Reactivity of the Ground and Excited Spin−Orbit States for the Reaction of the F(2P3/2,2P1/2) with D2

Development of the Time-Independent Methods for the Cl + H2/F + HD Reaction Using Hyper-Spherical Coordinates Including (Full) Spin-Orbit Characteristics

Recently, a combined study of high-resolution molecular crossed beam experiment and accurate full-dimensional time-dependent theory, including full spin-orbit characteristics on the effect of electronic spin and orbital angular momenta in the F + HD reaction, was reported by some of us, focusing on the partial wave resonance phenomenon (Science 2021, 371, 936-940). It revealed that the time-dependent theory could explain all of the details observed in the high-resolution experiment. Here, we develop two time-independent close-coupling methods using hyperspherical coordinates, including the two-state model, where only a part of the spin-orbit characteristics is considered, and the six-state model, where the full spin-orbit characteristics is considered. With these two newly developed theoretical models and the adiabatic theoretical model, the detailed reaction dynamics of the F + HD (v = 0, j = 0) reaction and the Cl + H2 (v = 0, j = 0) reaction are investigated and compared. Some of the results are compared with the time-dependent quantum wave packet theory and the experimental observations, and good agreements have been obtained, which suggests the validity of the pure-procession approximation in the six-state model using different theoretical methods. This work demonstrates the ability of the reactive scattering theory including full spin-orbit characteristics for describing the reactions of a halogen atom plus hydrogen molecule and its isotopologues.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H₂/D₂ reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H₂ and D₂) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H₂ and F + D₂ reactions are presented along with previous theoretical and experimental results.

An accurate NH2(X2A′′) CHIPR potential energy surface via extrapolation to the complete basis set limit and dynamics of the N(2D) + H2(X1+g) reaction

An accurate CHIPR potential energy surface for NH2(X2A′′) is structured to study the N(2D) + H2(X1Σ+g) reaction using the time-dependent wave packet and quasi-classical trajectory method.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Quasi-classical trajectory study of the reaction dynamics of calcium ground state and metastable atoms with CH2Cl2

The dynamics properties of the Ca(1S0,3P) + CH2Cl2 reaction system have been calculated by means of the quasi-classical trajectory method based on the extended London–Eyring–Polanyi–Sato potential energy surface. By the calculations, the vibrational distribution, reaction cross section, rotational alignment, and reaction rate constant are obtained. The peak location of vibrational quantum numbers is at ν = 0 when the collision energy is 2.302 kcal/mol, whether the calcium atom is at the ground state or metastable state. The product vibrational distribution agrees well with the experiment value in Han, K. L.; He, G. Z.; Lou, N. Q. Chem. Phys. Lett. 1991, 178, 528. The cross section thoroughly decreases with the increase of the collision energy. The rotational alignment of the product greatly deviates from –0.5. The reaction rate constant increases with rising temperature.

A THEORETICAL ANALYSIS OF THE DISSOCIATION OF OH RADICAL: FINE-STRUCTURE DISTRIBUTIONS OF THE O(3PJ) PRODUCT

A theoretical treatment is presented for the nonadiabatic photodissociation of hydroxyl radical. Five electronic states, X 2Π, A 2Σ+, 14Σ-, 12Σ- and 14Π, are included in this simulation. Based on the accurate ab initio calculations of the potential energy curves, transition dipole moments and nonadiabatic couplings between the relevant states, the dissociation dynamics are investigated using the time-dependent quantum wave packet approach. The direct dissociation, following the excitation from the specific vibrational levels of the ground state X 2Π to the repulsive state 12Σ- is examined, where the total and partial cross sections and the branching fractions of spin–orbit fine-structures of O (3 P J) are calculated over a wide range of the incident photon frequencies. For the predissociation via the bound excited state A 2Σ+, the influence of the nonadiabatic interactions in different internuclear regions and the role of the repulsive states in the dissociation starting at different vibrational levels are also analyzed through the spin–orbit branching fractions of products.

USING THE QUASI-CLASSICAL TRAJECTORY METHOD TO STUDY THE F + H2 AND ITS ISOTOPIC VARIANTS: VECTOR CORRELATIONS

The vector correlations between products and reagents for the reactions F + HH → HF + H , F + HD → HF + D and F + HT → HF + T , have been investigated using the quasi-classical trajectory (QCT) method on the Stark-Werner (SW) ab initio potential energy surface. The distribution P(θr) of angle between k′ and j′, the distribution P(ϕr) of dihedral angle denoting k-k′-j′ correlation are calculated. The polarization dependent generalized differential cross sections have also been studied. The evident influence of isotope substitution on the product polarization is revealed. This effect may be derived from the different mass factor of the three reactions and the barrier height of the F + H2 PES.

