QM-Cluster Calculations

Embedded QM calculations Embedded QM cluster calculations within bulk region minimised by pair potential methods ... 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

Thus, these simple QM-cluster calculations gave deep insight into Nature s design of the three families of mono-nuclear Mo oxo-transfer enzymes. We have found that the Mo ligands are not selected to make the oxo-transfer reactions as favourable as possible, but rather exothermic by a minimal amount of energy. This is important, because the active-site must be re-reduced or re-oxidized after the oxo-transfer reaction and the reaction must also be favourable. The reduction of DMSO is trivial and can be performed by all three families. The oxidation of sulfite is also rather simple, provided that the repulsion between the active site and the substrate can be overcome. However, the hydroxylation of xanthine is much more complicated and seems to require a unique MoOS active site, in which the S ligand makes the formal hydride-transfer reaction possible. 

Adsorption experiments with CO have conclusively shown that CO adsorbs weakly on the MgO terrace but more strongly on edges and corners sites. Using QM cluster calculations, Petterson et al.I l predicted CO adsorption values of 8, 18 and 48 kJ/mol for the terrace, corner and edge sites, respectively. The adsorption of CO at terrace, edge, and kink sites was found to lead to an upward shift in the CO stretching frequency by - -9, +27 and +50 cm , respectively. These results are consistent with the generally accepted experimental data on this system of Wichtendahl et al. . 

We have employed an embedded cluster approach in which a QM cluster was embedded into a finite nano-cluster representation of the polarisable host lattice via the shell model. Relaxation of both electronic and ionic subsystems of the host lattice is performed self-consistently with the charge density of the QM cluster calculated using the B3LYP density functional. The self-consistent scheme of calculations has been described in more details elsewhere [82,83], The QM cluster used in these studies is shown in Fig, 4,5a, All anions and all fully coordinated cations have been treated as all electron atoms using the standard 6-3IG basis set. Cations at the border of the QM cluster have been treated using Hay and Wadt effective core pseudopotentials [84] and one contracted s-function. 

Figure 3.6 Molecule-Ti02 interfaces used to investigate ultrafast interfacial electron transfer processes. Increased system interaction complexity is illustrated for periodic surface QM calculations of a binding ligand on a clean rutile (110) surface (left), QM cluster calculations of a complete dye molecule (RuN3) in a nanocrystalline environment (middle) and a multiscale MD simulation (right), highlighting both differences and similarities.

These QM/MM calculations are in contrast to a standard evaluation of chemical shielding for gas phase water clusters where the classical point charge environment is omitted entirely. The same solvation shell criterion as before was applied, and the system was treated purely quantum mechanically. 

The resulting data are shown in Fig. 1.4, in which is plotted the isotropic NMR chemical shift of all 128 protons, obtained from the QM/MM and the isolated cluster calculations as a function of the fully periodical quantum mechanical results. 

Figure 1.4 shows a significant deviation between the isolated cluster calculations and the full calculation. The situation is, however, considerably improved by the presence of the classical point charges in the QM/MM calculation. Here the whole bandwidth of chemical shielding constants is present, and correlation with the reference values is excellent. 

DFT calculations remarkably well reproduce the experimental bonding parameters which indicate that the protein environment does not impose an energetically unfavourable conformation on the active centre. Amara et al. (1999) report an effect of the protein environment in their QM/MM calculations. This may, however, be due to their convergence on an S =f spin state for the cluster in vacuo and on an S = I spin state when the protein environment is considered. 

The approaches based on explicit representations of the environment molecules include full quantum mechanical (QM) and hybrid QM/MM methods. In the former, the supramolecular system that is the object of the calculations cannot be very large for instance, it can be composed of the chromophore and a few solvent molecules ( cluster or microsolvation approach). A full QM calculation can be combined with PCM to take into account the bulk of the medium [5,13], which is also a way to test the accuracy of the PCM and of its parameterization, by comparing PCM only and PCM+microsolvation results. The full QM microsolvation approach is recommended when dealing with chromophore-environment interactions that are not easily modelled in the standard ways, such as those involving Rydberg states. An example is the simulation of the absorption spectrum of liquid water, by calculations on water clusters (all QM), clusters + PCM, and a single molecule + PCM only the cluster approach (with or without PCM) yielded results in agreement with experiment [13] (but we note that this example does not conform to the above requirement for a clear distinction between chromophore and environment). 

The periodic approach is not the only one available for atomistic simulations of these materials and we should first mention that much progress has been made in the application of molecular quantum chemical methods using cluster representations of the local structure of oxide materials [1, 2], More recently, this has given way to mixed quantum mechanics/molecular mechanics (QM/MM) calculations. In QM/MM simulations the important region, the active site for catalysis, is represented at a quantum chemical level while the influence of its environment, the extended solid, is represented using the computationally less-demanding atomistic force field approach. This allows complex structures such as metal particles supported on oxides to be tackled [3]. 

Even well-made TS-1 contains a small fraction of Si-vacancy defects [73,74]. Consistent with FTIR results on H2O2/TS-I [75], previous DPT calculations on nondefect (tetrapodal) and metal-vacancy defect (tripodal) Ti sites in TS-1 suggested that H2O2 attack on Ti-defect sites leads to Ti-OOH species (and water), while H2O2 attack on Ti-nondefect sites is kinetically and thermodynamically less favorable [76]. Moreover, Ti-OOH species can catalyze propylene epoxidation to PO [76-78]. Recent QM/MM calculations on adsorption of Aui 5 clusters inside the TS-1 pores suggest that the Ti-defect site is also the most favorable binding site for small Au clusters [66]. Therefore, defects in TS-1 are likely to stabilize adsorbed Au clusters and prevent sintering. 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

Perhaps the most accurate calculations performed to date are the MP2, LMP2, and LCCSD(TO) calculations on chorismate mutase (CM) and para hydroxy-benzoate-hydroxylase (PHBH) (the L in the acronyms indicates that local approximations were used, and TO is an approximate triples correction).41,42 These are coupled-cluster calculations that account for the effects of conformational fluctuations through an averaging over multiple pathways (16 for CM and 10 for PHBH). Initial structures were sampled from semiempirical QM/MM dynamics, using B3LYP/MM optimized reaction pathways. 

Fig. 2.2. Space partitioning in EPE embedded cluster calculations. I - internal region treated at a QM level II - shell model enviromnent of the QM cluster subdivided into regions of explicit optimization (Ila), of the effective (Mott-Littleton) polarization (lib) and of the external area (lie). The sphere indicates an auxiliary surface charge distribution which represents the Madelung field acting on the QM cluster (dashed line).

For our DF calculations of adsorption complexes on an a-Al203(0001) surface, discussed below, it is important to inspect how accurately the structure of the clean surface is described in the EPE embedding scheme. We demonstrated [74] that the force field [100], employed to model the environment of QM clusters, is able to reproduce fairly well the structure of both a-Al203 bulk and the strongly relaxed (0001) surface. This agreement between the results... 

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