Molecular Descriptors for Natural Diamondoid Hydrocarbons and Quan- titative Structure-Property Relationships for Their Chromatographic Data

Diamond hydrocarbons (or diamondoids) are hydrocarbons that have a carbon skeleton superimposable on the diamond lattice and contain one or more adamantane units. Recently it was found that many higher diamondoids (containing four to eleven adamantane units) are present in petroleum and can be isolated by a series of methods that include HPLC and GC techniques. We develop QSPR equations using molecular descriptors derived from the topology and geometry of diamondoids, by means of dualist graphs consisting of vertices placed at the centers of adamantane cells forming the diamondoid, and of edges connecting vertices centered in adamantane cells sharing faces. From distance (or distancedistance) matrices encoding the topology and geometry of diamondoids one can obtain distance-sums, distance-distance sums, or eigenvectors as molecular descriptors characterizing the diamondoids. These descriptors afford satisfactory correlations with GC and HPLC retention data, and may also facilitate the identification of diamondoid isomers. INTRODUCTION The surprising discovery and isolation of higher diamondoids (or polymantanes, hydrocarbons whose carbon scaffold is part of the diamond lattice) was recently reported [1,2]. Consequently one desires theoretical methods for correlating structures with properties for these unique and useful compounds, only available from petroleum [3]. Many applications of “nanotube diamondoids” in nano-devices and medicine have been proposed. Chiral diamondoids may be used in stereoselective syntheses. Individual diamondoids with many potential applications (such as antiviral compounds, field emitters, components of molecular motors, nanorods as spacers in pharmaceuticals), being the most stable among their isomers, can be isolated via thermal treatments. Diamondoids are more thermally stable than nondiamondoid hydrocarbons (e.g., acyclic hydrocarbons) in petroleum systems, and therefore become concentrated in the natural gas condensates as they form over geologic time [3].Thermal treatments are similarly used to produce fractions extremely rich in diamondoids [1,2]. Moreover, diamondoids are more stable than graphite in the sub-5 nm size range (contrary to the stability relationship of macroscopic diamond and graphite). MolecularDiamond Technologies of Chevron Technology Ventures measured various physical properties of the higher diamondoids during the development of methods for their isolation. These data are now used in this quantitative structure-property relationship (QSPR) study. Higher diamondoid hydrocarbons are 1 – 2 nm-sized structures that have carbon scaffolds corresponding to parts of the diamond lattice. Eleven higher diamondoids (not counting enantiomers) are shown in (Fig. 1), four on a grey octahedral diamond lattice and also as separate carbon framework structures, with higher members of their respective series radiating out from the lattice. *Address correspondence to this author at the Texas A&M University at Galveston, 5007 Avenue U, Galveston, TX 775651, USA; E-mail: [email protected] Fig. (1). Examples of separate structure series of higher diamondoids indicated by four different colored carbon frameworks superimposed on a grey diamond lattice and shown separately with their notation, and with successive “adamantanologs”. In the case of the red-colored chiral diamondoids (having primary helicity), enantiomers are displayed with P/M notations. Thence it seems appropriate that a systematic study of diamondoid structures and diamondoid property characterization be developed. This is initiated here – in particular, using the systematic nomenclature based on dualist graphs, and the complicit structural characterization is further for14 The Open Organic Chemistry Journal, 2007, Volume 1 Balaban et al. malized with idealized coordinates, and MM2 optimized coordinates, all of which are used to compute distancematrix-related invariants useful in correlations with chromatographic retention times. STRUCTURAL CHARACTERIZATION OF DIAMONDOIDS AND NOMENCLATURE Several decades ago, for encoding the structure of condensed benzenoids, dualist graphs have been used: they consist of vertices placed at the centers of each benzenoid ring and of edges connecting vertices corresponding to rings sharing a CC bond. Unlike the usual graphs in which bond angles do not matter, in dualists they do. Cata-condensed benzenoids (that contain no carbon atom common to three rings and no internal hydrogen atoms) have acyclic dualists, pericondensed benzenoids (that contain carbon atoms common to three rings) have dualists with 3-membered rings, and corona-condensed benzenoids (that have “holes” with internal hydrogen atoms) have larger rings in their dualists. A coding system was developed for cata-condensed benzenoids based on the geometry of their dualists. By analogy, diamondoid hydrocarbons have dualist graphs consisting of vertices placed at the centers of adamantane cells forming the diamondoid and of edges connecting vertices of adamantane cells sharing faces. The dualists of diamondoids have structures corresponding to staggered alkane or cycloalkane rotamers. A coding system was proposed for specifying uniquely the structure of diamondoids by associating the tetrahedral directions with digits 1 through 4, indicating these directions from one end of the alkane chain to the other end, to and choosing among all possible notations that one which yields the smallest number on reading sequentially the digits. A few other simple rules were formulated for cyclic or polycyclic dualists, and these rules were also relaxed when wishing to indicate not only the constitution but also the stereoisomerism. Adamantane, diamantane and triamantane have but one constitutional isomer, but higher diamondoids have two or more isomers, as shown in Table 1. Fig. (2). Adamantane and diamantane with their carbon (grey) and hydrogen atoms (blue). Adamantane (C10H16) (1) was isolated in the 1930s from petroleum where it is present in low amounts. Laborintensive chemical syntheses followed in the 1940s. The breakthrough occurred in 1957 when the serendipitous catalyzed isomerization of many other C10H16 tricyclic hydrocarbons to yield adamantane was discovered by Schleyer [4,5]. The complicated mechanisms involving 1,2-rearrangements of carbocations were elucidated by computations [6,7] and reaction graphs [8,9]. Soon afterwards, the next homologues up to triamantane were prepared via analogous isomerizations. Diamondoids are the most stable among all their isomers. However, no chemical syntheses are available for higher diamondoids than triamantane, other than one of the four tetramantanes, i.e., C2h-tetramantane, but many of them have now been isolated from petroleum and are available for scientific research from MolecularDiamond Technologies. Adamantane (1) and diamantane (2) are presented in (Fig. 2). Balaban and Schleyer [10] published a system for the enumeration and nomenclature of diamondoids that is being currently used by MolecularDiamond Technologies Co. The IUPAC name of adamantane (1) is tricyclo[3.3.1.1]decane and the IUPAC name of diamantane (with two fused adamantane units) is pentacyclo[7.3.1.1.0.0 ]tetradecane (2). The names and numbering schemes according to the IUPAC nomenclature for the higher diamondoids are exceptionally convoluted and prone to error. The coding and nomenclature system for diamondoids [10] uses the “dualist graph” and was first employed for benzenoids [11-14]. In the center of each unit (benzenoid ring or adamantane unit) one places a vertex of the dualist graph, and then one connects vertices sharing a bond (for benzenoids) or a face (for diamondoids). Dualist graphs Fig. (3). Stereo-views of the tetramantane isomers. From top to bottom: the achiral [121]-, the two enantiomers [123]and [124]-, and the achiral [1(2)3]-tetramantane. H H