Quantum Mechanical Treatment Research Articles

A hybrid approach to simulation of electron transfer in complex molecular systems

Electron transfer (ET) reactions in biomolecular systems represent an important class of processes at the interface of physics, chemistry and biology. The theoretical description of these reactions constitutes a huge challenge because extensive systems require a quantum-mechanical treatment and a broad range of time scales are involved. Thus, only small model systems may be investigated with the modern density functional theory techniques combined with non-adiabatic dynamics algorithms. On the other hand, model calculations based on Marcus's seminal theory describe the ET involving several assumptions that may not always be met. We review a multi-scale method that combines a non-adiabatic propagation scheme and a linear scaling quantum-chemical method with a molecular mechanics force field in such a way that an unbiased description of the dynamics of excess electron is achieved and the number of degrees of freedom is reduced effectively at the same time. ET reactions taking nanoseconds in systems with hundreds of quantum atoms can be simulated, bridging the gap between non-adiabatic ab initio simulations and model approaches such as the Marcus theory. A major recent application is hole transfer in DNA, which represents an archetypal ET reaction in a polarizable medium. Ongoing work focuses on hole transfer in proteins, peptides and organic semi-conductors.

Entanglement generation in a system of two atomic quantum dots coupled to a pool of interacting bosons

We discuss entanglement generation in a closed system of one or two atomic quantum dots (qubits) coupled via Raman transitions to a pool of cold interacting bosons. The system exhibits rich entanglement dynamics, which we analyze in detail in an exact quantum mechanical treatment of the problem. The bipartite setup of only one atomic quantum dot coupled to a pool of bosons turns out to be equivalent to two qubits which easily get entangled being initially in a product state. We show that both the number of bosons in the pool and the boson-boson interaction crucially affect the entanglement characteristics of the system. The tripartite system of two atomic quantum dots and a pool of bosons reduces to a qubit-qutrit-qubit realization. We consider entanglement possibilities of the pure system as well as of reduced ones by tracing out one of the constituents, and show how the entanglement can be controlled by varying system parameters. We demonstrate that the qutrit, as expected, plays a leading role in entangling of the two qubits and the maximum entanglement depends in a nontrivial way on the pool characteristics.

Implementation of non-equilibrium vertex corrections in KKR: transport through disordered layers

The theoretical description of modern nanoelectronic devices requires a quantum mechanical treatment and often involves disorder, e.g. from alloys. Therefore, the ab initio theory of transport using non-equilibrium Green’s functions is extended to the case of disorder described by the coherent potential approximation. This requires the calculation of non-equilibrium vertex corrections. We implement the vertex corrections in a Korringa–Kohn–Rostoker multiple scattering scheme. In order to verify our implementation and to demonstrate the accuracy and applicability we investigate a system of an iron-cobalt alloy layer embedded in copper. The results obtained with the coherent potential approximation are compared to supercell calculations. It turns out that vertex corrections play an important role for this system.

Dissociative chemisorption dynamics of small molecules on metal surfaces

Much progress has been achieved for both experimental and theoretical studies on the dissociative chemisorption of molecules on surfaces. Quantum state-resolved experimental data has provided unprecedented details for these fundamental steps in heterogeneous catalysis, while the quantitative dynamics is still not fully understood in theory. An in-depth understanding of experimental observations relies on accurate dynamical calculations, in which the potential energy surface and adequate quantum mechanical implementation are desired. This article summarizes the current methodologies on the construction of potential energy surfaces and the quantum mechanical treatments, some of which are promising for future applications. The challenges in this field are also addressed.

Structure and dynamics of the Th4+-ion in aqueous solution – An ab initio QMCF-MD study

An ab initio quantum mechanical charge-field molecular dynamics simulation of the tetravalent thorium ion in aqueous environment is presented. Including the first and second hydration shell in the quantum mechanical treatment to enhance accuracy, this study yields very good results for a wide range of characteristics, as compared to experimental data. 20ps of simulation time were used to investigate structural and dynamical properties of the hydrate by numerous methods, including radial and angular distribution functions, three-body distribution functions, ligand exchange analysis and vibrational spectra. The hydrate proved stable during the simulation and did not show hydrolysis. The first solvation shell was found to be a very flexible one, with a number of intrashell ligand rearrangements occurring along the simulation. The data of the simulation also indicated the existence of a third hydration layer. Vibrational analysis yielded an average ion–oxygen frequency of 420cm−1, which is in excellent agreement with experimental data.

