# 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 QM-only 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 solvent-solute molecular interactions.

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 $$N_B$$
• $$\delta\big[r-r_{A_iB_j}\big]=$$ 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)
$\frac{1}{V}g_{AB}(r)=\frac{1}{N_A\cdot N_B}\bigg\langle\sum\limits_{i=1}^{N_A}\sum\limits_{j=1}^{N_B}\delta\big[r-r_{A_iB_j}\big]\bigg\rangle$

In the plot below, the distances ($$r$$) of the shells of hydration are