Conformational Analysis of Thioether Musks Using Density Functional Theory

A conformational analysis of nine macrocyclic thioether musks has been carried out using molecular mechanics (MMFF), density functional theory (DFT) using both B3LYP and M06 functionals, as well as Hartree-Fock and post-Hartree-Fock (MP2) ab initio methods. 6-Thia-, 10-thia- and 4-methyl-5-thia-14-tetradecananolide, 4-thia-, 7-thia-, 11-thia- and 12-thia-15-pentadecanolide and 6-thia- and 12-thia-16-hexadecanolide were modeled. Unfortunately, there was little agreement between the computational methods at the levels of theory used in this study.


Introduction
Discrepancies in energy differences between density functional (B3LYP) and post Hartree-Fock (MP2) ab initio methods have been noted in large, conformationally mobile ring systems, including mesocyclic hydrocarbons [1,2] and macrocyclic sesquiterpenes [3]. In addition, the B3LYP functional has been found to give increased errors with increasing molecular size [4,5], and Schreiner and co-workers [4] have recommended using higher level (e.g., MP2 with a 6-31G** basis set) single-point energy calculations on DFT structures as a confirmation. In order to compare DFT methods with post-HF methods on conformationally mobile macrocycles, a conformational analysis of thioether musks has been carried out.

Results and Discussion
A Monte-Carlo molecular mechanics conformational search was carried out on each thioether macrocyclic lactone using the MMFF force field [10]. From the molecular mechanics conformational search, those conformations with relative energies (E rel , calculated energies relative to the lowest energy conformation) ≤ 3 kcal/mol were investigated using density functional theory (DFT) employing the popular hybrid B3LYP functional [11,12] and the 6-31G* basis set, as well as the recently developed M06 combination functional [13] and the 6-31G* basis set. The B3LYP functional was chosen because it is the popular choice for modeling organic compounds, the M06 functional was chosen because it was developed to predict accurate structures and energies of main-group-containing compounds and includes concovalent interactions. The 6-31G* basis set was chosen for its relatively rapid calculations. In order to confirm the energies from the B3LYP and M06 analyses, single-point Hartree-Fock (HF), followed by second-order Møller-Plesset electron correlation (MP2) calculations at the 6-31G** level were carried out using the B3LYP geometries [4]. (1) 6-Thia-14-tetradecanolide (1) had 30 conformations that had E rel (MMFF) ≤ 3.0 kcal/mol. The lowest-energy conformation, [13434], was also the lowest-energy conformation from the B3LYP analysis (see Figure 1). Note: macrocyclic conformations are designated according to the system of Dale [14]. In square brackets are indicated the number of bonds in the trans-configured edges of the macrocycle, starting with the shortest trans-chain, and progressing in the direction of the next shortest; the sum of the numbers in the square bracket is equal to the ring size. An alternative conformation, [13353], however, was the lowest-energy structure according to the MP2 calculations. The M06 calculations indicated a [23343] conformation to be lowest in energy, but this conformation was also very low in energy in the other three computational methods. The lowest-energy conformation for cyclopentadecane using molecular mechanics has been found to be the quinquangular [33333] conformation [14], but an X-ray crystal structure of cyclopentadecanone (exaltone) revealed a [13353] conformation [15]. The lowest-energy [33333] conformation was 1.15, 1.98, and 1.03 kcal/mol higher in energy than the respective lowest-energy conformations for MMFF, M06, and MP2, but only 0.37 kcal/mol higher than the [13434] for B3LYP. In each of the low-energy conformations ([13434], [13353], and [23343]) the thioether moiety can adopt a preferred gauche C-S-C-C torsion angle [16,17]. Additionally, the ester group adopts a preferred s-trans orientation [18][19][20] in each of these conformations.

10-Thia-14-tetradecanolide (2)
10-Thia-14-tetradecanolide (2) also showed disagreement between the computational methods. There were 32 low-energy conformations from the MMFF calculations, of which a [13434] was the lowest-energy from the MMFF analysis, but a [23343] conformation was shown to be the B3LYP lowest-energy conformation while an alternative [23343] conformation was favored by M06 ( Figure 2). The MP2 calculations indicated a fourth conformation, a [14334] conformation, to be the lowest energy form. A [13353] conformation was also low in energy. Although the C-S-C-C groups are gauche in each of these conformations, only in the [14334] and [13353] conformations do the sulfur atom adopt an exodentate "corner" position [21,22]. Similar to what was found for 1, the lowestenergy [33333] conformation is 1.44, 1.15, and 1.47 kcal/mol higher in energy than the respective lowest-energy conformations for MMFF, M06, and MP2, but only 0.65 kcal/mol higher than the [23342] for B3LYP.  (1). Values in parentheses are with diffuse basis sets (6-31+G* for B3LYP and M06, 6-311+G** for MP2).

Computational Methods
All calculations were carried out using SPARTAN'08 for Windows [30]. Initial conformational analyses were carried out on each macrocycle using a Monte-Carlo molecular mechanics conformational search using the MMFF force field [10]. For each macrocycle, all conformations with E rel less than 3 kcal/mol from the MMFF conformational analysis were then modeled using both density functional theory and Hartree-Fock and post-HF methods. Both the popular B3LYP [11,12] and the recently developed M06 [13] functionals and the 6-31G* basis set [31] were used for the optimization of all stationary points in the gas phase. Single-point Hartree-Fock ab initio energies were calculated using the DFT geometries (above) at the 6-31G** [31] level, followed by a correlation energy calculation using the second-order Møller-Plesset model (MP2) [31]. In addition, single point calculations were carried out on the low-energy conformations of the thioether musks at the B3LYP/6-31+G*//B3LYP/6-31G*, M06/6-31+G*//M06/6-31G*, and MP2/6-311+G**//B3LYP/6-31G* levels

Conclusions
The results from this study indicate that conformationally mobile macrocyclic ring systems remain difficult to computationally model, even with relatively large basis sets and diffuse functions. At the levels of theory used in these current calculations, there seems to be little agreement between the two DFT methods (B3LYP and M06) as well as with the MP2 ab initio method ( Table 2). With new and improving functionals, larger basis sets, and increased computational power, this situation will hopefully improve.