.. _qmmm:

=========================
ASE for QM/MM Simulations
=========================

QM/MM Simulations couple two (or, in principle, more) descriptions to get total energy
and forces for the entire system in an efficient manner.
ASE has a native Explicit Interaction calculator, :class:`~ase.calculators.qmmm.EIQMMM`, that uses an electrostatic embedding
model to couple the subsystems explicitly. See
:doi:`the method paper for more info <10.1021/acs.jctc.7b00621>`.

Examples of what this code has been used for can be seen
:doi:`here <10.1021/jz500850s>`,
and :doi:`here <10.1021/acs.inorgchem.6b01840>`.

This section will show you how to setup up various QM/MM simulations.
We will be using GPAW_ for the QM part. Other QM calculators should
be straightforwardly compatible with the subtractive-scheme SimpleQMMM
calculator, but for the Excplicit Interaction EIQMMM calculator, you
would need to be able to put an electrostatic external potential into
the calculator for the QM subsystem. This is often simply a matter of:

1. Making the ASE-calculator write out the positions and charge-values
   to a format that your QM calculator can parse.
2. Read in the forces on the point charges from the QM density.


ASE-calculators that currently support EIQMM:

1. GPAW_
2. DFTBplus_
3. CRYSTAL_
4. TURBOMOLE_

To see examples of how to make point charge potentials for EIQMMM,
have a look at the :class:`~ase.calculators.dftb.PointChargePotential`
classes in any of the calculators above.

.. _GPAW: https://gpaw.readthedocs.io/
.. _DFTBplus: https://ase-lib.org/ase/calculators/dftb.html
.. _CRYSTAL: https://ase-lib.org/ase/calculators/crystal.html
.. _TURBOMOLE: https://ase-lib.org/ase/calculators/turbomole.html

You might also be interested in the solvent MM potentials included in ASE.
The tutorial on :ref:`tipnp water box equilibration` could be relevant to
have a look at. For acetonitrile, have a look at :ref:`acetonitrile_md_box_equilibration`.

Some MD codes have more advanced solvators, such as AMBER_, and stand-alone
programs such as PACKMOL_ might also come in handy.

.. _AMBER: https://ambermd.org/AmberTools.php
.. _PACKMOL: http://m3g.iqm.unicamp.br/packmol/home.shtml


Electrostatic Embedding QM/MM
-----------------------------
The total energy expression for the full QM/MM system is:

.. math::  E_\mathrm{TOT} = E_\mathrm{QM} + E_\mathrm{I} + E_\mathrm{MM}.

The MM region is modelled using point charge force fields, with charges
`q_i` and `\tau_i` denoting their spatial coordinates, so the
QM/MM coupling term `E_\mathrm{I}` will be

.. math:: E_\mathrm{I} = \sum_{i=1}^C q_i \int \frac{n({\bf r})}{\mid\!{\bf r} -
                         \tau_i\!\mid}\mathrm{d}{\bf r} +
                         \sum_{i=1}^C\sum_{\alpha=1}^A
                         \frac{q_i Z_{\alpha}}{\mid\!{\bf R}_\alpha - \tau_i\!\mid} + E_\mathrm{RD}

where `n({\bf r})` is the spatial electronic density of the quantum
region, `Z_\alpha` and `{\bf R}_\alpha` are the charge and
coordinates of the nuclei in the QM region, respectively, and
`E_\mathrm{RD}` is the term describing the remaining, non-Coulomb
interactions between the two subsystems.

For the MM point-charge external potential in GPAW, we use the total pseudo-
charge density `\tilde{\rho}({\bf r})` for the coupling, and since the
Coloumb integral is evaluated numerically on the real space grid, thus the
coupling term ends up like this:

.. math:: E_\mathrm{I} = \sum_{i=1}^C q_i \sum_{g} \frac{\tilde{\rho}({\bf r})}{\mid\!{\bf r}_g  - \tau_i\!\mid} v_g + E_\mathrm{RD}

Currently, the term for `E_{\mathrm{RD}}` implemented is a Lennard-
Jones-type potential:

.. math:: E_\mathrm{RD} = \sum_i^C \sum_\alpha^A
                          4\epsilon\left[ \left(\frac{\sigma}{\mid\!{\bf R}_\alpha
                          - \tau_i\!\mid}\right)^{12}
                          - \left(\frac{\sigma}{\mid\!{\bf R}_\alpha
                          - \tau_i\!\mid}\right)^{6} \right]

Let's first do a very simple electrostatic embedding QM/MM single point
energy calculation on the water dimer. The necessary inputs are described in
the :class:`ase.calculators.qmmm.EIQMMM` class.


