# QM/MM methods¶

Modules: pyscf.qmmm

## Introduction¶

In the Quantum Mechanics - Molecular Mechanics (QM/MM) method, the system is divided into a QM region and an MM region. QM/MM models mainly differ in the treatment of the interaction between QM and MM regions.

The qmmm module implements the electronic embedding model, where classical point charges in the MM region are added into the QM Hamiltonian analogously to the nuclear charges:

$\begin{split}\mathbf{H}_{\mathrm{QMMM}} =&\ \mathbf{H}_{\mathrm{QM}} + \mathbf{V}_{\mathrm{nuc}-\mathrm{MM}} + \mathbf{V}_{\mathrm{elec}-\mathrm{MM}} \\ =&\ \mathbf{H}_{\mathrm{QM}} + \sum_{A}^{N_{\mathrm{MM}}} \sum_{B}^{N_{\mathrm{QM}}} \frac{Q_{A}Q_{B}}{|\mathbf{R}_A - \mathbf{R}_B|} - \sum_{A}^{N_{\mathrm{MM}}} \sum_i^{N_{\mathrm{elec}}} \frac{Q_{A}}{|\mathbf{R}_A - \mathbf{r}_i|}\end{split}$

The total energy calculated using the above model includes the regular QM energy, the interaction between the nuclei in QM region and the MM charges, and the static Coulomb interaction between the electron density and the MM charges. It does not include the static Coulomb interactions of the MM point charges, the MM energy, the vdw interaction or other bonding/non-bonding effects between QM region and MM particles.

Another QM/MM model - polarizable embedding model - is provided in the solvent module. See Solvation models for details.

## SCF methods with MM charges¶

MM background charges support SCF methods scf.RHF(), scf.UHF(), scf.ROHF(), scf.RKS(), scf.UKS() and scf.ROKS(), by decorating the underlying SCF objects with qmmm.mm_charge(). A minimal example of using the qmmm module is as follows.

>>> from pyscf import gto, scf, qmmm
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvdz')
>>> coords = [(0.5,0.6,0.8)]
>>> charges = [-0.3]
>>> mf = qmmm.mm_charge(scf.RHF(mol), coords, charges)
>>> mf.kernel()
converged SCF energy = -100.045455504517


In the above example, the coordinates (in the same unit as mol.unit) and charges of the point charges in the MM region are given by coords and charges, respectively.

Note

Currently, MM charges do not support scf.GHF() and scf.GKS().

Analytical nuclear gradients are calculated with the background charges.

>>> mf.nuc_grad_method().run()
x                y                z
0 H    -0.0157686538    -0.0189223846    -0.1102601870
1 F    -0.0830715173    -0.0996858207     0.1182587572
----------------------------------------------


Note

>>> from pyscf import grad


for a qmmm.mm_charge() decorated mf object will be missing the contributions from the background charges.

If MM charges and X2C correction are used together, function qmmm.mm_charge() needs to be applied after X2C decoration.

>>> qmmm.mm_charge(scf.RHF(mol).x2c(), coords, charges).run()
converged SCF energy = -100.126131355203
>>> qmmm.mm_charge(scf.RHF(mol).x2c1e(), coords, charges).run()
converged SCF energy = -100.126131355203
>>> qmmm.mm_charge(scf.RHF(mol).sfx2c1e(), coords, charges).run()
converged SCF energy = -100.126131355203


Note

X2C gradients with MM charges are not supported.

MM charges can also be used together with second order scf and solvation models.

## Post-SCF methods with MM charges¶

Once function qmmm.mm_charge() is applied on the SCF object, it affects all the post-HF calculations, eg. MP2, CCSD, MCSCF, etc.

>>> from pyscf import mcscf
>>> mf = qmmm.mm_charge(scf.RHF(mol), coords, charges).run()
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.run(conv_tol=1E-10)
CASSCF energy = -100.101848457578
CASCI E = -100.101848457578  E(CI) = -6.74400107375546  S^2 = 0.0000000