W e compare the performance of seven methods in computing or approximating service levels for nonstationary M t /M/s t queueing systems: an exact method (a Runge-Kutta ordinary-differential-equation solver), the randomization method, a closure (or surrogate-distribution) approximation, a direct infinite-server approximation, a modified-offered-load infinite-server approximation, an effective-arrival-rate approximation, and a lagged stationary approximation. We assume an exhaustive service discipline, where service in progress when a server is scheduled to leave is completed before the server leaves. We used all of the methods to solve the same set of 640 test problems. The randomization method was almost as accurate as the exact method and used about half the computational time. The closure approximation was less accurate, and usually slower, than the randomization method. The two infinite-server-based approximations, the effective-arrival-rate approximation, and the lagged stationary approximation were less accurate but had computation times that were far shorter and less problem-dependent than the other three methods.

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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.

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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.

High resolution electronic spectroscopy and an empirical potential energy surface for NeSH/D J. Chem. Phys. 110, 5065 (1999); 10.1063/1.478395High resolution electronic spectroscopy of KrOH/D and an empirical potential energy surface Experimental data from vibrationally and rotationally resolved laser induced fluorescence experiments have been used to produce potential energy surfaces ͑PES͒ for the excited à 2 ⌺ ϩ states of the Ar•SH and Kr•SH van der Waals complexes. This was done using a potential energy functional form first suggested by Bowman and co-workers ͓J. Phys. Chem. 94, 2226, 8858 ͑1990͒; Chem. Phys. Lett. 189, 487 ͑1992͔͒ for Ar•OH/D. A discrete variable representation ͑DVR͒ of the vibration-rotation Hamiltonian was used in combination with the implicitly restarted Lanczos method and sequential diagonalization truncation ͑SDT͒ of the DVR Hamiltonian. This approach takes advantage of the sparseness of the DVR Hamiltonian and the reduced order of the SDT representation. This combination of methods greatly reduces the amount of computational time needed to determine the eigenvalues of interest. This is important for the determination of the PES that results from minimizing the difference between the experimental and theoretically predicted values for the vibronic energy levels and their corresponding rotational constants. In addition this procedure was helpful in assigning the absolute vibrational quantum numbers for the deuterated species for which less experimental data was available. Plots of the calculated wavefunctions corresponding to various experimentally vibronic bands indicate that these states sample regions of the PES from 0 degrees, where the hydrogen atom is closest to the rare gas atom, to approximately the saddle point, near the T-shaped configuration. As a result this region of the surface is determined accurately whereas the region of the PES around 180 degrees, corresponding to the sulfur atom being closest to the rare gas atom, is determined only qualitatively.

We present a method for including the geometric phase in quantum reactive scattering computations based on the log derivative version of the Kohn variational principle. A new variational functional is developed which includes the influence of the geometric phase through modifications in the momentum operators. The system investigated is a two-dimensional reactive scattering model which includes the vector potential induced by the magnetic field of an infinitely long solenoid. The coordinates used in this model are analogous to Jacobi coordinates used in atom–diatom systems. Some interesting features of this study include the gauge invariance of the scattering probabilities, symmetry adaptation of the wave function, and the behavior of the probability density in the presence of the geometric phase.

Results of a six-dimensional treatment of the rotation–vibration Hamiltonian for (HF)2 are presented. Energies of 40(J+1) states for J⩽4 are reported. These energies and the corresponding wave functions are used to analyze rotation–vibration interactions in (HF)2. Over the range of energies probed in this study, Coriolis couplings are found to be relatively unimportant and for 94% of the states the wave functions and energies can be approximated by the solutions to a Hamiltonian in which the Coriolis coupling terms are neglected. Rotation–vibration interactions are investigated in greater detail for the ground state and for states with one and two quanta of excitation in the intermolecular stretching vibration ν4. Specifically, we study the K and n4 dependencies of the tunneling splitting and the effective rotational constant that corresponds to rotation about the intermolecular axis. Based on an analysis of the wave functions and the potential, we find that the observed trends can be attributed to the fact that (HF)2 behaves like a quasilinear molecule whose large amplitude bending motions lead to significant wave amplitude in linear configurations, even in the vibrational ground state.