Crystal structure, Hirshfeld surface and frontier molecular orbital analysis of 9-(3-bromo-4-hydroxy-5-methoxyphenyl)-3,3,6,6-tetramethyl-3,4,5,6,7,9-hexahydro-1H-xanthene-1,8(2H)-dione

In the xanthene moiety of the title compound, the central ring adopts a flattened-boat conformation whereas the cyclohexenone rings adopt envelope conformations. In the crystal, molecules are linked by pairs of O—H⋯O hydrogen bonds, forming inversion dimers with an (20) ring motif.

In the fused ring system of the title compound, C 24 H 27 BrO 5 , the mean plane and maximum deviations of the central pyran ring are 0.0384 (2) and 0.0733 (2) Å , respectively. The cyclohexenone rings both adopt envelope conformations with the tetra-substituted C atoms as flap atoms, whereas the central pyran ring adopts a flattened boat conformation. The central pyran and phenyl substituent rings are almost perpendicular to each other, making a dihedral angle of 89.71 (2) . In the crystal, pairs of molecules are linked via O-HÁ Á ÁO hydrogen bonds, forming inversion dimers with an R 2 2 (20) ring motif. A Hirshfeld surface analysis indicates that the most important contributions to the crystal packing are from HÁ Á ÁH (50.6%), OÁ Á ÁH/HÁ Á ÁO (22.9%) and CÁ Á ÁH/HÁ Á ÁC (11.1%) contacts. Quantum chemical calculations for the frontier molecular orbitals were undertaken to determine the chemical reactivity of the title compound.

Structural commentary
The title compound (I) (Fig. 1) crystallizes in the triclinic space group P1 with Z = 2. The central pyran ring B (O1/C1/C8-C10/ C17) is almost planar with a mean deviation from the mean plane of 0.0384 (2) Å and a maximum deviation of 0.0733 (3) Å for C9. Atoms C9 and O1 are displaced out of the mean plane in the the same direction so the ring may also be described as having a highly flattened boat conformation.

Figure 2
A view of the structure of (I) showing the O-HÁ Á ÁO hydrogen bonds, forming a centrosymmetric dimer with an R 2 2 (20) ring motif.

Figure 3
Packing view for (I), showing the formation of O-HÁ Á ÁO hydrogen bonds between molecules in the unit cell.

Figure 1
A view of the structure of (I), showing the atom-numbering scheme. Displacement ellipsoids are drawn at the 50% probability level.
To quantify the intermolecular contacts in the crystal, Hirshfeld surfaces (Spackman & Jayatilaka, 2009) and two-dimensional fingerprint plots were generated using Crystal Explorer 17.5 (Turner et al., 2017). The Hirshfeld surfaces mapped over d norm in the range À0.5451 to 1.6834 a.u. (Fig. 4) show the intermolecular contacts as red-coloured spots, which indicate the closer contacts of C-HÁ Á ÁO and O-HÁ Á ÁO hydrogen bonds. The bright-red spots indicate their roles as donors and/or acceptors in hydrogen bonding; they also appear as red and blue regions corresponding to negative and positive potentials on the Hirshfeld surface mapped over electrostatic potential (Spackman et al., 2008)  View of the three-dimensional Hirshfeld surface of (I) plotted over d norm in the range À0.5451 to 1.6834 a.u. The two O-HÁ Á ÁO hydrogen bonds forming the dimer are depicted as dashed lines.

Figure 5
View of the three-dimensional Hirshfeld surface of (I) plotted over electrostatic potential energy in the range À0.0500 to 0.0500 a.u. using the STO-3 G basis set at the Hartree-Fock level of theory. The hydrogenbond donors and acceptors are viewed as blue and red regions, respectively, around atoms, corresponding to positive and negative potentials.

Figure 6
The percentage contributions of close contacts of (I). The d i and d e values are the closest internal and external distances (in Å ) from given points on the Hirshfeld surface. and BrÁ Á ÁH/HÁ Á ÁBr (11.6%) interactions make a significant contribution to the total Hirshfeld surface. The percentage contributions of the BrÁ Á ÁO/OÁ Á ÁBr, OÁ Á ÁO and CÁ Á ÁC contacts are 1.8, 0.7 and 0.1%, respectively.

Frontier molecular orbital analysis
The chemical reactivity of the title compound was studied by frontier molecular orbital analysis. For the calculation, the starting structural geometry was taken from the refined experimental structure obtained from X-ray diffraction data. The energy levels for the compound were computed using the DFT-B3LYP/6-311G++(d,p) level of theory as implemented in Gaussian09W (Frisch et al., 2013). The calculated frontier molecular orbitals, HOMO, HOMOÀ1, LUMO and LUMO+1, are shown in Fig. 7. The energies of HOMO, HOMOÀ1, LUMO and LUMO+1 were calculated to be À5.8915, À6.2499, À1.9353 and À1.0419 eV, respectively, and the energies required to excite one electron from HOMO to LUMO and from HOMOÀ1 to LUMO+1 are 3.9562 and 5.2080 eV, respectively. The chemical potential, chemical hardness, chemical softness and electrophilicity index of the title molecule are listed in Table 2. Parr et al. (1999) have proposed the electrophilicity index as a quantitative measure of the energy lowering due to the maximal electron flow between donor and acceptor orbitals. The electrophilicity index value of 3.8711 eV shows the global electrophilic nature of the molecule. Based on the wide band gap and its chemical hardness value of 1.9781 eV, the title molecule seems to be hard.  Purushothaman & Thiruvenkatam, 2018). In the title compound, the dihedral angle between the phenyl and pyran rings is 89.71 (2) , similar to the values observed for LERZEP, the 2,4-dinitrophenyl analogue, YAVTAS, the 4hydroxy-3,5-dimethoxyphenyl analogue, and VITWEC, the 2,4-difluorophenyl analogue, for which the dihedral angles are 85.88 (2), 86.32 (2) and 87.55 (4) , respectively.

Figure 7
The frontier molecular orbitals of (I

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 3. Hydrogen atoms were fixed geometrically and treated as riding atoms, with C-H = 0.93-0.97 Å and U iso (H) = 1.2U eq (C) or 1.5U eq (C-methyl).    (Farrugia, 2012) and Mercury (Macrae et al., 2020); software used to prepare material for publication: SHELXL2018 (Sheldrick, 2015a) and publCIF (Westrip, 2010). 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 )
x y z U iso */U eq