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Nonadiabatic Molecular Dynamics (NAMD) provides a general framework for studying highly nonequilibrium processes in a broad range of systems, including electrons, phonons, photons, spins, and other relevant degrees of freedom. NAMD most closely mimics nature and parallels time-resolved spectroscopy experiments. In NAMD, electrons are treated quantum mechanically, e.g., by Time-Dependent Density Functional Theory, while atomic motions are (semi-) classical, because atoms are much heavier and slower than electrons.
Surface Hopping (SH) is the most common class of NAMD approaches. It captures key physical phenomena, such as quantum mechanical branching and approach to thermodynamic equilibrium, while remaining computationally efficient.
By considering quantum dynamics of open systems, we provided a physical justification of SH trajectory branching, while, at the same time, describing decoherence in the quantum subsystem induced by atomic motions. The developed Decoherence Induced Surface Hopping (DISH) approach is widely used to model excited state processes in large systems.
O. V. Prezhdo, “Mean field approximation for the stochastic Schrodinger equation”, J. Chem. Phys. 111 8366 (1999).
H. M. Jaeger, S. Fisher, O. V. Prezhdo “Decoherence induced surface hopping” J. Chem. Phys., 137, 22A545 (2012).
S. Gumber, O. V. Prezhdo, “Zeno and Anti-Zeno Effects in Nonadiabatic Molecular Dynamics”, J. Phys. Chem. Lett., 14 7274-7282 (2023).
D. Liu. B. Wang, A. S. Vasenko. O. V. Prezhdo “Decoherence Ensures Convergence of Non-adiabatic Molecular Dynamics with Number of States”, J. Chem. Phys., 161, 064104 (2024)
Ehrenfest dynamics is a basic NAMD approach. Rooted in Ehrenfest’s theorem, it couples quantum mechanical expectation values to classical variables. Due to its mean-field nature, it does not capture quantum mechanical branching and loss of coherence in the quantum subsystem. We modified the Ehrenfest approach to include these effects, which are particularly important in nanoscale and condensed phases.
A. V. Akimov, R. Long, O. V. Prezhdo, “Coherence penalty functional: A simple method for adding decoherence in Ehrenfest dynamics”, J. Chem. Phys., 140, 194107 (2014).
P. Nijjar, J. Jankowska, O. V. Prezhdo, “Ehrenfest and classical path dynamics with decoherence and detailed balance”, J. Chem. Phys., 150, 204124 (2019).
We borrowed ideas from many body physics to develop a hierarchy of approximations that generalize classical Hamiltonian dynamics to capture quantum effects, such as tunneling, zero-point energy and decoherence, with a few additional variables. Higher order quantum variables are decomposed into lower order ones via closures.
O. V. Prezhdo, “Quantized Hamilton dynamics”, Perspective Article "New Perspectives in Theoretical Chemistry", Theor. Chem. Acc., 116, 206 (2006).
Y. V. Pereverzev, A. Y. Pereverzev, Y. Shigeta, O. V. Prezhdo, “Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics”, J. Chem. Phys., 129, 144104 (2008).
E. M. Heatwole, O. V. Prezhdo, “Second-order Langevin equation in quantized Hamilton dynamics”, J. Phys. Soc. Japan, 77, 044001 (2008).
Quantum commutator and classical Poisson bracket are both Lie brackets. The Poisson bracket can be obtained from the commutator via the Wigner-Moyal expansion in Planck’s constant. We derived a mixed quantum-classical Lie bracket by defining two Planck’s constants and taking the limit of one of them to zero. The resulting quantum-classical Lie bracket is the starting point for various equations of motions.
O. V. Prezhdo and V. V. Kisil, “Mixing quantum and classical mechanics” Phys. Rev. A 56, 162 (1997).
O. V. Prezhdo, “A quantum-classical bracket that satisfies the Jacobi identity”, J. Chem. Phys. – Rapid. Comm., 124, 201104 (2006).
Tully’s Fewest Switches Surface Hopping (FSSH) is the most used NAMD algorithm. It defines transition rates based on state-to-state quantum mechanical fluxes. In higher order processes, such as super-exchange or many-particle transitions, there is no direct flux between initial and final states, and FSSH may err. We developed Global Flux Surface Hopping (GFSH) that solves this problem and provides a generalization of FSSH that is useful for studying complex systems with large numbers of states.
L. Wang, D. Trivedi, O. V. Prezhdo “Global flux surface hopping approach for mixed quantum-classical dynamics”, J. Theor. Comp. Chem., 10, 3598-3605 (2014).
D. J. Trivedi, L. J. Wang, O. V. Prezhdo, “Auger-mediated electron relaxation is robust to deep hole traps: time-domain ab initio study of CdSe quantum dots”, Nano Lett., 15, 2086-2091 (2015).
Surface Hopping is typically performed in Hilbert space. We developed Surface Hopping in quantum Liouville space, opening up additional transition pathways through quantum coherences and enabling modeling of new classes of processes, such as super-exchange and many-particle transitions.
L.-J. Wang, A. E. Sifain, O. V. Prezhdo, “Fewest switches surface hopping in Liouville space”, J. Phys. Chem. Lett., 6, 3827-3833 (2015).
L.-J. Wang, A. E. Sifain, O. V. Prezhdo, “Communication: Global flux surface hopping in Liouville space”, J. Chem. Phys., 143, 191102 (2015).
De Broglie-Bohm formulation of quantum mechanics provides an intuitive description of evolution of quantum particles, which follow deterministic trajectories subject to a highly non-local interaction. We coupled the classical subsystem to an individual trajectory in the ensemble of quantum Bohmian particles, rather than to the average as in the Ehrenfest approach. This way we provided a solution to the classical trajectory branching problem, alternative to Surface Hopping.
O. V. Prezhdo, C. Brooksby, “Quantum backreaction via the Bohmian particle”, Phys. Rev. Lett., 86 3215 (2001).
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