Theor Chem Acc (2007) 117: 153–161 DOI 10.1007/s00214-006-0159-4 REGULAR ARTICLE Shant Shahbazian · Rohoullah Firouzi Mansour Zahedi An ab initio quantum chemical comparative study of possible additive rules and linear relations in parent and extended sulfur diimide families Received: 9 April 2006 / Accepted: 2 June 2006 / Published online: 19 August 2006 © Springer-Verlag 2006 Abstract In this study, it has been demonstrated that there are additive rules corresponding to ab initio derived total elec- tronic energies between members of triple sets of some ex- tended sulfur diimides and their mono- and bi-derivatives. It has been shown that the additive rules are insensitive to the combination of methods and basis sets used to derive the total electronic energies. This insensitivity to the level of calcula- tion is demonstrated to be the case for some linear alkanes also. It has been found that the total electronic energies of certain members of extended sulfur diimide sets ((ZZ) k and (EE) k conformers) follow a linear relation although chemi- cal accuracy may be achieved only by excluding the smallest members of these sets. The details of this deviation have been employed to quantify the “Z-effect” proposed previously by the same authors. Keywords Sulfur diimides · Additive rules · Linear relations · Ab initio · Density functional theory 1 Introduction After a long-term ignorance of the community of theoret- ical chemists, there is a renewed interest in transferability problem and its possible consequences. Whereas transfer- ability and related concepts have a firm ground in the his- tory of chemistry and appeared soon in empirical theories of the nineteen century [1], less attention has been paid to their physical origins and quantitative aspects during the evolution of quantum chemistry. Thanks to Quantum Theory of Atoms in Molecules (hereafter abbreviated as QTAIM) [2], this sit- uation has been changed and a formal definition of molecu- lar fragments within the context of “quantum mechanics of open subsystems” [3] is now routine. Accordingly, based on such a firm theoretical ground, the putative concept of func- tional group and its quantitative aspects, as the cornerstones S. Shahbazian · R. Firouzi · M. Zahedi (B ) Department of Chemistry, Faculty of Sciences, Shahid Beheshti University, Evin, P.O. Box 19395-4716, Tehran 19839, Iran E-mail: m-zahedi@cc.sbu.ac.ir of organic chemistry, now seem to have a well-defined physics [4]. So, transferability of molecular fragments may be calculated and measured unambiguously employing QTAIM [5]. On the other hand, there were always empirical eviden- ces regarding the possibility to transfer certain properties of molecular fragments or functional groups in a class of related molecules (particularly the homologous series). As a famous example, this quantitative transferability is best manifested in measured thermodynamic [6–8] and magnetic [9,10] prop- erties of alkanes. In this case, methylene group (–CH 2 –) acts as a transferable moiety. The mathematical consequences of this transferability are the additive rules and linear relations among the physical properties of a selected class of related molecules (alkanes in this case). In recent years, theoretical calculations have also been employed to demonstrate these additive rules and linear relations. In this regard, one may note the interesting paper by Bad- er and Martin [11] that demonstrates the additive rule among total electronic energies (calculated by an ab initio method) of various substituted ethyl derivatives. In the three-member sets (H–CH 2 –CH 2 –H, H–CH 2 –CH 2 –R, R–CH 2 –CH 2 –R) with (R=CH 3 , NH 2 , OH, F) one may find a surprising addi- tive rule, namely, the arithmetic mean of total electronic energies of ethane and its bi-substituted derivative is equal within chemical accuracy (∼ 1–2 kcal mol -1 ) to the total electronic energy calculated independently (at the same com- putational level) for its mono-substituted derivative. On the other hand, the extensive quantum chemical study of Neu- gebauer and Häfelinger [12] demonstrates the prevalence of linear relations in numerous organic homologous series. In every homologous series studied by these researchers, an excellent (within chemical accuracy, namely, ∼ 1–2 kcal mol -1 ) linear regression has been found among total calcu- lated electronic energies of molecules of that series and the number of corresponding electrons. In a comment on Neu- gebauer and Häfelinger’s paper, Cortès-Guzmán and Bader [13] demonstrate elegantly that linear relations found by the above-mentioned researchers may be explained within QTAIM definition of functional group and compensatory