Benchmark quality

Pressurised pipes for water and gas provide an example of design lives being predicted with confidence on the basis of a large assembly of data, of benchmark quality control tests for existing products, and of two-parameter accelerated testing for new ones. Some types of pipe are particularly sensitive to pressure extremes. Lifetime prediction cannot however take into account poor installation conditions. 

Methods for Benchmark Quality Ab Initio Thermochemistry—W1 and W2 Theory. 

J. M. L. Martin and G. de Oliveira, Towards standard methods for benchmark quality abinitio thermochemistry-W1 and W2 theory../. Chem. Phys. Ill, 1843-56(1999). 

J.M.L. Martin, RR. Taylor, Benchmark quality total atomization energies of small polyatomic molecules,. Chem. Phys. 106 (20) (1997) 8620-8623. 

Harding, M. E. Gauss, J. Schleyer, P. v. R. Why benchmark-quality computations are needed to reproduce 1-adamantyl cation NMR chemical shifts accurately, 7. Phys. Chem. A, 2011,115, 2340-2344. 

Jurecka et al have published a database of accurate benchmark quality interaction energies of small model complexes, DNA base pairs, and amino acid pairs obtained from MP2 and CCSD(T) calculations together with estimates of the complete basis set limit. They examine interaction energies and geometries for more than 100 DNA base pairs, amino acid pairs and model complexes. Extrapolation to the complete basis set limit was carried out by these researchers using a two-point method in conjunction with correlation consistent basis sets. 

Direct comparison of force fields to benchmark-quality CCSD(T) energies is complicated by the fact that most standard, workhorse force fields do not include polarization terms. This leads to errors, but these errors can be partially compensated by other errors. Hence, a force field that compares poorly to CCSD(T) benchmarks for a set of van der Waals dimers may still perform fairly well for condensed-phase properties, due to error cancellation. This is the rationale for obtaining atomic charges in the AMBER force field using restrained electrostatic potential (RESP) fitting (Bayly, 1993) to modest-quality Hartree-Fock/6-31G quantum chemical computations this method tends to overestimate dipole moments, but this is considered beneficial for simulations in water, to approximately cancel errors from neglecting polarization effects... 

J.M.L. Martin andG.de Oliveira, Towards standard methods fior benchmark quality ab initio thermochemistry—W1 andW2 theory, J. Chon. Phys. Ill (1999), pp. 1843-1856. 

Martin JML, de Oliveira G. Towards standard methods for benchmark quality ab initio thermochemistry. J Chem Phys. 1999 111 1843-56. 

A scheme to calculate frequency-dependent first hyperpolarizabilities for general CC wavefunctions (CCSD, CC3, CCSDT, and CCSDTQ) has been presented by O Neill et al This analytical third derivative scheme exploits the similarities between response theory and analytic derivative theory. Illustrations have first confirmed that the inclusion of higher-than-double excitations is essential for a quantitative description of the first hyperpolarizabilities. Moreover, the CC3 approximation has been seen to provide good results for singly-bonded systems, with little multireference character, but that full triples contribution using CCSDT are required for benchmark quality results on other systems. Representative results of ref. 18 are given in Table 1. 

In common parlance, the word calibration calculation has come to acquire both meanings high-accuracy calculations on fairly small systems pursued in order to (i) gauge the accuracy of less accurate, but more economical, methods and obtain an estimate of residual error (ii) obtain results of benchmark quality in their own right. 

The importance of the former can hardly be overestimated indeed, calibration calculations comparing some new approximate method with experiment or benchmark quality calculations are the staple of any methodological paper. Now what would qualify a calculation as of benchmark quality ... 

Mere chemical accuracy (commonly defined as 1 kcal mol on total atomization energies) obviously does not qualify. Nor does the circumstance that a calculation represents the maximum in terms of computational feasibility at any point in time qualify a calculation in and of itself as of benchmark quality otherwise, crude minimal-basis set ab initio calculations on large peptides would qualify. Besides, the horizon of the computationally affordable moves so rapidly that today s tour de force is tomorrow s routine. 

We will arbitrarily define benchmark quality calculations here as those yielding results so accurate that they are generally more reliable than experiment. In the course of the article, we will focus on three principal properties total atomization energies (TAEs, Y,De values), geometries and related properties (such as rotational constants), and vibrational frequencies. We will show that it is presently possible, for small polyatomics, to obtain total atomization energies correct to 1 kJ mol (0.24 kcal mol ) on average, geometries to 0.001 A or better, and fundamental frequencies to a few cm . ... 

For instance, the quantum chemical literature is full of comparisons between computed harmonic frequencies and observed fundamental ones. While this may be acceptable in situations where an anharmonic force field calculation (see Anharmonic Molecular Force Fields) is technically impossible, the anharmonicity a>i — v, of a fundamental may easily range from 2 to 200 cm- and therefore such a comparison is essentially meaningless for benchmark quality results. Yet for polyatomics, the experimentally derived harmonic frequencies are often associated with large uncertainties (cf. the C2H4 example at the end of this article) due to indeterminacies, and often the only meaningful comparison will be between computed and observed fundamentals, requiring the ab initio calculation of the anharmonic part of the force field. 

For our reference sample, the mean absolute error is 1.32 kcal mol on the values. An improved version of the scheme known as G2M(RCC) brings down the mean absolute error to 0.82 kcal mol While this definitely qualifies as chemical accuracy, it does not pass muster as benchmark quality . 

The above results clearly illustrate that benchmark quality calculations on small poly atomics are definitely feasible. 

Coupled cluster, configuration interaction, and other correlated ab initio methods Small organic and inorganic molecules About ten atoms Structures and binding energies High computational effort, benchmark quality results, systematic (but slow) convergence towards exact solution... 

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