Accuracy benchmark

For the purpose of high-accuracy benchmarking, not all CCSD(T) computations are of equal accuracy. Just as in any electronic structure computation, the choice of one-particle basis set matters. 

Janowski, T, and Pulay, P. (2007). High accuracy benchmark calculations on the benzene dimer potential energy surface, Chem. Phys. Lett. 447, pp. 27-32. 

One sees that the two methods are complimentary. In fact, one major application of numerical calculations is to calibrate basis sets for determination of properties in situations where the relevant experience is lacking. A recent example involves testing new (unfamiliar) operators for spin densities (very sensitive to basis set). Another major application is the generation of very high accuracy benchmarks which can be used to analyze the accuracy and convergence properties of other methods. Numerical methods are highly unlikely ever to supplant BSE methods, even if completely satisfactory polyatomic HF methods eventually are developed. However,... 

Finally, we should mention that experimental data serving as a benchmark for the appraisal of computational methods must be highly accurate. Setting the goal of 2 kcal/mol for useful accuracy of calculated thermochemical data means of course, that a still better level of accuracy must be reached by experimental measurements. The high accuracy of... 

ONIOM can combine two MO levels like ONIOM(QM QM), which is a unique feature that is not available to QM/MM methods. However, the most popular combination is ONIOM(QM MM), combining QM with MM. This is essentially equivalent to generic QM/MM. However, there are some subtle cancellation or double-counting differences for the case where a covalent bond is cut. For this, we refer to a detailed discussion published elsewhere [8], QM MM or QM/MM applications have typically been used without appropriate accuracy or S-value tests, as the benchmark full QM calculation for the real system is often impossible. In Section 2.2.2, we will examine one such test in detail. 

The first benchmark of a QSAR model is usually to determine the accuracy of the fit to the training data. However, because QSAR models are often used for predicting the activity of compounds that have not yet been synthesized, the most important statistical measures are those giving an indication of their prediction accuracy. Common methods to test QSAR predictivity are listed below. 

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. 

Inner-shell correlation is a substantial part of the absolute correlation energy even for late first-row systems for second-row systems, it in fact rivals the absolute valence correlation energy in importance. However, its relative contribution to molecular TAEs is fairly small in benzene, for instance, it amounts to less than 0.7 % of the TAE. Even so, at 7 kcal/mol, its contribution is important by any reasonable thermochemical standard. By the same token, a 1 % relative error in a 7 kcal/mol contribution is tolerable even by benchmark thermochemistry standards, while the same relative error in a 300 kcal/mol contribution would be unacceptable even by the chemical accuracy standards. 

The importance of scalar relativistic effects for compounds of transition metals and/or heavy main group elements is well established by now [44], Somewhat surprisingly (at first sight), they may have nontrivial contributions to the TAE of first-row and second-row systems as well, in particular if several polar bonds to a group VI or VII element are involved. For instance, in BF3, S03) and SiF4, scalar relativistic effects reduce TAE by 0.7, 1.2, and 1.9kcal/mol, respectively - quantities which clearly matter even if only chemical accuracy is sought. Likewise, in a benchmark study on the electron affinities of the first-and second-row atoms [45] - where we were able to reproduce the experimental values to... 

Having verified the accuracy of the composite IRCMax CBS-QCI/ APNO QCISD/6-311G(d,p) method through comparison with experiment, we then employed these calculations as benchmarks to determine the accuracy of the less demanding CBS-4M and CBS-QB3 models. We employed six reactions [40],... 

The results of this study are somewhat atypical in the sense that the inferred re and tq structures of Sis are nearly the same. This is a somewhat fortuitous circumstance, which cannot be attributed entirely to the fact that Sis appears to be only weakly anharmonic (see cubic constants in Table I), since it has a relatively low-frequency bending mode that is potentially problematic. Nonetheless, it can be stated with some certainty that the structure obtained in the present research is accurate to within 0.002A and 0.2 . Hence, this structure can be used as a reference for benchmarking quantum chemical methods intended for high accuracy calculations on silicon clusters, as well as for comparison with structures of other silicon-containing molecules. 

Fig. 2. This figure shows the electronic energy of the ground state of H2 molecule, calculated in a crude approximation using only one configuration. The benchmark calculation of Kolos and Wolniewicz is exhibited for comparison. Accuracy can be seen to be improved by using more atomic orbitals even when a rough approximation is used for the interelectron repulsion matrix element.

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