Crystal structure, DFT and Hirshfeld surface analysis of N-acetyl-t-3-methyl-r-2,c-6-diphenylpiperidine

In the title compound, C20H23NO, the piperidine ring adopts a distorted boat conformation, while the phenyl rings subtend a dihedral angle 65.1 (2)°. In the crystal, molecules are linked by C—H⋯O hydrogen bonds into chains extending along the b-axis direction.


Chemical context
The structures of a wide array of heterocyclic derivatives have been analysed for their pharma-potentiality over the past three decades (Katritzky, 2010). Among these, derivatives of the six-membered heterocyclic base piperidine have proven to be successful pharmacophores. 2,6-Substituted piperidine derivatives have been found to be useful as tranquilizers and possess a wide range of biological activities such as anti-tumor (Vinaya et al., 2009), antiviral, antimalarial, antibacterial and antifungal activities (Aridoss et al., 2009;Mobio et al., 1989). These have spurred considerable awareness of the synthetic arena based on their structure, reactivity, synthesis and biological properties. We report herein the crystal structure, Hirshfeld surface analysis and DFT computational calculations of the title compound.

Structural commentary
The methyl-substituted piperidine title compound crystallizes in the monoclinic space group P2 1 . A perspective view of the ISSN 2056-9890 molecule is shown in Fig. 1. The bond lengths and angles are well within the expected limits (Roques et al., 1981), and agree with values observed in related structures (Sekar et al., 1990).
The piperidine ring [N1/C2-C6] makes dihedral angles of 82.0 (1) and 58.4 (1) , respectively, with the C13-C18 and C7-C12 phenyl rings, and confirms the fact that the moieties are in axial and equatorial orientations. It is to be noted that there is a possibility of resonance between atoms N1, C19 and O1 as a result of the delocalization of the hetero electrons of the carbonyl group, which is also confirmed by the torsion angles C2-N1-C19-O1 = 177.7 (2) and C6-N1-C19-O1 = 13.0 (3) .
The methyl group substituted at the 5-position of the piperidine ring is axially oriented, as confirmed by the torsion angles N1-C6-C5-C21 = À68.0 The molecular structure of the title compound, showing the atomic numbering and displacement ellipsoids drawn at the 30% probability level.

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).

Supramolecular features
The crystal packing features C-HÁ Á ÁO interactions (Table 1). Atom C20 of the molecule at (x, y, z) donates a proton to atom O1 of the molecule at (Àx + 1, y + 1 2 , Àz + 1), forming a C4 zigzag chain (Bernstein et al., 1995) running along the b-axis direction as shown in Fig. 2. The overall packing is shown in Fig. 3.

Density functional theory (DFT) study
The optimized molecular structure and frontier molecular orbitals (FMOs) (Figs. 4 and 5, respectively) were calculated using the DFT/B3LYP/6-311G(d,p) basis set implemented in the GAUSSIAN09 program package (Frisch et al., 2009). The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are called frontier molecular orbitals (FMOs) as they lie at the outermost boundaries of the electrons of the molecule. The electron distribution (ED) 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 represented in green and red, respectively.
The HOMO of the title molecule is localized on one aromatic ring and the C O group, while the LUMO is located over the whole molecule with the exception of the CH 3 group and some carbon and hydrogen atoms in the piperidine ring. Thus the HOMO/LUMO implies an ED transfer to the C O group from the ring. The energy band gap (ÁE = E HOMO À E LUMO ) of the molecule is 3.165 eV and the calculated frontier molecular orbital energies, E HOMO and E LUMO , are À5.212 and À2.047 eV, respectively. The title compound has a small frontier orbital gap, hence the molecule has high chemical reactivity and low kinetic stability. The electron affinity (A) and ionization potential (I) of the molecule were calculated using the DFT/B3LYP/6-311++G(d,p) basis set. The values of the hardness (), softness (), electronegativity () and electrophilicity index (!) for the title compound are given in Table 2.

Hirshfeld surface analysis
In order to visualize the intermolecular interactions in the crystal of the title compound, a Hirshfeld surface (HS) analysis (Spackman & Jayatilaka, 2009) was carried out and the associated two-dimensional fingerprint plots (McKinnon et al., 2007) were generated using CrystalExplorer17 (Turner et al., 2017). The Hirshfeld surface mapped over d norm using a standard surface resolution with a fixed colour scale of À0.2 (red) to 1.3 (blue) a.u. is shown in Fig. 6a Table 2 Physico-chemical properties.

Figure 4
The optimized molecular structure of the title compound.

Figure 5
The frontier molecular orbitals (FMOs) of the title compound.
longer contacts are indicated as red and blue spots, respectively, on the Hirshfeld surfaces, and contacts with distances approximately equal to the sum of the van der Waals radii are represented as white spots. The most important red spots on the d norm surface represent C-HÁ Á ÁO interactions. 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 surface with high curvedness is highlighted as dark blue 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 (Mohamooda Sumaya et al., 2017).
The two-dimensional fingerprint plots of (d i , d e ) points of all the contacts contributing to the Hirshfeld surface analysis in normal mode for all the atoms are shown in Fig. 7. The most important intermolecular interactions are HÁ Á ÁH contacts, contributing 73.2% to the overall crystal packing. Other interactions and their respective contributions are CÁ Á ÁH/ HÁ Á ÁC (18.4%) and OÁ Á ÁH/HÁ Á ÁO (8.4%), respectively.
The Hirshfeld surface analysis confirms the importance of H-atom contacts in establishing the packing. The large number of HÁ Á ÁH and CÁ Á ÁH/HÁ Á ÁC interactions suggest that van der Waals interactions and hydrogen bonding play the major roles in the crystal packing (Hathwar et al., 2015).

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.
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å 2 )