3D-RISM: 3D Reference Interaction Site Model
********************************************

**Introduction**

The three-dimensional reference interaction site model (3D-RISM)
provides the solvent structure in the form of a 3D site distribution
function, g_{\gamma}^{UV}(r), for each solvent site, \gamma.

It enables, at modest computational cost, the calculation of
thermodynamic and electronic properties and molecular solvation
structure of a solute molecule in a given molecular liquid or mixture.
Using 3D-RISM, one can study chemical reactions, including reaction
coordinates and transition state searches, with the molecular
solvation described from first principles based on a molecular-
mechanics type description of the solvent. The method yields all of
the features available by using other solvation approaches.

The 3D-RISM implementation has been revised and supplemented (AMS2022)
by a new option that uses the fitted electron density directly in the
interaction between the solvent and the solute. Without the use of
point charges, numerical stability has been improved. Using this
option, 3D-RISM can now be used for structure optimization, numerical
frequencies, vertical excitation energies and magnetic properties. The
code has also been parallelized. Details can be found in Ref. [1].
Starting from AMS2022, new point-charge-based options can be used in
combination with structure optimization, numerical frequencies and
vertical excitation energies.

Details on the original implementation of 3D-RISM-KH in ADF can be
found in Ref. [2], with applications in Ref. [3]. The theory of 3D-
RISM-KH in combination with DFT can be found in Refs. [4] [5] [6] [7].
A combination of 3D-RISM-KH with FDE (frozen-density embedding) can be
found in Ref. [8].

Similar to explicit solvent simulations, 3D-RISM properly accounts for
chemical peculiarities of both solute and solvent molecules, such as
hydrogen bonding and hydrophobic forces, by yielding the 3D site
density distributions of the solvent. Moreover, it readily provides,
via analytical expressions, all of the solvation thermodynamics,
including the solvation free energy potential, partial molar volume,
and compressibility. Starting from AMS2023, enthalpic and entropic
decomposition of the solvation free energy can be obtained
approximately using analytic expressions (which are exact for
CHRGLVL=MM or pure Lennard-Jones fluids), also including the
macroscopic dependence of the dielectric constant on temperature and
solvent density. [9] The expression for the solvation free energy (and
its derivatives) in terms of integrals of the correlation functions
follows from a particular approximation for the so-called closure
relation used to complete the integral equation for the direct and
total correlation functions.

**Solvation free energy**

The solvation free energy can be calculated as:
      Solvation Free Energy =
      [ (Total Bonding Energy) + (Internal Energy)
         - T * (Entropy) + (Excess Chemical Potential) ]_3D-RISM
      - [ (Total Bonding Energy) + (Internal Energy) - T * (Entropy) ]_Gas-Phase

If one assumes that the internal energy and the vibrational and
rotational entropy of the solute molecule are the same in solution and
in gas phase, then this simplifies to:
      Solvation Free Energy =
      [ (Total Bonding Energy) + (Excess Chemical Potential) ]_3D-RISM
      - [ (Total Bonding Energy)]_Gas-Phase

However, a formally accurate calculation should include the difference
between the thermal corrections from frequency calculations produced
by ADF in the SCF calculation with 3D-RISM solvation and in gas phase.

**Input**

When performing 3D-RISM simulations, each atom in the **ATOMS** block
in the AMS part of the input must have two Lennard-Jones parameters
specified, adf.SigU and adf.EpsU, for example:

   System
      ATOMS
        C     0.00    0.00    0.00     adf.SigU=3.50    adf.EpsU=0.066    adf.ChgU=-0.4000
        ...
      END
   End

They can be obtained from a Lennard-Jones force-field parameter set.
Atom-centered point charges adf.ChgU can optionally be set as well but
will only be used in combination with CHRGLVL=MM (see below).

All other 3D-RISM-related input keys are contained in a **RISM** input
block. Below, only the mandatory keywords are shown. Optional keywords
are described in the next section.

