Benchmark Geometries Research Articles

Two approximate solutions for the 3-D field in the ASA benchmark wedge

One of the current challenges to the underwater acoustics 3-D numerical modeling community is the development of benchmark geometries and solutions. Benchmark solutions to canonical problems provide a reference against which numerical models can be compared, as well as providing insight into regions or frequency regimes where the models fail. The 3-D penetrable wedge is a good candidate for a benchmark geometry because it corresponds to real-world environments (beaches and continental slopes), is tractable to a variety of numerical modelers, and has been studied analytically. Although there is no exact analytical solution available for the penetrable wedge, several approximate solutions have been developed, which may be regarded as secondary benchmarks. The results from 2 of these models for the 3-D extension of the ASA wedge benchmark will be presented.

The penetrable wedge as a three-dimensional benchmark

In 1989, members of the Acoustical Society of America developed a suite of range-dependent benchmark geometries, allowing the underwater acoustics community to compare the performance of analytical and numerical solutions to two-dimensional propagation problems. These benchmarks were successful in providing the acoustics community with a set of standards, and continue to be useful as reference geometries. Over the past decade, there have been significant advances in analytical and numerical solutions to three-dimensional propagation problems, and establishing three-dimensional benchmarks is a timely development. A useful benchmark must eliminate the undesired complications of a real-word environment but retain the essential physics of the problem while being tractable to a variety of modelers. A geometry which satisfies these constraints is the ocean wedge with a penetrable basement. The three-dimensional Green’s function for the penetrable wedge has already been studied by a number of investigators, and measured with scale-model tank experiments. The state of modeling and measurement for the wedge will be discussed in the context of its usefulness as a three-dimensional benchmark.

Structures and vibrational frequencies in the full configuration interaction limit: Predictions for four electronic states of methylene using a triple-zeta plus double polarization (TZ2P) basis

Benchmark energies, geometries, dipole moments, and harmonic vibrational frequencies are determined for four states of methylene (CH2) by solving the electronic Schrödinger equation exactly for a triple-ζ plus double polarization (TZ2P) basis with the restrictions that the core orbital remains doubly occupied and the highest-lying virtual orbital is deleted. Approximate models of electron correlation are evaluated based on their ability to match the exact, full configuration interaction results. Predictions from configuration interaction with all single, double, triple, and quadruple substitutions (CISDTQ) and coupled-cluster including singles, doubles, and triples (CCSDT) are virtually identical to the full CI results for all but the c̃ 1A1 state, which is poorly described by a single-configuration reference. In agreement with previous work, the c̃ state remains slightly bent at the TZ2P full CI level of theory, with a bond angle of 170.1° and a barrier to linearity of only 25 cm−1.

Full Configuration Interaction Energies, Geometries, and Quartic Force Fields of the Nitrenium Ion

Benchmark configuration interaction energies, geometries, dipole moments, and harmonic vibrational frequencies are obtained for four low-lying electronic states of NH2+ and for X2B1 NH2 by solving the electronic Schrodinger equation exactly within a double-ζ plus polarization (DZP) basis set and restricting the nitrogen 1s-like core orbital to remain doubly occupied. In addition, full quartic force fields have been determined, and sets of anharmonic spectroscopic constants and fundamental frequencies are reported for the ã 1A1 state of NH2+. Vertical and adiabatic ionization potentials of NH2 are also determined exactly within a DZP basis. The capability of less-complete electron correlation treatments to match these exact, full configuration interaction (full CI) results is assessed. The efficacy of obtaining anharmonic force fields at nonstationary geometries is also examined, and in agreement with previous work, it is found that the self-consistent field method can provide high quality cubic and quartic force constants when they are evaluated at the full CI equilibrium geometry. Both the CCSD(T) and CASSCF-SOCI methods provide geometric and spectroscopic data in excellent agreement with the Full CI results and are competitive in their reliability with more expensive procedures (e.g. CISDTQ). The second 1A1 state in C2v symmetry is predicted by the TZ2P(f,d) CASSCF-SOCI wavefunction to be linear (thus properly labeled as c1Σg+), even though it is found to be quasilinear at the DZP full CI level.

Full configuration interaction benchmarks for the ?3B1, ã 1A1, ? 1B1 and ? 1A1 states of methylene

Abstract Previous experimental and theoretical work on the four lowest lying electronic states of methylene is summarized and new benchmark energies, geometries, dipole moments and harmonic vibrational frequencies are obtained by solving the electronic Schrodinger equation exactly, given a double-ζ plus polarization (DZP) basis set and restricting the core orbital to remain doubly occupied. These full configuration interaction (CI) results are used to evaluate several approximate treatments of electron correlation. The predictions of a CI procedure including all single, double, triple and quadruple excitations (CISDTQ) are virtually identical to the full CI results for all but the c 1 A 1 state, which is the second state of its symmetry and as such is difficult to describe using standard single-reference methods.

Full configuration interaction benchmarks for the [formula omitted] states of methylene

Previous experimental and theoretical work on the four lowest lying electronic states of methylene is summarized and new benchmark energies, geometries, dipole moments and harmonic vibrational frequencies are obtained by solving the electronic Schrödinger equation exactly, given a double-ζ plus polarization (DZP) basis set and restricting the core orbital to remain doubly occupied. These full configuration interaction (CI) results are used to evaluate several approximate treatments of electron correlation. The predictions of a CI procedure including all single, double, triple and quadruple excitations (CISDTQ) are virtually identical to the full CI results for all but the c ̃ 1A 1 state, which is the second state of its symmetry and as such is difficult to describe using standard single-reference methods.

Determination of stress intensity factors for Battelle Benchmark geometries

The finite element method is applied to a series of three dimensional cracked configurations as proposed at the Three Dimensional Fracture Analysis Workshop at Battelle Columbus, in 1976. Results for these cases are presented showing crack opening displacements and stress intensity factors around the crack profiles, derived using several methods, for values of Poisson's ratio equal to both 0.3 and 0.49. The semicircular crack mesh was also applied to the embedded circular crack problem, for which an analytical solution exists, and agreement within 1% and 3% was obtained for Poisson's ratio equal to 0.3 and 0.49 respectively, demonstrating the accuracy of the chosen meshes and evaluation techniques.