5
1 Hybrid QM/MM Methods: Treating Electronic Phenomena …
give the electronic wave function. If this interaction is considered one speaks about
Electronic (or Electrostatic) Embedding, depending if it is included (or not) in the
QM Hamiltonian. Taking into account this embedding with the additive scheme is
straightforward. For the subtractive portioning, special care has to be taken. One has
to note that, independently of the partitioning, the charge distribution of the MM
system is not perturbed by the polarization of the QM part.
1.3.3 Polarizable Embedding (PE)
Rigorously speaking, if the MM part polarized the QM region, in turn the QM region
should polarize the MM part and so on until convergence is reached. Some specific
force fields, which allow such procedure, are said to be polarizable (AMOEBA,
TCPEp, SIBFA, …) [28–30, 49, 50, 52, 53]. Another approach, called Electronic
Response of the Surrounding (ERS), that uses the dynamical part of the dielectric
constant of a polarizable continuum, is developed in our group [9, 54–61]. One
speaks of Polarizable Embedding when such level of sophistication is used. Although, PE is certainly the most realistic possible QM/MM simulation, it is barely
used and EE is the standard. The reason behind is not the laziness of theoretical
chemists but the way force fields parameters are defined. In fact, most of the (nonpolarizable) force fields define the atomic point charges in such a way to reproduce
condensed phase properties. Thus the MM point charges are implicitly polarized
and the EE level is sufficient. It exist however some situations for which the PE approximation is mandatory: when the force field parameters are based on gas phase
data, or when the electronic variations of the QM part are drastic (for example for
some chemical reactions like Menshutkin’s one or for electronic transitions between
states of different nature). PE calculations with the additive partitioning are straightforward from a theoretical point of view. Within the subtractive decomposition of
the total Hamiltonian one has to modify further the initial methodology.
Up to now, the partitioning of the Hamiltonian and the Embedding of the QM
part are enough to discriminate between QM:MM methods (in addition to the trivial
differentiation induced by the methods used for the QM and the MM parts). For
QM–MM methods, one needs to go one step further and to consider the way they
connect the MM part to the QM one, since formally covalent bonds of the total
molecule are cut and have to be modeled.
1.4 QM–MM Junctions
Whatever the connection scheme, the frontier atom on the QM side must possess
classical parameters for the bonded terms linking the two fragments. The most common habit is to include all MM bonded interactions when at least one MM atom is
involved. However, this implies to define connectivity inside the QM region which
could be incompatible with the investigated chemical process. This induces an intrinsic limitation to the smallest size the QM part can have.
1 Hybrid QM/MM Methods: Treating Electronic Phenomena …
give the electronic wave function. If this interaction is considered one speaks about
Electronic (or Electrostatic) Embedding, depending if it is included (or not) in the
QM Hamiltonian. Taking into account this embedding with the additive scheme is
straightforward. For the subtractive portioning, special care has to be taken. One has
to note that, independently of the partitioning, the charge distribution of the MM
system is not perturbed by the polarization of the QM part.
1.3.3 Polarizable Embedding (PE)
Rigorously speaking, if the MM part polarized the QM region, in turn the QM region
should polarize the MM part and so on until convergence is reached. Some specific
force fields, which allow such procedure, are said to be polarizable (AMOEBA,
TCPEp, SIBFA, …) [28–30, 49, 50, 52, 53]. Another approach, called Electronic
Response of the Surrounding (ERS), that uses the dynamical part of the dielectric
constant of a polarizable continuum, is developed in our group [9, 54–61]. One
speaks of Polarizable Embedding when such level of sophistication is used. Although, PE is certainly the most realistic possible QM/MM simulation, it is barely
used and EE is the standard. The reason behind is not the laziness of theoretical
chemists but the way force fields parameters are defined. In fact, most of the (nonpolarizable) force fields define the atomic point charges in such a way to reproduce
condensed phase properties. Thus the MM point charges are implicitly polarized
and the EE level is sufficient. It exist however some situations for which the PE approximation is mandatory: when the force field parameters are based on gas phase
data, or when the electronic variations of the QM part are drastic (for example for
some chemical reactions like Menshutkin’s one or for electronic transitions between
states of different nature). PE calculations with the additive partitioning are straightforward from a theoretical point of view. Within the subtractive decomposition of
the total Hamiltonian one has to modify further the initial methodology.
Up to now, the partitioning of the Hamiltonian and the Embedding of the QM
part are enough to discriminate between QM:MM methods (in addition to the trivial
differentiation induced by the methods used for the QM and the MM parts). For
QM–MM methods, one needs to go one step further and to consider the way they
connect the MM part to the QM one, since formally covalent bonds of the total
molecule are cut and have to be modeled.
1.4 QM–MM Junctions
Whatever the connection scheme, the frontier atom on the QM side must possess
classical parameters for the bonded terms linking the two fragments. The most common habit is to include all MM bonded interactions when at least one MM atom is
involved. However, this implies to define connectivity inside the QM region which
could be incompatible with the investigated chemical process. This induces an intrinsic limitation to the smallest size the QM part can have.