Double Many-body Expansion Research Articles

Unraveling the effect of reagent vibrational excitation on the scattering mechanism of the benchmark H + H2 → H2 + H hydrogen exchange reaction in the coupled 12E' ground electronic manifold.

The hydrogen exchange reaction, H + H2 → H2 + H, along with its isotopic variants, has been the cornerstone for the development of new and novel dynamical mechanisms of gas-phase bimolecular reactions since the 1930s. The dynamics of this reaction are theoretically investigated in this work to elucidate the effect of reagent vibrational excitation on differential cross sections (DCSs) in a nonadiabatic situation. The dynamical calculations are carried out using a time-dependent quantum mechanical method, both on the lower adiabatic potential energy surface and employing a two-state coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 12E' ground electronic manifold of the H3 system. Towards this effort, the Boothroyd-Keogh-Martin-Peterson (BKMP2) surface of the lower adiabatic component is coupled with the double many-body expansion (DMBE) surface of the upper one. The smooth variation of energy along the D3h seam of the conical intersections is explicitly confirmed. The coupled two-state calculations are performed only for H2 (v = 3-4, j = 0), as the minimum of the conical intersections becomes energetically accessible for these vibrational levels in the considered energy range. Initial state-selected total and state-to-state DCSs are calculated to elucidate various mechanistic aspects of reagent vibrational excitation. The latter enhances the forward scattering and makes the backward scattering less prominent. Important roles of collision energy in the vibrational energy disposal of both forward- and backward-scattered products are examined. Analysis of the state-to-state DCSs of the vibrationally excited reagents reveals an important correlation among scattering angle, and the product rotational angular momentum and its helicity state. Such an analysis establishes a novel mechanism for the forward scattering of the reaction.

High-accuracy DMBE potential energy surface for CNO(A''4) and the rate coefficients for the C + NO reaction in the A'2, A''2, and A''4 states.

An accurate potential energy surface (PES) for the lowest lying A''4 state of the CNO system is presented based on explicitly correlated multi-reference configuration interaction calculations with quadruple zeta basis set (MRCI-F12/cc-pVQZ-F12). The abinitio energies are fitted using the double many-body expansion method, thus incorporating long-range energy terms that can accurately describe the electrostatic and dispersion interactions with physically motivated decaying functions. Together with the previously fitted lowest A'2 and A''2 states using the same theoretical framework, this constitutes a new set of PESs that are suitable to predict rate coefficients for all atom-diatom reactions of the CNO system. We use this set of PESs to calculate thermal rate coefficients for the C(P3) + NO(Π2) reaction and compare the temperature dependence and product branching ratios with experimental results. The comparison between theory and experiment is shown to be improved over previous theoretical studies. We highlight the importance of the long-range interactions for low-temperature rate coefficients.

SiS formation in the interstellar medium via SiH + S collisions

ABSTRACT One of the most important Si-bearing species in the intersellar medium is the SiS molecule. Thermal rate coefficients and other collisional properties are calculated for its formation via the title reaction using the quasi-classical trajectory method. An accurate representation of the HSiS potential energy surface is employed, which has been modelled from high-level ab initio calculations and a reliable description of long-range interactions as implied by the underlying double many-body expansion method. The calculated rate coefficients for the $\rm SiH + S \rightarrow SiS + H$ reaction can be modelled with k(T) = α(T/300)βe−γ/T where $\alpha =0.63\times 10^{-10}\, \rm cm^3\, s^{-1}$, β = -0.11, and $\gamma = 11.6\, \rm K$. This result is only slightly lower than that for SiS formation via Si + SH collisions. The contribution of each reaction mechanism and the rovibrational energy distributions of the nascent SiS molecule are also calculated. The title collision can also yield SH ($\rm SiH + S \rightarrow SH + Si$), but the corresponding rate coefficient is 20 to 27 times smaller than for SiS formation ($\alpha =0.025\times 10^{-10}\rm cm^3\, s^{-1}$, β =-0.13, and $\gamma = 9.38\, \rm K$). The role of intersections between excited electronic states is also discussed, based on novel calculations including eight electronic states.

