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Multiscale Modeling

Since the beginning of First-Principles (ab initio) Molecular Dynamics, about 20 years ago [Car and Parrinello, PRL 1985], an increasing number of problems in physics,  material science, chemistry, biophysics and biochemistry have been tackled through a detailed description of the electronic structure dynamics of atoms, solids and molecules. First-principles MD techniques, mostly based on Density Functional Theory and the Car-Parrinello method, allows us nowadays to explore the evolution in time of the electronic structure of hundred of atoms  on the pico-second time scale.
In order to study larger molecular systems, like the ones of interest in Molecular Biophysics, the methods has been recently extended to a mixed Quantum Mechanical / Molecular Mechanical (QM/MM) hybrid schemes [Laio,Vandevondele and Rothlisberger J.Chem.Phys. 2002, 116, 6941]. This approach is able to treat the atoms belonging to the reactive part of the full system (i.e. the active site of an enzyme) at the full quantum level, whereas the rest of the atoms are treated at the force-field level (i.e. the rest of the protein and the solvent).



Exploring Reactivity via Electronic Reaction Coordinates

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Chemical reactions are usually described using approximate reaction coordinates that are expressed as a function of the ionic positions (such as bonds, angles, dihedrals). Whereas for some chemical reactions the definition of partial reaction coordinates can be a reasonable assumption, for many others, that for instance involve ionic collective motions or dynamic solvent effects, a proper reaction coordinate cannot be easily expressed via a trivial combination of ionic degrees of freedom.
Reactivity indexes such as hardness, softness and Fukui Functions may provide interesting insights into the reactivity pathways, especially in their Density Functional Theory formulation [Parr, R. G.; Yang, W. J.A.C.S.1984, 106, 4049-4050]. Recently, [L. Guidoni, U. Rothlisberger, J. Chem. Theo. and Comp., in press 2005 (pdf)], we introduced in the DFT framework reaction coordinates that only explicitly depends on the electronic degrees of freedom of the reactive system. This ‘Electronic Reaction Coordinate’, which is expressed in terms of a penalty function of the one-electron orbital energies, has been applied to study reaction pathways of the butadiene in vacuo.
Using only electronic degrees of freedom, three reactive channels have been identified in s-cis-butadiene: the s-cis/s-trans isomerization, the cis/trans isomerization, and the symmetry allowed cyclization. Interestingly for the latter case, despite the fact that Woodward-Hoffmann rules are guided by the butadiene frontier orbitals, the introduction of an electronic reaction coordinate which involves only these orbitals is not enough to drive the system towards cyclization. A low-lying valence shell orbital (see figure) needs to be included. Thermodynamical quantities like the activation free energy are also calculated along the electronic reaction coordinates in fair agreement with previous reports.
This Orbital Biased Molecular Dynamics has been also implemented within the QM/MM framework to explore different chemical pathways in enzyme catalysis.  
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 Within 1ps of first-principles MD, Electronic Reaction coordinates drive  butadiene
  towards ciclization across a 45 kcal/mol-hight energy barrier
 

QMC/MM Quantum Monte Carlo / Molecular Mechanics

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Few biophysical systems require the choice of Quantum Mechanical methods which go beyond standard Density Functional techniques. Indeed, the latter show some limitations in delicate cases like: near-half-filled transition metal compounds (such as Cr,Co,Fe,Ni,Mn), systems where dispersion forces are relevant, and excited states. In particular, accurate calculations of molecular excitations in solution and in condensed complex environments like proteins are still a challenge for both Density Functional Theory and other more sophisticated quantum chemistry methods. Recently, has been shown that Quantum Monte Carlo (QMC) can accurately estimate excitation energies also in delicate cases like conjugated systems [Schautz, Buda, Filippi, J. Chem. Phys. 2004,120, 10931]. We are currently combining Quantum Monte Carlo calculations with QM/MM Car-Parrinello dynamics to allow a  many body study of electronic excitations of biological chromophores in situ. 

 

                  qmcmm

 Low energy excitation of acetone in water calculated by hybrid QMC/MM simulations


 



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