Coriolis Coupling Calculation Research Articles

Quantum dynamics study of reaction H+SiH using a new potential energy surface of SiH<sub>2</sub>(1<sup>1</sup>A′)

Initial state-selected and energy-resolved reaction probabilities, integral cross sections(ICSs), and thermal rate constants of the <inline-formula><tex-math id="M3">\begin{document}$ \text{H}{(}^{2}\text{S})+S\text{iH}({\text{X}}^{2}\Pi; \nu = 0\text{ },j = 0)\to \text{Si}{(}^{1}\text{D})+{\text{H}}_{2}({\text{X}}^{1} \Sigma_{g}^{+}) $\end{document}</tex-math></inline-formula> reaction are calculated within the coupled state(CS) approximation and accurate calculation with full Coriolis coupling(CC) by a time-dependent wave packet propagation method (Chebyshev wave packet method). Therefore, a new ab initio global potential energy surface (PES) of the electronic ground state (1<sup>1</sup>A′) of the system, which was recently reported by Li et al. [<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://pubs.rsc.org/en/content/articlelanding/2022/cp/d1cp05432e"> <i>Phys. Chem. Chem. Phys.</i> 2022 <b>24</b> 7759</ext-link>], is employed. The contributions of all partial waves to the total angular momentum <i>J</i> = 80 for CS approximation and <i>J</i> = 90 for CC calculation are considered to obtain the converged ICSs in a collision energy range of 1.0 ×10<sup>–3</sup>－1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH<sub>2</sub> well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of an SiH<sub>2</sub> complex supported by the stationary points of the SiH<sub>2</sub>(1<sup>1</sup>A′) PES. In addition, the results of the exact calculation including CC effect are compared with those calculated in the CS approximation. For the reaction probability, CC and CS calculations change with similar tends, shown by their observations at small total angular momentum <i>J</i> = 10, 20 and 30, and the CC results are larger than the CS results almost in the whole considered energy range at large total angular momentum <i>J</i> = 40, 50, 60 and 70. The gap between CS and CC probability get more pronounced with increasing of <i>J</i>, which reveals that Coriolis coupling effects become more and more important with <i>J</i> increasing for the title reaction<i>.</i> Moreover, the exact quantum-wave calculations show that the thermal rate constant between 300 K and 1000 K for the title reaction shows a similar temperature independent behavior to that for the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that for the H + CH reaction.

An accurate many-body expansion potential energy surface for AlH2 (22A') and quantum dynamics in Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) collisions.

An accurate potential energy surface is constructed for the excited state of AlH2 by fitting extensive ab initio points calculated at the multi-reference configuration interaction level based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. All the calculated energies are corrected via the many-body expansion method and extrapolated to the complete basis set limit. The various topographic features of the new potential energy surface are investigated to demonstrate the correct behavior of Al(3P) + H2(X1Σg+) and AlH(a3Π) + H(2S) dissociation limits. By employing the time-dependent wave packet approach, the integral scattering cross-sections obtained from the Coriolis coupling calculation and the centrifugal sudden approximation, respectively, are compared in detail and show that the former has a higher effect on the reaction. Moreover, the thermal rate constants for Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) in the temperature range of 0-5000 K are calculated, thereby providing insights into the influence of ro-vibrational quantum numbers on the thermal rate constants.

Quantum dynamics studies of the <inline-formula><tex-math id="M2">\begin{document}$\rm D+SiD^+ \to D_2+Si^ +$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M2.png"/></alternatives></inline-formula> reaction

