Solvation beyond continuum solvation models: 3D-RISM
****************************************************

ADF Solvation RISM

The three-dimensional reference interaction site model (3D-RISM) is a
solvation model that can be viewed as a bridge between continuum
solvation models such as COSMO and much more complex descriptions
based on QM/MM molecular simulations. It describes the solvent in
terms of interacting sites - such as H, O and CH3 in case of methanol
- that are assigned point charges and Lennard Jones parameters, as is
done in many force fields. Its output includes an estimate for the
free energy of solvation as well as the averaged solvent (site)
distribution around the solute. The AMS implementation [1] was heavily
extended [2] in AMS2022 and features a self-consistent combination of
the 3D-RISM approach and the (fitted) electron density obtained from
DFT. In this combination, it can give insights into changes of the
electronic structure of the solute upon solvation and related
properties such as dipole moments and vertical excitation energies as
required to investigate solvatochromism. [2]

In this tutorial, we show how to run self-consistent 3D-RISM-SCF
calculations and how to inspect the resulting solvent distributions
using the example of acetone in water

Note:

  The 3D-RISM implementation is fully compatible with the calculation
  of analytical gradients, numerical frequencies (to verify the nature
  of a stationary point), vertical excitation energies and the
  calculation of EPR and NMR parameters (although specific MO
  contributions from the solvent are missing). See also the ADF manual
  on 3D-RISM.


Setting up and running the calculation
======================================

Load the structure of the acetone molecule from the molecules database
and set up the calculation:

   Start AMSinput
   1. Press the [image: Search][image] button and search for Acetone and select "C3H6O: Acetone (ADF)"
   2. Symmetrize the molecule by clicking the [image: SymmTool][image] button
   3. In the **Main** panel set **Task** to **Single Point**
   4. Set **XC functional** to **GGA:PBE**
   5. Set the **Basis set** to **TZP**

   [image]

Since the 3D-RISM-SCF by default uses the fitted electron density to
describe the electrostatic interaction between solvent and solute, it
is highly recommended to increase the numerical quality of the density
fit, especially for large molecules and when analytical gradients are
computed. For this we set the Spline Zlm fit to better quality.

   6. Move to **Details** → **Numerical Quality** and set **Spline Zlm fit** to **Very Good**

   [image]

To set up the 3D-RISM part:

   1. Move to **Model** → **3D-RISM** and set **Solvent** to **Water**
   2. In the same menu enable **Show GF-, PC+, …**
   3. Set **Box size** to "24" "24" "24" Å
   4. Set **Box grid** to "96" "96" "96"

Note:

  The parameters used for the default solvents were taken from the SI
  of [2].

Note:

  The box - i.e., the cartesian grid, on which the 3D-RISM equations
  are solved - should extend far enough into space to allow for at
  least the first two or three solvation shells. Typically, adding 10
  Å in each direction to the extent of the molecules is a good
  starting point. The grid spacing should not be above 0.5 Å (2 grid
  points per Å) and should best be below 0.33 Å (3 grid points per Å).
  The number of grid points has to be even and should have no prime
  factor larger than seven for optimal performance.

   [image]

Now run the calculation:

   1. **File** → **Save**, choose for example "Acetone_in_water" as name
   2. **File** → **Run**
   3. Wait for the calculation to finish, it should only take a few minutes


Results
=======

A few interesting results have been written to the output file, such
as free energy of solvation or the dipole moment of the molecule.

   1. Open the output, **SCM** → **Output**
   2. In AMSoutput search for "Corrections based on the calculated distribution functions"

   [image]

The calculated free energy of solvation of 8.82 kcal/mol is indeed
much too positive for acetone in water (exp. -3.85 kcal/mol). The PC+
corrected value (-7.42 kcal/mol) gives the best agreement.

Note:

  For a formally correct free energy of solvation, the molecule should
  be optimized in both the gas phase and in solution and thermal
  corrections should be included!

For an inspection of dipole moment, search for "Dipole Moment" in
AMSoutput.

   [image]

The dipole moment of 4.14 Debye is very close to the COSMO value (4.03
Debye) and shows the polarization of the C=O bond upon solvation (gas
phase value at this level of theory: 2.87 Debye). Additional insight
into this effect can be obtained from the solvent site distribution
functions. They can be easily inspected using AMSview:

   1. **SCM** → **View**
   2. **Add** → **Isosurface**
   3. **Select Field ...** → **RISM...**
   4. Select the distribution of the second site (the water hydrogen) by clicking "RISM g(r) for site 2"
   5. Enter a Isosurface value of 1.7

   [image]

The isosurface shows the region in space, where the pair correlation
function is above 1.7 -- which corresponds to the local (site) density
being 70 % larger than the average bulk density. The picture can
straightforwardly be interpreted to show the hydrogen sited forming
the hydrogen bonds to the oxygen lone pairs, which in turn explains
the previously shown polarization of the C=O bond.


References
==========

[1] Sergey Gusarov, Tom Ziegler and Andriy Kovalenko J. Phy. Chem. A
    110, 6083-6090 (2006).

[2] Marc Reimann and Martin Kaupp J. Phys. Chem. A 124, 7439-7452
    (2020).
