Time correlation functions overview

While no general overview paper exists that compares all methods discussed above on the same grounds, several contributions have appeared that compare subsets of methods. In 2007, Heyden et al. compared the performance of Abmpt, Hot Spot, ONIOM-XS, PAP, and SAP for a system of argon in argon with two different classical (MM) potentials [33]. The observables compared were energy conservation, temperature conservation, and radial distribution functions. In 2013, the authors of this chapter compared the performance of Abrupt, SAP, DAS, BF, FIRES, and BF for a system of water in water with four permutations of two QM and two MM potentials [17]. They compared the results obtained with the various QM/MM simulations with a reference calculation, fuU QM. In 2015, Pezeshki et al. reviewed ONIOM-XS, PAP, SAP, DAS, Hot-Spot and BF [18]. However, they did not perform any new method comparison with respect to Ref. [33]. Below, we wiU summarize the results of these studies, separated into a section about dynamical performance (energy/temperature conservation, time correlation functions), a section about structural results, and a section about timings. The comparison is summarized in Table 2.2. 

In discussing a many-body stochastic model one needs an overview of the time evolution behavior of the system over a significantly large range of parameters, in order to explore physical regimes of interest. Thus, in all cases, we have obtained results for both first and second rank orientational correlation functions for the first body (the solute), while varying the energetic and frictional parameters for the inertial models, momentum correlation functions have also been computed. 

In summary, we have made an attempt to classify existing MQC strategies in formulations resulting from (i) a partial classical limit, (ii) a connection ansatz, and (iii) a mapping formalism. In this overview, we shall focus on essentially classical formulations that may be relatively easily applied to multidimensional surface-crossing problems. On the other hand, it should be noted that there also exists a number of essentially quantum-mechanical formulations which at some point use classical ideas. A well-known example are formulations that combine quantum-mechanical time-dependent perturbation theory with a classical evaluation of the resulting correlation functions, e.g. Golden Rule type formulations.Furthermore, several... 

---