Small molecules benchmark studies

AMI Atoms in Molecules Benchmark Studies on Small Molecules Computer Graphics and Molecular Modeling ... 

In the next two subsections, we describe collections of calculations that have been used to probe the physical accuracy of plane-wave DFT calculations. An important feature of plane-wave calculations is that they can be applied to bulk materials and other situations where the localized basis set approaches of molecular quantum chemistry are computationally impractical. To develop benchmarks for the performance of plane-wave methods for these properties, they must be compared with accurate experimental data. One of the reasons that benchmarking efforts for molecular quantum chemistry have been so successful is that very large collections of high-precision experimental data are available for small molecules. Data sets of similar size are not always available for the properties of interest in plane-wave DFT calculations, and this has limited the number of studies that have been performed with the aim of comparing predictions from plane-wave DFT with quantitative experimental information from a large number of materials. There are, of course, many hundreds of comparisons that have been made with individual experimental measurements. If you follow our advice and become familiar with the state-of-the-art literature in your particular area of interest, you will find examples of this kind. Below, we collect a number of examples where efforts have been made to compare the accuracy of plane-wave DFT calculations against systematic collections of experimental data. 

All molecules will show an MCD spectrum. The spectrum of many types of molecule can now be simulated, often through more than one theoretical approach. Several areas need further study however. It would be useful if all types of MCD spectrum could be calculated at a range of levels of theory so that a scientist interested in predicting a spectrum would be able to choose an approach that suitably fits their needs. More benchmark calculations are needed to improve our understanding of the limitations of the present methods. These calculations would be aided by the availability of more high-quality spectra of small molecules that would be suitable test cases. While the MCD spectra of many molecules can now be calculated, one area that probably still cannot be studied with confidence is paramagnetic molecules that include very heavy elements. In this case spin-orbit effects will be very large and perturbational treatments like those applied thus far are unlikely to provide accurate results. 

In order to render the chapter sufficiently self-contained, the reader will find a theory and methodology section immediately following this introduction (Sect. 2). Literature covering a broad range of applications is reviewed in the subsequent sections, grouped by topics as follows. Section 3 Benchmarks of functionals and basis sets, small molecule test cases. Section 4 Beyond gas phase and static structures. Section 5 (mainly) Assignment of absolute configuration case studies. Section 6 Analysis methods for chiroptical properties. Section 7 Case studies where a variety of methods was used to probe ECD,... 

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. 

Nowadays ab initio quantum chemical calculations can provide results approaching benchmark accuracy for small molecules in the gas phase [1], and they have proven to be very useful fo complement experimental studies. Small molecules in the gas phase are typically addressed by high-level methods such as CCSD(T), QCISD(T) and MRCI, which in many cases are equally accurate than experiments [2]. A wide variety of properties such as structures [3] thermochemistry [4] spectroscopic quantities [5,6], and kinetics [7] can be effectively computed. 

Few studies have employed configuration interaction with all singles, doubles, triples, and quadruples (CISDTQ) because the number of triple and quadruple substitutions grows very rapidly with the number of electrons and basis functions (cf. Table 3). CISDTQ results are most commonly reported in benchmark full Cl studies to indicate the fraction of the basis set correlation energy recovered by triples and quadruples.17,22,39,801234,241,264 Nevertheless, the CISDTQ method has occasionally been used for benchmarking in cases where the full Cl was not technically feasible, because the CISDTQ results are expected to be very close to full Cl for small molecules. For systems with eight electrons or less at their equilibrium geometries, the CISDTQ method recovers more... 

Most of the proof-of-concept studies to date have focused on small-molecule asthma drugs. These drugs are currently the most important class of inhalation medicine and conveniently, commercial inhaler devices and formulations with micronized materials are available for benchmark comparison. 

Polarizabilities and Hyperpolarizabilities of Small Molecules. - 5.2.1 Diatomic Molecules. - The methods usually employed for diatomic response function calculations are often identical with those used for polyatomic molecules but some features are more typical of diatomic studies the use of very large atomic basis sets, the more frequent use of complete Cl as a benchmark, the inclusion of relativistic effects and calculations that do not assume the Bom-Oppenheimer approximation. Work on diatomics is also... 

For most chemical applications, one is not interested in negative energy solutions of a four-component Dirac-type Hamiltonian. In addition, the computational expense of treating four-component complex-valued wave functions often limited such calculations to benchmark studies of atoms and small molecules. Therefore, much effort was put into developing and implementing approximate quantum chemistry methods which explicitly treat only the electron degrees of freedom, namely two- and one-component relativistic formulations [2]. This analysis also holds for a relativistic DFT approach and the solutions of the corresponding DKS equation. 

Ideally, one would apply these high-accuracy methods as a routine for thermochemistry and kinetics studies. However, these methods can be very expensive for even a moderate system. For example, a G2(MP2) calculation on a octane molecule exceeds 100 cpu hours on a CRAY-YMP supercomputer. Petersson (1998) did extensive benchmark study and his conclusion is that most of the CBS and G2 methods are not practical for systems that have more than a half dozen non-hydrogen atoms. Table 2 shows the summary of error measurements for the G2 test set of 125 reactions. Most of these reactions involve very small gas molecules. 

These benchmark studies demonstrate the importance of dispersion in computing structures in ruthenium-catalyzed olefin metathesis. Although B3LYP has been the method of choice for many years due to its great performance for small organic molecules, it has been shown to systematically underestimate the... 

Excited-state absorption (ESA) is a type of electronic spectroscopy for which only a few theoretical studies have been performed (for a recent study on the singlet-singlet ESA spectrum of azulene, see Ref. 130 and for some benchmark calculations on small molecules, see Ref. 131). From the experimental point of view ESA is a very important topic in photophysical (kinetic) investigations of energy, electron or hydrogen-transfer processes. Although in principle all excited states of a molecule show a distinct electronic absorption spectrum, only the ESA spectra of the lowest excited state in each multiplicity (i.e.. Si or Ti) are usually accessible experimentally. Because of the short... 

O Figure 11-1, taken from Bak et al. (2000), illustrates the accuracy of equilibrium geometry dipole moments calculated for a series of small molecules. In Bak et al. (2000), the dipole moments of 11 molecules were studied at various levels of approximation using a sequence of basis sets, with the CCSD(T)/aug-cc-pVQZ results providing the benchmark values. The normal distribution of errors with respect to the reference values, shown in O Fig. 11-1, demonstrates the systematic improvements of the computed results with increasing basis set and improved treatment of electron correlation effects. 

Basis Sets Correlation Consistent Sets Benchmark Studies on Small Molecules Coupled-cluster Theory Gradient Theory M0ller-Plesset Perturbation Theory NMR Chemical Shift Computation Ab Initio Spin Contamination Symmetry in Chemistry. 

---