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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.

Direct dynamics within the framework of DFT was used to study the long-time puzzling mechanism of the reaction between F2 and ethylene. Three types of reactions are widely accepted : F atom elimination reaction, HF elimination reaction and the addition reaction. Several reaction mechanisms have been proposed, but only the radical mechanism can reasonably explain the initial reaction at low temperature. In this article, our calculations support the radical mechanism and the reaction mechanisms of the three reactions, and they are described in detail by trajectory simulation. The reactions in a cryogenic matrix with the reaction mechanism were also discussed.

Classical trajectory calculations using the MERCURY/VENUS code have been carried out on the H+O(2) reactive system using the DMBE-IV potential energy surface. The vibrational quantum number and the temperature were selected over the ranges nu=0 to 15, and T=300 to 10 000 K, respectively. All other variables were averaged. Rate constants were determined for the energy transfer process, H+O(2)(nu)-->H+O(2)(nu(")), for the bimolecular exchange process, H+O(2)(nu)-->OH(nu('))+O, and for the dissociative process, H+O(2)(nu)-->H+O+O. The dissociative process appears to be a mere extension of the process of transferring large amounts of energy. State-to-state rate constants are given for the exchange reaction, and they are in reasonable agreement with previous results, while the energy transfer and dissociative rate constants have never been reported previously. The lifetime distributions of the HO(2) complex, calculated as a function of v and temperature, were used as a basis for determining the relative contributions of various vibrational states of O(2) to the thermal rate coefficients for recombination at various pressures. This novel approach, based on the complex's ability to survive until it collides in a secondary process with an inert gas, is used here for the first time. Complete falloff curves for the recombination of H+O(2) are also calculated over a wide range of temperatures and pressures. The combination of the two separate studies results in pressure- and temperature-dependent rate constants for H+O(2)(nu)(+Ar) right arrow over left arrow HO(2)(+Ar). It is found that, unlike the exchange reaction, vibrational and rotational-translational energy are liabilities in promoting recombination.

We report on a global potential energy hypersurface for the lowest triplet state of H3+ based on the double many-body expansion (DMBE) method and ab initio data points of V5Z quality. These data points are represented with a root mean square deviation of only 3.46 cm−1 in the energy region below the H2+(X2Σg+)+H(2S) dissociation threshold and with less than 15 cm−1 up to the three-particle breakup energy. As expected from a DMBE approach, all dissociation limits are represented accurately and are approached in a physically correct manner.

We report a new multi-sheeted double many-body expansion potential energy surface that reproduces most known topological features of the title system. Near spectroscopic accuracy is conveyed to the ground-state sheet of 2A1 (1 2A′ in Cs) symmetry in the vicinity of the minimum by merging it with a spectroscopically determined Taylor-series-expansion-type form via a novel multiple energy-switching scheme. A high energy ridge for C2v insertion of N(4S) into O2(X 3Σg−) has also been imposed to mimic the result of accurate ab initio complete active space self-consistent field and second-order perturbation theory on CAS wave function calculations carried out for such geometries. This ridge decreases for Cs geometries yielding a minimum barrier height for the N+O2 reaction of 0.273 eV at a bent N–O–O structure defined by RNO=3.107a0, ROO=2.513a0, and ∠NOO=113.5 deg. Both the location and height of this barrier are in good agreement with existing ab initio calculations and the recommended values. Another salient...

A simple theoretically motivated model to extrapolate the correlation energy based on correlation-consistent polarized X-tuple basis sets is suggested. It has the form EXcor=E∞cor[1+A3 X−3(1+A4 X−1)], where EXcor is the energy for the X-tuple basis set, E∞cor and A3 are parameters to be determined from a set (Xmin−Xmax) of correlation consistent basis sets at a given level of theory, and A4 is a function of A3. Even for the simple (2,3) extrapolation scheme, the method is shown to yield energies for 33 test data sets that are more accurate than those obtained from pure correlation consistent sextuple-zeta basis sets at a much lower computational cost. Other extrapolation schemes have also been investigated, including a simple one-parameter rule EXcor=E∞cor(1–2.4X−3).

