Structural Biochemistry/Chemical Bonding/ Electronic Structure Theories

Overview

Valence bond theory – this is used to describe hybrid orbitals and electron pairs. It is an extension of the electron dot and bybrid orbital representations. Crystal field theory – this is used to describe the split in metal d-orbitals, which approximates the energy levels from the ultraviolet and visible spectra, but it does not describe bonding Ligand field theory – this is an expansion of the crystal field theory that can be used to describe bonding between the metal ion and the ligands by focusing on the orbital interactions. Angular overlap method – this is used to estimate the orbital energies in a molecular orbital calculation.

Valence Bond Theory

Valence bond theory was originally proposed by Pauling as a way of hybridization between atomic orbitals. This was one of the major theory used to describing the bonding of coordination compounds, but it's rarely used today. The valence bond theory is filled by the Aufbau principle, which states that electrons are most stable when they filled each orbital with one electron before further filling it. This leads to the Madelung rule, which states that orbitals filled by n+l are filled first before orbitals filled by n+l of higher energy orbitals.

Period 4			Period 5			Period 6			Period 7
Element	Z	Electron Configuration	Element	Z	Electron Configuration	Element	Z	Electron Configuration	Element	Z	Electron Configuration
						Lanthanum	57	[Xe] 6s² 5d¹	Actinium	89	[Rn] 7s² 6d¹
						Cerium	58	[Xe] 6s² 4f¹ 5d¹	Thorium	90	[Rn] 7s² 6d²
						Praseodymium	59	[Xe] 6s² 4f³	Protactinium	91	[Rn] 7s² 5f² 6d¹
						Neodymium	60	[Xe] 6s² 4f⁴	Uranium	92	[Rn] 7s² 5f³ 6d¹
						Promethium	61	[Xe] 6s² 4f⁵	Neptunium	93	[Rn] 7s² 5f⁴ 6d¹
						Samarium	62	[Xe] 6s² 4f⁶	Plutonium	94	[Rn] 7s² 5f⁶
						Europium	63	[Xe] 6s² 4f⁷	Americium	95	[Rn] 7s² 5f⁷
						Gadolinium	64	[Xe] 6s² 4f⁷ 5d¹	Curium	96	[Rn] 7s² 5f⁷ 6d¹
						Terbium	65	[Xe] 6s² 4f⁹	Berkelium	97	[Rn] 7s² 5f⁹

Scandium	21	[Ar] 4s² 3d¹	Yttrium	39	[Kr] 5s² 4d¹	Lutetium	71	[Xe] 6s² 4f¹⁴ 5d¹	Lawrencium	103	[Rn] 7s² 5f¹⁴ 7p¹
Titanium	22	[Ar] 4s² 3d²	Zirconium	40	[Kr] 5s² 4d²	Hafnium	72	[Xe] 6s² 4f¹⁴ 5d²	Rutherfordium	104	[Rn] 7s² 5f¹⁴ 6d²
Vanadium	23	[Ar] 4s² 3d³	Niobium	41	[Kr] 5s¹ 4d⁴	Tantalum	73	[Xe] 6s² 4f¹⁴ 5d³
Chromium	24	[Ar] 4s¹ 3d⁵	Molybdenum	42	[Kr] 5s¹ 4d⁵	Tungsten	74	[Xe] 6s² 4f¹⁴ 5d⁴
Manganese	25	[Ar] 4s² 3d⁵	Technetium	43	[Kr] 5s² 4d⁵	Rhenium	75	[Xe] 6s² 4f¹⁴ 5d⁵
Iron	26	[Ar] 4s² 3d⁶	Ruthenium	44	[Kr] 5s¹ 4d⁷	Osmium	76	[Xe] 6s² 4f¹⁴ 5d⁶
Cobalt	27	[Ar] 4s² 3d⁷	Rhodium	45	[Kr] 5s¹ 4d⁸	Iridium	77	[Xe] 6s² 4f¹⁴ 5d⁷
Nickel	28	[Ar] 4s² 3d⁸ or [Ar] 4s¹ 3d⁹ (disputed)^[1]	Palladium	46	[Kr] 4d¹⁰	Platinum	78	[Xe] 6s¹ 4f¹⁴ 5d⁹
Copper	29	[Ar] 4s¹ 3d¹⁰	Silver	47	[Kr] 5s¹ 4d¹⁰	Gold	79	[Xe] 6s¹ 4f¹⁴ 5d¹⁰
Zinc	30	[Ar] 4s² 3d¹⁰	Cadmium	48	[Kr] 5s² 4d¹⁰	Mercury	80	[Xe] 6s² 4f¹⁴ 5d¹⁰