The quantum dynamics calculations are carried out for the title reaction D +SiD<sup>+</sup>→D<sub>2</sub>+Si<sup>+</sup> to obtain the initial (<inline-formula><tex-math id="M8">\begin{document}$ \nu = 0{\text{ }},j = 0 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_M8.png"/></alternatives></inline-formula>)reaction probability, integral cross section (ICS) and rate constant on the potential energy surface (PES) of Gao, Meng and Song. A total of 110 partial waves are calculated by using the Chebyshev wave packet method with full Coriolis coupling (CC) and centrifugal sudden (CS) approximation in a collision energy range from 1.0 × 10<sup>–3 </sup>to 1.0 eV. The calculated probability decreases with the collision energy increasing except for <i>J≤</i>40. The calculation results indicate that the CS approximation will overestimate or underestimate the reaction probability . The ICS decreases with the collision energy increasing and shows an oscillatory structure due to the<inline-formula><tex-math id="Z-20221114130407">\begin{document}$\rm{SiH_2^+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_Z-20221114130407.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_Z-20221114130407.png"/></alternatives></inline-formula>well on the reaction path. The results show that the neglect of the Coriolis coupling leads to the overestimation of the cross section and the rate constant. Besides, the discrepancy between the integral cross sections from the CC and CS calculations decreases clearly with collision energy increasing. Comparison with the corresponding results of H+CH<sup>+</sup> reaction indicates that isotope substitution reaction makes the cross section and the rate constant underestimated. The resulting integral reaction cross section displays less oscillatory structure, especially in the exact quantum calculation with the full Coriolis coupling effect taken into consideration. The kinetic isotope effect <inline-formula><tex-math id="Z-20221117061024-1">\begin{document}$(\kappa_{\rm H+SiH^+}(T)/\kappa_{\rm D+SiD^+}(T))$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_Z-20221117061024-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20221155_Z-20221117061024-1.png"/></alternatives></inline-formula>is found to decrease with temperature increasing. It can be seen that the reduced mass of reactant can exert a certain effect on dynamic behavior.

Quantum wave-packet studies on ion–molecule reaction with and without Coriolis-coupling effect

The time-dependent quantum scattering calculation with Chebyshev wave packet propagation scheme has been carried out based on an accurate electronic potential energy surface of H2O+(X4A″). Due to the influence of the deep potential well, the reaction probability of [Formula: see text] shows resonance structures regardless of the Coriolis-coupling (CC) effect or centrifugal sudden (CS) approximation. In the range of collision energy 0.0–1.0 eV, the integral cross section obtained by the CS approximation calculation is smaller than that by the CC calculation, which indicates that the CC effect plays a significant role in the title reaction.

Quantum dynamics calculations for O+ + H2 (vi = 0, ji = 0) → OH+ + H ion–molecule reaction on a new potential energy surface

The quantum dynamics calculations of O+ + H2 (vi = 0, ji = 0) → OH+ + H reaction have been performed using a Chebyshev wave packet method on a new potential energy surface constructed by Song et al. [Y.Z. Song et al., Chin. Phys. B 24, 063101 (2015)]. The reaction probabilities of partial wave J = 0–80 are calculated explicitly with the centrifugal sudden (CS) and Coriolis coupling (CC) calculations. The comparison between the CC and the corresponding CS results indicates that neglecting the Coriolis coupling will lead to the underestimation of the reaction probability. The comparison of theoretical integral cross sections (ICS) with the experimental results in the collision energy range of 0.0–1.0 eV indicates that the calculated values in this work agree well with the experimental data and other theoretical results, showing the reasonability of PES and dynamic calculations. The obtained ICSs are used to calculate the rate constants in the temperature range of 0–2000 K, and the results at room temperature reasonably agree with the experimental data.

Coriolis coupling effects in the [formula omitted] reaction: A time-dependent wave packet investigation

The time-dependent dynamics studies on the H+Li2(X1Σg+) reaction has been carried out by using the novel HLi2 (X2A′) potential energy surface [7]. The reaction probabilities from both Coriolis coupling and centrifugal sudden approximation calculation exhibit oscillations, being attributed to the existence of deep potential well in the reaction. The integral cross sections of the Coriolis coupling calculation are slightly larger than those of the centrifugal sudden approximation calculation over the collision energy range of 0–0.4eV, which demonstrates that the Coriolis coupling effect plays an important role in the H+Li2(X1Σg+) reaction.