In this work we apply the line-integral technique to study possible geometric phase effects in the 2×2 diabatic double many-body expansion (DMBE) potential energy surface of three hydrogenic systems, namely, H3, DH2, and HD2. First, we show that the phase obtained by employing the line-integral method is identical (up to a constant) to the ordinary diabatic angle of the orthogonal transformation that diagonalizes the diabatic potential matrix. Next this angle is studied numerically along the line formed by fixing the two hyperspherical coordinates ρ and θ and letting φ change along the interval [0, 2π]. We find that in the H3 system, where this line always encircles the seam, the corresponding line integral always produces the value π for the geometric (Berry) phase. In the cases of the two isotopic systems we usually find the same results, but we also verify that for substantial regions in configuration space these lines do not encircle the seam and that, therefore, the line integrals produce the value of zero for the geometric phase. Analyzing the results, we establish that the Longuet-Higgins phase, which is usually assumed to be equal to φ/2, is in general significantly different from this value for all studied mass combinations.

Based on the equivalence of the gauge transformations for the nuclear and electronic wave functions, the physical meaning of the geometric phase effect has been disclosed for a two coupled-state system. It is found that the geometric phase A(R) is defined by the argument of the complex electronic vector state in the complex plane spanned by the two real-valued electronic components. Such an angle is identical (up to a constant) to the mixing angle γ(R). Novel generalized Born–Oppenheimer equations for the two coupled-state problem in the vicinity of the crossing seam have been derived, and numerical calculations of vibrational spectra done for H3. The results demonstrate significant differences in relation to those obtained from the assumption that A(R)=φ/2.

We report detailed evidence on the crossing and avoided crossing between the X 1A′ and 2 1A′ potential energy surfaces of HCN from ab initio full valence complete active space calculations. The role of three-body effects on explaining the crossing seam and the implications of the latter on reaction dynamics are also briefly discussed.

A recently proposed two-valued energy switching potential energy surface for the water molecule [J. Chem. Phys. 107, 867 (1997)] is modified to incorporate the proper dissociation limits in all channels pertaining to the first excited 1A′ electronic state, in addition to those of the ground state. A brief analysis of the loci of conical intersections is also presented.

A single-valued double many-body expansion potential energy surface is reported for ground-state HCN based on a realistic representation of the long-range forces, and a fit to accurate ab initio calculations for the HCN↔CNH regions [J. M. Bowman, B. Gazdy, J. A. Bentley, T. J. Lee, and C. E. Dateo, J. Chem. Phys. 99, 308 (1993)] and novel full valence complete active space energies for CHN geometries. The various topographical features of the novel global potential energy surface are examined, and vibrational calculations are presented to characterize the minima associated to the HCN and CNH isomers. The quality of the new fit is compared with that of the seminumerical representation of Bowman et al. in terms of root-mean-squared deviations for stratified energy regimes.

A novel scheme is suggested to construct a global potential energy surface by switching between representations which are optimal for different energy regimes. The idea is illustrated for the electronic ground state of water for which we use as switched functions the many‐body expansion potential of Murrell and Carter [J. Chem. Phys. 88, 4887 (1984)] and the polynomial form of Polyansky, Jensen, and Tennyson, [J. Chem. Phys. 101, 7651 (1994)]. By also modifying the former to reproduce the Coulombic behavior at the collapsed molecular limits for vanishingly small interatomic distances and approximately account for the long range forces, the new potential energy surface has been given double many‐body expansion quality. The result is a global H2O potential energy surface which has spectroscopic accuracy and may be used for studies of reaction dynamics.

