Electronic structure,reactivity,and Hirshfeld surface analysis of carvone

Abstract

The density functional theory (at the B3LYP level using 6-311++G(2d,2p) basis set) was used for the investigation of the geometry and electronic properties of the carvone. The electronic properties and chemical activity of the titled compound were investigated by means of several theoretical approaches, molecular electrostatic potential surface, natural bond orbital, and frontier molecular orbital analyses. It was established that the oxygen atom in the structure characterized the electrophilic reactivity; the positive regions are localized on the hydrogen atoms, which can be considered as possible sites for nucleophilic attack. A detailed analysis of the intermolecular interactions via Hirshfeld surface analysis and fingerprint plots revealed that the carvone structure is stabilized mainly by the formation of O. . .H/H. . .O hydrogen bonds. However, close contacts were established between C. . .H/H. . .C and H. . .H contacts.

Keywords

carvone density functional theory electronic properties Hirshfeld surface analysis

Introduction

Carvone is a monocyclic monoterpene, which exists in two enantiomeric forms—S-(+)- and R-(−)-carvone. It is a colorless to pale yellowish liquid with a characteristic spicy odor of Carum carvi and with warm and sweet taste. They are natural products in the essential oils from dill (Anethum graveolens L.), caraway (Carum carvi L.) (S-(+)-carvone), and spearmint (Mentha spicata L.) (R-(−)-carvone).^1,2 The two forms have biological and pharmacological activities: antioxidant, antimicrobial, anticarcinogenic, antimutagenic, antidiabetic, and diuretic activities.^3,4

Essential oils containing carvone are used in foodstuffs for the flavoring of various food products and beverages, as well as in perfumery and cosmetics.²

The carvone is isolated from the oils that contain it in a larger quantity,⁵ but for industrial purposes it is synthesized.^6–8

From many years, the experimental and theoretical methods are used to investigate the structural and spectroscopic properties of molecules. The infrared, Raman, and vibrational circular dichroism spectra of S-(+)-carvone were calculated and compared to the experimental one with Hartree–Fock (HF) and density functional theory (DFT) methods from the study by Hoffmann.⁸ The experimental and theoretical studies of the optical activity of carvone were reported⁹ in order to elucidate the potential importance of solvent effects on its optical rotatory dispersion and circular dichroism spectrum. It is found that DFT with B3LYP functional and 6-311G(d,p) basis set gives good results.

The crystal structure of R-(−)-carvone (l-carvone) was presented in the work of Sane et al.¹⁰ The authors reported that the pure l-carvone displays complex polymorphic behavior.

Hence, in this work, a theoretical study on the geometry, electronic structure and chemical reactivity of the carvone by DFT calculations using the B3LYP/6-311++G(2d,2p) method was carried out for better understanding the molecular geometry, highest occupied molecular orbital (HOMO)–lowest occupied molecular orbital (LUMO), and electronic excitation. The intermolecular interactions were characterized on the basis of Hirshfeld surface analysis.

Experimental section

The S-(+)- and R-(−)-carvone were purchased from Fluka Chemical.

Fourier-transform infrared spectroscopy

For the identification of S-(+)- and R-(−)-carvone, the Fourier-transform infrared (FTIR) and UV-Vis spectroscopies were used. The infrared spectrum was recorded using a Nicolet iS 50 Thermo Scientific FTIR spectrometer equipped with a DTGS KBr detector (4 сm⁻¹) in the frequency region of 4000–400 сm⁻¹ at scan numbers of 32.

Characterization results for S-(+)-carvone: FTIR (ν, сm⁻¹) 3308.7, 3201.0, 3110.0, 3050.4, 3025.2, 2900.9, 2130.8, 1716.3, 1647.3, 1430.3, 1372.7, 1337.2, 1317.6, 1281.6, 1235.7, 1163.0, 1112.7, 1058.7, 1033.6, 897.2, 664.6, 614.9, 560.1, 518.4, 456.0, and 436.4.

Characterization results for R-(−)-carvone: FTIR (ν, сm⁻¹) 3335.7, 3319.7, 3074.6, 3010.6, 2968.3, 2952.4, 2925.3, 2883.4, 2350.7, 1669.2, 1648.3, 1446.3, 1435.3, 1371.3, 1324.7, 1270.7, 1244.5, 1201.7, 1137.7, 1105.4, 1057.5, 10.47.6, 1031.6, 999.7, 962.7, 903.3, 802.7, 706.7, 664.7, and 611.5.

