Cyclohexanone-Based Chalcones as Alternatives for Fuel Additives.

The use of small molecules, such as chalcones and their derivatives, for more efficient fuels is in increasing demand due to environmental factors. Here, three crystal structures (BH I, II, and III) of cyclohexanone-based chalcones were synthesized and described by single-crystal X-ray diffraction and Hirshfeld surface analysis. The supramolecular modeling analysis on the hyperconjugative interaction energies and QTAIM analysis at the ωB97XD/6-311++G(d,p) level of theory were carried out to analyze the intermolecular interactions in the solid-state. The structure-property relationship, frontier molecular orbital, molecular electrostatic potential, and the experimental calorific value analysis show that the three compounds are a good alternative to be used as an additive for some fuels. Our findings represent a further step forward in the development of cheaper and more efficient fuel additives and pose an opportunity for further investigation on similar analogues.

Introduction

The push from the exhaustion of fossil fuels and global warming problems has increased the demand for alternative bioenergy sources and improved the efficiency of current fuels.[1] Regarding currently used biofuels, their energetic efficacy is affected by inherent stability, oxidation, and energy availability limitations.[2] The use of small molecules for these purposes is an attractive alternative, once they usually are easily synthesized, cost-wise accessible, and serve for a myriad of different applications, including the modulation of protein–protein interactions, alteration of protein function, catalytic activity, and energy source for crucial chemical reactions.[3] In fact, due to its physicochemical properties similar to cellulose, the small molecule α-cyclodextrin has been investigated as an accurate way to unveil the chemical mechanisms involved during high-temperature conversion to biofuel.

Chalcones and their analogues are either found in plants or obtained from specific synthetic pathways and have shown numerous applications as liquid crystal materials,[4] pH sensors,[5,6] nonlinear optical materials,[7,8] as well as their remarkable biological properties: antitumor,[9,10] anti-inflammatory,[11] antifungal,[12−14] antibacterial,[12,15,16] and antioxidant.[17−20] Some of these properties can be related to fuel applications, such as energy efficiency or additives,[21−27] and often fuels such as ethanol and biofuels are prone to suffer from degradation and oxidation problems, mainly caused by micro-organisms[28−34] or even the lower combustion capacity, therefore, a lower energy efficiency.[35−39]

Chalcone molecular structures have stimulated studies of their spatial conformation systems, such as π-electronic conjugations,[40] cyclohexanone rings,[41] electronic effects of substituents in the aromatic rings,[42] interaction energies, and electronic properties obtained by density functional theory (DFT) calculations.[43] Understanding these interactions has been applied to comprehend these physical chemistry systems and pharmaceutical and material properties. X-ray crystallography, Hirshfeld surface analysis, and theoretical studies are handy tools for this subject.

Based on these potentials as fuel additives previously described for chalcones, we hypothesized that cyclohexanone-based analogues would present the same physicochemical features needed to improve biofuel’s efficiency. Here we report the results of the (2E,6E)-2,6-bis(4-ethylbenzylidene)cyclohexanone (BH I), (2E,6E)-2,6-bis(2,4-dichlorobenzylidene)cyclohexanone (BH II), and (2E,6E)-2,6-bis(4-chlorobenzylidene)cyclohexanone (BH III) from single-crystal X-ray diffraction (XRD) and Hirshfeld surface (HS) analysis in order to describe its molecular and supramolecular architectures. In addition to molecular structure studies, theoretical calculations such as frontier molecular orbital (FMO), molecular electrostatic potential (MEP) map, hyperconjugative interaction energies, counterpoise procedure, quantum theory of atoms in molecules (QTAIM), and vibrational infrared (IR) spectra assignments were carried out at the ωB97XD/6-311++G(d,p) level of theory. Finally, we quantified their energetic potential using a calorimetric pump, which was then compared to ethanol, biodiesel, diesel, and butanol.

Experimental and Computational Procedures

Synthesis and Crystallization

The reaction was carried out at room temperature where BH I, II, and III were prepared by the reaction of cyclohexanone (3.00 mmol) and substituted benzaldehydes (2.00 mmol) in a minimum amount of absolute methanol (10 mL) as shown in Scheme . Then a 30% KOH solution was added and after a few minutes of continuous stirring, the reaction was completed, and the precipitate obtained was collected by filtration. Yellow product was obtained in 75% yield.

Scheme 1

Chemical Scheme of the Synthesized BH I, II, and III

Crystals of BH I, II, and III were grown in dichloromethane inside a beaker with a known solvent volume. Then, the reaction mixture was kept at room temperature for slow evaporation for 96 h until the formation of crystals. All solvents and chemicals used in the synthesis were obtained from commercial sources and used without further purification. Thin-layer chromatography (TLC) was carried out using Silica gel 60 UV254 plates, and the solvent system was ethyl acetate–hexane (3:7). Infrared (IR) spectra were recorded using a PerkinElmer-8400S FT-IR (400–4000 cm–1) with the KBr pellet technique. 1H and 13C nuclear magnetic resonance (NMR) spectra were recorded on a Bruker 500 MHz NMR spectrometer using CDCl3 as solvent. IR, 1H, and 13C NMR data of the representative BH I, II, and III are given as follows:

BH I

C24H26O (330.462 g/mol); yellow solid, 75% yield. IR (KBr) (cm–1): 3084, 3048, 3023, 3001, 2965, 2929, 2853, 1663, 1606, 1580, 1508, 1457, 1165, 1140, 828; 1H NMR (500 MHz, CDCl3): δ 1.28 (6H, t, J = 7.5), 1.82 (2H, dtt, J = 14.2, 6.5, 2.8 Hz), 2.70 (4H, ddd, J = 14.6, 6.5, 2.8 Hz), 2.96 (4H, q, J = 7.5), 7.27 (4H, d, J = 7.99; 1.43; 0.46), 7.48 (4H, d, J = 8.1, 1.4, 0.5 Hz), 7.82 (2H, s), as shown in Figure S1. 13C NMR (125 MHz, CDCl3 δ (ppm): 190.19 (C-13), 136.71 (C-7/14), 135.85(C-8/12), 145.11 (C-1/18), 133.45 (C-4/15), 127.87 (C-3/5/16/20), 130.67 (C-2/6/17/19), 28.83 (C-21/23), 28.55 (C-9/11), 23.10 (C-10), 15.41 (C-22/24), as shown in Figure S4.