Spin decoherence due to a randomly fluctuating spin bath

We study the decoherence of a spin in a quantum dot due to its hyperfine coupling to a randomly fluctuating bath of nuclear spins. The system is modelled by the central spin model with the spin bath initially being at infinite temperature. We calculate the spectrum and time evolution of the coherence factor using a Monte Carlo sampling of the exact eigenstates obtained via the algebraic Bethe ansatz. The exactness of the obtained eigenstates allows us to study the non-perturbative regime of weak magnetic fields in a full quantum mechanical treatment. In particular, we find a large non-decaying fraction in the zero-field limit. The crossover from strong to weak fields is similar to the decoherence starting from a pure initial bath state treated previously. We compare our results to a simple semiclassical picture [Merkulov et al., Phys. Rev. B 65, 205309 (2002)] and find surprisingly good agreement. Finally, we discuss the effect of weakly coupled spins and show that they will eventually lead to complete decoherence.

Unified treatment of hadronic annihilation and protonium formation in slow collisions of antiprotons with hydrogen atoms

Antiproton ($\overline{p}$) collisions with hydrogen atoms, resulting in the hadronic process of particle-antiparticle annihilation and the atomic process of protonium ($\overline{p}p$) formation (or $\overline{p}$ capture), are investigated theoretically. As the collision energy decreases, the collision time required for the $\overline{p}$ capture becomes necessarily longer. Then, there is the possibility that the $\overline{p}$-$p$ annihilation occurs significantly before the $\overline{p}$ capture process completes. In such a case, one can no longer consider the annihilation decay separately from the $\overline{p}$ capture process. The present study develops a rigorous unified quantum-mechanical treatment of the annihilation and $\overline{p}$ capture processes. For this purpose, an $R$-matrix approach for atomic collisions is extended to have complex-valued $R$-matrix elements allowing for the hadronic annihilation. Detailed calculations are carried out at low collision energies ranging from ${10}^{\ensuremath{-}8}$ to ${10}^{\ensuremath{-}1}$ eV, and the annihilation and the $\overline{p}$ capture (total and product-state selected) cross sections are reported. Consideration is given to the difference between the direct annihilation occurring during the collision and the annihilation of $\overline{p}p$ occurring after the $\overline{p}$ capture. The present annihilation process is also compared with the annihilation in two-body $\overline{p}+p$ collisions.

Towards an accurate treatment of σ∗ ← σ transitions: Moving onto [formula omitted

Dimeric σ∗ radical anions are ubiquitous, and their formation, spectroscopy and outcome can often be elucidated by density functional theory. But for shorter interfragment distances, three-electron two-center systems can be reluctant to a single-determinant description, such as the hexanitrogen radical anion. For N6.-, we show that multireference configuration interactions calculations are required to recover its characteristic electronic excitation energy, while TDDFT fails even with modern exchange–correlation functionals. The effects of vibronic couplings on the absorption spectrum are delineated based on a full quantum mechanical dynamical treatment; this study opens the door towards an accurate description of the subtle solvatochromism of hemi-bonded systems.

Quantitative analysis of metabolic mixtures by two-dimensional 13C constant-time TOCSY NMR spectroscopy.

An increasing number of organisms can be fully (13)C-labeled, which has the advantage that their metabolomes can be studied by high-resolution two-dimensional (2D) NMR (13)C-(13)C constant-time (CT) total correlation spectroscopy (TOCSY) experiments. Individual metabolites can be identified via database searching or, in the case of novel compounds, through the reconstruction of their backbone-carbon topology. Determination of quantitative metabolite concentrations is another key task. Because strong peak overlaps in one-dimensional (1D) NMR spectra prevent straightforward quantification through 1D peak integrals, we demonstrate here the direct use of (13)C-(13)C CT-TOCSY spectra for metabolite quantification. This is accomplished through the quantum mechanical treatment of the TOCSY magnetization transfer at short and long-mixing times or by the use of analytical approximations, which are solely based on the knowledge of the carbon-backbone topologies. The methods are demonstrated for carbohydrate and amino acid mixtures.

Quantum mechanical treatment of binding energy between DNA nucleobases and carbon nanotube: A DFT analysis

The interactions between DNA and carbon nanotubes (CNTs) have been widely studied in recent years. The binding process of DNA with CNT as well as the electronic properties of DNA/CNT hybrids constitutes an interesting yet complicated problem. The binding energy (BE) of the hybridization is one of the most extensively studied parameters for the problem. In this work, density functional theory (DFT) was used to perform geometry optimization of neutral nucleobases including adenine, cytosine, guanine and thymine absorbed on a zigzag (7,0) single-walled CNT and to evaluate the basis set superposition error corrected BE of the optimized configuration. All DFT calculations were performed using the M05-2X functional. The 6-31G(d) basis set was used for the optimization step and single point energy calculations were done using the 6-31G(d,p) basis set. For each nucleobase, we examined the influence of the initial configuration (IC) on the BE value. In particular, we considered 24 different ICs for each nucleobase, and each IC was subjected to an independent optimization and BE calculation. Our results showed that different ICs result in very different BE values and can even change the order of the BE corresponding to different nucleobases. The difference in the BE for a particular nucleobase caused by changes in its IC can be comparable to the difference in the BE between different nucleobases at the same initial position relative to the CNT. This provides an explanation for the discrepancies that exist in the literature on the nucleobase/CNT BE, and suggests that the potential energy surface between the nucleobases and the CNT can have many local minima and care should be exercised in the calculation and interpretation of the BE.

