Dynamics of the C(D1)+D2 reaction: A comparison of crossed molecular-beam experiments with quasiclassical trajectory and accurate statistical calculations

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Gas-phase formation of silicon monoxide via non-adiabatic reaction dynamics and its role as a building block of interstellar silicates

Silicon monoxide (SiO) is classified as a key precursor and fundamental molecular building block to interstellar silicate nanoparticles, which play an essential role in the synthesis of molecular building blocks connected to the Origins of Life. In the cold interstellar medium, silicon monoxide is of critical importance in initiating a series of elementary chemical reactions leading to larger silicon oxides and eventually to silicates. To date, the fundamental formation mechanisms and chemical dynamics leading to gas phase silicon monoxide have remained largely elusive. Here, through a concerted effort between crossed molecular beam experiments and electronic structure calculations, it is revealed that instead of forming highly-stable silicon dioxide (SiO₂), silicon monoxide can be formed via a barrierless, exoergic, single-collision event between ground state molecular oxygen and atomic silicon involving non-adiabatic reaction dynamics through various intersystem crossings. Our research affords persuasive evidence for a likely source of highly rovibrationally excited silicon monoxide in cold molecular clouds thus initiating the complex chain of exoergic reactions leading ultimately to a population of silicates at low temperatures in our Galaxy.

Gas-Phase Preparation of Subvalent Germanium Monoxide (GeO, X1+) via Non-Adiabatic Reaction Dynamics in the Exit Channel

The subvalent germanium monoxide (GeO, X¹Σ⁺) molecule has been prepared via the elementary reaction of atomic germanium (Ge, ³P_j) and molecular oxygen (O₂, X³Σ_g^-) with each reactant in its electronic ground state by means of single-collision conditions. The merging of electronic structure calculations with crossed beam experiments suggests that the formation of germanium monoxide (GeO, X¹Σ⁺) commences on the singlet surface through unimolecular decomposition of a linear singlet collision complex (GeOO, i1, C_∞v, ¹Σ⁺) via intersystem crossing (ISC) yielding nearly exclusively germanium monoxide (GeO, X¹Σ⁺) along with atomic oxygen in its electronic ground state [p1, O(³P)]. These results provide a sophisticated reaction mechanism of the germanium-oxygen system and demonstrate the efficient "heavy atom effect" of germanium in ISC yielding (nearly) exclusive singlet germanium monoxide and triplet atomic oxygen compared to similar systems (carbon dioxide and dinitrogen monoxide), in which non-adiabatic reaction dynamics represent only minor channels.

Quantum Dynamics Study of the C(1D) + HD Reaction on the ã1A' and b̃1A″ Potential Energy Surfaces

We present an in-depth theoretical study of the C(¹D) + HD (v = 0, j = 0) → CD (CH) (v', j') + H (D) reaction using a time-dependent wave packet method with full Coriolis coupling on the Zhang-Ma-Bian potential energy surfaces (PESs) recently constructed by our group. The integral cross sections (ICS), differential cross sections, CD/CH branching ratios, and product state distributions are calculated over a wide range of collision energies. We find that the vibrational branching ratio defined as ICS(v'=1)/ICS(v'=0) obtained from the b̃¹A″ PES is much smaller than that from the ã¹A' PES for both product channels, which may be attributed to the dynamical effects of the conical intersection regulated (CI-R) intermediate on the b̃¹A″ PES. The collision energy dependence of CD/CH branching ratios displays oscillatory structures, which may be caused by the resonance states supported by the wells on the PESs. The high-temperature rate coefficients are also obtained and compared with previous results. The role of the excited-state PESs is also discussed.

Universal crossed beam imaging studies of polyatomic reaction dynamics

Crossed-beam imaging studies of polyatomic reactions show surprising dynamics not anticipated by extrapolation from smaller model systems.

Dynamical importance of van der Waals saddle and excited potential surface in C(1D)+D2 complex-forming reaction

Encouraged by recent advances in revealing significant effects of van der Waals wells on reaction dynamics, many people assume that van der Waals wells are inevitable in chemical reactions. Here we find that the weak long-range forces cause van der Waals saddles in the prototypical C(¹D)+D₂ complex-forming reaction that have very different dynamical effects from van der Waals wells at low collision energies. Accurate quantum dynamics calculations on our highly accurate ab initio potential energy surfaces with van der Waals saddles yield cross-sections in close agreement with crossed-beam experiments, whereas the same calculations on an earlier surface with van der Waals wells produce much smaller cross-sections at low energies. Further trajectory calculations reveal that the van der Waals saddle leads to a torsion then sideways insertion reaction mechanism, whereas the well suppresses reactivity. Quantum diffraction oscillations and sharp resonances are also predicted based on our ground- and excited-state potential energy surfaces.