BH II

C20H14Cl4O (412.136 g/mol); yellow solid, 75% yield. IR (KBr) (cm–1): 3095, 3030, 2972, 2943, 2845, 1600, 1580, 1468, 1139, 1049, 825, 742; 1H NMR (500 MHz, CDCl3): δ 1.80 (2H, dtt, J = 14.5; 6.54; 2.75), 2.76 (4H, ddd, J = 14.65; 6.5, 2.8 Hz), 7.28 (4H, dd, J = 8.28), 7.48 (2H, d, J = 8.28; 1.74 Hz), 7.84 (2H, s), as shown in Figure S2. 13C NMR (125 MHz, CDCl3 δ (ppm): 189.54 (C-13), 138.04 (C-7/14), 135.82 (C-8/12), 133.03 (C-1/18), 132.07 (C-4/15), 134.92 (C-3/16), 131.11 (C-5/20), 128.7–129.68 (C-2/6/17/19), 28.24 (C-9/11), 23.05 (C-10), as shown in Figure S5.

BH III

C20H16Cl2O (343.24 g/mol); yellow solid, 75% yield. IR (KBr) (cm–1): 3088, 3059, 3030, 2929, 2871, 2835, 1667, 1606, 1577, 1486, 1147, 1092, 836, 799; 1H NMR (500 MHz, CDCl3): δ 1.81 (2H, dtt, J = 14.2, 6.5, 2.8 Hz), 2.36 and 2.91 (4H, ddd, J = 14.6, 6.5, 2.8 Hz), 7.45–7.59 (10H, 7.72 (s), 7.32 (ddd, J = 8.1, 1.4, 0.5 Hz), 7.40 (ddd, J = 8.1, 1.4, 0.5 Hz), as shown in Figure S3. 13C NMR (125 MHz, CDCl3 δ (ppm): 189.75 (C-13), 136.49 (C-7/14), 135.8 (C-8/12), 134.55 (C-1/18), 131.75 (C-4/15), 130.89 (C-3/5/16/20), 128.30 (C-2/6/17/19), 28.03 (C-9/11), 23.07 (C-10), as shown in Figure S6.

Crystallographic Characterization

Single-crystal XRD intensity data collection was performed on a Bruker APEX II CCD diffractometer fitted with MoKα radiation (0.71073 Å) at 120 K. The structures, using the ShelXS[44] structure solution program, were solved by direct methods and refined by least-squares minimization using the ShelXL[45] refinement package. The non-hydrogen atoms were refined anisotropically. The hydrogen atoms were placed geometrically and refined using a riding model with their Uiso set to 1.2 Ueq of the bonded carbon, except for the CH3, whose Uiso(H) was set to 1.5 Ueq of the corresponding carbon. The crystallographic information file (CIF) was prepared using Olex2.[46] Also, the artwork representations for publication were prepared using the programs Ortep[47] and Mercury (version 3.0).[48] Intermolecular interactions were checked by the Platon software.[49] The BH I, II, and III structures were deposited in the Cambridge Structural Database under codes 2120122, 2120123, and 2120124. These data can be obtained free of charge via http://www.ccdc.cam.ac.uk/conts/retrieving.html.

Hirshfeld Surface

The HS consists of a spatial map to visualize the surface of the molecules.[50] It is a useful tool that compares the electron density of a molecule to the entire crystal and measures the distribution of close contact interactions. A weight function wa(r) for a molecule in a crystal was defined by eq ,where ρa(r) is the electron density function of the atom, centered on the nucleus a, defined by eq ,ρmol(r) defines the molecular electron density. In an HS, de is the distance from the nearest nucleus to a molecule outside the surface, which provides the close intermolecular contacts, while di is the distance from inside to the surface, which provides studies of the molecule itself. The normalized contact distance (dnorm), which combines the normalized de and di with the van der Waals radius for each atom involved in this close contact to the surface, is given by eq and was used to analyze intermolecular interactions.

In eq , the rivdw and revdw represent the van der Waals radii.

The shape index is a function of a surface that allows one to identify complementarity between molecules in the crystal packing structure and that can identify hydrophobic intermolecular interactions.[51] Fingerprint plots provide a quantitative value for the types of intermolecular contacts, also known as frequency occurrences. The software Crystal Explorer 21.5[52] was used to generate HS intermolecular interactions and calculated 2D fingerprint plots.

