Calculation of bound rovibrational states on the first electronically excited state of the H3 system

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.

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.

Cold atom-atom-anion three-body recombination of 4He4HexLi- (x = 6 or 7) systems

Atom-atom-anion three-body recombination (TBR) in mixed ⁴He and ^xLi^- (x = 6 or 7) is investigated in the adiabatic hyperspherical representation by quantum mechanically solving the Schrödinger equation. The distributions of product states following these TBR processes are found to be relatively different for the two systems when the collision energy is less than roughly 0.6 mK × k_B or 0.3 mK × k_B for ⁴He⁴He⁶Li^- and ⁴He⁴He⁷Li^- systems, respectively, with k_B being the Boltzmann constant. For ⁴He⁴He⁶Li^- systems, the rate of recombination into (v=0) l = 0⁴He⁶Li^- molecular anions is the largest with v and l denoting the rovibrational quantum numbers, while the TBR rate that leads to the formation of l = 1⁴He⁶Li^- molecular anions is a little smaller than that of neutral ⁴He₂ molecules. For ⁴He⁴He⁷Li^- systems, neutral ⁴He₂ molecules tend to be the most products, following the yields of l = 0 and 1 ⁴He⁷Li^- molecular anions. However, in spite of these distinctly different distributions, the products of molecular anions, the sum of l = 0 and 1 ⁴He^xLi^- products, are relatively larger than that of neutral ⁴He₂ molecules for both the two systems.

Role of sharp avoided crossings in short hyper-radial range in recombination of the cold 4He3 system

The role of sharp avoided crossings (SACs) in a short hyper-radial range R≤ 50 a.u. in the calculation of recombination for a cold ⁴He₃ system is investigated in the adiabatic hyperspherical representation by "turning off and on" the relevant nonadiabatic couplings. The influence of SACs on the recombination is related with the channels of the system and with the scattering energy. For J^Π = 0⁺ symmetry, the two-body recombination channel has an attractive potential well, which makes radial wave functions of both two-body recombination channel and three-body continuum channels accessible in the short hyper-radial range where SACs are located. The SACs consequently play an important role in coupled-channel calculations and this is particularly the case for lower scattering energies. However, for excited nuclear orbital momenta, i.e., J^Π = 1^-, 2⁺,…, 7^- symmetries, the two-body recombination channel has a repulsive interaction and the radial wave functions are not accessible in the short hyper-radial range. Therefore, omission of SACs in the short range for these symmetries has no effect on the numerical results, which leads to great savings on hyper-radial grid points in the practical numerical calculations. Moreover, to make the nonadiabatic couplings among channels to be continuous in the hyper-radius, different methods associated with the application of consistent phase convention are discussed.

Adiabatic hyperspherical study of weakly bound He(2)H(-), He(2)H, and HeH(2) systems

The He(2)H(-), He(2)H, and HeH(2) triatomic systems are studied using the adiabatic hyperspherical representation. By adopting the best empirical interaction potentials, we search for weakly bound states of (4)He(2) H(-), (4)He(2) H, and (4)HeH(2). We consider not only zero total nuclear orbital angular momentum, J=0, states but also J>0 states. We find no bound state for the (4)He(2) H systems, while the (4)He(2) H(-) and (4)HeH(2) systems are shown to possess three and one bound states, respectively, for J(Pi)=0(+). Interestingly, one bound state has been found each for the J(Pi)=1(-) and 2(+) symmetries of the (4)He(2) H(-) anion. We shall calculate the bound state energies and analyze the molecular structure of these species in detail.

Calculation of argon trimer rovibrational spectrum

Rovibrational spectra of Ar3 are computed for total angular momenta up to J=6 using row-orthonormal hyperspherical coordinates and an expansion of the wave function on hyperspherical harmonics. The sensitivity of the spectra to the two-body potential and to the three-body corrections is analyzed. First, the best available semiempirical pair potential (HFDID1) is compared with our recent ab initio two-body potential. The ab initio vibrational energies are typically 1-2 cm-1 higher than the semiempirical ones, which is related to the slightly larger dissociation energy of the semiempirical potential. Then, the Axilrod-Teller asymptotic expansion of the three-body correction is compared with our newly developed ab initio three-body potential. The difference is found smaller than 0.3 cm-1. In addition, we define approximate quantum numbers to describe the vibration and rotation of the system. The vibration is represented by a hyper-radial mode and a two-degree-of-freedom hyperangular mode, including a vibrational angular momentum defined in an Eckart frame. The rotation is described by the total angular momentum quantum number, its projection on the axis perpendicular to the molecular plane, and a hyperangular internal momentum quantum number, related to the vibrational angular momentum by a transformation between Eckart and principal-axes-of-inertia frames. These quantum numbers provide a qualitative understanding of the spectra and, in particular, of the impact of the nuclear permutational symmetry of the system (bosonic with zero nuclear spin). Rotational constants are extracted from the spectra and are shown to be accurate only for the ground hyperangular mode.

Incorporating the Geometric Phase Effect in Triatomic and Tetraatomic Hyperspherical Harmonics

Hyperspherical harmonics in the democratic row-orthonormal hyperspherical coordinates are very appropriate basis sets for performing reactive scattering calculations for triatomic and tetraatomic systems. The mathematical conditions for incorporating the geometric phase effect in these harmonics are given. These conditions are implemented for triatomic systems, and their explicit analytical expressions in terms of Jacobi polynomials, in both the absence and presence of the geometric phase effect, are given.

On the (E⊗e)-Jahn-Teller conical intersections in the 3p(E′) and 3d(E″) Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.

A Quantum Wave Packet Dynamical Study of the Electronic and Spin−Orbit Coupling Effects on the Resonances in Cl(2P) + H2 Scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.

Symmetry properties of rovibronic states of an X(3) molecule in an upright conical potential

The rovibronic structure of cone states of an X3 type molecule is investigated to provide a detailed understanding of the effect of the geometrical phase. When compared to the rovibronic structure of a system in which no geometrical effect is present, a dramatic duplication of the number of rotational levels (k not equal 0) is observed for certain vibrational states (l=0) including the vibrational ground state. Rotational structure may serve as a diagnostic tool to detect the presence of a conical intersection.