Double Many-body Expansion Research Articles

Effect of O2 + O ab initio and Morse additive pairwise potentials on dissociation and relaxation rates for nonequilibrium flow calculations

This work quantifies the sensitivity of O2 + O dissociation rates and relaxation to interatomic potential energy surfaces at high-enthalpy, nonequilibrium flow conditions. State-to-state cross sections are obtained by quasi-classical trajectory (QCT) calculations with two potential surfaces. The first is a Morse additive pairwise potential for O3 that is constructed based on O2(3Σg−) spectroscopic measurements and the second is a double many-body expansion potential by Varandas and Pais [Mol. Phys. 65, 843–860 (1988)]. The QCT calculations of cross sections and rates with the two surfaces are compared to each other and shock tube measurements. It is found that, at temperatures between 2500 K and 20 000 K, the equilibrium dissociation rates predicted by the two potentials agree within 12%, and they are bound by experimental dissociation measurements. In contrast, above 10 000 K, ab initio based equilibrium dissociation rates are about a factor of two higher than the widely used Park’s model. The nonequilibrium dissociation rates calculated by the two potentials are within 70% while phenomenological models differ by two orders of magnitude for vibrationally cold conditions of shocks. The analyses provide an approach for improving accuracy of nonequilibrium high-enthalpy flow modeling when ab initio potentials are not available.

Exploring NH (X3Σ−) + D (2S) → N (4S) + HD (X1Σg+) reaction with time-dependent wave packet method

For the title reaction, we performed the time-dependent wave packet calculations over the collision energy range from 0 to 1.0eV on the double many-body expansion 4A″ potential energy surface reported by Poveda and Varandas (2005) and combined many-body expansion and neural network 4A″ potential energy surface reported by Zhai and Han (2011), respectively. We obtained the initial state-selected reaction probabilities, reaction cross-sections, and rate constants. The calculated room-temperature rate constants on both potential energy surfaces agree with the experimental estimation.

Accurate adiabatic potential energy surface for 12A′ state of FH2 based on ab initio data extrapolated to the complete basis set limit

An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system. It is obtained by using the aug-cc-pVTZ and aug-cc-pVQZ basis sets with extrapolation of the electron correlation energy to the complete basis set limit, plus extrapolation to the complete basis set limit of the complete-active-space self-consistent field energy. The collinear and bending barrier heights of the new global potential energy surface is 2.301 and 1.768 kcal mol-1, in very good agreement with the values of 2.222 and 1.770 kcal mol-1 from the current best potential energy surface. In particular, the new potential energy surface describes well the important van der Waals interactions which is very useful for investigating the dynamics of the title system. Thus, the new potential energy surface can both be recommended for dynamics studies of the F + H2 reaction and as building block for constructing the potential energy surfaces of larger fluorine/hydrogen containing systems. Based on the new potential energy surface, a preliminary theoretical study of the reaction F(2P) + H2 (X1 Σ g +) → FH(X 1 Σ +) + H(2S) has been carried out with the methods of quasi-classical trajectory and quantum mechanical. The results have shown that the new PES is suitable for any kind of dynamics studies.

Dynamics of the O + ClO reaction: reactive and vibrational relaxation processes.

Classical trajectories have been integrated to study the O + ClO reaction, both reactive and vibrational energy transfer processes, for the range of temperatures 100 ≤ T/K ≤ 500 using momentum Gaussian binning. The employed potential energy surface is the recently proposed single-sheeted double many-body expansion potential energy surface for the (2)A" ground-state of ClO2 based on multireference ab initio data. A capture-type regime with a room-temperature rate constant of (17.8 ± 0.5) × 10(-12) cm(3) s(-1) and temperature dependence of k(T/K)/cm(3) s(-1) = 22.4 × 10(-12) × T(-0.81) exp(-39.2/T) has been found. Although the value reported here is half of the experimental and recommended one, tentative explanations are given. Other dynamical attributes are also examined for the title reaction, with state-to-all and state-to-state vibrational relaxation and excitation rate constants reported for temperatures of relevance in stratospheric chemistry.

Exploring the utility of many-body expansions: a consistent set of accurate potentials for the lowest quartet and doublet states of the azide radical with revisited dynamics.

Starting from reliable double many-body expansion potentials calibrated with energies calculated at the state-of-the-art ab initio level but of varying accuracies, it is shown that a single scaling parameter suffices to bring them into consistency while mimicking key experimental data and leaving mostly unaffected crossing seams of the conical type. This emerges as a valuable asset of their underlying formalism. Use of the novel potentials for studying the dynamics of the N(⁴S/²D) + N₂(¹Σ(g)⁺) reactions yields results in excellent agreement with the most accurate available data.

Accurate double many-body expansion potential energy surface for the 2(1)A' state of N2O.