Calorific Power

The calorific value of fuel indicates energy released by combustion per unit mass. The test to determine the calorific value was carried out in a calorimetric pump with a combustor surrounded by water. This analysis followed the ASTM D4809 standard[53] methodologies using an IKA C200 equipment. The combustor is pressurized (30 bar), and the sample is heated by an electric current that promotes burning. Burning releases energy into the environment and exchanges heat with water, generating a change in its temperature. A high precision resistive sensor measures the change in temperature as a function of time and, after correlation with the sample mass obtained prior to burning, the result of the calorific value of the sample is reported.[24,54]

Theoretical Calculation

The electronic structure calculations were carried out with the Gaussian 16[55] program package for BH I, II, and III. Full geometry optimization was carried out using DFT, with exchange-correlation functional ωB97XD[56] and basis set 6-311++G(d,p). This functional includes empirical dispersion with long-range corrections, making it suitable for noncovalent interactions. The wave function for the natural bond orbital (NBO) analysis was carried out at the same level of theory, and the basis set superposition errors (BSSE) were corrected using the counterpoise procedure as implemented in the g16 program.[57] Also, the studied electronic properties: the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO) and MEP were calculated. The QTAIM analysis, using the Multwfn program (version 3.7),[58] was performed using the non-hydrogen atoms taken from the crystallographic data, while the hydrogen atoms were optimized using the same level of theory and were also calculated assignments of infrared vibrational frequencies.

Results and Discussion

Solid-State Description

Table lists the main IR absorption bands and also Figure shows the overlapping of the theoretical and experimental FT-IR spectra for BH I, II, and III. The values of DFT in vibrational frequencies for the results obtained at the ωB97XD/6-311++G(d,p) level of theory were scaled by Wang et al. as 0.9461.[59] The experimental measurements of ν(C=O) for BH I, II, and III occur at 1663, 1660, and 1667 cm–1, respectively, while the theoretical measurements absorb at 1683, 1688, and 1682 cm–1, respectively, considering the molecule was in the gas phase.

Table 1

Vibrational Assignments of the Theoretical and Experimental FT-IR for BH I, II, and IIIa

	BH I		BH II		BH III
vibrational modes	exptl freqb	scaled freqb,c	exptl freqb	scaled freqb,c	exptl freqb	scaled freqb,c
ν (Csp2–H) Ard,Alke	3084–3001	3044–3001	3095–3030	3042–3000	3088–3030	3044–3000
ν (Csp3–H)	2965–2853	2957–2876	2972–2845	2935–2859	2929–2835	2932–2849
ν (C=C) Ard	1606, 1580, 1508, 1457	1607, 1482	1600, 1580, 1468	1620, 1575, 1440	1606, 1577, 1486	1617, 1591, 1457
ν (C=O) and ν (C=C) Alke	1663	1683	1660	1688	1667	1682
δ (C–H) Alke out of plane	828	822	825	817	836	815
ν (C–Cl)			742	746	799	785

These results were obtained at the ωB97XD/6-311++G(d,p) level of theory in the gas phase. ν = stretching; δ = bending.

cm–1.

Scale factor 0.9461.

Ar = aromatic ring.

Alk = alkene.

Figure 1

Overlapping of the theoretical (red) and experimental (black) FT-IR spectra of (a) BH I, (b) BH II, and (c) BH III.

Absorption peaks appear in the experimental ν(Csp2–H) aromatic ring for BH I at 1606 cm–1, 1580, 1508, and 1457 cm–1; for BH II these peaks appear at 1600, 1580, and 1468 cm–1; and for BH III they appear at 1606, 1577, and 1486 cm–1, while theoretically, these values appear for BH I at 1607 and 1482 cm–1; for BH II at 1620, 1575, and 1440 cm–1; and for BH III at 1617, 1591, and 1457 cm–1. It is observed that the ν(Csp3–H) for BH I, II, and III are in the range of 2965–2853 cm–1, 2972–2845 cm–1, and 2929–2835 cm–1, respectively, while the DFT calculations assigned to the regions of 2957–2876 cm–1, 2935–2859 cm–1, and 2932–2849 cm–1, respectively. Additionally, the experimental measurements of ν(C–Cl) for BH II and III are 742 and 799 cm–1, while the theoretical band appears in 746 and 785 cm–1.

Figure shows the BH I, II, and III asymmetric units as an Ortep diagram. With respect to BH I, the stereochemistry of the C5=C2 is on an (E)-configuration. This molecule appears in the cyclohexanone as an envelope conformation confirmed by the ring-puckering parameters Q = 0.5034 Å and ϕ = 360°, as described by Cremer and Pople.[60] Additionally, for BH I, the dihedral angle C2–C5–C6–C7 has −147.3°, as shown in Table . Also, for BH II and III, the stereochemistry of the C7=C8 and C12=C14 is on an (E,E)-configuration. These molecules appear in the cyclohexanone as a half boat conformation, which is confirmed by the ring-puckering parameters Q = 0.529 Å and ϕ = 136.2°, as well as Q = 0.5343 Å and ϕ = 282.02° for BH II and III, respectively. Furthermore, for BH II with dichloro-substituted, the dihedral angle C3–C4–C7–C8 and C12–C14–C15–C16 has 145.6° and −142.0°, respectively, as shown in Table . Likewise, for BH III, the dihedral angle C3–C4–C7–C8 has 149.76°. On the other hand, the dihedral angle C12–C14–C15–C16 between the terminal ring C15–C20 and the cyclohexanone has −173.12°, i.e., almost coplanar, as shown in Table .

Figure 2

Ortep diagram of ellipsoids at 50% probability level with the atomic numbering scheme for (a) BH I, (b) BH II, and (c) BH III. Hydrogen atoms are in arbitrary radii.

