Dr. Daniel Dundas

Lecturer in Applied Mathematics and Theoretical Physics


Rm: DBB.01.021
☎: +44 (0) 28 9097 3369
@: d.dundas@qub.ac.uk

Atomistic Simulation Centre Department of Physics and Astronomy School of Mathematics and Physics Queen's University Belfast University Road Belfast BT7 1NN Northern Ireland

Degrees, Awards and Honours


      Most Recent Publications

      1. Length Matters: Keeping Atomic Wires in Check, MRS Proceedings, 2015, 1753
        doi: 10.1557/opl.2015.197 Abstract
        Dynamical effects of non-conservative forces in long, defect free atomic wires are investigated. Current flow through these wires is simulated and we find that during the initial transient, the kinetic energies of the ions are contained in a small number of phonon modes, closely clustered in frequency. These phonon modes correspond to the waterwheel modes determined from preliminary static calculations. The static calculations allow one to predict the appearance of non-conservative effects in advance of the more expensive real-time simulations. The ion kinetic energy redistributes across the band as non-conservative forces reach a steady state with electronic frictional forces. The typical ion kinetic energy is found to decrease with system length, increase with atomic mass, and its dependence on bias, mass and length is supported with a pen and paper model. This paper highlights the importance of non-conservative forces in current carrying devices and provides criteria for the design of stable atomic wires.

      2. Multielectron effects in high harmonic generation in N2 and benzene: Simulation using a non-adiabatic quantum molecular dynamics approach for laser-molecule interactions http://dx.doi.org/10.1557/opl.2015.197, Journal of Chemical Physics, 2012, 136, No. 19, pp. 194303-1
        doi: 10.1063/1.4718590 Abstract
        A mixed quantum-classical approach is introduced which allows the dynamical response of molecules driven far from equilibrium to be modeled. This method is applied to the interaction of molecules with intense, short-duration laser pulses. The electronic response of the molecule is described using time-dependent density functional theory (TDDFT) and the resulting Kohn-Sham equations are solved numerically using finite difference techniques in conjunction with local and global adaptations of an underlying grid in curvilinear coordinates. Using this approach, simulations can be carried out for a wide range of molecules and both all-electron and pseudopotential calculations are possible. The approach is applied to the study of high harmonic generation in N2 and benzene using linearly polarized laser pulses and, to the best of our knowledge, the results for benzene represent the first TDDFT calculations of high harmonic generation in benzene using linearly polarized laser pulses. For N2 an enhancement of the cut-off harmonics is observed whenever the laser polarization is aligned perpendicular to the molecular axis. This enhancement is attributed to the symmetry properties of the Kohn-Sham orbital that responds predominantly to the pulse. In benzene we predict that a suppression in the cut-off harmonics occurs whenever the laser polarization is aligned parallel to the molecular plane. We attribute this suppression to the symmetry-induced response of the highest-occupied molecular orbital.

      3. Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approachhttp://dx.doi.org/10.1063/1.4718590 , Physical Review B, 2012, 85, pp. 245444
        doi: 10.1103/PhysRevB.85.245444 Abstract
        We derive and employ a semiclassical Langevin equation obtained from path integrals to describe the ionic dynamics of a molecular junction in the presence of electrical current. The electronic environment serves as an effective nonequilibrium bath. The bath results in random forces describing Joule heating, current-induced forces including the nonconservative wind force, dissipative frictional forces, and an effective Lorentz-type force due to the Berry phase of the nonequilibrium electrons. Using a generic two-level molecular model, we highlight the importance of both current-induced forces and Joule heating for the stability of the system. We compare the impact of the different forces, and the wide-band approximation for the electronic structure on our result. We examine the current-induced instabilities (excitation of runaway “waterwheel” modes) and investigate the signature of these in the Raman signals.

      All of Daniel's publications


      1. AMA2005: Fluid Mechanics
      2. AMA4006: Practical Methods for Partial Differential Equations


      1. Ultra-fast electron and photon driven dynamics in molecular systems

        The interaction of molecular systems with ultra short laser pulses provide fundamental examples of complex quantum many body systems driven far from equilibrium. A highly non perturbative and non adiabatic coupling exists between electronic and nuclear degrees of freedom which induces both charge and energy flow within the molecule. These charge and energy transfer processes occur on the femtosecond timescale, and are of extreme importance in the design of electronic devices, probes and sensors, and in the areas of condensed matter and plasma physics, medicine and biochemistry. The development of non adiabatic quantum approaches is therefore one of the great challenges in Physics. The challenge comes about through the diversity of time scales that occur in the problem. These time scales range from a few femtosecond for electron transfer through tens of femtoseconds for excitation processes to hundreds of femtoseconds characterizing the ionic motion. All these processes need to be described within a consistent dynamical picture.

        We have developed a number of approaches for describing the inteaction of molecules using both full quantum descriptions of electron and ions for small molecules and mixed, quantum classical approaches for large molecules.

        • Quantum electron-ion dynamics of small molecules

          For one- and two-electron diatomic molecules such as H2+ and H2 we can treat both the electronic and vibrational degrees of freedom exactly through the solution of the time-dependent Schroedinger equation (TDSE), assuming that the laser light is linearly polarised along the intermolecular axis. Studying such systems interacting with ultrashort intense laser pulse allows us to gain an understanding of the fundamental roles of electron-electron and electron-ion interactions in ultrafast processes and can act as a benchmark for high-precision laboratory experiment.

          We have developed computer codes based on a mixed Lagrange mesh and finite difference approach for solving the TDSE for these molecules. These include a code called THeREMIN (vibraTing HydRogEn Molecular IoN) for describing H2+ and a code called H2MOL for describing H2.

          This work is being carried out with Alejandro de la Calle.

          Pre-ionization dynamics of H2+ by an ultrashort laser pulse
          Dissociation of H2+ by a 6-cycle linearly polarized Ti:sapphire laser pulse. The molecule lies along the z-axis with the laser polarization aligned along this axis. The TDSE is solved in cylindrical coordinates with -150 ≤ z ≤ 150, 0 ≤ ρ ≤ 100, 0 ≤ R ≤ 20. In the plot the ρ coordiante has been integrated over and we focus on that part of the grid neat the atoms. We see electron wavepacket responding in antiphase to the field with very little ionization occuring. After the pulse has finished, we see wavepackets moving out in R which is indicative of dissociation.

          Relevant Papers