About

Craig Martens is a Professor at the University of California, Irvine, within the Department of Chemistry. His research interests encompass Physical Chemistry and Chemical Physics, with a focus on Polymer, Materials, and Nanoscience. His work involves theoretical and computational approaches to these fields, contributing to the understanding of complex chemical systems and advancing knowledge in material sciences.

Research topics

• Physics
• Quantum mechanics
• Geometry
• Classical mechanics
• Atomic physics
• Physical chemistry
• Economics
• Statistical physics
• Chemistry
• Mathematics

Selected publications

• Generalization of Quantum-Trajectory Surface Hopping to Multiple Quantum States

  Journal of Chemical Theory and Computation · 2025-03-10 · 6 citations

  articleCorresponding

  In this work, we present a generalization of the quantum trajectory surface hopping (QTSH) to multiple states and its implementation in the Libra package for nonadiabatic dynamics. In lieu of the ad hoc velocity rescaling used in many trajectory-based surface hopping approaches, QTSH utilizes quantum forces to evolve nuclear degrees of freedom continuously. It also lifts the unphysical constraint of enforcing the total energy conservation at the individual trajectory level and rather conserves the total energy at the trajectory ensemble level. Leveraging our new implementation of the multistate QTSH, we perform a comparative analysis of this method with the conventional fewest switches surface hopping approach. We combine the QTSH and decoherence corrections based on the simplified decay of mixing (SDM) and exact factorization (XF), leading to the QTSH-SDM and QTSH-XF schemes. Using the Holstein, superexchange, and phenol model Hamiltonians, we assess the relative accuracy of the resulting combined schemes in reproducing branching ratios, population, and coherence dynamics for a broad range of initial conditions. We observe that the decoherence correction in QTSH is crucial to improve energy conservation as well as the internal consistency between the population from the quantum probability and active state.

  PublisherDOI

• Nanopores with Ionic Memory in Oscillating Ion Current Signals

  Journal of the American Chemical Society · 2025-12-09 · 3 citations

  articleOpen access

  Nanopores provide controlled nanoconfinement that can be used to induce localized chemical reactions. Here, we present a nanopore exhibiting memory in the frequency of ion current oscillations induced by the dynamic formation and removal of nanoprecipitates within the pore volume. We find that the onset and characteristics of these current oscillations depend on the direction of the voltage scan, with memory effects evidenced in the frequency of switching between high and low conductance states and the probability of the pore to be in the open state. We have also emulated conductive synaptic switching behavior by applying voltage pulses and demonstrated an ability for the system to exhibit long-term potentiation (LTP) and long-term depression (LTD) that mimic learning and memory of synapses. A hypothesis is presented stating that the memory effects arise from the delayed formation and clearing of nanoprecipitates due to spatial-temporal asymmetry as well as from long-term variations in the effective surface charge. We propose a model in which precipitate formation is limited by the cation arrival rate. Our delayed logistic expression successfully recreates steady-state and oscillatory features in the transmembrane current. Nanopores with memory encoded in the frequency of ion current oscillations emulate how the brain stores information, open the possibility to achieve high-dimensional ionic memory, and move beyond the hysteresis in average conductance of ionic memristors.

  PublisherOA PDFDOI

• High-Dimension Ionic Memory in Oscillating Ion Current Signals

  Research Square · 2025-07-04

  preprintOpen access
  PublisherOA PDFDOI

• Nonadiabatic Coupling-Induced Quantum Coherence in Two-Dimensional Materials

  The Journal of Physical Chemistry Letters · 2024-06-10 · 4 citations

  articleOpen access

  Two-dimensional materials provide a rich platform demonstrating quantum effects, and the process of electron-hole recombination occurring in them has significant applications in the fields of the photocatalytic and optoelectronic community. Here, we present nonadiabatic coupling-induced quantum coherence and quantum beats in Al-doped blue phosphorene. The work improves our understanding and utilization of nonadiabatic coupling in low-dimensional materials from a new perspective. In addition, our investigations provide meaningful guidance for manipulating quantum coherence in low-dimensional materials and promoting their novel optoelectronic properties.

  PublisherDOI

• Zombie cats on the quantum–classical frontier: Wigner–Moyal and semiclassical limit dynamics of quantum coherence in molecules

  The Journal of Chemical Physics · 2023-11-22 · 2 citations

  articleSenior author

  In this paper, we investigate the time evolution of quantum coherence-the off-diagonal elements of the density matrix of a multistate quantum system-from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit-an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.

