Crystal structure, Hirshfeld surface analysis, interaction energy, and DFT studies of cholesteryl heptanoate

The title compound consists of cholesteryl and heptanoate units, in which the six-membered rings adopt chair and twisted-boat conformations, while the five-membered ring adopts an envelope conformation. In the crystal, the molecules are aligned along the a-axis direction and stacked along the b-axis direction.


Chemical context
Cholesterol is an important constituent of cell membranes with a rigid ring system and a short branched hydrocarbon tail. It modulates membrane fluidity over the range of physiological temperatures and also reduces the permeability of the plasma membrane to protons and sodium ions. In the liver, it is converted to bile, which is then stored in the gallbladder. It functions in intracellular transport, cell signaling and nerve conduction within the cell membrane and is an important precursor in several biochemical pathways within the cells, in the synthesis of vitamin D and steroid hormones, including the adrenal gland hormones cortisol and aldosterone as well as sex hormones progesterone, oestrogens, and testosterone, and their derivatives. Cholesteryl esters are formed between the carboxylate group of a fatty acid and the hydroxyl group of cholesterol and have a lower solubility in water than cholesterol. These esters are also important in many biological mechanisms and numerous experimental investigations have been performed on cholesterol derivatives (Faiman et al., 1976;Goheen et al., 1977;Bush et al., 1980;Di Vizio et al., 2008;Ikonen, 2008). Thus, due to the importance of cholesterol and its esters, we report herein the crystallization, the molecular and crystal structures along with the Hirshfeld surface analysis and the interaction energy and DFT studies of the title compound, (I), whose magnetic properties were previously ISSN 2056-9890 studied by electron paramagnetic resonance (EPR), (Sayin et al., 2013).

Supramolecular features
In the crystal, the molecules are aligned along the a-axis direction and stacked along the b-axis direction (Fig. 2).

Hirshfeld surface analysis
In order to visualize the intermolecular interactions in the crystal of the title compound, a Hirshfeld surface (HS) analysis (Hirshfeld, 1977;Spackman & Jayatilaka, 2009) was carried out by using Crystal Explorer 17.5 (Turner et al., 2017). In the HS plotted over d norm (Fig. 3), the white surface indicates contacts with distances equal to the sum of van der Waals radii, and the red and blue colours indicate distances shorter (in close contact) or longer (distinct contact) than the van der Waals radii, respectively (Venkatesan et al., 2016). The brightred spots indicate their roles as the respective donors and/or acceptors. The overall two-dimensional fingerprint plot, Fig. 4a, and those delineated into HÁ Á ÁH, HÁ Á ÁO/OÁ Á ÁH and HÁ Á ÁC/CÁ Á ÁH contacts (McKinnon et al., 2007) are illustrated in Fig. 4b-d, respectively, together with their relative contributions to the Hirshfeld surface. The most important interaction is HÁ Á ÁH (Table 1) contributing 92.4% to the overall crystal packing, which is reflected in Fig. 4b as widely scattered points of high density due to the large hydrogen content of the molecule with the tip at d e = d i = 1.11 Å . The pair of spikes in the fingerprint plot delineated into HÁ Á ÁO/OÁ Á ÁH contacts (Table 1) have a symmetrical distribution of points (6.1% contribution, Fig. 4c) with the tips at d e + d i = 2.66 Å . In the absence of C-HÁ Á Á interactions, the pair of characteristic wings in the fingerprint plot delineated into HÁ Á ÁC/CÁ Á ÁH A partial packing diagram viewed down the c axis.

Figure 3
View of the three-dimensional Hirshfeld surface of the title compound plotted over d norm in the range of 0.0196 to 1.7047 a.u.

Figure 1
The asymmetric unit of the title compound with the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.  Fig. 5a-b, respectively.
The Hirshfeld surface analysis confirms the importance of H-atom contacts in establishing the packing. The large number of HÁ Á ÁH and HÁ Á ÁO/OÁ Á ÁH interactions suggest that van der Waals interactions play the major role in the crystal packing (Hathwar et al., 2015).

