Quantum computers potential power

Another field where dielectric continuum models are extensively used is the statistical mechanical study of many particle systems. In the past decades, computer simulations have become the most popular statistical mechanical tool. With the increasing power of computers, simulation of full atomistic models became possible. However, creating models of full atomic detail is still problematic from many reasons (1) computer resources are still unsatisfactory to obtain simulation results for macroscopic quantities that can be related to experiments (2) unknown microscopic structures (3) uncertainties in developing intermolecular potentials (many-body correlations, quantum-corrections, potential parameter estimations). Therefore, creating continuum models, which process is sometimes called coarse graining in this field, is still necessary. 

However, despite of the great importance of quantum mechanical potentials from the purely theoretical point of view, simple effective two-body potential functions for water seem at present to be preferable for the extensive simulations of complex aqueous systems of geochemical interest. A very promising and powerful method of Car-Parrinello ah initio molecular dynamics, which completely eliminates the need for a potential interaction model in MD simulations (e.g., Fois et al. 1994 Tukerman et al. 1995, 1997) still remains computationally extremely demanding and limited to relatively small systems N < 100 and a total simulation time of a few picoseconds), which also presently limits its application for complex geochemical fluids. On the other hand, it may soon become a method of choice, if the current exponential growth of supercomputing power will continue in the near future. 

Historically, the potential power of quantum computation was first proclaimed in a talk of Richard Feynman at the first Conference on the Physics of Computation at MIT in 1981 [15]. He observed that it appeared to be impossible in general to simulate the evolution of a quantum system on a classical computer in an efficient way. The computer simulation of quantum evolution involves an exponential slowdown in time, compared with the natural evolution. The amount of classical information required to describe the evolving quantum state is exponentially larger than that required to describe the corresponding classical system with a similar accuracy. But, instead of regarding this intractability as an obstacle, Feynman considered it an opportunity. He explained that if it requires that much computation to find what will happen in a multi-particle interference experiment, then the amount of such an experiment and measuring the outcome is equivalent to performing a complex computation. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

The equation (3) generates the famous BO potential energy hypersurface. The practical power of this concept is well documented and it remains at the foundation of important domains in computational quantum chemistry. The theory of absolute reaction rates is entirely based upon it [32-34, 63] as well as all modem quantum theories of reaction rates [36, 39, 64-80],... 

In 1997, Ehlers and co-workers 76) extended these early studies by making use of vastly improved modern computational power. Quantum-mechanical ah initio calculations at the MP2 and CCSD(T) level of theory using effective core potentials for the heavy atoms as well as density functional calculations using various gradient corrections were... 

Two methods are mainly responsible for the breakthrough in the application of quantum chemical methods to heavy atom molecules. One method consists of pseudopotentials, which are also called effective core potentials (ECPs). Although ECPs have been known for a long time, their application was not widespread in the theoretical community which focused more on all-electron methods. Two reviews which appeared in 1996 showed that well-defined ECPs with standard valence basis sets give results whose accuracy is hardly hampered by the replacement of the core electrons with parameterized mathematical functions" . ECPs not only significantly reduce the computer time of the calculations compared with all-electron methods, they also make it possible to treat relativistic effects in an approximate way which turned out to be sufficiently accurate for most chemical studies. Thus, ECPs are a very powerful and effective method to handle both theoretical problems which are posed by heavy atoms, i.e. the large number of electrons and relativistic effects. 

Massively parallel (multiple instruction, multiple data) computers with tens or hundreds of processors are not readily accessible to the majority of quantum chemists at the present time. However the cost of currently available hypercube machines with tens of processors (each with about the power of a VAX) is comparable to that of superminis but with up to a hundred times the power. For applications of the type discussed above the performance of a machine with as few as 32 or 64 processors would be comparable to (or perhaps even exceed) that of a single processor supercomputer. Although computer requirements currently limit QMC applications (even with effective potentials) the proliferation of inexpensive massively parallel machines could conceivably make the application of relativistic effective potentials with C C quite competitive with more conventional electronic structure techniques. 

The input data for the shape analysis methods are provided by well-established quantum chemical or empirical computational methods for the calculation of electronic charge distributions, electrostatic potentials, fused spheres Van der Waals surfaces, or protein backbones. The subsequent topological shape analysis is equally applicable to any existing molecule or to molecules which have not yet been synthesized. This is precisely where the predictive power of such shape analysis lies based on a detailed shape analysis, a prediction can be made on the expected activity of all molecules in the sequence and these methods can select the most promising candidates from a sequence of thousands of possible molecules. The actual expensive and time-consuming synthetic work and various chemical and biochemical tests of... 

On the theoretical side, the tremendous increase of computer power has permitted to obtain very accurate ab initio global Potential Energy Surfaces (PES) for triatomic systems and to develop efficient classical and quantum dynamical methods. Thus, in the last decade, good agreement between theory and experiment has been obtained for elementary reactions such as H -h H2 —> H2 + H and F -I- Ho FH -I- H. 

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