Integrated Methods: Applications in Quantum ChemistryAuthorsPublication Date4/13/04Read full article onlineFull ArticleAbstractCoinciding with the discovery of the C_{60} buckminsterfullerene molecule, nanotechnology was envisioned in the mid1980s as the art of manipulating matter at the atomic level. Since then, nanotechnology rapidly became a growing interdisciplinary research area, driven by one promise: Regardless of the rate at which nanotechnology will be implemented, it holds the potential to change everything. Unfortunately, it has proven to be very difficult to obtain reliable structural data on nanostructures, and their chemical reaction mechanisms are still largely unknown, making it extremely difficult to create commercially successful applications. In addition to these difficulties, the quantum effects responsible for the properties and reactivity of nanoscale chemical systems are very often qualitatively different from those of either bulk material or atoms and molecules, thereby preventing us to make use of our knowledge of their electronic structures. We find ourselves today forced to study nanoscale electronic structures from the very beginning with the focus on a size domain where quantum mechanics and classical mechanics meet to create new fascinating phenomena and structural wonders. Unfortunately, the computational cost of traditional electronic structure methods remains by far too large even today at the age of ultrafast computers to permit direct investigation of realistic models relevant to the nanoscale at the quantum chemical level. The problem is the vast number of atoms involved in these structures. For instance, when one assumes an interatomic distance of ∼ 0.2 nm in the solid state, a 3D system only 10 nm in size involves ∼ 125,000 atoms. Although advances in massively parallel processing, linear scaling techniques, localized orbital methods, and sophisticated integral approximation methods have in recent years extended the applicability of ab initio molecular orbital (MO) and density functional theory (DFT) methods to larger and larger systems, calculations on the nanometer scale remains far beyond their reach. Atomic level modeling of systems of this size is only theoretically achievable by means of molecular mechanics force fields. Unfortunately, classical mechanical force field approaches are incapable of describing fundamental chemical processes such as oxidation, reduction, electronic excitation, and bond breaking. Band gaps, relative position of conduction and valence bands, lifetimes of electron/hole pairs, magnetic response, optical response, charge transfer rates, (photo)oxidation/reduction rates, and bond breaking/formation rates are important properties of quantum character that require a rigorous quantum chemical treatment where conventional molecular mechanics force field approaches naturally fail. Clearly, describing electronic structure at the nanoscale is a great challenge, which has been taken on by many research groups worldwide using a variety of different approaches. As a zeroorder approximation, computationally inexpensive and not very accurate semiempirical or tightbinding methods have been used to compute the electronic structures of large clusters and nanostructures, and in some cases DFT methods in combination with small basis sets were employed, unwillingly accepting a low level of accuracy. In very few cases, higheraccuracy methods such as secondorder Møller–Plesset perturbation theory (MP2) with reasonably sized basis sets were used to predict equilibrium geometries for highly symmetrical structures. In general, however, chemically accurate (within ∼ 3 kcal/mol) calculations for nanoscale systems cannot be performed using straightforward, highaccuracy quantum chemical methods. As a possible solution to this dilemma, socalled “integrated” or “hybrid” methods have recently become an attractive alternative for largescale quantum chemistry, by combining highaccuracy calculations for small parts of the nanostructures and less accurate lower levels of theory for the entire system. In fact, if applied carefully, these methods are capable of delivering chemical accuracy in the prediction of electronic structures and reactivities in the chemistry on the nanoscale. Their recent contributions toward a deeper and more accurate understanding of nanoscale quantum chemistry are subject of this review. At first we will introduce quantum chemical methods applicable to extended molecular systems or parts of them, describe in short the theory behind integrated methods, and in the second part discuss their applications to the most recognizable areas of nanochemistry, namely, the chemistry of fullerenes, nanotubes, and silica based nanosystems. Finally, we will give an outlook into the future development of integrated methods and their tremendous potential in the theoretical investigation of quantum chemistry on the nanoscale. 