Table 2

Relevant Experimental and Theoretical Dihedral Angles (deg) for BH I, II, and III

BH	experimental	theoretical
I
O1–C1–C2–C3	–171.9 (2)	–179.0
C1–C2–C3–C4	–33.4 (2)	–29.8
C1–C2–C5–C6	–176.2 (2)	–179.7
C2–C3–C4–C3	59.9 (3)	59.0
C2–C5–C6–C7	–147.3 (2)	–145.9
C2–C5–C6–C11	36.8 (3)	36.0
C5–C2–C3–C4	144.94 (18)	147.3
C8–C9–C12–C13	–165.1 (3)	–178.1
II
O1–C13–C8–C9	–173.7 (3)	169.1
O1–C13–C12–C11	–175.5 (3)	–169.1
C13–C8–C9–C10	17.6 (4)	35.4
C12–C11–C10–C9	64.2 (3)	58.7
C13–C8–C7–C4	179.6 (3)	179.2
C13–C12–C14–C15	–176.4 (3)	–179.2
C8–C13–C12–C14	–172.9 (3)	–164.5
C8–C9–C10–C11	–53.4 (4)	–58.7
C12–C14–C15–C16	–142.0 (3)	–134.0
C3–C4–C7–C8	145.6 (3)	134.0
C5–C4–C7–C8	–35.0 (5)	–48.3
C7–C8–C9–C10	–161.2 (3)	–141.0
Cl1–C1–C6–C5	–176.9 (3)	–179.8
Cl2–C3–C2–C1	178.9 (3)	–179.5
Cl3–C18–C17–C16	178.9 (3)	179.9
Cl4–C16–C17–C18	179.6 (3)	179.5
III
O1–C13–C8–C9	178.3 (1)	178.4
O1–C13–C12–C11	169.0 (1)	–178.4
C13–C8–C9–C10	36.6 (2)	30.1
C12–C11–C10–C9	51.1 (2)	59.0
C13–C8–C7–C4	178.2 (1)	179.9
C13–C12–C14–C15	–179.1 (1)	–179.9
C8–C13–C12–C14	165.6 (1)	–175.7
C8–C9–C10–C11	–63.1 (1)	–59.0
C12–C14–C15–C16	–173.1 (1)	–144.7
C3–C4–C7–C8	149.8 (1)	144.8
C5–C4–C7–C8	–32.4 (2)	–37.0
C7–C8–C9–C10	–140.6 (1)	–147.0
Cl1–C1–C6–C5	–177.6 (1)	–179.5
Cl2–C18–C19–C20	–179.6 (1)	179.5

Relevant experimental and theoretical dihedral angles are given in Table . The important crystallographic parameters of BH I, II, and III are shown in Table . Detailed intermolecular interactions observed in all crystal structures are given in Table .

Table 3

Important Crystallographic Parameters of BH I, II, and III

crystal data	BH I		BH II		BH III
empirical formula	C24 H26 O		C20 H14 O Cl4		C20 H16 O Cl2
formula weight/g mol–1	330.45		412.11		343.23
temperature/K	120(2)		120(2)		120(2)
radiation type	MoKα		MoKα		MoKα
crystal system	orthorhombic		orthorhombic		monoclinic
space group	Cmc21		Pbca		P21/n
unit cell dimensions	a = 20.72(4) Å	α = 90°	a = 14.26(2) Å	α = 90°	a = 9.82(9) Å	α = 90°
	b = 14.80(4) Å	β = 90°	b = 7.78(13) Å	β = 90°	b = 16.48(15) Å	β = 90°
	c = 6.03(12) Å	γ = 90°	c = 31.37(5) Å	γ = 90°	c = 10.46(10) Å	γ = 90°
volume/ Å3	1852.2(7)		3484.7(10)		1630.6(3)
Z	4		8		4
density (calculated)/ g cm–3	1.185		1.571		1.398
F(000)	712		1680		712
reflections collected	14571		61722		30834
independent reflections	2375 [R(int) = 0.0356]		4366 [R(int) = 0.0856]		4036 [R(int) = 0.0223]
data/restraints/parameters	2375/1/155		4366/0/238		4036/0/229
goodness-of-fit on F2	1.047		1.262		1.077
final R indexes [I > 2σ(I)]	R1 = 0.0357, wR2 = 0.0868		R1 = 0.0629, wR2 = 0.1289		R1 = 0.0325, wR2 = 0.0785
final R indexes [all data]	R1 = 0.0448, wR2 = 0.0917		R1 = 0.0793, wR2 = 0.1342		R1 = 0.0379, wR2 = 0.0816
extinction coefficient	n/a		n/a		n/a
largest diff. peak and hole/e Å–3	0.18/–0.19		0.53 and −0.41		0.36 and −0.26

Table 4

Hydrogen-Bond Geometry (Å, deg) in the Crystal Structure of BH I, II, and III

BH	D–H···A	D–H	D···A	H···A	D–H···A	symmetry code
I	C3–H3B···O1	0.98	3.277	2.55	130.08	x, y, −1 + z
	C13–H13B···H13B–C13	1.05	2.650	1.65	154.83	–1 + x, y, z
II	C10–H10A···O1	0.96	3.506	2.54	177.00	1/2 – x, 1/2 + y, z
	C20–H20···O1	0.95	3.225	2.33	157.00	1/2 – x, −1/2 + y, z
	C17–H17···Cl3	0.97	3.587	2.74	146.00	1 – x, −y, 1 – z
III	C6–H6···π	0.94	3.623	2.71	159.63	–1/2 + x, 1.5 – y, −1/2 + z
	C10–H10B···Cl1	0.97	3.799	2.89	154.87	–1 + x, y, z
	C18–Cl2···Cl1	1.74	5.023	3.30	169.18	–2 + x, y, −1 + z

The BH I is crystallized in the orthorhombic system with noncentrosymmetric space group Cmc21. In this case, being a centrosymmetric molecule and lying on a crystallographic mirror plane, its asymmetric unit comprises only one-half-molecule (Z′ = 0.5) of the compound. The crystal packing of BH I appears in an infinite chain formed by C3–H3B···O1 interaction along the c axis, which can be described as C11(5)[61] (Figure a). Further, C13–H13B···H13B–C13 dihydrogen contact is possible to observe along the a-axis, also generating an infinite chain (Figure b). Figure c shows the packing of BH I, formed by dihydrogen contact at the center of the unit cell and the C3–H3B···O1 interaction lying on a crystallographic mirror plane.

