# 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 4 | Period 4 | Period 5 | Period 5 | Period 5 | Period 6 | Period 6 | Period 6 | Period 7 | Period 7 | Period 7 |
| Element | Z | Electron Configuration | Element | Z | Electron Configuration | Element | Z | Electron Configuration | Element | Z | Electron Configuration |
| | | | | | | Lanthanum | 57 | [Xe] 6s$^2$ 5d$^1$ | Actinium | 89 | [Rn] 7s$^2$ 6d$^1$ |
| | | | | | | Cerium | 58 | [Xe] 6s$^2$ 4f$^1$ 5d$^1$ | Thorium | 90 | [Rn] 7s$^2$ 6d$^2$ |
| | | | | | | Praseodymium | 59 | [Xe] 6s$^2$ 4f$^3$ | Protactinium | 91 | [Rn] 7s$^2$ 5f$^2$ 6d$^1$ |
| | | | | | | Neodymium | 60 | [Xe] 6s$^2$ 4f$^4$ | Uranium | 92 | [Rn] 7s$^2$ 5f$^3$ 6d$^1$ |
| | | | | | | Promethium | 61 | [Xe] 6s$^2$ 4f$^5$ | Neptunium | 93 | [Rn] 7s$^2$ 5f$^4$ 6d$^1$ |
| | | | | | | Samarium | 62 | [Xe] 6s$^2$ 4f$^6$ | Plutonium | 94 | [Rn] 7s$^2$ 5f$^6$ |
| | | | | | | Europium | 63 | [Xe] 6s$^2$ 4f$^7$ | Americium | 95 | [Rn] 7s$^2$ 5f$^7$ |
| | | | | | | Gadolinium | 64 | [Xe] 6s$^2$ 4f$^7$ 5d$^1$ | Curium | 96 | [Rn] 7s$^2$ 5f$^7$ 6d$^1$ |
| | | | | | | Terbium | 65 | [Xe] 6s$^2$ 4f$^9$ | Berkelium | 97 | [Rn] 7s$^2$ 5f$^9$ |
| Scandium | 21 | [Ar] 4s$^2$ 3d$^1$ | Yttrium | 39 | [Kr] 5s$^2$ 4d$^1$ | Lutetium | 71 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^1$ | Lawrencium | 103 | [Rn] 7s$^2$ 5f$^{14}$ 7p$^1$ |
| Titanium | 22 | [Ar] 4s$^2$ 3d$^2$ | Zirconium | 40 | [Kr] 5s$^2$ 4d$^2$ | Hafnium | 72 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^2$ | Rutherfordium | 104 | [Rn] 7s$^2$ 5f$^{14}$ 6d$^2$ |
| Vanadium | 23 | [Ar] 4s$^2$ 3d$^3$ | Niobium | 41 | [Kr] 5s$^1$ 4d$^4$ | Tantalum | 73 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^3$ | | | |
| Chromium | 24 | [Ar] 4s$^1$ 3d$^5$ | Molybdenum | 42 | [Kr] 5s$^1$ 4d$^5$ | Tungsten | 74 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^4$ | | | |
| Manganese | 25 | [Ar] 4s$^2$ 3d$^5$ | Technetium | 43 | [Kr] 5s$^2$ 4d$^5$ | Rhenium | 75 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^5$ | | | |
| Iron | 26 | [Ar] 4s$^2$ 3d$^6$ | Ruthenium | 44 | [Kr] 5s$^1$ 4d$^7$ | Osmium | 76 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^6$ | | | |
| Cobalt | 27 | [Ar] 4s$^2$ 3d$^7$ | Rhodium | 45 | [Kr] 5s$^1$ 4d$^8$ | Iridium | 77 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^7$ | | | |
| Nickel | 28 | [Ar] 4s$^2$ 3d$^8$ or [Ar] 4s$^1$ 3d$^9$ (disputed) | Palladium | 46 | [Kr] 4d$^{10}$ | Platinum | 78 | [Xe] 6s$^1$ 4f$^{14}$ 5d$^9$ | | | |
| Copper | 29 | [Ar] 4s$^1$ 3d$^{10}$ | Silver | 47 | [Kr] 5s$^1$ 4d$^{10}$ | Gold | 79 | [Xe] 6s$^1$ 4f$^{14}$ 5d$^{10}$ | | | |
| Zinc | 30 | [Ar] 4s$^2$ 3d$^{10}$ | Cadmium | 48 | [Kr] 5s$^2$ 4d$^{10}$ | Mercury | 80 | [Xe] 6s$^2$ 4f$^{14}$ 5d$^{10}$ | | | |

## 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.