The quantum dynamics of the reactions N+H2(HD,D2) and their vibrational excitation effect

The N(4S)+H2 reaction and its isotopic variants have been investigated by means of time-dependent quantum wave packet with split operator method on the ground state potential energy surface (Zhai and Han, J. Chem. Phys. 2011, 135, 104314). The reaction probabilities, integral cross sections, branching ratio of the integral cross sections, and effect of vibrational excitation of H2, HD, and D2 diatomic molecules are presented and discussed. The results reveal that the intramolecular isotopic effect is greater than the intermolecular one, and that the vibrational excitation of the diatomic molecules can promote the progress of this reaction. In addition, a limited number of rigorous Coriolis coupling calculations of the integral cross sections of the N(4S)+H2 reaction have been carried out. Also shown is that since the Coriolis coupling plays a small part in this accurate quantum calculation, the cheaper centrifugal sudden calculations here reported are effective for this reactive system. © 2014 Wiley Periodicals, Inc.

Time-Dependent Wave Packet Quantum and Quasi-Classical Trajectory Study of He + H2+, D2+→ HeH++ H, HeD++ D Reaction on an Accurate FCI Potential Energy Surface

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H₂⁺ (v = 0-3, j = 1) → HeH⁺ + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D₂⁺ (v = 0-2, j = 0) → HeD⁺ + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.

Vibronic Analysis of the S1−S0 Transition of Phenylacetylene Using Photoelectron Imaging and Spectral Intensities Derived from Electronic Structure Calculations

The vibrational structure of the S(1)-S(0) electronic band of phenylacetylene has been recorded by 1 + 1 resonance-enhanced multiphoton ionization, accompanied by slow electron velocity map imaging photoelectron spectroscopy at each resonant vibrational band. Assignments of the S(1) vibrations (up to 2000 cm(-1) above the band origin) are based upon the relative intensities of the vibronic bands calculated by complete second-order vibronic coupling, vibration-rotation (Coriolis and Birss) coupling calculations, and the vibrational structure of the S(1) resonant photoelectron spectra. Although this is an allowed electronic transition, the relative intensities of the a(1) bands are often largely determined by vibronic coupling rather than simple Franck-Condon factors, and second-order coupling is substantial. Nonsymmetric vibrations have intensities obtained through either vibronic or Coriolis coupling, and the calculations have been instrumental in discriminating between alternate possibilities in the assignments. Strong vibronic effects are expected to be present in the spectra of most monosubstituted benzenes, and the calculations presented here show that theoretical treatments based upon electronic structure calculations will generally be useful in the analysis of their spectra.

Exact and truncated Coriolis coupling calculations for the S(1D)+HD reaction employing the ground adiabatic electronic state

We present exact quantum differential cross sections and exact and estimated integral cross sections and branching ratios for the title reaction. We employ a time-dependent wavepacket method as implemented in the DIFFREALWAVE code including all Coriolis couplings and also an adapted DIFFREALWAVE code where the helicity quantum number and with this the Coriolis couplings have been truncated. Our exact differential cross sections at 0.453 eV total energy, one of the experimental energies, show good agreement with the experimental results for one of the product channels. While the truncated calculation present a significant reduction in the computational effort needed they overestimate the exact integral cross sections.

