Parallelization with Minimal Modifications

Let us develop a simple performance model for the algorithm PI. The only time-consuming communication step is the global summation of the quarter-transformed integrals. This summation is performed times, each 

This yields the following expression for the speedup, S p) = ftotai(l)/ftotai(p) 

Send iN jS) and iN jR) contributions to process holding current ij pair End i, j loop 

The high-performance parallel direct MP2 algorithm P2. R, S, M, and N denote shells of atomic orbitals. Occupied orbitals, i, can be processed in batches, I, to reduce the storage requirement. Distributed indices are underlined. R, S pairs are distributed either statically or dynamically as explained in the text. 

The send operations employed are non-blocking and can be overlapped with computation to some extent. Our performance model will take this into account by using effective a and /3 values measured for overlapped communication and computation. From Eq. 9.12 it is clear that the overall communication requirement for the P2 algorithm, namely, the total amoimt of data that must be sent per process, O( sheii0 n / p), is roughly inversely proportional to the number of processes, which is a prerequisite for a strongly 

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In order to perform FEP calculations on optimized paths with a small number of images, extra images need to be added on the path between the previously optimized points. Once these extra images have been added, an optimization has to be performed to minimize them to the MEP. Here we have developed a modification to our NEB QM/MM implementation [27], This modification allows for the optimization of only selected images on the path while maintaining the points previously optimized with the parallel iterative path method or the combined procedure fixed. 

Concepts to minimize effects of Rq by capillary or cell modification were presented in [13, 14]. Thin wires (diameters around 10 pm) can be positioned very close to the working electrode with negligible shielding effect. They are either charged with stable redox systems (e.g., palladium/hydrogen [15] or gold/gold oxide [16]) or connected via capacitors in parallel to conventional reference electrode systems [17] to reduce or t, respectively Eqs. 1 and 2. 

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