COMPARATIVE STUDY OF REACTION RATE CONSTANTS FOR THE NH3 + H → NH2 + H2 REACTION WITH GLOBE DYNAMICS AND TRANSITION STATE THEORIES

The nine-dimension quasi-classical trajectory (QCT) calculations have been carried out for the title reaction with a global potential energy surface (PES) constructed by Corchado and Espinosa-García (J Chem Phys106:4013, 1997). The detailed dynamics calculations cover the specific collision energies falling in the range of 0.62–3.04 eV, which are sufficient to fit the calculated reactive cross-sections into a barrier-type excitation function and to obtain the thermal rate constants. The present QCT rate constants are in good agreement with the recent quantum dynamics (QD) results, both of which are much lower than that of the previous variational transition state theory (VTST).

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.

Spin-orbit effect in the energy pooling reaction O2(aΔ1)+O2(aΔ1)→O2(bΣ1)+O2(XΣ3)

Five-dimensional nonadiabatic quantum dynamics studies have been carried out on two new potential energy surfaces of S(2)((1)A(')) and T(7)((3)A(")) states for the title oxygen molecules collision with coplanar configurations, along with the spin-orbit coupling between them. The ab initio calculations are based on complete active state second-order perturbation theory with the 6-31+G(d) basis set. The calculated spin-orbit induced transition probability as a function of collision energy is found to be very small for this energy pooling reaction. The rate constant obtained from a uniform J-shifting approach is compared with the existing theoretical and experimental data, and the spin-orbit effect is also discussed in this electronic energy-transfer process.

Recent advances in crossed-beam studies of bimolecular reactions

A critical overview of the recent progress in crossed-beam reactive scattering is presented. This review is not intended to be an exhaustive nor a comprehensive one, but rather a critical assessment of what we have been learning about bimolecular reaction dynamics using crossed molecular beams since year 2000. Particular emphasis is placed on the information content encoded in the product angular distribution-the trait of a typical molecular beam scattering experiment-and how the information can help in answering fundamental questions about chemical reactivity. We will start with simple reactions by highlighting a few benchmark three-atom reactions, and then move on progressively to the more complex chemical systems and with more sophisticated types of measurements. Understanding what cause the experimental observations is more than computationally simulating the results. The give and take between experiment and theory in unraveling the physical picture of the underlying dynamics is illustrated throughout this review.

Time-Dependent Wave Packet Studies on the Cl + HCl Hydrogen Exchange Reaction

The initiation of the hydrogen exchange reaction Cl((2)P)+HCl --> ClH+Cl((2)P) by excitation of the HCl molecular stretch to v=2 is studied for total angular momentum quantum number J=(1)/(2) and both even and odd parity. The calculations were performed using a time-dependent propagation from an initial quasi-bound state and employed all three relevant potential energy surfaces and the nonadiabatic couplings between them. Coriolis and spin-orbit coupling were also taken into account. The electronic and HCl rotational distributions of the products in both dissociation channels are analyzed, and the results are interpreted using features of the potential energy surfaces.

Nonadiabatic reactant-product decoupling calculation for the F(P1∕22)+H2 reaction

In this paper we present a theoretical study using time-dependent nonadiabatic reactant-product decoupling method for the state-to-state reactive scattering calculation of F((2)P(1/2))+H(2) (nu=j=0) reaction on the Alexander-Stark-Werner potential energy surface. In this nonadiabatic state-to-state calculation, the full wave function is partitioned into reactant component and a sum of all product components. The reactant and product components of the wave function are solved independently. For the excited state reaction, the state-to-state reaction probabilities for J=0.5 are calculated. Comparing the state-to-state reaction probabilities, it is found that the vibrational population of the HF product is dominated by vibrational levels nu=2 and 3. The rotation specific reaction probabilities of HF product in j=1 and 2 are larger than those in other rotational levels. As the rotation quantum number j increases, the positions of the peak in the rotational reaction probability of HF product in nu=3 shift to higher collision energy.

Quantum Wave Packet Study of the H+ + D2 Reaction on Diabatic Potential Energy Surfaces

The exact three-dimensional nonadiabatic quantum dynamics calculations were carried out for the title reaction by a time-dependent wave packet approach based on a newly constructed diabatic potential energy surface (Kamisaka et al. J. Chem. Phys. 2002, 116, 654). Three processes including those of reactive charge transfer, nonreactive charge transfer, and reactive noncharge transfer were investigated to determine the initial state-resolved probabilities and reactive cross sections. The results show that a large number of resonances can be observed in the calculated probabilities due to the deep well on adiabatic ground surface and the dominant process is the reactive noncharge-transfer process. Some interesting dynamical features such as v-dependent and j-dependent behaviors of the probabilities are also revealed. In addition, a good agreement has been achieved in the comparison between the calculated quantum cross sections from the ground rovibrational initial state and the experimental measurement data.

