Time-independent Calculations Research Articles

Quantum and statistical state-to-state studies of cold Ar + H2+ collisions.

In this work we present new state-to-state integral scattering cross sections and initial-state selected rate coefficients for the 36Ar (1S) + H2+ (X2Σg+,v = 0,j) reactive system for collision energies up to 0.1 eV (with respect to the 36Ar (1S) + H2+ (X2Σg+,v = 0,j = 0) channel). To the best of our knowledge, these cross sections are the first fully state resolved ones that were obtained by performing time-independent quantum mechanical and quantum statistical calculations. For this purpose a new full-dimensional ground state 2A' adiabatic electronic potential energy surface was calculated at the MRCI+Q/aug-cc-pVQZ level of theory, which was fitted by means of machine learning methods. We find that a statistical quantum method and a statistical adiabatic channel model reproduce quantum mechanical initial-state selected cross sections fairly well, thus suggesting that complex-forming mechanisms seem to be playing an important role in the reaction dynamics of the reaction that was studied.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix-matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree-Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.

Two-wire junction of inequivalent Tomonaga-Luttinger liquids

We develop two novel numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infinite size matrix product state to minimize the finite-size effects. Due to the lack of the translational invariance, we focus on a finite-size window containing the junction. For time-independent calculations, we use infinite boundary conditions to evaluate the correlations within the window. For time-dependent calculations, we use the window technique to evaluate the local currents within the window. The numerical results obtained by both schemes show excellent agreement with the analytical predictions.

Influence of shape resonances on the angular dependence of molecular photoionization delays

Characterizing time delays in molecular photoionization as a function of the ejected electron emission direction relative to the orientation of the molecule and the light polarization axis provides unprecedented insights into the attosecond dynamics induced by extreme ultraviolet or X-ray one-photon absorption, including the role of electronic correlation and continuum resonant states. Here, we report completely resolved experimental and computational angular dependence of single-photon ionization delays in NO molecules across a shape resonance, relying on synchrotron radiation and time-independent ab initio calculations. The angle-dependent time delay variations of few hundreds of attoseconds, resulting from the interference of the resonant and non-resonant contributions to the dynamics of the ejected electron, are well described using a multichannel Fano model where the time delay of the resonant component is angle-independent. Comparing these results with the same resonance computed in e-NO+ scattering highlights the connection of photoionization delays with Wigner scattering time delays.

Collisional excitation of deuterated hydroxyl (OD) by molecular hydrogen

ABSTRACT Cross sections and rate coefficients for transitions between hyperfine levels associated with the 14 lowest rotational/fine-structure levels of OD induced by collisions with ortho-H2 and para-H2 are presented. These collisional parameters have been computed in time-independent close-coupling quantum-scattering calculations with a potential energy surface (PES) describing the OD–H2 interaction, which was obtained by transformation of the OH–H2 PES. Rate coefficients have been computed for temperatures from 5 to 200 K. Cross sections for OD transitions between rotational/fine-structure levels are found to be significantly larger than the corresponding transitions in OH, mainly because of the reduced energy gaps in OD. The hyperfine-resolved rate coefficients were employed in simple radiative transfer calculations for OD and compared with analogous calculations for OH.

Theoretical study of the T+D2 and D+T2 collisions in low-temperature hydrogen plasmas

The study of low-temperature hydrogen plasmas is relevant for many technological plasma applications. The theoretical investigation of elementary processes, especially those involving H, D, and T species, is crucial for the modeling of nonequilibrium plasma systems such as those found in fusion plasmas. We report fully quantum time-independent calculations of rate coefficients for the vibrationally inelastic and reactive collisions of T with ${\mathrm{D}}_{2}(v=0)$ and of D with ${\mathrm{T}}_{2}(v=0)$. Our calculations are based on the ${\mathrm{H}}_{3}$ global potential-energy surface of Mielke et al. [S. L. Mielke et al., J. Chem. Phys. 116, 4142 (2002)]. We obtain state-to-state rate coefficients for the formation of DT through $\mathrm{T}+{\mathrm{D}}_{2}$ and $\mathrm{D}+{\mathrm{T}}_{2}$ reactions and for the vibrational excitation of ${\mathrm{D}}_{2}$ by T and of ${\mathrm{T}}_{2}$ by D for temperatures up to 2500 K. The results are compared to existing ones for other hydrogen isotopes and significant differences are found between the different sets of results, confirming that specific data have to be obtained for all the collisional systems of interest of hydrogen plasmas. We expect that this data will allow a more accurate modeling of hydrogen plasmas of interest for technological applications.

