Accurate high level ab initio-based global potential energy surface and dynamics calculations for ground state of CH2(+)

Non-adiabatic dynamics studies of the C+(2P1/2, 3/2) + H2 reaction: Based on global diabatic potential energy surfaces of CH2

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 ab initio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the ab initio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study.

The temperature variation of the CH+ + H reaction rate coefficients: a puzzle finally understood?

CH+ was the first molecular ion identified in the interstellar medium and is found to be ubiquitous in interstellar clouds. However, its formation and destruction paths are not well understood, especially at low temperatures. A new theoretical approach based on the canonical variational transition state theory was used to study the H + CH+ reactive collisions. Rate coefficients for formation of C+ ions are calculated as a function of temperature. We considered the participation of a direct path and an indirect path in which the reactants should overcome an entropic barrier to form a van der Waals complex or pass through a CH2+ intermediate complex, respectively. We show that the contribution of both pathways to the formation of C+ has to be taken into account. The new reactive rate coefficients for the title reaction, complemented by reactive data for CH+/CH2+ in the H/H2/He mixture, have been used to simulate the corresponding kinetics experimentally measured using an Atomic Beam 22 Pole Trap apparatus at low temperature. A good agreement with the experimental findings was found at 50 K. At a lower temperature, the model overestimates the formation of C+. This shows that secondary reactions are not responsible for the weak C+ production in the experiments at such temperature. Then, we discuss the possible impact of non-adiabatic effects in the study of the H + CH+ reactive collisions and we found that such effects can be responsible for the decrease of the H + CH+ rate coefficients at low temperature. This study offers an explanation for the disagreement between H + CH+ theoretical and experimental rate coefficients which has been going on for 20 years and highlights the need for performing non-adiabatic studies for this simple chemical reaction.

Potential Energy Curves of the Low-Lying Five 1Σ+ and 1Π States of a CH+ Molecule Based on the Free Complement - Local Schrödinger Equation Theory and the Chemical Formula Theory

The potential energy curves (PECs) of the low-lying five 1Σ+ and 1Π states (X1Σ+, C1Σ+, 31Σ+, A1Π, and D1Π states) of a CH+ molecule, an important interstellar molecule, were calculated by the free complement (FC) - local Schrödinger equation (LSE) theory with the direct local sampling scheme. The FC wave functions were constructed based on the chemical formula theory (CFT), whose local characters correspond to the covalent dissociations: C+(2P°(s2p))) + H(2S) of the X1Σ+ and A1Π states and the ionic dissociations: C(1D(s2p2)) + H+ of the C1Σ+ and D1Π states. All the calculated PECs were obtained with satisfying the chemical accuracy, i.e., error less than 1 kcal/mol, as absolute total energy of the Schrödinger equation without any energy shift. The spectroscopic data calculated from the PECs agreed well with both experimental and other accurate theoretical references. We also analyzed the wave functions using the inverse overlap weights proposed by Gallup et al. with the CFT configurations. For the X1Σ+ and A1Π states, the covalent C+(sp2) and C+(p3) configurations played important roles for bond formation. In the small internuclear distances of the C1Σ+, D1Π, and 31Σ+ states, the covalent character was also dominant as a result of the electron charge transfer from C to H+. Thus, the present FC-LSE results not only are accurate but also can provide chemical understanding according to the CFT.

An accurate many-body expansion potential energy surface for AlH2 (22A') and quantum dynamics in Al(3P) + H2 (v0 = 0-3, j0 = 0, 2, 4, 6) collisions

An accurate potential energy surface is constructed for the excited state of AlH₂ by fitting extensive ab initio points calculated at the multi-reference configuration interaction level based on aug-cc-pV(Q+d)Z and aug-cc-pV(5+d)Z basis sets. All the calculated energies are corrected via the many-body expansion method and extrapolated to the complete basis set limit. The various topographic features of the new potential energy surface are investigated to demonstrate the correct behavior of Al(³P) + H₂(X¹Σ_g⁺) and AlH(a³Π) + H(²S) dissociation limits. By employing the time-dependent wave packet approach, the integral scattering cross-sections obtained from the Coriolis coupling calculation and the centrifugal sudden approximation, respectively, are compared in detail and show that the former has a higher effect on the reaction. Moreover, the thermal rate constants for Al(³P) + H₂ (v₀ = 0-3, j₀ = 0, 2, 4, 6) in the temperature range of 0-5000 K are calculated, thereby providing insights into the influence of ro-vibrational quantum numbers on the thermal rate constants.

