Simulation techniques quantum methods

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

Despite advent of theoretical methods and techniques and faster computers, no single theoretical method seems to be capable of reliable computational studies of reactivities of biocatalysts. Ab initio quantum mechanical (QM) methods may be accurate but are still too expensive to apply to large systems like biocatalysts. Semi-empirical quantum methods are not as accurate but are faster, but may not be fast enough for long time simulation of large molecular systems. Molecular mechanics (MM) force field methods are not usually capable of dealing with bond-breaking and formation... 

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

Molecular dynamics simulations, with quantum-mechanically derived energy and forces, can provide valuable insights into the dynamics and structure of systems in which electronic excitations or bond breaking processes are important. In these cases, conventional techniques with classical analytical potentials, are not appropriate. Since the quantum mechanical calculation has to be performed many times, one at each time step, the choice of a computationally fast method is crucial. Moreover, the method should be able to simulate electronic excitations and breaking or forming of bonds, in order to provide a proper treatment of those properties for which classical potentials fail. 

The accuracy achieved through ab initio quantum mechanics and the capabilities of simulations to analyze structural elements and dynamical processes in every detail and separately from each other have not only made the simulations a valuable and sometimes indispensable basis for the interpretation of experimental studies of systems in solution, but also opened the access to hitherto unavailable data for solution processes, in particular those occurring on the picosecond and subpicosecond timescale. The possibility to visualize such ultrafast reaction dynamics appears another great advantage of simulations, as such visualizations let us keep in mind that chemistry is mostly determined by systems in continuous motion rather than by the static pictures we are used to from figures and textbooks. It can be stated, therefore, that modern simulation techniques have made computational chemistry not only a universal instrument of investigation, but in some aspects also a frontrunner in research. At least for solution chemistry this seems to be recognizable from the few examples presented here, as many of the data would not have been accessible with contemporary experimental methods. 

Figure 2. Illustration of simulation techniques available at various time and length scales. QC means first principles, quantum chemical methods. MD refers to classical molecular dynamics methods. (Monte Carlo methods are useful in roughly the same range of time and distance.) Methods for connecting QC, MD, and continuum methods are indicated in parentheses.

The main goal of simulation methods is to obtain information on the spatial and temporal behavior of a complex system (a material), that is, on its structure and evolution. Simulation methods are subdivided into atomistic and phenomenological methods. Atomistic methods directly consider the evolution of the system of interest at the atomic level with regard to the microscopic structure of the substance. These methods include classical and quantum MD and various modifications of the MC technique. Phenomenological methods are based on macroscopic equations in which the atomistic nature of the material is not directly taken into account. Within the multiscale approach, both groups of methods mutually complement each other, which permits the physicochemical system under study to be described most comprehensively. 

The development of multiscale simulation techniques that involve the atomistic modeling of various structures and processes still remains at its early stage. There are many problems to be solved associated with more accurate and detailed description of these structures and processes. These problems include the development of efficient and fast methods for quantum calculations at the atomistic level, the development of transferable interatomic potentials (especially, reactive potentials) for molecular dynamic simulations, and the development of strategies for the application of multiscale simulation methods to other important processes and materials (optical, magnetic, sensing, etc.). 

Most molecular simulation techniques can be categorized as being among three main types (1) quantum mechanics, (2) molecular dynamics (MD) and (3) kinetic Monte Carlo (KMC) simulation. Quantum mechanics methods, which include ah initio, semi-empirical and density functional techniques, are useful for understanding chemical mechanisms and estimating chemical kinetic parameters for gas-phase... 

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