Protons and Path Integrals Landmark Simulation of Condensed Phase - PowerPoint PPT Presentation

Protons and Path Integrals Landmark Simulation of Condensed Phase Proton Transfer Thomas Allen (PI: Nancy Makri) Department of Chemistry University of Illinois May 13, 2015 Thomas Allen (PI: Nancy Makri) May 13, 2015 1 / 20

Introduction Charge transfer reactions are an important class of fundamental chemical reactions Thomas Allen (PI: Nancy Makri) May 13, 2015 2 / 20

Introduction Charge transfer reactions are an important class of fundamental chemical reactions ↽ A + + B − A + B ⇀ ↽ A − + BH + AH + B ⇀ Thomas Allen (PI: Nancy Makri) May 13, 2015 2 / 20

Introduction Charge transfer reactions are an important class of fundamental chemical reactions ↽ A + + B − A + B ⇀ ↽ A − + BH + AH + B ⇀ These reactions are ubiquitous in biology Transfer of H, H + , and H − is a major synthetic motif Cutting-edge materials for energy storage and transport Thomas Allen (PI: Nancy Makri) May 13, 2015 2 / 20

The Proton Transfer Problem Proton transfer is a condensed phase process Thomas Allen (PI: Nancy Makri) May 13, 2015 3 / 20

The Proton Transfer Problem Proton transfer is a condensed phase process Gas Phase 20 15 10 kcal/mol 5 0 -5 -10 0.8 1 1.2 1.4 1.6 1.8 Distance (Ang.) Thomas Allen (PI: Nancy Makri) May 13, 2015 3 / 20

The Proton Transfer Problem Proton transfer is a condensed phase process 20 15 10 kcal/mol 5 0 -5 -10 0.8 1 1.2 1.4 1.6 1.8 Distance (Ang.) Thomas Allen (PI: Nancy Makri) May 13, 2015 4 / 20

The Proton Transfer Problem Proton transfer is a condensed phase process 20 15 10 kcal/mol 5 0 -5 -10 0.8 1 1.2 1.4 1.6 1.8 Distance (Ang.) Many degrees of freedom, transfering species is quantum mechanical Separation into interacting system and environment is key Thomas Allen (PI: Nancy Makri) May 13, 2015 4 / 20

Quantum-Classical Approaches Fundamental idea of quantum-classical separation has been around for many years Thomas Allen (PI: Nancy Makri) May 13, 2015 5 / 20

Quantum-Classical Approaches Fundamental idea of quantum-classical separation has been around for many years Quantum Mechanics/Molecular Mechanics Surface Hopping Reduced Models (Spin-Boson, etc.) Thomas Allen (PI: Nancy Makri) May 13, 2015 5 / 20

Quantum-Classical Approaches Fundamental idea of quantum-classical separation has been around for many years Quantum Mechanics/Molecular Mechanics Surface Hopping Reduced Models (Spin-Boson, etc.) All of these methods make tradeoffs in rigor or representation We desire a rigorous method that works across many regimes of behavior Thomas Allen (PI: Nancy Makri) May 13, 2015 5 / 20

Quantum-Classical Approaches Fundamental idea of quantum-classical separation has been around for many years Quantum Mechanics/Molecular Mechanics Surface Hopping Reduced Models (Spin-Boson, etc.) All of these methods make tradeoffs in rigor or representation We desire a rigorous method that works across many regimes of behavior Capturing full system-bath interaction is especially important The Quantum-Classical Path Integral formalism is designed to achieve these goals Thomas Allen (PI: Nancy Makri) May 13, 2015 5 / 20

QCPI in a Nutshell Thomas Allen (PI: Nancy Makri) May 13, 2015 6 / 20

QCPI in a Nutshell Thomas Allen (PI: Nancy Makri) May 13, 2015 7 / 20

QCPI in a Nutshell Thomas Allen (PI: Nancy Makri) May 13, 2015 8 / 20

QCPI in a Nutshell Thomas Allen (PI: Nancy Makri) May 13, 2015 9 / 20

QCPI Equations � � e − i ˆ h ˆ ρ (0) e i ˆ s + N x + HN ∆ t / ¯ HN ∆ t / ¯ ρ red ( s ± dx ± � h � � s − N x − � � ˆ N ; N ∆ t ) = N N N R. Lambert, N. Makri, J. Chem. Phys. 137 , 22A552 and 22A553 (2012) Thomas Allen (PI: Nancy Makri) May 13, 2015 10 / 20

