Surrogate Hamiltonian Approach Research Articles

Dissipative quantum dynamics using the stochastic surrogate Hamiltonian approach.

Based on the original Stochastic Surrogate Hamiltonian approach for the simulation of open quantum system dynamics, we present a modified algorithm for the swap procedure. The implementation is tested with nuclear relaxation dynamics of model systems known from literature, i.e., the harmonic oscillator and the Morse oscillator. Finally, the stochastic surrogate Hamiltonian is applied to simulate the dynamical electronic excitation and relaxation of a photodesorption process. This is the first application of the stochastic surrogate Hamiltonian in an ab initio context. A comparison to a surrogate Hamiltonian benchmark allows us to evaluate the results obtained. For this purpose, the well-studied laser-induced desorption of NO from NiO(100) is chosen.

Quantum dynamics of a vibronically coupled linear chain using a surrogate Hamiltonian approach.

Vibronic coupling between the electronic and vibrational degrees of freedom has been reported to play an important role in charge and exciton transport in organic photovoltaic materials, molecular aggregates, and light-harvesting complexes. Explicitly accounting for effective vibrational modes rather than treating them as a thermal environment has been shown to be crucial to describe the effect of vibronic coupling. We present a methodology to study dissipative quantum dynamics of vibronically coupled systems based on a surrogate Hamiltonian approach, which is in principle not limited by Markov approximation or weak system-bath interaction, using a vibronic basis. We apply vibronic surrogate Hamiltonian method to a linear chain system and discuss how different types of relaxation process, intramolecular vibrational relaxation and intermolecular vibronic relaxation, influence population dynamics of dissipative vibronic systems.

Quantum dynamical study of femtosecond photodesorption of CO from TiO2(110).

The photodesorption of CO from TiO2(110) by femtosecond pulses is investigated with the Surrogate Hamiltonian approach. The aim of the study is to resolve the relaxation mechanism and forecast the lifetime of the exited state based on a microscopic description of the excitation and relaxation processes. The parameters characterizing the system are obtained from ab initio and Density Functional Theory-calculations with one parameter estimated from physical considerations and convergence studies. Two electronic states are considered and the relaxation is assumed to be due to the interaction of the excited adsorbate with electron hole pairs in the surface. Desorption probabilities and velocity distributions of the desorbing molecules are calculated and an exited state lifetime is predicted. Throughout this paper atomic units, i.e., ℏ = me = e = a0 = 1, have been used unless otherwise stated.

A Surrogate Hamiltonian study of femtosecond photodesorption of CO from NiO(100)

In this paper, the Surrogate Hamiltonian approach is employed in order to study electronic relaxation in femtosecond laser-induced desorption experiments of CO from NiO(100). The study is based on ab initio calculations and a microscopic description of the NiO(100)-surface and the relaxation mechanism developed by Koch et al. The relaxation mechanism is assumed to be of dipole–dipole interaction nature, where the transition dipole moment of the adsorbate interacts with surface electron-hole pairs. In the Surrogate Hamiltonian approach the electron-hole pairs are treated as two-level systems and are described by excitation energy and a dipole charge. The Surrogate Hamiltonian parameters and potential energy surfaces used are obtained from ab initio calculations. The desorption probability and the velocity distributions of the desorbing molecules are calculated and an excited state lifetime is predicted. Throughout this paper atomic units, i.e. ℏ︀ = m e = e = a 0 = 1, have been used unless otherwise stated.

Between Superexchange and Hopping: An Intermediate Charge-Transfer Mechanism in Poly(A)-Poly(T) DNA Hairpins

We developed a model for hole migration along relatively short DNA hairpins with fewer that seven adenine (A):thymine (T) base pairs. The model was used to simulate hole migration along poly(A)-poly(T) sequences with a particular emphasis on the impact of partial hole localization on the different rate processes. The simulations, performed within the framework of the stochastic surrogate Hamiltonian approach, give values for the arrival rate in good agreement with experimental data. Theoretical results obtained for hairpins with fewer than three A:T base pairs suggest that hole transfer along short hairpins occurs via superexchange. This mechanism is characterized by the exponential distance dependence of the arrival rate on the donor/acceptor distance, k(a) ≃ e(-βR), with β = 0.9 Å(-1). For longer systems, up to six A:T pairs, the distance dependence follows a power law k(a) ≃ R(-η) with η = 2. Despite this seemingly clear signature of unbiased hopping, our simulations show the complete delocalization of the hole density along the entire hairpin. According to our analysis, the hole transfer along relatively long sequences may proceed through a mechanism which is distinct from both coherent single-step superexchange and incoherent multistep hopping. The criterion for the validity of this mechanism intermediate between superexchange and hopping is proposed. The impact of partial localization on the rate of hole transfer between neighboring A bases was also investigated.