It is commonly held that van der Waals wells are inevitable in chemical reactions. Here, the authors show that weak van der Waals forces in the entrance channel of a prototypical complex-forming reaction cause a van der Waals saddle instead, with different dynamical effects from a well at low collision energies.

Quasiclassical trajectory study of the C(1D) + HD reaction

Isotopic branching ratios are investigated by detailed quasiclassical trajectory calculations on our recent singlet ground and excited potential energy surfaces.

An experimental and theoretical investigation of the C(1D) + D2 reaction

Rate constants derived from ring polymer molecular dynamics calculations confirm the validity of this method for studying low-temperature complex-forming reactions

A Combined Experimental and Theoretical Study on the Formation of the 2-Methyl-1-silacycloprop-2-enylidene Molecule via the Crossed Beam Reactions of the Silylidyne Radical (SiH; X(2)Π) with Methylacetylene (CH3CCH; X(1)A1) and D4-Methylacetylene (CD3CCD; X(1)A1)

The bimolecular gas-phase reactions of the ground-state silylidyne radical (SiH; X(2)Π) with methylacetylene (CH3CCH; X(1)A1) and D4-methylacetylene (CD3CCD; X(1)A1) were explored at collision energies of 30 kJ mol(-1) under single-collision conditions exploiting the crossed molecular beam technique and complemented by electronic structure calculations. These studies reveal that the reactions follow indirect scattering dynamics, have no entrance barriers, and are initiated by the addition of the silylidyne radical to the carbon-carbon triple bond of the methylacetylene molecule either to one carbon atom (C1; [i1]/[i2]) or to both carbon atoms concurrently (C1-C2; [i3]). The collision complexes [i1]/[i2] eventually isomerize via ring-closure to the c-SiC3H5 doublet radical intermediate [i3], which is identified as the decomposing reaction intermediate. The hydrogen atom is emitted almost perpendicularly to the rotational plane of the fragmenting complex resulting in a sideways scattering dynamics with the reaction being overall exoergic by -12 ± 11 kJ mol(-1) (experimental) and -1 ± 3 kJ mol(-1) (computational) to form the cyclic 2-methyl-1-silacycloprop-2-enylidene molecule (c-SiC3H4; p1). In line with computational data, experiments of silylidyne with D4-methylacetylene (CD3CCD; X(1)A1) depict that the hydrogen is emitted solely from the silylidyne moiety but not from methylacetylene. The dynamics are compared to those of the related D1-silylidyne (SiD; X(2)Π)-acetylene (HCCH; X(1)Σg(+)) reaction studied previously in our group, and from there, we discovered that the methyl group acts primarily as a spectator in the title reaction. The formation of 2-methyl-1-silacycloprop-2-enylidene under single-collision conditions via a bimolecular gas-phase reaction augments our knowledge of the hitherto poorly understood silylidyne (SiH; X(2)Π) radical reactions with small hydrocarbon molecules leading to the synthesis of organosilicon molecules in cold molecular clouds and in carbon-rich circumstellar envelopes.

Global analytical ab initio ground-state potential energy surface for the C((1)D)+H2 reactive system

A new global ab initio potential energy surface (called ZMB-a) for the 1(1)A' state of the C((1)D)+H2 reactive system has been constructed. This is based upon ab initio calculations using the internally contracted multireference configuration interaction approach with the aug-cc-pVQZ basis set, performed at about 6300 symmetry unique geometries. Accurate analytical fits are generated using many-body expansions with the permutationally invariant polynomials, except that the fit of the deep well region is taken from our previous fit. The ZMB-a surface is unique in the accurate description of the regions around conical intersections (CIs) and of van der Waals (vdW) interactions. The CIs between the 1(1)A' and 2(1)A' states cause two kinds of barriers on the ZMB-a surface: one is in the linear H-CH dissociation direction with a barrier height of 9.07 kcal/mol, which is much higher than those on the surfaces reported before; the other is in the C((1)D) collinearly attacking H2 direction with a barrier height of 12.39 kcal/mol. The ZMB-a surface basically reproduces our ab initio calculations in the vdW interaction regions, and supports a linear C-HH vdW complex in the entrance channel, and two vdW complexes in the exit channel, at linear CH-H and HC-H geometries, respectively.

