Classical-quantum hybrid approaches

This method can be successfully applied to the case of a solvation effect on the proton chemical shift. However, the effect cannot always be explained by this method. The quantity is very sensitive to the solute-solvent interaction and a serious drawback inherent in the classical-quantum hybrid approach is revealed. The result of ab initio MO analysis for small clusters suggests that electron exchange between solute and solvent is crucial to compute correct values of the chemical shift. A few attempts have been made to overcome this deficiency [18]. 

The study of chemical shift reveals a serious drawback inherent in the classical-quantum hybrid approach. The solvent effect on the oxygen chemical shift showed temperature dependence opposite to corresponding experimental results. An ab initio analysis with a small cluster suggested stongly that the ill behavior is originated from the lack of electron exchange between solute and solvent. Therefore an obvious direction of improvement of the RISM-SCF theory is to take the electron exchange into account. 

However, theories that are based on a basis set expansion do have a serious limitation with respect to the number of electrons. Even if one considers the rapid development of computer technology, it will be virtually impossible to treat by the MO method a small system of a size typical of classical molecular simulation, say 1000 water molecules. A logical solution to such a problem would be to employ a hybrid approach in which a chemical species of interest is handled by quantum chemistry while the solvent is treated classically. 

Finally, it must be remembered that DFT and AIMD can be incorporated into the so-called mixed quantum mechanical/molec-ular mechanical (QM/MM) hybrid schemes [12, 13]. In such methods, only the immediate reactive region of the system under investigation is treated by the quantum mechanical approach -the effects of the surroundings are taken into account by means of a classical mechanical force field description. These DFT/MM calculations enable realistic description of atomic processes (e.g. chemical reactions) that occur in complex heterogeneous envir-... 

Hybrid methods are characterized by a combination of quantum mechanical (QM) and molecular mechanical (MM) potentials. They treat the electronically important part of a large system by a quantum chemical method (e.g., ab initio, DFT, or semiempirical) and the remainder by a classical force field. They can provide an appropriate description for systems which are too large for a purely quantum chemical approach (even at the semiempirical level) and which contain regions that cannot be described classically (e.g., reactive centers with breaking and forming bonds, or chromophores where an electronic excitation takes place). 

The semi-empirical equivalent of the above scheme benefits strongly from the simplifications introduced by the basic assumptions of the semi-empirical quantum chemical methods. Owing to the assumed orthogonality of the atomic orbitals, the only requirement of the method is the orthogonalization of the atomic orbitals defined on atoms X to the hybrid orbital involved in the SLOs associated to the frontier bonds. Similarly, one can discard the atomic orbitals centered on the Y atoms and these atoms are considered as classical point charges like all the other classical atoms. This approach has been tested successfully at the NDDO level. 

Aqvist, J., Warshel, A. Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches. Chem. Rev. 93... 

Aqvist J and A Warshel 1993. Simulation of Enzyme Reactions Using Valence Bond Force Fields a Other Hybrid Quantum/Classical Approaches. Chemical Reviews 93 2523-2544. 

The modern approach to chemical education appears to be strongly biased toward theories, particularly quantum mechanics. Many authors have remarked that classical chemistry and its invaluable predictive rules have been downgraded since chemistry was put into orbit around physics. School and undergraduate courses as well as textbooks show an increasing tendency to begin with the establishment of theoretical concepts such as orbitals and hybridization. There is a continuing debate in the chemical literature on the relative merits of theory as opposed to qualitative or descriptive chemistry 1-6). To quote the late J. J. Zucker-man who supported the latter approach (3). 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

The inter/intramolecular potentials that have been described may be viewed as classical in nature. An alternative is a hybrid quantum-mechanical/classical approach, in which the solute molecule is treated quantum-mechanically, but interactions involving the solvent are handled classically. Such methods are often labeled QM/MM, the MM reflecting the fact that classical force fields are utilized in molecular mechanics. An effective Hamiltonian Hefl is written for the entire solute/solvent system ... 

I. Burghardt, K. B. Moller, G. Parlant, L. S. Cederbaum and E. R. Bittner. Quantum hydrodynamics Mixed states, dissipation and new hybrid quantum-classical approach. Int. J. Quantum Chem., 100 1153-1162, 2004. 

Burghardt, I., Parlant, G. On the dynamics of coupled Bohmian and phase-space variables a new hybrid quantum-classical approach. J. Chem. Phys. 120... 

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