Full-dimensional time-dependent wave packet dynamics of H2 + D2 reaction

Collision induced dissociation (CID), four center reaction (4C), and single exchange reaction (SE) in H(2) (v(1) = high) + D(2) (v(2) = low) were studied by means of time-dependent wave packet approach within a full-dimensional model. Initial state-selected total reaction probabilities for the three competitive processes have been computed on two realistic global potential energy surfaces of Aguado-Suárez-Paniagua and Boothroyd-Martin-Keogh-Peterson (BMKP) with the total angular momentum J = 0. The role of both vibrationally excited and rotationally excited reagents was examined by varying the initial vibrational and rotational states. The vibrational excitation of the hot diatom gives an enhancement effect on the CID process, while the vibrational excitation of the cold diatom gives an inhibition effect. The rotational excitation of both reagents has a significant effect on the reaction process. The 4C and SE probabilities are at least one order of magnitude smaller than the CID probabilities over the energy range considered. Isotope substitution effects were also studied by substituting the collider D(2) by H(2) and HD on the BMKP potential energy surfaces. The CID process is most efficient for the H(2) + D(2) combination and least efficient for the H(2) + H(2) combination and is different for the 4C and SE processes.     

Full-dimensional quantum dynamics study of exchange processes for the D + H2O and D + HOD reactions

The exchange processes of D + H(2)O and D + HOD reactions are studied using initial state-selected time-dependent wave packet approach in full dimension. The total reaction probabilities for different partial waves, together with the integral cross sections, are obtained both by the centrifugal sudden (CS) approximation and exact coupled-channel (CC) calculations, for the H(2)O(HOD) reactant initially in the ground rovibrational state. In the CC calculations, small resonance peaks in the reaction probabilities and quick diminishing of the resonance peaks with the increase of total angular momenta J do not lead to clear step-like features just above the threshold in the cross sections for the title reactions, which are different in other isotopically substituted reactions where the hydrogen atom was included as the reactant instead of the deuterium atom [B. Fu, Y. Zhou, and D. H. Zhang, Chem. Sci. 3, 270 (2012); B. Fu and D. H. Zhang, J. Phys. Chem. A 116, 820 (2012)]. It is interesting that the shape resonance-induced features resulting from the reaction tunneling are significantly diminished accordingly in the reactions of the deuterium atom and H(2)O or HOD, owing to the weaker tunneling capability of the reagent deuterium atom in the title reactions than the reagent hydrogen atom in other reactions. In the CS calculations, the resonance peaks persist in many partial waves but cannot survive the partial-wave summations. The cross sections for the D(') + H(2)O → D(')OH + H and D(') + HOD → D(')OD + H reactions are substantially larger than those for the D(') + HOD → HOD(') + D reaction, indicating that the D(')/H exchange reactions are much more favored than the D(')/D exchange.     

Full-dimensional quantum dynamics study of the H + H2O and H + HOD exchange reactions

The initial state-selected time-dependent wave packet approach is employed to study the H' + H(2)O → H'OH + H and H' + HOD → H'OD + H, HOH' + D exchange reactions with both OH bonds in the H(2)O reactant and OH(D) bond in the HOD reactant treated as reactive bonds. The total reaction probabilities for different partial waves, as well as the integral cross sections, which are the exact CC (coupled-channel) results, are first obtained in this study for the H(2)O(HOD) reactant initially in the ground rovibrational state. Because of the shallow C(3v) minimum along the reaction path, the reaction probabilities for the three reactions present several resonance peaks, with one dominant resonance peak just above the threshold. The cross sections for the H' + HOD → HOH' + D reaction are substantially smaller than those for the H' + H(2)O → H'OH + H and H' + HOD → H'OD + H reactions, indicating that the H'/H exchange reactions are much more favored. In the CC calculations, the resonance peaks in the reaction probabilities diminish quickly with the increase in total angular momenta J, resulting in the existence of a clear step-like feature just above the threshold in the cross sections for the title reactions, which manifests the signature of shape resonances in these reactions. In the CS calculations, the resonance peaks on reaction probabilities persist in many partial waves, and thus the resonance structures can no longer survive the partial-wave summation and are washed out completely in the CS cross sections for the title reactions.     