An accurate double many-body expansion potential energy surface is reported for the 2(1)A' state of N2O. The new double many-body expansion (DMBE) form has been fitted to a wealth of ab initio points that have been calculated at the multi-reference configuration interaction level using the full-valence-complete-active-space wave function as reference and the cc-pVQZ basis set, and subsequently corrected semiempirically via double many-body expansion-scaled external correlation method to extrapolate the calculated energies to the limit of a complete basis set and, most importantly, the limit of an infinite configuration interaction expansion. The topographical features of the novel potential energy surface are then examined in detail and compared with corresponding attributes of other potential functions available in the literature. Exploratory trajectories have also been run on this DMBE form with the quasiclassical trajectory method, with the thermal rate constant so determined at room temperature significantly enhancing agreement with experimental data.

Single-Sheeted Double Many-Body Expansion Potential Energy Surface for Ground-State ClO2

A global single-sheeted double many-body expansion potential energy surface is reported for the ground electronic state of ClO2. The potential energy surface is obtained by fitting 3200 energy points that map all atom-diatom dissociation channels as well as all relevant stationary points, including the well-known OClO and ClOO structures. The ab initio calculations are obtained at the multireference configuration interaction level of theory, employing the cc-pVXZ (X = D, T) Dunning basis sets, and then extrapolated to the complete basis set limit with the generalized uniform singlet- and triplet-pair protocol. The topographical features of the novel global potential energy surface are examined in detail.

Quantum dynamics on S(1D) + H2 reaction: effect of orientation and rotation

Time-dependent quantum mechanical wave packet calculations have been carried out to study the effect of orientation and rotation of the hydrogen molecule on the reaction S (1D) + H2(X1 Σ + )(v = 0, j = 0–3) → SH(X2 Π) + H(2S) using the double many-body expansion (DMBE)/complete basis set (CBS) potential energy surface (PES) by Song and Varandas [J. Chem. Phys. 130, 134317 (2009)]. Reaction probability and integral cross section values were calculated over a range of collision energy values. The cross section values are compared with the experimental values as well as with the other quantum mechanical results. Our calculation shows that reaction probability values strongly depend on the orientation and rotation of the hydrogen molecule. It was also found that rotational excitation of H2 molecule significantly enhances integral reaction cross section values contrary to earlier reported quasi-classical trajectory calculation results.

A typical slow reaction H(2S) + S2(X3Σ−g) → SH(X2Π) + S(3P) on a new surface: Quantum dynamics calculations

Quantum dynamics calculations for the title reaction H(2S) + S2(X3Σ−g) → SH(X2Π) + S(3P) are performed by using a globally accurate double many-body expansion potential energy surface [J. Phys. Chem. A 115 5274 (2011)]. The Chebyshev real wave packet propagation method is employed to obtain the dynamical information, such as reaction probability, initial state-specified integral cross section, and thermal rate constant. It is found not only that there is a reaction threshold near 0.7 eV in both reaction probabilities and integral cross section curves, but also that both the probability and cross section increase firstly and then decrease as the collision energy increases. The existence of the resonance structure in both the probability and cross section curves is ascribed to the deep potential well. The calculation of the rate constant reveals that the reaction occurring on the potential energy surface of the ground-state HS2 is slow to take place.

Quasiclassical Trajectory Study of the Atmospheric Reaction N(2D) + NO(X 2Π) → O(1D) + N2(X 1Σg+)

Quasiclassical trajectories have been run for the title atmospheric reaction over the range of temperatures 5 ≤ T/K ≤ 3000 on a recently proposed single-sheeted double many-body expansion (DMBE) potential energy surface for ground-state N2O((1)A'). As typical in a capture-like reaction, the rate constant decreases with temperature for 50 ≤ T/K ≤ 800 K, while showing a small dependence at higher temperature regimes. At room temperature, it is predicted to have a value of (20.1 ± 0.2) × 10(-12) cm(3) s(-1). The calculated cross sections show a monotonic decay with temperature and translational energy. Good agreement with the experimental data has been observed, providing more realistic rate constants and hence support of enhanced accuracy for the DMBE potential energy surface with respect to other available forms.

Accurate ab initio-based DMBE potential energy surface for HLi2(X 2A′) via scaling of the external correlation

A globally accurate potential energy surface is reported for the electronic ground-state HLi2 by fitting ab initio energies to double many-body expansion formalism. The total 3726 ab initio energies used to map the HLi2 potential energy surface are calculated using the multi-reference configuration interaction method, with their dynamical correlation being semiempirically corrected by the double many-body expansion-scaled external correlation method. The current potential energy surface generates an excellent fit of the ab initio energies, showing a small root-mean squared derivation of 0.636 kcal mol-1. The topographical features of the HLi2 potential energy surface are examined in detail, which concludes that the H + Li2(X 1 Σ g ) → Li + LiH(X 1 Σ) reaction is essentially barrierless and the exothermicity is calculated to be 33.668 kcal mol-1, thus corroborates the available experimental and theoretical results.

