Reduced Density Matrix Approach Research Articles

First-Principles Study on Optoelectronic Properties of Fe-Doped Montmorillonite Clay.

A theoretical investigation is conducted to describe optoelectronic properties of Fe-doped montmorillonite nanoclay under spin states of low spin (LS), intermediate spin (IS), and high spin (HS). Ground state electronic properties are studied using spin-polarized density functional theory calculations. The nonradiative and radiative relaxation channels of charge carriers are studied by computing nonadiabatic couplings (NACs) using an "on-the-fly" approach from adiabatic molecular dynamics trajectories. The NACs are further processed using a reduced density matrix approach with the Redfield formalism. The computational results are presented for electronic density of states, absorption spectra, charge carrier dynamics, and photoluminescence (PL) by comparing various spin multiplicities. Results on spin α and spin β components are independent and quite different because of the partial occupation of Fe 3d states. Overall, HS is the most stable with the largest Fe-O distances. One finds different nonradiative relaxation pathways in space and on the time scale for electrons and holes. The Redfield PL reveals obvious Fe 3d-3d transitions for LS and IS.

Reduced density matrix approach to ultracold few-fermion systems in one dimension

The variational determination of the two-fermion reduced density matrix (2-RDM) is described for harmonically trapped, ultracold few-fermion systems in one dimension with equal spin populations. This is accomplished by formulating the problem as a semi-definite program, with the 2-RDM being subject to well-known N-representability conditions. The ground-state energies, as well as the density, pair-correlation function, and lower-order eigenvalues of the 2-RDM of various fermionic systems are found by utilising an augmented Lagrangian method for semi-definite programming. The ground-state energies are found to match well to those determined by full-configuration interaction and coupled-cluster calculations and the density, pair-correlation function, and eigenvalue results demonstrate that the salient features of these systems are well-described by this method. These results collectively demonstrate the utility of the reduced density matrix method firstly in describing strong correlation arising from short-range interactions, suggesting that the well-known N-representability conditions are sufficient to model ultracold fermionic systems, and secondly in illustrating the prospect of treating larger systems currently out of the reach of established methods.

Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where the complex dynamics of interacting fermions is replaced by a statistical average of mean-field like trajectories is able to grasp some correlations beyond the mean-field. We explore the possibility to use alternative equations of motion in the phase-space approach. Guided by the BBGKY hierarchy, equations of motion that already incorporate part of the correlations beyond mean-field are employed along each trajectory. The method is called Hybrid Phase-Space (HPS) because it mixes phase-space techniques and the time-dependent reduced density matrix approach. The novel approach is applied to the one-dimensional Fermi-Hubbard model. We show that the predictive power is improved compared to the original stochastic mean-field method. In particular, in the weak-coupling regime, the results of the HPS theory can hardly be distinguished from the exact solution even for long time.

On uncorrelated inter-monomer Förster energy transfer in Fenna-Matthews-Olson complexes.

The Fenna-Matthews-Olson (FMO) light-harvesting antenna protein of green sulfur bacteria is a long-studied pigment-protein complex which funnels energy from the chlorosome to the reaction centre where photochemistry takes place. The structure of the FMO protein from Chlorobaculum tepidum is known as a homotrimeric complex containing eight bacteriochlorophyll a per monomer. Owing to this structure FMO has strong intra-monomer and weak inter-monomer electronic coupling constants. While long-lived (sub-picosecond) coherences within a monomer have been a prevalent topic of study over the past decade, various experimental evidence supports the presence of subsequent inter-monomer energy transfer on a picosecond time scale. The latter has been neglected by most authors in recent years by considering only sub-picosecond time scales or assuming that the inter-monomer coupling between low-energy states is too weak to warrant consideration of the entire trimer. However, Förster theory predicts that energy transfer of the order of picoseconds is possible even for very weak (less than 5 cm-1) electronic coupling between chromophores. This work reviews experimental data (with a focus on emission and hole-burned spectra) and simulations of exciton dynamics which demonstrate inter-monomer energy transfer. It is shown that the lowest energy 825 nm absorbance band cannot be properly described by a single excitonic state. The energy transfer through FMO is modelled by generalized Förster theory using a non-Markovian, reduced density matrix approach to describe the electronic structure. The disorder-averaged inter-monomer transfer time across the 825 nm band is about 27 ps. While only isolated FMO proteins are presented, the presence of inter-monomer energy transfer in the context of the overall photosystem is also briefly discussed.

