Previous Semiclassical Calculations Research Articles

Signatures of Plexcitonic States in Molecular Electroluminescence

We develop a quantum master equation (QME) approach to investigate the electroluminesence (EL) of molecules confined between metallic electrodes and coupled to quantum plasmonic modes. Within our general state-based framework, we describe electronic tunneling, vibrational damping, environmental dephasing, and the quantum coherent dynamics of coupled quantum electromagnetic field modes. As an example, we calculate the STM-induced spontaneous emission of a tetraphenylporphyrin (TPP) molecule coupled to a nanocavity plasmon. In the weak molecular exciton-plasmon coupling regime we find excellent agreement with experiments, including above-threshold hot luminescence, an effect not described by previous semiclassical calculations. In the strong coupling regime, we analyze the spectral features indicative of the formation of plexcitonic states.

Efficiency of Collisional O2 + N2 Vibrational Energy Exchange.

By following the scheme of the Grid Empowered Molecular Simulator (GEMS), a new O2 + N2 intermolecular potential, built on ab initio calculations and experimental (scattering and second virial coefficient) data, has been coupled with an appropriate intramolecular one. On the resulting potential energy surface detailed rate coefficients for collision induced vibrational energy exchanges have been computed using a semiclassical method. A cross comparison of the computed rate coefficients with the outcomes of previous semiclassical calculations and kinetic experiments has provided a foundation for characterizing the main features of the vibrational energy transfer processes of the title system as well as a critical reading of the trajectory outcomes and kinetic data. On the implemented procedures massive trajectory runs for the proper interval of initial conditions have singled out structures of the vibrational distributions useful to formulate scaling relationships for complex molecular simulations.

Rovibrational coupling in molecular nitrogen at high temperature: An atomic-level study

This article contains an atomic-level numerical investigation of rovibrational relaxation in molecular nitrogen at high temperature (>4000 K), neglecting dissociation. We conduct our study with the use of pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC), verified to produce statistically identical results at the conditions of interest here. MD and CTC DSMC solely rely on the specification of a potential energy surface: in this work, the site-site Ling-Rigby potential. Additionally, dissociation is prevented by modeling the N–N bond either as a harmonic or an anharmonic spring. The selected molecular model was shown to (i) recover the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predict well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduce vibrational relaxation times in excellent accordance with the Millikan-White correlation and previous semi-classical trajectory calculations in the low temperature range, i.e., between 4000 K and 10 000 K. By simulating isothermal relaxations in a periodic box, we found that the traditional two-temperature model assumptions become invalid at high temperatures (>10 000 K), due to a significant coupling between rotational and vibrational modes for bound states. This led us to add a modification to both the Jeans and the Landau-Teller equations to include a coupling term, essentially described by an additional relaxation time for internal energy equilibration. The degree of anharmonicity of the N2 bond determines the strength of the rovibrational coupling. Although neglecting N2 dissociation only provides a partial description of a nitrogen system at very high temperatures, high-energy trends for bound-bound transitions are essential to understand nonequilibrium gas flows, with possible implications on rovibration/chemistry interaction at the onset of N2 dissociation.

The AdS3 × S3 × S3 × S1 Hernández–López phases: a semiclassical derivation

This note calculates the Hernández–López phases for strings in AdS3 × S3 × S3 × S1 by semiclassical methods using the d(2, 1; α)2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3 × S3 × T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrization, cutoffs and surface terms which could safely be ignored in AdS5 × S5, and some issues about the terms c1, s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 × S3 × T4 case, and exactly 1/2 this in the general case AdS3 × S3 × S3 × S1, for any α and any (light) polarizations.