Importance of Coriolis Coupling in Isotopic Branching in (He, HD+) Collisions

A three-dimensional time-dependent quantum mechanical wave packet approach is used to calculate the reaction probability (P(R)) and integral reaction cross section values for both channels of the reaction He + HD(+)(v = 1; j = 0) --> HeH (D)(+) + D (H) over a range of translational energy (E(trans)) on the McLaughlin-Thompson-Joseph-Sathyamurthy potential energy surface including the Coriolis coupling (CC) term in the Hamiltonian. The reaction probability plots as a function of translational energy for different J values exhibit several oscillations, which are characteristic of the system. The sigma(R) values obtained by including CC and not including it are nearly the same over the range of E(trans) investigated for the HeD(+) channel. For the HeH(+) channel, on the other hand, sigma(R) values obtained from CC calculations are significantly smaller than those obtained from coupled state calculations. These results are compared with the available experimental results. The computed branching ratios (Gamma(sigma) = sigma(R) (HeH(+))/sigma(R) (HeD(+))) are also compared with the available experimental results.

A time-dependent wave-packet quantum scattering study of the reaction H2+(v=–2,4,6;j=1)+He→HeH++H

The quantum scattering dynamics calculation was carried out for the titled reaction in the collision energy range of 0.0-2.4 eV with reactant H(2) (+) in the rotational state j = 1 and vibrational states v = 0-2, 4, and 6. The present time-dependent wave-packet calculation takes into account the Coriolis coupling (CC) and uses the accurate ab initio potential-energy surface of Palmieri et al. [Mol. Phys. 98, 1835 (2000)]. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC calculation and the previous coupled state (CS) calculation. The CC total cross sections for the v = 2, 4, and 6 states show collision energy-dependent behaviors different from those based on the CS calculation. Furthermore, the collision energy dependence of the total cross sections obtained in the present CC calculation only exhibits minor oscillations, indicating that the chance is slim for reactive resonances in total cross sections to survive through the partial-wave averaging. The magnitude and profile of the CC total cross sections for v = 0-2 in the collision energy range of 0.0-2.5 eV are found to be consistent with experimental cross sections obtained recently by Tang et al. [J. Chem. Phys. 122, 164301 (2005)] after taking into account the experimental uncertainties.

Coriolis coupling in the rotational bands of deformed odd-odd nuclei

Evidence is presented for the existence of odd-even staggering in ${K}^{\mathrm{\ensuremath{-}}}$ rotational bands (with Kg0) of odd-odd nuclei in the rare-earth and actinide regions. Coriolis-coupling calculations have been carried out for rotational bands in $^{168}\mathrm{Tm}$, $^{176}\mathrm{Lu}$, $^{182}\mathrm{Ta}$, and $^{182}\mathrm{Re}$. With these calculations, we are able to reproduce the odd-even staggering observed in these nuclei. In particular, the unusually strong staggering observed in the K${=2}^{+}$ and ${4}^{\mathrm{\ensuremath{-}}}$ bands of $^{182}\mathrm{Re}$ can be understood. Unusual features in the wave functions of some bands reflect the importance of couplings due to terms other than Coriolis in the Hamiltonian.

Odd-even staggering in the K = 1, 2, 3 and 4 rotational bands of deformed odd-odd nuclei

An analysis of the rotational structure of the K = |Ω p − Ω n | bands in the odd-odd nuclei from the rare earth region reveals an odd-even staggering in the level energies. Such an odd-even effect is present, sometimes very prominently, in almost all the K − bands with K values ranging from 1 to 4. We find that complete Coriolis coupling calculations are able to explain most of the staggering in the four nuclei studied. However, the K = 2 + and K = 4 − bands in 182Re cannot be explained satisfactory.

228Th nuclear states fed in 228Ac decay.

