Time-independent Approach Research Articles

Quantum reactive scattering of O(3P)+H2 at collision energies up to 4.4 eV.

We report the results of quantum scattering calculations for the O((3)P)+H2 reaction for a range of collision energies from 0.4 to 4.4 eV, important for astrophysical and atmospheric processes. The total and state-to-state reactive cross sections are calculated using a fully quantum time-independent coupled-channel approach on recent potential energy surfaces of (3)A' and (3)A″ symmetry. A larger basis set than in the previous studies was used to ensure single-surface convergence at higher energies. Our results agree well with the published data at lower energies and indicate the breakdown of reduced dimensionality approach at collision energies higher than 1.5 eV. Differential cross sections and momentum transfer cross sections are also reported.

Spectroscopic and quantum chemical analysis of Isonicotinic acid methyl ester

In this present study, an organic compound Isonicotinic acid methyl ester (INAME) was structurally characterized by FTIR, FT-Raman, and NMR and UV spectroscopy. The optimized geometrical parameters and energies of all different and possible conformers of INAME are obtained from Density Functional Theory (DFT) by B3LYP/6-311++G(d,p) method. There are three conformers (SI, SII-1, and SII-2) for this molecule (ground state). The most stable conformer of INAME is SI conformer. The molecular geometry and vibrational frequencies of INAME in the ground state have been calculated by using HF and density functional method (B3LYP) 6-311++G (d,p) basis set. Detailed vibrational spectral analysis has been carried out and assignments of the observed fundamental bands have been proposed on the basis of peak positions and relative intensities. The computed vibrational frequencies were compared with the experimental frequencies, which yield good agreement between observed and calculated frequencies. A study on the electronic properties, such as HOMO and LUMO energies were performed by time independent DFT approach. Besides, molecular electrostatic potential (MEP) and thermodynamic properties were performed. The electric dipole moment (μ) and first hyper polarizability (β) values of the investigated molecule were computed using ab initio quantum mechanical calculations. The calculated results show that the INAME molecule may have microscopic nonlinear optical (NLO) behavior with non zero values. The 1H and 13C nuclear magnetic resonance (NMR) chemical shifts of the molecule were calculated by gauge independent atomic orbital (GIAO) method.

A comparative study between present and palaeo-heat flow in the Qiangtang Basin, northern Tibet, China

The Qiangtang Basin is a significant prospective area for hydrocarbon and gas hydrate resources in the Tibetan Plateau, China. However, relatively little work has been performed to characterise heat flow in this basin, which has restricted petroleum and gas hydrate exploration. In this study, we compare present and palaeo-heat flow in the Qiangtang Basin to provide information on geothermal regime, hydrocarbon generation and permafrost that is necessary for further petroleum and gas hydrate exploration. We base our study on temperature data from a thermometer well, thermal conductivity tests, vitrinite reflectance data, homogenisation temperature data from fluid inclusions, stratigraphic information and a time-independent modelling approach. Our results indicate that in the central Qiangtang Basin, the present thermal gradient is approximately 15.5 °C/km, and heat flow is approximately 46.69 mW/m2. Heat flow in the Qiangtang Basin is not relatively stable since the Early Jurassic, as previous research has suggested, and it is generally decreasing with time. Additionally, there is a clear difference between the hottest thermal regime of the southern and northern Qiangtang Depressions during Cretaceous to Pleistocene time. In the southern Qiangtang Depression, the palaeogeothermal gradient is approximately 32.0 °C/km, and palaeo-heat flow is approximately 70 mW/m2. However, in the northern Qiangtang Depression, the palaeogeothermal gradient exceeds 81.8 °C/km, and palaeo-heat flow is greater than 172.09 mW/m2. The high thermal regime in the northern Qiangtang Depression is driven mainly by hydrothermal convection. Gas reservoirs are possible targets for hydrocarbon exploration in this depression. Currently, the northwestern part of the northern Qiangtang Depression is the most favourable area for gas hydrate exploration in the Qiangtang Basin.

Rotational excitation of HCN by para- and ortho-H₂.