Effect of vibrational and rotational excitation on the stereodynamics of the C(1D) + H2 (v, j) → CH + H reaction

The stereodynamics of the title reaction on the ab initio1A′ potential energy surface (PES) (B. Bussery-Honvault, P. Honvault, and J.-M. Launay. 2001. J. Chem. Phys. 115: 10701) at a collision energy of 16 kJ/mol have been studied using quasi-classical trajectory (QCT) method. Vector properties including angular momentum alignment parameters and four polarization-dependent differential cross sections (PDDCS) of the product CH are presented. Furthermore, the influence of reagent vibrational and rotational excitations on the product vector properties have also been studied in the present work. The calculated results indicate that the angle distributions of the CH product are mainly dominated by backward–forward scattering.

Effect of collision energy on cross sections and product alignments for the C(1D) + H2 (v = 0, j = 0) insertion reactions

Quasi-classical trajectory (QCT) calculations of total reaction probabilities and vibrationally state-resolved reaction probabilities at total angular momentum J = 0 as a function of collision energy for the C(1D) + H2 (v = 0, j = 0) reactions have been performed on an ab initio potential-energy surface [ J. Chem. Phys. 2001, 115, 10701]. In addition, the integral cross sections as a function of collision energy have been carried out for the same reaction. The product rotational alignments have also been calculated, which are almost invariant with respect to collision energies.

Crossed-beam and theoretical studies of the S(1D) + C2H2 reaction

The reaction dynamics of excited sulfur atoms, S((1)D), with acetylene has been investigated by the crossed-beam scattering technique with mass spectrometric detection and time-of-flight (TOF) analysis at the collision energy of 35.6 kJ mol(-1). These studies have been made possible by the development of intense continuous supersonic beams of S((3)P,(1)D) atoms. From product angular and TOF distributions, center-of-mass product angular and translational energy distributions are derived. The S((1)D) + C(2)H(2) reaction is found to lead to formation of HCCS (thioketenyl) + H, while the only other energetically allowed channels, those leading to CCS((3)Sigma(-), (1)Delta) + H(2), are not observed to occur to an appreciable extent. The dynamics of the H-elimination channel is discussed and elucidated. The interpretation of the scattering results is assisted by synergic high-level ab initio electronic structure calculations of stationary points and product energetics for the C(2)H(2)S ground-state singlet potential energy surface. In addition, by exploiting the novel capability of performing product detection by means of a tunable electron-impact ionizer, we have obtained the first experimental information on the ionization energy of thioketenyl radical, HCCS, as synthesized in the reactive scattering experiment. This has been complemented by ab initio calculations of the adiabatic and vertical ionization energies for the ground-state radical. The theoretically derived value of 9.1 eV confirms very recent, accurate calculations and is corroborated by the experimentally determined ionization threshold of 8.9 +/- 0.3 eV for the internally warm HCCS produced from the title reaction.

Probing the dynamics of polyatomic multichannel elementary reactions by crossed molecular beam experiments with soft electron-ionization mass spectrometric detection