   RISM title
     RISM1D
       FLUIDPARAM temper=298. DielConst=78.497 UTotDens=1/A3 0.03333
     SUBEND
     SOLVENT ArbitrarySolventName
       UNITS uWeight=g/mol  ULJsize=A  ULJenergy=kcal/mol Ucoord=A Udens=1/A3
       PARAMETERS Weight=weight nAtoms=NSiteTypes
         N1    Z_alpha1   Sigma_alpha1   Eps_alpha1   X1_1 Y1_1 Z1_1
                                                      X1_2 Y1_2 Z1_2
                                                      ...  ...  ...
         N2    Z_alpha2   Sigma_alpha2   Eps_alpha2   X2_1 Y2_1 Z2_1
                                                      X2_2 Y2_2 Z2_2
                                                      ...  ...  ...
         ...
         DENSPE=density
     SUBEND
     SOLUTE ArbitrarySoluteName
       BOXSIZE   sizeX  sizeY  sizeZ
       BOXGRID    npX    npY    npZ
     SUBEND
   END

The **RISM1D** sub-block contains general parameters for the preceding
1D-RISM calculation of the solvent(s) to create the bulk
susceptibility function. Even though all technical RISM1D sub-keys
have reasonable defaults, the FLUIDPARAM sub-key will most likely
require attention because its default values for density and
dielectric constant are only applicable if the solvent is water. Thus,
you may need to change these values when modeling a different solvent.
Note that even when using all default values from the RISM1D sub-
block, the sub-block itself must be specified, even if empty. See
below for a complete description of the RISM1D sub-block.

The **SOLVENT** sub-block can be repeated for each component if the
solvent is a mixture. Each SOLVENT sub-block contains parameters for
one solvent. First, each solvent has a name, which is specified on the
SOLVENT keyword's line and is arbitrary. The first line in the SOLVENT
sub-block must contain the UNITS key. Usually, only the Udens part
should be changed. Then follow the actual solvent parameters. In
principle, each solvent consists of multiple atoms and functional
groups (so-called sites). For example, in 3D-RISM terms, methanol
consists of 3 sites: CH_3, O, and H. Each such site has a set of three
parameters, shared between all sites of the same type, and the
coordinates. These parameters follow the PARAMETERS keyword. The line
with the PARAMETERS keyword itself must specify the molecular weight
of the solvent and the number of site types that follow. The first
line for each site type contains, in this order: number of equivalent
sites of this type, z_\alpha (the point charge assigned),
\sigma_\alpha, \epsilon_\alpha (the Lennard-Jones parameters
assigned), three coordinates for the first site of this type. If there
is more than one site of this type, then the coordinates for the
second and other sites follow on subsequent lines. The SOLVENT sub-
block is concluded by the specific density of this solvent, by
default, in molecules per cubic Angstrom. This number should be equal
to the total density for mono-component solvents. Using Udens=MOL, the
specific density needs to be given in molar fractions, and should
therefore be one for mono-component solvents.

For example, the SOLVENT block for water would typically look like
this:

   SOLVENT water
     UNITS      uWeight=g/mol  ULJsize=A  ULJenergy=kcal/mol Ucoord=A Udens=1/A3
     PARAMETERS Weight=18.015   nAtoms=2
       1    -0.8476   3.166    0.1554       0.000000  0.00000 -0.064605
       2     0.4238   1.000    0.0560      -0.816495  0.00000  0.512747
                                            0.816495  0.00000  0.512747
     DENSPE=0.03333
   SUBEND

The **SOLUTE** sub-block specifies 3D-RISM parameters for your
molecule. The BOXSIZE and BOXGRID sub-keys specify dimensions of the
simulation box, in Angstrom, and the number of grid points in each
direction. The box should at least be twice as large as the molecule
and the BOXGRID values must be even numbers. Due to the 3D-FFT
routines, the largest prime factor of the BOXGRID values should be 7
for optimal performance. The size/np ratio defines the grid spacing in
each direction and this should not be larger than 0.5 Angstrom for
energy calculations and not larger than 0.35 Angstrom for structure
optimizations. When the BOXSIZE and BOXGRID keywords are not
specified, the grid is calculated based on the GRIDSTEP and BOXEXTENT
values; see below. The number of grid points along the Cartesian
coordinate *i* will then be determined as N_i = (range(i) +
2*BOXEXTENT)/GRIDSTEP + 1, where *range(i)* is the span of Cartesian
coordinate *i* of the solute molecule. The number of grid points may
be increased to be a product of prime numbers not larger than 7.

The **optional** 3D-RISM keys for the RISM1D and SOLUTE sub-blocks are
listed below together with their defaults.

