Crystal structure, Hirshfeld surface analysis and DFT studies of 1-[r-2,c-6-diphenyl-t-3-(propan-2-yl)piperidin-1-yl]ethan-1-one

The dihedral angles between the mean plane of the piperidine ring, which adopts a chair conformation, and the phenyl rings are 89.72 (8) and 48.32 (8)°. In the crystal, molecules are linked into chains along the b-axis direction by C—H⋯O hydrogen bonds.


Chemical context
Piperidine is a heterocyclic six-membered ring containing nitrogen as a hetero atom and is an essential structural part of many important drugs including paroxetine, raloxifene, haloperidol, droperidol and minoxidiln (Wagstaff et al., 2002). Piperidine derivatives exhibit a wide range of biological activities, such as antimicrobial, anti-inflammatory, antiviral, antimalarial and general anesthetic (Aridoss et al., 2009). The biological properties of piperidines are highly dependent on the type and position of substituents on the heterocyclic ring. 2,6-Disubstituted piperidine derivatives have been found to possess fungicidal, bactericidal and herbicidal activities (Mobio et al., 1989). Piperidine derivatives are the intermediate products in agrochemicals, pharmaceuticals, rubber vulcanization accelerators and are widely used as building block molecules in many industries. Various piperidine derivatives are present in numerous alkaloids (Badorrey et al., 1999).
This wide range of biological activities prompted us to synthesize novel 2,6-diphenyl piperdine derivatives. Against this background, the structure of the title compound has been determined.

Structural commentary
The molecular structure of the title compound is shown in Fig. 1. The diphenyl-substituted piperidine compound crystallizes in the monoclinic space group P2 1 /n. The bond lengths and angles are well within the expected limits and comparable with literature values (Allen et al., 1998).

Supramolecular features
In the crystal, molecules are linked into C(8) chains along the b-axis direction by C-HÁ Á ÁO hydrogen bonds (Table 1, Fig. 2). The overall crystal packing of the title compound is shown in Fig. 3.

DFT study
The optimized structure of the molecule in the gas phase was generated theoretically via density functional theory (DFT) using standard B3LYP functional and 6-311G(d,p) basis-set Symmetry code: (i) x À 1 2 ; Ày þ 1 2 ; z À 1 2 .

Figure 2
A partial view along the b axis of the crystal packing of the title compound, showing the formation of a molecular chain by C-HÁ Á ÁO interactions (dotted lines).

Figure 3
The overall crystal packing of the title compound, viewed along the b-axis direction. Hydrogen bonds are shown as dashed lines, and only the H atoms involved in hydrogen bonding have been included.

Figure 1
The molecular structure of the title compound, showing the atomic numbering and displacement ellipsoids drawn at the 30% probability level.
calculations (Becke et al., 1993), as implemented in GAUS-SIAN09 (Frisch et al., 2009). The overlay diagram for the optimized structure (purple) and the structure in solid state (green) with respect to the piperidine ring is shown in Fig. 4. The piperidine rings in the two phases have an r.m.s deviation of 0.434 Å for the nonhydrogen atoms. The conformation of the molecules in the two phases differs with respect to the central piperidine ring, as seen in the disparity of about 38.5 in the N1-C6-C5-C4 torsion angles (39.88/1.38 ) and 2.25 in the N1-C2-C3-C4 torsion angles (44.41/39.81 ) for the optimized and solid-state molecules, respectively.
The highest-occupied molecular orbital (HOMO), acting as an electron donor, and the lowest-unoccupied molecular orbital (LUMO), acting as an electron acceptor, are known as frontier molecular orbitals (FMOs). The FMOs play an important role in the optical and electric properties, as well as in quantum chemistry (Fleming, 1976). When the energy gap is small, the molecule is highly polarizable and has high chemical reactivity. The electron distribution of the HOMOÀ1, HOMO, LUMO and LUMO+1 energy levels and the energy values are shown in Fig. 5. The positive and negative phases are shown in green and red, respectively.
The HOMO of the title molecule is localized on the C O group, one aromatic ring and the piperidine ring, while the LUMO is located over the whole molecule expect for the isopropyl group. The DFT study shows that the FMO energies E HOMO and E LUMO are À4.804 and À1.694 eV, respectively, and the HOMO-LUMO energy gap is 3.110 eV. The title compound has a small frontier orbital gap, hence the molecule has high chemical reactivity and low kinetic stability.
The electron affinity (I) and ionization potential (A) of the molecule were calculated using the DFT/B3LYP/6-311++G(d,p) basis set. A high value of the electrophilicity index describes a good electrophile, while a small value of electrophilicity index describes a good nucleophile. The values of the hardness (), softness (), electronegativity () and electrophilicity index (!) for the title compound are given in Table 2.

Hirshfeld surface analysis
CrystalExplorer17 (Turner et al., 2017) was used for the Hirshfeld surface (HS) analysis (Spackman & Jayatilaka, 2009) and to generate the associated two-dimensional fingerprint plots (McKinnon et al., 2007) to quantify the various intermolecular interactions in the structure of the title compound. In the HS plotted over d norm (Fig. 6), the white surface indicates contacts with distances equal to the sum of the 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 HS mapped over curvedness and shape-index, introduced by Koendrink (Koenderink, 1990;Koenderink & van Doorn, 1992), give further chemical insight into molecular packing. A surface with low curvedness designates a flat region and may be indicative ofstacking in the crystal. A The frontier molecular orbitals (FMOs) of the title compound.   Hirshfeld surface with high curvedness is highlighted as darkblue edges, and is indicative of the absence ofstacking (Fig. 6). The nearest neighbour coordination environment of a molecule is identified from the colour patches on the Hirshfeld surface, depending on their closeness to adjacent molecules  et al., 2004). In these compounds, the piperidine ring adopts a chair conformation as the title compound. The phenyl rings substituted at the 2-and 6-positions of the piperidine ring subtend dihedral angles of 89.78 (7) and 48.30 (8) , respectively, with the best plane of the piperidine ring in the title compound and 81.04 (7) and 81.10 (7) , respectively, in NIKYEN, whereas in BIHZEY they are equatorially oriented. The C-HÁ Á ÁO interaction leads to the formation of a C(8) chain in the title compound, while it forms dimers in the other two structures.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 3. H atoms were positioned geometrically (N-H = 0.88-0.90 Å and C-H = 0.93-0.98 Å ) and allowed to ride on their parent atoms,with U iso (H) = 1.5Ueq(C) for methyl H 1.2Ueq(C) for other H atoms.

N-acetyl-3-isopropyl-2,6-diphenylpiperidine
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.