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.

Benchmarking an improved statistical adiabatic channel model for competing inelastic and reactive processes

Inelastic collisions and elementary chemical reactions proceeding through the formation and subsequent decay of an intermediate collision complex, with an associated deep well on the potential energy surface, pose a challenge for accurate fully quantum mechanical approaches, such as the close-coupling method. In this study, we report on the theoretical prediction of temperature-dependent state-to-state rate coefficients for these complex-mode processes, using a statistical quantum method. This statistical adiabatic channel model is benchmarked by a direct comparison using accurate rate coefficients from the literature for a number of systems (H₂ + H⁺, HD + H⁺, SH⁺ + H, and CH⁺ + H) of interest in astrochemistry and astrophysics. For all of the systems considered, an error of less than factor 2 was found, at least for the dominant transitions and at low temperatures, which is sufficiently accurate for applications in the above mentioned disciplines.

Accurate High-Level Ab Initio-Based Global Potential Energy Surface and Quantum Dynamics Calculation for the First Excited State of CH2. J Phys Chem A 2021;125:5490-5498. [PMID: 34137628 DOI: 10.1021/acs.jpca.1c02413]

A full three-dimensional global potential energy surface (PES), covering the whole configuration space, is reported first for the title system by fitting high-level ab initio energies at the multireference configuration interaction level with the aug-cc-pV6Z basis set. In this work, the many-body expansion method is invoked to fit the innate character of the CH₂⁺(1²A″) PES. The topographical features are examined in detail based on the new global PES and in accordance with the other calculations from the ab initio energies, which show the correct behavior at the C⁺(²P) + H₂(X¹Σ_g⁺) and CH⁺(a³Π) + H(²S) dissociation limits. Using a time-dependent wave packet method, we provide insights into the dynamics behavior for reaction of C⁺(²P) + H₂(X¹Σ_g⁺) → CH⁺(a³Π) + H(²S). The integral cross sections and reaction probabilities increase monotonically in terms of the collision energy.

Experimental study of the proton-transfer reaction C + H2+ → CH+ + H and its isotopic variant (D2+)

We report absolute integral cross section (ICS) measurements using a dual-source merged-fast-beams apparatus to study the titular reactions over the relative translational energy range of Er ∼ 0.01-10 eV. We used photodetachment of C- to produce a pure beam of atomic C in the ground electronic 3P term, with statistically populated fine-structure levels. The H2+ and D2+ were formed in an electron impact ionization source, with well known vibrational and rotational distributions. The experimental work is complemented by a theoretical study of the CH2+ electronic system in the reactant and product channels, which helps to clarify the possible reaction mechanisms underlying the ICS measurements. Our measurements provide evidence that the reactions are barrierless and exoergic. They also indicate the apparent absence of an intermolecular isotope effect, to within the total experimental uncertainties. Capture models, taking into account either the charge-induced dipole interaction potential or the combined charge-quadrupole and charge-induced dipole interaction potentials, produce reaction cross sections that lie a factor of ∼4 above the experimental results. Based on our theoretical study, we hypothesize that the reaction is most likely to proceed adiabatically through the 14A' and 14A'' states of CH2+via the reaction C(3P) + H2+(2Σ+g) → CH+(3Π) + H(2S). We also hypothesize that at low collision energies only H2+(v ≤ 2) and D2+(v ≤ 3) contribute to the titular reactions, due to the onset of dissociative charge transfer for higher vibrational v levels. Incorporating these assumptions into the capture models brings them into better agreement with the experimental results. Still, for energies ⪅0.1 eV where capture models are most relevant, the modified charge-induced dipole model yields reaction cross sections with an incorrect energy dependence and lying ∼10% below the experimental results. The capture cross section obtained from the combined charge-quadrupole and charge-induced dipole model better matches the measured energy dependence but lies ∼30-50% above the experimental results. These findings provide important guidance for future quasiclassical trajectory and quantum mechanical treatments of this reaction.

