Crystal structure, Hirshfeld surface analysis, calculations of crystal voids, interaction energy and energy frameworks as well as density functional theory (DFT) calculations of 3-[2-(morpholin-4-yl)ethyl]-5,5-diphenylimidazolidine-2,4-dione

In the title molecule, the imidazolidine ring slightly deviates from planarity and the morpholine ring exhibits the usual chair conformation. In the crystal, N—H⋯O and C—H⋯O hydrogen bonds form helical chains of molecules extending parallel to the c axis that are connected by C—H⋯π(ring) interactions into a tri-periodic network.

In the title molecule, C 21 H 23 N 3 O 3 , the imidazolidine ring slightly deviates from planarity and the morpholine ring exhibits the chair conformation.In the crystal, N-H� � �O and C-H� � �O hydrogen bonds form helical chains of molecules extending parallel to the c axis that are connected by C-H� � ��(ring) interactions.A Hirshfeld surface analysis reveals that the most important contributions for the crystal packing are from H� � �H (55.2%),H� � �C/C� � �H (22.6%) and H� � �O/O� � �H (20.5%) interactions.The volume of the crystal voids and the percentage of free space were calculated to be 236.78A ˚3 and 12.71%, respectively.Evaluation of the electrostatic, dispersion and total energy frameworks indicates that the stabilization is dominated by the nearly equal electrostatic and dispersion energy contributions.The DFT-optimized molecular structure at the B3LYP/6-311 G(d,p) level is compared with the experimentally determined molecular structure in the solid state.Moreover, the HOMO-LUMO behaviour was elucidated to determine the energy gap.

Chemical context
The investigation of compounds comprising the hydantoin moiety has gained interest in the quest for the development of new drugs because of their similarity to natural amino acids (S ´ladowska et al., 2016).Such compounds show various pharmacological properties, including antibacterial (Pandeya et al., 2000;Sangeetha et al., 2016), anticonvulsant (Emami et al., 2021), antidiabetic (Salem et al., 2018), antitumor (Z ˙esławska et al., 2021), antinociceptive and anti-inflammatory (Abdel-Aziz et al., 2016;da Silva Guerra et al., 2011) activities.One of the foremost pharmaceutical drugs in the hydantoin class is phenytoin, also known as 5,5-diphenylhydantoin (systematic name: 5,5-diphenylimidazolidine-2,4dione).This compound and its derivatives are considered to be potential pharmaceutical agents due to their extended shelf life.However, their optimum efficacy depends on how easily they break down in the body (Al-Nuzal et al., 2018).With respect to the biological importance of phenytoin, we were interested in the synthesis of a new derivative thereof, viz.
3-[2-(morpholin-4-yl)ethyl]-5,5-diphenylimidazolidine-2,4-dione, (I), C 21 H 23 N 3 O 3 , through an alkylation reaction under the conditions of phase transfer catalysis.We report here the molecular and crystal structures as well as the Hirshfeld surface analysis of this compound, as well as intermolecular interaction energies, energy frameworks, and a comparison of the experimentally determined molecular structure in the solid state with that of an optimized structure obtained by density functional theory (DFT).

Figure 1
The title molecule with the labelling scheme and displacement ellipsoids drawn at the 50% probability level.
Cg3 is the centroid of the C4-C9 benzene ring.agreement with the calculation of a relatively small void space (vide infra).

Hirshfeld surface analysis
In order to visualize the intermolecular interactions in the crystal of (I), a Hirshfeld surface (HS) analysis (Hirshfeld, 1977;Spackman & Jayatilaka, 2009) was carried out using CrystalExplorer (Spackman et al., 2021).In the HS plotted over d norm (Fig. 4), 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 (distant contact) than the sum of the van der Waals radii, respectively (Venkatesan et al., 2016).The bright-red spots on the surface indicate the roles of adjacent atoms as the respective donors and/or acceptors and they also appear as blue and red regions corresponding to positive (hydrogenbond donors) and negative (hydrogen-bond acceptors) potentials on the HS mapped over electrostatic potential (Spackman et al., 2008;Jayatilaka et al., 2005), as shown in View of the three-dimensional Hirshfeld surface of (I) plotted over d norm .

