Explicit Solvation¶
Abstract
Rules for explicit solvation¶
1. It takes a LOT of solvent molecules to look like a solution¶
 too few and it looks like a cluster, which is not a solution
 This makes it incredibly expensive
 We have tools to make this more simple  PBC, Ewald sums, QM/MM, split basis?
Benefits:¶
 The solvent IS actually there, so we can performa a solvent density analysis (molecules per unit\(^2\))
 Density differences mean that you can look at the specific interactions with regions of the molecule (favourable/unfavourable solvation conditions)
E.g. Solvation of tRNA¶
In this example, we can see that while there is typically only favourable solvation along the \(\ce{PO4}\) spine in RNA (2AA:IsoC and G:C), in this case (G:U), we have hydration in the typically hydrophobic minor groove.
This extra solvation also correlates with enzymatic methylation of the base pair in this particular species.
2. Equilibrium properties (e.g. free energies) require averaging over phase space (MM/MD)¶
 There are far too many minima if we do this though optimisation, making a QMonly solvation process near impossible to do rigorously

Solvation really should be done through MC or MD, until ergodic behaviour is identified.
 To make this more rigorous, different starting trajectories should be chosen and the system should converge to the same average geometry
 This also allows for averages of flexible molecules with dynamic structures (particularly biopolymers)
 You could also choose a small portion of MD steps to then run QM calculations on, reducing the amount of possible configurations
 You can obtain structural details that are associated specifically with the solvation shell. Specific solventsolute molecular interactions.
Radial distribution function¶
Tells us the distribution of distances between atoms \(A\) and \(B\). (The probability of finding an atom at distance \(r\))
Where:
 \(V=\) Volume that all the atoms take up
 \(g_{AB}=\) Radial distribution of atoms \(A\) to \(B\)
 \(r=\) The distance between the atoms
 \(\frac{1}{N_A\cdot N_B}=\) A normalisation value for the numbers of atoms \(A\) (\(N_A\)) and \(B\) (\(N_B\))
 \(\sum\limits_{i=1}^{N_A}\sum\limits_{j=1}^{N_B}=\) Summing over all the occurrences of atoms \(A\), from \(i=1\) to \(N_A\) and \(B\), from \(j=1\) to \(N_B\)
 \(\delta\big[rr_{A_iB_j}\big]=\) Kronecker delta function  Checking whether the distance between the atoms is equal to the value of \(r\) we’ve specified (spits out a True/False statement)
\[
\frac{1}{V}g_{AB}(r)=\frac{1}{N_A\cdot N_B}\bigg\langle\sum\limits_{i=1}^{N_A}\sum\limits_{j=1}^{N_B}\delta\big[rr_{A_iB_j}\big]\bigg\rangle
\]
In the plot below, the distances (\(r\)) of the shells of hydration are