Figure 3

Intermolecular interactions depicting (a) C3–H3B···O1, (b) C13–H13B···H13B–C13 dihydrogen contact, and (c) the crystalline packing of BH I.

The BH II is crystallized in the orthorhombic system with centrosymmetric space group Pbca, with one molecule in the asymmetric unit (Z = 8). The crystal packing of BH II is formed by C10–H10A···O1 and C20–H20···O1 interactions, appearing as bifurcated interaction along the b axis, which can be described as C21(9), as shown in Figure a. Further, C17–H17···Cl3 appears as a dimer around the inversion center along the c axis, which can be described as R22(8) (Figure b). Figure c shows the packing of BH II, formed by C17–H17···Cl3 lying at the center of the unit cell and around the inversion centers.

Figure 4

Intermolecular interactions depicting (a) C10–H10A···O1 and C20–H20···O1, (b) C17–H17···Cl3, and (c) the crystalline packing of BH II.

The BH III crystallized in the monoclinic system with centrosymmetric space group P21/n, with one molecule in the asymmetric unit (Z = 4). The crystal packing of BH III, differently from the other BHs, is formed by C6–H6···π interaction appearing in a zigzag chain along the a axis (Figure a). Further, bifurcated contacts through C10–H10B···Cl1 and C1–Cl1···Cl2–C18 appears in an infinite chain along the a axis, as shown in Figure b. Figure c shows the packing of BH III, formed by a zigzag chain lying on a crystallographic glide plane. On the other hand, at the center of the unit cell and around the inversion center, no interaction is observed.

Figure 5

Intermolecular interactions depicting (a) C6–H6···π, (b) C10–H10B···Cl1 and C18–Cl2···Cl1, and (c) the crystalline packing of BH III.

In order to interpret the intermolecular interactions, we employed HS dnorm analysis. These interactions are verified in de and di, indicating the distance within the molecule between the external and internal nucleus of the HS, respectively. Additionally, de and di correspond to acceptor and donor regions, respectively. The HS mapped over dnorm (range of −0.511 to 1.470 Å) is shown in Figure .

Figure 6

Hirshfeld surfaces indicating (a and b) C3–H3B···O1 and C13–H13B···H13B–C13 intermolecular contacts for BH I; (c–e) C10–H10A···O1, C20–H20···O1, C17–H17···Cl3 intermolecular contacts and π···π stacking for BH II and (f–h) C6–H6···π, C10–H10B···Cl1, and C18–Cl2···Cl1 intermolecular contacts for BH III are represented by dotted lines.

For BH I, the red spots correspond to a stronger C3–H3B···O1 contact (Figure a), which is also related to the shorter H···H contact (Figure b). In the same way, for BH II, the red spots correspond to C10–H10A···O1 and C20–H20···O1 interactions, as shown in Figure c. Also, Figure d is related to a dimer C17–H17···Cl3 interaction. The shape index HS also is a tool for the identification of hydrophobic interactions like π···π. The π···π stacking in the BH II is identified by the red and blue triangle in the shape index surface, as shown in Figure e. The distance between centroids, formed between the center of aromatic rings C1–C6 (Cg1) and C15–C20 (Cg3), is 3.88 Å providing additional stability for the structure. For BH III, the red spots correspond to C6–H6···π and C10–H10B···Cl1 interactions, as shown in Figure f,g, respectively. Also, Figure h is related to a halogen Cl···Cl contact.

The 2D fingerprint plot of BH I, II, and III is shown in Figure . From the 2D fingerprint plot, most contact is due to H···H interaction, which makes up 68.1% of the HS of BH I and is characterized by the thin spike of the fingerprint 2D plot. The contribution of O···H/H···O interactions of BH I represents 5.6% of the HS (Figure a). For BH II, the contribution of H···H and C···H/H···C contacts represents 23.5% and 15.3% of the HS, respectively. The polar dimer interactions Cl···H/H···Cl represents 32.7%. Another feature is the existence of C···C interaction, which is responsible for 5.1% of HS. The interaction O···H/H···O is characterized by the small spikes in the bottom of the fingerprint plot, representing 6.0% of the HS, as shown in Figure b. For BH III, most contact is due to H···H interaction which makes up 33.5% of the HS. The contribution of C···H/H···C interactions of BH III represents 27.4% of the HS. The polar interaction Cl···H/H···Cl represents 22.5%. The contribution of Cl···Cl contacts are characterized by the thin spike at the center of the 2D fingerprint plot (Figure c).

Figure 7

Fingerprint plot quantifies the contacts for (a) BH I, (b) BH II, and (c) BH III.

The root mean squared (RMS) values predicted by the Mercury program package,[48] comparing calculated and experimental geometries, were 0.0047, 0.0131, and 0.0061 for BH I, II, and III, respectively. The overlay depicts a good correlation between the geometric parameters for all the structures. The difference for BH I (Figure a), representing about 7.29%, is around C8–C9–C12–C13 with experimental (−165.1°) and theoretical (−178.1°) dihedral angles, as shown in Table . The difference for BH II (Figure b), representing about 7.90%, is around C3–C4–C7–C8 with experimental (145.6°) and theoretical (−134.0°) dihedral angles. Additionally, another difference for BH II, representing about 12.5%, is around C7–C8–C9–C10 with experimental (−161.2°) and theoretical (−141.0°) dihedral angles, as shown in Table . The difference for BH III (Figure c), representing about 16.40%, is around C12–C14–C15–C16 with experimental (−173.1°) and theoretical (−144.7°) dihedral angles, as shown in Table .

