Research Objectives
Our research focuses on the development of methods to attack the three principal bottlenecks to extending molecular simulations: (1) the timescale bottleneck in molecular simulations, (2) the particle number bottleneck in electronic structure calculations, and (3) the dimensionality bottleneck in quantum reactive scattering.
Computational Approach and Accomplishments
We have developed action functionals for directed paths that connect reactants and products via rare crossings of transition states. With the algorithms for sampling these functionals we have developed over the past year, this is now a practical computational method for obtaining meaningful simulations of reactive processes which occur on timescales far too long for conventional simulations. A range of problems of increasing realism and complexity have been studied, facilitated by use of the NERSC T3E. These include hydrogen bond breaking in liquid water, and the dissociation of NaCl in water.
We have developed improved methods for constructing the effective Hamiltonian in electronic structure theory with effort scaling only linearly with molecule size. This includes exchange interactions, and Coulomb interactions for periodic systems. We have also addressed the related problem of converting an effective Hamiltonian into a density matrix in linear scaling effort, via a novel Chebyshev analysis, which is of both formal and practical value.
Simulation methods based on the direct and correct evaluation of rate constants for chemical reactions have been generalized to approximately include the effect of pressure on a primary chemical reaction of interest. This has been applied to the O + OH -> HO2 -> O2 + H reaction, which is of central importance in modeling hydrocarbon combustion.
Additionally we have made progress of semiclassical initial value representations as a general way of including quantum effects in molecular simulations without the prohibitive cost of a formally exact treatment. Particularly interesting is the generalization we have made that provides a description also of electronically non-adiabatic processes.
Significance
Progress in these areas leads to better possibilities for leveraging new supercomputing capabilities into changes in the scale of simulations that are feasible. For example, consider the particle number bottleneck. A method whose complexity rises as the cube of molecular size means that the availability of a computer eight times faster translates into the ability to study a molecule that is only two times larger. By contrast, a linear scaling method would permit a system eight times larger to be modeled. Similar considerations apply in our other two areas of focus, and illustrate the need for improvements in the algorithms of molecular simulations to go hand in hand with improvements in supercomputing resources.
Publications
Schwegler, E., M. Challacombe, and M. Head-Gordon. 1997. Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build. Journal of Chemical Physics 106:9708-9717.
Baer, R., and M. Head-Gordon. 1997. Sparsity of the density matrix in Kohn-Sham density functional theory and an assessment of linear system-size scaling methods. Phys. Rev. Lett. 79:3962-3965.
German, T. C., and W. H. Miller. 1997. Quantum mechanical pressure-dependent reaction and recombination rates for O+OH -> H+O2, HO2. Journal of Physical Chemistry 101:6358-6367.
(upper) Schematic energy landscape with reactant region A and product region B. The chain of
beads is a discretized path as used in our path simulation. It reproduces the correct reacti
on
coordinate which depends both on q and on q'.
(lower) Schematic free energy along coordinate q. The coordinate q adequately characterizes the
stable states near q=qA and q=qB. The free energy F(q) has a maximum at q=q*. This
value of q is far from that associated with the dynamical bottleneck separating the two
stable states.