Full Quantum Calculations Research Articles

Non-linear spectral splitting of Rydberg sodium in external fields**Project supported by the National Basic Research Program of China (Grant No. 2013CB922003) and the National Natural Science Foundation of China (Grant Nos. 11174329 and 91121005).

We have studied highly excited sodium in various electric fields, parallel electric and magnetic fields, with one σ and π photon irradiation, and even in a magnetic field with a complex laser polarization configuration. The σ spectra shows a simple linear Stark effect with the applied electric field, while the π spectra exhibits a strong non-linear dependence on the electric field. The π transitions in parallel fields show a similar behavior to that in a pure electric field but the spectra get more smooth due to the magnetic field. The diamagnetic spectrum with laser polarization angles between 0 and π/2 proves that it can be reproduced by simple linear combination of π and σ components, indicating there is no interference between the π and σ channels. A full quantum calculation considering the quantum defects accounts for all the observations. The quantum defects, especially for the channel np, play an important role in the spectral profile.

Rubidium D1 and D2 atomic lines’ pressure broadened by ground-state helium atoms

Full quantum calculations are performed to determine the spectral broadening of the rubidium D1 and D2 lines induced by collisions with helium perturbers. The potential curves of the low-lying RbHe molecular states, as well as the corresponding transition dipole moments, are generated theoretically with ab initio methods based on SA-CASSCF-MRCI calculations, including the spin–orbit effects. The absorption and emission coefficients at wavelengths lying between 650 and and temperatures ranging from 100 to 3000 K are determined. The absorption profile reveals it is dominated by the free–free transitions, whereas the emission spectral shape arises from the free–free and bound–free transitions. The resulting red- and blue-wing profiles are compared with previous experimental and theoretical works.

Nonlinear spectroscopy of barium in parallel electric and magnetic fields

We report on the experimental spectral observations of barium in parallel electric and magnetic fields. The laser pulse is linearly polarized along or perpendicular to the fields, leading to the states m = 0 and the states m = ±1 populated, respectively, by one photon excitation. By sweeping the electric field, we observe the linear and nonlinear splitting of the diamagnetic spectrum as the electric field increases. The spectral anticrossing is induced by the atomic core effect. The Stark spectrum also shows an obvious nonlinear quadratic behavior when the applied magnetic field varies strongly. All spectra are well explained by the full quantum calculation after taking the quantum defect effects of the channel ns up to nf into account.

Full-quantum chemical calculations of the absorption maxima of oxyluciferin in the catalytic center of firefly luciferase containing adenosine monophosphate

Absorption maxima of firefly oxyluciferin (Oxyln) were calculated by taking into account all atoms (10,467–10,473) of Luciola cruciata luciferase (Luc) containing Oxyln, a cofactor adenosine monophosphate (AMP) and water molecules based on its X-ray diffraction data (PDB code: 2D1R). Energy minimization and absorption peak calculations were executed by the Quantum/Molecular Mechanics (QM/MM) method, and by the Intermediated Neglect of Differential Overlap for Spectroscopy (INDO/S) method, respectively. The present study focused on the charge of AMP present in the catalytic center of Luc and investigated the effect of its change on the absorption maxima of Oxyln. As a result, the tendencies of the absorption peaks were found to differ greatly according to the protonation state of Oxyln and to depend on the AMP charge: the absorption maxima of the monoanion and the neutral Oxyln shifted to the longer-wavelength region (approximately 600nm) and to the shorter-wavelength region (around 400–500nm), respectively. Although this trend does not differ from the calculation results for the isolated Oxyln, directly taking into account the specific interaction with the catalytic center of Luc, the absorption maxima of the monoanion and the neutral Oxyln shifted to the longer-wavelength region. The absorption maxima of both monoanion and neutral Oxyln shifted toward the longer-wavelength region on reducing the AMP negative charge from dianion to neutral. According to the results obtained by our “Full-QM” calculations considering the Oxyln–Luc interaction, it was concluded that the red light (∼620nm) and the yellow–green light (∼560nm) emission for the acidic and the neutral/basic pH, respectively, could be assigned to the monoanion and the neutral Oxyln. It was also concluded that the charge of AMP significantly affects the luminescent color.

Harmonic Generation and Nonlinear Propagation: When Secondary Radiations Have Primary Consequences

In this Letter, it is experimentally and theoretically shown that weak odd harmonics generated during the propagation of an infrared ultrashort ultra-intense pulse unexpectedly modify the nonlinear properties of the medium and lead to a strong modification of the propagation dynamics. This result is in contrast with all current state-of-the-art propagation model predictions, in which secondary radiations, such as third harmonic, are expected to have a negligible action upon the fundamental pulse propagation. By analysing full three-dimensional ab initio quantum calculations describing the microscopic atomic optical response, we have identified a fundamental mechanism resulting from interferences between a direct ionization channel and a channel involving one single ultraviolet photon. This mechanism is responsible for wide refractive index modifications in relation with significant variation of the ionization rate. This work paves the way to the full physical understanding of the filamentation mechanism and could lead to unexplored phenomena, such as coherent control of the filamentation by harmonic seeding.