In this Perspective we highlight developments in the field of chemical reaction dynamics. Focus is on the advances recently made in the investigation of the dynamics of elementary multichannel radical-molecule and radical-radical reactions, as they have become possible using an improved crossed molecular beam scattering apparatus with universal electron-ionization mass spectrometric detection and time-of-flight analysis. These improvements consist in the implementation of (a) soft ionization detection by tunable low-energy electrons which has permitted us to reduce interfering signals originating from dissociative ionization processes, usually representing a major complication, (b) different beam crossing-angle set-ups which have permitted us to extend the range of collision energies over which a reaction can be studied, from very low (a few kJ mol(-1), as of interest in astrochemistry or planetary atmospheric chemistry) to quite high energies (several tens of kJ mol(-1), as of interest in high temperature combustion systems), and (c) continuous supersonic sources for producing a wide variety of atomic and molecular radical reactant beams. Exploiting these new features it has become possible to tackle the dynamics of a variety of polyatomic multichannel reactions, such as those occurring in many environments ranging from combustion and plasmas to terrestrial/planetary atmospheres and interstellar clouds. By measuring product angular and velocity distributions, after having suppressed or mitigated, when needed, the problem of dissociative ionization of interfering species (reactants, products, background gases) by soft ionization detection, essentially all primary reaction products can be identified, the dynamics of each reaction channel characterized, and the branching ratios determined as a function of collision energy. In general this information, besides being of fundamental relevance, is required for a predictive description of the chemistry of these environments via computer models. Examples are taken from recent on-going work (partly published) on the reactions of atomic oxygen with acetylene, ethylene and allyl radical, of great importance in combustion. A reaction of relevance in interstellar chemistry, as that of atomic carbon with acetylene, is also discussed briefly. Comparison with theoretical results is made wherever possible, both at the level of electronic structure calculations of the potential energy surfaces and dynamical computations. Recent complementary CMB work as well as kinetic work exploiting soft photo-ionization with synchrotron radiation are noted. The examples illustrated in this article demonstrate that the type of dynamical results now obtainable on polyatomic multichannel radical-molecule and radical-radical reactions might well complement reaction kinetics experiments and hence contribute to bridging the gap between microscopic reaction dynamics and thermal reaction kinetics, enhancing significantly our basic knowledge of chemical reactivity and understanding of the elementary reactions which occur in real-world environments.

A comparative study of the Si+O(2)-->SiO+O reaction dynamics from quasiclassical trajectory and statistical based methods

The dynamics of the singlet channel of the Si+O(2)-->SiO+O reaction is investigated by means of quasiclassical trajectory (QCT) calculations and two statistical based methods, the statistical quantum method (SQM) and a semiclassical version of phase space theory (PST). The dynamics calculations have been performed on the ground (1)A(') potential energy surface of Dayou and Spielfiedel [J. Chem. Phys. 119, 4237 (2003)] for a wide range of collision energies (E(c)=5-400 meV) and initial O(2) rotational states (j=1-13). The overall dynamics is found to be highly sensitive to the selected initial conditions of the reaction, the increase in either the collisional energy or the O(2) rotational excitation giving rise to a continuous transition from a direct abstraction mechanism to an indirect insertion mechanism. The product state properties associated with a given collision energy of 135 meV and low rotational excitation of O(2) are found to be consistent with the inverted SiO vibrational state distribution observed in a recent experiment. The SQM and PST statistical approaches, especially designed to deal with complex-forming reactions, provide an accurate description of the QCT total integral cross sections and opacity functions for all cases studied. The ability of such statistical treatments in providing reliable product state properties for a reaction dominated by a competition between abstraction and insertion pathways is carefully examined, and it is shown that a valuable information can be extracted over a wide range of selected initial conditions.

Unraveling the dynamics of the C(3P,1D) + C2H2 reactions by the crossed molecular beam scattering technique

A detailed investigation of the dynamics of the reactions of ground- and excited-state carbon atoms, C(3P) and C(1D), with acetylene is reported over a wide collision energy range (3.6-49.1 kJ mol-1) using the crossed molecular beam (CMB) scattering technique with electron ionization mass spectrometric detection and time-of-flight (TOF) analysis. We have exploited the capability of (a) generating continuous intense supersonic beams of C(3P, 1D), (b) crossing the two reactant beams at different intersection angles (45, 90, and 135 degrees ) to attain a wide range of collision energies, and (c) tuning the energy of the ionizing electrons to low values (soft ionization) to suppress interferences from dissociative ionization processes. From angular and TOF distribution measurements of products at m/z=37 and 36, the primary reaction products of the C(3P) and C(1D) reactions with C2H2 have been identified to be cyclic (c)-C3H + H, linear (l)-C3H + H, and C3 + H2. From the data analysis, product angular and translational energy distributions in the center-of-mass (CM) system for both the linear and cyclic C3H isomers as well as the C3 product from C(3P) and for l/c-C3H and C3 from C(1D) have been derived as a function of collision energy from 3.6 to 49.1 kJ mol-1. The cyclic/linear C3H ratio and the C3/(C3 + c/l-C3H) branching ratios for the C(3P) reaction have been determined as a function of collision energy. The present findings have been compared with those from previous CMB studies using pulsed beams; here, a marked contrast is noted in the CM angular distributions for both C3H- and C3-forming channels from C(3P) and their trend with collision energy. Consequently, the interpretation of the reaction dynamics derived in the present work contradicts that previously proposed from the pulsed CMB studies. The results have been discussed in the light of the available theoretical information on the relevant triplet and singlet C3H2 ab initio potential energy surfaces (PESs). In particular, the branching ratios for the C(3P) + C2H2 reaction have been compared with the available theoretical predictions (approximate quantum scattering calculations and quasiclassical trajectory calculations on ab initio triplet PESs and, very recent, statistical calculations on ab initio triplet PESs as well as on ab initio triplet/singlet PESs including nonadiabatic effects, that is, intersystem crossing). While the experimental branching ratios have been corroborated by the statistical predictions, strong disagreement has been found with the results of the dynamical calculations. The astrophysical implications of the present results have been noted.