   ! optional RISM1D subkeys with their default values:
   RISM1D Theory=RISM Closure=KH NOSPEEDUP
     FLUIDPARAM temper=298. DielConst=78.497 UTotDens=1/A3 0.03333
     OUTPUT PrintLev=5 File=solvent
     GRID   Nr=8192  dR=0.025 MaxRout=100.0 MaxKout=0.0
     MDIIS  N=20 Step=0.5 Tolerance=1.e-12
     ELSTAT LRsmear=1.0 Adbcor=0.5
     ITER   Ksave=-1 Kshow=1 Max=10000
     DODEPS alpha=-1.0 kappa=-1.0 dedtp=-1.0 dedpt=-1.0
     Restart1D=restartfile
   SUBEND

"RISM1D"
   Theory - Version of 1D-RISM used: RISM - extended RISM, DRISM -
   dielectrically consistent RISM (should be used for solvents with a
   static dipole moment).

   Closure - Closure for the 1D problem: KH - Kovalenko-Hirata, HNC -
   hypernetted chain, PSEn - partial series expansion of HNC up to
   order n (n=1 is identical to KH), PY - Percus-Yevick, KGK - Kobryn-
   Gusarov-Kovalenko.

   NOSPEEDUP - Switch off the automatic adjustment of the MDIIS step
   width.

"FLUIDPARAM"
   Temper - temperature.

   DielConst - dielectric constant (only used when theory=DRISM).

   UTotDens - units for total density: G/CM3, KG/M3, 1/A3 are valid
   units followed by the density value.

"OUTPUT"
   PrintLev - print level.

   File - common base name for output files.

   OutList - which information will be written to additional output
   files (no additional information will be written by default): G -
   distribution function, C - direct correlation function, H - total
   correlation function, U - interaction function, X - ".xvv" file
   (only required up to ADF2019), T - thermodynamics, D - density and
   temperature derivatives of all correlation functions (automatically
   set when DERIV option is chosen in the SOLUTE block).

"GRID"
   Nr - the size of the 1D-RISM grid, must be a power of 2 (max.
   value: 16384).

   dR - mesh size in Angstrom.

   MaxRout - plot range in direct space.

   MaxKOut - plot range in reciprocal space.

"MDIIS"
   N - number of vectors in the DIIS space.

   Step - step size.

   Tolerance - convergence criterion.

"ELSTAT"
   LRsmear - smearing parameters for Coulomb potential.

   Abdcor - switching parameter for dielectric correction (only used
   if theory=DRISM).

"ITER"
   Ksave - save the current solution every Ksave steps (0 - do not
   save).

   Kshow - print convergence progress every Kshow steps.

   Max - maximum number of iterations.

"DODEPS"
   If this block is set, the temperature and density dependence of the
   dielectric constant is included in the calculation of temperature
   and density derivatives (OutList=D).

   Alpha - isobaric thermal expansion coefficient of the solvent (in
   1/K, not set by default!).

   Kappa - isothermal compressibility of the solvent (in 1/Pa, not set
   by default!).

   dedtp - temperature derivative of the dielectric constant at
   constant pressure (in 1/K, not set by default!).

   dedpt - pressure derivative of the dielectric constant at constant
   temperature (in 1/Pa, not set by default!).

Restart1D - use the given restart file (of the RISMDATA type) to
restart the 1D-RISM calculation.

   SOLUTE ArbitrarySoluteName
     outlist=M  closure=KH  xvvfile=solvent.xvv outfile=rism3d
     Nis=10  DELOZ=0.5 TOLOZ=2.0e-6
     Ksave=-1  Kshow=1  Maxste=10000
     Output=4
     CHRGLVL=ZLM
     GRIDSTEP=0.33
     BOXEXTENT=12.0
   SUBEND

Outlist - output requested: M - detailed output for the excess
chemical potential, F - some corrections (GF, PC+, UC, ...) to the
excess chemical potential, G - distribution function, C - direct
correlation function, H - total correlation function.

Closure - closure for the 3D problem: KH – Kovalenko-Hirata, HNC -
hypernetted chain approximations, PSEn - partial series expansion of
HNC up to order n (n=1,2,...; n=1 is identical to KH), KGK - Kobryn-
Gusarov-Kovalenko.

RBC - Use the current closure in combination with the repulsive bridge
correction (incompatible with analytical gradients).

UCA - The value of the a-parameter in the universal correction (a*V +
b, mandatory to compute the UC correction).

