Reactive chemical dynamics through conical intersections

Electronic nonadiabatic effects in the state-to-state dynamics of the H + H2 → H2 + H exchange reaction with a vibrationally excited reagent

Out of the many major breakthroughs that the hydrogen-exchange reaction has led to, electronic nonadiabatic effects that are mainly due to the geometric phase has intrigued many. In this work we investigate such effects in the state-to-state dynamics of the H + H2 (v = 3, 4, j = 0) → H2 (v', j') + H reaction with a vibrationally excited reagent at energies corresponding to thermal conditions. The dynamical calculations are performed by a time-dependent quantum mechanical method both on the lower adiabatic potential energy surface (PES) and also using a two-states coupled diabatic theoretical model to explicitly include all the nonadiabatic couplings present in the 1E' ground electronic manifold of the H3 system. The nonadiabatic couplings are considered here up to the quadratic term; however, the effect of the latter on the reaction dynamics is found to be very small. Adiabatic population analysis showed a minimal participation of the upper adiabatic surface even for the vibrationally excited reagent. A strong nonadiabatic effect appears in the state-to-state reaction probabilities and differential cross sections (DCSs). This effect is manifested as "out-of-phase" oscillations in the DCSs between the results of the uncoupled and coupled surface situations. The oscillations persist as a function of both scattering angle and collision energy in both the backward and forward scattering regions. The origins of these oscillations are examined in detail. The oscillations that appear in the forward direction are found to be different from those due to glory scattering, where the latter showed a negligibly small nonadiabatic effect. The nonadiabatic effects are reduced to a large extent when summed over all product quantum states, in addition to the cancellation due to integration over the scattering angle and partial wave summation.

Time-dependent quantum mechanical wave packet dynamics

Starting from a model study of the collinear (H, H₂) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH₄. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H₂) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H₂ (v = 0-4, j = 0-3) → H₂ (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.

Excited electronic states and nonadiabatic effects in contemporary chemical dynamics

The question of how to describe the crossing of molecular electronic states is one of the most challenging issues in contemporary chemical dynamics. In recent years, the fundamental concept of conical intersections (CIs) of electronic potential energy surfaces (PESs) has emerged, which allows extremely fast and efficient switching of a molecule between its excited and ground electronic states. CIs are ubiquitous in polyatomic molecules. Because they generically allow the crossings of the Born-Oppenheimer (BO) adiabatic PESs, they have become the crucial mechanistic elements of the rapidly growing area of nonadiabatic chemistry. The most critical consequence of CIs is a complete breakdown of the adiabatic BO approximation. That means that the reorganization of fast-moving electrons and nuclear vibrations must be treated concurrently. Ideally, the theoretical description should be quantum mechanical in this situation. However, because of the complexity, the necessary approximations often make it difficult to conclusively predict dynamic behavior of large polyatomic molecules. In addition, a nonunique diabatic electronic representation (describing coupling between states in the electronic Hamiltonian) is essential to avoid the singular nature of the nuclear kinetic coupling terms of the unique adiabatic electronic representation. This Account describes both the challenges and some recent advances in quantum mechanical studies of nonadiabatic molecular processes, highlighting results from our recent work examining the static aspects of CIs and their dynamical consequences. The spectroscopic implications of the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) intersections in complex molecular systems are discussed. Our work probes the underlying details of complex vibronic spectra of systems of growing sizes in terms of both electronic and nuclear degrees of freedom. The necessity of extension of the theoretical treatment beyond a linear vibronic coupling approach is addressed. Our results establish highly overlapping band structures due to JT and PJT CIs, a bimodal distribution of spectral intensity that originates from strong JT coupling, and the role of intermode bilinear coupling in the progressions of vibronic bands. Investigations of the quantum dynamics of the prototypical naphthalene radical cation were aimed at understanding its photostability, lack of fluorescence emissions, and diffuse interstellar bands. This work established extremely fast relaxation of this radical cation through CIs. Simulations of the interplay of electronic and relativistic spin-orbit coupling in the photodetachment spectroscopy of ClH(2)(-), in conjunction with experimental data, support the existence of a shallow van der Waals well in the reactive Cl + H(2) PES. These results also reveal a quenching of electronic coupling by the relatively strong spin-orbit coupling. In addition, we studied the dynamics of the prototypical H + H(2) reaction from a new perspective by explicitly including the coupling between the two energy surfaces of its JT split degenerate ground electronic state. Although individual reaction probabilities show partial sensitivity to nonadiabatic effects, the theoretical results reveal that they are not important for the dynamical outputs such as integral reaction cross sections and thermal rate constants.