`QMMM` incorporates environmental effects in terms of
the QM/MM approach. This keyword, its description, and implementation into
MOPAC was based on materials developed and provided by Prof Arieh Warshel and Dr
Nikolay Plotnikov, University of Southern California.

This option is intended for use with other software, and
requires a knowledge of how to construct a mol.in file. Users should
become familiar with MM software before attempting to use `QMMM`.

To use `QMMM`, a file called mol.in must be present in the folder
that contains the data set. The format of of mol.in is described below.

A hybrid quantum mechanics/ molecular mechanics
approach QM/MM^{1 }has become a powerful modeling technique^{2-4}.
This method allows one to capture the electrostatic effects of surrounding
“solvent” in complex polar and microscopically inhomogeneous environment (e.g.
water, protein, zeolites, etc.) on “solute” (e.g. reactants, enzyme active
center, chromophore, etc.) “Solute” is treated at the QM level of theory, while
“solvent” is described with a MM model. The QM/MM approach is particularly
effective when less expensive implicit solvation models are inapplicable^{5}.

In the QM/MM approach, it is crucial to describe
coupling between the QM and the MM regions, in particular polarization of solute
by polar environment. Not doing so will for example lead to having NaCl
dissociating to Na and Cl instead of Na^{+} Cl^{-} in water^{6}.

In the case of semi-empirical Hamiltonians it is
quite simple to incorporate the effect of solvent into semi-empirical QM/MM
Hamiltonian by adding the interaction energy of an electron with the
electrostatic potential created by solvent (MM atoms) to the one-electron
diagonal elements of Hamiltonian^{1,7,8}:

here* h _{νν}* is the gas phase
one-electron Hamiltonian elements with the ν-

This simple modification is implemented^{5 }in
MOPAC.The required electrostatic potentials on QM atoms from all MM atoms are
calculated with the MOLARIS-XG simulation package, which also calculates the
corresponding QM/MM electrostatic energy derivatives using the charges provided
by MOPAC. This allows to perform almost any QM/MM calculation (e.g. activation
free energy barrier, average dipole moments, absorption and emission spectra).
Furthermore, this functionality allows for a general interface between MOPAC and
any MM program (e.g. GROMACS)

Note that MM program must provide an additional input file mol.in in the following format:

<empty line>

n1 n2

0 0 0 0 φ(*1*)

…

0 0 0 0 φ(*n*)

where
n1 is the number of
atoms, n1 is the number of linked atoms, *n* is number of QM atoms (including link
atoms), and

*
φ(i)* units
are kcal/(mol∙*e*) where *e* is the elementary charge. If the atomic
distance, *r _{ij}*, is given in Ångstroms,
and

This file should be in the directory where MOPAC is
being executed.

The output created by MOPAC includes the effect of environment on energy, heat of formation, charge distribution, dipole moments. Energy derivatives include only QM intra-molecular contributions. However, the QM charge distribution can be used to calculate electrostatic QM/MM contribution to force according to the MM force-field formalism.

The file mol.in provides the various
*
φ(i)*.
These are given in lines 3 on, in column 5, as shown in the following example.
The first line is is skipped, the second line of mol.in should have two integer numbers
that add to the total the total number of atoms. If you are building this
file using an editor, a useful default is to set the first number equal to the
total number of atoms and to make the second number zero. Typically,
this file would be created by the MM program, in which case do not edit the
file.

empty_line 6 0 # of qmmm atoms, # of link atoms in Region I CL -1.591010336 -3.497323620 -4.177329152 119.381953977 C 0.623273531 -3.927769978 -4.243650888 88.802327810 H 0.627631085 -3.831528682 -5.334074435 77.449540155 H 0.737788528 -3.010768158 -3.634868517 83.899739734 H 0.444587282 -4.863821218 -3.677635261 90.477795343 CL 2.837655032 -4.254371189 -4.197078072 120.024810232

Reading is activated by keyword QMMM, that is the PM6.mop input file looks like:

PM6 1SCF CHARGE=-1 GRAD QMMM snapshot of MD step 0 CL -1.5910103360 1 -3.4973236200 1 -4.1773291520 1 C 0.6232735310 1 -3.9277699780 1 -4.2436508880 1 H 0.6276310850 1 -3.8315286820 1 -5.3340744350 1 H 0.7377885280 1 -3.0107681580 1 -3.6348685170 1 H 0.4445872820 1 -4.8638212180 1 -3.6776352610 1 CL 2.8376550320 1 -4.2543711890 1 -4.1970780720 1

Advanced users interested in
implementing the QM/MM interface with MM-packages should use the MOPAC2016 keyword`
AUX` to create an auxiliary file which contains all
the data necessary
for propagating MD trajectories and for MC sampling. To use this function in a
MOPAC job, simply include keyword `AUX`. An example of a typical
keyword line would be:

PM6 1SCF CHARGE=-1 GRAD AUX QMMM

(the keywords `1SCF` and
`GRAD` are both necessary; `1SCF` because the gradients
of the supplied geometry are needed, and `GRAD` because, by default, gradients are
not calculated when `1SCF` is used.)

In the <file>.aux file the corresponding entries for energies, heat of formation, atomic charges and gradients can be found under Final SCF results, e.g.:

# Final SCF results #

….

HEAT_OF_FORMATION:KCAL/MOL=-0.218242D+03

ENERGY_ELECTRONIC:EV=-0.161973D+04

ENERGY_NUCLEAR:EV=+0.938798D+03

DIPOLE:DEBYE=+0.297586D+00

DIP_VEC:DEBYE[3]=
+0.16008D+00 -0.85662D-01 -0.23579D+00

**…
**TOTAL_ENERGY:EV=-0.680928D+03

-0.82604 +0.13275 +0.18844 +0.16625 +0.14813 -0.80953

GRADIENTS:KCAL/MOL/ANGSTROM[0018]=

6.6683 0.2249 1.9733 0.9287 -5.8534 -16.0747 0.2434 6.4429 -7.0648 -3.0670

8.3435 6.1962 -3.9386 -9.9628 13.9620 -0.8348 0.8050 1.0079

The QM/MM approach nowadays is an extremely popular
approach^{2-4}. Due to its low computational cost semi-empirical QM/MM
methods are widely used in molecular dynamics, Monte Carlo and minimization
approaches with variety of different program-specific implementations^{9,10}.
Modeling with the explicit solvent is the most accurate and physically
meaningful way to describe environmental effects, but it comes at a higher
computational cost. For example, the activation free energy barrier calculated^{5}
for a S_{N}2 reaction between methyl chloride and chloride in water is
predicted by the COSMO model to be ~18 kcal/mol, while the PM3/MM
estimate, at 27-29 kcal/mol (for ESP charges and Mulliken charges models ,
respectively) is in perfect agreement with the experimental estimate of 26.6).
Another application is the calculation of vertical excitation energies in polar
environment, e.g. in fluorescent proteins and photoactive dyes, where atomistic
polarizable solvent models are critical for a reliable prediction of
the solvatochromic shift^{11}. Another area where QM/MM with explicit
solvation is advantageous (and essential ) is the evaluation of the binding
free energy in enzymatic binding pockets^{12}

While the treatment of the entire system quantum
mechanically is still very computationally expensive, the QM/MM approach allows
one to explore a numerous problems in biochemistry with a reasonable computational
cost. The accuracy of the semi-empirical QM/MM description can be further improved
by perturbatively moving to a higher level of theory using the Paradynamics
approach^{5}.

In the described QM/MM implementation, the heat of formation and energies reported by MOPAC contain all electrostatic QM/MM coupling terms, including interaction between QM and MM nuclei.

The derivatives, which are read from MOPAC, contain only QM contributions, and the QM/MM electrostatic term is evaluated by the MM program, using the derived charge distribution for QM atoms from MOPAC.

The charge model for QM from MOPAC can be Mulliken or ESP, Mulliken charges are obtained faster but ESP charges are more physical.

(5) Plotnikov, N. V.; Warshel, A.
Exploring, Refining, and Validating the Paradynamics QM/MM Sampling. *The
Journal of Physical Chemistry B***2012**, *116*, 10342-10356. **DOI**: 10.1021/jp304678d. Web-article:
http://dx.doi.org/10.1021/jp304678d