A quantum wave-packet study of intersystem crossing effects in the O(P2,1,03,D21)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.

Comparison of experimental time-of-flight spectra of the HF products from the F+H2 reaction with exact quantum mechanical calculations

High resolution HF product time-of-flight spectra measured for the reactive scattering of F atoms from n-H2(p-H2) molecules at collision energies between 69 and 81 meV are compared with exact coupled-channel quantum mechanical calculations based on the Stark-Werner ab initio ground state potential energy surface. Excellent agreement between the experimental and computed rotational distributions is found for the HF product vibrational states v'=1 and v'=2. For the v'=3 vibrational state the agreement, however, is less satisfactory, especially for the reaction with p-H2. The results for v'=1 and v'=2 confirm that the reaction dynamics for these product states is accurately described by the ground electronic state 1 (2)A' potential energy surface. The deviations for HF(v'=3, j' > or =2) are attributed to an enhancement of the reaction resulting from the 25% fraction of excited ((2)P(12)) fluorine atoms in the reactant beam.

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.

A Quantum Wave Packet Dynamical Study of the Electronic and Spin−Orbit Coupling Effects on the Resonances in Cl(2P) + H2 Scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.

Nonadiabatic energy transfer studies of O(1D)+N2(X 1Σg+)→O(3P)+N2(X 1Σg+) by time-dependent wave packet

Three-dimensional time-dependent quantum calculations have been performed on two/three coupled potential surfaces, including the singlet surface 1 (1)A(') and two triplet surfaces 1 (3)A(') and 1 (3)A("), for the electronic quenching process of O((1)D)+N(2)(X (1)Sigma(g) (+))-->O((3)P)+N(2)(X (1)Sigma(g) (+)). An extended split-operator scheme was employed to study this nonadiabatic process. Two types of singlet surface 1 (1)A('), namely, double many body expansion (DMBE2) were used in the calculations, along with spin-orbit couplings of Nakamura-Kato and with a constant value of 80 cm(-1). All the calculated probabilities are resonance dominated, with a general decreasing trend within the investigated collision energy range. The probability involving three potential energy surfaces is approximately two times as high as that on two potential energy surfaces. At low collision energies, the calculations on the ZPM2 surface produced much larger probability than that on the DMBE2 surface, but the difference was diminishing as the collision energy became high. The behavior of the probability on DMBE2/ZPM2 surfaces at low energies indicates that the ZPM2 surface dominates over the DMBE2 surface in the description of the process. However, the DMBE2 surface has been modified by removing the unreasonable barrier. The estimated quenching cross sections both on the ZPM2 surface and on the modified DMBE2 surface in the three-coupled-surface calculations agree with the experimental measurement. Also, a rather insensitive characteristic of the probability relative to the analytical function form of spin-orbit coupling is revealed.

A resonance-mediated non-adiabatic reaction: F*(2P1/2) + HD --> HF(v' = 3) + D

The reaction of F(2P3/2,1/2) + HD --> HF(v' = 3) + D was investigated in a rotating-source, crossed-beam machine. The high translational energy resolution afforded by the Doppler-selected time-of-flight technique enabled us to distinguish the differential attributes of the HF(v' = 3) + D products of the ground state (2P3/2) reaction from those due to the spin-orbit excited (2P1/2) one. It was found that the F*(2P1/2) reactivity is significantly smaller than that for F(2P3/2), and the two state-to-state angular distributions exhibit remarkable similarities, though some differences were noted. Comparing the results with those concluded previously, we assert that both the adiabatic (F(2P3/2) + HD) and, in particular, the non-adiabatic (F*(2P1/2) + HD) reactions are predominantly mediated by a resonance mechanism for the formation of the HF(v' = 3) + D channel.

The investigation of spin–orbit effect for the F(2P)+HD reaction

In this paper, we employ the time-dependent quantum wave packet method to study the reaction of F((2)P(3/2), (2)P(1/2)) with HD on the Alexander-Stark-Werner potential energy surface. The reaction probabilities and total integral cross sections of the spin-orbit ground and excited states for the two possible products of the system are calculated. Because the reaction channel of the excited spin-orbit state is closed at the resonance energy, the resonance feature does not appear in the reaction probabilities and cross section for the F((2)P(1/2))+HD(v=j=0)-->HF+D reaction, in contrast with that found for the ground spin--orbit state. We also compare the average cross sections of the two possible products with the experimental measurement. The resonance peak in the present average cross section for the HF+D product is slightly larger than the experimental result, but much smaller than that of the single-state calculations on the potential energy surface of Stark and Werner. It seems that the spin--orbit coupling would play a relatively important role in this reaction. Moreover, the isotope effects of the ground and excited spin--orbit states and the reactivity of the two product channels from the excited spin--orbit state are presented.