A study of conical intersections for the H3(+) system

A parametrization of the three asymptotic conical intersections between the energies of the H3(+) ground state and the first excited singlet state is presented. The influence of an additional, fourth conical intersection between the first and second excited states at the equilateral geometry on the connection between the three conical regions is studied, for both diatomics-in-molecules and ab initio molecular data.     

Quantum wave packet study of the H+ + D2 reaction on diabatic potential energy surfaces

The exact three-dimensional nonadiabatic quantum dynamics calculations were carried out for the title reaction by a time-dependent wave packet approach based on a newly constructed diabatic potential energy surface (Kamisaka et al. J. Chem. Phys. 2002, 116, 654). Three processes including those of reactive charge transfer, nonreactive charge transfer, and reactive noncharge transfer were investigated to determine the initial state-resolved probabilities and reactive cross sections. The results show that a large number of resonances can be observed in the calculated probabilities due to the deep well on adiabatic ground surface and the dominant process is the reactive noncharge-transfer process. Some interesting dynamical features such as v-dependent and j-dependent behaviors of the probabilities are also revealed. In addition, a good agreement has been achieved in the comparison between the calculated quantum cross sections from the ground rovibrational initial state and the experimental measurement data.     

Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials

We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, η, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A(3) system. The application of this methodology to AB(2) and ABC systems is also discussed.     

Ab initio adiabatic and diabatic energies and dipole moments of the CaH+ molecular ion

The diabatic and adiabatic potential-energy curves and permanent and transition dipole moments of the highly excited states of the CaH(+) molecular ion have been computed as a function of the internuclear distance R for a large and dense grid varying from 2.5 to 240 au. The adiabatic results are determined by an ab initio approach involving a nonempirical pseudopotential for the Ca core, operatorial core-valence correlation, and full valence configuration interaction. The molecule is thus treated as a two-electron system. The diabatic potential energy curves have been calculated using an effective metric combined to the effective Hamiltonian theory. The diabatic potential-energy curves and their permanent dipole moments for the (1)∑(+) symmetry are examined and corroborate the high imprint of the ionic state in the adiabatic representation. Taking the benefit of the diabatization approach, correction of hydrogen electron affinity was taken into account leading to improved results for the adiabatic potentials but also the permanent and transition electric dipole moments.     

Combinatorial invariants and covariants as tools for conical intersections

The combinatorial invariant and covariant are introduced as practical tools for analysis of conical intersections in molecules. The combinatorial invariant is a quantity depending on adiabatic electronic states taken at discrete nuclear configuration points. It is invariant to the phase choice (gauge) of these states. In the limit that the points trace a loop in nuclear configuration space, the value of the invariant approaches the corresponding Berry phase factor. The Berry phase indicates the presence of an odd or even number of conical intersections on surfaces bounded by these loops. Based on the combinatorial invariant, we develop a computationally simple and efficient method for locating conical intersections. The method is robust due to its use of gauge invariant nature. It does not rely on the landscape of intersecting potential energy surfaces nor does it require the computation of nonadiabatic couplings. We generalize the concept to open paths and combinatorial covariants for higher dimensions obtaining a technique for the construction of the gauge-covariant adiabatic-diabatic transformation matrix. This too does not make use of nonadiabatic couplings. The importance of using gauge-covariant expressions is underlined throughout. These techniques can be readily implemented by standard quantum chemistry codes.     