Pitfall in Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation of Small Solutes in Solution

Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem.

Theory of atomistic simulation of spin-transfer torque in nanomagnets

In spin-transfer torque (STT) for technological applications, the miniaturization of the magnet may reach the stage of requiring a fully quantum-mechanical treatment. We present an STT theory which uses the quantum macrospin ground and excited (magnon) states of the nanomagnet. This allows for energy and angular momentum exchanges between the current electron and the nano-magnet. We develop a method of magnetization dynamics simulation which captures the heating effect on the magnet by the spin-polarized current and the temperature-dependence in STT. We also discuss the magnetostatics effect on magnon scattering for ferromagnetic relaxation in a thin film. Our work demonstrates a realistic step towards simulation of quantum spin-transfer torque physics in nano-scale magnets.

Oscillator-field model of moving mirrors in quantum optomechanics

We present a microphysics model for the kinematics and dynamics of optomechanics describing the coupling between an optical field, modeled here by a massless scalar field, and the internal and mechanical degrees of freedom of a movable mirror. Instead of implementing boundary conditions on the field, we introduce an internal degree of freedom and its dynamics to describe the mirror's reflectivity. Depending on parameter values, the internal degrees of freedom of the mirror in this model capture a range of its optical activities, from those exhibiting broadband reflective properties to those reflecting only in a narrow band. After establishing the model we show how appropriate parameter choices lead to other well-known optomechanical models, including those of Barton and Calogeracos [Ann. Phys. (NY) 238, 227 (1995)], Calogeracos and Barton, Ann. Phys. (NY) 238, 268 (1995), Law [Phys. Rev. A 51, 2537 (1995)], and Golestanian and Kardar [Phys. Rev. Lett. 78, 3421 (1997); Phys. Rev. A 58, 1713 (1998)]. As a simple illustrative application we derive classical radiation pressure cooling from this model. We then connect our microphysics model to the common descriptions of a moving mirror coupled to radiation pressure (e.g., with $Nx$ coupling, where $N$ is the photon number and $x$ is the mirror displacement), making explicit the underlying assumptions made in these phenomenological models. Our model is also applicable to the lesser explored case of small $N$, which existing models based on sideband approximations [Kimble et al., Phys. Rev. D 65, 022002 (2001)] have not addressed. Interestingly, we also find that slow-moving mirrors in our model can be described by the ubiquitous Brownian motion model of quantum open systems. The scope of applications of this model ranges from a full quantum-mechanical treatment of radiation pressure cooling and quantum entanglement between macroscopic mirrors to the back reaction of Hawking radiation on black-hole evaporation in a moving mirror analog.

Quantum stabilization of a closed Nielsen-Olesen string

We revisit the classical instability of closed strings in the Abelian Higgs model. The instability is expressed by a vanishing energy as the torus-like configuration shrinks to zero size. We treat the radius of the torus as a collective coordinate and demonstrate that a quantum-mechanical treatment of this coordinate leads to a stabilization of the closed string at small radii.

QM/MM Excited State Molecular Dynamics and Fluorescence Spectroscopy of BODIPY

Absorption and emission spectra arising from the lowest energy transition in BODIPY have been simulated in the gas phase and water using a quantum mechanics/molecular mechanics (QM/MM) approach. Kohn-Sham density functional theory (DFT) is used to calculate both ground (So) and first excited (S1) states using the maximum overlap method to obtain the S1 state. This approach gives ground and excited state structures in good agreement with structures found using multiconfigurational perturbation theory (CASPT2). Application of a post-self-consistent field spin-purification relationship also yields transition energies in agreement with CASPT2 and available experimental data. Spectral bands were simulated using many structures taken from ab initio molecular dynamics simulations of the ground and first excited states. In these simulations, DFT is used for BODIPY, and in the condensed phase simulations the water molecules are treated classically. The resulting spectra show a blue shift of 0.3 eV in both absorption and emission bands in water compared to the gas phase. A Stokes shift of about 0.1 eV is predicted, and the width of the emission band in solution is significantly broader than the absorption band. These results are consistent with experimental data for BODIPY and closely related dyes, and demonstrate how both absorption and emission spectra in solution can be simulated using a quantum mechanical treatment of the electronic structure of the solute.

