Multiscale Modeling and Simulation

O(n) and O(Log n) Constrained Molecular Dynamics

(initial development started on September, 1996)

In the study of molecular systems using Molecular Dynamics (MD) simulations it is often desired to impose relative or absolute motion constraints on atoms or groups of atoms. This offers several different advantages depending on the type of constraint involved, i.e. absolute or relative, and on the type of generalized coordinates used to describe the equations of motion (EOM) of the system, i.e. Cartesian or internal. Indistinctively, both approaches involve the formulation of mixed systems of differential EOM and nonlinear algebraic equations of constraint.

Our approach involves the use of internal coordinates, even though this  increases the complexity of the solution to the EOM (mainly because we now have a highly coupled molecular system with highly non-linear, non inertial terms in velocity, a dense mass matrix operator and potential numerical conditioning of the formulation solution) hence requiring efficient algorithms to compute the algebraic differential solution in linear, or better, computation time, it offers several advantages over the conventional Cartesian constrained dynamics methods (the Figure to the left depicts an NVT@300K of a polymer chain that results in an order of magnitude increase in simulation time-step in comparison to conventional atomistic Cartesian MD). 

Non-adiabatic force fields for explicit electron molecular dynamics

Our research involves developing and using first principles based methods to examine the chemical processes of matter at extreme conditions that may have significant concentrations of molecules, atoms, ions, and electrons exposed to transient mechanical, thermal and electrical fields. In particular we want to understand the processes for heterogeneous systems and interfaces in systems with temperatures ranging from ~0.1-100’s eV [~103-106’sK] and densities up to 10 times standard value (often referred to as warm-dense-matter - WDM - see top-left figure). Studies of such systems have mainly been the province of physics and astrophysics. We want to bring in the chemistry to bridge the transition regimes from solid to liquid to plasma driven by extreme conditions, using a first-principles-based modeling and simulation methodology capable of accurately expressing the non-adiabatic energetics and dynamics of excited electronic states. For this, we have been developing the first-principles-based electron force field (eFF) methodology, which enables modeling of the simultaneous dynamics of electrons and nuclei (eMD) evolving nonadiabatically under transient extreme conditions.  In eFF the N-electron wavefunction is described as a product of one-electron Gaussian functions, whose size is a dynamical variable and whose position is not constrained to a nuclear center. This form allows for straightforward propagation of the wavefunction, with time, using a simple formulation. The nuclei are described as point charges.  The full Hamiltonian has then a standard description for electrostatic interactions between a set of delocalized point and Gaussian charges which include, nuclei-nuclei, electron-electron, and nuclei-electron.  In addition to the electrostatics, eFF introduces QM effects through an electron kinetic energy from the Gaussians and a spin-dependent Pauli repulsion potential term between Gaussians. 

Thus eFF is a simplified QM method rather than a conventional force field method, in which electron motions are averaged out into ground state nuclear motions (i.e a single electronic state) described by empirically parameterized interatomic potential functions. 

We have demonstrated the applicability of eFF to multiple problems, including: predicting the single shock Hugoniots for Hydrogen [Su and Goddard, 2007], Lithium [Kim, Su, and Goddard, 2010; Jaramillo-Botero, Su, An, and Goddard, 2010], Carbon [An, Su, Jaramillo-Botero, and Goddard, 2010], Beryllium, Auger dynamics [Su and Goddard, 2010], among others.  Bottom figure shows the shock wave kinematics, including mass velocities (Up) and shock wave velocities (Us) , and the corresponding single shock Hugoniot for lithium metal, obtained from a pEFF dynamics simulation.

Current effort focused on: