Real Wave Packet Method Research Articles

Isotope Effects on State-to-State Photodissociation Dynamics of D2S in Its First Absorption Band.

State-to-state photodissociation dynamics of D2S in its first absorption band were explored by utilizing recently developed diabatic potential energy surfaces (PESs). Quantum dynamics calculations, involving the first two strongly coupled 1A″ states, were executed employing a Chebyshev real wavepacket method. The nonadiabatic channel via the conical intersection (CI) is facile, direct, and fast, leading to the production of rotationally and vibrationally cold SD(X̃2Π). The calculated absorption spectrum, product state distributions, and angular distributions are in reasonable agreement with the experimental results, although some discrepancies exist at 193.3 nm. Compared with H2S, there are obvious isotope effects on rotational state distributions for D2S photodissociation in its first absorption band. Moreover, we scrutinize the variation of product state distributions as a function of photon energy and the vibrational mediated photodissociation of the parent molecule. Due to the diverse shapes of the three fundamental vibrational wave functions, photoexcited wavepackets access distinct segments of the upper-state PES, resulting in a disparate absorption spectrum and ro-vibrational distributions via the nonadiabatic transition. This study provides a comprehensive figure of the isotopic effect and wavelength dependence on the photofragmentation behaviors from D2S photodissociation, which should attract more experimental and theoretical attention to this prototypical system.

Theoretical study on photodissociation dynamics of vibrational excited states of H2S in the first absorption band

The photodissociation quantum dynamics for the first absorption band of H2S in different initial vibrational states have been investigated using Chebyshev real wave packet method. Because of the difference of the wave functions for the initial vibrational states, the calculated absorption spectra and the distributions of vibrational and rotational state of the products display different dynamic characteristics. The width and peak position of the absorption spectra for initial stretching excited states (1,0,0) and (0,0,1) are different from that of the vibrational ground state, while the (0,1,0) vibrational state has two almost equally high peaks in its absorption spectrum because of the change of wave function in angular coordinate. The product vibrational state distribution for (0,1,0) initial state weakly depends on the excitation energy and is dominated by the products of v=0, but SH(v=1) fragment is dominant at lower energy for (1,0,0) and (0,0,1) vibrational states. The rotational state distributions of products are very cold with the peak at j=l for these four states and weakly depend on the total energy. Besides, the rotational state distribution from (0,1,0) vibrational state displays strong oscillation, and its anisotropic parameter with rotational quantum numbers is also different from that of the other three vibrational states.

Quantum Dynamics of Nonadiabatic Renner-Teller Effects in Atom + Diatom Collisions.

We review the quantum nonadiabatic dynamics of atom + diatom collisions due to the Renner-Teller (RT) effect, i.e., to the Hamiltonian operators that contain the total spinless electronic angular momentum L̂. As is well-known, this rovibronic effect is large near collinear geometries when at least one of the interacting states is doubly degenerate. In general, this occurs in insertion reactions and at short-range, where the potential wells exhibit deep minima and support metastable complexes. Initial-state-resolved reaction probabilities, integral cross sections, and thermal rate constants are calculated via the real wavepacket method, solving the equation of motion with an approximated or with an exact spinless RT Hamiltonian. We present the dynamics of 10 single-channel or multichannel reactions showing how RT effects depend on the product channels and comparing with the Born-Oppenheimer (BO) approximation or coexisting conical-intersection (CI) interactions. RT effects not only can significantly modify the adiabatic dynamics or correct purely CI results, but also they can be very important in opening collision channels which are closed at the BO or CI level, as in electronic-quenching reactions. In the OH(A2Σ+) + Kr electronic quenching, where both nonadiabatic effects (CI and RT) coexist, they are in competition because CI dominates the reactivity but RT couplings reduce the large CI cross section and open a CI-forbidden evolution toward products, so that CI + RT quantum results are in good agreement with experimental or semiclassical findings. The different roles of these couplings are due to the unlike nuclear geometries where they are large: rather far from or near to linearity for CI or RT, respectively. The OH(A2Σ+) + Kr electronic quenching was investigated with the exact RT Hamiltonian, validating the approximated one, which was employed for all other collisions.