A full dimensional time-dependent wave packet study for the H4 four-center, collision induced dissociation, and single exchange reactions: reaction probabilities for J=0

A time-dependent initial state selected wave packet method has been developed to study the H2(v(1)=10-11,j1=0)+H2'(v2=0,j2=0)-->HH'+HH' four-center (4C) reaction, and two other competing reactions: the H2+H2'-->H+H+H2' collision induced dissociation (CID) and the H2+H2'-->H+HH'+H' single exchange (SE) reaction, in full six dimensions. Initial state-specific total reaction probabilities for these three competing reactions are presented for total angular momentum J=0 and the effects of reagent vibration on reactions are examined. It is found that (a) the CID process is the dominant process over the whole energy range considered in this study, but the 4C and SE processes also have non-negligible probabilities; (b) the SE process has a lower threshold energy than the 4C process, but the SE probability increases slower than the 4C probability as collision energy increases; (c) the vibrational excitation of H2(v1) is much more efficient than translational motion for promoting these processes, in particular to the CID process.     

A time-dependent wave packet quantum scattering study of the reaction HD+ (v = 0 - 3;j0 = 1) + He --> HeH+(HeD+) + D(H)

Time-dependent wave packet quantum scattering (TWQS) calculations are presented for HD(+) (v = 0 - 3;j(0)=1) + He collisions in the center-of-mass collision energy (E(T)) range of 0.0-2.0 eV. The present TWQS approach accounts for Coriolis coupling and uses the ab initio potential energy surface of Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. For a fixed total angular momentum J, the energy dependence of reaction probabilities exhibits quantum resonance structure. The resonances are more pronounced for low J values and for the HeH(+) + D channel than for the HeD(+) + H channel and are particularly prominent near threshold. The quantum effects are no longer discernable in the integral cross sections, which compare closely to quasiclassical trajectory calculations conducted on the same potential energy surface. The integral cross sections also compare well to recent state-selected experimental values over the same reactant and translational energy range. Classical impulsive dynamics and steric arguments can account for the significant isotope effect in favor of the deuteron transfer channel observed for HD(+)(v<3) and low translational energies. At higher reactant energies, angular momentum constraints favor the proton-transfer channel, and isotopic differences in the integral cross sections are no longer significant. The integral cross sections as well as the J dependence of partial cross sections exhibit a significant alignment effect in favor of collisions with the HD(+) rotational angular momentum vector perpendicular to the Jacobi R coordinate. This effect is most pronounced for the proton-transfer channel at low vibrational and translational energies.     

Nonadiabatic time-dependent wave packet study of the D+ + H2 reaction system

A theoretical investigation on the nonadiabatic processes of the D(+) + H(2) reaction system has been carried out by means of exact three-dimensional nonadiabatic time-dependent wave packet calculations with an extended split operator scheme (XSOS). The diabatic potential energy surface newly constructed by Kamisaka et al. (J. Chem. Phys. 2002, 116, 654) was employed in the calculations. This study provided quantum cross sections for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, which contrasted markedly to many previous quantum theoretical reports on the (DH(2))(+) system restricted to the total angular momentum J = 0. These quantum theoretical cross sections derived from the ground rovibrational state of H(2) show wiggling structures and an increasing trend for both the reactive charge transfer and the nonreactive charge transfer but a decreasing trend for the reactive noncharge transfer throughout the investigated collision energy range 1.7-2.5 eV. The results also show that the channel of the reactive noncharge transfer with the largest cross section is the dominant one. A further investigation of the v-dependent behavior of the probabilities for the three channels revealed an interesting dominant trend for the reactive charge transfer and the nonreactive charge transfer at vibrational excitation v = 4 of H(2). In addition, the comparison between the centrifugal sudden (CS) and exact calculations showed the importance of the Coriolis coupling for the reactive system. The computed quantum cross sections are also compared with the experimental measurement results.     

