Recent Advances in Computing Heteroatom-Rich Five- and Six-Membered Ring Systems

Guntram Rauhut    Institut für Theoretische Chemie, Universität Stuttgart, D-70569 Stuttgart, Germany

I Introduction

Recent developments in computer technology in combination with increasingly accurate quantum chemical methods allow for the detailed investigation of molecular reactions, properties, and bulk effects. However, studies of systems with several (adjacent) heteroatoms are hampered owing to strong electron correlation effects, spin contamination in open-shell molecules, and strong charge polarization which requires very flexible basis sets. These problems limit the reliability of semiempirical methods and simple Hartree–Fock ab initio calculations for this class of molecules. Nevertheless, many questions could be solved based on such calculations. But the accuracy of modern gradient-corrected density functionals and a new generation of fast ab initio post-Hartree–Fock methods allow the investigation of molecules of up to 50 atoms on standard personal computers at much higher levels. Since these methods now permit a quantitative interpretation rather than a qualitative one, computational chemistry has become increasingly important in traditional heterocyclic chemistry, life sciences, and drug design. It is thus the purpose of this contribution to provide an overview of the recent advances of modern quantum chemical methods in heterocyclic chemistry. Many of these methods are no longer “blackbox” in nature, they require a sound knowledge of quantum mechanics. Thus particular care must attend the choice of method and the interpretation of results. The last aspect is even more important when reference data are lacking.

The choice for the correct method depends on several parameters. (1) What do I want to know? (2) How large is the system I am interested in? (3) What are my computer resources? The first aspect leads to a preselection of the computational methods in principle. For instance, if one is interested in computing a UV spectrum, one may choose several standard methods including (1) time-dependent density functional theory (TD-DFT), (2) equation-of-motion coupled-cluster theory [EOM-CCSD(T)], (3) multireference perturbation theory (CASPT2), or (4) configuration-interaction methods (CISD and MRCI). These methods differ strongly with respect to their computational demands and accuracy. For a good guess, TD-DFT will be sufficient in most cases. If one wants to predict experimentally unknown data of a difficult system, EOM-CCSD(T) or MRCI calculations may be more reliable. However, if the molecule is large or possesses a strongly delocalized π system, these methods may be prohibitive, so that TD-DFT remains the only feasible choice. The size of the molecule is not the only factor that influences the method; another is the choice of the basis set. Much larger basis sets are required for anions than for neutral species, thus very demanding methods cannot be afforded very often. Therefore, the computer architecture finally determines the level of accuracy and hence the choice of the method. Consequently, many applications are still out of range even for the fastest supercomputers and thus require the development of new quantum chemical methods. A short example may illustrate this. An energy calculation of indene at the coupled-cluster, CCSD(T), level with a satisfying cc-pVTZ basis (i.e., 388 basis functions) may need one day (which would require a multiprocessor high-performance computer). Because the number of operations in the CCSD(T) approaches scales with the seventh order with respect to the number of basis functions N [i.e. O(N7)], the calculation of the corresponding dimer would require about 128 days. Extrapolating the extreme increase in computer power by assuming an optimistic annual processor speedup by a factor of 2, one would have to wait for at least 5 years until this calculation becomes feasible by virtue of developments in modern computer technology. Therefore, there is still a strong need for faster algorithms, especially for high-level ab initio methods. Among the most promising concepts is the local correlation approach introduced by Pulay and Saebø [83CPL151, 84JCP1901, 87JCP914]. The principal ideas of Pulay’s approximations can be applied to any existing ab initio method and are already available up to local CCSD(T) level. For instance, the conventional MP2 approach scales with the fifth order of the basis functions, while the local MP2 (LMP2) scales with an order of about 1.5. This means that the calculation of the correlation calculation is no longer the dominating step, but rather the Hartree–Fock iterations, which scale effectively with an order of 2.3. However, new developments have also led to a linear scaling of this method. On average, the local correlation calculations are as accurate as conventional methods, and thus much larger systems can be computed owing to the tremendous reduction of CPU time. In other words, if a Hartree–Fock calculation can be performed, there are essentially no arguments for not performing an MP2 calculation.

Whereas density functional methods are widely used by experimentally working heterocyclists, high-level ab initio methods are mainly the tools of computational chemists, since the latter offer the possibility of a systematic improvement of the results. It is one of the major drawbacks of the density functional theory that the accuracy of the results depends solely on the exchange-correlation functional, which is parametrized on physical models and thus may fail in certain situations. The most prominent example in this respect is the absence of long-range dispersion interactions as they are of particular importance for the calculation of molecular clusters [94CPL175]. Nevertheless, DFT functionals provide excellent results for molecular geometries and vibrational frequencies. Consequently, a combination of DFT and high-level ab initio calculations has proven to be the most successful in computational chemistry. Owing to the much higher accuracy of the mentioned methods, the following sections will primarily focus on computational studies that deal with DFT or post-HF methods. This is necessary because heterocycles with at least two heteroatoms are usually much more sensitive to the theoretical level than are hydrocarbons or simple heterocycles. Since the power of quantum chemical methods as an interpretive tool has been recognized by very many research groups, this review is restricted to the last few years and to the heteroatoms N, O, and S. Moreover, in addition to chemical aspects, computational details are provided in most cases. Very often, quantum chemical methods were used for the investigation of molecular properties rather than for studying the reactivity of a species. Consequently, this review differs from others by a stronger emphasis on the physical properties of a molecule.

II Recommendations

The following sections provide examples of recent quantum chemical studies in heterocyclic chemistry. As can be seen from these studies, the quality of the results depends strongly on the applied methods and the knowledge of the users. Since most of the readers of this book are experimentalists whose primary focus is not quantum chemistry but experimental heterocyclic chemistry that should be supported by quantum chemical calculations, it is the purpose of this section to provide some crude guidelines for the less experienced users on how to use modern quantum chemical methods.

The recommendations provided below are grounded on the following premises: (1) The user has access to a standard personal computer (PC) rather than high-performance workstations. (2) The fast-growing efficiency of modern PCs enables ab initio investigations of systems up to 50 atoms with few limitations at the moment. Within the next five years, much larger systems can be envisaged. (3) Well established quantum chemical methods, such as the perturbational MP2 approach, will be replaced by more efficient variants. For example, with respect to the standard MP2 method, much larger systems can be studied using the RI-MP2 [93CPL359, 97TCA331], LT-MP2 [92JCP489, 99JCP3660], LMP2 [87JCP914, 98JCP5185], and related methods [95JCP1481, 98CPL102]. These methods certainly will be preferred over the conventional methods in the near future. (4) Multiprocessor PCs can run quantum chemical calculations in parallel, permitting the study of much larger systems. (5) Recommendations can be provided only for standard applications. For more detailed aspects, collaborations with computational chemistry groups are highly recommended. This usually prevents mis-interpretations of computational results and enables the use of more sophisticated methods.

Certainly, in ten years these recommendations will cause readers to smile; therefore, they must be considered my personal view in December 2000, which should not be generalized immoderately.

Basis Sets: For determining structural parameters, basis sets of at least double-ζ quality should be used. The most popular basis sets of this quality are Pople’s 6-31G** [71JCP724] and Dunning’s cc-pVDZ bases [89JCP1007]. In any case, the basis should include polarization functions (i.e., 6-31G** vs. 6-31G). For the study of through-space interactions (e.g.,...