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A. Monari and X. Assfeld
1.3 QM/MM Embeddings
The way the QM part feels the presence of the MM surroundings is called embedding. Prior to detail the various possible embeddings, it is important to recall the
elementary particles of each part and how they interact.
The MM force fields consider a set of connected atoms (point masses). The
atomic interactions are divided in two families: the bonded ones (stretching, bending, torsion) and the non-bonded ones (mainly electrostatic and van der Waals interactions). Some elaborated force fields allow the atomic point charges to vary
according to their environment (polarization). Albeit the lack of explicit description
of the electrons and nuclei is a strong limitation of MM methods, the main restriction of the MM representation is the predefined and fixed connectivity between the
atoms.
The QM part is composed by a set of nuclei surrounded by electrons, and in absence of external field, solely the coulombic interaction is considered.
The QM/MM interactions are classified in three categories listed below.
1.3.1 Mechanical Embedding (ME)
The surroundings create geometrical constrains on the QM part. For QM:MM methods, only non-bonded interactions are responsible for these constrains (mainly van
der Waals, but electrostatic repulsion or attraction can also have a non-negligible
effect). They define regions of space that exclude the QM atoms and consequently
modify its geometry. For QM–MM methods, the terms corresponding to bonded
interactions between the QM part and the close-by MM atoms also play a major
role. One has to note that van der Waals parameters need to be attributed to QM
atoms (most of the time these parameters are those of the used force field, but one
can optimize them [51]). If the QM part doesn’t feel the electrostatic field of the
MM surroundings, i.e. only when bonded and van der Waals QM/MM interactions
are considered, one speaks about Mechanical Embedding. In this approximation the
additive and the subtractive partitioning would give the same answer, since the QM
electronic wave function is only affected through geometrical polarization. This approximation is suitable only for very weak polar, or isotropic, environment.
1.3.2 Electrostatic Embedding (EE)
Most of the time, the charge distribution of the MM region is anisotropic and this
results in a non uniform external electrostatic field felt by the QM fragment. As a
consequence, the electronic cloud of the QM region is polarized and the physical
properties are then greatly modified. This electrostatic QM/MM interaction is then
of primary importance and has to be taken into account for, of course, the calculation of the total energy of the whole system, but also in the Hamiltonian which will
A. Monari and X. Assfeld
1.3 QM/MM Embeddings
The way the QM part feels the presence of the MM surroundings is called embedding. Prior to detail the various possible embeddings, it is important to recall the
elementary particles of each part and how they interact.
The MM force fields consider a set of connected atoms (point masses). The
atomic interactions are divided in two families: the bonded ones (stretching, bending, torsion) and the non-bonded ones (mainly electrostatic and van der Waals interactions). Some elaborated force fields allow the atomic point charges to vary
according to their environment (polarization). Albeit the lack of explicit description
of the electrons and nuclei is a strong limitation of MM methods, the main restriction of the MM representation is the predefined and fixed connectivity between the
atoms.
The QM part is composed by a set of nuclei surrounded by electrons, and in absence of external field, solely the coulombic interaction is considered.
The QM/MM interactions are classified in three categories listed below.
1.3.1 Mechanical Embedding (ME)
The surroundings create geometrical constrains on the QM part. For QM:MM methods, only non-bonded interactions are responsible for these constrains (mainly van
der Waals, but electrostatic repulsion or attraction can also have a non-negligible
effect). They define regions of space that exclude the QM atoms and consequently
modify its geometry. For QM–MM methods, the terms corresponding to bonded
interactions between the QM part and the close-by MM atoms also play a major
role. One has to note that van der Waals parameters need to be attributed to QM
atoms (most of the time these parameters are those of the used force field, but one
can optimize them [51]). If the QM part doesn’t feel the electrostatic field of the
MM surroundings, i.e. only when bonded and van der Waals QM/MM interactions
are considered, one speaks about Mechanical Embedding. In this approximation the
additive and the subtractive partitioning would give the same answer, since the QM
electronic wave function is only affected through geometrical polarization. This approximation is suitable only for very weak polar, or isotropic, environment.
1.3.2 Electrostatic Embedding (EE)
Most of the time, the charge distribution of the MM region is anisotropic and this
results in a non uniform external electrostatic field felt by the QM fragment. As a
consequence, the electronic cloud of the QM region is polarized and the physical
properties are then greatly modified. This electrostatic QM/MM interaction is then
of primary importance and has to be taken into account for, of course, the calculation of the total energy of the whole system, but also in the Hamiltonian which will