The following script will calculate the QM/MM single point energy of the
water dimer from the :ref:`s22`, using LDA and TIP3P, for illustration purposes.

.. literalinclude:: water_dimer.py

Here, we have just used the TIP3P LJ parameters for the QM part as well. If
this is a good idea or not isn't trivial. The LJInteractions module needs
combined parameters for all possible permutations of atom types in your
system, that have LJ parameters. A list of combination rules can be found
`here <http://www.sklogwiki.org/SklogWiki/index.php/Combining_rules>`_.
Here's a code snippet of how to combine LJ parameters of atom types A and B
via the Lorentz-Berthelot rules::

   import itertools as it

   parameters = {'A': (epsAA, sigAA),
                 'B': (epsBB, sigBB)}

   def lorenz_berthelot(p):
       combined = {}
       for comb in it.product(p.keys(), repeat=2):
          combined[comb] = ((p[comb[0]][0] * p[comb[1]][0])**0.5,
                           (p[comb[0]][1] + p[comb[1]][1])/2)
       return combined

   combined = lorenz_berthelot(parameters)
   interaction = LJInteractions(combined)

This will (somewhat redundantly) yield::

    >>>combined
    {('A', 'A'): (epsAA, sigAA),
     ('A', 'B'): (epsAB, sigAB),
     ('B', 'A'): (epsAB, sigAB),
     ('B', 'B'): (epsBB, sigBB)}


It is also possible to run structural relaxations and molecular dynamics
using the electrostatic embedding scheme::

    from ase.constraints import FixBondLengths
    from ase.optimize import LBFGS

    mm_bonds = [(3, 4), (4, 5), (5, 3)]
    atoms.constraints = FixBondLengths(mm_bonds)
    dyn = LBFGS(atoms=atoms, trajectory='dimer.traj')
    dyn.run(fmax=0.05)

Since TIP3P is a rigid potential, we constrain all interatomic distances.
QM bond lengths can be constrained too, in the same manner.

The implementation was developed with the focus of modelling ions and complexes
in solutions, we're working on expanding its functionality to encompass
surfaces.

In broad strokes, the steps to performing QM/MM MD simulations for thermal
sampling or dynamics studies, these are the steps:

QM/MM MD General Strategy for A QM complex in an MM solvent:

1. Equillibrate an MM solvent box using one of the MM potentials built into
   ASE (see :ref:`tipnp water box equilibration` for water potentials), one
   of the compatible external MM codes, or write your own potential
   (see :ref:`Adding new calculators`)
2. Optimize the gas-phase structure of your QM complex in GPAW, analyze what
   level of accuracy you will need for your task.
3. Place the relaxed structure of the QM molecule in your MM solvent box,
   deleting overlapping MM molecules.
4. Re-equillibrate the QM/MM system.
5. Run production runs.

For these types of simulations with GPAW, you'd probably want two cells: a QM (non-
periodic) and and MM cell (periodic)::

    atoms.set_pbc(True)
    # Set up calculator
    atoms.calc = EIQMMM(
        qm_idx,
        GPAW(txt='qm.out'),
        TIP3P(),
        interaction,
        embedding=embedding,
        vacuum=4.,  # Now QM cell has walls min. 4 Å from QM atoms
        output='qmmm.log')


This will center the QM subsystem in the MM cell. For QM codes with no single
real-space grid like GPAW, you can still use this to center your QM subsystem,
and simply disregard the QM cell, or manually center your QM subsystem, and leave
vacuum as ``None``.