Quasiclassical Trajectory Study of the Si + SH Reaction on an Accurate Double Many-Body Expansion Potential Energy Surface

An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R-4, R-5, R-6, R-8, R-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.

Accurate DMBE potential-energy surface for CNO(2A″) and rate coefficients in C(3P)+NO collisions.

A realistic double many-body expansion potential energy surface (PES) is developed for the 2A″ state of the carbon-nitrogen-oxygen (CNO) system based on MRCI-F12/cc-pVQZ-F12 ab initio energies. The new PES reproduces the fitted points with chemical accuracy (root mean square deviation up to 0.043 eV) and explicitly incorporates long range energy terms that can accurately describe the electrostatic and dispersion interactions. Thermal rate coefficients were computed for the C(3P) + NO(2Π) reaction for temperatures ranging from 15 K to 10 000 K, and the values are compared to previously reported results. The differences are rationalized, and the major importance of long range forces in predicting the rate coefficients for barrierless reactions is emphasized.

A theoretical investigation of the $${{\rm SO}}({{B}^{3}\Sigma ^{-}{-}{X}^{3}\Sigma ^{-}}$$) vibronic transition using accurate analytical potential energy functions

In the present investigation, we report new analytical potential energy curves (APECs) for three triplet electronic states $${{X}^{3}\Sigma ^{-}}$$, $${{B}}^{3}\Sigma ^{-},$$ and $${{C}}^{3}\Pi$$ of sulfur monoxide. For such, ab initio electronic energies have been calculated employing the highly accurate multireference configuration interaction method with Davidson modification associated with aug-cc-pV(5+d)Z basis set. The novel analytical representations have been constructed by fitting such accurate energies utilizing a least-squares fitting procedure. By considering our APECs, molecular properties as spectroscopic parameters, rovibrational levels, and classical turning points were derived. Our results show good agreement when compared with available experimental and theoretical data. The vibronic (vibration–electronic) transition parameters like Franck–Condon factors, Einstein coefficients, transition dipole moment, and r-centroids for the $${{B}^{3}\Sigma ^{-}{-}{X}^{3}\Sigma ^{-}}$$ band system were also examined. The present findings provide a reliable theoretical reference that could be employed in interpretations of astrochemical and astrophysical observations. Based on the results, we recommend these functional forms to represent the two-body fragments within the double many-body expansion method to develop potential energy surfaces for larger S-bearing species.

Accurate Potential Energy Surface for Quartet State HN2 and Interplay of N(4S) + NH(X̃3Σ–) versus H + N2(A3Σu+) Reactions

A global potential energy surface for the lowest quartet state of HN2 is reported for the first time from accurate multireference ab initio calculations extrapolated to the complete basis set limit using the double many-body expansion method. All its stationary points are characterized, with the lowest quartet of HN2 predicted to have a bent global minimum 36 kcal mol-1 below the N(4S) + NH(X̃3Σ-) asymptote, from which it is barrierlessly achievable. The entire set of calculated ab initio points has been fitted for energies up to 1000 kcal mol-1 above the global minimum with an RMSD of 0.89 kcal mol-1, a gap comprising all identified stationary points. Special care is taken in modeling the involved long-range forces and cusps caused by crossing seams. The novel PES prompts for the calculation of rate constants for several unexplored reactions that are relevant for combustion, plasma, and atmospheric chemistry.

The effect of collision energy on the stereodynamics of the reaction triatomic NH2 system

The stereodynamics of the reaction H(2S) + NH (v = 0, 1, 2, 3; j = 0) → N(4S) + H2 are studied using the quasi-classical trajectory method on a double many-body expansion potential energy surface to understand the alignment and orientation of the product molecules in the collision energy range of 2–20 kcal·mol−1. The vibrational–rotational quantum number of the NH molecules is specifically investigated for v = 0, 1, 2, and 3 and j = 0. The differential cross section [DCS; ], and average rotational alignment factor are calculated. The stereodynamics results indicate that the reagent vibrational quantum number and initial collision energy significantly affect the distributions of the k–j′, k–k′–j′ and k–k′ vector correlations along with In addition, while DCS is extremely sensitive to the collision energy, it is not significantly affected by the vibrational excitation of the reagents.

