# Model Chemistry¶

• Additional theories can be implemented:
• Møller-Plesset perturbation theory
• Configuration Interaction
• Coupled Cluster
• Everything is a trade off between accuracy (large basis set, higher level of theory) and computational cost/time

• The higher the theory and basis set, the more realistic the results
• It’s worth noting that DFT

Electron Configuration * We define electron configuration in comp chem much like we do in physical chem * We use symmetry and number the order however, to describe the orbitals * E.g. for water:

$1(A_1 )^2 2(A_1 )^2 1(B_2 )^2 3(A_1 )^2 1(B_1 )^2 4(A_1 )^0 2(B_2 )^0$
• We use the terms HOMO and LUMO to describe these and can often describe the surrounding orbitals as HOMO-1 and LUMO+1

#### Koopman’s Theorem¶

• States that the ionisation energy of an atom or molecule is equal to the energy from the orbital of which the electron is ejected
$I_i=−\epsilon_t$
• In HF, the energies are more exactly calculated, however in DFT, we can only say that the energy is approximately equal to the ionisation energy (meta Koopman’s theory)
$I_i≈−\epsilon_t$

#### Coordinates¶

• The general rule of thumb is that the fewer coordinates there are, the less variables there are for the computer to have to optimise
• The connectivity is determined by the atom’s behaviour, so we don’t need to specify it explicitly
• We can depict geometry in two primary ways:

#### Cartesian Coordinates¶

• Use the cartesian system of X, Y and Z values for each atom
• E.g.
C       x     y     z
C       x     y     z
H       x     y     z
H       x     y     z
...


#### Z-Matrix¶

• Uses a system of internal coordinates of bond lengths, angles and dihedrals to define the geometry
• E.g.
C1
C2     R1     1
H3     R2     1     𝜃1     2
H4     R3     1     𝜃2     2     D1     6
H5     R4     1     𝜃3     2     D2     6
H6     R5     2     𝜃4     1     D3     3
H7     R6     2     𝜃5     1     D4     3
H8     R7     2     𝜃6     1     D5     3

R1=
R2=
...
𝜃1=
𝜃2=
...
D1=
D2=
...