Quantum wave-packet dynamics of H+HLi scattering: reaction cross section and thermal rate constant

The channel specific and initial state-selected reaction cross section and temperature-dependent rate constant for the title system is calculated with the aid of a time-dependent wave-packet approach and using the ab initio potential energy surface of Dunne et al. [Chem. Phys. Lett. 336, 1 (2001)]. All partial-wave contributions up to the total angular momentum J=74 are explicitly calculated within the coupled states (CS) approximation. Companion calculations are also carried out employing the standard as well as the uniform J-shifting (JS) approximation. The overall variation of reaction cross sections corresponds well to the behavior of a barrierless reaction. The hydrogen exchange channel yielding HLi+H products is seen to be more favored over the HLi depletion channel yielding Li+H(2) products at low and moderate collision energies. Sharp resonance features are observed in the cross-section results for the HLi depletion channel at low energies. Resonance features in the reaction cross sections average out with various partial-wave contributions, when compared to the same observed in the individual reaction probability curve. Except near the onset of the reaction, the vibrational and rotational excitation of the reagent HLi, in general, does not dramatically influence the reactivity of either channel. The thermal rate constants calculated up to 4000 K show nearly Arrhenius type behavior. The rate constant decreases with vibrational excitation of the reagent HLi, indicating that the cold HLi molecules are efficiently depleted in the reactive encounter with H at relatively low temperatures. The results obtained from the JS approximation are found to agree well qualitatively with the CS results.     

Quantum wave packet dynamics of N(2D)+H2 reaction

The quantum wave packet dynamics of the title reaction within the coupled state approximation is examined here and initial state-selected reaction probabilities, integral reaction cross sections, and thermal rate constants are reported. The ab initio potential energy surface of the electronic ground state (1(2)A(")) of the system recently reported by Ho et al. [J. Chem. Phys., 119, 3063 (2003)] is employed in this investigation. All partial wave contributions up to the total angular momentum J=55 were necessary to obtain converged integral reaction cross sections up to a collision energy of 1.0 eV. Thermal rate constants are calculated from the reaction cross sections and compared with the available theoretical and experimental results. Typical resonances formed during the course of the reaction and elucidating the insertion type mechanism for the product formation are calculated. Vibrational energy levels supported by the deep well (approximately 5.5 eV) of the 1(2)A(") potential energy surface of NH(2) are also calculated for the total angular momentum J=0. A statistical analysis of the spacing between the adjacent levels of this energy spectrum is performed and the extent of irregularity in the spectral sequence is assessed.     

Time-dependent quantum study of the kinetics of the H(2S) + FO(2II) OH(2II) + F(2P) reaction

Quantum mechanical wave packet calculations are carried out for the H((2)S) + FO((2)II) --> OH((2)II) + F((2)P) reaction on the adiabatic potential energy surface of the ground (3)A' triplet state. The state-to-state and state-to-all reaction probabilities for total angular momentum J = 0 have been calculated. The probabilities for J > 0 have been estimated from the J = 0 results by using J-shifting approximation based on a capture model. Then, the integral cross sections and initial state-selected rate constants have been calculated. The calculations show that the initial state-selected reaction probabilities are dominated by many sharp peaks. The reaction cross section does not manifest any sharp oscillations and the initial state-selected rate constants are sensitive to the temperature.     

Coriolis coupling effects on the initial-state-resolved dynamics of the N(2D)+H2-->NH+H reaction

We present Coriolis coupling effects on the initial-state-resolved dynamics of the insertion reaction N((2)D)+H(2)(X (1)Sigma(g) (+))-->NH(X (3)Sigma(-) and a (1)Delta)+H((2)S), without and with nonadiabatic Renner-Teller (RT) interactions between the NH(2) X (2)B(1) and A (2)A(1) electronic states. We report coupled-channel (CC) Hamiltonian matrix elements, which take into account both Coriolis and RT couplings, use the real wave-packet and flux methods for calculating initial-state-resolved reaction probabilities, and contrast CC with centrifugal-sudden (CS) results. Without RT interactions, Coriolis effects are rather small up to J=40, and the CS approximation can be safely employed for calculating initial-state-resolved, integral cross sections. On the other hand, RT effects are associated with rather large Coriolis couplings, mainly near the linearity of NH(2), and the accuracy of the CS approximation thus breaks down at high collision energies, when the reaction starts on the excited A (2)A(1) surface. We also present the CC-RT distribution of the X (3)Sigma(-) and a (1)Delta electronic states of the NH products.     

