MCI TIMINGS

Warning

This page is under construction, and thus the results should not be taken as a direct reference.

The ESIpy code provides an improved algorithm for the generation of permutations in the MCI calculation. ESI-3D used a Nested Summation Symbol (NSS) to compute all the ring connectivities. In ESIpy, two separate algorithms are used: S and M. Both algorithms only generate the (n-1)!/2 permutations of a given n-lenghted list for non-symmetric AOMs and (n-1)! for symmetric AOMs (i.e., Mulliken). In order to obtain the non-cyclic permutations, one approach computes the (n-1) cyclic permutations and appends the nth term, resulting in the non-cyclic ring connectivities. Moreover, due to the topology of the permutations, a factor of 2 is present if the first (n-1) elements of the list of length n are reversed. Hence, the algorithms check this reversability and gets rid of the \(2\) factor.

Both S and M perform slices of the original list using the itertools.islice module. The S algorithm computes the Iring for each permutatation, while the M separates them into different chunks as iterators. Then computes the MCI for each chunk and sums up all the MCIs. The storage of the slices as iterators allows for multiprocessing without memory requirements, although the speed-up is non-linear.

By default, ESIpy works on a single core unless specified otherwise in the num_threads variable (if it is not specified or it is equal to one). To use the other algorithm, M, set the variable to an integer greater than 1. The following tests have been performed by generating and computing the MCI for 35x35 AOMs (a [10]annulene molecule) in an Intel(R) Xeon(R) W-2123 CPU @ 3.60Hz) machine.

Time (in seconds) for the MCI calculation of an n-membered ring in single-core processing, computed as an average of three timings.

n	TIME AT 1 CORE (s)
	S ALG.	M ALG.
6	0.002	0.022
7	0.010	0.042
8	0.077	0.116
9	0.664	0.778
10	6.525	7.166
11	71.694	78.580
12	869.263	894.523