Chapter 14
Simulating Quantum Dynamics in
Classical Nanoscale Environments
Gabriel Hanna and Alessandro Sergi
Abstract In this chapter, we describe a mixed quantum-classical approach for
simulating the dynamics of quantum mechanical phenomena occurring in nanoscale
systems. This approach is based on the quantum-classical Liouville equation
(QCLE), which prescribes the dynamics of a quantum subsystem coupled to a
classical environment. We explain how the QCLE can be solved using a stochastic
surface-hopping algorithm and how expectation values of observables can be
computed. Schemes for reducing the number of trajectories required in these
computations and for ensuring the continuous evolution of the quantum subsystem
states along the trajectories are also outlined. To demonstrate the utility of these
techniques, we describe two recent applications: vibrational energy transfer in
an alpha-helical polypeptide and the field-driven dynamics of a plasmonic metamolecule.
Keywords Mixed quantum-classical dynamics · Quantum-classical Liouville
equation · Nonadiabatic transitions · Surface hopping · Vibrational energy
transfer · Plasmonic metamolecule
G. Hanna ()
Department of Chemistry, University of Alberta, Edmonton, AB, Canada
e-mail: gabriel.hanna@ualberta.ca
A. Sergi
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra,
Università degli Studi di Messina, Messina, Italy
Institute of Systems Science, Durban University of Technology, Durban, South Africa
Istituto Nazionale di Fisica Nucleare, Sez. di Catania, Catania, Italy
e-mail: asergi@unime.it
© Springer Nature Singapore Pte Ltd. 2020
T. Onishi (ed.), Theoretical Chemistry for Advanced Nanomaterials,
https://doi.org/10.1007/978-981-15-0006-0_14
515
Simulating Quantum Dynamics in
Classical Nanoscale Environments
Gabriel Hanna and Alessandro Sergi
Abstract In this chapter, we describe a mixed quantum-classical approach for
simulating the dynamics of quantum mechanical phenomena occurring in nanoscale
systems. This approach is based on the quantum-classical Liouville equation
(QCLE), which prescribes the dynamics of a quantum subsystem coupled to a
classical environment. We explain how the QCLE can be solved using a stochastic
surface-hopping algorithm and how expectation values of observables can be
computed. Schemes for reducing the number of trajectories required in these
computations and for ensuring the continuous evolution of the quantum subsystem
states along the trajectories are also outlined. To demonstrate the utility of these
techniques, we describe two recent applications: vibrational energy transfer in
an alpha-helical polypeptide and the field-driven dynamics of a plasmonic metamolecule.
Keywords Mixed quantum-classical dynamics · Quantum-classical Liouville
equation · Nonadiabatic transitions · Surface hopping · Vibrational energy
transfer · Plasmonic metamolecule
G. Hanna ()
Department of Chemistry, University of Alberta, Edmonton, AB, Canada
e-mail: gabriel.hanna@ualberta.ca
A. Sergi
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra,
Università degli Studi di Messina, Messina, Italy
Institute of Systems Science, Durban University of Technology, Durban, South Africa
Istituto Nazionale di Fisica Nucleare, Sez. di Catania, Catania, Italy
e-mail: asergi@unime.it
© Springer Nature Singapore Pte Ltd. 2020
T. Onishi (ed.), Theoretical Chemistry for Advanced Nanomaterials,
https://doi.org/10.1007/978-981-15-0006-0_14
515