Mixed Upper Exciton State of the Special Pair in Bacterial Reaction Centers.

Excitonic interactions between two closely separated bacteriochlorophyll a molecules (BChls) in the special pair of the reaction center (RC) of purple bacteria determine the positions and relative oscillator strengths of its two excitonic components. While the absorption of the lower excitonic band is well-defined, the position and the intensity of the upper excitonic band ( PY+) are still under debate. Recent 77 K two-dimensional electronic spectroscopy data on Rba. capsulatus suggested that the PY+ component absorbs at ∼840 nm, i.e., at a significantly lower energy than previously suggested. In the present work, we argue that the PY+ state is mixed with the excited states of the accessory BChls ( B*/ P Y+) leading to excitons contributing to the 785-825 nm spectral region which is consistent with previously published data. This conclusion is based on hole-burning/linear dichroism data and modeling studies of the excitonic structure of the RC using a non-Markovian reduced density matrix approach.

Development and application of a 2-electron reduced density matrix approach to electron transport via molecular junctions.

Can an electronic device be constructed using only a single molecule? Since this question was first asked by Aviram and Ratner in the 1970s [Chem. Phys. Lett. 29, 277 (1974)], the field of molecular electronics has exploded with significant experimental advancements in the understanding of the charge transport properties of single molecule devices. Efforts to explain the results of these experiments and identify promising new candidate molecules for molecular devices have led to the development of numerous new theoretical methods including the current standard theoretical approach for studying single molecule charge transport, i.e., the non-equilibrium Green's function formalism (NEGF). By pairing this formalism with density functional theory (DFT), a wide variety of transport problems in molecular junctions have been successfully treated. For some systems though, the conductance and current-voltage curves predicted by common DFT functionals can be several orders of magnitude above experimental results. In addition, since density functional theory relies on approximations to the exact exchange-correlation functional, the predicted transport properties can show significant variation depending on the functional chosen. As a first step to addressing this issue, the authors have replaced density functional theory in the NEGF formalism with a 2-electron reduced density matrix (2-RDM) method, creating a new approach known as the NEGF-RDM method. 2-RDM methods provide a more accurate description of electron correlation compared to density functional theory, and they have lower computational scaling compared to wavefunction based methods of similar accuracy. Additionally, 2-RDM methods are capable of capturing static electron correlation which is untreatable by existing NEGF-DFT methods. When studying dithiol alkane chains and dithiol benzene in model junctions, the authors found that the NEGF-RDM predicts conductances and currents that are 1-2 orders of magnitude below those of B3LYP and M06 DFT functionals. This suggests that the NEGF-RDM method could be a viable alternative to NEGF-DFT for molecular junction calculations.

Ultrafast energy transfer with competing channels: Non-equilibrium Förster and Modified Redfield theories.

We derive equations of motion for the reduced density matrix of a molecular system which undergoes energy transfer dynamics competing with fast internal conversion channels. Environmental degrees of freedom of such a system have no time to relax to quasi-equilibrium in the electronic excited state of the donor molecule, and thus the conditions of validity of Förster and Modified Redfield theories in their standard formulations do not apply. We derive non-equilibrium versions of the two well-known rate theories and apply them to the case of carotenoid-chlorophyll energy transfer. Although our reduced density matrix approach does not account for the formation of vibronic excitons, it still confirms the important role of the donor ground-state vibrational states in establishing the resonance energy transfer conditions. We show that it is essential to work with a theory valid in a strong system-bath interaction regime to obtain correct dependence of the rates on donor-acceptor energy gap.

Photoinduced Charge Transfer at Interfaces of Carbon Nanotube and Lead Selenide Nanowire

Photoinduced generation of excitons and their nonradiative relaxation dynamics are simulated at the interface of (10, 0) carbon nanotubes (CNT) and a PbSe nanowire (NW). Possible pathways of photoinduced excitations are explored by combining a reduced density matrix approach in the basis of Kohn–Sham orbitals and on-the-fly nonadiabatic couplings. A range of neutral photoexcitations localized on the CNT is followed by formation of charge transfer (CT) states involving PbSe NW. Depending on the wavelength of the incident light, the initial photoexcitation can be followed by two directions of charge transfer: either (PbSe)+(CNT)− or (PbSe)−(CNT)+. Excitation of a hot electron results in the CT state with an electron located at the NW and the hole at the CNT with shorter lifetime, while excitation of a hot hole leads to the CT state with an electron at the CNT and the hole at the PbSe having much longer lifetime. Observed ability to control the direction and the lifetime of the CT state makes the CNT/PbSe NW composites promising for photovoltaic applications.