Deuterium Enrichment of Interstellar Methanol Explained by Atom Tunneling

We calculate, down to low temperature and for different isotopes, the reaction rate constants for the hydrogen abstraction reaction H + H(3)COH → H(2) + CH(2)OH/CH(3)O. These explain the known abundances of deuterated forms of methanol in interstellar clouds, where CH(2)DOH can be almost as abundant as CH(3)OH. For abstraction from both the C- and the O-end of methanol, the barrier-crossing motion involves the movement of light hydrogen atoms. Consequently, tunneling plays a dominant role already at relatively high temperature. Our implementation of harmonic quantum transition state theory with on the fly calculation of forces and energies accounts for these tunneling effects. The results are in good agreement with previous semiclassical and quantum dynamics calculations (down to 200 K) and experimental studies (down to 295 K). Here we extend the rate calculations down to lower temperature: 30 K for abstraction from the C-end of methanol and 80 K for abstraction from the OH-group. At all temperatures, abstraction from the C-end is preferred over abstraction from the O-end, more strongly so at lower temperature. Furthermore, the tunneling behavior strongly affects the kinetic isotope effects (KIEs). D + H(3)COH → HD + CH(2)OH has a lower vibrationally adiabatic barrier than H + H(3)COH → H(2) + CH(2)OH, giving rise to an inverse KIE (k(H)/k(D) < 1) at high temperature, in accordance with previous experiments and calculations. However, since tunneling is more facile for the light H atom, abstraction by H is favored over abstraction by D below ~135 K, with a KIE k(H)/k(D) of 11.2 at 30 K. The H + D(3)COD → HD + CD(2)OD reaction is calculated to be much slower than the D + H(3)COH → HD + CH(2)OH, in agreement with low-temperature solid-state experiments, which suggests the preference for H (as opposed to D) abstraction from the C-end of methanol to be the mechanism by which interstellar methanol is deuterium-enriched.

Ultra-fast converging path-integral approach for rotating ideal Bose–Einstein condensates

A recently developed efficient recursive approach for analytically calculating the short-time evolution of the one-particle propagator to extremely high orders is applied here for numerically studying the thermodynamical and dynamical properties of a rotating ideal Bose gas of 87Rb atoms in an anharmonic trap. At first, the one-particle energy spectrum of the system is obtained by diagonalizing the discretized short-time propagator. Using this, many-boson properties such as the condensation temperature, the ground-state occupancy, density profiles, and time-of-flight absorption pictures are calculated for varying rotation frequencies. The obtained results improve previous semiclassical calculations, in particular for smaller particle numbers. Furthermore, we find that typical time scales for a free expansion are increased by an order of magnitude for the delicate regime of both critical and overcritical rotation.

Photoinduced quantum dynamics of ortho- and para-fulvene: Hindered photoisomerization due to mode selective fast radiationless decay via a conical intersection

In this study, we investigate the photoinduced nonadiabatic dynamics of para- and ortho-fulvene by a combination of quantum chemical ab initio calculations and quantum dynamical simulations. We explore the competition between two different pathways, the photoisomerization and radiationless decay via a conical intersection (CI) at planar configuration. For this purpose, we extend a previous two-dimensional model which included the molecular torsion and the antisymmetric stretch as a coupling mode [Grohmann et al., Chem. Phys. 338, 252 (2007)] to a three-dimensional model, taking into account also the symmetric stretch as additional vibrational mode. Quantum dynamical simulations show that upon excitation with a single short laser pulse, the mode selective motion along the symmetric stretch drives the system to the CI, followed by radiationless decay before photoisomerization of fulvene can take place, thus confirming previous semiclassical calculations [Bearpark et al., J. Am. Chem. Soc. 118, 5253 (1996)]. Moreover, we show that the competition between photoisomerization and radiationless decay at a planar geometry depends on the nonadiabatic coupling strength.

