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# 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, `EIQMMM`, that uses an electrostatic embedding model to couple the subsystems explicitly. See the method paper for more info.

Examples of what this code has been used for can be seen here, and here.

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 `PointChargePotential` classes in any of the calculators above.

You might also be interested in the solvent MM potentials included in ASE. The tutorial on Equilibrating a TIPnP Water Box could be relevant to have a look at. For acetonitrile, have a look at Equilibrating an MD box of acetonitrile.

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

## Electrostatic Embedding QM/MM

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

\[E_\mathrm{TOT} = E_\mathrm{QM} + E_\mathrm{I} + E_\mathrm{MM}.\]

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

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

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:

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

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

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

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 `ase.calculators.qmmm.EIQMMM` class.

The following script will calculate the QM/MM single point energy of the water dimer from the S22 database of weakly interacting dimers and complexes, using LDA and TIP3P, for illustration purposes.

    from gpaw import GPAW

    from ase.calculators.qmmm import EIQMMM, Embedding, LJInteractions
    from ase.calculators.tip3p import TIP3P, epsilon0, sigma0
    from ase.data import s22

    # Create system
    atoms = s22.create_s22_system('Water_dimer')
    atoms.center(vacuum=4.0)

    # Make QM atoms selection of first water molecule:
    qm_idx = range(3)

    # Set up interaction & embedding object
    interaction = LJInteractions({('O', 'O'): (epsilon0, sigma0)})
    embedding = Embedding(rc=0.02)  # Short range analytical potential cutoff

    # Set up calculator
    atoms.calc = EIQMMM(qm_idx,
                        GPAW(txt='qm.out'),
                        TIP3P(),
                        interaction,
                        embedding=embedding,
                        vacuum=None,  # if None, QM cell = MM cell
                        output='qmmm.log')

    print(atoms.get_potential_energy())

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. 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 Equilibrating a TIPnP Water Box for water potentials), one of the compatible external MM codes, or write your own potential (see 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 `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