The combined Jahn-Teller plus pseudo-Jahn-Teller [(E'+A1')⊗e'] problem is discussed for the tricarbon radical (C3) by means of ab initio calculations at the multireference configuration interaction level of theory. For the (1)E' electronic state arising from a e'(2) valence configuration, three additional symmetry-equivalent C2v seams are found to lie in close proximity to the D3h symmetry-required seam over the entire range of the breathing coordinate here considered. As the perimeter of the molecule increases, the C2v disjoint seams approach the D3h one almost linearly and ultimately coalesce with it at Q1 = 5.005 a0, thence forming an intersection node or confluence. By further increasing the size of the molecular triangle, the C2v seams get rotated by ±π in the g-h plane. A three-state vibronic Hamiltonian is also proposed to model locally the title system and shown to accurately mimic the calculated data over the region close to the minimum energy crossing point. No net geometric phase effect is observed when the associated electronic wave functions are adiabatically transported along closed paths encircling the four singularity points. For all paths enclosing the intersection node, the sign reversal criterion is shown to be not fulfilled, even for infinitesimal loops. The results so obtained are expected to be valid for other ring systems experiencing similar topological attributes.

A method for calculating quasiclassical trajectories on potential energy surfaces defined using a sequence of model quadratic surfaces (QCT/GH) is suggested, and tested for atom–diatom collisions against the traditional quasiclassical trajectory approach. A simple model is also suggested to constrain the classical energy of a bound vibrational mode to be greater than a specified amount, namely, its zero‐point energy value. Essentially the model consists of assuming that the sum of the energies in the nonrelevant vibrational modes (typically unbound modes) of the supermolecular complex acts as a pool from which energy may be taken to compensate any leak of vibrational energy in the relevant bound modes, hence preventing the latter from falling below zero‐point value. Extensive QCT/GH trajectory calculations carried out for the H+H2 exchange reaction, which occurs over an energy barrier, as well as exploratory trajectories for the reaction O+OH→O2+H, which occurs on a potential energy surface with a deep ch...

The excitation function of the H+O2 (v=0)→OH+O reaction has been determined from trajectory calculations using the HO2 DMBE IV potential energy surface. Reactive cross sections for thirteen translational energies, corresponding to a total of a quarter of a million trajectories, have been computed covering the range 65≤Etr/kJ mol−1≤550. Various schemes for analyzing the trajectories, three of which aim to correct approximately for the zero‐point energy problem of classical dynamics, have been investigated. One of these schemes aims to correct also for known requirements on rotational distributions, e.g., for the fact that by Hund’s rules for the coupling of angular momentum the product OH (2Π) molecule always rotates. It has been found that zero‐point energy effects and lowest‐J constraints on rotational distributions may have a crucial role, especially close to the threshold energy of reaction. Agreement with recent measurements of absolute reactive cross sections is generally satisfactory but, unlike exp...

The quasiclassical trajectory (QCT) method has been used for a detailed study of the state‐to‐state dynamics of the reaction O(3P) + OH(2Π)→O2(X33Σ−g) + H(2S) over the range of translational energies 0.125 ≤ Etr/kcal mol−1≤2.0, corresponding to the temperature range 40≤T/K≤680. A novel variant of this method insuring that trajectory calculations properly account for the zero‐point energy of the diatomic molecules, the so‐called quasiclassical trajectory–internal‐energy quantum‐mechanical‐threshold method, is also suggested and applied to the title reaction. The most recent and accurate double many‐body expansion potential‐energy surface for the ground doublet state of the hydroperoxyl radical has been employed in all calculations. The computed reactive cross sections for initial quantum rotational states of OH varying from J=0 to J=10 (the vibrational quantum number is kept fixed at v=0) are shown to have a marked decreasing dependence on translational energy, thus suggesting that long‐range forces play ...

A recently proposed coupled three-dimensional time-dependent wave-packet formalism in hyperspherical coordinates is shown to yield accurate results for the reactive non-charge transfer process in the title system at collision energies as low as 100 K, where the lowest sheet of the accurate double many body expansion form for the singlet H3 (+) is used. The results are compared with available experimental data as well as time-independent calculations, and the agreement shown to be generally good.