Difficulties and Virtues in Assessing the Potential Energy Surfaces of Carbon Clusters via DMBE Theory: Stationary Points of Cκ (κ = 2-10) at the Focal Point.

The previously reported potential energy surfaces (PESs) of ground-state singlet C3 and triplet C4 are here utilized as input for the construction of approximate cluster expansions for larger Cκ (κ = 5-10) species. Relying primarily on the double many-body expansion (DMBE) approach, global potentials are obtained by summing the total interaction energies of all atomic subclusters up to four-body terms. The notable capability of the final forms in predicting good estimates of the linear global minima and their thermochemical/structural properties may provide important insights into the structure-determining nature of the (2 + 3 + 4) terms. The main difficulties and virtues in assessing Cκ's via DMBE theory are analyzed and new prospects given for the construction of global reliable PESs for the target species.

A theoretical study of energy transfer in Ar(1S) + SO2( ') collisions: Cross sections and rate coefficients for vibrational transitions.

Vibrational transitions, induced by collisions between rare-gas atoms and molecules, play a key role in many problems of interest in physics and chemistry. A theoretical investigation of the translation-to-vibration (T-V) energy transfer process in argon atom and sulfur dioxide molecule collisions is presented here. For such a purpose, the framework of the quasi-classical trajectory (QCT) methodology was followed over the range of translational energies 2 ≤ Etr/kcal mol-1 ≤ 100. A new realistic potential energy surface (PES) for the ArSO2 system was developed using pairwise addition for the four-body energy term within the double many-body expansion. The topological features of the obtained function are compared with a previous one reported by Hippler et al. [J. Phys. Chem. 90, 6158 (1986)]. To test the accuracy of the PES, additional coupled cluster singles and doubles method with a perturbative contribution of connected triples calculations were carried out for the global minimum configuration. From dynamical calculations, the cross sections for the T-V excitation process indicate a barrier-type mechanism due to strong repulsive interactions between SO2 molecules and the Ar atom. Corrections to zero-point energy leakage in QCT were carried out using vibrational energy quantum mechanical threshold of the complex and variations. Rate coefficients and cross sections are calculated for some vibrational transitions using pseudo-quantization approaches of the vibrational energy of products. Main attributes of the title molecular collision are discussed and compared with available information in the literature.

Accurate Explicit-Correlation-MRCI-Based DMBE Potential-Energy Surface for Ground-State CNO.

We report a new global double many-body expansion potential energy surface for the ground state of the CNO(2A') manifold, calculated by the explicit correlation multireference configuration interaction method. The functional form was accurately fitted to 3701 ab initio points with a root mean squared deviation of 0.99 kcal mol-1. All stationary points reported in previous forms are systematically described and improved, in addition to three new ones and a characterization of an isomerization transition state between the CNO and NCO minima. The novel proposed form gives a realistic description of both short-range and long-range interactions and hence is commended for dynamics studies.

Energy-switching potential energy surface for ground-state [formula omitted

The multiple energy switching scheme [J. Chem. Phys. 119 (2003) 2596] has been used to improve the double many-body expansion (DMBE II) potential energy surface of C3 near its linear global minima by morphing it with an accurate Taylor-series expansion [J. Chem. Phys. 144 (2016) 044307]. The final ES form attains the accuracy of the local form in reproducing the rovibrational spectrum of C3 while keeping unaltered all key attributes of the original DMBE II, namely conical intersection seams and dissociative channels. The ES form is therefore commended for adiabatic spectroscopic and reaction dynamics studies.

Theoretical insight into the effect of collision energy on the S(3P) + SH(X2∏) → S2(X3∑g−) + H(2S) reaction

In this work, the dynamics of reaction S(3P) + SH(X2∏) → S2(X3∑g−) + H(2S) has been investigated using quasi-classical trajectories method on a newly constructed accurate double many-body expansion potential energy surface of Song et al. [J. Phys. Chem. A 115, 5274 (2011)]. The integral cross section and the rate constant are obtained. Furthermore, the distribution reflecting vector correlation and the polarization-dependent differential cross section are investigated. The results show a decreasing behavior of the integral cross section as the increasing of the collision energy, and dominate complex forming mechanism at lower energies, as well as the stripping mechanism at higher energies. Those results indicate that the product S2 is sensitively affected by the collision energy.

