Continuum Solvent Non-Electrostatics¶

Abstract

Rules for implicit solvation¶

3. Electrostatics are only part of the free energy of solvation¶

Consequence:¶

You also need to somehow account for cavitation, dispersion, solvent structural changes etc.

Tools:¶

You can always make electrostatics better at the same time

How to account for non-electrostatic terms¶

• (worst) You could ignore them completely, though this would only really be valid for systems where electrostatic effects will dominate
• Attempt to compute them separately e.g. one property, one calculation
• (best) Assume proportionality to the solvent-accessible surface area and parameterise microscopic surface tensions
• Continuum solvation is inherently semiempirical, so parameterisation should not be feared.

First solvation-shell contributions¶

One way to approximate the Solvent Accessible Surface Area (SASA) is to “roll a ball” over the surface of the molecule and the volume it takes up defines the

Where:

• $$\sum\limits_k^{atoms}=$$ Adding up the influence of each atom $$k$$
• $$A_k=$$ Surface area exposed of the atom $$k$$
• $$\sigma_k=$$ A characteristic surface tension, based on atomic number
• $$\sum\limits_{k'}^{atoms}\sigma_{kk'}(R)=$$ A modifier for the interaction of functional groups
• $$\sum\limits_{k'}^{atoms}=$$ Adding up the influence of each other atom ($$k'$$)
• $$\sigma_{kk'}(R)=$$ looks at the distance between the two atoms ($$k$$ and $$k'$$) and modifies the value of $$\sigma$$
$G_{CDS}=\sum\limits_k^{atoms}A_k\bigg(\sigma_k+\sum\limits_{k'}^{atoms}\sigma_{kk'}(R)\bigg)$

The value of $$\sigma_{kk'}$$ varies over distance, which will result in a gradual switching behaviour. In the figure below, the short distances might represent a ketone (the switch is on) and the longer distance might represent an ether (the switch is off)

Microscopic surface tensions¶

This simple equation shows the non-electrostatic solvation energy $$G_{CDS}$$ is equal to the sum of the exposed surface area of each atom $$A_k$$ times some proportionality constant $$\sigma_k$$.

$G_{CDS}=\sum\limits_kA_k\sigma_k$

E.g. 1. SMx universal solvation model¶

These are universal, because the surface tension ($$\sigma_k$$) will change based on the solvent

• Surface tensions are treated as functions, rather than parameters
• The value arrives from running over a series of descriptors ($$\sum_j^{descr}$$) and taking a parameter associated with that descriptor ($$\hat{\sigma}_{Z_i}$$) and multiplying it with the descriptor ($$\xi_j$$\$)
$\sigma_i=\sum\limits_j^{descr}\hat{\sigma}_{Z_i}\xi_j$

The descriptors could be (incomplete list):

• $$n=$$ solvent index of refraction (is a direct measure of polarisability of the solvent)
• $$\gamma=$$ solvent macroscopic surface tension (how hard it is to cavitate the solvent)
• $$\alpha=$$ Abraham h-bonding acidity (the ability of the solvent to h-bond as a proton donor)
• $$\beta=$$ Abraham h-bonding basicity (the ability of the solvent to h-bond as a proton acceptor)

To create these parameters¶

Take the experimental data, subtract the electrostatics to get the $$G_{CDS}$$, we know the surface area, since we can calculate it, which leaves the unknown parameters.

After doing a big multilinear regression, we can determine the universal parameters of the solvent

$\Delta G_{aq,\:expt}-\Delta G_{ENP}=G_{CDS}=\sum\limits_kA_k\sigma_k$

The result¶

SM8 has about 72 parameters for 2500 data (H, C, N, O, F, S, P, Cl, Br based compounds) in 91 solvents.

There is a mean error of $$\sim\pm0.6\:kcal\:mol^{-1}$$ for neutral species and $$\pm3-6\:kcal\:mol^{-1}$$ for ions (depending on the solvent)

Examples of solvent descriptors¶

$$\ce{H2O}$$ $$\ce{C6H6}$$ $$\ce{CH2Cl2}$$
Dielectric constant ($$\varepsilon$$) 78.36 2.27 8.93
Abraham h-bonding acidity ($$\alpha$$) 0.82 0.00 0.10
Abraham h-bonding basicity ($$\beta$$) 0.38 0.141 0.05
Refractive index ($$n$$) 1.33 1.50 1.42
Surface tension ($$cal\cdot mol^{-1}\cdot\unicode{x212B}^{-2}$$) 104.71 40.62 39.15
Carbon aromaticity 0.00 1.00 0.00
Electronegative halogenicity 0.00 0.00 0.67

SM8 Performance¶

Mean unsigned errors (kcal/mol) for SM8 compared to other models

Solute Class Data N SM8 IEFPCM (G03/UA0) C-PCM GAMESS PB Jaguar All Equal to Mean2
Aqueous neutrals 274 0.5 4.9 1.6 0.9 2.7
Non-aqueous neutrals 666 0.6 6.0 2.8 2.3 1.5
Aqueous ions 112 3.2 12.4 8.4 4.0 8.6
Non-aqueous ions 220 4.9 8.4 8.4 8.1 8.6

1. Benzene’s $$\pi$$ cloud can actually accept a proton to some extent.

2. Assumes no difference in atom types.