Quantum scattering calculations of the O((3)P)+OH((2)Π)⇌O2((3)Σg (-))+H((2)S) reactions are presented using the combined-hyperbolic-inverse-power-representation potential energy surface [A. J. C. Varandas, J. Chem. Phys. 138, 134117 (2013)], which employs a realistic, ab initio-based, description of both the valence and long-range interactions. The calculations have been performed with the ABC time-independent quantum reactive scattering computer program based on hyperspherical coordinates. The reactivity of both arrangements has been investigated, with particular attention paid to the effects of vibrational excitation. By using the J-shifting approximation, rate constants are also reported for both the title reactions.

In this work is reported the first quantum mechanical treatment of the atmospheric atom–triatom O+O3→2O2 reaction. Temperature‐dependent rate constants were calculated and were found to be in good agreement with the experiment.

The purpose is to fit an accurate smooth function of the many-body expansion type to a multidimensional large data set using a basis-set type method. By adopting a combined-hyperbolic-inverse-power-representation for the basis, the novel approach is tested in detail for the ground electronic state of tri-hydrogen and hydroperoxyl systems, assuming that their potential energy surfaces are single-sheeted representable. It is also shown that the method can be easily applicable to potential energy curves by considering as prototypes molecular oxygen and the hydroxyl radical.

The core electron temperature (T(e0)) of neutral beam heated plasmas is determined in TJ-II stellarator by using soft x ray detectors with beryllium filters of different thickness, based on the method known as the foil absorption technique. T(e0) estimations are done with the impurity code IONEQ, making use of complementary information from the TJ-II soft x ray tomography and the VUV survey diagnostics. When considering the actual electron density and temperature profile shapes, an acceptable agreement is found with Thomson scattering measurements for 8 different magnetic configurations. The impact of the use of both neutral beam injectors on the T(e0) measurements is addressed. Also, the behaviour of T(e0) during spontaneous profile transitions is presented.

The spin-component-scaling second-order Møller-Plesset theory proposed by Grimme, the scaled opposite-spin variant of Head-Gordon and co-workers, and other variants of the theory to treat the electron correlation energy are examined. A refinement of scaled opposite-spin theory for strong chemical interactions is suggested where the scaled correlation contribution is chosen such as to mimic closely the one obtained by more sophisticated methods of the coupled cluster type. With the scaling factor chosen to vary in a simple statistical manner with the number of opposite-spin electron pairs of the system, the parameters have been calibrated from standard coupled cluster type calculations for a chosen ab initio test data set. The new approach, termed as variable-scaling opposite spin, aims to be applicable at any regions of the molecule configuration space where second-order Møller-Plesset perturbation theory converges. It thus benefits of all advantages inherent to the original theory, which makes it an attractive approach on a computational cost basis. Because the method in one of its formats fails size-extensivity, the consequences and remedies of this are analyzed. Illustrations are presented for many molecules utilizing Dunning-type basis sets, in particular, for a detailed analysis of N(3) in its lowest quartet state, which does not belong to the test set. Extrapolations of the calculated raw energies to the complete one-electron basis set limit are also reported, giving the most reliable estimates available thus far of the energetics for the N((4)S)+N(2) exchange reaction. All spin-component-scaling schemes are known to show difficulties in dealing with weak interactions of the van der Waals type, which has justified the design of specific variants of the theory according to the property and regime of interactions. Several variants of the theory are then examined using a second test set of molecules, and shown to be linked via a coordinate that evolves gradually between two known extreme regimes. It is further shown that such a coordinate can be specified via a constrained Feenberg-type scaling approach, a theory whose merits are also explored.