Calculations of V−V Transfer Rates in H2 and Comparison with Experiment

Recent observations on VV transfer in H(2) have shown interesting results. For nonresonant processes, comparison of the experimental rate constants with the results of previous semiclassical calculations, quantum oscillators/classical rotors coupled via classical collisions, showed the theoretical rate constants to be too slow by a factor of 3 or more. The semiclassical rate constant of the resonant VV process (v = 1 + v = 0 --> v = 0 + v = 1) was also found to be too slow, by more than an order of magnitude, compared with the experimental rate. Further, the semiclassical model predicted the value of k(1,1-->0,2) to exceed that of k(1,0-->0,1), but the experimental data shows it to be a factor of approximately 2 less. In this work we employ an accurate interaction potential for the H(2)-H(2) system, and treat both rotation and vibration of the diatoms as coupled quantum-mechanical degrees of freedom. These new calculated results are in better overall agreement with the near-resonant experimental values, but the calculated rate constants are a factor of 2 to 3 larger than experiment for the nonresonant processes.

Stimulated Raman scattering measurements of V–V transfer in oxygen

We present new sets of V–V energy transfer rates for vibrational levels 0–5 in O 2 at 300 K, using a stimulated Raman – spontaneous Raman pump/probe apparatus. Inferred rate coefficients, k 0 , 1 v , v - 1 , equal to 2.6 ± .5, 4.3 ± 1.1 × 10 −13 cm 3 s −1 for levels v = 2 and 3 are found to agree, within the combined quoted uncertainty, with the recent data of Kalogerakis. For v = 4 and 5, k 0 , 1 v , v - 1 is found to equal 7.1 × 10 −13 cm 3 s −1 and 2.0 × 10 −13 cm 3 s −1±, respectively. In agreement with earlier observations by Diskin, it is found that previous semi-classical trajectory calculations underestimate O 2 V–V kinetics by approximately one order of magnitude. New calculations, invoking the same semi-classical formalism, require an increase in the attractive part of the intermolecular potential by a factor of approximately 1.75, in order to replicate the experimental data, a result which is considered non-physical. The purely repulsive Forced Harmonic Oscillator – Free Rotator model of Adamovich is found to under predict the absolute rates by a factor of approximately eight, but to predict the relative rates with reasonable accuracy.

Cascade approach to current fluctuations in a chaotic cavity

We propose a simple semiclassical method for calculating higher-order cumulants of current in multichannel mesoscopic conductors. To demonstrate its efficiency, we calculate the third and fourth cumulants of current for a chaotic cavity with multichannel leads of arbitrary transparency and compare the results with ensemble-averaged quantum-mechanical quantities. We also explain the discrepancy between the quantum-mechanical results and previous semiclassical calculations.

Low-energy muon-transfer reaction from hydrogen isotopes to helium isotopes

Direct muon transfer in low-energy collisions of the muonic hydrogen H μ and helium (He ++) is considered in a three-body quantum-mechanical framework of coordinate-space integro-differential Faddeev–Hahn-type equations within two- and six-state close coupling approximations. The final-state Coulomb interaction is treated without any approximation employing appropriate Coulomb waves in the final state. This procedure of treating Coulomb interaction leads to much improved results for low-energy transfer rates. The present results agree reasonably well with previous semiclassical calculations.

Quantum energy levels and classical periodic orbits: discreteness and statistical duality

It is shown that both universal and non-universal correlations must exist between classical periodic orbits in order that Gutzwiller's semiclassical trace formula is consistent with a real, discrete quantum energy spectrum. Formulae for the two-point correlations are derived. The universal correlations are consistent with those conjectured by Argaman et al. (1993). Likewise, both universal and non-universal correlations must exist between quantum energy levels in order that the trace formula be consistent with the fact that periodic orbit actions are real and discrete. In this case, the two-point correlations implied are consistent with random matrix theory and previous semiclassical calculations. These ideas are illustrated with reference to the primes and the Riemann zeros.

