Molecular Orbital Theory

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Virgil Black
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1 Molecular Orbital Theory 1. MO theory suggests that atomic orbitals of different atoms combine to create MOLECULAR ORBITALS 2. Electrons in these MOLECULAR ORBITALS belong to the molecule as whole 3. This contrasts to VB theory which suggests that electrons are shared by simple overlap atomic orbitals or hybridized atomic orbitals Molecular orbital can be constructed from linear combination of atomic orbitals MO = LCAO

2 In terms of approximate solutions to the Scrödinger equation Molecular Orbitals are linear combinations of atomic orbitals (LCAO) Y= caψa + cbψb (for diatomic molecules) As the distance between atoms decreases Atomic orbitals overlap Bonding takes place if: the orbital symmetry must be such that regions of the same sign overlap the energy of the orbitals must be similar the interatomic distance must be short enough but not too short

3 Bonding and Antibonding Orbitals When two atomic orbitals are added together 1. A set of lower energy BONDING orbitals are created Bonding orbitals have most of the electron (negative) density between the 2 positive nuclei 2. A set of higher energy ANTI-BONDING orbitals are created Antibonding orbitals have most of the electron density on the opposite side from the region where the bond must be formed Nonbonding Orbital: the energy of which is essentially that of an atomic orbital

7 No interaction different symmetry

11 magnetism The orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields. When an external magnetic field is applied to a material, these current loops will tend to align in such a way as to oppose the applied field: induced magnetic fields tend to oppose the change which created them. Materials in which this effect is the only magnetic response are called diamagnetic. All materials are inherently diamagnetic, but if the atoms have some net magnetic moment as in paramagnetic materials, or if there is long-range ordering of atomic magnetic moments as in ferromagnetic materials, these stronger effects are always dominant. Diamagnetism is the residual magnetic behavior when materials are neither paramagnetic nor ferromagnetic.

14 Covalent radius N > O> F, bond distance N2 < O2< F2, because of the increasing population of antibonding electrons Chapter 5 p129

15 The covalent radius of the atoms decrease as the number of valence electrons increase because the increasing nuclear charge pulls the electrons closer to the nucleus

16 Photoelectron Spectroscopy Photoelectron spectroscopy utilizes photo-ionization and energy-dispersive analysis of the emitted photoelectrons to study the composition and electronic state of the surface region of a sample. Traditionally, when the technique has been used for surface studies it has been subdivided according to the source of exciting radiation into : X-ray Photoelectron Spectroscopy (XPS) Ultraviolet Photoelectron Spectroscopy (UPS) - using soft ( ev) x-ray excitation to examine core-levels. - using vacuum UV (10-45 ev) radiation from discharge lamps to examine valence levels.

17 In this technique, UV light or X-rays dislodge electrons from molecules: O2 + hv (photons) O2+ + ethe kinetic energy of the expelled electrons can be measured: the difference between the energy of the incident photons and this kinetic energy equal the ionization energy (bonding energy) of the electrons: Ionization energy = hv photons kinetic energy of the expelled electrons UV removes outer electrons, usually from gases; X-rays are more energetic and remove inner electrons as well, from any physical state

18 O2 N2 σg (2p) πu (2p) σ*u (2s) π u (2p) σg (2p) σ*u (2s) πu (2p) Very involved in bonding (vibrational fine structure) (Energy required to remove electron, lower energy for higher orbitals)

19 Note subscripts g and u symmetric/antisymmetric upon i

20 Place labels g or u in this diagram σ u π g πu σg

21 A correlation diagram shows the calculated effect of moving two atoms together, from a large interatomic distance on the right, with no interatomic interaction, to zero interatomic distance on the right, where the two nuclei become, in effect, a single nucleus. The simplest example has two H atoms on the right and a He atom on the left.

22 Symmetry is used to connect the molecular orbitals with the atomic orbital of the united atom. 1 u* 2pz on the left 1 u 2px or 2py 1 g* 3d (dxz or dyz) Another consequence of this phenomenon is called the noncrossing rule, which states that orbitals of the same symmetry interact so that their energy never cross

23 Heteronuclear diatomic molecules Heteronuclear diatomic molecules follow the same general bonding pattern as the homonuclear molecules, but a greater nuclear charge on one of the atoms lowers its atomic energy levels and shifts the resulting MO levels. The potential energies are negative because they represent attraction between the valences and the nuclei

24 The atomic orbitals of homonuclear diatomic molecules have identical energies and both atoms contributes equally to a given MO. Therefore, in the equation for the MO, the coefficients for the two atomic orbitals are identical. In heteronuclear diatomic molecules, the coefficients are different. The atomic orbital closer in energy to an MO contributes more to the MO and its coefficient is larger in the wave functions.

25 Using C2V point group, the s and pz orbital have A1 symmetry, and form MO with σsymmetry, while px and py orbitals have B1 and B2 symmetry and for MO. M-C-O: The HOMO of CO is 3σ, with a higher electron density and a larger lobe on carbon. The LUMo are the 2 * and concentrated on carbon

26 LiF Ionic compounds can be considered the limiting form of polarity in heteronuclear molecules.

27 Molecular Orbitals for Larger molecules: 1. Determine the point group for the molecule. Substitute D2h for D h and C2v for C v 2. Assign x, y and z coordinate to the atoms. Highest order rotation axis of the molecule is chosen as the z axis of the central atom 3. Find the characters of the representation for the combination of 2s and 2p orbitals: change position 0, same position and same sign 1, same position but reversed sign Reduce the representation from step 3 to irreducible representations. This is equivalent to finding the symmetry of the group orbitals or the symmetry-adapted linear combinations (SALCs) 5. Find the atomic orbitals of the central atom with the same symmetries 6. Combine the atomic orbitals of the central atom and those of the group orbitals with the same symmetry and similar energy to form molecular orbitals.

28 Group orbitals for F----F of F-H-F-

30 Atomic orbitals and group orbitals of the same symmetry can combine to form molecular orbitals, just as atomic orbitals of the same symmetry can combine to form group orbitals. The energy match of the 1s orbital of H atom (-13.16ev) is much better with the 2pz of F (-18.7ev) than with 2s of F (-40.2 ev)

32 Chapter 5 p148

33 Symmetry-adapted linear combinations --- SALCs Projection operator --- The fundamental, universally applicable tool for constructing SALCs

37 NH3

43 Group theory approach Sp3 or sd3

The symmetry properties & relative energies of atomic orbitals determine how they react to form molecular orbitals. These molecular orbitals are then

1 The symmetry properties & relative energies of atomic orbitals determine how they react to form molecular orbitals. These molecular orbitals are then filled with the available electrons according to