Adsorption patterns of caffeic acid on titania: affinity, charge transfer and sunscreen applications

ABSTRACTSeveral photo-induced processes contribute to titania-catalysed photodegradation of organic UV-absorbing compound, caffeic acid (CA), utilised as skin photoprotector in sunscreens containing titania. Optical transitions, channels of photoexcitations, and charge transfer state formation in anatase TiO2 nanowire sensitised by CA are computed and analysed. Trends of charge transfer state formation are explored through modelling of non-adiabatic dynamics using reduced density matrix approach combined with density functional theory with Perdew–Burke–Ernzerhof functional, in the basis of plane waves, using Vienna Ab initio Simulation Package software. The electronic structure of the explored model shows signatures of quantum confinement of TiO2 nanowire. A change of excitation energy provides control of either one of the possible channels for photoexcitations: (1) local excitation at either nanowire or CA-adsorbate or (2) photo-induced electron transfer from CA-adsorbate to titania. The conclusions obtained from this computational modelling deliver further understanding of the adsorption of catechol groups on the surface of titania nanowire that will help in designing titania-based materials least damaging to CA and skin.

XMVB 2.0: A new version of Xiamen valence bond program

Xiamen valence bond (XMVB), which is an ab initio nonorthogonal valence bond program, has been progressively developed and refined during the last 25 years. As the release of XMVB 1.0 in 2004, a number of significant enhancements and improvements have been made to the program. As a consequence, a new version, XMVB 2.0, has been released and will be described in this article. In XMVB 2.0, the nonorthogonal orbital‐based reduced density matrix approach for the valence bond (VB) theory is implemented, based on the second quantization scheme for nonorthogonal orbitals. The present article also describes the recently developed algorithms for orbital optimization in the VB self‐consist field (VBSCF) method, in which the internal contraction of wave function is used for computing energy gradients. Moreover, several newly implemented ab initio VB methods, such as VBSCF(CAS), internally contracted VB second‐order perturbation theory (icVBPT2), VB polarizable continuum model, VB effective fragment potential (VBECP), and density‐functional‐based VB, are briefly reviewed in this article. Finally, test calculations of several planar arenes, in which up to 18 active electrons are involved, are performed with XMVB 2.0. © 2014 Wiley Periodicals, Inc.

Heat current characteristics in nanojunctions with superconducting baths

As a fundamental requisite for thermotronics, controlling heat flow has been a longstanding quest in solid state physics. Recently, there has been a lot of interest in nanoscale hybrid systems as possible candidates for thermal devices. In this context, we study the heat current in the simplest hybrid device of a two level system weakly coupled to two heat baths. We use the reduced density matrix approach together with a simple Born-Markov approximation to calculate the heat current in the steady state. We consider different kinds of reservoirs and show that the nature of the reservoir plays a very important role in determining the thermal characteristics of the device. In particular, we investigate the effectiveness of a conventional superconductor as a reservoir with regard to manipulating the heat current. In the emergent temperature characteristics, we find that superconductivity in the reservoirs leads to enhanced thermal currents and that the superconducting phase transition is clearly visible in the heat current. We observe negative differential thermal conductance and a pronounced rectification of the heat current, making this a good building block for a quantum thermal diode.

Electron Dynamics of Solvated Ti(OH)4

ABSTRACTIncreasing interest in the photocatalytic activity of TiO2 has led to considerations of using TiO2 nanoparticles in energy generation. In order to better understand the electron-hole relaxation of nano scale TiO2 structures, it is important to start with an understanding of TiO2 synthesis building blocks. The solvated titanium (IV) ion is a precursor found in synthesis methods of colloidal TiO2 nanostructures. This simplest test compound may reflect some common basic electronic features for larger structures composed of Ti(IV) coordinated with oxygen. For this computational study, a model of Ti(OH)4 with tetrahedral coordination was created. To simulate the electronic properties of a solution of Ti(IV), the model was surrounded with 27 H2O molecules. The model was explored by means of standard density functional theory (DFT) molecular dynamics (MD) followed by nonadiabatic electron dynamics computed with Reduced Density Matrix approach combined with “on-the-fly coupling”. Results were generated with Vienna ab initio Simulation Package (VASP) using the Perdew-Burke-Ernzerhof (PBE) functional, plane wave basis set, and projector augmented wave (PAW) potentials. The absorption spectra, MD, and electron-hole relaxation rates are presented for the Ti(OH)4 model at various ambient temperatures. The electron-hole relaxation rates show a non-linear dependence on temperature and were found to be near the same order of magnitude as electron-hole relaxation rates in bulk TiO2 calculations. A video of the geometry optimization can be found online.[1]

