Publications

"Quantum Reactive Scattering in Three Dimensions. Using Tangent-Sphere Coordinates to Smoothly Transform from the Hyperspherical to Jacobi Regions.'' 

G. A. Parker, Mark Keil, Michael A. Morrison and Stefano Crocchianti, 

J. Chem. Phys. 113 , 957-970 (2000).

  064 TangentSphere.pdf

Abstract: Hyperspherical coordinates are well suited for treating rearrangement processes in the strong interaction region, and several different hyperspherical coordinates have been used successfully for quantum reactive scattering by various research groups. However, it is well known that asymptotically the appropriate set of coordinates for a three particle system! are the three sets of Jacobi coordinates. In this paper we show how one can smoothly connect the hyperspherical coordinates in the rearrangement region to Jacobi coordinates in the nonrearrangement region using tangent-sphere coordinates. This procedure reduces the computational time required to solve the quantum Schrodinger equation and eliminates the need for numerical projection. To illustrate this method, we apply it to the F+H ₂ --> HF+F reaction, comparing reaction probabilities to those from previous benchmark calculations based on a conventional formulation.

G. A. Parker, S. Crocchianti and M. Keil, 

Lagana, A. and Riganelli A. Eds., Lecture Notes in Chemistry, 75, 88 (2000).

063 LectureNotes.pdf

Abstract:  Quantum reactive scattering or rearrangement processes continues to be of considerable theoretical and experimental interest. A review of our Adiabatically-adjusting, Principal Axes Hyperspherical (APH) coordinates method will be presented. Basis functions defined as a product of Wigner rotation matrices times surfaces functions will be defined. We will briefly describe four methods for obtaining accurate surface functions and give relative merits of each. The surface functions methods are:  Finite Element Method (FEM)  Discrete Variable Representation (DVR) Analytic Basis set Method (ABM)  Distributed Approximating Functions (DAF) Our choice of product basis functions give rise to a set of second-order differential equations. We will outline the solution to these equations and present a new method for smoothly transforming from hyperspherical to Jacobi coordinates outside the rearrangement region. This new procedure eliminates the two dimensional projection used previously. We will demonstrated that Quantum resonances are important for some rearrangement processes. We also argue that it is important for theoreticians to properly model the experimental parameters for a complete comparison with experiment.

"On the Effect of Increasing the Total Angular Momentum on Li+HF Reactivity.''

Antonio Lagana, Alessandro Bolloni, Stefano Crocchianti and Gregory A. Parker

Chem. Phys. Lett. 324, 466-474 (2000).

062 LiFHReactivity.pdf

Abstract:  The effect of increasing the total angular momentum J on the value of the reaction probability has been investigated theoretically using exact quantum calculations. The contribution of higher J probabilities to the calculated value of the cross-section has been treated as a correction to its J-shifting model formulation. Two interesting features of the calculated  . cross-section have been evidenced in this way: a as more exact quantum contributions are added to the calculation, the  . agreement between theory and experiment improves; b the resonance structure characterizing low-energy probabilities survives the averaging over partial waves.

"Symmetry Adapted Distributed Approximating Functionals: Theory and Application to the ro-vibrational states of H₃⁺.''

S. S. Iyengar, G. A. Parker, D. J. Kouri, and D. K. Hoffman 

J. Chem. Phys., 110, 10283-10298, (1999).

059 SADAF.pdf

Abstract:  Symmetry-adapted Distributed Approximating Functionals ~SADAFs! are derived and used to obtain a coordinate representation for the Adiabatically Adjusting Principal Axis Hyperspherical ~APH! coordinates kinetic energy operator. The resulting expressions are tested by computing ( J 50) ro-vibrational states for the well-studied H 3 1 molecular ion system, by iterative diagonalization of the Hamiltonian matrix using the Arnoldi procedure. The SADAF representation and APH coordinate system are found to be computationally robust and accurate.

"The Quantum Threshold Behavior of the Na+HF Reaction.''

R. Gargano, S. Crocchianti, and A. Lagana, 

J. Chem. Phys., 108}, 6266-6271, (1998).

058 NaHF.pdf

Abstract:  Full three dimensional quantum calculations of reactive properties of the Na1HF system have been performed at zero total angular momentum (J50) to investigate the energy dependence of the reactive probability of this reaction. The effect of increasing the vibrational excitation of reactants is also discussed.