A new hybrid numerical technique which utilizes both the DVR (Discrete Variable Representation) and FBR (Finite Basis Representation) to solve for the full 5D surface functions in the three-atom problem in hyperspherical coordinates for nonzero total angular momentum (J≠0) is reported. This method accurately treats the Eckart singularities in the kinetic energy operator which occur at both the north pole and equator of the 2D hypersphere in body-frame coordinates. The effects of the Eckart singularities on the surface function energies for HD2 are investigated and it is shown that an accurate treatment of these singularities is crucial in order to obtain the correct results. An improper treatment of the Eckart singularities could be a source for some of the discrepancies between recent experimental results and theory for the reaction H+D2→HD+D.

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An efficient parallel algorithm is reported for determining all bound rovibrational energy levels for the HO 2 molecule for nonzero angular momentum values, Jϭ1, 2, and 3. Performance tests on the CRAY T3D indicate that the algorithm scales almost linearly when up to 128 processors are used. Sustained performance levels of up to 3.8 Gflops have been achieved using 128 processors for J ϭ3. The algorithm uses a direct product discrete variable representation ͑DVR͒ basis and the implicitly restarted Lanczos method ͑IRLM͒ of Sorensen to compute the eigenvalues of the polyatomic Hamiltonian. Since the IRLM is an iterative method, it does not require storage of the full Hamiltonian matrix-it only requires the multiplication of the Hamiltonian matrix by a vector. When the IRLM is combined with a formulation such as DVR, which produces a very sparse matrix, both memory and computation times can be reduced dramatically. This algorithm has the potential to achieve even higher performance levels for larger values of the total angular momentum.

Articles you may be interested inCross sections and rate constants for OH + H2 reaction on three different potential energy surfaces for rovibrationally excited reagents J. Chem. Phys. 135, 194302 (2011); 10.1063/1.3660222 Predicting observables on different potential energy surfaces using feature sensitivity analysis: Application to the collinear H+H2 exchange reaction J. Chem. Phys. 97, 6240 (1992); 10.1063/1.463685 Distributed complex Gaussian basis sets: A useful function space for the solution of predissociation problems via the complex eigenvalue Schrödinger equation. Application to the isotope effect of NeH, NeD J. Chem. Phys. 93, 6642 (1990); 10.1063/1.458932 Potential energy surface for the collinear reaction of Ne and HeHThree different functional forms are fit to a calculated coupled electron pair approach potential energy surface for the reaction Ne+Ht ..... NeH+ +H. Minimum energy pathways and stationary points of the various fits are discussed.represents the H-H distance.

Recently, Klemperer, et al,,2-4 have used the electric quadrupole deflection of molecular beams to detect molecules possessing permanent dipole moments.

Theoretical studies of the reactivity and spectroscopy of H+CO=HCO. I. Stabilization and scattering studies of resonances for J=0 on the Harding a b i n i t i o surfaceThe bending-corrected rotating linear model (BCRLM) is used to investigate the reaction of neon with Hi (v=0-3) using three different fits to the ab initio potential-energy surface computed by Urban, Jaquet, and Staemmler. Numerous long-liy~d scattering resonances are found for each surface. The number and position of these scattering resonances are found to be sensitive to the relatively small differences among these three surfaces. These BCRLM results demonstrate how the rich resonance structure that appears in the partial cross sections is washed out in the total cross section. The integrated rates for reactivity from v=O and 1 are nearly identical for all three potential-energy surfaces over a wide range of temperatures. However, the integrated rates from v=2 and 3 exhibit significant differences among the potential-energy surfaces. A vibrationally adiabatic hyperspherical model of the trapped resonance states provides insight into the nature and contribution of these resonances to reactive scattering. The more accurate of the three fits to the ab initio potential-energy surface (obtained using the functional form of Aguado and Paniagua) is also used to obtain converged results for total angular momentum J=O employing the adiabatically adjusting, principal axis, hyperspherical (APH) formulation of Pack and Parker for quantum reactive scattering in three dimensions (3D). An eigenlifetime analysis of these 3D scattering results reveals numerous resonances with lifetimes of 1 ps or more. While this resonance structure is sensitive to the details of the potential energy surface, with appropriate Gaussian averaging over the total scattering energy, the cumulative reaction probabilities (CRPs) are not very sensitive to changes in the potential energy surface. Moreover, these quantum CRPs agree rather well with CRPs predicted using variational Rice-Ramsperger-Kassel-Marcus (RRKM) calculations.2728

Nonempirical LCAO MO SCF calculations are reported for the ground, C 2 " states of the Group IIa dihalides, BeF 2 , MgF2' and CaF 2 . These calculations demonstrate the importance of 3d orbitals in the bonding trends of the dihalides and, hence, in the determination of the equilibrium bond angles and the bending force constants. The calculations on BeF 2 indicate that d orbitals play an important role in the bonding but do not preferentially alter the general features of the total energy curve at any bond angle. In the case of MgF2' d orbitals are found to preferentially lower the energy of the nonlinear configurations. However, for both species, the ground-state equilibrium bond angle is predicted to be 180°. Configuration interaction studies also support the fact that, in the gas phase, the linear configuration is most stable. On the basis of s (1 s, 2s, 3s, 4s, 2p, and 3p orbitals on Ca) basis set calculations, it is predicted that CaF2 is linear. However, when 3d orbitals are added to the s basis set, the predicted equilibrium bond angle is 145°. This is in good agreement with the value of 141° deduced from matrix-isolation spectroscopy. The bonding in these molecules is discussed with reference to the nonempirical molecular correlation diagram.

The discrete variable representation (DVR) method has been modified in three major ways to produce a more efficient scheme for calculating the rotational−vibrational energies of van der Waals molecules. First, the implicitly restarted Lanczos method (IRLM) of Sorensen (SIAM J. Matrix Anal. Appl. 1992, 13, 357) is used to determine the eigenpairs of interest. Second, Chebychev polynomial preconditioning is applied to make it easier to project out unwanted eigenfunctions and thus speed up the convergence of the IRLM. Finally, a very efficient matrix−vector algorithm is introduced that makes maximum use of the underlying sparsity of the DVR Hamiltonian. Calculations for a protypical system Ar−HCl are reported. For the 20 lowest Ar−HCl eigensolutions corresponding to angular momentum J = 1 and using only a single processor of a Cray YMP, the modified DVR approach is about 6 times faster than the original DVR method and 14 times faster than the collocation method of Peet and Yang (J. Chem. Phys. 1989, 91, 6598). As the total angular momentum is increased, the relative performance of the modified DVR approach improves dramatically. For instance, with J = 5 the modified method is about 45 times faster than the original DVR and 100 times faster than the collocation method on a single processor of a Cray YMP. This modified DVR approach also runs significantly faster on a range of workstations such as DEC Alpha and the IBM RS/6000. Application of this method is also shown to be effective in obtaining an improved interaction potential for the A 2Σ+ state of Ar−HO.