12.3 Stand-Alone QM/MM Calculations

12.3.1 Available QM/MM Methods and Features

Three modes of operation are available:

  • MM calculations only (no QM)

  • QM/MM calculations using a two-layer ONIOM model with mechanical embedding

  • QM/MM calculations using the Janus model for electronic embedding

Q-Chem can carry out purely MM calculations, wherein the entire molecular system is described by a MM force field and no electronic structure calculation is performed. The MM force fields available at present are AMBER,958 CHARMM,268 and OPLSAA.438

As implemented in Q-Chem, the ONIOM model948 is a mechanical embedding scheme that partitions a molecular system into two subsystems (layers): an MM subsystem and a QM subsystem. The total energy of an ONIOM system is given by

Etotal=EtotalMM-EQMMM+EQMQM (12.34)

where EtotalMM is the MM energy of the total system (i.e., QM + MM subsystems), EQMMM is the MM energy of the QM subsystem, and EQMQM is the QM energy of the QM subsystem. MM energies are computed via a specified MM force field, and QM energies are computed via a specified electronic structure calculation.

The advantage of the ONIOM model is its simplicity, which allows for straightforward application to a wide variety of systems. A disadvantage of this approach, however, is that QM subsystem does not interact directly with the MM subsystem. Instead, such interactions are incorporated indirectly, in the EtotalMM contribution to the total energy. As a result, the QM electron density is not polarized by the electrostatic charges of the MM subsystem.

If the QM/MM interface partitions the two subsystems across a chemical bond, a link atom (hydrogen) must be introduced to act as a cap for the QM subsystem. Currently, Q-Chem supports only carbon link atoms, of atom type 26, 35, and 47 in the CHARMM27 force field.

The Janus model824 is an electronic embedding scheme that also partitions the system into MM and QM subsystems, but is more versatile than the ONIOM model. The Janus model in Q-Chem is based upon the “YinYang atom” model of Shao and Kong.831 In this approach, the total energy of the system is simply the sum of the subsystem energies,

Etotal=EMM+EQM (12.35)

The MM subsystem energy, EMM, includes van der Waals interactions between QM and MM atoms but not QM/MM Coulomb interactions. Rather, EQM includes the direct Coulomb potential between QM atoms and MM atoms as external charges during the QM calculation, thus allowing the QM electron density to be polarized by the MM atoms. Because of this, Janus is particularly well suited (as compared to ONIOM) for carrying out excited-state QM/MM calculations, for excited states of a QM model system embedded within the electrostatic environment of the MM system. Within a Janus calculation, Q-Chem first computes EMM with the specified force field and then computes EQM with the specified electronic structure theory.

When the Janus QM/MM partition cuts across a chemical bond, a YinYang atom831 is automatically introduced by Q-Chem. This atom acts as a hydrogen cap in the QM calculation, yet also participates in MM interactions. To retain charge neutrality of the total system, the YinYang atom has a single electron and a modified nuclear charge in the QM calculation, equal to qnuclear=1+qMM (i.e., the charge of a proton plus the charge on the YinYang atom in the MM subsystem).

Because this modified charge will affect the bond containing the YinYang atom, an additional repulsive Coulomb potential is applied between the YinYang atom and its connecting QM atom to maintain a desirable bond length. The additional repulsive Coulomb energy is added to EMM. The YinYang atom can be an atom of any kind, but it is highly recommended to use carbon atoms as YinYang atoms.

Q-Chem’s stand-alone QM/MM capabilities also include the following features:

  • Analytic QM/MM gradients are available for QM subsystems described with density functional theory (DFT) or Hartree-Fock (HF) electronic structure theory, allowing for geometry optimizations and QM/MM molecular dynamics.

  • Single-point QM/MM energy evaluations are available for QM subsystems described with most post-HF correlated wave functions.

  • Single-point QM/MM calculations are available for excited states of the QM subsystem, where the latter may be described using CIS, TDDFT, or correlated wave function models. Analytic gradients for excited states are available for QM/MM calculations if the QM subsystem is described using CIS.

  • Single-point MM or QM/MM energy evaluations and analytic gradients are available using periodic boundary conditions with Ewald summation.

  • Implicit solvation for both Janus QM/MM calculations as well as MM-only calculations is available using the Polarizable Continuum Models (PCMs) discussed in Section 12.2.2.

  • Gaussian blurring of MM external charges is available for Janus QM/MM calculations.

  • User-defined MM atoms types, MM parameters, and force fields.