Quantum mechanics, classical algorithm

The algorithms of the mixed classical-quantum model used in HyperChem are different for semi-empirical and ab mi/io methods. The semi-empirical methods in HyperChem treat boundary atoms (atoms that are used to terminate a subset quantum mechanical region inside a single molecule) as specially parameterized pseudofluorine atoms. However, HyperChem will not carry on mixed model calculations, using ab initio quantum mechanical methods, if there are any boundary atoms in the molecular system. Thus, if you would like to compute a wavefunction for only a portion of a molecular system using ab initio methods, you must select single or multiple isolated molecules as your selected quantum mechanical region, without any boundary atoms. 

Semi-empirical methods could thus treat the receptor portion of a single protein molecule as a quantum mechanical region but ab mdio methods cannot. However, both semi-empirical and ab initio methods could treat solvents as a perturbation on a quantum mechanical solute. In the future, HyperChem may have an algorithm for correctly treating the boundary between a classical region and an ab mdio quantum mechanical region in the same molecule. For the time being it does not. 

The previous subsections defined the AIMS method, the various approximations that one could employ, and the resulting different limits classical mechanics, Heller s frozen Gaussian approximation, and exact quantum mechanics. As emphasized throughout the derivation, the method can be computationally costly, and this is one of the reasons for developing and investigating the accuracy of various approximations. Alternatively, and often in addition, one could try to develop algorithms that reduce the computational cost of the method without compromising its accuracy. In this subsection we discuss two such extensions. Each of these developments has been extensively discussed in a publication, and interested readers should additionally consult the relevant papers (Refs. 125 and 41, respectively). We conclude this subsection with a discussion of the first steps... 

Quantum mechanical methods can now be applied to systems with up to 1000 atoms 87 this capacity is not only from advances in computer technology but also from improvements in algorithms. Recent developments in reactive classical force fields promise to allow the study of significantly larger systems.88 Many approximations can also be made to yield a variety of methods, each of which can address a range of questions based on the inherent accuracy of the method chosen. We now discuss a range of quantum mechanical-based methods that one can use to answer specific questions regarding shock-induced detonation conditions. 

Future directions in the development of polarizable models and simulation algorithms are sure to include the combination of classical or semiempir-ical polarizable models with fully quantum mechanical simulations, and with empirical reactive potentials. The increasingly frequent application of Car-Parrinello ab initio simulations methods " may also influence the development of potential models by providing additional data for the validation of models, perhaps most importantly in terms of the importance of various interactions (e.g., polarizability, charge transfer, partially covalent hydrogen bonds, lone-pair-type interactions). It is also likely that we will see continued work toward better coupling of charge-transfer models (i.e., EE and semiem-pirical models) with purely local models of polarization (polarizable dipole and shell models). 

The non-adiabatic quantum simulation procedures we employ have been well described previously in the literature, so we describe them only briefly here. The model system consists of 200 classical SPC flexible water molecules," and one quantum mechanical electron interacting with the water molecules via a pseudopotential. 2 The equations of motion were integrated using the Verlet algorithm with a 1 fs time step in the microcanonical ensemble, and the adiabatic eigenstates at each time step were calculated with an iterative and block Lanczos scheme. Periodic boundary conditions were employed using a cubic simulation box of side 18.17A (water density 0.997 g/ml). 

The exponential increase in computer power and the development of highly efficient algorithms has distinctly expanded the range of structures that can be treated on a first-principle level. Using parallel computers, AIMD simulations of systems with few hundred atoms can be performed nowadays. This range already starts to approach the one relevant in biochemistry. Indeed, some simulations of entire biomolecules in laboratory-realizable conditions (such as crystals or aqueous solutions) have been performed recently [25-28]. For most applications however, the systems are still too large to be treated fully at the AIMD level. By combining AIMD simulations with a classical MD force field in a mixed quantum mechanical/molecular mechanical fashion (Hybrid-AIMD) the effects of the protein environment can be explicitly taken into account and the system size can be extended. 

Nuclear motion can be described by quantum mechanical propagation of the vibrational wave function or classical motion on the time-dependent adiabatic potentials. In our approach, the classical equations of motion are solved by the velocity Verlet algorithm. The typical time increment for integration. At, was 0.5 fs. 

Increases in computer power and improvements in algorithms have greatly extended the range of applicability of classical molecular simulation methods. In addition, the recent development of Internal Coordinate Quantum Monte Carlo (ICQMC) has allowed the direct comparison of classical simulations and quantum mechanical results for some systems. In particular, it has provided new insights into the zero point energy problem in many body systems. Classical studies of non-linear dynamics and chaos will be compared to ICQMC results for several systems of interest to nanotechnology applications. The ramifications of these studies for nanotechnology applications will be discussed. 

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