QCPI Equations � � e − i ˆ h ˆ ρ (0) e i ˆ s + N x + HN ∆ t / ¯ HN ∆ t / ¯ ρ red ( s ± dx ± � h � � s − N x − � � ˆ N ; N ∆ t ) = N N N � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = N , x 0 , p 0 ; N ∆ t ) dx 0 R. Lambert, N. Makri, J. Chem. Phys. 137 , 22A552 and 22A553 (2012) Thomas Allen (PI: Nancy Makri) May 13, 2015 10 / 20

QCPI Equations � � e − i ˆ h ˆ ρ (0) e i ˆ s + N x + HN ∆ t / ¯ HN ∆ t / ¯ ρ red ( s ± dx ± � h � � s − N x − � � ˆ N ; N ∆ t ) = N N N � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = N , x 0 , p 0 ; N ∆ t ) dx 0 R. Lambert, N. Makri, J. Chem. Phys. 137 , 22A552 and 22A553 (2012) Thomas Allen (PI: Nancy Makri) May 13, 2015 10 / 20

The Azzouz-Borgis Model Our goal is to extend previous work to treat atomistic systems H. Azzouz, D. Borgis, J. Chem. Phys. 98 , 7361 (1993) Thomas Allen (PI: Nancy Makri) May 13, 2015 11 / 20

The Azzouz-Borgis Model Our goal is to extend previous work to treat atomistic systems A test system for our method should have several properties Simple MD description Realistic interactions and energetics Rigorous approach is beneficial H. Azzouz, D. Borgis, J. Chem. Phys. 98 , 7361 (1993) Thomas Allen (PI: Nancy Makri) May 13, 2015 11 / 20

The Azzouz-Borgis Model Our goal is to extend previous work to treat atomistic systems A test system for our method should have several properties Simple MD description Realistic interactions and energetics Rigorous approach is beneficial The Azzouz-Borgis model of proton transfer is just such a system H. Azzouz, D. Borgis, J. Chem. Phys. 98 , 7361 (1993) Thomas Allen (PI: Nancy Makri) May 13, 2015 11 / 20

The Azzouz-Borgis Model H. Azzouz, D. Borgis, J. Chem. Phys. 98 , 7361 (1993) Thomas Allen (PI: Nancy Makri) May 13, 2015 12 / 20

QCPI Challenges � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = dx 0 N , x 0 , p 0 ; N ∆ t ) Thomas Allen (PI: Nancy Makri) May 13, 2015 13 / 20

QCPI Challenges � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = dx 0 N , x 0 , p 0 ; N ∆ t ) Huge number of calculations required It is possible to parallelize these efficiently Thomas Allen (PI: Nancy Makri) May 13, 2015 13 / 20

QCPI Challenges � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = dx 0 N , x 0 , p 0 ; N ∆ t ) Thomas Allen (PI: Nancy Makri) May 13, 2015 14 / 20

QCPI Challenges � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = dx 0 N , x 0 , p 0 ; N ∆ t ) Huge number of calculations required It is possible to parallelize these efficiently Forward-Backward paths must interface with MD BW staff and LAMMPS developers helped incorporate this behavior efficiently Thomas Allen (PI: Nancy Makri) May 13, 2015 15 / 20

QCPI Challenges � � ρ red ( s ± dp 0 P ( x 0 , p 0 ) Q ( s ± ˆ N ; N ∆ t ) = dx 0 N , x 0 , p 0 ; N ∆ t ) Huge number of calculations required It is possible to parallelize these efficiently Forward-Backward paths must interface with MD BW staff and LAMMPS developers helped incorporate this behavior efficiently Further refinements suggested by BW staff Using memory for file storage Investigating multi-level parallelism Thomas Allen (PI: Nancy Makri) May 13, 2015 15 / 20

Results Thomas Allen (PI: Nancy Makri) May 13, 2015 16 / 20

Results Thomas Allen (PI: Nancy Makri) May 13, 2015 16 / 20

Results Thomas Allen (PI: Nancy Makri) May 13, 2015 17 / 20

Future Directions Complete converged anharmonic calculations Investigate bath ensemble properties Extending results to complex systems, including proteins and biomolecules Although these systems are larger, their couplings may be more manageable Thomas Allen (PI: Nancy Makri) May 13, 2015 18 / 20

Acknowledgements Thomas Allen (PI: Nancy Makri) May 13, 2015 19 / 20