The Hybrid Quantum Trajectory/Electronic Structure DFTB-based Approach to Molecular Dynamics
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Transcript of The Hybrid Quantum Trajectory/Electronic Structure DFTB-based Approach to Molecular Dynamics
The Hybrid Quantum Trajectory/Electronic Structure DFTB-based Approach toMolecular Dynamics
Lei WangDepartment of Chemistry and BiochemistryUniversity of South Carolina
James W. Mazzuca University of South CarolinaSophya Garashchuk University of South CarolinaJacek Jakowski NICS & UTK
XSEDE14, Atlanta, GAJuly, 17th, 2014
Chemical Reaction Process
Molecules
Electrons Nuclei
(a) Quantum method: explicitlysolve Schrödinger equation for reactive system at low energy(b) Force field method: empirical parameters
Density functional tight binding (DFTB): approximate quantum chemical method1) cheap and accuracy2) can do hundreds or a few thousand electrons
Classical - Molecular Dynamics
Light particles: Proton or Deuterium at low energy reactive process
Include quantum effects for nuclei into MD: Zero Point Energy
Tunneling
Example of ZPE and Tunneling
One-dimensional harmonic oscillator
ZPE
Quantum Tunneling
E > V
E < V
Outline
Bohmian dynamics and Linearized Quantum Force (LQF) method
Implementation in real/imaginary time dynamics
Collision of hydrogen with graphene sheet
Proton transfer in soybean lipoxygenase-1
Bohmian Dynamics: Mixed Quantum/Classical Trajectory Dynamics
The polar form of time-dependent Schrödinger equation (TDSE):
tyxHtyxt
i ,,ˆ,,
where x describes light quantum particles and y heavy “classical” particles.
yxVMm
H yx ,22
ˆ 22
22
tyxSityxAtyx ,,exp,,,,
D. Bohm. Phys. Rev., 85, 166-179, 1952
Trajectories follow reduced Newton’s Eqs and extra quantum correction :
UVpmpx
VpMp
y
xxx
xyyy
,
,
Linearized Quantum Force and Imaginary Time Dynamics
Expectation values are computed by sums over the trajectories,
cq
tttyxw
,
,ˆ
U is called quantum potential: AmA
U x2
2
2
And fitting with a linear function of x.AA
S. Garashchuk and V. Rassolov. J. Chem. Phys. 120, 1181-1190, 2004
,ˆ, xHx
Boltzmann evolution/Imaginary Time Dynamics can be propagated through imaginary time:
Cooling the system to temperature:Tkit B1
Where kB is the Boltzmann constant.
Reaction rate constant or ZPE
Implementation Quantum correction is included
for selected DoFs The QT code is merged with DFTB
method Electronic energy evaluation is
parallelized Multiple independent sub-
ensembles represent nearly classical DoFs
Fig 1: CPU time as a function of the number of cores. 4800 trajectories were propagated for 25 steps
Interaction of H+C37H15
“A Quantum Trajectory-Electronic Structure Approach for Exploring Nuclear Effects in the Dynamics of Nanomaterials”, S. Garashchuk, J. Jakowski, L. Wang, B. Sumpter, J. Chem. Theory Comput., 9 (12), 5221–5235 (2013)
DFTB Accuracy Test at Different Collision Sites
Fig 2: The electronic potential energy curves for H+C37H15 obtained with the DFT and with the DFTB at zero impact parameter with respect a) lattice-center, b) hexagon-center and c) bond-center geometries.
Energy Transfer: Adsorbed Trajectories
Fig 3: the collision energies Ecoll ={0.2,0.4,0.8} eV are plotted as a solid line, dash and dot-dash, respectively: (a) the kinetic energy of adsorbing hydrogen, (b) the kinetic energy of C37H15, (c) the position of the colliding proton along the reactive coordinate z and (d) the potential energy of the system along the trajectories are shown as functions of time.
Energy Transfer: Reflected Trajectories
Fig 4: collision energies Ecoll ={ 0.05,1.2,1.6} eV are plotted as a solid line, dash and dot-dash,respectively: (a) the kinetic energy of reflected hydrogen, (b) the kinetic energy of C37H15,(c) the z-coordinate of the colliding proton, and (d) the potential energy of the system along the trajectories are shown as functions of time.
Movement of Hydrogen and Selected Carbons
Fig 5: Positions of the colliding hydrogen and selected carbons along the z-axis for Ecoll={ 0.05,0.8,1.6} eV represented as a solid line, dash and dot-dash, respectively: (a) the proton, (b) the central carbon and (c) the nearest-neighbor carbon.
“Adsorption of a Hydrogen Atom on a Graphene Flake Examined with a Quantum Trajectory/Electronic Structure Dynamics”, L. Wang, J. Jakowski, S. Garashchuk, J. Phys. Chem. C, accepted.
Three-dimensional proton
Classical Quantum
Three-dimensional Proton Dynamics
Fig 6: Left: Adsorption probability; Right: Displacement of the central carbon. a) C37H15 and b) C87H23
Adsorption Probability Averaged over Multiple Ensembles of Trajectories
• The ensembles are independent of each other• Converged probabilities are obtained with 11 ensembles for the hydrogen and with 14 ensembles for the deuterium
Fig 7: Adsorption probability of H on C37H15 obtained with multiple ensembles: a) Hydrogen and b) Deuterium
Conclusion
Hybrid quantum/classical trajectory dynamics: reduced dimensionality quantum corrections on dynamics for light/heavy particles. It is suitable for up to 200 atoms.
QTES-DFTB simulation of H+C37H15: the dominant QM effect is due to delocalization of initial wavepacket; neglect of nuclear effects can lead to an overestimation of adsorption.
Biological Environment with Real & Imaginary Time Dynamics: Proton transfer in soybean lipoxygenase-1
Fig 8: DFTB potential energy as the hydrogen moves from carbon to oxygen.
The effect of local substrate vibrations on the H/D primary kinetic isotope effect (KIE):QT = 51, QM = 49, Experimental value = 81
J. W. Mazzuca, S. Garashchuk, J. Jakowski. Chem. Phys. Lett. submitted
Thermal Evolution of the Proton Wavefunction
Real-time calculations are initialized using the trajectories in b)
Rate Constant and Kinetic Isotopic Effect
dttCTQTk ff
k(T): rate constantQ(T): quantum partition function of reactantsCff(t): flux-flux correlation function
Conclusion
Substrate vibrations in SLO-1 active site increase the rate constant by 15%, and the kinetic isotope effect increases by 5-10%.
The increase is moderate because the reaction is fast ~0.1ps.
Acknowledgement Dr. Sophya Garashchuk Dr. Jacek Jakowski Dr. Vitaly Rassolov Dr. James Mazzuca Dr. David Dell’Angelo Bing Gu Brett Cagg Bryan Nichols