Accurate global adiabatic potential energy surfaces for three low-lying electronic states of AlH2 free radicals

In order to obtain the all-round molecular properties of the AlH2 system and the corresponding dynamical characteristics of the Al + H2 (v = 0, j = 0) → H + AlH reaction, three significant global adiabatic potential energy surfaces of AlH2 (X2A1, 2B1, and 2B2) free radicals were constructed for the first time. Ab initio energies were calculated under the multi-reference configuration interaction method and the aug-cc-pV(T,Q)Z basis sets; then the ab initio energies were extrapolated to the complete basis sets limit. The three adiabatic potential energy surfaces were constructed by the many-body expansion theory. The maximum root-mean square error was just 50 cm-1, which was small enough to ensure that the potential energy surfaces were accurate. The concerned T-type insertion topographical features, dissociation schemes, C2v geometry reaction mechanisms, and minimum energy curve paths were investigated and are discussed in detail. Several differences from previous studies are also pointed out. Eventually, the integral cross-sections of Al + H2 (v = 0, j = 0) → H + AlH reaction as calculated by quasi-classical trajectory method were employed to predict the dynamical properties of AlH2, providing the most reliable theoretical reference of the dynamical characteristics known thus far for such a reaction. These new potential energy surfaces can be treated as a reliable basis for investigation of the dynamics and as a component for constructing larger aluminum-/hydrogen-containing systems.

Accurate global potential energy surface for SiH2 +(X2A1) and quantum dynamics of related reaction H(2S) + SiH+(X1Σ+)

With the many-body expansion method, an accurate global potential energy surface (PES) is constructed for SiH₂ ⁺(X²A₁) by mapping 4762 ab initio energy points calculated on the multireference configuration interaction level including Davidson corrections with aug-cc-pV6Z Dunning's basis set. The dissociation energies and equilibrium geometries of SiH⁺(X¹Σ⁺) and H₂(X¹Σ_g ⁺) agree well with the experimental results. The topographical characteristics of all stationary points for the SiH₂ ⁺(X²A₁) PES are discussed in detail and compared with other theoretical and experimental results. In order to verify the validity and usability of the present PES, the dynamics calculations based on the Chebyshev quantum wave packet method are performed for the H(S2)+SiH⁺(X¹Σ⁺)→Si⁺(P2)+H₂(X¹Σ_g ⁺) reaction. The probabilities, the total integral cross sections, and the rate constants are computed, and the analogies with the corresponding ones of reaction H(S2) + CH⁺(X¹Σ⁺)→C⁺(P2) + H₂(X¹Σ_g ⁺) are also made. The reasonable dynamical behavior throughout the entire configuration space indicates that the PES is suitable for relevant dynamics investigations and serves as a building block for constructing the PES of larger molecular systems containing Si⁺/H.

Accurate potential energy surface of H2S+(X 2 A″) via extrapolation to the complete basis set limit and its use in dynamics study of S + ( D 2 ) + H 2 ( X 1 Σ g + ) reaction

The single-sheeted potential energy surface (PES) of H 2 S + ( X   2 A ' ' ) is developed based on the ab initio energies calculated by the multi-reference configuration interaction method including the Davidson correction. All the ab initio energies are first calculated using aug-cc-pVQdZ and aug-cc-pV5dZ basis sets, which are then extrapolated to the complete basis set (CBS) limit. A switching function is developed to model the transition of S + D 2 to S + S 4 . The many-body expansion formalism is employed to obtain the H 2 S + ( X   2 A ' ' ) PES by fitting such CBS energies and the root-mean square derivation is 0.0367 eV. The topographical features of the present PES are examined in detail, which are well consistent with previous studies. The quasiclassical trajectory method is subsequently utilized to study the S + D 2 + H 2 ( X 1 Σ g + )   →   S H + ( X   3 Σ - ) + H ( S 2 ) reaction. The capture time, integral cross sections, and rovibrational distributions are calculated. By examining the capture time, it can be concluded that the title reaction is mainly controlled by the indirect mechanism for lower collision energies, while the direct and indirect mechanisms coexist and the latter plays a dominant role for higher collision energies.