Interaction energy calculations
The intermolecular interaction energies are calculated using the CE-B3LYP/6-31G(d,p) energy model available in Crystal Explorer 17.5 (Turner et al., 2017), where a cluster of molecules is generated by applying crystallographic symmetry operations with respect to a selected central molecule within the radius of 3.8 Å by default (Turner et al., 2014). The total intermolecular energy (E tot ) is the sum of electrostatic (E ele ), polarization (E pol ), dispersion (E dis ) and exchange-repulsion (E rep ) energies (Turner et al., 2015) with scale factors of 1.057, 0.740, 0.871 and 0.618, respectively (Mackenzie et al., 2017). The evaluation of the energies indicates that the stabilizations in the title compound are dominated by the dispersion energy contributions.

DFT calculations
The optimized structure (Fig. 6) of the title compound was generated theoretically via density functional theory (DFT) using standard B3LYP functional and 6-31 G(d) basis-set calculations (Becke, 1993) as implemented in GAUSSIAN 09 (Frisch et al., 2009). The theoretical and experimental results were in good agreement ( Table 2). As is common in these studies, there are differences between the observed and calculated values because the former pertain to the solid state while the latter are for an isolated molecule in the gas phase. The correlation graphs based on the calculations of the bond lengths and angles for comparison with the experimental results are shown in Fig. 7a     The optimized structure of the title compound, (I).

Figure 7
The correlation graphs of the calculated and experimental (a) bond lengths and (b) bond angles of the title compound, (I).
occupied molecular orbital (HOMO), acting as an electron donor, and the lowest-unoccupied molecular orbital (LUMO), acting as an electron acceptor, are very important parameters for quantum chemistry. When the energy gap is small, the molecule is highly polarizable and has high chemical reactivity and it is characterized as soft. The DFT calculations provide some important information on the reactivity and site selectivity of the molecular framework. E HOMO and E LUMO clarify the inevitable charge exchange collaboration inside the studied material, electronegativity (), hardness (), potential (), electrophilicity (!) and softness () are recorded in Table 3. The significance of and is to evaluate both the reactivity and stability. The HOMO and LUMO energy levels are shown in Fig. 8. The HOMO is localized in the plane extending over the whole cholesteryl heptanoate ring, while the LUMO is localized on the oxygens and their surrounding atoms. The energy band gap [ÁE = E LUMO À E HOMO ] of the molecule is 6.49 eV, and the frontier molecular orbital energies, E HOMO and E LUMO are À7.05 and À0.56 eV, respectively. The molecular electrical potential surfaces or electrostatic potential energy maps illustrate the charge distributions of the molecules in three dimensions, allowing one to visualize variably charged regions of the molecule, which may be used to determine how molecules interact with one another. Electrostatic potential maps (MEPs) are invaluable in predicting the behaviour of complex molecules. The MEP of the title compound is shown in Fig. 9, where the negative electrostatic potential formed around O1 and O2 atoms and positive   Table 2 Comparison of the selected (X-ray and DFT) geometric data (Å , ).

Figure 9
The MEP plot of the title compound, (I).

Figure 8
The LUMO and HOMO energies of the title compound, (I).
potential (green) formed around the hydrogen atoms. The MEP values of atoms O1 and O2 are À0.050 and À0.017 a.u., respectively. Thus, atoms O1 and O2 are the most appropriate ones for electrophilic attacks while H atoms are more appropriate for nucleophilic attacks.

Synthesis and crystallization
The white fine crystalline powder of cholesteryl heptanoate (C 34 H 58 O 2 ) was purchased from Merck, and single crystals were grown by slow evaporation of a concentrated ethyl acetate solution.

Refinement
Crystal data, data collection and structure refinement details are summarized in   (Farrugia, 2012); software used to prepare material for publication: WinGX publication routines (Farrugia, 2012) and PLATON (Spek, 2020).

Cholesteryl heptanoate
Crystal data Special details Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.