Quenching of Li (2P) by H2: potential energy surfaces, conical intersection seam, and diabatic bases

The quenching of Li (1s ²2p; ²P) to Li (1s ²2s; ²S) by H₂ is considered using coupled-cluster and multireference configuration-interaction techniques. C _{2 v} (²A₁, ²B₂) and C _{∞ v} (²Π,²Σ⁺) sections of the 1²A^′ and 2²A^′ potential energy surfaces are determined. The C _{2 v} portion of the 1²A^′−2²A^′ seam of conical intersection is studied. Perhaps the most significant finding is a surprising trifurcation of this seam into a portion with only C _s symmetry and the aforementioned C _{2 v} portion. The adiabatic-to-diabatic state transformation is considered in the vicinity of the seam of conical intersection using both perturbation theory and the dipole moment operator. The ²B₂ section of the 2²A^′ potential energy surface exhibits an exciplex in the general vicinity of the seam of conical intersection. The ²Π section of the 2²A^′ potential energy surface possesses a global minimum lying 1.86kcal/mol below the Li (²P)+H₂ asymptote. A van der Waals-like minimum with C _{∞ v} symmetry was found on the 1²A^′ potential energy surface. Received: 14 August 1998 / Accepted: 20 August 1998 / Published online: 11 November 1998     

Jahn-Teller effect in CH3D+ and CD3H+: conformational isomerism, tunneling-rotation structure, and the location of conical intersections

High-resolution pulsed-field-ionization zero-kinetic-energy photoelectron spectra of CH(3)D and CD(3)H have been recorded at rotational resolution from the adiabatic ionization energy up to 600 cm(-1) of internal energy of the respective cations. The spectra are characterized by the effects of a large-amplitude pseudorotational motion exchanging the equivalent nuclei in each molecule. With increasing internal energy, a transition from the tunneling regime with splittings of the order of 1-10 cm(-1) to the free pseudorotation regime is observed. A theoretical model that treats the simultaneous rotational and pseudorotational motions and incorporates the effects of the geometric phase has been developed. The model provides the appropriate rovibronic symmetries in the C(3v)(M) molecular symmetry group and reaches a near-quantitative agreement with the experimental data. The complete group-theoretical analysis of the rovibronic problem is also given. The analysis of the spectra has revealed the existence of two different isomers for both CH(3)D(+) and CD(3)H(+), which differ in the bond length between the carbon atom and the unique ligand atom. All isomers are subject to a fast pseudorotational motion between three equivalent minima with a period of 3-5 ps in CH(3)D(+) and 18-28 ps in CD(3)H(+). The analysis has also provided the ordering of the tunneling sublevels for each isomer, which enables the location of the twofold conical intersections on the potential energy surface that could not be determined from experiments on CH(4) (+).     

Ab initio nonadiabatic dynamics study of ultrafast radiationless decay over conical intersections illustrated on the Na3F cluster

We present a theoretical approach for the ultrafast nonadiabatic dynamics based on the ab initio molecular dynamics carried out "on the fly" in the framework of the configuration interaction method combined with Tully's surface hopping algorithm for nonadiabatic transitions. This approach combined with our Wigner distribution approach allows us to perform accurate simulations of femtosecond pump-probe spectra in the systems where radiationless transitions among electronic states take place. In this paper we illustrate this by theoretical simulation of ultrafast processes and nonradiative relaxation in the Na(3)F cluster, involving three excited states and the ground electronic state. Furthermore, we show that our accurate simulation of the photoionization pump-probe spectrum is in full agreement with the experimental signal. Based on the nonadiabatic dynamics at high level of accuracy and taking into account all degrees of freedom, the nonradiative lifetime for the 1 (1)B(1) excited state of Na(3)F has been determined to be approximately 900 fs.     