Quantum Interferences and Electron Transfer in Photosystem I

We have studied the electron transfer occurring in the photosystem I (PSI) reaction center from the special pair to the first iron-sulfur cluster. Electronic structure calculations performed at the DFT level were employed to determine the on-site energies of the fragments comprising PSI, as well as the charge transfer integrals between neighboring pairs. This electronic Hamiltonian was then used to compute the charge transfer dynamics, using the stochastic surrogate Hamiltonian approach to account for the coherent propagation of the electronic density but also for its energy relaxation and decoherence. These simulations give reasonable transfer time ranging from subpicoseconds to nanoseconds and predict coherent oscillations for several picoseconds. Due to these long-lasting coherences, the propagation of the electronic density can be enhanced or inhibited by quantum interferences. The impact of random fluctuations and asymmetries on these interferences is then discussed. Random fluctuations lead to a classical transport where both constructive and destructive quantum interferences are suppressed. Finally it is shown that an energy difference of 0.15 eV between the on-site energies of the phylloquinones leads to a highly efficient electron transfer even in presence of strong random fluctuations.

Optimal control of open quantum systems: A combined surrogate Hamiltonian optimal control theory approach applied to photochemistry on surfaces

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., ℏ = m(e) = e = a(0) = 1, have been used unless otherwise stated.

A stochastic surrogate Hamiltonian approach of coherent and incoherent exciton transport in the Fenna-Matthews-Olson complex

The capture and transduction of energy in biological systems is clearly necessary for life, and nature has evolved remarkable macromolecular entities to serve these purposes. The Fenna-Matthews-Olson (FMO) complex serves as an intermediate to transfer the energy from the chlorosome to the special pairs of different photo systems. Recent observations have both suggested the importance of coherent exciton transport within the FMO and motivated an elegant and appropriate theoretical construct for interpreting these observations. Here we employ a different approach to exciton transport in a relaxing environment, one based on the stochastic surrogate Hamiltonian method. With it, we calculate the quantum trajectories through the FMO complex both for the model involving seven bacteriochlorophylls that has been used before, and for one involving an eighth bacteriochlorophyll, which has been observed in some new and very important structural work. We find that in both systems, efficient energy transfer to the ultimate receptor occurs, but that because of the placement of, and energy relaxation among, the different bacteriochlorophyll subunits in the FMO complex, the importance of coherent oscillation that was discussed extensively for the seven site system is far less striking for the eight site system, effectively because of the weak mixing between the initial site and the remainder of the system. We suggest that the relevant spectral densities can be determinative for the energy transport route and may provide a new way to enhance energy transfer in artificial devices.

Optimal Control of Open Quantum Systems Applied to the Photochemistry of Surfaces

A quantum system in a condensed phase undergoes strong dissipative processes. The last decades have seen the rise of experimental and theoretical approaches for gaining control over dissipative phenomena. From a theoretical viewpoint it is important to model such processes in a rigorous way. An efficient and accurate method to find control fields is optimal control theory (OCT). In this Letter, a control scheme relying on OCT with time-dependent targets is employed to minimize dissipation, modeled within the surrogate Hamiltonian approach, on adsorbate-surface systems.

Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations

The recently developed quantum-classical method has been applied to the study of dissipative dynamics in multidimensional systems. The method is designed to treat many-body systems consisting of a low dimensional quantum part coupled to a classical bath. Assuming the approximate zeroth order evolution rule, the corrections to the quantum propagator are defined in terms of the total Hamiltonian and the zeroth order propagator. Then the corrections are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary part is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on two model systems coupled to a harmonic bath: (i) an anharmonic (Morse) oscillator and (ii) a double-well potential. The simulations have been performed at zero temperature. The results have been compared to the exact quantum simulations using the surrogate Hamiltonian approach.

Calculation of thermal effects in the photodesorption of NO from NiO(100)

The influence of temperature in the photodesorption of NO from a NiO(100)-surface is studied with a two-dimensional quantum wave packet approach. The complete process including laser-induced excitation and subsequent relaxation is treated explicitly from first principles. The electronic quenching caused by the interaction of the excited adsorbate–substrate system with electron–hole-pairs in the surface is treated with the surrogate Hamiltonian approach. We have implemented a parallelization scheme of the wave packet propagation based on a one-dimensional data decomposition to perform simulations in a reasonable computing time. The results are compared with mixed quantum-classical simulations and with experimental measurements. Both desorption yield and mean velocity of the desorbing molecules were enhanced with increasing temperature. The calculated rotational temperatures are consistent with experimental results.

