Enumeration of the Conformers of Unbranched Aliphatic Alkanes Gyula Tasi,* ,²,‡ Fujio Mizukami, ² Istva ´ n Pa ´ linko ´ , § Jo ´ zsef Csontos, ‡ Werner Gyo _ rffy, ‡ Padmakumar Nair, ² Kazuyuki Maeda, ² Makoto Toba, ² Shu-ichi Niwa, ² Yoshimichi Kiyozumi, ² and Imre Kiricsi ‡ Department of Surface Chemistry, National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan, Applied Chemistry Department, Jo ´ zsef Attila UniVersity, Rerrich B. te ´ r 1, H-6720 Szeged, Hungary, and Department of Organic Chemistry, Jo ´ zsef Attila UniVersity, Do ´ m te ´ r 8, H-6720 Szeged, Hungary ReceiVed: April 15, 1998; In Final Form: June 8, 1998 An effective one-electron quantum chemical method was applied to enumerate the conformers of unbranched aliphatic alkanes. The results obtained for butane, pentane, hexane, and heptane were utilized to derive four rules with which the number and sequences of the existing conformers up to undecane could be reproduced. The validity of the rules was confirmed at Hartree-Fock and second-order Moeller-Plesset levels too. Full ab initio conformational analyses were performed for the butane, pentane, hexane, heptane, and octane molecules. The rules demonstrate that the most important factors governing the conformational behavior of unbranched aliphatic alkanes are the nonbonded repulsive-attractive (van der Waals) interactions between the hydrogen atoms attached to the carbon atoms at positions 1,4; 1,5; 1,6; and 1,7. The calculated gas- phase standard heats of formation of the unbranched aliphatic alkanes closely matched the experimental values. Introduction Theoretical study of the conformational flexibility of biologi- cally active molecules is of utmost importance. A knowledge of each possible conformer is essential, since it is far from certain that the biologically active conformer corresponds to the global minimum of the molecular potential-energy surface. The conformational flexibility of molecules with potential pharmacological activity must also be taken into account in similarity studies. 1 The simplest class of molecules with high conformational flexibility is the unbranched aliphatic alkanes. Despite numer- ous studies 2-4 and even books 5 on this topic, it is still not clear how many conformers exist for the individual members of this homologous series. According to Tsuzuki et al., the number of possible conformers is probably larger than 3 n , where n is the number of the rotatable C-C bonds (i.e., the number of free C-C-C-C torsional angles). 3 The following methods can be applied to study the confor- mational properties of large molecules: molecular dynamics, molecular mechanics, and semiempirical quantum chemistry. Molecular mechanics and dynamics methods provide results quickly, but the results are generally less reliable than those of the traditional quantum chemical methods. However, an appreciable number of examples demonstrate that even the widely used semiempirical quantum chemical methods do not always provide satisfactory results. For instance, the AM1 method 6 cannot reproduce the conformational spectrum of R,R′- diaminoacetone, and its suitability for investigating the confor- mational properties of oligopeptides is therefore questionable. 7 It has recently been shown that the MNDO 8 and AM1 methods overestimate the stabilities of the all-trans conformers of unbranched aliphatic alkanes. 4 It has also been suggested that large molecules must be taken into consideration on the parametrization of new semiempirical methods, since the AM1 and PM3 9 standard heats of formation for large ring systems are clearly not satisfactory. 10 We recently studied the ground-state equilibrium molecular geometries and permanent electric dipole moments of aliphatic hydrocarbons. 11 Accurate molecular total energies and zero- point vibrational energy (ZPVE) corrections were additionally obtained by the Gaussian-2 (G2) method 12 for several aliphatic alkane molecules. 13 On the basis of these results, we param- etrized an effective one-electron quantum chemical model for aliphatic alkanes. 13 The method was named the scaled effective one-electron method (SEOEM). For aliphatic alkane molecules, the SEOEM gas-phase standard heats of formation closely matched the experimental values. For 63 molecules, the average absolute deviation and maximum absolute deviation were 0.83 and 3.70 kcal/mol, respectively. 13 In this work, SEOEM model quantum chemistry is applied to investigate the conformational properties of unbranched aliphatic alkanes. For the butane, pentane, hexane, heptane, and octane molecules, full ab initio conformational analyses were performed at Hartree-Fock (HF) and second-order Moeller-Plesset (MP2) levels. Theoretical Background The SEOEM model takes into consideration all the electrons of the system (all-electron method). 13 For the calculation of molecular integrals and their derivatives, the STO-3G basis set is used for aliphatic alkanes. The details of the parametrization and the optimized parameters of the SEOEM model for aliphatic alkanes can be found elsewhere. 13 To calculate the ZPVE corrections within the SEOEM approximation, the harmonic vibrational frequencies are used ² National Institute of Materials and Chemical Research. ‡ Applied Chemistry Department, Jo ´zsef Attila University. § Department of Organic Chemistry, Jo ´zsef Attila University. 7698 J. Phys. Chem. A 1998, 102, 7698-7703 S1089-5639(98)01866-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 09/09/1998