Computational study on the reaction CH2CH2 + F --> CH2CHF + H

Previous ab initio studies on reactions involving radical addition to alkenes showed that such reactions are very sensitive to theoretical levels, and thus are difficult to deal with. This motivates us to theoretically reexamine the title reaction thoroughly, which has been studied only at several low levels of theory. In the present work, the geometry optimizations and energy calculations for all species involved in the title reaction were performed at several high levels of theory. The reaction mechanism of the title reaction is discussed at the CCSD(T)/aug-cc-pVDZ//CCSD/6-31G(d,p) theoretical level. According to our study, the fluorine addition to ethylene occurs via the formation of a prereaction complex with C2v symmetry, which is pointed out for the first time. The prereaction complex evolves into a fluoroethyl radical almost without a barrier, with an exothermicity of 41.49 kcal/mol. The fluoroethyl radical can further decompose into a hydrogen atom and fluoroethylene, with an energy release of 10.33 kcal/mol. Besides the direct departure of the hydrogen atom from the fluoroethyl radical, an indirect decomposition pathway may also be open, which has not been reported before. In addition, the formation of a fluoroethyl radical from a separate fluorine atom and ethylene is described pictorially via the molecular intrinsic characteristic contour (MICC) and the electron density mapped on it. Thereby, strong interpolarization and evident electron transfer between the fluorine atom and ethylene are observed as they approach each other. The transition structure for the fluorine addition to ethylene is clearly shown to be reactant-like. This provides new and intuitional insight into the title reaction.     

Ab initio investigation of the potential energy surfaces of C2H2F2 and C2H2F2+

Ab initio MO calculations have been performed for neutral and cationic C₂H₂F₂ structures. Olefinic and carbene structures are investigated for the neutral isomers, while olefinic, carbene, and fluoronium-type cations are found. Stability orders and rotational barriers are discussed in terms of orbital and Coulomb interaction. Contrary to previous studies, the higher stability of the geminal isomers is interpreted to be caused by Coulomb attraction.     

Renner-Teller/Jahn-Teller intersections along the collinear axes of polyatomic molecules: C2H2 + as a case study

Recently we discussed the Renner-Teller effect in triatomic molecules [J. Chem. Phys. 125, 094102 (2006)]. In that article the main message is that the Renner-Teller phenomenon, just like the Jahn-Teller phenomenon, is a topological effect. Now we extend this study to a tetra-atomic system, namely, the C(2)H(2) (+) ion, for which topological effects are revealed when one atom surrounds the triatom axis or when two atoms surround (at a time) the two-atom axis. The present study not only supports the findings of the previous study, in particular, the crucial role played by the topological D matrix for diabatization, but it also reveals new features which are expected to be more and more pronounced the larger the original collinear molecule. As already implied, shifting away two atoms from the collinear molecular axis does not necessarily abolish the ability of the remaining two atoms to form topological effects. Moreover, the study indicates that when the two hydrogens are shifted away, the CC axis produces two kinds of topological effects: (1) a Renner-Teller effect (characterized by a topological phase of 2pi) which is revealed when the two hydrogens surround, rigidly, this axis (as mentioned above), and (2) a Jahn-Teller effect (characterized by a topological phase of pi) which is revealed when one of the hydrogens surrounds this axis while the other hydrogen is clamped to its position.     

An improved potential energy surface for the F+H2 reaction

A new ground state potential energy surface has been developed for the F+H₂ reaction. Using the UCCSD(T) method, ab initio calculations were performed for 786 geometries located mainly in the exit channel of the reaction. The new data was used to correct exit channel errors that have become apparent in the potential energy surface of Stark and Werner [J. Chem. Phys. 104 (1996) 6515]. While the entrance channel and saddlepoint properties of the Stark–Werner surface are unchanged on the new potential, the exit channel behavior is more satisfactory. The exothermicity on the new surface is much closer to the experimental value. The new surface also greatly diminishes the exit channel van der Waals well that was too pronounced on the Stark–Werner surface. Several preliminary dynamical scattering calculations were carried out using the new surface for total angular momentum equal to zero for F+H₂ and F+HD. It is found that gross features of the reaction dynamics are quite similar to those predicted by the Stark–Werner surface, in particular the reactive resonance for F+HD and F+H₂ survive. However, the most of the exit channel van der Waals resonances disappear on the new surface. It is predicted that the differential cross-sections at low collision energy for the F+H₂ reaction may be drastically modified from the predictions based on the Stark–Werner surface.     

A surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H₂⁺ + H₂ → H₃⁺ + H and the isotopic variants (H₂⁺ + D₂ and D₂⁺ + H₂). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number (v⁺) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v⁺ = 0 and reductions in cross sections of up to 30% for v⁺ = 3 trajectories.     

Explorations of conical intersections and their ramifications for chemistry through the Jahn-Teller effect

Much recent progress has been made theoretically and computationally towards understanding the importance of conical intersections for chemical reactions. Nonetheless, experimental characterization of conical intersections has proven extremely difficult with one striking exception: the Jahn-Teller conical intersection. This article overviews the fundamental similarity of a variety of conical intersections and demonstrates how the spectroscopy of Jahn-Teller active molecules can be used to characterize them. Specific results are reviewed for four representative Jahn-Teller active molecules, C5H5, C6H6+, Ag3 and CH3O.     

Molecular beam study of F2+I2

Crossed molecular beam techniques have been used to study the endoergic reaction between F₂ and I₂. Above a threshold energy of 4 kcal/mole the observed products are I₂F and F. At higher energies IF is also produced. Angular and velocity distributions indicate that the IF does not result from a four-center exchange reaction.     

The microscopic reaction dynamics and branching ratio in the F + HCOOH and F + H2CO reactions

Infrared chemiluminescence under conditions of arrested relaxation has been applied to the study of the hydrogen and deuterium abstraction reactions of HCOOH, DCOOH and H₂CO with F atoms. Two distinctly different modes of product excitation are observed, depending upon whether the reaction proceeds via the formyl or carboxyl hydrogen. Reaction at the formyl hydrogen (or deuterium) causes substantial inversion in the diatomic product internal energy distributions. The F + H₂CO and F + DCOOH reactions respectively channel 56% and 54% of the available energy into vibration in the product diatomic when they occur at the formyl site. In both cases the product energy distributions are qualitatively similar to those observed in direct reactions of triatomic systems on repulsive energy surfaces. In contrast to these, reaction at the carboxyl hydrogen of DCOOH gives an HF2 product vibrational distribution having a Boltzmann equilibrium shape at a temperature of 4300 K. The ratio of HF to DF product from the F + DCOOH study shows that reaction occurs at the carboxyl hydrogen approximately twice as often as at the formyl site. Comparison with triatomic reactions involving the same mass-combinations implies that abstraction of the formyl hydrogen occurs via single-collision, direct encounters, whereas reaction at the carboxyl site involves a long-lived complex in which extensive randomisation of the reaction exoergicity among all the product vibrational modes can occur.     

Rate constant for H+H+Ar = H2 + Ar from 1300 to 1700 K

Shock tube experiments on the decay of OH-radical concentration after shock-initiated combustion of H₂:O₂:Ar = 10:1:89 mixtures were analyzed to give the rate constant 1 × 10¹⁵ cm⁶mol^?2s^?1for the reaction H + H + Ar = H₂ + Ar overthe temperature range 1300 to 1700 K.     

An eight-degree-of-freedom quantum dynamics study for the H2+C2H system

An eight-degree-of-freedom (8DOF) time-dependent wave-packet approach has been developed to study the H(2)+C(2)H-->H+C(2)H(2) reaction system. The 8DOF model is obtained by fixing one of the Jacobi torsion angle in the nine-degree-of-freedom AB+CDE reaction system. This study is an extension of the previous seven-degree-of-freedom (7DOF) computation [J. Chem. Phys. 119, 12057 (2003)] of this reaction system. This study shows that vibrational excitations of H(2) enhance the reaction probability, whereas the stretching vibrational excitations of C(2)H have only a small effect on the reactivity. Furthermore, the bending excitation of C(2)H, compared to the ground-state reaction probability, hinders the reactivity. A comparison of the rate constant between the 7DOF calculation and the present 8DOF results has been made. The theoretical and experimental results agree with each other very well when the present 8DOF results are adjusted to account for the lower transition state barrier heights found in recent ab initio calculations.