A quantum wavepacket study of state-to-state photodissociation dynamics of HOBr/DOBr

Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere. Here, we report the first three-dimensional potential energy surfaces for the lowest three singlet states for HOBr, based on high level multi reference configuration interaction calculations. Quantum dynamics calculations are performed with a real wavepacket method, yielding not only absorption spectra but also internal state and angular distributions of the photodissociation fragments. Our results agree quantitatively with the measured total absorption cross sections of HOBr in the ultraviolet region and reproduce well the observed vibrationally cold and rotationally hot OH/OD fragments via photodissociation of HOBr/DOBr at 266 nm. In addition, we predict that the recoil anisotropy parameters for OH/OD are close to the limiting value of a parallel transition, suggesting a rapid dissociation process at 266 nm following an in-plane transition from the ground state (11A′) to the 21A′ state. This is consistent with the experimental conclusion derived from the measured rotational alignment. However, spin and electronic angular momenta need to be taken into account in the future to achieve a more quantitative agreement with experiment. Our work is expected to motivate further experimental investigations for this benchmark system.

Non-adiabatic quantum dynamics of the electronic quenching OH(A2Σ+) + Kr.

We present the dynamics of the electronic quenching OH(A2Σ+) + Kr(1S) → OH(X2Π) + Kr(1S), with OH(A2Σ+) in the ground ro-vibrational state. This study relies on a new non-adiabatic quantum theory that uses three diabatic electronic states Σ+, Π', and Π'', coupled by one conical-intersection and nine Renner-Teller matrix elements, all of which are explicitly considered in the equation of the motion. The time-dependent mechanism and initial-state-resolved quenching probabilities, integral cross sections, thermal rate constants, and thermally-averaged cross sections are calculated via the real wavepacket method. The results point out a competition among three non-adiabatic pathways: Σ+ ↔ Π', Σ+ ↔ Π'', and Π' ↔ Π''. In particular, the conical-intersection effects Σ+-Π' are more important than the Renner-Teller couplings Σ+-Π', Σ+-Π'', and Π'-Π''. Therefore, Π' is the preferred product channel. The quenching occurs via an indirect insertion mechanism, opening many collision complexes, and the probabilities thus present many oscillations. Some resonances are still observable in the cross sections, which are in good agreement with previous experimental and quasi-classical findings. We also discuss the validity of more approximate quantum methods.

Non-adiabatic Quantum Dynamics of the Dissociative Charge Transfer He++H2 → He+H+H.

We present the non-adiabatic, conical-intersection quantum dynamics of the title collision where reactants and products are in the ground electronic states. Initial-state-resolved reaction probabilities, total integral cross sections, and rate constants of two H2 vibrational states, v0 = 0 and 1, in the ground rotational state (j0 = 0) are obtained at collision energies Ecoll ≤ 3 eV. We employ the lowest two excited diabatic electronic states of and their electronic coupling, a coupled-channel time-dependent real wavepacket method, and a flux analysis. Both probabilities and cross sections present a few groups of resonances at low Ecoll, whose amplitudes decrease with the energy, due to an ion-induced dipole interaction in the entrance channel. At higher Ecoll, reaction probabilities and cross sections increase monotonically up to 3 eV, remaining however quite small. When H2 is in the v0 = 1 state, the reactivity increases by ~2 orders of magnitude at the lowest energies and by ~1 order at the highest ones. Initial-state resolved rate constants at room temperature are equal to 1.74 × 10−14 and to 1.98 × 10−12 cm3s−1 at v0 = 0 and 1, respectively. Test calculations for H2 at j0 = 1 show that the probabilities can be enhanced by a factor of ~1/3, that is ortho-H2 seems ~4 times more reactive than para-H2.

The functional states of angular quantum numbers and Ne + H2+(ν= 0,j= 2) → NeH++ H reaction mechanism

The behaviors of Legendre polynomials representing angular movements are independent of the type of reaction and can be studied in detail paying attention to the changes on effective and centrifugal potentials. For the title reaction, dynamic calculations taking into account the effects of potential energy surfaces have been investigated using the real wave packet method on the most realistic potential energy surface (LZHH) recently obtained. The total electrical dipoles and energies were also calculated in the corresponding quantum states of the molecular system.

