Coupling of QMC and MD: Basic Idea

average distance made by an ion in one MD time step 10 -4 … 10 -3 a.u. average distance by an electron in a typical DMC time step 10 -2 … 10 -1 a.u. Instead of discrete sampling of each point with a new QMC run: calculate QMC energies “on-the-fly” during the dynamic simulation !

Continuously update the DMC walkers so that they correctly represent the evolving wave function (CDMC method) Evolution of both configuration spaces is coupled: as the ionic dynamical trajectories evolve, so does the population of DMC electrons J.C. Grossman/LLNL, L. Mitas/NCSU

Stable CDMC simulation

• Stable DMC population • How accurate is it?

• Benchmark against discrete DMC

Successful CDMC Algorithm

ab initio MD Step

R

,  (

R

) Compute orbital overlaps with current DMC walkers do VMC then DMC yes Orbital swapping or rotation?

no Check for node crossings compute weights Take DMC step(s) and calculate energy J.C. Grossman/LLNL, L. Mitas/NCSU

CDMC: Number of DMC step needed per MD step

• Use large discrete sampled runs (1000 steps each) for comparison • As simulation progresses, 1-step CDMC energies begin to differ significantly from discrete DMC • Using 3 steps corrects time “lag” • 33 times more efficient than discrete sampling Thermal Averages (over 1 ps) E(discrete DMC) E(1 step continuous) = -6.228(2) = -6.220(2) E(2 steps continuous) = -6.220(2) E(3 steps continuous) = -6.226(2) E(10 steps continuous)= -6.230(2) E(20 steps continuous)= -6.228(2) • Thermal averages are converged for N≥3 • Same convergence (3 CDMC steps) observed for Si 2 H 6 and Si 5 H 12 J.C. Grossman/LLNL, L. Mitas/NCSU

CDMC: Si

2

H

6

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As for SiH 4 , asymmetrically stretch molecule and let go Average temperature ~ 1500 K J.C. Grossman/LLNL, L. Mitas/NCSU

CDMC: Si

2

H

6

Results

ForSi 2 H 6 , 3 steps appears to lead to stability as for SiH 4 # steps looks like a function of dynamics rather than size Can pinpoint specific types of strain that lead to wf lag J.C. Grossman/LLNL, L. Mitas/NCSU

Test of quantum Monte Carlo/molecular dynamics method on water dissociation

“QMC only” molecular dynamics, with no external input from DFT SiH 4 at 1500 K H 2 O Dissociation • DMC forces in very good agreement with DFT forces • DMC-MD and DFT-MD trajectories are in excellent agreement J.C. Grossman/LLNL, L. Mitas/NCSU

New continuous quantum Monte Carlo/molecular dynamics method

• we propose a new method for coupling ab initio molecular dynamics ionic with stochastic DMC electronic steps to provide accurate DMC energies “on-the-fly” • exploits the slowness of MD evolution which enables to update the QMC sampling process very efficiently • accurate for both thermal averages and description of energies along the pathways • we have carried out the first QMC/MD both forces and energies from QMC simulations using J.C. Grossman/LLNL, L. Mitas/NCSU