Rotational excitation of the hydrogen cyanide (HCN) molecule by collisions with para-H2(j = 0, 2) and ortho-H2(j = 1) is investigated at low temperatures using a quantum time independent approach. Both molecules are treated as rigid rotors. The scattering calculations are based on a highly correlated ab initio 4-dimensional (4D) potential energy surface recently published. Rotationally inelastic cross sections among the 13 first rotational levels of HCN were obtained using a pure quantum close coupling approach for total energies up to 1200 cm(-1). The corresponding thermal rate coefficients were computed for temperatures ranging from 5 to 100 K. The HCN rate coefficients are strongly dependent on the rotational level of the H2 molecule. In particular, the rate coefficients for collisions with para-H2(j = 0) are significantly lower than those for collisions with ortho-H2(j = 1) and para-H2(j = 2). Propensity rules in favor of even Δj transitions were found for HCN in collisions with para-H2(j = 0) whereas propensity rules in favor of odd Δj transitions were found for HCN in collisions with H2(j ⩾ 1). The new rate coefficients were compared with previously published HCN-para-H2(j = 0) rate coefficients. Significant differences were found due the inclusion of the H2 rotational structure in the scattering calculations. These new rate coefficients will be crucial to improve the estimation of the HCN abundance in the interstellar medium.

Thermal properties of a DNA denaturation with solvent interaction

In this work we study the effects of the solvent interaction on the nonlinear dynamical structure of a DNA segment, by using a time-independent perturbation approach. Considering a well-known set of values for the spring constant (k) and the Morse (solvent) potential parameters Dn and an (fs and λs), we investigate the denaturation temperature profiles of some DNA’s thermodynamical functions, such as the stretching of the hydrogen bonds, the specific heat and the entropy. Besides a sharp thermal profile behavior of these functions, we observe also that the DNA’s melting temperature decreases as the solvent potential increases.

Duschinsky, Herzberg-Teller, and Multiple Electronic Resonance Interferential Effects in Resonance Raman Spectra and Excitation Profiles. The Case of Pyrene.

We show that a recently developed time-independent approach for the calculation of vibrational resonance Raman (vRR) spectra is able to describe Duschinsky and Herzberg-Teller (HT) effects acting on a single resonant state, together with interferential contributions arising from multiple electronic resonances, allowing us to investigate in detail how their interplay determines both the vRR spectra at selected wavelengths and the Raman excitation profiles. We apply this methodology to the study of the spectra of pyrene in acetonitrile, an ideal system since it exhibits three close-lying electronic transitions that are bright but also subjected to HT effects. To single out the different contributions to vRR line shapes we adopted two different adiabatic models for resonant-state potential energy surfaces, namely, Adiabatic Shift (only accounting from equilibrium geometry displacements) and Adiabatic Hessian (AH, including also the Duschinsky effects), and Franck-Condon (FC) or HT approximations for the transition dipole. We show that, on balance, FC+HT calculations within the AH model provide the best agreement with experiment. Moreover, our methodology permits to individuate bands in the experimental spectra due to the simultaneous contribution of more than one resonant state and to point out and analyze interferential effects between the FC and HT terms in each resonance Raman process, together with FC-HT and HT-HT interferences between different electronic states.

Electron-Nuclear Motion in the Cope Rearrangement of Semibullvalene: Ever Synchronous?

The effect of nuclear motion on the synchronicity of the pincer motion type electronic rearrangement associated with bond making and bond breaking and vice versa is investigated for the degenerate Cope rearrangement of semibullvalene using a time-independent quantum chemical approach. We find that distinct paths along the potential energy surface corresponding to synchronous nuclear rearrangement involve asynchronous electronic fluxes out of the old and into the new bond while synchronous electronic fluxes entail asynchronous nuclear rearrangement. In order to demonstrate the robustness of the results, various high-level quantum chemical methods including full structure optimizations up to second order multireference perturbation theory using triple-ζ basis sets (RS2/cc-pVTZ), which are subsequently refined at the RS3/cc-pVTZ and MRCI+Dav/cc-pVTZ levels of theory, are used for solving the electronic Schrödinger equation. These benchmark results extend previous quantum chemical data for the degenerate Cope rearrangement of semibullvalene and are tested against lower level methods (e.g., density functional theory calculations using the B3LYP and B3PW91 functionals).

State-to-State Quantum Mechanical Calculations of Rate Coefficients for the D+ + H2 → HD + H+ Reaction at Low Temperature

The dynamics of the D(+) + H2 → HD + H(+) reaction on a recent ab initio potential energy surface (Velilla, L.; Lepetit, B.; Aguado, A.; Beswick, J. A.; Paniagua, M. J. Chem. Phys. 2008, 129, 084307) has been investigated by means of a time-independent quantum mechanical approach. Cross-sections and rate coefficients are calculated, respectively, for collision energies below 0.1 eV and temperatures up to 100 K for astrophysical application. An excellent accord is found for collision energy above 5 meV, while a disagreement between theory and experiment is observed below this energy. We show that the rate coefficients reveal a slightly temperature-dependent behavior in the upper part of the temperature range considered here. This is in agreement with the experimental data above 80 K, which give a temperature independent value. However, a significant decrease is found at temperatures below 20 K. This decrease can be related to quantum effects and the decay back to the reactant channel, which are not considered by simple statistical approaches, such as the Langevin model. Our results have been fitted to appropriate analytical expressions in order to be used in astrochemical and cosmological models.