The decay of radiochemically-separated /sup 228/Ac sources has been reinvestigated using high-resolution coaxial HPGe detectors and ..gamma..-..gamma.. coincidence measurements. Energies and intensities of more than 240 photons were accurately measured, 80 of them for the first time. A /sup 228/Th level scheme, built on the bases of good energy fits and on ..gamma..-..gamma.. coincidence data, involves 58 excited states, of which 17 are new, up to 2159 keV with spin 0less than or equal toIless than or equal to6. Collective properties of low-energy states belonging to K/sup ..pi../ = 0/sup -/,2/sup +/,2/sup -/ bands are discussed in the framework of the Bohr-Mottelson model. Decay modes of a K/sup ..pi../ = 0/sup +/ excited band at 831.82 keV favor strong two octupole phonon K/sup ..pi../ = 0/sup -/ components. The K/sup ..pi../ = 1/sup -/ band is expected to have I = 2 and 3 members at 938.5 and 968.4 keV. Coriolis coupling calculations involving the four K/sup ..pi../ = 0/sup -/, 1/sup -/, 2/sup -/, and 3/sup -/ bands were carried out. Tentative K/sup ..pi../ = 2/sup +/ two-quasiparticle bands at 1638.23 and 1899.99 keV are discussed in terms of Nilsson orbitals.

Octupole state properties in 168Er and the two-neutron {

Detailed spectroscopy measurements have been made of the gamma rays that follow the deexcitation of $^{168}\mathrm{Er}$ levels populated in the electron capture decay of $^{168}\mathrm{Tm}$. These results, when combined with a reanalysis of Coulomb excitation and inelastic scattering data, provide level lifetime information and support octupole-state Coriolis-coupling calculations. The {[521 (1/2)][633 (7/2)]} two-neutron configurational pair deexcitation rates are compared and some evidence for K mixing among the octupole bands is presented.

High-spin particle states in 151Sm studied with the (α, 3He) reaction

High-spin states have been located in 151Sm by means of the (α, 3He) reaction with 40 MeV α-particles. The scattered particles were momentum analyzed in a QMG/2 magnetic spectrometer and recorded in a position sensitive detector. Several high-spin states were observed in the energy range below 1.7 MeV excitation. The previously unknown strongly populated levels at 867 and 1480 keV can most likely be interpreted as 13 2 + states. Both the deduced nuclear structure factors and the energy location of these levels are in excellent agreement with a simple Coriolis coupling calculation.

A study of 172Yb following the 170Er(α, 2n) reaction

Six side bands have been identified up to high spin in 172Yb. Four of these, with K π = 1 −, 4 −, 6 − and possibly 9 −, involve an i 13 2 neutron, and have high moments of inertia. The properties of these bands are reproduced in a two-quasiparticle-plus-rotor Coriolis coupling calculation. A well-known band with K π = 3 +; is extended to I = 14; its properties suggest a mixed neutron-proton configuration. The first excited K π = 0 + band is extended to I = 14. It has a rapidly rising moment of inertia, and is predicted to cross the g.s.b. at about I = 20 +. These K = 0 + states could be the low-spin members of an ( i 13 2 ) 2 band.

Single-neutron transfer reactions 76, 78, 80, 82Se(p,d) 75, 77, 79, 81Se at EP = 33MeV

Single-neutron transfer reactions on even-even Se nuclei have been studied using 33 MeV incident proton energy from the ANU cyclograaff facility. A total of 120 levels have been seen below 4 MeV excitation energy in 75, 77, 79, 81Se isotopes. Angular distributions for 88 states were extracted and analysed with DWBA theory yielding a number of new l n assignments. Coriolis coupling calculations have been carried out for low-level spin states in all four isotopes.

The excited states of 79Kr

Abstract The β + decay of 79 Rb has been studied with Ge(Li) detectors in singles and coincidence modes. The half-life of the 147.06 keV level in 79 Kr has been determined to be 78 ± 6 nsec. The relative electron intensities of seventeen transitions have been measured with a Si(Li) spectrometer. The internal conversion coefficients have been determined and the transition multipolarities have been deduced. Spin-parity assignments have been made for excited states of 79 Kr and the β + decaying ground state of 79 Rb ( 5 2 + ) . A Coriolis-coupling calculation using the Woods-Saxon potential together with a residual pairing and spin-spin interaction has been made. This model predicts the ground-state spin and parity of 79 Rb nucleus as well as the occurence and behaviour of most of 79 Kr states.