Figure 8

Overlapping of theoretical (ωB97XD/6-311++G(d,p)) (black) and X-ray structures for (a) BH I (green), (b) BH II (purple), and (c) BH III (blue) in respect to the aromatic ring.

Supramolecular Modeling Analysis and Energy

The investigation into the chalcones’ chemical structure and its properties[62−65] helps us to understand the activity of these molecules as a possible application in fuels.[22] Actually, the world energy matrix has some fuels with advantages over fossil fuels. However, these fuels have stability, oxidation, and energy availability problems, as with ethanol and biodiesel.[28,33] The calorific value test for BH I, II, and III shows values of 7284.0 kcal/kg, 6430.2 kcal/kg, and 7298.7 kcal/kg, respectively (Table ). In addition, we performed calorific value tests for gasoline (common type C), hydrated ethanol, and n-butanol for comparative parameters. Table also presents different calorific values for various types of biodiesel.

Table 5

Calorific Value for BH I, II, III, and Some Fuelsa

cmpd	calorific value	fuel	calorific value
BH I	7284.0	gasoline	9775
BH II	6430.2	ethanol	6906
BH III	7298.7	butanol	8509

All units for calorific power are in kcal/kg. BD: Biodiesel. BD BX, where X refers to the percentage by volume of the biodiesel.

The calorific value results reveal that BH I, II, and III have good energy availability, even a little lower than biodiesel (Figure ). However, BH I and III (7284.0 and 7298.7 kcal/kg) have a higher calorific value than ethanol (6906.0 kcal/kg), while BH II presents a small difference compared to ethanol. Due to the susceptibility and good energy availability of chalcones, they can be associated with fuels, since the high calorific value in fuels is associated with better performance.

Figure 9

Calorific value for BH I, II, III, and fuels: biodiesel, diesel, hydrated ethanol, and n-butanol. The calorific value of biodiesel varies with its composition; therefore, we have a comparative parameter. We performed an average of the values described in Table . Average of the values described in Table .

The FMO obtained from Kohn–Sham analysis for BH I, II, and III was carried out at ωB97XD/6-311++G(d,p) level of theory, and they are shown in Figure . The FMO analysis of bond-antibonding interactions is a good approximation for ionization (Lewis base) and electron affinity (Lewis acid) energies. The HOMO, the electron donor for BH I, II, and III, is located mainly on the aromatic rings. It is a π-bonding orbital, which is characteristic of the electrophilic region. The HOMO energy for BH I, II, and III is negative (−185.79, −200.34, and −194.86 kcal/mol, respectively). The LUMO for BH I, II, and III is an π-antibonding orbital, and it is spread out through the molecular rings and the carbonyl group. The LUMO energy for BH I, II, and III is −10.69, −20.34, and −19.69 kcal/mol, respectively. These results show that the BH I, II, and III compounds are electrophilic species.

Figure 10

Frontier molecular orbitals derived from Kohn–Sham analysis at ωB97XD/6-311++G(d,p) level of theory with the isovalue of 0.02 atomic units: the HOMO π-bonding orbital and the LUMO π-antibonding orbital for (a) BH I, (b) BH II, and (c) BH III.

NBO analysis helps us better understand the nature of intermolecular interactions in the solid state. For the reason that one of the aims of this work is to explain the supramolecular arrangement of the BH I, II, and III compounds, the atomic coordinates of non-hydrogen atoms were taken directly from the crystallographic data. However, as the coordinates of the hydrogen atoms were not experimentally determined, it was necessary to optimize them using the wB97XD/6-311++G(d,p) level of theory. The same level of theory was used to obtain the wave function for the NBO analysis. The hyperconjugative interaction energies were estimated from the second-order perturbation formula, as described in eq :where ⟨σ|F|σ⟩2 is the Fock matrix element between the i and j NBO orbitals. εσ* and εσ are the energies of σ* and σ NBO orbitals, respectively, and nσ stands for the σ donor orbital population. NBO analysis provides a method for studying hyperconjugative interaction in a molecular system.[91,92] The higher the E(2) value, the more intensive the interaction between electron donor and acceptor, respectively. Figure shows the calculated NBO orbitals.

Figure 11

Intermolecular donor–acceptor natural bond interactions in (a and b) C3–H3B···O1 and C13–H13B···H13B–C13 for BH I; (c–e) C10–H10A···O1, C20–H20···O1, and C17–H17···Cl3 for BH II; and (f–h) C6–H6···π, C10–H10B···Cl1, and C18–Cl2···Cl1 for BH III.

For BH I, Figure a shows the orbital interaction between the lone pair orbital of the O1 atom and the σ* antibonding orbital of the C3–H3B with a stabilization energy of 0.38 kcal mol–1. Along with the dihydrogen contacts (Figure b), higher stabilization energy is observed (1.00 kcal mol–1). For BH II, Figure c shows the orbital interaction between the π bonding orbital of the O1 atom and the σ* antibonding orbital of the C10–H10A with a stabilization energy of 0.96 kcal mol–1. The orbital interaction between the lone pair orbital of the O1 atom and the σ* antibonding orbital of the C20–H20 is shown in Figure d with a stabilization energy of 1.52 kcal mol–1. Along with the dimer interaction (Figure e) between the lone pair orbital of the Cl3 atom and the σ* antibonding orbital of the C17–H17, it is observed a stabilization energy of 0.53 kcal mol–1.

For BH III, Figure f shows the orbital interaction between the σ bonding orbital of the C6–H6 atom and the π* antibonding orbital of the O1–C13 with a stabilization energy of 0.49 kcal mol–1. The orbital interaction between the lone pair orbital of the Cl1 atom and the σ* antibonding orbital of the C10–H10B is shown in Figure g with a stabilization energy of 0.65 kcal mol–1. Along with the halogen contact (Figure h) between the lone pair orbital of the Cl1 atom and the σ antibonding orbital of the Cl2, a stabilization energy of 0.63 kcal mol–1 is observed.