A new bioassay for the ecotoxicological testing of VOCs on groundwater invertebrates and the effects of toluene on Niphargus inopinatus

A protocol was developed for testing the ecotoxicological effects of volatile organic compounds (VOCs) on groundwater invertebrates. Test substance volatility was addressed in a “closed from start to analysis”-design. Since manifestation of toxic effects may be delayed in ‘slower metabolizing’ organisms such as groundwater fauna, a time-independent (TI-) approach was adopted. Toluene was used as a model substance and its toxicity to the groundwater amphipod Niphargus inopinatus was assessed as an example. The method evaluation process considered various methodological issues such as partitioning of the toxicant between the water and the gas phase (Henry equilibrium), the possible depletion of oxygen in closed test vials, as well as microbial biodegradation of the test substance. For N. inopinatus, an LC50,14 days of 46.6mgL−1 toluene was obtained. The ultimate LC50 value was estimated at 23.3mgL−1 toluene. No oxygen depletion occurred in the test vials and Henry equilibrium was found to be established after 6h. The new test system proposed now awaits broad practical application.

A new theoretical method for calculating the radiative association cross section of a triatomic molecule: application to N2–H−

We present a new theoretical method to treat the atom-diatom radiative association within a time independent approach. This method is an adaptation of the driven equations method developed for photodissociation. The bound state energies and wave functions of the molecule are calculated exactly and used to propagate the overlap with the initial scattering wave function. In the second part of this paper, this approach is applied to the radiative association of the N2H(-) anion. The main features of the radiative association cross sections are analysed and the magnitude of the calculated rate coefficient at 10 K is used to discuss the existence of the N2H(-) in the interstellar medium which could be used as a tracer of both N2 and H(-).

The He + ${\rm H}_2^+$H2+ → HeH+ + H reaction: Ab initio studies of the potential energy surface, benchmark time-independent quantum dynamics in an extended energy range and comparison with experiments

In this work we critically revise several aspects of previous ab initio quantum chemistry studies [P. Palmieri et al., Mol. Phys. 98, 1835 (2000); C. N. Ramachandran et al., Chem. Phys. Lett. 469, 26 (2009)] of the HeH(2)(+) system. New diatomic curves for the H(2)(+) and HeH(+) molecular ions, which provide vibrational frequencies at a near spectroscopic level of accuracy, have been generated to test the quality of the diatomic terms employed in the previous analytical fittings. The reliability of the global potential energy surfaces has also been tested performing benchmark quantum scattering calculations within the time-independent approach in an extended interval of energies. In particular, the total integral cross sections have been calculated in the total collision energy range 0.955-2.400 eV for the scattering of the He atom by the ortho- and para-hydrogen molecular ion. The energy profiles of the total integral cross sections for selected vibro-rotational states of H(2)(+) (v = 0,...,5 and j = 1,...,7) show a strong rotational enhancement for the lower vibrational states which becomes weaker as the vibrational quantum number increases. Comparison with several available experimental data is presented and discussed.

Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: A time-independent approach

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping. We proceed further to evaluate the rate of escape of the driven particle from the metastable state in the high-temperature limit. We also envisage a resonance phenomena, a true hallmark of the system-reservoir quantization. This development would thus serve as a model template to investigate the trapping mechanism, as well as an appropriate analog to understand the dynamics of a fluctuation-induced escape process from the trap.

A time-independent approach for the study of spectral shift function

In this Note, we give a new proof of a pointwise asymptotic expansion in powers of h of the derivative of the spectral shift function corresponding to the pair (−h2Δ+V(x),−h2Δ), near a non-trapping energy. Here the potential V is smooth, real-valued and O(|x|−δ) for some δ>n, and h>0 is a small parameter. This result is originally due to D. Robert and H. Tamura and their proof is based on the construction of a long-time parametrix for the time-dependent Schrödinger equation. Here we give a time-independent method.