UV-Vis spectroscopy

UV-Vis spectrum of the sample was recorded in the range from 190 to 500 nm at 298 K using Evolution 300 UV-Vis spectrophotometer equipped with a silicon photodiode detector.

Characterization results for S-(+)-carvone: UV-Vis (λ, nm) for S-(+)-carvone in ethanol: 201 and 234.

Characterization results for R-(−)-carvone: UV-Vis (λ, nm) for R-(−)-carvone in ethanol: 223 and 240.

Computational methods

All quantum chemical calculations of the title compound were performed using the hybrid B3LYP method¹¹ of DFT with 6-311++G(2d,2p)¹² basis set by means of Gaussian 16.¹³ The optimized geometries (converged to 10⁻⁸ a.u.) were used in the vibrational frequency calculations to characterize the stationary point as minima. The absence of imaginary frequencies confirms that the structure corresponds to the minimum energy. GaussView program, Version 6¹⁴ was used to visualize the computed outputs.

Natural bond orbital (NBO) analysis was carried out in order to know the charge distribution and the intrinsic property of carvone. The stabilization energy (E⁽²⁾) associated with $i \to j$ delocalization for a donor NBO (i) and an acceptor NBO (j) was calculated by the following equation

E^{(2)} = q_{i} \frac{F^{2} (i, j)}{ε_{i} - ε_{j}}

(1)

where q_i is the ith donor orbital occupancy, $ε_{i}$ and $ε_{j}$ are diagonal elements, and $F (i, j)$ is the Fock matrix element.¹⁵

Molecular electrostatic potential (MEP) was calculated using the B3LYP/6-311++G(2d,2p) level of theory. By this analysis can be visualized the sites or regions of a molecule where an approaching electrophile or nucleophile will be attracted. Moreover, the study of interactions that involve a certain optimum relative orientation of the reactants could also be successfully carried out by means of MEP.¹⁶ The distribution of electrical charge creates an electrostatic potential (V(r)) in the surrounding space. If a molecule has an electron density function ρ(r), then its electrostatic potential at any point r can be calculated by the expression

V (r) = \sum_{A} \frac{Z_{A}}{| R_{A} - r |} - \int \frac{ρ (r^{'})}{| r^{'} - r |} d r^{'}

(2)

where Z_A is the charge on the nucleus A, located at distance R_A. The presented equation is an exact formula for the electrostatic potential due to the set of nuclei (Z_A) and the electronic density function ρ(r′).

Frontier molecular orbital (FMO) analysis was realized. The most important parameters in quantum chemistry—HOMO and LUMO—allow the investigation of stability and reactivity of the molecules.¹⁷ A smaller energy difference between them would determine a larger reactivity between two molecules. The HOMO acts as an electron donor and the LUMO acts as an electron acceptor.¹⁸

The reactivity parameters (chemical hardness, chemical potential, softness, electrophilicity, and nucleophilicity) are calculated with natural population charges obtained from the B3LYP/6-311++G(2d,2p) method. Using the restricted method, the energy calculations of the N-electron species were done, while the energies of the N − 1 and N + 1 electronic species were calculated by the open shell-restricted method using the optimized geometry of the N-electron species. By using Fukui function (f(r)), the reactivity of a chemical system can be measured as follows¹⁹

f (r) = {(\frac{\partial ρ (r)}{\partial N})}_{v (r)}

(3)

where ρ(r) is the electron density at each point r, N—electrons, and v(r)—potential acting on an electron due to all present nuclei. Yang and Mortier²⁰ proposed three different condensed forms of the Fukui function for an atom k in a molecule, based on atomic charges of N, N+ 1, and N − 1 electron systems

for nucleophilic attack : f_{k}^{+} (r) = q_{k} (N + 1) - q_{k} (N)

(4)

for electrophilic attack : f_{k}^{-} (r) = q_{k} (N) - q_{k} (N - 1)

(5)

\begin{array}{l} for free radical attack : \\ f_{k}^{0} (r) = \frac{1}{2} q_{k} (N + 1) - q_{k} (N - 1) \end{array}

(6)

where q_k is the atomic charge, evaluated from the natural population analysis (NPA) by the NBO method, in the neutral (N), anionic (N + 1), and cationic (N − 1) chemical species. To predict the reactivity of molecule, Yang and Parr²¹ introduced local softness s(r), which is obtained by Fukui function f(r) and global softness S

s (r) = S f (r)

