Quantum mechanical/free energy

In this chapter the basic theory of the structurally coupled QM/MM is summarized. This is followed by some technical points important in the practical use of the method. In particular, details about the treatment of the QM/MM boundary are discussed. The thermodynamically coupled quantum mechanical/ free energy (QM/FE) method is then introduced. Some representative applications of QM/MM methods are then described. The examples are selected to provide a representative picture of the potential applications of QM/MM methods on studies of reaction mechanisms. Here there is special emphasis on recent advances in the computational methodologies and in the future developments needed to improve the applicability of the methods. 

Jorgensen et al. [49] developed a combined quantum mechanical and molecular mechanical approach for study of organic reactions and applied it with success to many solution reactions. Inspired by this Kollman et al. [50, 51] developed the approach further for study of enzyme reactions. This quantum mechanical/free energy (QM/... 

Kollman, P. A. Kuhn, B. Donini, O. Perakyla, M. Stanton, R. Bakowies, D. Elucidating the nature of enzyme catalysis utiUzing a new twist on an old methodology Quantum mechanical-free energy calculations on chemical reactions in enzymes and in aqueous solution, Acc. Chem. Res. 2000, 34, 72-79. 

The quantum mechanical free energy barrier, A.g, can be evaluated by Feynman s path integral formulation [59], where each classical coordinate is replaced by a ring of quasiparticles that are subjected to the effective quantum mechanical potential... 

Wood, R. H. Yezdimer, E. M. Sakane, S. Barriocanal, J. A. Doren, D. J., Free energies of solvation with quantum mechanical interaction energies from classical mechanical simulations, 7. Chem. Phys. 1999,110, 1329-37... 

Ridder, L. Rietjens, I.M. Vervoort, J.A. Mulholland, A., Quantum mechani-cal/molecular mechanical free energy simulations of the glutathione S-transferase (Ml-1) reaction with phenanthrene 9,10-oxide, J. Am. Chem. Soc. 2002,123, 9926-9936. 

A new, more general, way to combine ab initio quantum mechanical calculations with classical mechanical free-energy perturbation approach (QM/FE approach) to calculate the energetics of enzyme-catalysed reactions and the same reaction in solution has been reported." The calculated free energies were in fairly good agreement with the experimental data for the activation energies of the first test case, amide hydrolysis in trypsin and in aqueous solution. 

Woods, C.J., Manby, F.R., Mulholland, A.J. An efficient method for the calculation of quantum mechanics/molecular mechanics free energies. J. Chem. Phys. 2008,128, 014109. 

With these expressions we can calculate thermodynamic averages, for instance the energy of the quantum mechanical free particle, which involves matrix elements of the hamiltonian in the position representation given by... 

Yao, Y, Liu, J., Zhan, C.G., 2012. Why does the G117H mutation considerably improve the activity of human butyrylcholinesterase against sarin Insights from quantum mechanical/molecular mechanical free energy calculations. Biochemistry 51, 8980-8992. 

The second model is a quantum mechanical one where free electrons are contained in a box whose sides correspond to the surfaces of the metal. The wave functions for the standing waves inside the box yield permissible states essentially independent of the lattice type. The kinetic energy corresponding to the rejected states leads to the surface energy in fair agreement with experimental estimates [86, 87],... 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

Torsional barriers are referred to as n-fold barriers, where the torsional potential function repeats every 2n/n radians. As in the case of inversion vibrations (Section 6.2.5.4a) quantum mechanical tunnelling through an n-fold torsional barrier may occur, splitting a vibrational level into n components. The splitting into two components near the top of a twofold barrier is shown in Figure 6.45. When the barrier is surmounted free internal rotation takes place, the energy levels then resembling those for rotation rather than vibration. 

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