INFLUENCE OF SPIN-FLIP ON THE PERFORMANCE OF THE SPIN-DIODE

We study spin-dependent transport through a spin diode in the presence of spin-flip by means of reduced density matrix approach. The current polarization and the spin accumulation are computed and influence of spin-flip on the current polarization is also analyzed. Analytical relations for the current polarization and the spin accumulation are obtained as a function of polarization of ferromagnetic lead and the spin-flip rate. It is observed that the current polarization becomes zero under fast spin-flip and the spin accumulation decreases up to 85% when the time of spin-flip is equal to the tunneling time. It is also observed that the current polarization increases linearly when the dot is singly occupied, whereas its behavior is more complicated when the dot is doubly occupied.

Decoherence and Thermalization of Quantum Spin Systems

In this review, we discuss the decoherence and thermalization of a quantum spin system interact- ing with a spin bath environment, by numerically solving the time-dependent Schrodinger equation of the whole system. The effects of the topologic structure and the initial state of the environment on the decoherence of the two-spin and many-spin system are discussed. The role of different spin-spin coupling is considered. We show under which conditions the environment drives the reduced density matrix of the system to a fully decoherent state, and how the diagonal elements of the reduced density matrix approach those expected for the system in the microcanonical or canonical ensemble, depending on the character of the additional integrals of motion. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the microcanonical distribution (in each eigenenergy subspace) and canonical ensemble are states that may result from pure quantum dynamics, suggesting that quan- tum mechanics may be regarded as the foundation of quantum statistical mechanics. Furthermore, our numerical results show that a fully decoherent quantum system prefers to stay in an equilibrium state with a maximum entropy, indicating the validity of the second law of thermodynamics in the decoherence process.

Polarized atomic radiative emission in electric and magnetic fields1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.

A reduced density matrix approach is employed to provide a general theoretical description of polarized radiative emission during single-photon transitions from bound and auto-ionizing states of many-electron atomic systems in the presence of a general arrangement of static (or quasi-static) electric and magnetic fields. Polarized radiative emission from partially ionized atomic systems can occur as a result of the excitation of the radiating atomic states by electrons or ions with an anisotropic velocity distribution, which can be produced in an electron or ion beam experiment, and in a non-equilibrium plasma environment. Polarized radiative emission can also be produced or modified during the excitation of the atomic system in the presence of electric and magnetic fields, and electromagnetic fields. In electric and magnetic fields, the normally overlapping angular momentum projection components of atomic spectral lines can be substantially shifted from their field-free positions and split into spectroscopically resolvable (and inherently polarized) features. Because of the breakdown of the field-free angular momentum and parity selection rules, otherwise forbidden components of atomic spectral lines can be generated. Using a representation based on the field-free many-electron atomic states, the Stark–Zeeman patterns can be determined by a diagonalization of the atomic Hamiltonian in the presence of electric and magnetic fields. In the density operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic bound or auto-ionizing states. A general expression for the matrix elements of the detected-photon density operator is obtained and provides a unified framework for the analysis of the spectral intensity, angular distribution, and polarization of the Stark–Zeeman patterns. From a unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the more comprehensive reduced density matrix approach, the non-equilibrium atomic state kinetics and the homogeneous spectral line shapes can be systematically and self-consistently described.

A heuristic model of damped quantum rotation effects in nuclear magnetic resonance spectra

The damped quantum rotation (DQR) theory describes temperature effects in NMR spectra of hindered molecular rotators composed of identical atoms arranged in regular N-gons. In the standard approach, the relevant coherent dynamics are described quantum mechanically and the stochastic, thermally activated motions classically. The DQR theory is consistent. In place of random jumps over one, two, etc., maxima of the hindering potential, here one has damping processes of certain long-lived coherences between spin-space correlated eigenstates of the rotator. The damping-rate constants outnumber the classical jump-rate constants. The jump picture is recovered when the former cluster appropriately around only as many values as the number of the latter. The DQR theory was confirmed experimentally for hindered methyl groups in solids and even in liquids above 170 K. In this paper it is shown that for three-, four-, and sixfold rotators, the Liouville space equations of NMR line shapes, derived previously with the use of the quantum mechanical reduced density matrix approach, can be be given a heuristic justification. It is based on an equation of motion for the effective spin density matrix, where the relevant spin hamiltonian contains randomly fluctuating terms. The occurrence of the latter can be rationalized in terms of fluctuations of the tunneling splittings between the torsional sublevels of the rotator, including momentary liftings of the Kramers degeneracies. The question whether such degeneracy liftings are physical or virtual is discussed. The random terms in the effective hamiltonian can be Monte Carlo modeled as piecewise constant in time, which affords the stochastic equation of motion to be solved numerically in the Hilbert spin space. For sixfold rotators, this way of calculating the spectra can be useful in the instances where the Liouville space formalism of the original DQR theory is numerically unstable.