Quantum approaches for the insertion dynamics of the H+ + D2 and D+ + H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.

A statistical quasiclassical trajectory model for atom-diatom insertion reactions

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.

Dynamics of insertion reactions of H2 molecules with excited atoms

Recent progress in the study of insertion reactions of hydrogen molecules with excited atoms is reviewed in this article. In particular, the dynamics of the reaction of O(1D), N(2D), C(1D), and S(1D) with H2 and its isotopomers, which have received a great deal of attention over the past decade, are examined in detail. All of these systems have in common the existence of several potential energy surfaces (PES) correlating with the reagents' states, and consequently, they can give rise to reaction following different adiabatic and nonadiabatic pathways. The main contribution, however, arises from their ground singlet PESs which feature the existence of deep wells with small or null barriers for insertion. Accordingly, these reactions proceed mainly via formation of relatively long-lived collision complexes and display an overall nearly statistical behavior. In spite of their similarities, the various reactions have peculiar characteristics caused by important differences of their respective PESs. The contribution of excited PES to the global reactivity, which has also become an important issue and a challenge both for theory and experiment, is also examined. The different theoretical approaches are discussed in the text, along with the experimental results obtained by a variety of techniques. The recent exact quantum treatments of these reactive systems together with the development of a rigorous statistical model have contributed to a very accurate description which in many cases matches very well the detailed measurements. The quasi-classical trajectory (QCT) method has also provided a fairly accurate description of the reaction dynamics for these systems. In particular, the analysis in terms of collision times has yielded interesting clues about the reaction mechanisms.

Time dependent wave packet and statistical calculations on the H + O(2) reaction

The H + O(2)--> OH + O reaction has been theoretically investigated by means of an exact time dependent wave packet method and two statistical approaches: a recently developed statistical quantum model and phase-space theory. The exhaustive analysis of reaction probabilities at a zero total angular momentum would, in principle, reveal the existence of a complex-forming mechanism at low collision energies (E(c) = 1.15 eV), whereas deviations from a statistical behaviour at higher energies may be interpreted as the onset of a direct abstraction pathway which favours the production of highly excited rotational states of the OH fragment in its ground vibrational state. The good description by statistical means of previously measured product rotational distributions and excitation functions seems to support such an interpretation. However the statistical predictions clearly overestimate both existing and present exact quantum mechanical reaction probabilities and total cross sections, thereby precluding to conclude definitely the statistical nature of the collision. The exact time dependent method yields values of the integral cross sections in agreement with results by Goldfield and Meijer, and below the experimental findings.

On the theory of complex-forming chemical reactions: effect of parity conservation on the polarization of differential cross sections

For complex-forming triatomic reactions such as the prototypical insertion reactions intensively studied in the last few years, quantum mechanical differential cross sections (DCS) present sharp forward/backward polarization peaks when the reagent rotational angular momentum quantum number j is zero. Moreover, the size of the peaks decreases rapidly with increasing j values so that for j = 3, they are no longer visible. In contrast, the polarization peaks are always missing in the classical mechanical DCSs. Apart from the peaks, however, the quantum and classical DCSs are usually in good agreement. In a recent rapid communication, we showed that the fundamental reason for the previous differences in the quantum and classical scenarios is that parity conservation leads in quantum mechanics to an angular momentum constraint without equivalent in classical mechanics. We also proposed a parity-restoring approximation leading to an accurate semi-classical description of the peaks. While only the main lines of the demonstration were given in the communication, we report here the whole developments. We also analyse why the peaks disappear when the reagent diatom is rotationally excited. As a by-product of the previous developments, we finally discuss the possibility of a general statistico-dynamical semiclassical approach.