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 + H?? (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 + D?? (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.     

Time-dependent reactive scattering for the system H- + D2 <--> HD + D- and comparison with H- + H2 <--> H2 + H-

This work presents results of quantum mechanical calculations of reaction probabilities for the ion-neutral molecule collisions H- + D2 <--> HD + D-. Time-dependent wave packet propagations for total angular momentum J not equal to 0, including the full Coriolis coupling, are performed. The calculated state-to-state reaction probabilities using product Jacobi coordinates are compared with energy-resolved reaction probabilities calculated with the flux-operator using reactant Jacobi coordinates and with time-independent calculations. Differences between nearly converged integral cross sections and those using the J-shifting method and centrifugal sudden approximation and comparison with experimental results will be presented.     

Effect of reagent rotation on isotopic branching in (He, HD+) collisions

A three-dimensional time-dependent quantum mechanical wave packet approach is used to calculate reaction probability (P(R)) and integral reaction cross section (sigma(R)) values for both the channels of the reaction He + HD(+) (v = 1; j = 0, 1, 2, 3) --> HeH(D)(+) + D(H), over a range of translational energy (E(trans)) on the McLaughlin-Thompson-Joseph-Sathyamurthy (MTJS) potential energy surface using centrifugal sudden approximation for nonzero total angular momentum (J) values. The reaction probability plots as a function of translational energy for different J values exhibit several oscillations, which are characteristic of the system. It is shown that HeH(+) is preferred over HeD(+) for large J values and that HeD(+) is preferred over HeH(+) for small J values for all the rotational (j) states studied. The integral reaction cross section for both the channels and therefore the isotopic branching ratio for the reaction depend strongly on j in contrast to the marginal dependence shown by earlier QCT calculations. The computed results are in overall agreement with the available experimental results.     

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.     

Three dimensional quantum dynamics of (H-, H2) and its isotopic variants

We present the results of a time-dependent quantum mechanical investigation using centrifugal sudden approximation in the form of reaction probability as a function of collision energy (E(trans)) in the range 0.3-3.0 eV for a range of total angular momentum (J) values and the excitation function sigma(E(trans)) for the exchange reaction H(-) + H(2) (v = 0, j = 0) --> H(2) + H(-) and its isotopic variants in three dimensions on an accurate ab initio potential energy surface published recently (J. Chem. Phys. 2004, 121, 9343). The excitation function results are shown to be in excellent agreement with those obtained from crossed beam measurements by Zimmer and Linder for H(-) + D(2) collisions for energies below the threshold for electron detachment channel and somewhat larger than the most recent results of Haufler et al. for (H(-), D(2)) and (D(-), H(2)) collisions.     

Dynamical properties of S(3P) + HD reaction on 13A″state and their quantum wavepacket calculation

The time‐dependent wavepacket method is used to study the reaction dynamics of S(³P) + HD (v = 0, 1, 2) on the adiabatic 1³A″ potential energy surface constructed by Han and coworkers [J. Chem. Phys. 2012, 136, 094308]. The reaction probabilities and integral cross sections as a function of collision energy are obtained and discussed. The results calculated by using the CC and the CS approximation have been compared, which suggests that for this direct abstraction reaction, the cheaper CS approximation calculation is valid enough in the quantum calculation. The investigation also shows that the reaction probabilities and integral cross sections tend to increase with collision energy. By analyzing the v‐dependent behavior of the integral cross sections, the significant effect of the vibrational excitation of HD is found. Also found in the calculation is a significant resonance feature in the reaction probabilities versus collision energy. © 2014 Wiley Periodicals, Inc.     