Figure 5
View of the three-dimensional Hirshfeld surface of (I) plotted over electrostatic potential energy using the STO-3 G basis set at the Hartree-Fock level of theory.Hydrogen-bond donors and acceptors are shown as blue and red regions around the atoms corresponding to positive and negative potentials, respectively.

Figure 6
Hirshfeld surface of the title compound plotted over shape-index.

Figure 7
The  8a-c.The Hirshfeld surface analysis confirms the importance of H-atom contacts in establishing the packing.The large number of H� � �H, H� � �C/C� � �H and H� � �O/O� � �H interactions suggest that van der Waals interactions and hydrogen-bonding interactions play the major roles in the crystal packing (Hathwar et al., 2015).

Crystal voids
The strength of the crystal packing is important for determining the response to an applied mechanical force.If significant voids are present in the crystal, the molecules are not tightly packed and a small amount of applied external mechanical force may easily break the crystal.To check the mechanical stability of the crystal, a void analysis was performed by adding up the electron densities of the spherically symmetric atoms contained in the asymmetric unit (Turner et al., 2011).The void surface is defined as an isosurface of the procrystal electron density and is calculated for the whole unit cell where the void surface meets the boundary of the unit cell, and capping faces are generated to create an enclosed volume.The volume of the crystal voids (Fig. 9a,b) and the percentage of free space in the unit cell were calculated as 236.78A ˚3 and 12.71%.

Interaction energy calculations and energy frameworks
The intermolecular interaction energies were calculated using the CE-B3LYP/6-31G(d,p) energy model available in Crys-talExplorer (Spackman et al., 2021) where a cluster of molecules is generated by applying crystallographic symmetry operations with respect to a selected central molecule within a radius of 3.8 A ˚ (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).Hydrogenbonding interaction energies (in kJ mol À 1 ) were calculated to

Figure 10
The energy frameworks for a cluster of molecules of (I) viewed down the b axis, showing (a) electrostatic energy, (b) dispersion energy and (c) total energy diagrams.The cylindrical radius is proportional to the relative strength of the corresponding energies and they were adjusted to the same scale factor of 80 with cut-off value of 5 kJ mol-1 within 2�2�2 unit cells.
be À 50.2(E ele ), À 12.7 (E pol ), À 27.6 (E dis ), 58.2 (E rep ) and À 50.5 (E tot ) for N2-H2� � �O3 and À 17.4 (E ele ), À 3.7 (E pol ), À 56.2 (E dis ), 43.2 (E rep ) and À 43.4 (E tot )] for C14-H14� � �O2.Energy frameworks combine the calculation of intermolecular interaction energies with a graphical representation of their magnitude (Turner et al., 2015).Energies between molecular pairs are represented as cylinders joining the centroids of pairs of molecules with the cylinder radius proportional to the relative strength of the corresponding interaction energy.Energy frameworks were constructed for E ele (red cylinders), E dis (green cylinders) and E tot (blue cylinders) and are displayed in Fig. 10a-c.The evaluation of the electrostatic, dispersion and total energy frameworks indicate that the stabilization is dominated by nearly equal electrostatic and dispersion energy contributions in the crystal structure of (I).

DFT calculations
The optimization of the molecular gas-phase structure of (I) was conducted using density functional theory (DFT) with the B3LYP functional and 6-311G(d,p) basis-set calculations, as implemented in GAUSSIAN09 (Becke, 1993;Frisch et al., 2009).The comparison between theoretical and experimental results revealed good agreement (Table 2).Essential parameters, such as the highest-occupied molecular orbital (HOMO) serving as an electron donor and the lowest-unoccupied molecular orbital (LUMO) acting as an electron acceptor, were examined, whereby a small energy gap indicates high molecular polarizability and reactivity.Numerical parameters of E HOMO , E LUMO , electronegativity (�), hardness (�), potential (�), electrophilicity (!), and softness (�) are detailed in Table 3.The values of � and � are particularly significant for assessing both reactivity and stability.The electron transition from the HOMO to the LUMO energy level is shown in Fig. 11.Both the HOMO and LUMO are localized in the molecular plane.The energy band gap (E = E LUMO À E HOMO ) is approximately 4.62 eV, with frontier molecular orbital (FMO) energies, E HOMO and E LUMO , determined as À 5.36 and À 0.73 eV, respectively.