The role of laser pulse duration in the photodesorption of NO/NiO(1 0 0)

The influence of the duration of the stimulating laser pulse in the photodesorption of NO from a NiO(1 0 0)-surface is studied theoretically within a two-dimensional quantum wave packet approach. The complete event including laser-induced excitation and subsequent electronic relaxation is treated consistently from first principles within the surrogate Hamiltonian approach for open quantum systems. We demonstrate that the common assumption of time-scale separation of excitation and relaxation does not hold if ultrashort femtosecond laser pulses are used. We predict a significant effect on rotational distributions of desorbing molecules if the time scales of electronic excitation and relaxation are similar.

Two-dimensional surrogate Hamiltonian investigation of laser-induced desorption of NO∕NiO(100)

The photodesorption of NO from NiO(100) is studied from first principles, with electronic relaxation treated by the use of the surrogate Hamiltonian approach. Two nuclear degrees of freedom of the adsorbate-substrate system are taken into account. To perform the quantum dynamical wave-packet calculations, a massively parallel implementation with a one-dimensional data decomposition had to be introduced. The calculated desorption probabilities and velocity distributions are in qualitative agreement with experimental data. The results are compared to those of stochastic wave-packet calculations where a sufficiently large number of quantum trajectories is propagated within a jumping wave-packet scenario.

Dissipative dynamics of a system passing through a conical intersection: Ultrafast pump-probe observables

The dynamics of a system incorporating a conical intersection, in the presence of a dissipative environment, is studied with the purpose of identifying observable ultrafast spectroscopic signatures. A model system consisting of two vibronically coupled electronic states with two nuclear degrees of freedom is constructed. Dissipation is treated by two different methods, Lindblad semigroup formalism and the surrogate Hamiltonian approach. Pump-probe experimental expectation values such as transient emission and transient absorption are calculated and compared to the adiabatic and diabatic population transfer. The ultrafast population transfer reflecting the conical intersection is not mirrored in transient absorption measurements such as the recovery of the bleach. Emission from the excited state can be suppressed on the ultrafast time scale, but the existence of a conical intersection is only one of the possible mechanisms that can provide ultrafast damping of emission.

Dissipative quantum dynamics with the surrogate Hamiltonian approach. A comparison between spin and harmonic baths

The dissipative quantum dynamics of an anharmonic oscillator coupled to a bath is studied with the purpose of elucidating the differences between the relaxation to a spin bath and to a harmonic bath. Converged results are obtained for the spin bath by the surrogate Hamiltonian approach. This method is based on constructing a system-bath Hamiltonian, with a finite but large number of spin bath modes, that mimics exactly a bath with an infinite number of modes for a finite time interval. Convergence with respect to the number of simultaneous excitations of bath modes can be checked. The results are compared to calculations that include a finite number of harmonic modes carried out by using the multiconfiguration time-dependent Hartree method of Nest and Meyer [J. Chem. Phys. 119, 24 (2003)]. In the weak coupling regime, at zero temperature and for small excitations of the primary system, both methods converge to the Markovian limit. When initially the primary system is significantly excited, the spin bath can saturate restricting the energy acceptance. An interaction term between bath modes that spreads the excitation eliminates the saturation. The loss of phase between two cat states has been analyzed and the results for the spin and harmonic baths are almost identical. For stronger couplings, the dynamics induced by the two types of baths deviate. The accumulation and degree of entanglement between the bath modes have been characterized. Only in the spin bath the dynamics generate entanglement between the bath modes.

Simulating dissipative phenomena with a random phase thermal wavefunctions, high temperature application of the Surrogate Hamiltonian approach

A scheme for calculating thermally averaged observables for quantum dissipative systems is presented. The method is based on a wavefunction with equal amplitude and random phase composed of a complete set of states, which is then propagated in imaginary time β/2. Application to a Surrogate Hamiltonian simulation of a molecule subject to an ultrafast pulse coupled to a bath is studied. Compared to Boltzmann thermal averaging the method scales more favorably with an increase in the number of bath modes. A self-averaging phenomenon was identified which reduces the number of random sets required to converge the thermal average.