A theoretical study on the C + OH reaction dynamics and product energy disposal with vibrationally excited reagent

State-to-state dynamics of the C(3 P) + OH(X2 Π , v = 0– 2, j = 0) → CO (a3 Π ) + H (2 S), reaction on the first (12 A″ ) and second (14 A″ ) excited states is studied by the real wave packet method of Gray and Balint-Kurti [S.K. Gray et al., J. Chem. Phys. 108 , 950 (1998)]. Product state-resolved (both vibrational and rotational) and total reaction probabilities are calculated for the total angular momentum, J = 0. Product vibrational and rotational distributions are also examined at five different collision energies to elucidate the reaction mechanism. Reagent vibrational excitation is found to decrease the reactivity on the 12 A″ state and enhance the same on the 14 A″ state. While the excess reagent vibrational energy releases mainly as product translation on the 12 A″ state, the same releases as product vibration and rotation on the 14 A″ state. The product rotational distribution is relatively cold on the 14 A″ state. Despite same mass combination and same exoergicity, the drastic differences of the dynamics of the reaction on the two excited states are related to the microscopic topology of the underlying reaction path. The late barrier present on the 14 A″ state plays crucial role on the reaction dynamics at the state-to-state level. The results of the present study are compared with the available literature data.

Vibration Dynamics of H+F2 Reactive Scattering

In this paper the vibration distributions of H+F2 reaction on the ground electronic state, which are important for chemical laser, have been discussed. The HF molecule formed by this reaction has been examined depending on the initial and final vibration states in particular collision energies. The results have been obtained using time dependent quantum mechanical Real Wave Packet (RWP) method on Potential Energy Surface (PES) [Chemical Physics Letters, Vol. 496, 2010, 248-263], which can be given more realistic values in the strong interaction region. The state to state reaction distributions have been calculated to be able to compare with both experimental results at the collision energy of 0.105 eV and Quasi-Classical Trajectories (QCT) results depended on LEPS potential at the collision energies of 0.494 eV and 0.086 eV. Also in this study, the obtained rate constants have been compared by theoretical and experimental values in the literature and are found to be in good agreement to each other.

Quantum real wave packet method by using spectral difference for a triatomic reactive scattering

Along with the increasing power of computer, the molecules which can be studied within quantum mechanics principle in the field of reaction dynamics become more complicated. The shortcoming of the discrete variable representation method, i.e., the full matrix and huge inter-computer communication in MPI calculations, becomes more significant. The spectral difference method is an excellent compromise. In this work, a spectral difference approach for angular coordinate, which leads to banded kinetic matrix similar to the spectral difference method for the radial degrees of freedom, is proposed. Using the Chebyshev real wave packet approach, we demonstrate that for all three degrees of freedom for a triatomic reactive scattering process, spectral difference is able to boost much computational efficiency. The numerical advantage of our proposed method was illustrated with the reactions of H + H2, O + O2, N + O2.

Quantum reaction dynamics of C(1D) + HD → CH(CD) + D(H) on the ground state potential energy surface

We present accurate quantum dynamic calculations of the reaction C(1D) + HD on the latest version of the potential energy surface [Zhang et al., J. Chem. Phys. 140, 234301 (2014)]. Using a Chebyshev real wave packet method with full Coriolis coupling, we obtain the initial state-specified ( ) reaction probabilities, integral cross sections, and rate constants. The resulting probabilities display oscillatory structures due to numerous long-lived resonances supported by the deep potential well. The calculated rate constants and CD/CH product branching ratio at room temperature are in reasonably good agreement with the experimental measurements.

Nonadiabatic Renner-Teller quantum dynamics of OH(X2Π) + H+ reactive collisions.

