Benchmarking Results

A considerable number of methods showed results not significantly different from the AAM model, i.e. these methods failed to provide predictive models. 

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Quantum mechanical effects—tunneling and interference, resonances, and electronic nonadiabaticity— play important roles in many chemical reactions. Rigorous quantum dynamics studies, that is, numerically accurate solutions of either the time-independent or time-dependent Schrodinger equations, provide the most correct and detailed description of a chemical reaction. While hmited to relatively small numbers of atoms by the standards of ordinary chemistry, numerically accurate quantum dynamics provides not only detailed insight into the nature of specific reactions, but benchmark results on which to base more approximate approaches, such as transition state theory and quasiclassical trajectories, which can be applied to larger systems. 

Manganese (IV) oxide enjoys numerous applications in modem technologies. The most widely known areas of its usage are sorption processes one could recall that co-precipitation of contaminating cations with manganese oxide is still employed as part of the in-tank precipitation in processes of treatment of supernatant wastes at high concentration. Furthermore, co-precipitation data are usually used as benchmark results in studies of novel sorbents for strontium [4],... 

If affordable, there is a range of very accurate coupled-cluster and symmetry-adapted perturbation theories available which can approach spectroscopic accuracy [57, 200, 201]. However, these are only applicable to the smallest alcohol cluster systems using currently available computational resources. Near-linear scaling algorithms [192] and explicit correlation methods [57] promise to extend the applicability range considerably. Furthermore, benchmark results for small systems can guide both experimentalists and theoreticians in the characterization of larger molecular assemblies. 

The development of these explicit-rjj methods has yielded a database of benchmark results for small polyatomic molecules. These calculations are listed as MP2-R12 and CCSD(T)-R12 in our tables. We have selected the version called MP2-R12/A as a benchmark reference for our study of the convergence to the MP2 limit. This is the version that Klopper et al. found to agree best with our interference effect. The close agreement with extrapolations of one-electron basis set expansions justifies this choice. 

A. Silane a-Complexes. A Short Historical Overview of Benchmark Results.. 219... 

We consider a situation where two single bonds are simultaneously broken, modelled by symmetrically stretching the two OH bonds in H2O molecule. As we did before, two spaces have been considered, [4e/4o] and [8e/7o], The bonds are stretched up to twice the equilibrium distance Re, and the results are compared to FCI as benchmark. Results are collected in Table 2. 

The initial benchmark results obtained with the full CCSD-R12 method [34] testified that the various simplified CCSD-R12 methods reported earlier were highly accurate approximations to the full CCSD-R12 method unless the basis set was too small. The assumptions about the relative importance of diagrammatic terms made in these simplified methods were proven to be valid. However, these neglected terms do not increase the computational cost scaling of CCSD-R12 and there appears no need to eliminate them from full CCSD-R12, once they are implemented. In other words, it is important to distinguish whether a certain approximation is motivated by a compromise between accuracy and the computational cost or by that between accuracy and the development cost. The latter has become increasingly unjustifiable with the advent of computerized derivation and implementation. 

As already discussed, the optimum catalyst efficiency is obtained for a N02/NOx ratio of 50%. The ESC and ETC simulation outputs for these input conditions can be regarded as a benchmark result, disregarding the NH3 slip. The comparison with the baseline simulation without N02 in Fig. 54 reveals that N02 improves the SCR efficiency significantly. The total conversion efficiency is increased from 90.7% to 94.0% for the ESC and from 87.5% to 94.9% for the ETC, cf. Table VII. The improvements can mainly be attributed to the higher conversion rates in the colder parts of the test cycles (e.g., 850s-l, 000s in the ESC). 

MH Locke, "The ASPEN PLUS Pressure Relief System Technical Details and Benchmark Results", Attachment 69 Minutes of 17th DIERS Users Group Meeting, Orlando, January 1995... 

The development of TDDFT has shown that, in order to obtain better results, getting closer to the accurate xc potential vxca is relatively more important than better modeling of the xc kernel/ 1. Some benchmark results have been obtained in [24], where an essentially accurate vxc constructed numerically from the ab initio (Cl) density p for some closed-shell prototype sys-... 

Nonsequential double and multiple ionization are to a large part classical phenomena. Indeed, the S-matrix approach suggests a pertinent classical limit. We have summarized evidence that the latter reproduces the fully quantum-mechanical results very well in parameter regions where this can be expected. Finally, we have extended such classical avenues to a statistical description of nonsequential triple and quadruple ionization. For neon, such a classical statistical model yields a fair description of the available data. While a more microscopic description of these extremely involved phenomena lies in the future, we believe that the simple models summarized in this paper will remain valuable as benchmark results. 

Mardirossian, N. Parkhill, J. A. Head-Gordon, M. Benchmark results for empirical post-GGA functionals difficult exchange problans and independent tests, Phys. ChertL Chem. Phys. 2011,13, 19325-19337. 

Cotta, R.M., and Mikhailov, MD. (2001) Hybrid Approaches in Convective Heat Transfer, in Benchmark Results for Convective Heat Transfer in Ducts - The Integral Transjorm Approach, eds. C.A.C. Santos, J.N.N. Quaresma, and J.A. Lima, ABCM Mechanical Sciences Series, Editora E-Papers, Rio de Janeiro, Part 1, Chapter II, pp. 17-38. 

Ejt = l,463cm ) are considered to be benchmark results for the determination of the JT parameters. They also identitied three dominant normal modes necessary to explain their results. These were recently confirmed by Stanton et al. using Equation-of-motion ionization potential coupled-cluster (EOMIP-CCSD) calculations [45]. Thus, this system is a good test case for both our multideterminental DFT approach in studies of the JT effect and for our model of the analysis of the multimode JT effect. 

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