Quantum Molecular Dynamics techniques

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

After 14 years on the faculty of Imperial College, Jacobs moved from London, England, to London, Ontario, where his research program focused on the optical and electrical properties of ionic crystals, as well as on the experimental and theoretical determination of thermodynamic and kinetic properties of crystal defects.213 Over the years his research interests have expanded to include several aspects of computer simulations of condensed matter.214 He has developed algorithms215 for molecular dynamics studies of non-ionic and ionic systems, and he has carried out simulations on systems as diverse as metals, solid ionic conductors, and ceramics. The simulation of the effects of radiation damage is a special interest. His recent interests include the study of perfect and imperfect crystals by means of quantum chemical methods. The corrosion of metals is being studied by both quantum chemical and molecular dynamics techniques. 

In order to study a system, one first has to assume a model interaction potential between the particles that are defined as the constituents of the fluid under investigation. Such a modelization is necessary if it is desired not to perform a quantum mechanical description of the system at the level of a first principle Hamiltonian composed of elementary forces. In the latter case, the ab initio molecular dynamics technique, developed by Car and Parrinello [1, 2], was revealed to be a powerful investigation tool that was adopted by many authors the last two decades. 

ZSM-5 (Al-MFI) is used as a catalyst in petroleum refining, in the production of synthetic fuels, and in other petrochemical processes, whereas TS-1 (Ti-MFI) is applied as a catalyst in fine chemical processes. The orthorhombic MFI structure exhibits 12 crystallographically unique tetrahedral sites. Calculations have been carried out on substitution preferences using classical as well as quantum models. " In most studies 12 simulations were conducted, and in each run, one or more crystallographically equivalent sites of the subsequently crystallographically unique tetrahedral sites were substituted. Energy minimization and molecular dynamics techniques were employed to calculate... 

Recently, semiempirical molecular-orbital methods have been combined with force-field-based molecular-dynamics techniques into hybrid schemes The interesting part of the system is described by quantum chemistry, while the surroundings are treated by a classical force field. These hybrid schemes allow calculation of the energy and gradients fast enough for molecular dynamics simulations of hundreds of picoseconds (10s time steps) duration to be feasible. This provides sufficient sampling for the calculation of many statistical-mechanical properties. A short synopsis is given of work carried out at ETH Zurich on conformational equilibria in solution, reactions in solution and enzyme reactions. 

Latterly, increasing use has also been made of Quantum Molecular Dynamics (QMD), based on the pioneering work of Car and Parrinello (1985) (see Chapter 8). The Car-Parrinello method makes use of Density Functional Theory to calculate explicitly the energy of a system and hence the interatomic forces, which are then used to determine the atomic trajectories and related dynamic properties, in the manner of classical MD. As an ab initio technique, QMD has the advantage over classical simulation methods that it is not reliant on interatomic potentials, and should in principle lead to far more accurate results. The disadvantage is that it demands far greater computing resources, and its application has thus far been limited to relatively simple systems. 

Quantum molecular dynamics is a natural offshoot of quantum mechanics whereby the fate of an encounter between atoms or molecules is determined by experiment or by numerical simulation. Simulation essentially involves solution of the Schrodinger equation. The potential energy of interaction is assumed to have already been determined previously by variational techniques and the initial wavefunctions (energy and geometrical structure) of... 

Some of the most widely used computational approaches will be briefly described below, namely some quantum chemical methods, classical simulations by Monte Carlo and Molecular Dynamics techniques and a few mesoscale methods. 

Tossell JA, Vaughan DJ (1992) Theoretical Geochemistry Applications of Quantum Mechanics in the Earth and Mineral Sciences. Oxford University Press, New York Tuckerman ME, Martyna GJ (2000) Understanding modem molecular dynamics Techniques and applications. J Phys ChemB 104 159-178... 

With respect to the dynamical properties of the hydrated electron in cluster systems, the first principle dynamics using ab initio molecular dynamics and so on have been extensively applied. [135, 180, 371, 408, 446] They revealed information about the structure and relative stabilities of the isomer clusters. Nonadiabatic dynamics of a solvated electron in various photochemical processes has also been studied experimentally. [62, 123, 294, 329] Rossky and co-workers [327, 468] also studied the relaxation dynamics of excess electrons using quantum molecular dynamics simulation techniques. Here the nonadiabatic interactions were taken into account basically within the scheme of surface hopping technique. [444]... 

Fifteen years ago Roberto Car of Princeton Uiuversity and Michele Parrinello of Max Planck Institute introduced a method that revolutionized electronic structure calculations for molecules, liquids and solids. In addition, this method called the Car-Parrinello Method also opened the field of quantum molecular dynamics for physicists. The Car-Parrinello algorithm allows for rigorous evaluation of molecular dynamics in clusters, solids and surfaces. Ursula Rothlisberger, a former member of the Parrinello s group, reviews the formations of the methods in its most common implementations in chapter two. She provides a munber of examples of applications of this powerful technique. Also, predictions of future directions of the methods are given in her chapter. 

Computational spectroscopy can take great advantage from weU-cahhrated molecular dynamics techniques, which can provide a direct and controlled interpretation of results and a deep understanding of the structure/spectroscopic relationship. Such theoretical approaches can be very helpful in several spectroscopic techniques ranging from magnetic, optical, to X-ray diffraction/absorption techniques for both equilibrium (steady-state) and nonequilibrium (time-resolved) experiments. Results obtained for challenging prototype applications encourage us to improve and further develop connections to more sophisticated full-quantum mechanical approaches. 

The most detailed molecular dynamics simulation technique is the ab-initio (quantum) molecular dynamics simulation approach that explicitly models the electrons of the particles within the system. Whereas, force-field molecular dynamics simulations model the nuclear interactions of the particles within the system, and therefore do not explicitly model each electron. Then the method that incorporates the least amount of detail is that of coarse grain molecular dynamics models where multiple particles are grouped together before being represented by a single interaction bead. ... 

AMI AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semiempirical MO Methods Electrostatic Catalysis Force Fields A General Discussion Force Fields CFF GROMOS Force Field Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Mixed Quantum-Classical Methods MNDO MNDO/d Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields Parameterization of Semiempirical MO Methods PM3 Protein Force Fields Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM) SINDOI Parameterization and Application. 

Equilibrium properties for a quantum particle in a classical solvent can be calculated by immersing the polymer in the classical solvent and treating the combined many-particle system by standard Monte Carlo or molecular dynamics techniques the latter often provide a viable alternative to importance sampling methods. 

There are two main methods in this field. One is Molecular Dynamics and the other is Monte Carlo. Additional simulation methods are either closely related to one or the other aforementioned methods or they apply on spatial scales far beyond the molecular scale. Molecular Dynamics techniques model a small amount of material (system sizes usually are on the nm-scale) based on the actual equations of motion of the atoms or molecules in this system. Usually this is done on the basis of mechanical inter- and intra-particle potential functions. In certain cases however quantum mechanics in needed. Monte Carlo differs from Molecular Dynamics in that its systems do not follow their physical dynamics. Monte Carlo estimates thermodynamic quantities via intelligent statistical sampling of (micro)states. Capabilities and applications of both methods overlap widely. But they both also have distinct advantages depending on the problem at hand. Here we concentrate on Monte Carlo—which is the more thermodynamic method of the two. 

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