Conformational energies of reference organic molecules: benchmarking of common efficient computational methods against coupled cluster theory

Abstract

We selected 145 reference organic molecules that include model fragments used in computer-aided drug design. We calculated 158 conformational energies and barriers using force fields, with wide applicability in commercial and free softwares and extensive application on the calculation of conformational energies of organic molecules, e.g. the UFF and DREIDING force fields, the Allinger's force fields MM3-96, MM3-00, MM4-8, the MM2-91 clones MMX and MM+, the MMFF94 force field, MM4, ab initio Hartree-Fock (HF) theory with different basis sets, the standard density functional theory B3LYP, the second-order post-HF MP2 theory and the Domain-based Local Pair Natural Orbital Coupled Cluster DLPNO-CCSD(T) theory, with the latter used for accurate reference values. The data set of the organic molecules includes hydrocarbons, haloalkanes, conjugated compounds, and oxygen-, nitrogen-, phosphorus- and sulphur-containing compounds. We reviewed in detail the conformational aspects of these model organic molecules providing the current understanding of the steric and electronic factors that determine the stability of low energy conformers and the literature including previous experimental observations and calculated findings. While progress on the computer hardware allows the calculations of thousands of conformations for later use in drug design projects, this study is an update from previous classical studies that used, as reference values, experimental ones using a variety of methods and different environments. The lowest mean error against the DLPNO-CCSD(T) reference was calculated for MP2 (0.35 kcal mol^-1), followed by B3LYP (0.69 kcal mol^-1) and the HF theories (0.81-1.0 kcal mol^-1). As regards the force fields, the lowest errors were observed for the Allinger's force fields MM3-00 (1.28 kcal mol^-1), ΜΜ3-96 (1.40 kcal mol^-1) and the Halgren's MMFF94 force field (1.30 kcal mol^-1) and then for the MM2-91 clones MMX (1.77 kcal mol^-1) and MM+ (2.01 kcal mol^-1) and MM4 (2.05 kcal mol^-1). The DREIDING (3.63 kcal mol^-1) and UFF (3.77 kcal mol^-1) force fields have the lowest performance. These model organic molecules we used are often present as fragments in drug-like molecules. The values calculated using DLPNO-CCSD(T) make up a valuable data set for further comparisons and for improved force field parameterization.

Keywords: B3LYP; Conformational energies; DLPNO-CCSD(T); Force fields; Organic molecules.

Fig. 1

Hyperconjugative interactions in trans and gauche n-butane. There are four hyperconjugative σ_C-Η → σ*_C-H interactions in trans conformation but two σ_C-H → σ*_C-Η and two σ_C-Η → σ*_C-C in gauche conformation

Fig. 2

The stabilisation of staggered configuration with respect to eclipsed in ethane comes from the hyperconjugative orbital interactions σ_C-H → σ*_C-H

Fig. 3

1,1,2,2-Tetrasubstituted ethane conformations. The opening up of bond angles R-C-R caused by steric crowding of methyl groups does not lead to additional unfavourable interactions in gauche conformation (F → H) but it causes stereochemical tension in anti conformation (E → G)

Fig. 4

Conformations of 1-butene

Fig. 5

Low energy conformations for tetraethylmethane, tetramethylhexane, tetrabenzylethene and tri-(neopentyl)benzene

Fig. 6

Conformers of cyclohexane, cyclohexene and cyclooctane

Fig. 7

A Shows the stabilization of the gauche conformation by rotation about C2-C3 bond in 1-fluoropropane through attractive electrostatic interactions (left) and/or via hyperconjugative interaction (right). B Shows destabilisation of the anti conformer because of shaping bended bond C-C (left) and stabilisation of gauche conformation in 1,2-difluoroethane via hyperconjugative phenomenon (right). C Shows the conformarions of 1,3-dichloropropane

Fig. 8

Top: equilibrium between low energy conformers in methylcyclohexane and the C-H bonds which participated (in bold) in the most important hyperconjugative interactions. Bottom: C-H bond participates in two hyperconjugative interactions in axial methylcyclohexane and in four hyperconjugative interactions in equatorial conformer

Fig. 9

Diaxial conformations of 1,4-dihalo cyclohexane (left) and di-equatorial conformation in 1,2-dihalo cyclohexane (right)

Fig. 10

Low energy conformers of 2-butanone, vinyl alcohol, vinyl methyl ether, glycolic acid and propenol

Fig. 11

Conformations of cyclodecanone

Fig. 12

Top: stabilization of gauche conformation of 1-propanol over anti conformation by rotation of C2-C3 bond is likely due to electrostatical interactions (left) and hyperconjugative interactions (right). Middle and bottom: the same conformational preferences are observed for the O-C1-C_exo-C dihedral in C- and O-glycosides

Fig. 13

The buttressing effect of methyl groups forces the O-Me group in cis-2,6-dimethyl-1-methoxycyclohexane eclipsing tertiary C-H bond

Fig. 14

Conformations around central C-O bonds in acetals R₁CH(OR₂)(OR₃)

Fig. 15

Conformations of 1,2-ethanediol and description of the conformarional space of trehalose by rotation around dihedral angles φ and φ′

Fig. 16

Conformations of hexahydropyrimidine and of its 3-OH analogue

Fig. 17

Conformations of diamines H₂N(CH₂)_xNH₂ (x = 2–4) around N-C-C-N (G or T) and lp-N-C-C (g or g+ and g' or g−) dihedral angles

Fig. 18

Low energy conformers of β-aminotropane and its cations

Fig. 19

Low energy conformers of N-acetylalanine-N-methylamide and of N-acetylphenylalaninyl-amide (NAPA) by rotation around φ (OC-N-C-CO), ψ (N-C-CO-N) and χ (N-C-C-Cipso) dihedral angles; Ramachandran and IUPAC definitions are used

Fig. 20

Low energy conformers of EtSH, MeSEt, i-PrSH and of the sulfones MeSO₂Et and cyclopentanesulfone (sulfolane)

Fig. 21

Conformations of ethyldimethylphosphine and trimethoxyphosphate

Fig. 22

Possible structures for the transition state by rotation around CO-N bond

Fig. 23

Ring inversion transition states for cyclohexane, cyclohexene and N-methylpiperidine

Fig. 24

Comparative performance (mean error in kcal mol⁻¹) of different theories using 158 conformational energies and barriers from 145 standard organic molecules compared to the DLPNO-CCSD(T)/cc-pVTZ calculated values