7
1 Hybrid QM/MM Methods: Treating Electronic Phenomena …
the QM method considered. Hence, this scheme cannot be considered as universal
neither.
1.4.3 Frozen Density (And Related Schemes)
Finally, the third class of approaches encompasses all methods dealing with frozen
electronic density (see Fig. 1.1c). Generally, the electronic density is obtained from
orbitals (hybrid orbitals or localized molecular orbitals) determined on small molecules which contain the bond of interest [9, 19, 20]. It is then possible to cut bonds
of any polarity (P–O in DNA for example), or multiplicity. It is even possible to cut
peptide bond, which represent a serious advantage for the study of proteins. The
universality of these methods is however accompanied by an inherent coding complexity. Among these methods, the Local Self-Consistent Field approach (LSCF)
developed in our group since more than fifteen years is detailed in the next section.
1.5 The LSCF Method
The first published QM/MM method using an ab initio Hamiltonian was based on
the LSCF method [19]. The basic ideas of the Local Self Consistent Field, i.e. using frozen strictly localized bond orbitals (SLBO) to describe the bonds separating
the quantum to the classical subsystems, already developed for the semi-empirical
level, have been applied to the ab initio or density functional levels of computation
[20, 62–71]. In the latter cases a difficulty appears due to the fact that overlap between atomic orbital is no longer neglected. Therefore, the molecular orbitals of the
quantum subsystem have to be kept orthogonal to each SLBO. This can be achieved
by an orthogonalization of the basis set to the SLBOs, but owing to the fact that
some functions of the set enter the SLBOs, a linear dependency appears between
the orthogonalized functions. This inconvenience can be overcome by means of a
canonical orthogonalization which yields a set of orthogonal, linearly independent
basis functions which can be used to develop the molecular orbitals of the quantum
subsystem. In order to recall to the reader the general equations used in the LSCF
method, we present below the very basic theory [20].
Solving the LSCF problem implies optimizing a monodeterminantal wavefunction in the orbital approximation knowing that some predefined orbitals are given,
and that these “external” orbitals should remain constant during the optimization
procedure, i.e. frozen. The type of frozen orbitals is completely free. They can be
monatomic, diatomic or polyatomic. In addition they can be occupied or empty. Of
course to link the QM and MM together, they are doubly occupied SLBOs. The
coefficients defining these frozen orbitals, are the only data needed to start the computation and are generally obtained on a simple molecule containing the bond to be
mimicked. Let say that the user gives L frozen orbitals
1,
{ }
i i L
ψ = expanded on the
initial basis set
1,
{ } K
µ µ
ϕ = composed of K real functions.
1 Hybrid QM/MM Methods: Treating Electronic Phenomena …
the QM method considered. Hence, this scheme cannot be considered as universal
neither.
1.4.3 Frozen Density (And Related Schemes)
Finally, the third class of approaches encompasses all methods dealing with frozen
electronic density (see Fig. 1.1c). Generally, the electronic density is obtained from
orbitals (hybrid orbitals or localized molecular orbitals) determined on small molecules which contain the bond of interest [9, 19, 20]. It is then possible to cut bonds
of any polarity (P–O in DNA for example), or multiplicity. It is even possible to cut
peptide bond, which represent a serious advantage for the study of proteins. The
universality of these methods is however accompanied by an inherent coding complexity. Among these methods, the Local Self-Consistent Field approach (LSCF)
developed in our group since more than fifteen years is detailed in the next section.
1.5 The LSCF Method
The first published QM/MM method using an ab initio Hamiltonian was based on
the LSCF method [19]. The basic ideas of the Local Self Consistent Field, i.e. using frozen strictly localized bond orbitals (SLBO) to describe the bonds separating
the quantum to the classical subsystems, already developed for the semi-empirical
level, have been applied to the ab initio or density functional levels of computation
[20, 62–71]. In the latter cases a difficulty appears due to the fact that overlap between atomic orbital is no longer neglected. Therefore, the molecular orbitals of the
quantum subsystem have to be kept orthogonal to each SLBO. This can be achieved
by an orthogonalization of the basis set to the SLBOs, but owing to the fact that
some functions of the set enter the SLBOs, a linear dependency appears between
the orthogonalized functions. This inconvenience can be overcome by means of a
canonical orthogonalization which yields a set of orthogonal, linearly independent
basis functions which can be used to develop the molecular orbitals of the quantum
subsystem. In order to recall to the reader the general equations used in the LSCF
method, we present below the very basic theory [20].
Solving the LSCF problem implies optimizing a monodeterminantal wavefunction in the orbital approximation knowing that some predefined orbitals are given,
and that these “external” orbitals should remain constant during the optimization
procedure, i.e. frozen. The type of frozen orbitals is completely free. They can be
monatomic, diatomic or polyatomic. In addition they can be occupied or empty. Of
course to link the QM and MM together, they are doubly occupied SLBOs. The
coefficients defining these frozen orbitals, are the only data needed to start the computation and are generally obtained on a simple molecule containing the bond to be
mimicked. Let say that the user gives L frozen orbitals
1,
{ }
i i L
ψ = expanded on the
initial basis set
1,
{ } K
µ µ
ϕ = composed of K real functions.