Collisional energy transfer in the HeH+-H reactive system.

The HeH+ molecule is the first to be formed in the Universe. Its recent detection, in the interstellar medium, has increased the interest in the study of the physical and chemical properties of this ion. Here, we report exact quantum time-independent calculations of the collisional cross sections and rate coefficients for the rotational excitation of HeH+ by H. Reactive and exchange channels are taken into account in the scattering calculations. Cross sections are computed for energies of up to 10 000 cm-1, enabling the computation of rate coefficients for temperatures of up to 500 K. The strongest collision-induced rotational HeH+ transitions are those with Δj = 1. Previous results obtained using approximate treatment are compared to the new ones, and significant differences are found. The new rate coefficients are also compared to those for electron-impact rotational excitation, and we found that collisions with H dominate the excitation of HeH+ in media where the electron fraction is less than 10-4. In the light of those results, we recommend the use of the new HeH+-H collisional data in order to accurately model HeH+ excitation in both the interstellar media and early Universe.

Atomic and molecular suite of R-matrix codes for ultrafast dynamics in strong laser fields and electron/positron scattering

SynopsisWe describe and illustrate a number of recent developments of the atomic and molecular ab initio R-matrix suites for both time-dependent calculations of ultrafast laser-induced dynamics and time-independent calculations of photoionization and electron scattering.

Excitation transport in quasi-one-dimensional quantum devices: a multiscale approach with analytical time-dependent non-equilibrium Green’s function

Under the wide-band limit approximation for electrodes, this research proposes analytical time-dependent non-equilibrium Green’s function (TD-NEGF) formulae to investigate dynamical functionalities of quasi-one-dimensional quantum devices, especially for (microwave) photon-assisted transports. Together with a multiscale approach by lumped element model, we also study the effects of transiently-transferring charges to reflect the non-conservation of charges in open quantum systems, and implement numerical calculations in hetero-junction systems composed of functional quantum devices and electrode-contacts (to the environment). The results show that (i) the current calculation by the analytical algorithms, versus those by conventional numerical integrals, presents superior numerical stability on a large-time scale, (ii) the correction of charge transfer effects can better clarify non-physical transport issues, e.g. the blocking of AC signaling under the assumption of conventional constant hamiltonian, (iii) the current in the long-time limit validly converges to the steady value obtained by standard time-independent density functional calculations, and (iv) the occurrence of the photon-assisted transport is well-identified.

The physical structure and surface reactivity of graphene oxide

The structural configuration of graphene oxide and its surface reactivity were investigated experimentally and clarified on the bases of time-independent density functional calculations (DFT). The physical structure was examined by transmission electron microscopy, infrared absorption, and X-ray diffraction parallel to radial distribution analysis. Surface reactivity was examined using N2-adsorption at 77 K and the kinetic of the adsorption of Ni2+, Cd2+, and Pb2+ ions at 300 K. The lattice structure of the material was hexagonal with unit cell a = 2.455 Å and c = 8.64 Å and with layer-layer distance of 4.32 Å. This structure is undulated in response to existence of oxygen atoms that shape surface topological imperfections and breaks the planner regularity. The undulation distance comprises 0.3 Å. The specific surface area was found 60.3 m2/g with about 50% of this area were available to adsorption of 2+ ions due to surface polarization. The vibration frequencies observed in FTIR are identified by DFT calculations and showed that the structure acts as an extended quantum system for which Pauli blocking prevents existence of two modes of marginal hydrogen vibrations within the same sheet.

State-to-state inelastic rotational cross sections in five-atom systems with the multiconfiguration time dependent Hartree method.

We present a MultiConfiguration Time Dependent Hartree (MCTDH) method as an attractive alternative approach to the usual quantum close-coupling method that approaches some computational limits in the calculation of rotational excitation (and de-excitation) between polyatomic molecules (here collisions between triatomic and diatomic rigid molecules). We have performed a computational investigation of the rotational (de-)excitation of the benchmark rigid rotor H2O-H2 system on a recently developed Potential Energy Surface of the complex using the MCTDH method. We focus here on excitations and de-excitations from the 000, 111, and 110 states of H2O with H2 in its ground rotational state, looking at all the potential transitions in the energy range 1-200 cm-1. This work follows a recently completed study on the H2O-H2 cluster where we characterized its spectroscopy and more generally serves a broader goal to describe inelastic collision processes of high dimensional systems using the MCTDH method. We find that the cross sections obtained from the MCTDH calculations are in excellent agreement with time independent calculations from previous studies but does become challenging for the lower kinetic energy range of the de-excitation process: that is, below approximately 20 cm-1 of collision energy, calculations with a relative modest basis become unreliable. The MCTDH method therefore appears to be a useful complement to standard approaches to study inelastic collision for various collision partners, even at low energy, though performing better for rotational excitation than for de-excitation.

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF.

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

Electronic spectroscopy of carbon chains (C2n+1, n = 7–10) of astrophysical importance. II. Quantum dynamics

In continuation with Paper I [S. R. Reddy et al., J. Chem. Phys. 151, 054303 (2019)], the vibronic structure and dynamics of the 1Σu+ electronic state of C15, C17, C19, and C21 chains in the coupled manifold of 1Σu+–1Πg–1Πu– 1Σg+ electronic states have been investigated in this paper. The model vibronic Hamiltonian developed through extensive ab initio quantum chemistry calculations in Paper I is employed, and first principles nuclear dynamics calculations are carried out to obtain the photoabsorption band of the 1Σu+ electronic state. Both time-independent and time-dependent quantum mechanical calculations are carried out to precisely locate the vibrational levels, assign them with the progression of vibrational modes, and elucidate the impact of both Renner-Teller and pseudo-Renner-Teller couplings on them. The nonradiative decay of the 1Σu+ electronic state is studied, and it is found that the decay rate is comparable with the prediction made for them to be qualified as a carrier of diffuse interstellar bands in the literature. The theoretical results are found to be in good accord with the available experimental results.

Collisional Excitation of CF+ by H2: Potential Energy Surface and Rotational Cross Sections

The CF+ molecule is considered one of the key species for the study of fluorine chemistry in the interstellar medium (ISM). Its recent detection, as well as its potential use as a tracer for atomic fluorine in the ISM, has increased the interest in the study of the physical and chemical properties of this cation. Accurate determination of the CF+ abundance in the ISM requires detailed modeling of its excitation from both radiation and collisions with the most dominant species, which are usually atomic and molecular hydrogen. Here, we report a new highly accurate potential energy surface (PES) describing the interaction between CF+ and the H2 molecule. Exact quantum time-independent calculations of the rotational excitation cross sections for collisions of CF+ with both para- and ortho-H2 are reported. Results obtained for collisions with para-H2 are compared to previous calculations performed using an approximate PES averaged over H2 rotation. Excitation data for collisions with ortho-H2 are provided for the first time.

GET-based time-dependent lattice homogenization using a global-local approach

To reduce computational effort, production-type full-core neutronic calculations are usually performed using few-group diffusion theory and a node-homogenized core model, whereby each homogenized node is assumed to have uniform neutronic properties. Homogenized-node properties are determined such that the flux and reaction rates obtained from few-group diffusion calculations using the node-homogenized model are as close as possible to their counterparts obtained using a detailed-geometry, many-group, full-core transport calculation; what constitutes the heterogeneous, reference results. Generalized Equivalence Theory (GET) is widely used to determine the node-homogenized neutronic properties, namely macroscopic cross sections and discontinuity factors. For time-independent calculations, if the reference results are available, then GET provides a way to generate node-homogenized few-group macroscopic cross sections and discontinuity factors such that the node-homogenized diffusion model produces node fluxes and reaction rates identical to the reference node-integrated fluxes and reaction rates. Since full-core reference results are not usually available, node-homogenized parameters are usually generated from single-node detailed-geometry many-group transport calculations using reflective boundary conditions. The corresponding (approximate) discontinuity factors are known as “assembly” discontinuity factors (ADFs). Methods have also been proposed to account for the true node-boundary conditions without resorting to full-core reference calculations. This work extends the equivalence between the heterogeneous model and the node-homogenized model to time-dependent problems and investigates, specifically, the effect of accounting for the time dependence of discontinuity factors compared to the case of using ADFs. A simple, one-dimensional, two-group diffusion model is used for this preliminary investigation. The heterogeneous reference solution is found using fine-mesh finite differences, whereas the node-homogenized solution is found using coarse-mesh (one mesh per node) finite differences. Results show that accounting for the time dependence of the discontinuity factors can reduce node-flux errors from ∼30% to ∼0.025%.

Intermolecular rovibrational bound states of H2O[sbnd]H2 dimer from a MultiConfiguration Time Dependent Hartree approach

We compute the rovibrational eigenstates of the H2OH2 Van der Waals complex using the accurate rigid-rotor potential energy surface of Valiron et al. (2008) with the MultiConfiguration Time Dependent Hartree (MCTDH) method. The J=0–2 rovibrational bound states calculations are done with the Block Improved Relaxation procedure of MCTDH and the subsequent assignment of the states is achieved by inspection of the wavefunctions’ properties. The results of this work are found to be in close agreement with previous time independent calculations reported for this complex and therefore supports the use of the MCTDH approach for the rovibrational spectroscopic study of such weakly bound complexes.

Rotational Excitation of HD by Hydrogen Revisited.

The HD molecules are key species for the cooling of pristine gas at temperatures below 100 K. They are also known to be key tracers of H2 in protoplanetary disks and thus, they can be used as a measure of protoplanetary disks mass. Accurate modeling of the cooling mechanism and of HD abundance in astrophysical media requires a proper modeling for its excitation by both radiative and collisional processes. Here, we report quantum time-independent calculations of collisional rate coefficients for the rotational excitation of HD by H for temperatures ranging from 10 to 1000 K. The reactive and hydrogen exchange channels are taken into account in the scattering calculations. New exact quantum results are compared to previous calculations performed neglecting reactive and exchange channels. We found that for temperatures higher than ∼300 K, the impact of these channels on the rate coefficients cannot be neglected. Such results suggest that the new HD-H collisional data have to be used for properly modeling HD cooling function and HD abundance in all the astrophysical environments where HD plays a role, e.g. in photon-dominated regions, protoplanetary disks, early Universe chemistry, and primordial star forming regions.

An improved coupled-states approximation including the nearest neighbor Coriolis couplings for diatom-diatom inelastic collision.

Solving the time-independent close coupling equations of a diatom-diatom inelastic collision system by using the rigorous close-coupling approach is numerically difficult because of its expensive matrix manipulation. The coupled-states approximation decouples the centrifugal matrix by neglecting the important Coriolis couplings completely. In this work, a new approximation method based on the coupled-states approximation is presented and applied to time-independent quantum dynamic calculations. This approach only considers the most important Coriolis coupling with the nearest neighbors and ignores weaker Coriolis couplings with farther K channels. As a result, it reduces the computational costs without a significant loss of accuracy. Numerical tests for para-H2+ortho-H2 and para-H2+HD inelastic collision were carried out and the results showed that the improved method dramatically reduces the errors due to the neglect of the Coriolis couplings in the coupled-states approximation. This strategy should be useful in quantum dynamics of other systems.

Geometric phase of light-induced conical intersections: adiabatic time-dependent approach

ABSTRACTConical intersections are degeneracies between electronic states and are very common in nature. It has been found that they can also be created both by standing or by running laser waves. The latter are called light-induced conical intersections. It is well known that conical intersections are the sources for numerous topological effects which are manifested, e.g. in the appearance of the geometric or Berry phase. In one of our former works by incorporating the diabatic-to-adiabatic transformation angle with the line-integral technique, we have calculated the Berry-phase of the light-induced conical intersections. Here, we demonstrate that by using the time-dependent adiabatic approach suggested by Berry the geometric phase of the light-induced conical intersections can also be obtained and the results are very similar to those of the time-independent calculations.