Fundamental limit to qubit control with coherent field

The ultimate accuracy as regards controlling a qubit with a coherent field is studied in terms of degradation of the fidelity by employing a fully quantum mechanical treatment. While the fidelity error accompanied by pi/2 pulse control is shown to be inversely proportional to the average photon number in a way similar to that revealed by the Gea-Banacloche's results. Our results show that the error depends strongly on the initial state of the qubit. When the initial state of the qubit is in the ground state, the error is about 20 times smaller than that of the control started from the exited state, no matter how large N is. This dependency is explained in the context of an exact quantum mechanical description of the pulse area theorem. By using the result, the error accumulation tendency of successive pulse controls is found to be both non-linear and initial state-dependent.

Cavity-enhanced long-distance coupling of an atomic ensemble to a micromechanical membrane

We discuss a hybrid quantum system where a dielectric membrane situated inside an optical cavity is coupled to a distant atomic ensemble trapped in an optical lattice. The coupling is mediated by the exchange of sideband photons of the lattice laser, and is enhanced by the cavity finesse as well as the square root of the number of atoms. In addition to observing coherent dynamics between the two systems, one can also switch on a tailored dissipation by laser cooling the atoms, thereby allowing for sympathetic cooling of the membrane. The resulting cooling scheme does not require resolved sideband conditions for the cavity, which relaxes a constraint present in standard optomechanical cavity cooling. We present a quantum mechanical treatment of this modular open system which takes into account the dominant imperfections, and identify optimal operation points for both coherent dynamics and sympathetic cooling. In particular, we find that ground state cooling of a cryogenically pre-cooled membrane is possible for realistic parameters.

Evidence for aT-Shape Break-Up Pattern in the Triple Photoionization of Li

We examine the angular distributions of all three electrons ionized from Li by a single photon near the triple ionization threshold using a fully quantum-mechanical treatment. We find strong evidence for a T-shape break-up pattern at a 5 eV excess energy as previously predicted by quasiclassical simulations [A. Emmanouilidou and J. M. Rost, J. Phys. B 39, 4037 (2006); A. Emmanouilidou, P. Wang, and J. M. Rost, Phys. Rev. Lett. 100, 063002 (2008)]. This finding is in conflict with the expected Wannier break-up dynamics of three electrons moving at mutual angles of 120°, which is expected to hold at energies a few eV above threshold. We use our quantum-mechanical approach to explore the physical mechanisms behind this unusual break-up configuration.

Electron dynamics in Na4 clusters under femtosecond laser irradiation

The electron dynamics in metal clusters under femtosecond laser irradiation yield excited nonlinear phenomena under the control of laser parameters. In this study, metal clusters Na4 as an example under femtosecond laser irradiation have been observed within the framework of time-dependent density functional theory molecular dynamics (TDDFT-MD), which self-consistently couples a quantum-mechanical TDDFT treatment of valence electrons with a classical molecular dynamics description of ionic cores. The specific excitation frequencies and polarization directions of the laser have been chosen to investigate the behavior of the dipole response and ionization process. We found that it is necessary to explore the electron dynamics of metal clusters by matching the laser frequency and polarization direction. In addition, resonant dipole oscillations induced by suitable laser parameters show pronounced enhancement of the ionization behavior.

Criterion of applicable models for planar type Cherenkov laser based on quantum mechanical treatments

A generalized theoretical analysis for amplification mechanism in the planar-type Cherenkov laser is given. An electron is represented to be a material wave having temporal and spatial varying phases with finite spreading length. Interaction between the electrons and the electromagnetic (EM) wave is analyzed by counting the quantum statistical properties. The interaction mechanism is classified into the Velocity and Density Modulation (VDM) model and the Energy Level Transition (ELT) model basing on the relation between the wavelength of the EM wave and the electron spreading length. The VDM model is applicable when the wavelength of the EM wave is longer than the electron spreading length as in the microwave region. The dynamic equation of the electron, which is popularly used in the classical Newtonian mechanics, has been derived from the quantum mechanical Schrödinger equation. The amplification of the EM wave can be explained basing on the bunching effect of the electron density in the electron beam. The amplification gain and whose dispersion relation with respect to the electron velocity is given in this paper. On the other hand, the ELT model is applicable for the case that the wavelength of the EM wave is shorter than the electron spreading length as in the optical region. The dynamics of the electron is explained to be caused by the electron transition between different energy levels. The amplification gain and whose dispersion relation with respect to the electron acceleration voltage was derived on the basis of the quantum mechanical density matrix.