A quasi-classical study of energy transfer in collisions of hyperthermal H atoms with SO2 molecules.

A deep understanding of energy transfer processes in molecular collisions is at central attention in physical chemistry. Particularly vibrational excitation of small molecules colliding with hot light atoms, via a metastable complex formation, has shown to be an efficient manner of enhancing reactivity. A quasi-classical trajectory study of translation-to-vibration energy transfer (T-V ET) in collisions of hyperthermal H(2S) atoms with SO2(X̃1A') molecules is presented here. For such a study, a double many-body expansion potential energy surface previously reported for HSO2(2A) is used. This work was motivated by recent experiments by Ma et al. studying collisions of H + SO2 at the translational energy of 59 kcal/mol [J. Ma et al., Phys. Rev. A 93, 040702 (2016)]. Calculations reproduce the experimental evidence that during majority of inelastic non-reactive collision processes, there is a metastable intermediate formation (HOSO or HSO2). Nevertheless, the analysis of the trajectories shows that there are two distinct mechanisms in the T-V ET process: direct and indirect. Direct T-V processes are responsible for the high population of SO2 with relatively low vibrational excitation energy, while indirect ones dominate the conversion from translational energy to high values of the vibrational counterpart.

Isotope Effect of the Stereodynamics for the Reactions N(<sup>4</sup>S)+HD→NH+D and N(<sup>4</sup>S)+HD→ND+H

Quasi-classical trajectory calculations have been employed to investigate the influence of isotope effect on the stereodynamics of the title reactions N(4S)+HD→NH+D and N(4S)+HD→ND+H on the 4A" double many-body expansion (DMBE) potential energy surface (PES) newly constructed by L. A. Poveda et al. [Phys. Chem. Chem. Phys. 7 (2005) 2867]. The generalized polarization-dependent differential cross sections (PDDCSs) and the three angular distributions of P(θr), P(φr) and P(θr,φr) are presented and discussed. It is revealed isotope effect exert a substantial influence on the product polarizations.

Effects of collision energy and rotational quantum number on stereodynamics of the reactions: H(2S) + NH(υ = 0, j = 0, 2, 5, 10)→N(4S) + H2**Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. 2016ZRB01066) and the University Student’s Science and Technology Innovation Fund of Ludong University, China (Grant No. 131007).

The stereodynamical properties of H(2S) + NH(v = 0, j = 0, 2, 5, 10) → N(4S) + H2 reactions are studied in this paper by using the quasi-classical trajectory (QCT) method with different collision energies on the double many-body expansion (DMBE) potential energy surface (PES) (Poveda L A and Varandas A J C 2005 Phys. Chem. Chem. Phys. 7 2867). In a range of collision energy from 2 to 20 kcal/mol, the vibrational rotational quantum numbers of the NH molecules are specifically investigated on v = 0 and j = 0, 2, 5, 10 respectively. The distributions of P(θr), P(ϕr), P(θr,ϕr), (2π/σ)(dσ00/dωt) differential cross-section (DCSs) and integral cross-sections(ICSs) are calculated. The ICSs, computed for collision energies from 2 kcal/mol to 20 kcal/mol, for the ground state are in good agreement with the cited data. The results show that the reagent rotational quantum number and initial collision energy both have a significant effect on the distributions of the k–j′, the k–k′–j′, and the k–k′ correlations. In addition, the DCS is found to be susceptible to collision energy, but it is not significantly affected by the rotational excitation of reagent.