UCB - The value of the b-parameter in the universal correction (a*V +
b, mandatory to compute the UC correction).

Xvvfile - name of the file with the results of the 1D-RISM calculation
specified in the RISM1D keyword above, with .xvv appended to it (only
used up to ADF2019).

Outfile - name of the output text files.

Output - print level.

CHRGLVL - which charges computed by ADF should be used. This can be
ZLM - use the electron density (default), CHELPG - use point charges
fitted to the electron density in analogy to the CHELPG procedure,
RESP - same as CHELPG but with a harmonic restraint to keep the
charges small, MM - use constant point charges given in the System
block, MDCq, MDCd, MDCm, or EXMDC (labeled EXACT in older versions).
The MDCq, MDCd, MDCm, or EXMDC levels cannot be combined with
analytical gradients.

OLDZLM - reproduce the exact ZLM results obtained with ADF2019 and
ADF2020;

RESPWEIGHT - pre-factor of the harmonic restraint in the RESP-like
procedure, default value: 0.05.

VDWTYPE - functional form of the van der Waals interaction requested:
12-6 (default), 9-6.

SPHINT - calculate the spherically averaged distribution function
around the given atom: 1,2,... - atom in input order, 0 - center of
mass.

SOLVPOS - find the most likely positions of a solvent site: 1,2,... -
site in input order, 0 - all sites.

OLDCODE - run the old version of the code (ADF2019 and older), should
only be used by experts.

DERIV - compute the temperature and density derivative of the excess
chemical potential analytically (only exact for CHRGLVL=MM or pure
Lennard-Jones fluids). When DODEPS is set in the RISM1D block,
enthalpy and entropy of solvation are calculated as well.

NOSPEEDUP - switch off the automatic adjustment of the MDIIS step
width.

GRIDSTEP - grid spacing, in Angstrom.

BOXEXTENT - extent of the grid, in Angstrom, beyond the space occupied
by atoms in each direction.

The Nis, DELOZ, and TOLOZ have the same meaning for 3D-RISM as the
parameters of the MDIIS keyword of the RISM1D block. Likewise, Ksave,
Kshow, and Maxste are analogous to the parameters of the ITER key in
RISM1D.

**Parameters for some solvents**

The following, compiled set of solvent parameters is taken from the
literature (see Ref. [1] and references therein for these and
additional solvents).


**Water Weight=18.015 nAtoms=2**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.8476        | 3.166          | 0.1554         | 0.000000       | 0.000000       | -0.064605      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.4238         | 1.000          | 0.0560         | 0.000000       | 0.816495       | 0.512747       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | 0.000000       | -0.816495      | 0.512747       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Methanol Weight=32.04 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.435          | 1.000          | 0.0560         | 0.00000        | 0.00000        | 0.00000        |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.700         | 3.070          | 0.1700         | 0.00000        | 0.00000        | 0.94500        |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.265          | 3.775          | 0.2070         | 1.35136        | 0.00000        | 1.39716        |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Ethanol Weight=47.07 nAtoms=4**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.435          | 1.000          | 0.0560         | 0.000000       | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.700         | 3.070          | 0.1700         | 0.000000       | 0.000000       | 0.945000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH2            | 0.265          | 3.775          | 0.2070         | 1.356103       | 0.000000       | 1.398746       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.000          | 3.905          | 0.1750         | 1.342751       | 0.000000       | 2.928687       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Isopropanol Weight=60.10 nAtoms=4**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.435          | 1.000          | 0.0560         | 0.000000       | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.700         | 3.070          | 0.1700         | 0.000000       | 0.000000       | 0.945000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH             | 0.265          | 3.850          | 0.0800         | 1.356103       | 0.000000       | 1.398746       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.000          | 3.910          | 0.1600         | 1.578230       | 1.268465       | 2.224915       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | 1.578230       | -1.268465      | 2.224915       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Acetonitrile Weight=41.052 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.150          | 3.775          | 0.2070         | 1.458000       | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| C              | 0.280          | 3.650          | 0.1500         | 0.000000       | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| N              | -0.430         | 3.200          | 0.1700         | -1.157000      | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Dimethylsulfoxide Weight=78.13 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.459         | 2.930          | 0.2800         | 0.000000       | 0.000000       | 1.530000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| S              | 0.139          | 3.560          | 0.3950         | 0.000000       | 0.000000       | 0.000000       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.160          | 3.810          | 0.1600         | 0.000000       | 1.716700       | -0.541300      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | -1.665300      | -0.416800      | -0.541300      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Acetone Weight=58.08 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| O              | -0.424         | 2.960          | 0.2100         | 0.000000       | 0.000000       | -1.208737      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| C              | 0.300          | 3.750          | 0.1050         | 0.000000       | 0.000000       | 0.013263       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| CH3            | 0.062          | 3.910          | 0.1600         | 0.000000       | 1.286301       | 0.798425       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | 0.000000       | -1.286301      | 0.798425       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Dichloromethane Weight=84.93 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| C              | -0.364         | 3.400          | 0.1094         | 0.000000       | 0.000000       | -0.814053      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.218          | 2.293          | 0.0157         | -0.926635      | 0.000000       | -1.406798      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | 0.926635       | 0.000000       | -1.406798      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Cl             | -0.036         | 3.564          | 0.2550         | 0.000000       | -1.451416      | 0.177892       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | 0.000000       | 1.451416       | 0.177892       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+