Theoretical investigation of vibrational relaxation of highly excited O3 in collisions with HO2

We report calculations of the relaxation process involving highly excited O3 with vibrationally cold HO2. The initial vibrational energies of O3 between 9 and 21 kcal mol−1 are considered. All calculations employ the quasi-classical trajectory method and the realistic double many-body expansion potential energy surface for HO5(2A). Both the traditional histogram boxing and momentum Gaussian binning schemes are utilized in examining the energy transfer process, the latter for the first time in the case of triatomic fragments. The results indicate that it may notable in studying the stratospheric ozone budget.

Accurate ab initio-based adiabatic global potential energy surface for the 22A″ state of NH2 by extrapolation to the complete basis set limit

A full three-dimensional global potential energy surface is reported first time for the title system, which is important for the photodissociation processes. It is obtained using double many-body expansion theory and an extensive set of accurate ab initio energies extrapolated to the complete basis set limit. Such a work can be recommended for dynamics studies of the N((2)D) + H2 reaction, a reliable theoretical treatment of the photodissociation dynamics and as building blocks for constructing the double many-body expansion potential energy surface of larger nitrogen/hydrogen containing systems. In turn, a preliminary theoretical study of the reaction N((2)D)+H2(X(1)Σg (+))(ν=0,j=0)→NH(a(1)Δ)+H((2)S) has been carried out with the method of quasi-classical trajectory on the new potential energy surface. Integral cross sections and thermal rate constants have been calculated, providing perhaps the most reliable estimate of the integral cross sections and the rate constants known thus far for such a reaction.

Quasi-classical trajectory study of the reaction N(4S) + H2 and its reverse reaction: Role of initial vibrational and rotational excitations in chemical stereodynamics

To investigate the effects of reagent vibrational and rotational states on the stereodynamical properties of the N(4S) + H2(v, j) → NH + H reaction and its reverse reaction of H(2S) + NH(v, j) → N(4S) + H2, we reported a detailed quasiclassical trajectory study using the 4A″ double many-body expansion potential energy surface and at the collision energy of 35 kcal/mol. The density distribution of P(θ r) as a function of the angle between \(\boldsymbol{k}\) and \(\boldsymbol{j^\prime} \), and that of P(ϕ r) as a function of the dihedral angle between the plane containing \(\boldsymbol{k}\)–\({\boldsymbol{k^\prime}} \) and the plane containing \(\boldsymbol{k^\prime}\)–\(\boldsymbol{j^\prime} \), the normal differential cross-sections as well as the averaged product rotational alignment parameter \(\left\langle {P_2 \left({\boldsymbol{j^\prime} \cdot \boldsymbol{k}} \right)} \right\rangle \) are calculated and reported. Comparison between the two reactions has showed that the degrees of alignment and orientation of products related to reagent rovibrational state have marked differences for the two reactive systems. The calculated average rotational alignment parameter \(\left\langle {P_2 \left({\boldsymbol{j^\prime} \cdot \boldsymbol{k}} \right)} \right\rangle \) as a function of the initial vibrational and rotational quantum numbers for the N(4S) + H2 and NH + H(2S) reactions, illustrating the dependence of the product alignment on initial vibrational and rotational excitations.

Accurate double many-body expansion potential energy surface by extrapolation to the complete basis set limit and dynamics calculations for ground state of NH2

An accurate single-sheeted double many-body expansion potential energy surface is reported for the title system. A switching function formalism has been used to warrant the correct behavior at the H2(X1Σg+)+N(2D) and NH (X3Σ-)+H(2S) dissociation channels involving nitrogen in the ground N(4S) and first excited N(2D) states. The topographical features of the novel global potential energy surface are examined in detail, and found to be in good agreement with those calculated directly from the raw ab initio energies, as well as previous calculations available in the literature. The novel surface can be using to treat well the Renner-Teller degeneracy of the 12A″ and 12A' states of NH 2. Such a work can both be recommended for dynamics studies of the N(2D)+H2 reaction and as building blocks for constructing the double many-body expansion potential energy surface of larger nitrogen/hydrogen-containing systems. In turn, a test theoretical study of the reaction N(2D)+H2(X1Σg+)(ν=0,j=0)→NH (X3Σ-)+H(2S) has been carried out with the method of quantum wave packet on the new potential energy surface. Reaction probabilities, integral cross sections, and differential cross sections have been calculated. Threshold exists because of the energy barrier (68.5 meV) along the minimum energy path. On the curve of reaction probability for total angular momentum J = 0, there are two sharp peaks just above threshold. The value of integral cross section increases quickly from zero to maximum with the increase of collision energy, and then stays stable with small oscillations. The differential cross section result shows that the reaction is a typical forward and backward scatter in agreement with experimental measurement result.