Accurate double many-body expansion potential energy surface of HS2A2A′) by scaling the external correlation**Project supported by the National Natural Science Foundation of China (Grant No. 11304185), the Taishan Scholar Project of Shandong Province, China, the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014AM022), the Shandong Province Higher Educational Science and Technology Program, China (Grant No. J15LJ03), the China Postdoctoral

A globally accurate single-sheeted double many-body expansion potential energy surface is reported for the first excited state of HS2 by fitting the accurate ab initio energies, which are calculated at the multireference configuration interaction level with the aug-cc-pVQZ basis set. By using the double many-body expansion-scaled external correlation method, such calculated ab initio energies are then slightly corrected by scaling their dynamical correlation. A grid of 2767 ab initio energies is used in the least-square fitting procedure with the total root-mean square deviation being 1.406 kcal·mol−1. The topographical features of the HS2(A2A′) global potential energy surface are examined in detail. The attributes of the stationary points are presented and compared with the corresponding ab initio results as well as experimental and other theoretical data, showing good agreement. The resulting potential energy surface of HS2(A2A′) can be used as a building block for constructing the global potential energy surfaces of larger S/H molecular systems and recommended for dynamic studies on the title molecular system.

Master Equation Study of Vibrational and Rotational Relaxations of Oxygen

Transition rates in collisions for each vibrational and rovibrational state are generated by means of the quasi-classical trajectory method using potential energy surfaces of different fidelities. The first potential energy surface, obtained via the double many-body expansion method, is adopted to obtain vibrational transition rates assuming transrotational equilibrium. The trajectory simulation on a simpler potential surface, based on the two-body pairwise interaction, generates a complete set of rates for each internal state. Vibrational and rotational relaxations of oxygen in a heat bath of parent atoms are modeled by a system of master equations at translational temperatures between 1000 and 20,000 K. It is shown that the vibrational relaxation becomes less efficient at high temperatures, in contrast with the conventional equation for relaxation time proposed by Millikan and White (“Systematics of Vibrational Relaxation,” Journal of Chemical Physics, Vol. null, No. null, 1963, Paper 3209). Rotational and vibrational relaxation times are the same order of magnitude in the range of temperatures observed in hypersonic flows. The excitation of the vibrational mode in collisions under typical postshock conditions occurs earlier than in other molecular systems. The exchange channel plays an important role in the internal energy randomization.

Coupled 3D Time-Dependent Wave-Packet Approach in Hyperspherical Coordinates: The D(+)+H2 Reaction on the Triple-Sheeted DMBE Potential Energy Surface.

We implement a coupled three-dimensional (3D) time-dependent wave packet formalism for the 4D reactive scattering problem in hyperspherical coordinates on the accurate double many body expansion (DMBE) potential energy surface (PES) for the ground and first two singlet states (1(1)A', 2(1)A', and 3(1)A') to account for nonadiabatic processes in the D(+) + H2 reaction for both zero and nonzero values of the total angular momentum (J). As the long-range interactions in D(+) + H2 contribute significantly due to nonadiabatic effects, the convergence profiles of reaction probabilities for the reactive noncharge transfer (RNCT), nonreactive charge transfer (NRCT), and reactive charge transfer (RCT) processes are shown for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. The total and state-to-state cross sections are presented as a function of the collision energy for the initial rovibrational state v = 0, j = 0 of the diatom, and the calculated cross sections compared with other theoretical and experimental results.

Accurate ab initio-based double many-body expansion potential energy surface for the adiabatic ground-state of the C3 radical including combined Jahn-Teller plus pseudo-Jahn-Teller interactions.

A fully ab initio-based potential energy surface is first reported for the ground electronic state of the C3 radical using the double many-body expansion (DMBE) method. The DMBE form so obtained mimics the full set of energies calculated at the multireference configuration interaction level of theory with chemical accuracy. To account for the incompleteness of the one- and N-electron bases, the calculated external correlation energies have been scaled prior to the fitting procedure via DMBE-scaled external correlation method. Furthermore, the novel potential energy surface reproduces accurately dissociation energies, diatomic potentials, long-range interactions at all asymptotic channels, and the correct topological behavior at the region of 4 conical intersections with the partner state of the same symmetry near equilateral triangular geometries due to combined Jahn-Teller (E' ⊗ e') plus pseudo-Jahn-Teller [(E'+A1')⊗e'] interactions. Rovibrational calculations have also been performed, unveiling a good match of the vibrational spectrum of C3 for 53 calculated levels. The present DMBE form is, therefore, commended for both spectroscopic and reaction dynamics studies, some also performed in the present work.