The MEP is a physicochemical tool that gives information about molecular interactions and helps predict the reactive sites to be targeted in a chemical reaction. The electrostatic potential at a given point ρ(r) in the vicinity of a molecule can be calculated by eq :where V(r) is the potential energy by a positive unit charge at point r; Zα is the nuclear charge of the atom α located at position Rα, and ρ(r′) is the electron density.

The tridimensional MEP representation (Figure ) for BH I, II, and III shows that the most negative region (red) is located on the oxygen atom of the carbonyl group, with a value of −35.76, −30.93, and −30.12 kcal/mol, respectively. On the other hand, the positive region (blue) is around the cyclohexanone hydrogen atoms, with a value of 12.29, 22.02, and 19.39 kcal/mol, respectively. In conclusion, due to C–H···O interactions in the crystal structures, we can assume an electrophilic attack on this carbonyl group’s region.

Figure 12

Molecular electrostatic potential surface mapped for (a) BH I, (b) BH II and (c) BH III showing the red-colored region rich in electrons and the blue-colored region, which is electron depleted. The density isovalue of 4.0 × 10–4 electrons/bohr3 was used to generate the molecular electrostatic potential surfaces.

Also, the supramolecular modeling analysis on the hyperconjugative interaction energies and QTAIM analysis, using theoretical calculations at the ωB97XD/6-311++G(d,p) level of theory, were calculated to prove the existence of intermolecular interactions and to classify their nature. Figure shows that, in quantum mechanic calculations, there are two types of interaction for BH I, II, and III in the solid-state, which we call here as side-to-side and head-to-head dimers. The basis set superposition errors (BSSE) were corrected using the counterpoise procedure as implemented in the g16 program.[57] For BH I, Figure a shows that the side-to-side dimer interaction energy is −10.60 kcal/mol, showing powerful and attractive energy for dimers. The head-to-head interaction energy (Figure b) for BH I dimer is 1.19 kcal/mol. This interaction energy is negligible and repulsive for the dimers. Consequently, we can assume that the side-to-side interaction energies are the driving forces for the BH I molecular arrangement in the solid-state.

Figure 13

Complexation energies obtained at the ωB97XD/6-311++G(d,p) level of theory: side-to-side and head-to-head dimers, respectively, (a and b) C3–H3B···O1 and C13–H13B···H13B–C13 for BH I; (c and d) C10–H10A···O1, C20–H20···O1, and C17–H17···Cl3 for BH II; and (e and f) C6–H6···π, C10–H10B···Cl1, and C18–Cl2···Cl1 for BH III.

For BH II, Figure c shows that the side-to-side dimer interaction energy is −19.59 kcal/mol, showing powerful and attractive energy for dimers. The head-to-head interaction energy (Figure d) for the BH II dimer is −0.53 kcal/mol. Consequently, we can assume that both the side-to-side and head-to-head interaction energies are the driving forces for the BH II molecular arrangement in the solid-state.

For BH III, Figure e shows that the side-to-side dimer C6–H6···π interaction energy is −10.73 kcal/mol. Further, another side-to-side dimer (i.e., C10–H10B···Cl1) interaction energy is −5.48 kcal/mol, showing powerful and attractive energy for the molecule. As well as BH I, the head-to-head C18–Cl2···Cl1 dimer interaction energy (Figure f) for BH III is 0.31 kcal/mol. This interaction energy is also negligible and repulsive for the dimers. Consequently, we can assume that the side-to-side interaction energies are the driving forces for the BH III molecular arrangement in the solid state.

The QTAIM analysis was carried out to understand the chemical nature of dimers’ interactions.[93,94] The interactions that occur in BH I are of type C3–H3B···O1 short contact and C13–H13B···H13B–C13 dihydrogen contact, as shown by bond critical point (BCP) analysis (Figure ). The BCP describes the stationary point between donor and acceptor atoms, confirming the existence of hydrogen bonding interaction. The QTAIM’s electron density ρ(r) at the BCP of proton-acceptor is 0.032 and 0.050 au for C3–H3B···O1 and C13–H13B···H13B–C13, respectively. The positive Laplacians, 0.040 and 0.28 au for C3–H3···O1 and C13–H13B···H13B–C13, respectively, are observed for noncovalent hydrogen bonds interactions. The total energy density value E(r) is small and negative for C3–H3···O1 and C13–H13B···H13B–C13, as shown in Table .

Figure 14

Molecular graph for BH I: (a) side-to-side C3–H3B···O1 interaction and (b) head-to-head C13–H13B···H13B–C13 contact, showing the BCP in yellow.

Table 6

QTAIM Parameters Describing Contacts and Intermolecular Interactions for BH I, II, and III [Electron Density at BCP (ρ(r)), Laplacian (▽2 ρ(r)), The Potential Electron Energy Density (V(r)), The Kinetic Electron Energy Density (G(r)), and The Total Electron Energy Density (E(r)). All Values Are Given in Atomic Units (a.u.)]

