CB VII. Molecular Orbital (MO) Theory. General. Basic Principles. Basic Ideas. further improvement on Lewis, VSEPR & VB theory;

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1 chem101/3, wi010 po 14 1 CB VII Molecular Orbital (MO) Theory chem101/3, wi010 po 14 General further improvement on Lewis, VSEPR & VB theory; resulting in better info on: bond energy bond order magnetic properties of molecules Ref 11: Prob FUP: 11: 3, 4 E of C: 11: 3 37, 51 Adv Rdg 5: 1-5 chem101/3, wi010 po 14 3 Wave mechanical theory Basic Principles chem101/3, wi010 po 14 4 problem very complex Basic Ideas is applied to bonding in a molecule as a whole i.e., includes interaction of all nuclei & e s no exact solutions exist Schroedinger equ n is solved for allowed wave states, or wave functions, Ψ, which, in turn, provide a description molecular orbitals (MO s) as a result we get a set of discrete MO s various approximations are applied, esp. LCAO method ( linear combination of atomic orbitals ) start off w/ AO s of bound atoms describing energy & location of e s important to realize that MO s cover the molecule as a whole (e s are delocalized ), rather than being strictly located on or between individual atoms generally, combine AO s that are close in: proximity, orientation, energy to form MO s

2 chem101/3, wi010 po 14 5 basic ideas... chem101/3, wi010 po 14 6 basic ideas... use wavemechanical concepts, esp. aspects of wave interference (constructive and destructive) to construct MO s apply principles you know from AO Theory to fill a set MO s w/ e s as follows: generally, # of MO s = # of originating AO s Aufbau in ground state lowest energy MO s are occupied half of MO s are lower in energy than the originating AO s = bonding MO s half of MO s are higher in energy... = antibonding MO s Pauli max. of e s per MO; if are present, they have opposite spins Hund if MO s are degenerate, fill MO s singly first (w/ same spin) before doubling up chem101/3, wi010 po 14 7 Application to H Molecule chem101/3, wi010 po 14 8 H molecule... E AH - H B Energy Diagram MO(1), σ 1s equivalent expression : 1s A & 1s B AO s combine 1s B MO(1), σ 1s 1s A in - phase to form bonding MO s & out - of - phase to form antibonding MO s MO(1) = 1 s A + 1 s B MO() = 1 s A 1 s B e s available, only the bonding MO, σ 1s, will be filled, H stable!!

3 chem101/3, wi010 po 14 9 chem101/3, wi010 po Orbital Diagrams for H Pet. Fig.11.0 MO Theory for H chem101/3, wi010 po Bond Order by MO Theory chem101/3, wi010 po 14 1 Other Row 1 Species General: B.O. = bonding e s antibonding e s see Pet. Fig evaluate for B.O. and stability: species B.O. Existence for H : B.O. = 0 = 1 ( single bond) H + He known 0.5 expected in this case, agrees w/ Lewis theory He 0 unknown, not expected

4 chem101/3, wi010 po Pet. Fig MO diagrams for diatomic row 1 species chem101/3, wi010 po MO Theory for Row Molecules (diatomic, homonuclear) Generally, can ignore core AO s ( i.e., 1s AO s) (because weak interaction; also, bonding & antibonding MO s cancel) i.e., work w/ valence e s significant combinations in row orbitals: s AO s σ s MO p AO s σ p MO π p MO chem101/3, wi010 po Combination of p AO s chem101/3, wi010 po Pet. Fig MO s from p AO s

5 chem101/3, wi010 po MO Energy Diagrams σ s lower than σ p, π p (b/c originating s AO s are lower than p AO) chem101/3, wi010 po General MO Energy Diagram Expected valid for O, F, (Ne ) expect that σ p is lower than π p (σ p has more overlap than π p ) expected MO diagram (HT Fig. 14.1) HT Fig σ pz π π px py p z p x p y π px π py but exceptions are common modified MO diagram (HT Fig. 14.) σ pz σ s σ s s chem101/3, wi010 po General MO Energy Diagram Modified chem101/3, wi010 po 14 0 Practice Complete MO Energy Diagrams for valid for Li... N HT Fig.14. Li, B, N, O fill MO diagrams w/ e s determine B.O. assess magnetism σ pz π px π py p z p x p y For completeness sake, you may want to do Be, C, F, Ne also σ pz π px π py σ s s σ s

6 chem101/3, wi010 po 14 1 chem101/3, wi010 po 14 MO Energy Diagram for Li MO Energy Diagram for B σ pz σ pz π px π py π px π py p z p x p y p z p x p y σ pz σ pz π px π py π px π py σ s s σ s B.O. = 0 =1 all e s paired diamagnetic σ s B.O. = 4 =1 e s unpaired paramagnetic σ s s chem101/3, wi010 po 14 3 chem101/3, wi010 po 14 4 MO Energy Diagram for N MO Energy Diagram for O σ pz σ pz π px π py p z p x p y π px π py σ pz π px π py p z p x p y π px π py σ pz σ s σ s s s B.O. = 8 = 3 all e s paired diamagnetic σ s B.O. = 8 4 = e s unpaired paramagnetic σ s

7 chem101/3, wi010 po 14 5 Summary chem101/3, wi010 po 14 6 Pet.Fig Summary of MO theory for row diatomics Pet. Fig provides a summary of MO s for all row diatomic homonuclear molecules. Derive, don t memorize chem101/3, wi010 po 14 7 Comments Use the same diagrams to analyze (stability, B.O., magnetism ) charged homonuclear species, such as N +, O, etc. similar analysis applies to row 3 diatomic molecules Na. Ar Combine 3s and 3p AO s to get σ 3s, σ 3p, π 3p MO s (again bonding & antibonding etc.) chem101/3, wi010 po 14 8 Heteronuclear Diatomics (e.g., CO, NO) when molecule contains O apply expected MO energy diagram, but in a distorted form (originating AO s of more e/n atom are lower in energy, causing this distortion) see CO as an example, HT Fig.14.3

8 chem101/3, wi010 po 14 9 HT Fig MO Energy Diagram for CO chem101/3, wi010 po Overall Comment on Bonding C O MO theory generally gives best results, but often very complicated in many cases, simpler theories are satisfactory p practicing chemists use a mixture of all theories, whatever works best s B.O. = 6 0 =3 all e s paired diamagnetic e.g., in organic chem.: for σ bonds: use VB theory, including hybridization of AO s for π bonds: use MO theory, including resonance ideas from Lewis theory