QM/MM simulations

Mo, Y., Gao, J. Polarization and charge-transfer effects in aqueous solution via ah initio QM/MM simulations. J. Phys. Chem. E Lett. 2006, no, 2976-2980. 

Mo Y, Gao J (2000) Ab initio QM/MM simulations with a molecular orbital-valence bond (MOVB) method application to an SN2 reaction in water. J Comput Chem 21(16) 1458—1469... 

In the following, we first briefly review the SCC-DFTB method and comment on a few issues related to the implementation of SCC-DFTB/MM, such as the multi-scale SCC-DFTB/MM-GSBP protocol. Next, a few specific examples of SCC-DFTB/MM simulations are given. The basic motivation is to highlight a number of issues that might impact either the quantitative or even qualitative nature of the result. We hope that the chapter is particularly instructive to researchers who are relatively new to the field and able to help them carry out meaningful QM/MM simulations. 

As in classical simulations of biomolecules, there are two general frameworks for setting up QM/MM simulations for a biological system periodic boundary condition (PBC) and finite-size boundary condition (FBC). When the system of interest is small ( 200-300 amino acids), PBC is well suited because the entire system can be completely solvated and therefore structural fluctuations ranging from the residue level to domain scale can potentially be treated at equal footing, within the limit... 

In this section, we use examples to illustrate several key issues that may significantly impact the reliability of QM/MM simulations of biological systems. In addition, we also discuss calculations that are useful for validating the simulation protocols in realistic applications. 

As discussed in many previous studies of biomolecules, the treatment of electrostatic interactions is an important issue [69, 70, 84], What is less widely appreciated in the QM/MM community, however, is that a balanced treatment of QM-MM electrostatics and MM-MM electrostatics is also an important issue. In many implementations, QM-MM electrostatic interactions are treated without any cut-off, in part because the computational cost is often negligible compared to the QM calculation itself. For MM-MM interactions, however, a cut-off scheme is often used, especially for finite-sphere type of boundary conditions. This imbalanced electrostatic treatment may cause over-polarization of the MM region, as was first discussed in the context of classical simulations with different cut-off values applied to solute-solvent and solvent-solvent interactions [85], For QM/MM simulations with only energy minimizations, the effect of over-polarization may not be large, which is perhaps why the issue has not been emphasized in the past. As MD simulations with QM/MM potential becomes more prevalent, this issue should be emphasized. 

Although water structure and sidechain flexibilities are useful gauges for the simulation protocol, more quantitative measures are needed for reliable QM/MM simulations of enzyme systems. In this regards, we have found that reduction potential [78] and pKa [73,91] calculations are particularly useful benchmark calculations because the results are likely very sensitive to the simulation details. 

The AMl/d-PhoT model [33] is a parameterization of a modified AMl/d Hamiltonian developed specifically to model phosphoryl transfer reactions catalyzed by enzymes and ribozymes for use in linear-scaling calculations and combined QM/MM simulations. The model is currently parametrized for H, O, and P atoms to reproduce... 

Variational electrostatic projection method. In some instances, the calculation of PMF profiles in multiple dimensions for complex chemical reactions might not be feasible using full periodic simulation with explicit waters and ions even with the linear-scaling QM/MM-Ewald method [67], To remedy this, we have developed a variational electrostatic projection (VEP) method [75] to use as a generalized solvent boundary potential in QM/MM simulations with stochastic boundaries. The method is similar in spirit to that of Roux and co-workers [76-78], which has been recently... 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

In typical QM-MM simulations, no dielectric constant is included. Orientational dielectric effects come naturally from reorienting and translation of the elements of the system, providing the system comes to equilibrium. What is left out of the model is electronic polarization of molecules, which makes a minor contribution. 

The authors will provide an all-atom GROMOS topology file, which will greatly facilitate laboratories interested in pursuing QM-MM simulations of voltage-dependent optical responses. 

Callis PR, Vivian JT (2003) Understanding the variable fluorescence quantum yield of tryptophan in proteins using QM-MM simulations. Quenching by charge transfer to the peptide backbone. Chem Phys Lett 369 409-414... 

Callis PR, Liu T (2006) Short range photoinduced electron transfer in proteins QM-MM simulations of tryptophan and flavin fluorescence quenching in proteins. Chem Phys 326 (l) 230-239... 

When a biomolecular system is separated into QM and MM regions one must usually cut amino acid side chains or the protein backbone at covalent bonds (Fig. 5.2 a). The construction of the covalent boundary between the QM and MM parts is key to accurate results from QM/MM calculations. Because there is no unique way to treat the covalent boundary, several different approaches have been described. In the first applications of coupled QM/MM simulations link atoms were used to create the covalent QM/MM boundary (Fig. 5.2b). Link atoms are atoms added to the QM part to fill the broken valences of the boundary QM atoms. These atoms are placed along the broken QM/MM bond at a distance appropriate for the QM bond added. The link atoms have usually been hydrogen atoms but methyl groups and pseudohalogen atoms have also been used [35]. 

Gao, J. Combined QM/MM simulation study of the Claisen rearrangement of allyl vinyl ether in aqueous solution, JAm.Chem.Soc., 116(1994), 1563-1564... 

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

According to these considerations three subregions are defined as depicted in Fig. 1. The inner and outer parts of the QM region are termed the QM core and QM layer zone, respectively. As discussed solutes in the QM core do not require the application of non-Coulombic potentials—composite species with complex potential energy surfaces can be treated in a straightforward way, while complex potential functions are required in the case of classical and even conventional QM/MM simulation studies. Interactions at close solute-solvent distances are treated exclusively via quantum mechanics and account for polarization, charge transfer, as well as many-body effects. The solute-solvent... 

The study of composite cations encounters further problems for classical and conventional QM/MM simulations, as their lower symmetry makes the evaluation of interaction energy surfaces and analytical potential functions describing them difficult. In these cases the QMCF MD method provides an elegant solution as well, renouncing solute-solvent potential functions. This advantage could be well demonstrated in studies on the dimer of Hg(I) (39), the titanyl ion (64), and the uranyl ions of U(V) (65) and U(VI) (66). Whereas the Hg + ion still has a fairly regular hydration structure although with a quite peculiar shape, the... 

Of course, the rich information available from a QM/MM simulation does not come without cost. The QM/MM Claisen simulation required several million AMI calculations to be carried out while AMI is a very efficient level of QM theory for a molecule as small as allyl vinyl ether, that still represents an enormous investment of computational resources. As a result, the application of QM/MM methodologies based on the formalism of Eqs. (13.4) and (13.5) has tended not to be especially systematic, i.e., choices of QM and MM models and necessary coupling parameters have tended to be made on an ad hoc basis, without regarding parameter transferability as being an issue of paramount concern. 

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