Computational benchmarking

It is not always possible to classify a computational study of chiroptical properties as purely theoretical, solely of benchmarking character (e.g., testing basis sets, or comparing electronic structure methods), or as being only of the applications type where an established method is selected and the main focus is to support the interpretation of experimental data by computations. This section is concerned with theoretical studies that are predominantly of benchmark character. These also often involve some method development. 

Regarding TDDFT benchmark studies of chiroptical properties prior to 2005, the reader is referred to some of the initial reports of TDDFT implementations and early benchmark studies for OR [15,42,47,53,98-100], ECD [92,101-103], ROA [81-84], and (where applicable) older work mainly employing Hartree-Fock theory [52,55, 85,104-111], Often, implementations of a new quantum chemistry method are verified by comparing computations to experimental data for relatively small molecules, and papers reporting new implementations typically also feature comparisons between different functionals and basis sets. The papers on TDDFT methods for chiroptical properties cited above are no exception in this regard. In the following, we discuss some of the more recent benchmark studies. One of the central themes will be the performance of TDDFT computations when compared to wavefunction based correlated ab initio methods. Various acronyms will be used throughout this section and the remainder of this chapter. Some of the most frequently used acronyms are collected in Table 1. 

B3LYP Three-parameter hybrid GGA functional with 20% HF exchange 

CCSD Coupled-cluster with singles and doubles 

COSMO Conductor-like screening solvation model 

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The elucidation of actinide chemistry in solution is important for understanding actinide separation and for predicting actinide transport in the environment, particularly with respect to the safety of nuclear waste disposal.72,73 The uranyl CO + ion, for example, has received considerable interest because of its importance for environmental issues and its role as a computational benchmark system for higher actinides. Direct structural information on the coordination of uranyl in aqueous solution has been obtained mainly by extended X-ray absorption fine structure (EXAFS) measurements,74-76 whereas X-ray scattering studies of uranium and actinide solutions are more rare.77 Various ab initio studies of uranyl and related molecules, with a polarizable continuum model to mimic the solvent environment and/or a number of explicit water molecules, have been performed.78-82 We have performed a structural investigation of the carbonate system of dioxouranyl (VI) and (V), [U02(C03)3]4- and [U02(C03)3]5- in water.83 This study showed that only minor geometrical rearrangements occur upon the one-electron reduction of [U02(C03)3]4- to [U02(C03)3]5-, which supports the reversibility of this reduction. 

H is the smallest ligand and the only one to form a pure single bond to a metal, Le., a crucial computational benchmark [Pg.62]

J WAGNER, Computational Benchmark for Estimation of Reactivity Margin from Fission Products and Minor Actinides in PWR Butnup Credit , 2001, NUREG/CR-6747, ORNL/TM-2000/306. 

Fig. 3. Average computation time for one step using EGO.VIII on a DEC-Alpha 3300L workstation (175 MHz) for simulation systems of varying size. The insets show some of the protein-water systems used for the benchmark simulations.

The program can be run either in a serial or parallel execution mode. Both execution modes were stable when tested on a multiprocessor Linux system. Parallel calculations can be run either on parallel computers or networked workstations. Benchmark information is available at the website listed below. 

In Table 2, the computers ia the MOPAC benchmark are grouped as they are to reflect differing floatiag-poiat machine represeatatioas. AH these computers use 64 bits to represeat a double precisioa floatiag-poiat aumber. Differeat behavior arises from the slightly differeat ways ia which the bits are allocated. 

This decreasing efficiency is a general characteristic of shared memory, shared bus computers. This example shows unusually high efficiency compared with many other programs. This may be because LINPACK is such a common benchmark that much effort has been devoted to optimising it for both vector and parallel computers. 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

AuH and Au2 serve as benchmark molecules to test the performance of various relativistic approximations. Figure 4.7 shows predictions for relativistic bond contractions of Au2 from various quantum chemical calculations over more than a decade. In the early years of relativistic quantum chemistry these predictions varied significantly (between 0.2 and 0.3 A), but as the methods and algorithms became more refined, and the computers more powerful, the relativistic bond contraction for Au2 converged and is now at 0.26 A. 

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... 

On the subject of comparing iterative methods a word of caution is in order. Clearly in any quantitative comparison, the termination criteria should be comparable and the benchmark problems should be run on the same computer. Yet even for simple problems and methods, these two requirements prove to be difficult to enforce and insufficient to ensure meaningful comparisons. To allow for the fact that different methods do not terminate at exactly the same point even when the same termination criterion is used, Broyden (B13) introduced a mean convergence rate, R, which is... 

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