57th Annual Report on Research 2012 Under Sponsorship of the ACS Petroleum Research Fund

A suite of programs called Accelerated Molecular Dynamics with Chemistry (AMolDC) has been written, tested, and employed in order to perform adaptive, multilevel QM/MM simulations for complex chemical processes in the gas-phase.  A paper that examines the properties of this new method was published recently.¹  The method is formulated to give a time-dependent, multilevel representation of the total potential that is derived from spatially-resolved quantum mechanical (QM) regions.  Ref. 1 shows that the AMolDC method scales linearly with system size due to the fact that at a constant temperature and pressure, the average system size will remain approximately constant regardless of the number of atoms in the simulation.

Fig. 1  Accuracy in the interpolant as a function of underlying grid density

The last year of work has been centered on two items:  i.)  continued improvement in the accuracy of the interpolant by a new method of optimizing the interpolant and ii.) running computational studies of AMolDC for parallelly executed QM calculations both with and without the interpolant.  Each of these is examined in turn.

Fig. 2  Computational studies of the AMolDC  program on hydrated organic clusters.

Much work over the last year has continued go into finding a general interpolation method that is both accurate and fast.  In order to make the interpolation module more accurate and have less scatter in the accuracy with increasing grid density, a new method of optimizing the interpolant has been employed.  The new method is the so-called leave-one-out method of optimization,^1-5 where the closest grid point to the point of interpolation is used as a basis for doing 1D line searches to solve for the optimum value of D in:  .  The result of this effort as been a much more stable interpolation module and the ability for the user to a priori set up criterion for both the energy and gradient interpolation accuracy, where no interpolation will be performed if the interpolant cannot be formulated to give accuracy below the input thresholds.  Shown in Fig. 1 are the results of the improved interpolant for the energy and forces of the bicyclohept-2-ene system, where the inset shows the grid density and interpolation error on a log-log scale.

Second, AMolDC was rewritten to submit the QM jobs in parallel and timing tests were performed.  Shown in Figure 1 is a log-log plot of CPU time for various system sizes of small condensed phase system of water, n-propanol (np), cyclohexanol (ch), and orthoxylene (ox).  The systems varied in sizes from 1 molecule of each to 6 molecules of each, giving system sizes from 52 atoms to 312 atoms.  The parallel QM calculations were submitted over an 18 node cluster.  Figure 1 shows the tremendous cost savings associated with performing interpolations (symbols) over performing parallel QM calulations with no interpolations (lines).  Levels of theory from B3LYP with cc-pVTZ basis sets to HF with 6-31G** basis sets were used for the various groups formed in these simulations.  Figure 1 also demonstrates that system sizes of multiple hundreds of atoms may be studied with total CPU times of about 6 hours while interpolating on DFT and HF potential and force surfaces.

Two manuscripts have been written and submitted to the Journal of Chemical Physics.  The first manuscript is on the interpolation module, how to perform accurate and fast interpolations for large chemical systems.  The second paper is using this interpolation methodology within AMolDC to perform computational studies of small hydrated organic clusters.  The papers were submitted together as back-to-back publications in the same issue.

References:

1.  Fasshauer, G.; Zhang, J. Numer. Algorithms, 2000, 45, 345-368.

2.  Franke, R. Math. Comput., 1982, 38, 181-200.

3.  Carlson, R.E.; Foley, T.A., Comput. Math. Appl. 1991, 21, 29-42.

4.  Rippa, S. Adv. Comput. Math. 1999, 11, 193-210.

5.  Kansa, E.J.; Carlson, R.E., Comput. Math. Appl. 1992, 24, 99-120.