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G. Hanna and A. Sergi
14.1 Introduction
Nanotechnologies have attracted the attention of many over the last several decades
due to their versatility and advanced functionality. Optoelectronics [24, 88], molecular electronics [62] and quantum computing/information [8, 58, 59] are just a
few prominent examples of fields that have benefitted tremendously from nanotechnologies. Nowadays, researchers are faced with the challenge of designing
high-performance, efficient and environmentally friendly materials and devices.
This challenge could translate into, for example, constructing devices that are
capable of highly efficient transfer of energy [43, 57], charge [30, 54] or quantum
information [58, 59] in complex nanostructures. To achieve such goals, however,
one must gain a fundamental understanding of the dynamical processes involved
and how these processes are influenced by their nanoscale environments. In this
regard, molecular simulation has proven to be an indispensable tool for probing the
structure and dynamics of nanoscale systems.
When the process under study is of a quantum nature and occurs in a complex,
many-particle system such as a nanomaterial, a fully quantum approach to modelling the dynamics will be computationally intractable. In this case, an approximate
treatment of the dynamics is required to gain insight into the process. Mixed
quantum-classical dynamics methods, which treat a subsystem of interest quantum
mechanically and the particles in its environment (or bath) in a classical-like fashion,
can provide tremendous computational savings over fully quantum methods. For
example, the subsystem could be a key proton/electron in a charge transfer reaction,
a chromophore involved in a vibrational/electronic energy transfer process or an
exciton in a light-harvesting system, while the environment could be a molecule,
solvent or crystal.
The partitioning of a system into different sets of degrees of freedom (DOF)
lies at the heart of the Born–Oppenheimer (BO) approximation, which assumes
a time/energy scale separation between the motions of the nuclei and electrons.
In quantum chemistry, the BO approximation greatly simplifies calculations of
molecular energies and wave functions by enabling one to solve the electronic
Schrödinger equation for a fixed configuration of the nuclei to obtain electronic
energies and wave functions that depend on the nuclear configuration. By repeating
this calculation for a sufficiently large number of nuclear configurations, one can
then construct the potential energy surfaces (PESs) of the electronic subsystem.
These PESs give rise to forces (known as Hellmann-Feynman forces) that act on
the nuclei over the course of their dynamics. When the energy scale separation
between the nuclei and electrons is sufficiently large, the nuclei will evolve subject
to the forces obtained from the PES corresponding to the current state of the
electrons (which will not change because the electrons will not have enough energy
to hop to another PES). This is known as adiabatic dynamics. However, when
their energy scales become comparable, the nuclei can evolve subject to the forces
obtained from another PES (because the electrons may acquire enough energy from
the nuclei to hop to another PES). This breakdown of the BO approximation is
G. Hanna and A. Sergi
14.1 Introduction
Nanotechnologies have attracted the attention of many over the last several decades
due to their versatility and advanced functionality. Optoelectronics [24, 88], molecular electronics [62] and quantum computing/information [8, 58, 59] are just a
few prominent examples of fields that have benefitted tremendously from nanotechnologies. Nowadays, researchers are faced with the challenge of designing
high-performance, efficient and environmentally friendly materials and devices.
This challenge could translate into, for example, constructing devices that are
capable of highly efficient transfer of energy [43, 57], charge [30, 54] or quantum
information [58, 59] in complex nanostructures. To achieve such goals, however,
one must gain a fundamental understanding of the dynamical processes involved
and how these processes are influenced by their nanoscale environments. In this
regard, molecular simulation has proven to be an indispensable tool for probing the
structure and dynamics of nanoscale systems.
When the process under study is of a quantum nature and occurs in a complex,
many-particle system such as a nanomaterial, a fully quantum approach to modelling the dynamics will be computationally intractable. In this case, an approximate
treatment of the dynamics is required to gain insight into the process. Mixed
quantum-classical dynamics methods, which treat a subsystem of interest quantum
mechanically and the particles in its environment (or bath) in a classical-like fashion,
can provide tremendous computational savings over fully quantum methods. For
example, the subsystem could be a key proton/electron in a charge transfer reaction,
a chromophore involved in a vibrational/electronic energy transfer process or an
exciton in a light-harvesting system, while the environment could be a molecule,
solvent or crystal.
The partitioning of a system into different sets of degrees of freedom (DOF)
lies at the heart of the Born–Oppenheimer (BO) approximation, which assumes
a time/energy scale separation between the motions of the nuclei and electrons.
In quantum chemistry, the BO approximation greatly simplifies calculations of
molecular energies and wave functions by enabling one to solve the electronic
Schrödinger equation for a fixed configuration of the nuclei to obtain electronic
energies and wave functions that depend on the nuclear configuration. By repeating
this calculation for a sufficiently large number of nuclear configurations, one can
then construct the potential energy surfaces (PESs) of the electronic subsystem.
These PESs give rise to forces (known as Hellmann-Feynman forces) that act on
the nuclei over the course of their dynamics. When the energy scale separation
between the nuclei and electrons is sufficiently large, the nuclei will evolve subject
to the forces obtained from the PES corresponding to the current state of the
electrons (which will not change because the electrons will not have enough energy
to hop to another PES). This is known as adiabatic dynamics. However, when
their energy scales become comparable, the nuclei can evolve subject to the forces
obtained from another PES (because the electrons may acquire enough energy from
the nuclei to hop to another PES). This breakdown of the BO approximation is