Rotational quenching of H2O by He: Mixed quantum/classical theory and comparison with quantum results

The mixed quantum/classical theory (MQCT) formulated in the space-fixed reference frame is used to compute quenching cross sections of several rotationally excited states of water molecule by impact of He atom in a broad range of collision energies, and is tested against the full-quantum calculations on the same potential energy surface. In current implementation of MQCT method, there are two major sources of errors: one affects results at energies below 10 cm(-1), while the other shows up at energies above 500 cm(-1). Namely, when the collision energy E is below the state-to-state transition energy ΔE the MQCT method becomes less accurate due to its intrinsic classical approximation, although employment of the average-velocity principle (scaling of collision energy in order to satisfy microscopic reversibility) helps dramatically. At higher energies, MQCT is expected to be accurate but in current implementation, in order to make calculations computationally affordable, we had to cut off the basis set size. This can be avoided by using a more efficient body-fixed formulation of MQCT. Overall, the errors of MQCT method are within 20% of the full-quantum results almost everywhere through four-orders-of-magnitude range of collision energies, except near resonances, where the errors are somewhat larger.

Mixed quantum/classical calculations of total and differential elastic and rotationally inelastic scattering cross sections for light and heavy reduced masses in a broad range of collision energies.

The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H2 and Na + N2. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.

Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory.

For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

Fast transport of two ions in an anharmonic trap

We design fast trajectories of a trap to transport two ions using a shortcut-to-adiabaticity technique based on invariants. The effects of anharmonicity are analyzed first perturbatively, with an approximate, single relative-motion mode, description. Then we use classical calculations and full quantum calculations. This allows to identify discrete transport times that minimize excitation in the presence of anharmonicity. An even better strategy to suppress the effects of anharmonicity in a continuous range of transport times is to modify the trajectory using an effective trap frequency shifted with respect to the actual frequency by the coupling between relative and center of mass motions.

Quantum phases of strongly interacting Rydberg atoms in triangular lattices

We present a theoretical study on the system of laser-driven strongly interacting Rydberg atoms trapped in a two-dimensional triangular lattice, in which the dipole-dipole interactions between Rydberg states result in exotic quantum phases. By using the mean-field theory, we investigate the steady state solutions and analyze their dynamical stabilities. We find that in the strong-interaction limit, the dynamics of the system is chaotic and exhibits random oscillations under appropriate laser detunings. Lyapunov exponent criterion is introduced to confirm the existence of this chaotic behavior. In addition, we present a full quantum calculation based on a six-atom model, and find that the system exhibits some bi-antiferromagnetic properties in every triangular cell when the one-photon detuning is exactly resonant or blue-shifted.

Calibrated multi-subband Monte Carlo modeling of tunnel-FETs in silicon and III–V channel materials

We present a semiclassical model for Tunnel-FET (TFET) devices capable to describe band-to-band tunneling (BtBT) as well as far from equilibrium transport of the generated carriers. BtBT generation is implemented as an add-on into an existing multi-subband Monte Carlo (MSMC) transport simulator that accounts as well for the effects typical to alternative channel materials and high-κ dielectrics. A simple but accurate correction for the calculation of the BtBT generation rate to account for carrier confinement in the subbands is proposed and verified by comparison with full 2D quantum calculation.

Quantum transport with two interacting conduction channels

The transport properties of a conduction junction model characterized by two mutually coupled channels that strongly differ in their couplings to the leads are investigated. Models of this type describe molecular redox junctions (where a level that is weakly coupled to the leads controls the molecular charge, while a strongly coupled one dominates the molecular conduction), and electron counting devices in which the current in a point contact is sensitive to the charging state of a nearby quantum dot. Here we consider the case where transport in the strongly coupled channel has to be described quantum mechanically (covering the full range between sequential tunneling and co-tunneling), while conduction through the weakly coupled channel is a sequential process that could by itself be described by a simple master equation. We compare the result of a full quantum calculation based on the pseudoparticle non-equilibrium Green function method to that obtained from an approximate mixed quantum-classical calculation, where correlations between the channels are taken into account through either the averaged rates or the averaged energy. We find, for the steady state current, that the approximation based on the averaged rates works well in most of the voltage regime, with marked deviations from the full quantum results only at the threshold for charging the weekly coupled level. These deviations are important for accurate description of the negative differential conduction behavior that often characterizes redox molecular junctions in the neighborhood of this threshold.