Global diabatic potential energy surfaces for the BeH2 + system and dynamics studies on the Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction

The Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction has great significance for studying diabatic processes and ultracold chemistry. The first global diabatic potential energy surfaces (PESs) which are correlated with the lowest two adiabatic states 12A' and 22A' of the BeH2 + system are constructed by using the neural network method. Ab initio energy points are calculated using the multi-reference configuration interaction method with the Davidson correction and AVQZ basis set. The diabatic energies are obtained from the transformation of ab initio data based on the dipole moment operators. The topographical characteristics of the diabatic PESs are described in detail, and the positions of crossing between the V d 11 and V d 22 are pinpointed. On new diabatic PESs, the time-dependent quantum wave packet method is carried out to study the mechanism of the title reaction. The results of dynamics calculations indicate the reaction has no threshold and the product BeH+ is excited to high vibrational states easily. In addition, the product BeH+ tends to backward scattering at most collision energies.

Dynamical resonances of the deuterated CH2+ complex in the electronic ground state: A quantum wavepacket study

We here investigate the effects of isotopic substituents on the vibrational energy levels of the CH₂⁺ complex, supported by the electronic ground (1 ²A') potential energy surface (PES) of the H + CH⁺ reaction. We calculate the transition state spectrum by Fourier transforming the time-autocorrelation function of the initial wavepacket (WP) chosen in the interaction region of the PES. Using the time-dependent WP approach, the dynamical resonances are identified as bound and quasibound in nature, and they are characterized in terms of the eigenfunctions and lifetimes. The present work on the isotopic variants [CHD⁺(CDH⁺) and CD₂⁺] is compared with our earlier work [P. Sundaram et al., Phys. Chem. Chem. Phys. 19, 20172 (2017)] on the parent CH₂⁺ species. The isotopic variants reveal a large number of peaks in the spectra and the eigenfunctions exhibit the systematic nodal progressions and periodic orbits, the same as in CH₂⁺. While the CD₂⁺ complex exactly mimics the resonance behaviors (local and hyperspherical modes) of the bound and quasibound CH₂⁺ complex, the CHD⁺(CDH⁺) complex reveals only the local mode behaviors at low energies and significantly less number of resonance structures at high energies. Lifetime analysis of the isotopic variants implies that the CD₂⁺ complex survives much longer than the CHD⁺(CDH⁺) complex and concludes the work by noting the following order in the decay profile of the deuterated CH₂⁺ resonances as CH₂⁺>CHD⁺(CDH⁺) >CD₂⁺.

Accurate global potential energy surface for the ground state of CH2 + by extrapolation to the complete basis set limit

A full three-dimensional global potential energy surface is reported for the ground state of CH2 + by fitting accurate multireference configuration interaction energies calculated using aug-cc-pVQZ and aug-cc-pV5Z basis sets with extrapolation of the electron correlation energy to the complete basis set limit. The topographical characteristics have been compared in detail with a potential energy surface of the same type recently reported [J. Chem. Phys., 2015, 142, 124302] based on a least-squares fit to accurate high level ab initio MRCI(Q) energies, calculated using AV6Z basis set. The new three-dimensional global potential energy surface is then used in quasiclassical trajectory calculations for H(2S) + CH+(X 1Σ+) → C+(2P) + H2(X 1Σg +) reaction. The integral cross sections, differential cross sections and the rate coefficients have been computed. A comparison shows that our potential energy surface can be applied to any type of dynamic study.

Dynamics and resonances of the H(2S) + CH+(X1Σ+) reaction in the electronic ground state: a detailed quantum wavepacket study

