Potential computational quantum mechanics

Clementi, J. Chem. Phys., 64, 1351 (1976) the full details of the computed X-ray diffraction intensity are available in G. C. Lie, M. Yoshimine, and E. Clementi, J. Chem. Phys., 64, 2314 (1976). The previous computations by Stillinger and Rahman did not use a quantum-mechanically derived potential, but an empirical potential. Present quantum-mechanical techniques, if properly used, can yield remarkably accurate potentials. This fact is not fully appreciated by a large number of chemists, possibly discouraged by the rather large amount of poor theoretical chemistry computations currently in the literature. It is notable that the repulsive part of a potential can be inferred from experiments, in general, with poor accuracy. 

Car-Parrinello methods contrasted wilhslalic (0 Ktemperature) computational quantum mechanical methods They can treat entropy accurately without the need to use models such as the harmonic approximation for degrees of freedom of atomic motions. They can be used to sample potential energy surfaces on picosecond time scales, which is essential for treating liquids and aqueous systems. Tliey can be used to sample reaction pathways or other chemical processes with a minimum of a priori assumptions. In addition, they can be used to find global minima [in conjunction with methods of optimization such as simulated annealing (Kirkpatrick et at, 1983)] and to step out of local minima. 

Integral to Car-Parrinello methods is the use of computational quantum mechanics to determine the state of a number of electrons in the presence of any conhguration of atomic nuclei. Determining the electronic state of the system quantum mechanically can be contrasted with using empirically derived potentials, such as Lennard-Jones or Morse potentials, used in classical methods. Once the electronic state has been computed, all properties of the system can be found. For molecular dynamics simulations, the most important properties are the absolute energy of the system and the forces on the individual atomic nuclei. Once these forces are computed, the nuclei can be propagated using classical equations of motion. 

Hu, H., Lu, Z., and Yang, W. (2007). Fitting molecular electrostatic potentials from quantum mechanical calculations, youma/ of Chemical Theory and Computation 3, 3, pp. 1004-1013. 

Hao Hu ZL, Weitao Y (2007) Eitting molecular electrostatic potentials from quantum mechanical calculations. J Chem Theor Comput 3 1004-1013... 

Exploiting the fact that the molecular electrostatic potential is an observable directly accessible from a wavefunction, Cox and Williams have proposed a clever method that allows sets of atomic charges to be determined easily. Their approach requires the definition of a grid of A pnt points, over which the electrostatic potential is computed quantum mechanically ... 

Combined Quantum Mechanical and Molecular Mechanical Potentials Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Har-tree-Fock (HF), and the Self-consistent Field Force Fields A General Discussion Force Fields CFF Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods NMR Chemical Shift Computation Ab Initio Transition Metals Applications TVRBOMOLE Transition State Theory. 

The theory coimecting transport coefficients with the intemiolecular potential is much more complicated for polyatomic molecules because the internal states of the molecules must be accounted for. Both quantum mechanical and semi-classical theories have been developed. McCourt and his coworkers [113. 114] have brought these theories to computational fruition and transport properties now constitute a valuable test of proposed potential energy surfaces that... 

The relative shift of the peak position of the rotational distiibution in the presence of a vector potential thus confirms the effect of the geometric phase for the D + H2 system displaying conical intersections. The most important aspect of our calculation is that we can also see this effect by using classical mechanics and, with respect to the quantum mechanical calculation, the computer time is almost negligible in our calculation. This observation is important for heavier systems, where the quantum calculations ai e even more troublesome and where the use of classical mechanics is also more justified. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

Field, M.J., Bash, P.A., Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem. 11 (1990) 700-733. 

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-... 

Using Jacobi coordinates and reduced masses, the Hydrogen-Chlorine interaction is modeled quantum mechanically whereas the Ar-HCl interaction classically. The potentials used, initial data and additional computational parameters are listed in detail in [16]. 

Amara P and M J Field 1998. Combined Quantum Mechanical and Molecular Mechanical Potentials. In Schleyer, P v R, N L Allinger, T Clark, J Gasteiger, P A Kolhnan H F Schaefer HI and P R Schreiner (Editors). The Encyclopedia of Computational Chemistry. Chichester, John Wiley Sons. 

Gao J 1995. Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials. In Lipkowitz K B and D B Boyd (Editors) Reviews in Computational Chemistry Volume 7. New York, VCH Publishers, pp. 119-185. 

Field M J, P A Bash and M Karplus 1990. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. Journal of Computational Chemistry 11 700-733. 

The electron alfinity (FA) and ionization potential (IP) can be computed as the difference between the total energies for the ground state of a molecule and for the ground state of the appropriate ion. The difference between two calculations such as this is often much more accurate than either of the calculations since systematic errors will cancel. Differences of energies from correlated quantum mechanical techniques give very accurate results, often more accurate than might be obtained by experimental methods. 

The quantum mechanics methods in HyperChem differ in how they approximate the Schrodinger equation and how they compute potential energy. The ab initio method expands molecular orbitals into a linear combination of atomic orbitals (LCAO) and does not introduce any further approximation. 

Reality suggests that a quantum dynamics rather than classical dynamics computation on the surface would be desirable, but much of chemistry is expected to be explainable with classical mechanics only, having derived a potential energy surface with quantum mechanics. This is because we are now only interested in the motion of atoms rather than electrons. Since atoms are much heavier than electrons it is possible to treat their motion classically. Quantum scattering approaches for small systems are available now, but most chemical phenomena is still treated by a classical approach. A chemical reaction or interaction is a classical trajectory on a potential surface. Such treatments leave out phenomena such as tunneling but are still the state of the art in much of computational chemistry. 

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