Replica Hamiltonian

Obviously it is much easier to perform averaging of a power instead of the logarithm. Replicating the system (Hamiltonian H) n-times allows rewriting Z" ( r ) in terms of multiple integrals (replica... 

Fukunishi, O. Watanabe Takada, S., On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems application to protein structure prediction, J. Chem. Phys. 2002,116, 9058-9067... 

This chapter highlighted the use of replica exchange molecular dynamics calculations for the investigation of the performance of the PM3, PDDG/PM3 and PM3PC Hamiltonians as applied for the conformational equilibrium of alanine dipeptide in the gas phase and water solution, a convenient model system for the study of biological molecules. 

Therefore, on the basis of the averaged Hamiltonian (5.2.4), a resonance of the standard mapping located at I = 2m7r overlaps with its next replica located at I = 2 m -I- 1)7T if Al = 2tt. This yields... 

Additionally, non-Hamiltonian d5mamics can be used in applications/ methodologies such as Path-integral MD, replica-exchange methods, variable transformation techniques, free energy dynamics methods, and other new applications. Generating these alternative statistical ensembles from simulation requires the use of extended systems or extended phase space [9]. In these systems, the simulations do not only include the N coordinate and momentum vectors that are needed to describe a classical Ai-particle system, but they also include a set of additional control or extended variables that are used to drive the fluctuations required by the ensemble of interest. 

The quantity ( Jj(f)l I j(O)) is the autocorrelation function of the electronic-vibrational state function created at time t = 0 with a replica of itself evolved from time 0 to time t under the influence of the excited state vibrational Hamiltonian. Thus, the standard Eq. (9.1.9) expression, in terms of individual transition frequencies and transition relative intensities, for a complete e, v e <— g, v" absorption spectrum, may alternatively be viewed as the Fourier transform of the autocorrelation function, Eq. (9.1.16). 

If we take a three chain system, the corresponding effective Hamiltonian will involve only the three chain term but no four chain interaction of Eq. (76). There is now the possibility of a disorder induced multicritical behavior. The four chain attractive interaction is marginal at d = 1 and so is the three chain interaction. The presence of these two marginal operators (at d = 1) however remain decoupled mainly because for directed polymers, higher order interactions (order = number of chains involved) do not renormalize lower order interactions. This has already been seen in the overlap problem for the random medium case in Sec. 6. Therefore the resulting renormalization of the two new couplings are independent of each other, and, in fact they are the same by virtue of the nature of the interaction. Because of the four body interaction, we expect a disorder induced criticality as for the two chain quenched case, but here this happens for a real four chain system - no replica is involved. 

Here, Greek indices denote replicas. Comparing this expression with the Hamiltonian of the pure model (13), we notice an additional interaction of the order parameter field the last term presents the effective interaction between different replicas. The coupling constant vq is proportional to the variance of the disorder distribution. The coupling Uq must be positive, otherwise the pure system undergoes a 1st order transition. For final results the replica limit n 0 has to be taken. 

Applying the replica method in order to average the free energy over different configurations of quenched disorder one finds the effective Hamiltonian of the m-vector model with long-range-correlated disorder [65] ... 

Affentranger, R., Tavernelli, I., Di lorio, E. E. (2006). A novel Hamiltonian replica exchange MD protocol to enhance protein conformational space sampling. Journal of Chemical Theory and Computation, 2, 217. 

Curuksu, J., Zacharias, M. (2009). Enhanced conformational sampling of nucleic acids by a new Hamiltonian replica exchange molecular dynamics approach. Journal of Chemical Physics, 130,104110. 

Zacharias, M. (2008). Combining elastic network analysis and molecular dynamics simulations by Hamiltonian replica exchange. Journal of Chemical Theory and Computation, 4, 477. 

Widmalm et al. have studied conformational sampling for a set of ten a- or p-(l - 6)-linked oligosaccharides using explicit solvent Hamiltonian replica exchange (HREX) simulations and NMR spectroscopy techniques. In this work the authors have evaluated 7(H,H), using... 

Widmalm and coworkers combine NMR transglycosidic J coupling constants and explicit solvent Hamiltonian replica exchange simulations to improve and validate the CHARMM36 force field as well as their simulation method on a set of a- or p-(l- 6)-linked oligosaccharides. The experimental trends in rotamer distributions are reproduced in simulations. Walker and coworkers report a new AMBER14 FF for lipids which is validated against NMR data. The philosophy is to be compatible with AMBER FFs for proteins and nucleic acids. ... 

H. Fukunishi, O. Watanabe, and S. Takada,/. Chem. Phys., 116(20), 9058-9067 (2002). On the Hamiltonian Replica Exchange Method for Efficient Sampling of Biomolecular Systems Application to Protein Structure Prediction. 

W. Jiang and B. Roux,/. Chem. Theory Comput., 6(9), 2559-2565 (2010). Free Energy Perturbation Hamiltonian Replica-Exchange Molecular Dynamics (FEP/H-REMD) for Absolute Ligand Binding Free Energy Calculations. 

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