Abstract. A new parametrization for carbon is proposed within the framework of the complete neglect of dierential overlap molecular orbital theory in a scheme for systems with periodic boundary conditions using large-unit-cells and C point sampling, with an accurate treatment of the long-range Coulomb tails of the interaction potentials. The new parametrization is obtained by fitting simultaneously experimental and theoretical data for electronic and structural properties of diamond and graphite. Remarkably, compared with other parametrizations existing in the literature and typically based on molecular data, it provides a better description of the relative stability between the two phases, but it is still unsatisfactory in the description of the elastic properties. Key words: Semi-empirical methods – Tight binding – Periodic systems 1 Introduction Carbon has always attracted the attention of both physicists and chemists for its fundamental role in the living world as well as in technology. Recently, the interest has been revived by the discovery of a new form of elemental carbon, i.e., fullerenes, and by the produc- tion and characterization of a wide variety of carbon- based nanostructures such as nanotubes, onions, and other low-dimensional structures. Understanding the physical and chemical properties of many of these structures requires accurate electronic- structure calculations, but the size and the complexity of the systems ask for a compromise between accuracy and computational burden. These considerations point to semi-empirical methods as very promising tools for this kind of problem. Among the semi-empirical methods, tight binding (TB) [1, 2] is the most widely used by the solid-state physics community. It was originally developed to model atoms in simple and perfect crystals, and, typ- ically, a particular tight-binding parametrization is optimized for a single crystalline structure. The vari- ous geometries and dierent chemical environments characterizing the wide variety of carbon-based sys- tems ask, conversely, for a highly transferable para- metrization. Although good TB Hamiltonians are nowadays available for some elements (e.g. for carbon [3, 4]), extensive transferability remains an open problem. This limitation is intrinsic to the method, and it is due to the crude treatment of the electron- electron interaction, which is not included explicitly in the standard TB Hamiltonians. The repulsive energy is taken into account empirically, typically with a pair- wise potential. Additional terms (usually in the form of a Hubbard-like term [2]) are sometimes added to the Hamiltonian in order to improve the description of systems involving large charge rearrangements. This type of ad hoc correction, however, is not satisfactory, and often not sucient to ensure transferability. Re- cent attempts have been made to include in a TB framework the many-body character of the bond: satisfactory results for the structural properties of di- amond and graphite are obtained [5], but with a high computational price. Another class of semi-empirical methods is the family of Hartree-Fock-based methods, originated from the pioneering work of Pople and coworkers in the late 1960s, and developed in the computational chemistry community also for large and complex molecules. These methods range from the simplest one, the complete ne- glect of dierential overlap (CNDO) [6], to the more sophisticated methods like the modified neglect of dif- ferential overlap (MNDO) method [7], the Austin model 1 (AM1) method [8], and the parametric method number 3 (PM3) [9]. They all make use of a linear combination of atomic orbitals for the one-electron wave functions to *Present address: Universita¨t Konstanz, Fakulta¨t fu¨r Chemie, Universita¨tsstrasse 10, D-78462 Konstanz, Germany Correspondence to: M. Peressi Letter Toward a transferable parametrization for carbon in a periodic semi-empirical molecular orbital scheme L. De Maria 1;2; *, M. Peressi 1;2 , S. Baroni 1;3 1 Istituto Nazionale di Fisica della Materia (INFM) 2 Dipartimento di Fisica Teorica, Universita` di Trieste, Strada Costiera 11, I-34014 Trieste, Italy 3 Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Beirut 2–4, I-34014 Trieste, Italy Received: 15 July 1998 / Accepted: 9 September 1998 / Published online: 16 November 1998 Theor Chem Acc (1998) 100:333–338 DOI 10.1007/s00214980m132