Kinetic energy release in fragmentation processes following electron emission: A time-dependent approach

A time-dependent approach for the kinetic energy release (KER) spectrum is developed for a fragmentation of a diatomic molecule after an electronic decay process, e.g., Auger process. It allows one to simulate the time-resolved spectra and provides more insight into the molecular dynamics than the time-independent approach. Detailed analysis of the time-resolved emitted electron and KER spectra sheds light on the interrelation between wave packet dynamics and spectra.

Time-dependent density functional study of transport in molecular junctions

Electron transport in nanostructures is calculated and compared using a time-independent and a time-dependent first-principles framework. The time-independent approach uses the nonequilibrium Green's-function technique to calculate the current, while the time-dependent method extracts the current from the time propagated wave function. The approaches have been tested using gold-benzene-dithiolate-gold and gold-bipyridine-gold molecular junctions. The reasons for the differences in the current-voltage curves predicted by the two methods are discussed.

Time-dependent approaches for the calculation of intersystem crossing rates

We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S(1) ⇝ T(1) transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.

Pulsed flow for enhanced cleaning in food processing

The use of slow (∼1 Hz) flow oscillation imposed on a stationary flow of liquid has been shown to enhance shear stresses imposed on a surface and to mitigate fouling or enhance cleaning. Examples of the application of pulsed flow are presented in this paper. A new measuring technique in combination with tailored CFD simulations was developed for monitoring the cleaning of complex piping equipment with pulsed flow. A time-independent and isotropic approach to model the wall shear stress is introduced. The optical monitoring procedure uses a model food soil consisting of starch as matrix material and phosphorescent zinc sulfide crystals as optical tracer. Investigations of pulsed flow cleaning published prior to this work focused on tests with straight pipes, whereas difficulties in industrial cleaning operations more often arise while operating piping systems and plant components with complex geometries. Therefore cleaning experiments were performed in a CIP test rig simulating industrial cleaning processes. The results with pulsed flow show an enhancement of cleaning efficiency at locations difficult to access using stationary flow.

A time-independent Hermitian Floquet approach for high harmonic generation in H2+ and HD+: Effect of nonadiabatic interaction in HD+

We have theoretically investigated the high harmonic generation (HHG) in H(2)(+) and HD(+) using a time-independent Hermitian nonperturbative three-dimensional Floquet approach for continuous wave monochromatic lasers of intensities of 2.59x10(13), 4.0x10(13), and 5.6x10(13) W/cm(2), and wavelengths of 1064, 532, and 355 nm. For the moderate intensities and the wavelengths used, the Keldysh parameter gamma > 1 and no tunnel ionization occurs. We have endeavored to explain the dynamics of HHG in H(2)(+) and HD(+) within the framework of transitions due to electronic as well as intrinsic (for HD(+)) dipole moments and the nuclear motion on the field coupled ground and the first excited electronic states of these single-electron molecular ions, without considering any ionization. To evaluate the HHG spectra, the resonance Floquet quasienergy and the Fourier components of the Floquet state corresponding to the initial vibrational-rotational level v = 0, J = 0 have been calculated by solving the time-independent close-coupled Schrödinger equation following the Floquet ansatz. For HD(+), we have taken into account the symmetry breaking effect of the nonadiabatic interaction or coupling [beyond the Born-Oppenheimer (BO) dynamics] in our calculations of the HHG spectra and have compared the results with the HHG spectra of HD(+) obtained with the BO approximation.

General Approach to Compute Vibrationally Resolved One-Photon Electronic Spectra

An effective time-independent approach to compute vibrationally resolved optical spectra from first principles is generalized toward the computation of one-photon electronic spectra induced by eith...

On the importance of inner-shell processes in two-photon ionization of Ne+

We have investigated two-photon ionization of ground-state Ne+ using the time-independent R-matrix Floquet approach and the time-dependent R-matrix approach. The R-matrix Floquet approach enables the detailed study of the influence of atomic structure on the magnitude of the ionization rates. It is found that excitation processes involving the inner 2s electron substantially enhance the two-photon ionization rates of Ne+. For photon energies above 37.5 eV, emission of the 2s electron becomes significant as demonstrated by the large probability that the residual Ne2+ ion is left in the 2s2p5 configuration. Time-dependent calculations of the ionization probability as a function of pulse length correspond well with the R-matrix Floquet ionization rates. However, the ionization probability is enhanced by single-photon ionization during the turn-on and turn-off of the laser pulse. In addition, the laser pulse leads to the population and depopulation of autoionizing states above the Ne2+ ground state during the pulse, and the final population left in these states strongly depends on pulse length.