Crystal Field Theory

Crystal field theory was originally developed to describe the structure of metal ions in crystals. The energies of the d orbitals are split by electrostatic field. This was developed in the 1930s, which ignored the covalent bonding since ionic crystals didn't describe it. When the ligands come close to the metal, a big destabilization occurs. The dx^2-y^2 and dz^2 have eg symmetry whereas the dxy, dxz, dyz have t2g symmetry, which implies that they're triply degenerate. eg accounts for 40% of the energy difference while t2g accounts for 60% of the energy. While eg's energy rises, t2g's energy falls to accounts for the difference in rising so that their energies cancel out. This energy difference is called crystal field stabilization energy. This also leads to the idea of high spin and low spin. High spin occurs when Δo > the pairing energy with a weak ligand field and low spin occurs when Δo < pairing energy with a strong ligand field.

Factors that influence Δo: 1) charge : the greater the charge on the central ion, the greater the pull from the ion, which results in an increase in oxidation state.

2) identity of the metal : the greater #d orbitals will have a greater Δo. For example, the 5d orbital can interact more efficiently than 3d, which results in a greater Δo.

3) identity of the ligand : stronger Lewis bases have greater Δo

Ligand Field Theory

Ligand field theory is used to describe ligand-metal orbital interactions. The metal's d-orbitals match the irreducible representations Eg and T2g. The metal's s and p orbitals have the symmetry A1g and T1u. This leads to a total of 3 bonding orbitals.

Coordination Numbers

Factors involved in determining the overall shape of a coordination compound

1) the number of bonds – since most bonds are exothermic, the creation of bonds will lead to a greater stabilization of the structure

2) VSEPR considerations

3) Occupancy of d-orbitals – the number of d electrons affect the geometry of the coordination compound

4) Steric interference – occurs when large ligands surround the central metal

5) Crystal packing effects – the regular shape is distorted when packed into a crystal. This would hinder the understanding of the original structure since it'd be unclear as if the distortion came from the crystallization process or naturally.

Coordination number 4 – this is usually obtained from square planer and tetrahedral structures with four ligands. Some examples are: CrO4 2-, Ni(CO)4, [Cu{py)4]+. Coordination number 5 – this is usually obtained from trigonal bipyramid, square pyramid, and pentagonal planes. Some examples are: Fe(CO)5 and PF5. Coordination number 6 – this is the most common coordination number since it is usually obtained from the structure of an octahedral. Some examples are: [Co(en)3]3+ and [Co(NO2)6]3-. Coordination number 7 – this is usually obtained from pentagonal bipyramid, capped trigonal prism, and capped octahedron. Some examples of molecules in this structure are: [NiF7]2- and [NbF7]2-. Coordination number 8 – this is usually only obtained in simple ionic lattice structures like CsCl.

References

Miessler, Gary. Inorganic Chemistry. 4th Edition.

↑ Scerri, Eric R. (2007). The periodic table: its story and its significance. Oxford University Press. pp. 239–240. ISBN 0-19-530573-6.

[1] Scerri, Eric R. (2007). The periodic table: its story and its significance. Oxford University Press. pp. 239–240. ISBN 0-19-530573-6.

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