Initial state-selected and energy resolved channel-specific reaction probabilities, integral cross sections and thermal rate constants of the H(²S) + CH⁺(X¹Σ⁺) reaction are calculated within the coupled states approximation by a time-dependent wave packet propagation method. The new ab initio global potential energy surface (PES) of the electronic ground state (1 ²A') of the system, recently reported by Li et al. [J. Chem. Phys., 2015, 142, 124302], is employed for this purpose. All partial wave contributions up to the total angular momentum J = 60 are considered to obtain the converged integral reaction cross section up to a collision energy of 1.0 eV. Thermal rate constants are calculated by averaging the reaction cross sections over the Boltzmann distribution of energies and compared with the available theoretical and experimental results for the temperature range 10-1000 K. Investigation of the channel-specific reaction attributes shows that the H abstraction (CH⁺ destruction) channel is highly favored over the H exchange channel. The effect of rotational and vibrational excitations of the CH⁺ reagent on the dynamics is also studied. The resonances formed during the course of the reaction are also identified by calculating the transition state spectrum and characterized in terms of the eigenfunctions and lifetimes. More than 260 vibrational levels are obtained and their eigenfunctions are calculated, which are represented in terms of the nodal assignments and the eigenenergies. They reveal both the local and hyperspherical behavior for the bound and quasibound states of the CH₂⁺ complex in the ground 1 ²A' surface. The lifetime analysis of the quasibound states indicates that the CH₂⁺ resonances survive for as long as ∼400 fs at high energies (E ∼ 2.0 eV) and are expected to decay faster with further increasing energy. Finally, the type of mechanism for the formation of the product (C⁺ + H₂) is elucidated.

State-to-state chemistry and rotational excitation of CH+ in photon-dominated regions

We present a detailed theoretical study of the rotational excitation of CH+ due to reactive and nonreactive collisions involving C+(2P), H2, CH+, H and free electrons. Specifically, the formation of CH+ proceeds through the reaction between C+(2P) and H2(νH2 = 1, 2), while the collisional (de)excitation and destruction of CH+ is due to collisions with hydrogen atoms and free electrons. State-to-state and initial-state-specific rate coefficients are computed in the kinetic temperature range 10-3000 K for the inelastic, exchange, abstraction and dissociative recombination processes using accurate potential energy surfaces and the best scattering methods. Good agreement, within a factor of 2, is found between the experimental and theoretical thermal rate coefficients, except for the reaction of CH+ with H atoms at kinetic temperatures below 50 K. The full set of collisional and chemical data are then implemented in a radiative transfer model. Our Non-LTE calculations confirm that the formation pumping due to vibrationally excited H2 has a substantial effect on the excitation of CH+ in photon-dominated regions. In addition, we are able to reproduce, within error bars, the far-infrared observations of CH+ toward the Orion Bar and the planetary nebula NGC 7027. Our results further suggest that the population of νH2 = 2 might be significant in the photon-dominated region of NGC 7027.

Globally accurate potential energy surface for the ground-state HCS(X2A') and its use in reaction dynamics

A globally accurate many-body expansion potential energy surface is reported for HCS(X²A') by fitting a wealth of accurate ab initio energies calculated at the multireference configuration interaction level using aug-cc-pVQZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical features of the present potential energy surface are examined in detail and is in good agreement with the raw ab initio results, as well as other theoretical results available in literatures. By utilizing the potential energy surface of HCS(X²A'), the dynamic studies of the C(³P) + SH(X²Π) → H(²S) + CS(X¹∑⁺) reaction has been carried out using quasi-classical trajectory method.

Low temperature rate coefficients of the H + CH(+) → C(+) + H2 reaction: New potential energy surface and time-independent quantum scattering

The observed abundances of the methylidyne cation, CH(+), in diffuse molecular clouds can be two orders of magnitude higher than the prediction of the standard gas-phase models which, in turn, predict rather well the abundances of neutral CH. It is therefore necessary to investigate all the possible formation and destruction processes of CH(+) in the interstellar medium with the most abundant species H, H2, and e(-). In this work, we address the destruction process of CH(+) by hydrogen abstraction. We report a new calculation of the low temperature rate coefficients for the abstraction reaction, using accurate time-independent quantum scattering and a new high-level ab initio global potential energy surface including a realistic model of the long-range interaction between the reactants H and CH(+). The calculated thermal rate coefficient is in good agreement with the experimental data in the range 50 K-800 K. However, at lower temperatures, the experimental rate coefficient takes exceedingly small values which are not reproduced by the calculated rate coefficient. Instead, the latter rate coefficient is close to the one given by the Langevin capture model, as expected for a reaction involving an ion and a neutral species. Several recent theoretical works have reported a seemingly good agreement with the experiment below 50 K, but an analysis of these works show that they are based on potential energy surfaces with incorrect long-range behavior. The experimental results were explained by a loss of reactivity of the lowest rotational states of the reactant; however, the quantum scattering calculations show the opposite, namely, a reactivity enhancement with rotational excitation.