Electrostatic Interaction of the Electrostatic-Embedding and Mechanical-Embedding Schemes for QM/MM Calculations

The geometries of the system including two waters have been optimized by the full quantum calculations with the constraints of the O―O distance. The HF and B3LYP density function levels with STO-3G, 6-31G, 6-31G*, and 6-31++G** four basis sets were used in the optimizations. At the optimized geometries, the QM/MM single point interaction energies of the electrostatic-embedding and mechanical-embedding schemes were calculated. The QM/MM interaction energies were compared with the full quantum calculations. The results reveal that the basis sets could be important in the QM/MM calculations. The QM/MM method of the two schemes could not accurately describe the energy of the structure. The electrostatic and VDW interaction energy between QM and MM regions of the electrostatic-embedding scheme is better than that of the mechanical-embedding scheme at the 6-31G and 6-31G* levels. At the 6-31++G** level, the energies of the two schemes are in good agreement with the full quantum calculations. Present investigation suggests that the electrostatic-embedding scheme could be more suitable in the QM/MM simulations of very large systems, e.g. emzyme reaction. The cutoff radius of the electrostatic-embedding scheme is at least 25a0. AMS subject classifications: 80A50, 92C40

Nonadiabatic Nuclear Dynamics in the Ammonia Cation Studied by the Branching Classical Trajectory Method

The photoinduced nonadiabatic nuclear dynamics of the ammonia cation is studied by the branching classical trajectory approach. The time-dependent populations of different electronic states of the ammonia cation are calculated and are in good agreement with the results of full quantum calculations.

Nonadiabatic Nuclear Dynamics of Atomic Collisions Based on Branching Classical Trajectories

The nonadiabatic nuclear dynamics of low-energy Na + H collisions is studied by the branching classical trajectory approach. The calculated inelastic cross sections are in good agreement with the results of full quantum calculations.

Semiclassical Hybrid Approach to Condensed Phase Molecular Dynamics: Application to the I2Kr17 Cluster

We study the vibrational decoherence dynamics of an iodine molecule in a finite krypton cluster comprising the first solvation shell. A normal mode analysis allows us to successively increase the complexity of the description. For the ground state dynamics, comparison with experimental matrix results shows that already four degrees of freedom are sufficient to capture the main decoherence mechanism. For electronically excited iodine, we model the vibrational dynamics of initial Schrödinger cat-like states by the semiclassical hybrid dynamics [Grossmann, F. J. Chem. Phys. 2006, 125, 014111] and full quantum calculations, where available. Good agreement of the results is found for a reduced model with three degrees of freedom. We find non-Gaussian distortions of the bath density matrix, which is a necessary condition, if Schrödinger catlike states in the bath are to be identified. However, in contrast to the experiment [Segale, D.; et al. J. Chem. Phys. 2005, 122, 111104], we observe only incoherent superpositions of bath vibrational states.

Raman scattering from molecular conduction junctions: Charge transfer mechanism

We present a model for the charge transfer contribution to surface-enhanced Raman spectroscopy (SERS) in a molecular junction. The model is a generalization of the equilibrium scheme for SERS of a molecule adsorbed on a metal surface [B. N. J. Persson. Chem. Phys. Lett. 82, 561 (1981)]. We extend the same physical consideration to a nonequilibrium situation in a biased molecular junction and to nonzero temperatures. Two approaches are considered and compared: a semiclassical approach appropriate for nonresonance Raman scattering, and a quantum approach based on the nonequilibrium Green's function method. Nonequilibrium effects on this contribution to SERS are demonstrated with numerical examples. It is shown that the semiclassical approach provides an excellent approximation to the full quantum calculation as long as the molecular electronic state is outside the Fermi window, that is, as long as the field-induced charge transfer is small.

Detailed model study of dissipative quantum dynamics of K2 attached to helium nanodroplets

We thoroughly investigate vibrational quantum dynamics of dimers attached to He droplets, motivated by recent measurements with K2 (Claas et al 2006 J. Phys. B: At. Mol. Opt. Phys.39 S1151). For those femtosecond pump–probe experiments, the crucial observed features are not reproduced by gas-phase calculations, but agreement is found using a description based on dissipative quantum dynamics, as briefly shown in the work by Schlesinger et al (2010 Chem. Phys. Lett.490 245–8). Here we present a detailed study of the influence of possible effects induced by the droplet. The helium droplet causes electronic decoherence, shifts of potential surfaces and relaxation of wave packets in attached dimers. Moreover, a realistic description of (stochastic) desorption of dimers off the droplet needs to be taken into account. Step by step, we include and study the importance of these effects in our full quantum calculation of the effective dimer dynamics. This approach allows us to reproduce and explain all major experimental findings. We find that desorption is fast and occurs within 2–10 ps after electronic excitation. A further finding is that slow vibrational motion in the ground state can be considered frictionless.

Quantum spectrum of Cherenkov glue

Full quantum calculation of Cherenkov gluon radiation by quark and gluon currents and a Cherenkov decay of a gluon into a pair of Cherenkov gluons in transparent media is performed. Energy losses due to Cherenkov gluon radiation in high energy nuclear collisions are calculated. The angular distribution of the energy flow due to the radiation of Cherenkov gluons is analyzed.

Surface hopping with Ehrenfest excited potential

Given the exponentially scaling cost of full quantum calculations, approximations need to be employed for the simulation of the time evolution of chemical systems. We present a modified version of surface hopping that has the potential to treat larger systems. This is accomplished through an Ehrenfest-like treatment of the excited states, thereby reducing the dynamics to transitions between the ground state and a mean-field excited state. A simplified description of the excited states is achieved, while still allowing for an accurate description of disparate reaction channels. We test our mean-field approximation for the excited states on a series of model problems. Results are compared to the standard surface hopping procedure, with its explicit treatment of all excited states, and the traditional Ehrenfest approach, with its averaging together of all states.