Simple Molecular Orbital Theory
Simple Molecular Orbital TheoryChapter 5Wednesday, October 7, 2015
Using Symmetry: Molecular OrbitalsOne approach to understanding the electronic structure of moleculesis called Molecular Orbital Theory. MO theory assumes that the valence electrons of the atoms withina molecule become the valence electrons of the entire molecule. Molecular orbitals are constructed by taking linear combinationsof the valence orbitals of atoms within the molecule. For example,consider H2:1s 1s Symmetry will allow us to treat more complex molecules byhelping us to determine which AOs combine to make MOs
LCAO MO Theory
MO Math for Diatomic Molecules 1 2A ------ BEach MO may be written as an LCAO: c1 1 c2 2Since the probability density is given by the square of the wavefunction:probability of finding theelectron close to atom Aditto atom Boverlap term, importantbetween the atoms
MO Math for Diatomic Molecules1The individual AOs are normalized:1S100% probabilityof finding electronsomewhere foreach free atom
MO Math for Homonuclear Diatomic MoleculesFor two identical AOs on identical atoms, the electrons are equally shared, so:221 12 212 c c In other words:c cc1 c2So we have two MOs from the two AOs: c ,1 ( 1 2 ) c ,1 ( 1 2 )After normalization (setting2 d 11 ( 1 2 )1/2[2(1 S )]where S is the overlap integral:and2 d 1 ):1( 1 2 ) 1/2[2(1 S )]0 S 1
LCAO MO Energy Diagram for H2H2 molecule: two 1s atomic orbitals combine to make onebonding and one antibonding molecular orbital.Energy E2 E1Ha H-HHb E2 E1, so the antibonding orbital is always more anti-bonding than the bondingorbital is bonding
MOs for H2 1( 12 22 2 1 2 ) 2(1 S )2 in phase combinationconstructive interferencelarge e- density in the internuclear region (bonding)an electron in this MO lowers the molecule’s energy 1( 12 22 2 1 2 ) 2(1 S )2 out of phase combinationdestructive interferencesmall e- density in the internuclear region (antibonding)nodal plane between atomsan electron in this MO raises the molecule’s energy
MO NotationSchematic representations of the MOs: shading indicates sign of AOsize of AO reflects the magnitude of its coefficient in the MO
Basic Rule #1 of MO TheoryRule #1: The interaction of n AOs leads to the formation of nMOs. If n 2, one MO is bonding and one antibonding. Thebonding orbital is more stable than the lower-energy AO. Theantibonding orbital is less stable than the higher-energy AO. Thebonding orbital is stabilized less than the antibonding orbital isdestabilized. 1 2 E E
H2 vs. He2dihydrogenbond order: 1stable moleculediheliumbond order: 0unstable molecule1BO # bonding e # anti-bonding e 2
Basic Rule #2 of MO TheoryRule #2: If the AOs are degenerate, their interaction isproportional to their overlap integral, S. 1 2 large overlap 1 2 small overlapThe greater the degree of overlap, the stronger the bonding/antibonding.
Basic Rule #3 of MO TheoryRule #3: Orbitals must have the same symmetry (sameirreducible representation) to have non-zero overlap. S 0 if orbitals have different irreducible representations. If S 0, then bonding and antibonding MOs result.If the overlap integral between two orbitals centered on differentatoms is zero, then there is no interaction between them. If an orbital has S 0 with all other orbitals in themolecule, then it is a 100% non-bonding orbital.
Overlap and Bond Type
Overlap and SymmetryThe extent of overlap depends on the internuclear separation, thenature of the orbitals involved (s, p, or d), and their relative orientation.S1s/1ssigmaS“parallel” 2p/2ppi“perpendicular” 2p/2p have zero overlap by symmetryS 0S 0
Overlap and Symmetry1s/2p overlap depends on the angle θ:overlap goes as cosθ:θ 90 θ 0 SS 01s/2p
Overlap and Symmetryd orbitalssigmapideltazero overlap bysymmetry
Basic Rule #4 of MO TheoryRule #4: If the AOs are non-degenerate, their interaction isproportional to S2/ΔE, where ΔE is the energy separationbetween the AOs. In this case the bonding orbital is mostlylocalized on the atom with the deeper lying AO, usually themore electronegative atom. The antibonding orbital is mostlylocalized on the atom with the higher AO. c1 1 c2 2c c2122 1 2 Orbitals with ΔE 12-14 eV have essentially zero interaction.
Basic Rule #4 of MO Theorystronginteractionbonding andantibondingweakinteractionalmostnonbonding
Using Symmetry: Molecular Orbitals One approach to understanding the electronic structure of molecules is called Molecular Orbital Theory. MO theory assumes that the valence electrons of the atoms within a mole
Topic 2: Molecular Orbital Theory Reading: Ch. 1 of your sophomore organic chemistry textbook I. Fleming Molecular Orbitals and Organic Chemical Reactions, Ch. 2 & 3 Bradley, J. D.; Gerrans, G. C. “Frontier molecular orbitals. A link between kinetics and bonding theory.” J .
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’s point group atom X’s p x and p y atomic orbitals symmetry label given to identify the p x and p y orbitals of atom X (central atom) symmetry label given to identify the p z orbital of atom X (central atom) atom X’s p z atomic orbitals atom X’s s–orbital s-orbital symmetry label C 2 1 –1
to the understanding and application of approximate molecular orbital calculations to chemical problems. The remainder of this chapter is a cursory and informal discussion of certain quantum-mechanical principles and an introduction to the orbital description of electronic structure. In Chap. 2, the methods of molecular orbital theory are
referred to as "FMO-MD," is an ab initio MD method (Komeiji et al., 2003) based on FMO, a highly parallelizable ab initio molecular orbital (MO) method (Kitaura et al., 1999). Like any ab initio MD method, FMO-MD can simulate molecular phenomena involving electronic structure changes such as polarization, electron transfer, and reaction.
Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20. 2 Review of the Previous Lecture 1. Discussed crystal field theory, an electrostatic theory that treats ligands as point charges. Ligands create an electric field
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