Following previous studies on the O(3P) + H2+(X2Σg+) collisions, we present the nonadiabatic quantum dynamics of the reactions OH(X2Π) + H'+ → OH'(X2Π) + H+, exchange (e), → OH+(X3Σ-) + H'(2S), quenching (q), and → OH'+ (X3Σ-) + H(2S), exchange-quenching (eq). The reactants and products correlate via the ground X[combining tilde]2A'' and first excited Ã2A' electronic states of OH2+, which are the degenerate components of linear 2Π species. Therefore, they are strongly perturbed by nonadiabatic Renner-Teller (RT) effects, opening the (q) and (eq) channels that are closed in the Born-Oppenheimer approximation. Using accurate potential energy surfaces (PESs) and RT matrix elements, initial-state-resolved reaction probabilities, real-time dynamics, cross sections, and rate constants of the product channels are obtained through the time-dependent real wavepacket (WP) method and full coupled-channel calculations. Owing to the nonadiabatic couplings, the WP jumps from the excited Ã2A' surface to the X[combining tilde]2A'' ground PES, avoiding any barrier, opening the quenching channels, and giving many collision complexes into the deep minima of both PESs, as it is clearly shown by the oscillations of the reaction probabilities and by the time-dependent WP dynamics. All the results show that the nonadiabatic-RT channels (q) and (eq) are highly reactive, much more than the adiabatic one (e), pointing out large RT effects. The reactivity of the quenching channels is similar, accounting for 97% of the overall reactivity. In fact, the maximum values of the (q) and (eq) cross sections σq and σeq are equal to 31.6 Å2, whereas the maximum σe value equals 1.34 Å2, and the maximum values of the rate constants kq, keq, and ke are 2.07 × 10-10, 2.45 × 10-10, and 0.23 × 10-10 cm3 s-1. Some calculations show that the centrifugal-sudden and the truncated coupled-channel approximations cannot be employed for the (q) channel. After a sharp increase at the threshold, σq and σeq decrease at larger collision energies while σe and the rate constants depend slightly on the collision energy and temperature, respectively. These findings are consistent with the barrierless nature of both PESs and the exoergicity of the quenching products, with the small role played by the centrifugal and RT barriers in the reactant channel, and with the large RT couplings in the OH2+ intermediates. Finally, we contrast the present results with those for the opposite reactions O + H2+ and for the nonadiabatic-induced quenchings NH + H' and OH + H'.

State to State Photodissociation Dynamics of Vibrationally Excited D2O in B Band

The state-to-state photodissociassion dynamics for the B band of D2O have been explored from quantum dynamical calculations including the electronic ̃X and ̃B states. The calculations were carried out using a Chebyshev real wave packet method. The calculated absorption spectra, product state distributions, and branching ratios from different initial vibrational states show different dynamic features, due to the different shapes of the vibrational wavefunctions. The initial bending mode (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum and a slight inverted vibrational population of OD(̃X) product at high total energies. The rotational state distributions of OD(̃X, v=0) product are highly inverted and depend weakly on the initial state and total energy. On the other hand, the ro-vibrational distributions of OD(̃A) product strongly oscillate with the total energy, which are dominated by the long-living resonances and depend sensitively on the potential surfaces. The antisymmetric stretching mode (0,0,1) has large OD(̃A)/OD(̃X) branching ratios at high total energies, which indicates that the B band dissociation proceeds mainly via the adiabatic pathway in some cases.

Full-Dimensional Quantum Dynamics of Vibrational Mediated Photodissociation of HOD in Its B Band.

The photodissociation dynamics for the ground and three fundamental vibrational states of HOD were explored from quantum dynamical calculations including the electronic X̃, Ã, and B̃ states. The calculations were based on a Chebyshev real wave packet method. Due to the different shapes of the initial vibrational wave functions and isotopic effect, the calculated absorption spectra, product state distributions, and branching ratios show different dynamic features. The initial bending excited vibtaional state (0, 1, 0) generates a bimodal behavior on the absorption spectrum and an inverted vibrational population of OD(X̃) fragment at some total energies. The rotational state distributions from four vibrational states have two different behaviors. One has a single broad peak, whereas the other one has a bimodal structure. Large OD(Ã)/OD(X̃) ratios are found for photodissociation from four vibrational states at high total energies, which indicate that the H atom dissociates mainly via the adiabatic pathway. We also calculated the OD/OH isotopic branching ratios from four vibrational states and found that the OD + H production channel is dominant over the OH + D channel in the energy range considered. The calculated results are consistent with the available observed ones.

Vibrational and Rotational Mode Specificity in The Cl + H2O → HCl + OH Reaction: A Quantum Dynamical Study.

The vibrational and rotational mode specificity of the Cl + H2O → HCl + OH reaction is studied on a recently constructed ab initio based global potential energy surface using an initial state selected Chebyshev real wave packet method. The full-dimensional quantum dynamical results under the centrifugal sudden and/or J-shifting approximations indicate that this reaction is enhanced strongly by excitations of the stretching modes of the H2O reactant but only weakly by bending excitations. On the other hand, combination modes are found to enhance the reaction more than the sum of individual excitations. In addition, rotational excitation of the H2O reactant slightly inhibits the reactivity. The observed mode specificity is consistent with the predictions of the recently proposed Sudden Vector Projection model, which attributes the promotional effects of the reactant modes to their couplings with the reaction coordinate at the transition state.

