10
A. Monari and X. Assfeld
contrast to the initial approach called LSCF + 1. Many results have shown that the
LSCF + 3 scheme reproduces satisfactorily the position of the minimum as well as
the curvature obtained with the full quantum results, the error on the equilibrium
distance being less than 0.1 Å [9]. Of course, no agreement can be obtained for long
interatomic distances because the SLBO is only valid in the vicinity of the distance
at which it has been obtained. This scheme has been extended successfully to the
peptide bond where the C atom is at the MM frontier. It has also been extended to
the same bonds in which the quanto-classical atom is the nitrogen atom. In this case,
adding two extra valence electrons, those contained in the orbital conjugated with
the C=O π orbital, is mandatory. The acronym is then trivially LSCF + 5. This method is free of fitted parameters and allows a symmetric description of the amino acid
residues without the arbitrariness of adjusting the classical point charges to obtain
an integer value. This procedure is particularly attractive for QM/MM calculations
on proteins since it permits to directly cutting through a peptide bond, keeping the
electron delocalization occurring at the amide bond. Indeed by using LSCF + 3 and
LSCF + 5 cutting scheme we have shown that the QM/MM equilibrium geometry
of a tripeptide in which only the central monomer is treated with QM reproduces
well the equilibrium geometry of the full QM systems, both for bond lengths and
angles. In particular the planarity of the amide groups is always perfectly respected
confirming the fact that the electron delocalization is taken into account whatever
atom between C and N is treated as quanto-classical. The link atom approaches
which use hydrogen atom to saturate the dangling bond are of course not able to
reproduce this feature.
Several localization procedures exist and many have been tested in the LSCF
framework [73–80]. It has been shown that, when one is interested in relative energies, the results do not depend on the localization scheme.
One can thus consider that the LSCF method is universal in the sense that it can
be applied to any MM and QM methods, to bonds of any polarity and multiplicity.
1.6 Applications
We will present here some applications of QM/MM methods to the treatment of
problems related to biological systems. Although these methods have been initially
developed to deal with enzymatic catalysis or biochemical reactivity in general [81,
82], they are nowadays also applied to study the photophysics or photochemistry
of complex biological systems. In this chapter, we will focus on the calculations
of electronic excited states and on the different effects of the environment induced
on the different chromophores [83–85]. We will consider systems in which the
chromophore being covalently bounded to the macromolecule the use of QM–MM
methods will be necessary, together with different cases in which QM:MM allows
to treat non-covalently bounded systems. Finally the role and the necessity of a
proper sampling of different conformations with using MD techniques using MD
techniques will be tackled and discussed.
A. Monari and X. Assfeld
contrast to the initial approach called LSCF + 1. Many results have shown that the
LSCF + 3 scheme reproduces satisfactorily the position of the minimum as well as
the curvature obtained with the full quantum results, the error on the equilibrium
distance being less than 0.1 Å [9]. Of course, no agreement can be obtained for long
interatomic distances because the SLBO is only valid in the vicinity of the distance
at which it has been obtained. This scheme has been extended successfully to the
peptide bond where the C atom is at the MM frontier. It has also been extended to
the same bonds in which the quanto-classical atom is the nitrogen atom. In this case,
adding two extra valence electrons, those contained in the orbital conjugated with
the C=O π orbital, is mandatory. The acronym is then trivially LSCF + 5. This method is free of fitted parameters and allows a symmetric description of the amino acid
residues without the arbitrariness of adjusting the classical point charges to obtain
an integer value. This procedure is particularly attractive for QM/MM calculations
on proteins since it permits to directly cutting through a peptide bond, keeping the
electron delocalization occurring at the amide bond. Indeed by using LSCF + 3 and
LSCF + 5 cutting scheme we have shown that the QM/MM equilibrium geometry
of a tripeptide in which only the central monomer is treated with QM reproduces
well the equilibrium geometry of the full QM systems, both for bond lengths and
angles. In particular the planarity of the amide groups is always perfectly respected
confirming the fact that the electron delocalization is taken into account whatever
atom between C and N is treated as quanto-classical. The link atom approaches
which use hydrogen atom to saturate the dangling bond are of course not able to
reproduce this feature.
Several localization procedures exist and many have been tested in the LSCF
framework [73–80]. It has been shown that, when one is interested in relative energies, the results do not depend on the localization scheme.
One can thus consider that the LSCF method is universal in the sense that it can
be applied to any MM and QM methods, to bonds of any polarity and multiplicity.
1.6 Applications
We will present here some applications of QM/MM methods to the treatment of
problems related to biological systems. Although these methods have been initially
developed to deal with enzymatic catalysis or biochemical reactivity in general [81,
82], they are nowadays also applied to study the photophysics or photochemistry
of complex biological systems. In this chapter, we will focus on the calculations
of electronic excited states and on the different effects of the environment induced
on the different chromophores [83–85]. We will consider systems in which the
chromophore being covalently bounded to the macromolecule the use of QM–MM
methods will be necessary, together with different cases in which QM:MM allows
to treat non-covalently bounded systems. Finally the role and the necessity of a
proper sampling of different conformations with using MD techniques using MD
techniques will be tackled and discussed.