Dynamics of Photoinduced Proton-Coupled Electron Transfer at Molecule−Semiconductor Interfaces: A Reduced Density Matrix Approach

A theoretical model for describing the dynamics of photoinduced proton-coupled electron transfer (PCET) at molecule−semiconductor interfaces is presented. In this model, the electron is photoexcited to a molecular electronic state near the semiconductor surface, and the subsequent electron transfer to the conduction band of the semiconductor is coupled to a proton transfer reaction. The electron could be photoexcited from the ground to an excited electronic state within a dye molecule at the interface or from the defect band in the semiconductor to a molecular adsorbate layer. A model Hamiltonian is developed to describe this PCET process, and the equations of motion for the reduced density matrix elements in the basis of electron−proton vibronic states are derived. This formulation is used to calculate the time-dependent electronic and vibronic state populations for a series of model systems. These calculations provide insight into the hydrogen/deuterium isotope effect on the dynamics of the donor state population decay for ultrafast interfacial PCET. This isotope effect depends on the initial proton wavepacket and the relative time scales of the donor electronic state population decay and proton vibrational relaxation. The effects of the electronic coupling, temperature, and energy of the donor state on the population dynamics are also investigated for photoinduced interfacial electron transfer and PCET. The resulting theoretical predictions about the qualitative impact of altering system properties on the population decay time scales could be useful for designing catalysts that activate bonds containing hydrogen atoms.

Origin of the Canonical Ensemble: Thermalization with Decoherence

We solve the time-dependent Schrodinger equation for the combination of a spin system interacting with a spin bath environment. In particular, we focus on the time development of the reduced density matrix of the spin system. Under normal circumstances we show that the environment drives the reduced density matrix to a fully decoherent state, and furthermore the diagonal elements of the reduced density matrix approach those expected for the system in the canonical ensemble. We show one exception to the normal case is if the spin system cannot exchange energy with the spin bath. Our demonstration does not rely on time-averaging of observables nor does it assume that the coupling between system and bath is weak. Our findings show that the canonical ensemble is a state that may result from pure quantum dynamics, suggesting that quantum mechanics may be regarded as the foundation of quantum statistical mechanics.

Selective subsurface absorption of hydrogen in palladium using laser distillation

A theoretical model for the selective subsurface absorption of atomic hydrogen in a Pd(111) surface by infrared (IR) laser pulses is presented. The dynamics of the adsorbate is studied within the reduced density matrix approach. Energy and phase relaxation of the hydrogen atom are treated using the semigroup formalism. The vibrational excitation leading to subsurface absorption is performed using rationally designed pulses as well as IR laser pulses optimized on-the-fly. It is shown that dissipation can be used as a tool to transfer population to an otherwise inaccessible state via a mechanism known as "laser distillation." We demonstrate that when the reaction path is generalized from a reduced one-dimensional to full three-dimensional treatment of the system, the laser control strategy can prove very different.

Tip-enhanced secondary emission of a semiconductor quantum dot

We present a theoretical study of the luminescence enhancement in a semiconductor quantum dot in the near field of a metallic tip. The electric near field induced by a plane electromagnetic wave near the apex of the perfectly conducting conical tip has been calculated analytically. The results obtained have been used to evaluate the interband matrix element which determines the electron-hole pair generation rate and luminescence intensity of a semiconductor quantum dot. Secondary emission calculations have been carried out using a reduced density matrix approach assuming a radiation frequency close to resonance with the quantum dot fundamental transition. In order to establish the most favorable experimental conditions, we have analyzed the dependence of the interband matrix element and luminescence spectra intensity on the quantum dot size and the distance between the quantum dot and the tip apex. It has been demonstrated that the presence of the metallic tip results in a significant enhancement of the luminescence intensity and leads to a partial violation of the standard selection rules.