BCP	interaction	ρ(r)	▽2ρ(r)	V(r)	G(r)	E(r)	kind of interaction
BH I
1	C3–H3B···O1	0.03258	0.04070	–0.01958	0.01488	–0.00470	weak
2	C13–H13B···H13B–C13	0.05043	0.28115	–0.10856	0.08942	–0.01913	weak
BH II
3	C10–H10A···O1	0.05882	0.07459	–0.03009	0.02437	–0.00572	weak
4	C20–H20···O1	0.08763	0.30248	–0.08025	0.07793	–0.00231	weak
5	C17–H17···Cl3	0.01996	0.09355	–0.02006	0.02172	0.00166	weak
BH III
6	C6–H6···π	0.06380	0.12316	–0.03976	0.03527	–0.0044	weak
7	C10–H10B···Cl1	0.05321	0.19465	0.01753	0.01556	0.03309	weak
8	C18–Cl2···Cl1	0.02586	0.01479	–0.00782	0.00576	–0.00206	weak

The interactions that occur in BH II are of type C10–H10A···O1 and C20–H20···O1 short contact and C17–H17···Cl3 dimer interaction, as shown by BCP analysis (Figure ). The QTAIM’s electron density ρ(r) at the BCP of proton-acceptor is 0.058, 0.087, and 0.019 au for C10–H10A···O1, C20–H20···O1, and C17–H17···Cl3, respectively. The positive Laplacians, 0.074, 0.30, and 0.093 au for C10–H10A···O1, C20–H20···O1, and C17–H17···Cl3, respectively, are observed for noncovalent hydrogen bonds interactions. The total energy density value E(r) is small and negative for C10–H10A···O1 and C20–H20···O1, as shown in Table . On the other hand, for C17–H17···Cl3, the total energy density value E(r) is small and positive.

Figure 15

Molecular graph for BH II: (a) side-to-side C10–H10A···O1 and C20–H20···O1 short contacts and (b) head-to-head C17–H17···Cl3 dimer interaction, showing the BCP in yellow.

The interactions in BH III are of type C6–H6···π, C10–H10B···Cl1 short contact and halogen contact C18–Cl2···Cl1 as shown by BCP analysis (Figure ). The QTAIM’s electron density ρ(r) at the BCP of proton-acceptor is 0.063, 0.053, and 0.025 au for C6–H6···π, C10–H10B···Cl1, and C18–Cl2···Cl1, respectively. The positive Laplacians, 0.12, 0.19, and 0.014 au for C6–H6···π, C10–H10B···Cl1, and C18–Cl2···Cl1, respectively, are observed for noncovalent hydrogen bonds interactions. The total energy density value E(r) is small and negative for C6–H6···π and C18–Cl2···Cl1, as shown in Table . On the other hand, for C10–H10B···Cl1, the total energy density value E(r) is small and positive. We can conclude from the QTAIM analysis that these interactions for all BH I, II, and III dimers can be classified as van der Waals or closed-shell interactions.

Figure 16

Molecular graph for BH III: (a and b) side-to-side C6–H6···π and C10–H10B···Cl1 short contacts and (c) head-to-head C18–Cl2···Cl1 contact, showing the BCP in yellow.

Energy availability is directly dependent upon the molecular structure, such as the number of carbons, chemical energy bond interactions, chemical stability, and molecular sites susceptible to the occurrence of reactions. Thus, its thermodynamic properties influence fuel energy efficiency. The difference in the calorific values between BH I, II, and III is related to their supramolecular arrangement formed by chemical energy interactions presented in these compounds. MEP calculation indicates the carbonyl group’s region where the burning reactions can occur, which can be involved with higher energy values.[95−97] Additionally, the HOMO and LUMO are related to excitation energies and GAP energy (EGAP = ELUMO – EHOMO) in some situations can be an indicator of kinetic stability (large GAP values are associated with kinetic stability).[98−107] For some compounds used to preserve fuels properties, this parameter is described in the literature (toluene derivative [EGAP = 114.1 kcal/mol],[108] butylated hydroxytoluene [EGAP = 130.5 kcal/mol],[109] thiazolidinone [EGAP = 115.1 kcal/mol],[110] ether molecules [EGAP = 96.7 kcal/mol][111]). Note that, according to the GAP values, the molecules analyzed in this work are kinetically more stable (BH I 175.1 kcal/mol, BH II 180 kcal/mol, BH III 175.17 kcal/mol). The structural description of these molecules, theoretical parameters, and experimental analysis of the calorific value provides a good understanding of the structure and its relationship with some properties. This information can support application studies or more specific theoretical analyses.

Conclusions

In this work, three crystal structures of chalcone based on cyclohexanone core have been extensively characterized. All these molecules appear as the dienones in the (E,E)-configuration. For BH I, the cyclohexanone appears as an envelope conformation, and for BH II and III, it appears as a half-boat conformation. The crystal packing for BH I was investigated by C–H···H–C dihydrogen contact and nonclassical hydrogen bonding C–H···O, which were observed on HS topological analysis (68.1% of H···H interaction and 5.6% of O···H interaction). The crystal packing for BH II was investigated by nonclassical hydrogen bonding C–H···O, C–H···Cl, and π···π stacking, which were observed on HS topological analysis (6.0% of O···H interaction, 32.7% of Cl···H interaction, and 5.1% π···π stacking). The crystal packing for BH III was investigated by C–H···π interaction, nonclassical hydrogen bonding C–H···Cl, and halogen Cl···Cl contacts, which were observed on HS topological analysis (27.4% of C···H interaction, 22.5% of Cl···H interaction, and 2.9% Cl···Cl contacts). The calculated and experimental geometries parameters depict a good correlation for all the structures.

The calorific value indicated good energy availability for these compounds, thus being able to support other studies of this application. Theoretical calculations using the counterpoise procedure conclude that the side-to-side interaction energies are the driving forces for the BH I, II, and III molecular arrangements in the solid state. We can conclude from the QTAIM analysis that these interactions for all BH I, II, and III dimers can be classified as van der Waals or closed-shell interactions. Additionally, FMO calculation indicates that the BH I, II, and III compounds are electrophilic species. Also, MEP calculation indicates the susceptible electrophilic attack on this carbonyl group’s region.