electrondelocalizationin Benzene,but sometimes not so easytovisualize/imagineaMOmodele.g.,for CH4!
Chapter 5 Structures of Polyatomic Molecules (I) Molecular Orbital Theory vs. Valence Bond Theory • VB theory: focusing on the (localized) bonds formed between valence electrons/atomic orbitals of neighboring atom(s), easier to visualize/imagine VB model of a molecule, i.e., “of chemical intuition!”. e.g., CH4 • MO theory: more powerful and more sophisticated than VB theory in many aspects, e.g., description of electron delocalization in Benzene, but sometimes not so easy to visualize/imagine a MO model e.g., for CH4 ! Introduction
Comparison of MO and VB theoriesVBTheoryMolecular orbital theory. The electrons pair to localize in a. MOs are formed by the overlap ofbond. ybond ~AO,AO2AOs. yMO ~ Zc,AO;Electrons are delocalized"within·Demands hybridization of AOMOs consisting of AOs·Basis of Lewis structures,Electrons fill up the MOsresonance,and hybridizationaccording to the aufbau principle· Good theory for predictingGive accuratebond dissociationmolecular structureenergies,IP, EA,and spectral data: Sometimes not so easy to·Easierto visualize/imagine VBvisualize/imagine a MO modelmodel for a molecule, i.e., “ofchemicalintuition!"foramolecule!
Comparison of MO and VB theories VB Theory Molecular orbital theory • Demands hybridization of AO • MOs are formed by the overlap of AOs. MO ciAOi • The electrons pair to localize in a bond. bond AO1 AO2 • Good theory for predicting molecular structure. • Basis of Lewis structures, resonance, and hybridization. • Easier to visualize/imagine VB model for a molecule, i.e., “of chemical intuition!”. • Electrons fill up the MOs according to the aufbau principle. • Electrons are “delocalized” within MOs consisting of AOs. • Sometimes not so easy to visualize/imagine a MO model for a molecule! • Give accurate bond dissociation energies, IP, EA, and spectral data
Electron Delocalizationin Benzene三个节面节有C节面VB description:have to introduce resonance of无节面localizedVB structuresMO description:inherently describingelectron delocalization!
Electron Delocalization in Benzene MO description： inherently describing electron delocalization! VB description: have to introduce resonance of localized VB structures
Molecular Orbital (MO)Theory Treatmentof Polyatomic Molecules LCAO-MO & group Theory (in part B of Chapter 3)Mean-field ApprInitial guessBasis set:& LCAO-MO(SALC)yCMO = Zc;ΦAOs ()SCF-HF[8, ,=Zc,Canonical molecularorbitals of CH(valence electrons only!)CAOsH ls AOsCMOW(A))±= ca(Φ1 + Φ2 + Φ3 + Φ4 )/2 ± C,C2syV(T2)x±= c(Φ1 - Φ2 - Φ + Φ4 )/2 ± caC2pxV(T2)± = c(Φ1 - Φ2 + Φ3 - Φ4 )/2 ± cCaC2pydV(T2)± = cc(Φ1 + Φ2 -Φ3 -Φ4 )/2 ± CaC2pAlldelocalized!
Molecular Orbital (MO) Theory Treatment of Polyatomic Molecules • LCAO-MO & group Theory (in part B of Chapter 3) Basis set: AOs {i } Mean-field Appr. & LCAO-MO(SALC) Initial guess CMO = cii SCF-HF {j , j = ci (j)i } Canonical molecular orbitals of CH4 (valence electrons only!) z x y a b c d All delocalized! (A1 ) = ca (1 + 2 + 3 + 4 )/2 cbC2s (T2 )x = cc (1 – 2 – 3 + 4 )/2 cdC2px (T2 )y = cc (1 – 2 + 3 – 4 )/2 cdC2py (T2 )z = cc (1 + 2 – 3 – 4 )/2 cdC2pz CMO H 1s AOs C AOs
How to get the CMOs of a molecule?CH, TaGroup theory treatment- SALCs:2s(A),(T2)2px,2py,2pz4H:1sΦn2Z2ETa8C,3C,65.60dpn111A.11-AETT-111V22010301-1(R..R..R)X30111(x,y. z)3Φh3０2I(4H) 41 0h4(4H)= A +TPsALc=Plg=Zx(R)ROZg(R)x(R)x(R)=R0=(Φ+Φ2+Φ3+Φ4)/2 ~As± = ca(Φ,+Φ2+Φ3+Φ4 )/2 ± c,C2sb= (Φ1-Φ2-Φ3+Φ4)/2 ~ x-like Tx± = cc(Φ1-Φ2-Φ3+Φ4 )/2 ± caC2px0。= (Φ1-Φ2+Φ3-Φ4)/2 ~ y-like T2V± = cc(Φ1-Φ2+Φ3-Φ4 )/2 ± caC2p)a= (Φi+Φ2-Φ3-Φ4)/2 ~ z-like T2± = c(Φ+Φ2-Φ3-Φ4 )/2 ± caC2p
How to get the CMOs of a molecule? • Group theory treatment– SALCs: h1 h2 h4 h3 z x y 1 2 3 4 C: 2s (A1 ), (T2 ) 2px , 2py , 2pz CH4 , Td 4 H: 1s (4H1s) 4 1 0 0 2 1 a g( R) ( R) ( R ) h R i i 4H A1 T2 ( ) i R j j i j j SALC R R h l P ˆ ( ) ˆ s = ca (1+2+3+4 )/2 cbC2s x = cc (1–2–3+4 )/2 cdC2px y = cc (1–2+3–4 )/2 cdC2py z = cc (1+2–3–4 )/2 cdC2pz a= (1+2+3+4 )/2 ~A1 b= (1–2–3+4 )/2 ~ x-like T2 c= (1–2+3–4 )/2 ~ y-like T2 d= (1+2–3–4 )/2 ~ z-like T2