Splitting method efficiency

Janezic, D., Merzel, F. An Efficient Split Integration Symplectic Method for Molecular Dynamics Simulations of Complex Systems. In Proceedings of the... 

A key feature required of a Hamiltonian system that leads to an efficient method based on splitting is the ability to separate the Hamiltonian into p-dependent and g-dependent terms. 

One of the most efficient algorithms known for evaluating the Ewald sum is the Particle-mesh Ewald (PME) method of Darden et al. [8, 9]. The use of Ewald s trick of splitting the Coulomb sum into real space and Fourier space parts yields two distinct computational problems. The relative amount of work performed in real space vs Fourier space can be adjusted within certain limits via a free parameter in the method, but one is still left with two distinct calculations. PME performs the real-space calculation in the conventional manner, evaluating the complementary error function within a cutoff... 

Multistep Thermochemical Water Splitting. Multistep thermochemical hydrogen production methods are designed to avoid the problems of one-step water spHtting, ie, the high temperatures needed to achieve appreciable AG reduction, and the low efficiencies of water electrolysis. Although water electrolysis itself is quite efficient, the production of electricity is inefficient (30—40%). This results in an overall efficiency of 24—35% for water electrolysis. 

A detailed discussion of thermochemical water splitting is available (155,165—167). Whereas many problems remain to be solved before commercia1i2ation is considered, this method has the potential of beiag a more efficient, and hence more cost-effective way to produce hydrogen than is water electrolysis. 

This is a method which is very attractive in principle and which has been applied to yield approximate barriers for a number of molecules. There are, however, difficulties in its use. In the first place, it is not easy to measure the intensities of microwave lines with accuracy. There are unsolved problems of saturation, reflections in the wave guide, and variation of detector efficiency with frequency which are presumably reponsible for the fact that measurements made with ordinary wave guide spectrometers are not very reproducible. In addition, both the spectral lines may be split into components by tunnelling from one potential minimum to another and this splitting, even though it is not resolved, can alter the apparent intensity. Furthermore, it is often difficult to find pairs of lines such that neither is obscured by Stark lobes from the other. 

These conceptual goals are attained by several combinatorial methods and tools. Characteristic for combinatorial chemistry is the synthesis on solid support or by polymer-supported synthesis, allowing for much higher efficiency in library production. Synthesis can be conducted either in automated parallel synthesis or by split-and-recombine synthesis. Centerpieces of combinatorial methods further include specific analytical methods for combinatorial... 

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