QUASI-CLASSICAL TRAJECTORY STUDY OF THE REACTION N + NH (v = 0–3, j=0) → N2 + H

The quasi-classical trajectory (QCT) calculations have been carried out for the reaction N + NH (v = 0–3, j=0) → N2 + H on the ground state of double many-body expansion (DMBE) potential energy surface [Caridade, PJSB, Poveda LA, Rodrigues SPJ, Varandas AJC, J Phys Chem A111:1172, 2007]. The influence of reagent vibrational excitation on reaction probability for total angular momentum J = 0 and integral cross section (ICS) at collision energies ranging from 0.1 eV to 1.0 eV has been investigated. The reaction probability tends to decrease with increasing collision energy and increase with the rising of initial vibration state, although some fluctuations appear. The ICS declines monotonously with the increase of collision energy and v. The product rotational alignment factor 〈P2(j′•k)〉 has also been calculated, and its value has a declining trend with the increase of collision energy. In spite of that, the results still show that the product is highly aligned. In addition, the vibrational excitation effect on the product polarization has also been studied. All the distributions of P(ϕr), P(θr), and the generalized polarization dependent differential cross sections indicate dependent behaviors on v.

INFLUENCE OF VIBRATIONAL EXCITATION AND COLLISION ENERGY ON THE STEREO DYNAMICS OF THE REACTIONS:N(4S)+H2(v = 0-3,j = 0) →NH(X3Σ-)+H

Quasi-classical trajectory (QCT) calculations have been carried out to study the stereodynamics of the title reactions, using the double many-body expansion (DMBE) potential energy surface (PES) constructed by Poveda [Poveda LA, Varandas AJC, Phys. Chem. Chem. Phys.7:2867, 2005]. Vector correlations, such as the distributions of the polarization-dependent differential cross-sections (PDDCSs), the angular distributions of P(θr), P(ϕr), P(θr,ϕr), and the product alignment parameter P2( cos θr) are reported within the energy range of 25–140 kcal mol-1. The influences of the collision energy and the initial state-selected vibrational excitation are discussed in detail. In addition, Validity of the current QCT calculations is also examined and compared with the revelant results reported by Pascual et al. [Pascual RZ, Schatz GC, Lendvay G, Troya D, J. Phys. Chem. Aਠ106:4125, 2002].

The Rate Constant Calculations for the Reaction H(2S)+NH(X3Σ−) to N(4S)+H2 by using Quantum Mechanics Method

The quantum reactive scattering dynamics calculations are carried out over the collision energy range of 0–1.0 eV on the double many-body expansion (DMBE) potential energy surface reported by Poveda and Varandas [Phys. Chem. Chem. Phys. 7(2005) 2867]. The reaction probabilities, integral cross-section and rate constants for the title reaction are calculated. The calculated rate constants are in agreement with the available experimental results at high temperature but lower than the experimental results at low temperature.

Ab initio-based double many-body expansion potential energy surface for the first excited triplet state of the ammonia molecule

A global single-sheeted double many-body expansion potential energy surface is reported for the first excited triplet state of NH(3). It employs an approximate cluster expansion of the molecular potential that utilizes previously reported functions of the same family for the triatomic fragments. Four-body energy terms have been calibrated from extensive accurate ab initio data so as to reproduce the main features of the title system. A new switching function formalism has been reported to approximate the true multisheeted nature of NH(3)((3)A(2) ('')) potential energy surface, thus allowing the correct behavior at the NH(2)((2)A(")) + H((2)S) and NH(2)((4)A(")) + H((2)S) dissociation limits. The resulting fully six-dimensional potential energy function reproduces the correct symmetry under the permutation of identical atoms, and predicts the correct behavior at all dissociation channels while providing a realistic representation at all interatomic separations. The major attributes of the NH(3) double many-body expansion potential energy surface have also been characterized, and found to be in good agreement, both with the calculated ones from the raw ab initio energies and the theoretical results available in the literature.

Ab Initio-Based Global Double Many-Body Expansion Potential Energy Surface for the First 2A″ Electronic State of NO2

An ab initio-based global double many-body expansion potential energy surface is reported for the first electronic state of the NO(2)((2)A") manifold. Up to 1700 ab initio energies have been employed to map the full configuration space of the title molecule, including stationary points and asymptotic channels. The calculated grid energies have been scaled to account for the incompleteness of the basis set and truncation of the MRCI expansion and fitted analytically with a total root-mean-squared-deviation smaller than 1.0 kcal mol(-1). The lowest point of the potential energy surface corresponds to the (2)B(1) linear minimum, which is separated from the C(s) distorted minimum by a C(2v) barrier of ≈9.7 kcal mol(-1). As usual, the proposed form includes a realistic representation of long-range interactions. Preliminary work indicates its reliability for reaction dynamics.