Force-assisted velocity selective coherent population trapping

We present a fully quantum analysis of velocity selective coherent population trapping (VSCPT) in two schemes for which there is a force which assists in the accumulation of atoms in the trapping state. In the first scheme, the Fg=2 to Fe=2 transition was studied where the existence of a semiclassical polarization gradient force even for a pure sigma +- sigma - configuration has been demonstrated which gives cooling for blue detuning. We also verify that cooling may be obtained for the F=2 to 1 and F=3 to 2 transitions; our fully quantum mechanical calculations yield a result which is consistent with recent experimental results of Valentin et al. (1992) but differ from previous semiclassical calculations. Secondly, we discuss a scheme of force-assisted VSCPT which combines VSCPT on the Fg=1 to Fe=1 transition with the coupling to another transition for which a strong sub-Doppler cooling force is present. This scheme allows velocity selective coherent population trapping and the polarization-gradient force to work under optimum conditions simultaneously. We find that both of these two schemes lead to efficient cooling of atoms.

Adsorption of NH 3 on MgO(100): a comparative study of ab initio and semi-classical calculations

Three ab initio approaches (i.e., molecular Hartree-Fock, periodic crystal Hartree-Fock and embedded perturbed cluster Hartree-Fock) were used to determine the adsorption site and energy of ammonia molecules on an ideal MgO(100) surface. Each approach is discussed by comparing it with previous semi-classical calculations and with data from laser-induced thermal desorption and low-energy electron diffraction experiments. It is shown that the latter two ab initio methods offer complementary information and their results are fairly consistent with the available data.

Coupled states calculations on vibrational relaxation of N +2 in collisions with He

Coupled states calculations on the vibrational relaxation in collisions of N + 2 ( v=1) with He are carried out over a wide range of collision energies. The results are compared with previous semiclassical calculations and with experimental measurements.

Quantum mechanical calculation of the electron screening in d-D fusion

We present the first quantum mechanical calculation of the electron screening effect for collisions between deuterons (d) and deuterium atoms (D) at finite collision velocity. The calculation has been performed within the framework of the adiabatic representation of the three-body problem. The results are in good agreement with the previous semi-classical calculations based on the classical trajectory Monte Carlo method. Our results allow one to extract from laboratory experiments the fusion cross sections for bare nuclei, which are of interest for the study of stellar interiors and of fusion machines.

Quantum fluctuations in superconducting arrays.

We study quantum-fluctuation effects on the critical behavior of superconducting arrays via the Feynman path-integral formalism. We compute the path-integral approximately and obtain an effective classical Hamiltonian. The renormalization-group technique is then applied, leading to the result that there exists a reentrant transition only for intermediate quantum fluctuations. Unlike previous semiclassical calculations, this is consistent with the known exact result at zero temperature. Effects of quantum fluctuations together with external magnetic fields are also discussed.

Semiclassical vibrational eigenvalues of H 2O and SO 2 by the adiabatic switching method

The adiabatic switching method is used to calculate semiclassical vibrational eigenvalues for H 2O and SO 2. Hyperspherical coordinates are utilized and a semiclassical correction rule, analogous to the Langer method in WKB theory is proposed and tested. Results calculated without the correction rule are in good agreement with previous semiclassical calculations, results obtained with the correction rule are significantly more accurate.

Macroscopic quantum-mechanical contributions to radiative polarization in electron storage rings.

We present a complete first-order quantum electrodynamics calculation of the spin polarization in a relativistic electron storage ring. The result differs from previous semiclassical calculations of other authors in several respects. Under ideal conditions a maximum polarization of 99.2% may be obtained.

.SCRIPTL.2 solution of the quantum mechanical reactive scattering problem. The threshold energy for D + H2(v = 1) .fwdarw. HD + H

The first results of a new method for quantum mechanical calculations of chemical reaction probabilities are presented. The method involves the expansion of the amplitude density due to the difference between the true interaction potential and a distortion potential in a square integrable basis set and the solution of a large set of coupled equations for the basis function coefficients. They find a threshold energy for D + H/sub 2/(upsilon = 1) ..cap alpha.. HD + H, where upsilon is the vibrational quantum number, in good agreement with previous semiclassical tunneling calculations.