The Periodic Table & Bonding

The Elements (song) by Tom Lehrer on YouTube

Electrons in isolated atoms

From school chemistry and physics (GCSE, A-level, 14-19 Diploma or equivalent), we know most matter on Earth and much of the matter in the rest of the universe is made of atoms. Atoms consist of a nucleus of positive protons and neutral neutrons surrounded by negative electrons. To better explain and understand chemical bonding and reactivity (which is at the heart of chemistry), we need a more advanced description of the inner workings of atoms than school-level electrostatics alone allows.

To explain the observed behaviour of electrons in even the simplest atoms (the hydrogen atom and monatomic ions with only one electron), we need quantum mechanics
(see also Wikipedia's gentle introduction to quantum mechanics, basic concepts of quantum mechanics and the fascinating history of quantum mechanics)
- Bohr model (1913)
- de Broglie wavelength (1924)
  - Standing waves:
    - Vibrating strings
    - Vibrations of a circular drum
    - Electron waves in atoms (all matter exhibits wave–particle duality)
    - Wave equations
      - The Schrödinger equation is the wave equation that describes the wave-like behaviour electrons in atoms.
        We'll focus on the time independent version (which is simpler but widely applicable) and not worry too much about the nitty-gritty of why scientists believe in the Schrödinger equation.
        There is a gentle introduction to the Schrödinger equation on Wikipedia if you want to know a bit more without getting bogged down in the swampy depth of advanced physics.
      - Boundary conditions
      - Nodes
- Quantum numbers:
  - Principal quantum number, n
  - Azimuthal quantum number, l
    - Spectroscopic notation (s, p, d, f, etc.)
  - Magnetic quantum number, m_l
  - Spin quantum number, m_s
Wavefunctions
Electron orbitals
Atomic orbitals
Electron shells
Electron configurations
Valence electrons

The periodic table

Periodic table
- Periodic trends: "Periodic Patterns", G. Rayner-Canham, J. Chem. Ed. (2000) 77, 1053–1056
- Periodic table groups
  1. alkali metals
  2. alkaline earth metals
  3. scandium family
  4. titanium family
  5. vanadium family
  6. chromium family
  7. manganese family
  8. iron family
  9. cobalt family
  10. nickel family
  11. copper family (the coinage metals)
  12. zinc family
  13. boron group
  14. carbon group
  15. nitrogen group (the pnictogens)
  16. chalcogens (oxygen family)
  17. halogens
  18. Group 18 elements (the noble gases)

Note:
Groups 3–11 are the transition metals.
Group 12 elements are considered transition metals by some chemists and post-transition metals by others.

Atomic electron configurations and the periodic table

Periodic table (electron configurations): the relationship between electron configurations and the layout of the periodic table
- First row of transition metals (Period 4, 3d orbitals filling) show two anomalies in the gas-phase electron configurations
- Expect to find Cr is [Ar] 3d⁴ 4s² but Cr is actually [Ar] 3d⁵ 4s¹
- Expect to find Cu is [Ar] 3d⁹ 4s² but Cu is actually [Ar] 3d¹⁰ 4s¹
- At A-level, they say a half-full or full d subshell has extra stability
- Due to a quantum mechanical effect called the exchange interaction (based on the principle of exchange symmetry)
- Detailed explanation: "The Full Story of the Electron Configurations of the Transition Elements", W. H. E. Schwarz, J. Chem. Ed. (2010) 87, 444–448

Element	Protons	Electron configuration	Diagram
Cr	24	[Ar] 3d⁴ 4s² (expected) [Ar] 3d⁵ 4s¹ (observed)
Cu	29	[Ar] 3d⁹ 4s² (expected) [Ar] 3d¹⁰ 4s¹ (observed)

Effective nuclear charge and shielding

Effective nuclear charge is not equal to actual nuclear charge because core electrons shield valence electrons
Slater's rules
- named after John C. Slater
- are a quick way to estimate effective nuclear charge
Brief mention of relativistic effects in the periodic table, such as:
- Hg is a liquid
- Au and Cs are coloured: J. Chem. Ed. (1999) 76, 200
- the inert pair effect
- the lanthanide contraction (relativistic effects are 10% of the cause, the rest being poorly shielding f orbitals)

Electrons in molecules

VSEPR theory

History

Valence shell electron pair repulsion theory has its origins in a 1940 lecture by Nevil Sidgwick and Herbert Marcus Powell: N. V. Sidgwick, H. M. Powell, Proc. R. Soc. Lond. A (1940) 176 153–180. The concepts that relate the number of valence electrons around a central atom in a molecule to its geometry were refined into VSEPR theory by Gillespie and Nyholm in 1957.

Scope

VSEPR is appropriate for predicting the structures of most main group molecules and ions. It doesn't work very well for species containing transition metals because d orbitals complicate matters - they are often stereochemically inactive. There are minor modifications to VSEPR to choose between several possible structures that all meet the main criteria. They consider the relative strength of electrostatic repulsions between double bonds, single bonds and lone pairs.

Notation

VSEPR only predicts a small number of different structures, but can be applied to a huge number of different molecules. It is therefore sometimes convenient to generalise and categorise the predictions. A common notation is as follows:

A = the central atom
X = a ligand atom
E = an unshared electron pair (or lone pair)

You can then categorise a molecule like ammonia, NH₃, as AX₃E₁. Ammonia has A = nitrogen and X = hydrogen.

This AXE notation doesn't distinguish between molecules like ammonia with only single bonds and ones like carbon dioxide or acetylene with double or triple bonds. This is because VSEPR predicts the same geometry for a molecule, whether or not an A–X bond is single or multiple. Nonetheless, it is important to know whether you have multiple bonds in your molecule, because this affects the number of valence electron pairs you count. A double bond comprises two valence electron pairs, but only one of those pairs is counted for the sake of determining the structure.

Instructions

Decide which atom is the central atom. If unsure, assume it's the most electropositive one
List the contributions of each atom to the valence shell of the central atom
1. The central atom (A) contributes all its valence electrons, e.g. phosphorus (group 15) contributes 5 valence electrons
2. Outer atoms (ligands, X) contribute one electron each if they are singly bonded to the central atom A
3. Outer atoms that are doubly bonded to the central atom A contribute two electrons each
4. Outer atoms that are triply bonded to the central atom A contribute three electrons each
5. A single negative charge on the overall molecule increases the valence electron count around A by one
6. A single positive charge on the overall molecule decreases the valence electron count around A by one
7. Multiply charges alter the valence electron count proportionally (e.g. a double negative charge on the molecule increases the valence electron count around A by two)
Add the valence electrons you have counted and write down the sum total
Halve the valence electrons total to get the number of valence electron pairs
Reduce the valence electron pair total by one for each double bond present, and by two for each triple bond present
The remaining number determines the underlying electron pair geometry (sometimes termed the electron arrangement)
1. 2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral, etc.
Lone pairs (E) occupy positions in the underlying geometry but are not mentioned explicitly in the final answer
1. e.g. if the underlying geometry is tetrahedral but there is one lone pair (AX₃E), the final answer is trigonal pyramidal
If more than one structure that adopts the predicted geometry is possible, they all need to be drawn and compared with the extra criteria below

Extra criteria

Strength of repulsion: lone pair-lone pair > lone pair-bonding pair > bonding pair-bonding pair, i.e. lp-lp > lp-bp > bp-bp
Two or more lone pairs are placed as far apart as possible (greatest E-A-E angle possible) except for trigonal bipyramidal where they should occupy equatorial positions as far as possible
Double bonds follow the same rules: they stay as far apart as possible, and repel each other more than they repel singly-bonded pairs