**Chloroform Weight=119.38 nAtoms=3**
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Atom           | z_\alpha /     | \sigma_\alpha  | \epsilon_\alp  | X/Å            | Y/Å            | Z/Å            |
|                | a.u.           | / Å            | ha / kcal/mol  |                |                |                |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| C              | -0.386         | 3.400          | 0.1094         | 0.000000       | 0.000000       | 0.463135       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| H              | 0.266          | 2.115          | 0.0157         | 0.000000       | 0.000000       | 1.563010       |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
| Cl             | 0.040          | 3.564          | 0.2550         | 1.607217       | -0.475149      | -0.067114      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | -0.392118      | 1.629465       | -0.067114      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+
|                |                |                |                | -1.215099      | -1.154317      | -0.067114      |
+----------------+----------------+----------------+----------------+----------------+----------------+----------------+

**OPLS-AA Parameters for common atoms and atom groups**

The table below contains possible sigma and epsilon parameters for
some of the most common solvent groups collected from Ref. [10] [11]
[12]. These parameters are kindly provided by Leonardo Costa.


**All atoms model**
^^^^^^^^^^^^^^^^^^^

+----------------------+----------------------+----------------------+----------------------+----------------------+
| Atom                 | Example              | \sigma_\alpha / Å    | \epsilon_\alpha /    | Reference            |
|                      |                      |                      | kcal/mol             |                      |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C (SP3)              | methane              | 3.73                 | 0.294                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C (SP3)              | neopentane           | 3.80                 | 0.050                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C (SP2)              | isobutene            | 3.75                 | 0.105                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C (SP)               | acetonitrile         | 3.40                 | 0.099                | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C (arom)             | benzene              | 3.55                 | 0.07                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| C                    | chloroform           | 4.10                 | 0.05                 | [12]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| H                    | O---H                | 0.7                  | 0.046                | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| H                    | hydrocarbons         | 2.42                 | 0.03                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| O                    | water                | 3.166                | 0.1554               | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| O                    | alcohol              | 3.07                 | 0.17                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| O                    | sulfoxide            | 2.93                 | 0.28                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| N (SP)               | acetonitrile         | 3.3                  | 0.099                | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| S                    | sulfoxide            | 3.56                 | 0.395                | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| Cl                   | chloroform           | 3.40                 | 0.300                | [12]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+


**United atom model**
^^^^^^^^^^^^^^^^^^^^^

+----------------------+----------------------+----------------------+----------------------+----------------------+
| Atom                 | Example              | \sigma_\alpha / Å    | \epsilon_\alpha /    | Reference            |
|                      |                      |                      | kcal/mol             |                      |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH (SP3)             | isobutane            | 3.850                | 0.080                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH (SP2)             | 2-butene             | 3.800                | 0.115                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH (arom)            | benzene              | 3.750                | 0.110                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH2 (SP3)            | n-butane             | 3.905                | 0.118                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH2 (SP2)            | 1-butene             | 3.850                | 0.140                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH3                  | hydrocarbon          | 3.775                | 0.207                | [10]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH3                  | acetonitrile         | 3.6                  | 0.38                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| CH3                  | sulfoxide            | 3.81                 | 0.16                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+
| NH2                  | amine                | 3.3                  | 0.17                 | [11]                 |
+----------------------+----------------------+----------------------+----------------------+----------------------+

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