LJInteractionsGeneral - For More Intricate Systems
--------------------------------------------------
It often happens that you will have different 'atom types' (an element in a
specific environment) per element in your system, i.e. you want to assign
different LJ-parameters to the oxygens of your solute molecule and the oxygens
of water. This can be done using
:class:`~ase.calculators.qmmm.LJInteractionsGeneral`, which takes in NumPy
arrays with sigma and epsilon values for each individual QM and MM atom,
respectively, and combines them itself, with Lorentz-Berthelot.
. I.e., for our water dimer from before::

    from ase.calculators.qmmm import LJInteractionsGeneral
    from ase.calculators.tip3p import epsilon0, sigma0


    # General LJ interaction object for the 'OHHOHH' water dimer
    sigma_mm = np.array([sigma0, 0, 0])  # Hydrogens have 0 LJ parameters
    epsilon_mm = np.array([epsilon0, 0, 0])
    sigma_qm = np.array([sigma0, 0, 0])
    epsilon_qm = np.array([epsilon0, 0, 0])
    interaction = LJInteractionsGeneral(sigma_qm, epsilon_qm,
                                        sigma_mm, epsilon_mm,
                                        qm_molecule_size=3,
                                        mm_molecule_size=3)

The ``qm_molecule_size`` and ``mm_molecule_size`` should be the number of atoms
per molecule. Often the ``qm_molecule_size`` will simply be the total number of
atoms in your QM subsystem. Here, our MM subsystem is comprised of a single
water molecule, but say we had N water molecules in the MM subsystem, we wouldn't
need to repeat e.g. the ``sigma_mm`` array N times, we can simply keep it as it is
written in the above.


EIQMMM And Charged Systems - Counterions
----------------------------------------
If your QM subsystem is charged, it is good to charge-neutrialize the entire
system. This can be done in ASE by adding MM 'counterions', which are simple,
single-atomic particles that carry a charge, and interact with the solvent and solute
through a Coulomb and an LJ term. The implementation is rather simplified and should only
serve to neutralize the total system. It might be a good idea to restrain them
so they do not diffuse too close to the QM subsystem, as the effective concentration
in your simulation cell might be a lot higher than in real life.

To use the implementation, you need to 'Combine' two MM calculators, one for the
counterions, and one for your solvent. This is an example of combining two Cl-
ions with TIP3P water, using the TIP3P LJ-arrays from the previous section::

    from ase import units
    from ase.calculators.combine_mm import CombineMM
    from ase.calculators.counterions import AtomicCounterIon as ACI

    # Cl-:  10.1021/ct600252r
    sigCl = 4.02
    epsCl = 0.71 * units.kcal / units.mol

    # in this sub-atoms object, CombineMM only sees Cl and Water,
    # and Cl is here atom 0 and 1
    mmcalc = CombineMM([0, 1],  # indices of the counterion atoms
                       apm1=1, apm2=3,  # atoms per 'molecule' of each subgroup
                       calc1=ACI(-1, epsCl, sigCl),  # Counterion calculator
                       calc2=TIP3P(),  # Water calculator
                       sig1=[sigCl], eps1=[epsCl],  # LJ Params for subgroup1
                       sig2=sigma_mm, eps2=epsilon_mm)  # LJ params for subgroup2


The charge of the counterions is defined as -1 in the first input in ``ACI``, which
then also takes LJ-parameters for interactions with other ions beloning to this calculator.

This ``mmcalc`` object is then used in the initialization of the ``EIQMMM`` calculator.
But before we can do that, the QM/MM Lennard-Jones potential needs to understand that
the total MM subsystem is now comprised of two subgroups, the counterions and the water.
That is done by initializing the ``interaction`` object with a tuple of NumPy arrays for the MM
part. So if your QM subsystem has 10 atoms, you'd do::

    sigma_mm = (np.array([sigCl]),  np.array([sigmaO, 0, 0]))
    epsilon_mm = (np.array([epsCl]),  np.array([epsilonO, 0, 0]))

    interaction = LJInteractionsGeneral(sigma_qm, epsilon_qm,
                                        sigma_mm, epsilon_mm, 10)


Current limitations:

* No QM PBCs
* There is currently no automated way of doing QM/MM over covalent bonds (inserting cap-atoms, redistributing forces ...)


Other tips:
___________

If you are using GPAW and water, consider having a look at the
`much faster RATTLE constraints for water here <https://gitlab.com/gpaw/gpaw/blob/master/gpaw/test/rattle.py>`__