The three-dimensional nonadiabatic dynamics calculation of DH(2)(+) and HD(2)(+) systems by using the trajectory surface hopping method based on the Zhu-Nakamura theory

A theoretical investigation on the nonadiabatic processes of the full three-dimensional D(+)+H(2) and H(+)+D(2) reaction systems has been performed by using trajectory surface hopping (TSH) method based on the Zhu-Nakamura (ZN) theory. This ZN-TSH method refers to not only classically allowed hops but also classically forbidden hops. The potential energy surface constructed by Kamisaka et al. is employed in the calculation. A new iterative method is proposed to yield the two-dimensional seam surface from the topography of the adiabatic potential surfaces, in which the inconvenience of directly solving the first-order partial differential equation is avoided. The cross sections of these two systems are calculated for three competing channels of the reactive charge transfer, the nonreactive charge transfer, and the reactive noncharge transfer, for ground rovibrational state of H(2) or D(2). Also, this study provides reaction probabilities of these three processes for the total angular momentum J=0 and ground initial vibrational state of H(2) or D(2). The calculated results from ZN-TSH method are in good agreement with the exact quantum calculations and the experimental measurements.     

A time-dependent wave-packet quantum scattering study of the reaction H2+(v = 0-2,4,6;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.     

Accurate time-dependent wave packet study of the Li + H₂⁺ reaction and its isotopic variants

The dynamics and kinetics of the Li + H?? reaction and its isotopic variants (D?? and T??) have been studied by using a time-dependent wave packet (TDWP) coupled-channel (CC) method on the ab initio potential energy surface (PES) of Martinazzo et al. [J. Chem. Phys. 2003, 119, 21]. Total initial v = 0, j = 0 state-selected reaction probabilities for the Li + H?? reaction and its isotopic variants have been calculated from the threshold up to 1 eV for total angular momenta J from 0 to 90. Integral cross sections have been evaluated from the reaction probabilities at collision energies from threshold (≈0.2 eV) up to 1.0 eV collision. The calculated rate constants as a function of temperature show an Arrhenius type behavior in the 200 ≤ T ≤ 1000 K temperature interval. It has been found to be a considerable large intermolecular kinetic isotope effect. The TDWP-CC results are in overall good agreement with those obtained applying the TDWP Centrifugal-Sudden (CS) approximation, showing that the CS approximation is rather accurate for the title reaction.     

Influence of reagent rotation on (H-, D2) and (D-, H2) collisions: a quantum mechanical study

Time-independent quantum mechanical (TIQM) approach (helicity basis truncated at k = 2) has been used for computing differential and integral cross sections for the exchange reaction H- + D2 (v = 0, j = 0-4) --> HD + D- and D- + H2 (v = 0, j = 0-3) --> HD + H- in three dimensions on an accurate ab initio potential energy surface. It is shown that the j-weighted differential reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder at four different relative translational energies (Etrans = 0.55, 0.93, 1.16 and 1.48 eV) for (H-, D2) and at one relative translational energy (Etrans = 0.6 eV) by Haufler et al. for both (H-, D2) and (D-, H2) collisions. The j-weighted integral reaction cross section values are in good agreement with the crossed beam measurements by Zimmer and Linder in the Etrans range 0.5-1.5 eV and close to the guided ion beam results by Haufler et al. for (H-, D2) in the range 0.8-1.2 eV. Time-dependent quantum mechanical (TDQM) results obtained using centrifugal sudden approximation are reported in the form of integral reaction cross section values as a function of Etrans in the range 0.3-3.0 eV for both reactions in three dimensions on the same potential energy surface. The TDQM reaction cross section values decline more sharply than the TIQM results with increase in the initial rotational quantum number (j) for the D2 molecules in their ground vibrational state (v = 0) for (H-, D2) collisions. The computed j-weighted reaction cross section values are in good agreement with the experimental results reported by Zimmer and Linder for (H-, D2) collisions and guided ion beam results by Haufler et al. for both (H-, D2) and (D-, H2) collisions for energies below the threshold for electron detachment channel.