Properties of Atomic Orbitals and Intro to Molecular Orbital Theory

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1 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, m l = - l,,, l (i.e p x, p y, p z ) Spin quantum number, m s = +1/2 or -1/2 Pauli Exclusion Principle No two electrons can have the same set of quantum numbers (each orbital can hold 2 e - ) Hund s Rule For degenerate orbitals the lowest energy configuration maximizes the electron spin (no pairing of electrons if avoidable) 1

2 Radial Nodes For a given atomic orbital there are n- l -1 radial nodes. p and d-orbitals orbitals: : Nodal planes For a given atomic orbital there are l nodal planes. 2

3 Relative Sizes of Atomic Orbitals Atom Radius s Radius p C 64 pm 65 pm Si 115 pm 95 pm Ge 120 pm 96 pm Sn 140 pm 114 pm Pb 148 pm 121 pm Values correspond to radial expectation values based on Hartree-Fock calculations, taken from webelements.com/.com/webelements Relative Sizes of Atomic Orbitals Atom Radius s Radius d Ti 162 pm 53 pm Zr 179 pm 84 pm Hf 178 pm 88 pm Cu 137 pm 33 pm Ag 153 pm 55 pm Au 156 pm 64 pm Values correspond to radial expectation values based on Hartree-Fock calculations, taken from webelements.com/.com/webelements 3

4 Relative Sizes of Atomic Orbitals Atom Radius s Radius d Nd 222 pm 35 pm Yb 199 pm 25 pm U 226 pm 53 pm No 215 pm 40 pm Values correspond to radial expectation values based on Hartree-Fock calculations, taken from webelements.com/.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 (1 st ionization energy increases). The electronegativity increases. Relative Orbital Sizes 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]. Lanthanide Contraction 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 2 nd row transition metal (i.e. Nb) ) to a 3 rd row transition metal (i.e. Ta) 4

5 Special Properties associated with filling a subshell for the first time Filling the 2p orbitals (B Ne) Short internuclear separation allows for effective p overlap, allows for strong π bonding to occur s and p orbitals have similar spatial extent which favors bonding geometries well suited for both orbitals (hybridization) Filling the 3d orbitals (Sc Zn) Overlap of 3d orbitals with ligand orbitals is not large, gives rise to high spin configurations and Curie-Weiss magnetism Filling the 4f orbitals (La Lu) The spatial extent of the 4f orbitals leads to negligible overlap with other orbitals.. Thus the chemistry of the lanthanides is fairly constant, and the magnetism of these elements in compounds is similar to that of a free ion. 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? The heavier elements, particularly the 6th period and beyond (Cs, Ba,, La, ). Are all orbitals affected equally? No. The s orbitals are most strongly affected, while the p-orbitals are affected to a lesser extent. Relativistic effects have little direct influence on the d and f orbitals. 5

6 Element Group 14 Orbital Energies E p (ev) non-relat. E s (ev) non-relat. E p (ev) Relativistic E s (ev) Relativistic C Si Ge Sn Pb 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 Reaction Potential (V) CO CO SiO SiO GeO GeO Ge Ge 0.00 SnO SnO Sn Sn 0.15 Pb Pb 1.69 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 π-bonding.] Structure & Properties of the Group 14 Elements Element Structure E g (ev) C Diamond 5.5 Si Diamond 1.1 Ge Diamond 0.7 α-sn Diamond 0.1 β-sn Tetragonal Metal Pb FCC Metal As you go proceed down the group the tendency for the s-orbitals to become involved in bonding diminishes. This destabilizes tetrahedral coordination and semiconducting/insulating behavior. 6

7 Relativistic Effects: Bonding Implications Contraction of the s-orbitals decreases their spatial overlap with other atoms decreases their contribution to bonding Energetic stabilization of the s-orbitals Stabilizes the +2 oxidation state for the heavier elements Combined effects 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 +, Pb 2+, Bi 3+, Sn 2+, Sb 3+, Te 4+. The tendency for sp 3 hybridization is reduced, which impacts coordination preferences Oxidation state = +4: tetrahedral octahedral Oxidation state = 0: tetrahedral close packed Orbital Overlap: Molecular Orbital (MO) Theory Antibonding Orbital, σ * Bonding Orbital, σ 7

8 Overlap of p-orbitals MO Diagram for 2nd Row Diatomic Molecule 8

9 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 The spatial overlap in a bond depends upon symmetry It decreases as the number of nodal planes increases, σ > π > δ π and particularly δ bonds are more sensitive to changes in bond angle 9

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