State‐to‐state reaction dynamics for the reactions of atom N with radicals

Much progress has been achieved in the developments of accurate and efficient algorithms for quantum dynamics calculations in the past two decades. Based on the reliable potential energy surfaces (PESs) constructed with state‐of‐the‐art ab initio calculations, quantum reactive scattering calculations for the atom‐diatom collisions can be performed accurately at the state‐to‐state level. In this review, we described the general strategies of constructing a PES and the Chebyshev real wave packet method briefly, and summarized our recent studies on the PESs and state‐to‐state reaction dynamics for the reactions of the atom N with radicals OH, CH, and C2. Such barrierless complex‐forming reactions are very important for understanding low‐temperature reaction dynamics and still difficult to treat accurately. © 2014 Wiley Periodicals, Inc.

State-to-state quantum dynamics of the N(4S) + C2( $$\tilde{X}$$ X ~ 1Σ+) → CN( $$\tilde{X}$$ X ~ 2Σ+) + C(3P) reaction

Quantum dynamics of the N(4S) + C2( $$\tilde{X}$$ 1Σ+) → CN( $$\tilde{X}$$ 2Σ+) + C(3P) reaction was investigated on a global potential energy surface for the $$\tilde{a}$$ 4 A″ state of C2N using a Chebyshev real wave packet method. This reaction is barrierless and has two deep wells corresponding to the CCN and CNC species, respectively. The numerous oscillations in reaction probabilities and highly excited ro-vibrational states of the product CN reflect the large exothermicity of the reaction and the feature of the potential. As expected for a complex-forming reaction, the rotational state distributions of the CN product were highly excited. The calculated vibrational state distributions of the CN product are in reasonably good agreement with the experimental results. The differential cross sections were found to be dominated by scattering in both forward and backward directions with a forward bias, suggesting that the reaction is not completely statistic and the lifetime of the reaction intermediate is not particularly long.

State-to-State Reaction Dynamics in Collision of Deuterium Molecule with Excited-State Nitrogen Atom

Abstract The collision dynamics of deuterium molecule with excited-state nitrogen atom has been investigated at a state-to-state dynamic level by using the real wave packet method. The energy-dependent behavior of the differential and integral cross sections, especially from the reactant quantum states of v = 0, j = 0 to the product quantum states of j′ = 0–7, v′ = 0–5, is presented and discussed for total energies up to 0.4 eV. The present study predicted noninverted vibrational populations and inverted rotational populations in product rovibrational distributions. Comparison of the theoretical total differential cross section with the previous experimental measurement has also been presented and discussed.

Theoretical study of the state-to-state photodissociation dynamics of the vibrationally excited water molecule in the B band.

The state-to-state photodissociation dynamics for the vibrationally excited H2O in its second absorption band has been investigated on the recent three-dimensional potential energy surfaces based on a large number of high-level ab initio points. The photodissociassion dynamics from three fundamental vibrational states of H2O were explored from quantum dynamical calculations including the electronic X̃ and B̃ states on the basis of a Chebyshev real wave packet method. Because of the different shapes of various initial vibrational wave functions, the photoexcited wavepackets access different portions of the upper-state potential energy surface, which yields different absorption spectra, ro-vibrational distributions, and branching ratios. The bending excited vibrational state (0,1,0) generates two lobes with a shallow minimum on the absorption spectrum, a dominant vibrational inverted population OH(X̃, ν = 1) fragment at higher energy, and a nearly single rotational product propensity. The bond-stretching vibrational states (0,0,1) and (1,0,0) show a high OH(Ã)/OH(X̃) ratio at short photon wavelength, which indicates that dissociation proceeds mainly via the adiabatic channel.

State to state photodissociation dynamics of D2O in the B band

State-to-state photodissociation dynamics of D2O in the B band has been investigated using the recently developed diabatic potential energy surfaces. Quantum dynamical calculations including the electronic X and B states were carried out using a Chebyshev real wave packet method. The nonadiabatic channel via the DOD conical intersection is facile, direct, and fast, which produces rotationally hot and vibrationally cold OD(X) product. On the other hand, the adiabatic channel on the excited state, leading to the OD(Ã) product, is dominated by long-lived resonances, which depend sensitively on the potential energy surface. The calculated absorption spectra, product state distributions, branching ratios, and angular distributions are in reasonably good agreement with the latest experimental results.