The uniform singlet- and triplet-pair extrapolation scheme and its generalized variant are utilized to describe bond breaking of the C(2) molecule in the ground electronic state, as well as in two other excited states of the same spin symmetry by extrapolating multireference configuration interaction energies calculated with the correlation consistent basis sets of Dunning to the complete-basis set limit. It is shown that the correlation energy changes drastically (with a symmetric sigmoidal-type shape) near the geometry (R approximately 1.6 A) where the two lowest (1)Sigma(g)(+) adiabatic states show the avoided crossing. The implications of such a feature on extrapolating the dynamical correlation are then analyzed, and the attributes of the extrapolated ground electronic state shown to be in excellent agreement with the most recent experimental data available in the literature.

The potential energy surface of H(3) (+) in the lowest electronic triplet state, a (3)Sigma(u) (+), shows three equivalent minima at linear nuclear configurations. The vibrational levels of H(3) (+) and D(3) (+) on this surface can therefore be described as superimposed linear molecule states. Owing to such a superposition, each vibrational state characterized by quantum numbers of an isolated linear molecule obtains a one- and a two-dimensional component. The energy splittings between the two components have now been rationalized within a hyperspherical picture. It is shown that nuclear motion along the hyperangle phi mainly accounts for the splittings and provides upper bounds. This hyperspherical motion can be considered an extension of the antisymmetric stretching motion of the individual linear molecule.

The state-to-state dynamics of the H+D2 reaction is studied by the reactant-product decoupling method using the double many-body expansion potential energy surface. Two approaches are compared: one uses only the lowest adiabatic sheet while the other employs both coupled diabatic sheets. Rotational distributions for the reaction H+D2 (upsilon = 0, j = 0)--HD(upsilon' = 3, j')+D are obtained at eight different collision energies between 1.49 and 1.85 eV; no significant difference are found between the two approaches. Initial state-selected total reaction probabilities and integral cross sections are also given for energies ranging from 0.25 up to 2.0 eV with extremely small differences being observed between the two sets of results, thus showing that the nonadiabatic effects in the title reaction are negligible at least for small energies below 2.0 eV.

We present a consistent analytic representation of the two lowest potential energy surfaces for H3 and their nonadiabatic coupling. The surfaces are fits to ab initio calculations published previously by Liu and Siegbahn and also to new ab initio calculations reported here. The analytic representations are especially designed to be valid in the vicinity of the conical intersection of the two lowest surfaces, at geometries important for the H+H2 reaction, and in the van der Waals regions.

A new potential energy surface for H3 of the London–Eyring–Polanyi–Sato type has been obtained which reproduces the best available estimates for the geometry, classical barrier height, and quadratic force constants of the D∞h saddle point. Other attributes of the surface, e.g., minimum energy profile for the exchange process, spherically averaged potential V0, and leading anisotropic potential V2, are also shown to be in good agreement with the best available estimates. The simplicity of its functional form further commends it for future dynamical studies.

A method recently proposed by Brown and Truhlar to correct large‐scale configuration interaction calculations for incomplete dynamic correlation of electrons is reformulated using the formalism of the double many‐body expansion method. Rather than making the assumption that large‐basis‐set multireference configuration interaction calculations including all single and double excitations from a complete‐active space recover an approximately constant fraction of the external correlation, it is suggested that this fraction is approximately constant for the various n‐body terms which arise in a cluster expansion of the total molecular energy. A new variant of this method in which the assumption of geometry‐independent fraction of the external correlation is relaxed for the diatomics is also examined. Results are reported for the ground electronic states of the H3 and HO2 systems.

We study low‐energy quantal phenomena in the rearrangement of three‐atom systems composed of H and D. All calculations are carried out on the double many‐body expansion potential energy surface for the hydrogen trimer. The unimolecular rearrangements of van der Waals molecules, such as D⋅⋅⋅H2→HD⋅⋅⋅H, are studied as a model for the exchange transfer reaction in condensed phases, and the gas‐phase bimolecular reactions, such as D+H2→HD+H, are studied to probe the limiting low‐temperature threshold behavior, which is compared to that predicted by quantum mechanical threshold laws. The reaction rates are studied down to temperatures of 10−3 K. We also predict the spectroscopic tunneling shift on the lowest energy levels of the H⋅⋅⋅H2 complex.