  PublisherDOI

• Zombie Cats on the Quantum-Classical Frontier: Wigner-Moyal and Semiclassical Limit Dynamics of Quantum Coherence in Molecules

  arXiv (Cornell University) · 2023-09-08

  preprintOpen accessSenior author

  In this paper, we investigate the time evolution of quantum coherence -- the off-diagonal elements of the density matrix of a multistate quantum system -- from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is exactly soluble for both fully quantum and semiclassical descriptions. We highlight serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrodinger's cat state. The alive and dead cats of the exact two state quantum evolution collapses into a "zombie" cat in the semiclassical limit -- an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.

  PublisherOA PDFDOI

• Quantum and Semiclassical Trajectories: Development and Applications

  Frontiers research topics · 2023-01-01

  book

  Trajectory-based approaches to quantum dynamics have been developed and applied to describe a range of quantum processes, including nonadiabatic dynamics, quantum tunneling, quantum entanglement, geometric phase effects, and others. Such quantum trajectory methodologies have computational advantages for the numerical simulation of large quantum problems, particularly in many-dimensional systems, where “on the fly

  PublisherDOI

• A First Principles Derivation of Energy Conserving Momentum Jumps in Surface Hopping Simulations

  arXiv (Cornell University) · 2023-09-26

  preprintOpen accessSenior author

  The fewest switches surface hopping (FSSH) method proposed by Tully in 1990 [J. C Tully, J. Chem. Phys. 93, 1061 (1990)] -- along with its many later variations -- is basis for most practical simulations of molecular dynamics with electronic transitions in realistic systems. Despite its popularity, a rigorous formal derivation of the algorithm has yet to be achieved. In this paper, we derive the energy conserving momentum jumps characterizing FSSH from the perspective of quantum trajectory surface hopping (QTSH [C. C. Martens, J. Phys. Chem. A 123, 1110 (2019)]. In the limit of localized nonadiabatic transitions, simple mathematical and physical arguments allow the FSSH algorithm to be derived from first principles. For general processes, the quantum forces characterizing the QTSH method provides accurate results for nonadiabatic dynamics with rigorous energy conservation at the ensemble level within the consistency of the underlying stochastic surface hopping without resorting to the artificial momentum rescaling of FSSH.

  PublisherOA PDFDOI

• A first principles derivation of energy-conserving momentum jumps in surface hopping simulations

  The Journal of Chemical Physics · 2023 · 7 citations

  Senior authorCorresponding
  • Statistical physics
  • Physics
  • Mathematics

  The fewest switches surface hopping (FSSH) method proposed by Tully in 1990 [Tully, J. Chem. Phys. 93, 1061 (1990)]-along with its many later variations-forms the basis for most practical simulations of molecular dynamics with electronic transitions in realistic systems. Despite its popularity, a rigorous formal derivation of the algorithm has yet to be achieved. In this paper, we derive the energy-conserving momentum jumps employed by FSSH from the perspective of quantum trajectory surface hopping (QTSH) [Martens, J. Phys. Chem. A 123, 1110 (2019)]. In the limit of localized nonadiabatic transitions, simple mathematical and physical arguments allow the FSSH algorithm to be derived from first principles. For general processes, the quantum forces characterizing the QTSH method provide accurate results for nonadiabatic dynamics with rigorous energy conservation, at the ensemble level, within the consistency of the underlying stochastic surface hopping without resorting to the artificial momentum rescaling of FSSH.

  PublisherDOI

• Photofragmentation dynamics study of ArBr$$_2$$ $$(v=16,\ldots ,25)$$ using two theoretical methods: trajectory surface hopping and quasiclassical trajectories

  The European Physical Journal D · 2022 · 4 citations

  Senior authorCorresponding
  • Physics
  • Atomic physics
  • Chemistry
  PublisherOA PDFDOI

Recent grants

• Methods for Simulating Nonadiabatic Dynamics with Trajectories

  NSF · $420k · 2018–2022

• Nonlinear Dynamics of Nanopore Current Oscillations

  NSF · $347k · 2008–2011

• Theory and Simulation of Many-Body Quantum Coherence

  NSF · $395k · 2006–2011

Frequent coauthors

• Gregory S. Ezra

  Cornell University

  12 shared

• Arnaldo Donoso

  National University of Ireland, Maynooth

  12 shared

• Zuzanna S. Siwy

  Walker (United States)

  10 shared

• V. A. Apkarian

  University of California, Irvine

  9 shared

• R. Zadoyan

  MKS Instruments (United States)

  9 shared

• Ernesto García‐Alfonso

  8 shared

• Matthew Powell

  University of California, Irvine

  8 shared

• Nadine Halberstadt

  Université de Toulouse

  7 shared