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Unformatted text preview: Properties of Atomic Orbitals and Intro to Molecular Orbital Theory
Chemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #15 Atomic Orbitals Four quantum numbers define the properties of each atomic orbital Principle quantum number, n = 1,2,3,... Azimuthal quantum number, l = 0(s), 1(p), 2(d), 3(f), n-1 Magnetic quantum number, ml = - l, ..., l (i.e px, py, pz) , .e Spin quantum number, ms = +1/2 or -1/2 Pauli Exclusion Principle Hund's Rule No two electrons can have the same set of quantum numbers (each orbital can hold 2 e-) For degenerate orbitals the lowest energy configuration maximizes the electron spin (no pairing of electrons if avoidable) 1 Radial Nodes For a given atomic orbital there are n- l -1 radial nodes. p and d-orbitals: Nodal planes For a given atomic orbital there are l nodal planes. 2 Relative Sizes of Atomic Orbitals Atom C Si Ge Sn Pb Radius s 64 pm 115 pm 120 pm 140 pm 148 pm Radius p 65 pm 95 pm 96 pm 114 pm 121 pm Values correspond to radial expectation values based on Hartree-Fock calculations, Hartreetaken from http://www.webelements.com/webelements http://www.webelements.com/webelements Relative Sizes of Atomic Orbitals Atom Ti Zr Hf Cu Ag Au Radius s 162 pm 179 pm 178 pm 137 pm 153 pm 156 pm Radius d 53 pm 84 pm 88 pm 33 pm 55 pm 64 pm Values correspond to radial expectation values based on Hartree-Fock calculations, Hartreetaken from http://www.webelements.com/webelements http://www.webelements.com/webelements 3 Relative Sizes of Atomic Orbitals Atom Nd Yb U No Radius s 222 pm 199 pm 226 pm 215 pm Radius d 35 pm 25 pm 53 pm 40 pm Values correspond to radial expectation values based on Hartree-Fock calculations, Hartreetaken from http://www.webelements.com/webelements http://www.webelements.com/webelements Periodic Trends As you move either up a group (i.e. Pb C) or left to right across a period (i.e. K Kr). The effective nuclear charge increases. The orbitals become more contracted (smaller). The valence electrons become more tightly bound to the nucleus (1st ionization energy increases). The electronegativity increases. The spatial extent (size) of the valence shell orbitals decrease from (n)s (largest) (n)p (n-1)d (n-2)f [on a given atom]. Due to the ineffective shielding of the 4f electrons there is only a very small increase in the spatial extent of the orbitals as you go from a 2nd row transition metal (i.e. Nb) to a 3rd row transition metal (i.e. Ta) Nb) Relative Orbital Sizes Lanthanide Contraction 4 Special Properties associated with filling a subshell for the first time Filling the 2p orbitals (B Ne) Ne) Short internuclear separation allows for effective p overlap, allows for strong bonding to occur s and p orbitals have similar spatial extent which favors bonding geometries well suited for both orbitals (hybridization) Overlap of 3d orbitals with ligand orbitals is not large, gives rise to high spin configurations and Curie-Weiss magnetism The spatial extent of the 4f orbitals leads to negligible overlap with other orbitals. Thus the chemistry of the orbitals. lanthanides is fairly constant, and the magnetism of these elements in compounds is similar to that of a free ion. Filling the 3d orbitals (Sc Zn) Filling the 4f orbitals (La Lu) Relativistic Effects What are relativistic effects? For very heavy nuclei the electron velocities approach the speed of light, which causes them to get heavier according to the Theory of Relativity. The increased mass leads to a contraction of the orbital, which in turn lowers it's energy. What elements are most affected by relativistic effects? Are all orbitals affected equally? The heavier elements, particularly the 6th period and beyond (Cs, Ba, La, ...). Ba, No. The s orbitals are most strongly affected, while the p-orbitals are affected to a lesser extent. Relativistic p-orbitals effects have little direct influence on the d and f orbitals. orbitals. 5 Group 14 Orbital Energies
Element C Si Ge Sn Pb Ep (eV) non-Relat. -5.42 -4.17 -4.08 -3.93 -3.86 Es (eV) Ep (eV) Es (eV) non-Relat. Relativistic Relativistic -13.63 -5.42 -13.64 -10.83 -11.61 -10.05 -9.72 -4.16 -4.05 -3.87 -3.70 -10.87 -11.92 -10.78 -12.17 For Pb Relativistic Effects lower the energy of the 6s orbitals by 2.35 eV, while the 6p are only stabilized by 0.16 eV! Relativistic Effects - Implications
Standard Reduction Potentials
CO CO2 `SiO' SiO2 GeO GeO2 Ge2+ Ge4+ SnO SnO2 Sn2+ Sn4+ Pb2+ Pb4+ Structure & Properties of the Group 14 Elements
C Si Ge -Sn -Sn Pb Potential (V)
-0.11 -0.97 -0.37 0.00 -0.09 0.15 1.69 Structure
Diamond Diamond Diamond Diamond Tetragonal FCC 5.5 1.1 0.7 0.1 Metal Metal Eg(eV) eV) As you go from Ge Sn Pb the +2 oxidation state becomes more stable, as it requires more energy to remove electrons from this orbital. [CO is stabilized by -bonding.] As you go proceed down the group the tendency for the s-orbitals s-orbitals to become involved in bonding diminishes. This destabilizes tetrahedral coordination and semiconducting/insulating semiconducting/insulating behavior. 6 Relativistic Effects: Bonding Implications Contraction of the s-orbitals s-orbitals decreases their spatial overlap with other atoms decreases their contribution to bonding Stabilizes the +2 oxidation state for the heavier elements Inert pair effect (distorted coordination environment for ions which retain their valence s-electrons, due to formation of an sp-hybrid). This effect is pronounced for the following ions Tl+, Pb2+, Bi3+, Sn2+, Sb3+, Te4+. The tendency for "sp3 hybridization" is reduced, which impacts coordination preferences Oxidation state = +4: tetrahedral octahedral Oxidation state = 0: tetrahedral close packed Energetic stabilization of the s-orbitals s-orbitals Combined effects Orbital Overlap: Molecular Orbital (MO) Theory
Antibonding Orbital, * Bonding Orbital, 7 Overlap of p-orbitals MO Diagram for 2nd Row Diatomic Molecule 8 Orbital Interactions: Key Points The overlap of two atomic orbitals is dependent upon: symmetry of the orbitals distance between the orbitals spatial extent of the orbitals the energy difference between orbitals Increasing the overlap (spatial and energetic) leads to the following: Stabilization of the bonding MO Destabilization of the antibonding MO The antibonding MO is destabilized to a greater extent than the bonding MO is stabilized It decreases as the number of nodal planes increases, > > and particularly bonds are more sensitive to changes in bond angle The spatial overlap in a bond depends upon symmetry 9 ...
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