Database survey
A search of the Cambridge Structural Database (CSD; Groom et al., 2016; updated January 2024) with the fragment (II) (Fig. 12) gave ten hits, one of which (LUHFID; Ooms et al.,

Figure 12
The molecular moiety used for the CSD search procedure.

Figure 11
The energy band gap of the title compound.Guerrab et al., 2023).In all cases, the five-membered ring is close to planarity and the nitrogen lone pairs are involved in N!C � bonding.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 4. H atoms attached to C atoms were placed in calculated positions (C-H = 0.95-0.99A ˚) and were included as riding contributions with isotropic displacement parameters 1.2-1.5 times those of the attached atoms.The H atom attached to N2 was found in a difference-Fourier map and refined with a distance of 0.91 (1) A ˚. Two reflections, 111 and 011, affected by the beamstop were omitted from the final refinement.Computer programs: APEX4 and SAINT (Bruker, 2021), SHELXT (Sheldrick, 2015a), SHELXL (Sheldrick, 2015b), DIAMOND (Brandenburg & Putz, 2012), SHELXTL (Sheldrick, 2008) and PLATON (Spek, 2020).

Special details
Experimental.The diffraction data were obtained from 13 sets of frames, each of width 0.5° in ω or φ, collected with scan parameters determined by the "strategy" routine in APEX4.The scan time was 10 sec/frame.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.Refinement.Refinement of F 2 against ALL reflections.The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 .The threshold expression of F 2 > 2sigma(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement.R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.H-atoms attached to carbon were placed in calculated positions (C-H = 0.95 -0.99 Å) and were included as riding contributions with isotropic displacement parameters 1.2 -1.5 times those of the attached atoms.That attached to nitrogen was placed in a location derived from a difference map and refined with a DFIX 0.91 0.01 instruction.Two reflections affected by the beamstop were omitted from the final refinement.

Figure 2 A
Figure 2 A portion of one helical chain in the crystal structure viewed along the b axis.N-H� � �O and C-H� � �O hydrogen bonds are depicted by violet and black dashed lines, respectively.Non-interacting hydrogen atoms are omitted for clarity.

Figure 3
Figure 3The crystal packing viewed along the a axis with N-H� � �O and C-H� � �O hydrogen bonds depicted by violet and black dashed lines, respectively, and with C-H� � ��(ring) interactions depicted by green dashed lines.Non-interacting hydrogen atoms are omitted for clarity.

Fig. 5 .
Figure 4 full two-dimensional fingerprint plots for (I), showing (a) all interactions, and delineated into (b) H� � �H, (c) H� � �C/C� � �H, (d) H� � �O/ O� � �H and (e) H� � �N/N� � �H interactions.The d i and d e values are the closest internal and external distances (in A ˚) from given points on the Hirshfeld surface.the overall crystal packing, are shown in Fig. 7c with the tips at d e + d i = 2.74 A ˚and are attributed to C-H� � �� interactions.The symmetrical pair of spikes in the fingerprint plot delineated into H� � �O/O� � �H contacts with the tips at d e + d i = 1.84A ˚(Fig.7d) make a 20.5% contribution to the HS.Finally, the tiny pair of spikes with the tips at d e + d i = 2.70 A ˚in the fingerprint plot delineated into H� � �N/N� � �H contacts (Fig. 7e) contributes only 1.7% to the HS.The nearest neighbour coordination environment of a molecule can be determined from the colour patches on the HS based on how close to other molecules they are.The Hirshfeld surface representations with the function d norm plotted onto the surface are shown for the H� � �H, H� � �C/ C� � �H and H� � �O/O� � �H interactions in Fig.

Figure 9
Figure 9Graphical views of voids in the crystal packing of (I), (a) along the a axis and (b) along the c axis.

Table 2
Comparison of the selected (X-ray and DFT) geometric data (A ˚, � ).

Table 4
Experimental details.