(7)

For investigation and visualization of intermolecular interactions in R-(−)-carvone, Hirshfeld surface analysis was used.^22,23 Using the program CrystalExplorer,²⁴ Hirshfeld surfaces and fingerprint plots were generated. The crystallographic information file (.cif) was retrieved from the Cambridge Crystallographic Data Center as supplementary publication no. CCDC 131923.²⁵ In the field of this analysis, a given molecule is defined by a set of points in three-dimensional (3D) space where the contribution to the electron density from the molecule of interest is equal to the contribution from all other molecules.²⁶ The intermolecular interactions are obtained by mapping normalized contact distance ( $d_{norm}$ ), which is expressed by the following equation²⁷

d_{n o r m} = \frac{d_{i} - r_{i}^{v d W}}{r_{i}^{v d W}} + \frac{d_{e} - r_{e}^{v d W}}{r_{e}^{v d W}}

(8)

where $r_{i}^{v d W}$ and $r_{e}^{v d W}$ are the van der Waals radii of the atoms (i—atom inside, e—atom outside of the surface), $d_{i}$ and $d_{e}$ are the distances between the points on the surface and the nearest atoms present inside and outside of the surface, respectively.²⁸

Results and discussion

Structural properties

The optimized geometrical parameters—bond lengths and bond angles for R-(−)-carvone and S-(+)-carvone—were computed by the DFT using the B3LYP method with 6-311++G(2d,2p) basis set. The experimental (X-ray diffraction (XRD)) crystal data obtained by Sane et al.¹⁰ are added for comparison. Results showed that the theoretically calculated values correlate well with obtained experimentally (Figure S1 and Table S1). The calculated energy values, dipole moments, polarizability, and hyperpolarizability of R-(−)-carvone and S-(+)-carvone with B3LYP/6-311++G(2d,2p) are presented in Table S2. It can be seen that the energies of the two enantiomeric forms are the same. There are small differences in the values for dipole moment, polarizability, and hyperpolarizability. Dipole moment in a molecule is an important property, which is used to study the intermolecular interactions. As shown in Table S2, the title compound has larger dipole moments (3.5610 D for S-(+)-carvone and 3.5609 D for R-(−)-carvone), and the stronger dipole moments in the cases of title compound are mainly attributed to an overall imbalance in the charge from one side of a molecule to the other. The calculated polarizability values are equal to 18.2485 × 10⁻²⁴ esu (123.13433 a.u.) for S-(+)-carvone and 18.2484 × 10⁻²⁴ esu (123.13367 a.u.) for R-(−)-carvone. The S-(+)-carvone is slightly softer and has more polarizability than R-(−)-carvone.

Figure 1 illustrates the optimized molecular structure and atom numbering of S-(+)-carvone (d-carvone).

Figure 1.

Optimized molecular structures and atom numbering of S-(+)-carvone.

It is visible from the data presented in Table S1 that the double bonds C¹=C² and C⁸=C⁹ are characterized with lengths of 1.342 and 1.332 Å, respectively. The double bond C¹=C² is longer than the C⁸=C⁹ because the π C⁶–O²⁴ orbital is involved in the conjugation with the antibonding σ* C¹–C² orbital. On the contrary, slightly higher values were calculated as lengths for the single C³–C⁴, C⁴–C⁵, and C⁵–C⁶ bonds (1.539, 1.538, and 1.520 Å, respectively) in comparison with other single C–C bonds. This may be attributed to the conjugation of π C⁸–C⁹ with the antibonding σ* C³–C⁴ and σ* C⁴–C⁵orbitals (1), on the contrary (2) it is known that the length of a given bond strongly depends on the hybridization state of the atoms formed that bond and it increases in the following order: sp³ < sp² < sp.^29,30 For this reason, an NBO analysis was used to confirm the differences between the bond lengths in the title compound.

It was presented earlier that the distance (1.342 Å) between the atoms C¹ and C² is slightly longer than that observed for the C⁸=C⁹ (1.332 Å) interaction (Table S1). According to NBO analysis, the σ component of the double C¹=C² bond (1.980e) possessed a contribution of 50.83% sp^1.64(C¹) and 49.17% sp^1.55(C²), whereas the π component (1.862e) was expressed via 52.34% p(C¹) and 47.66% p(C²) (Table 1). The data obtained for the C⁸=C⁹ bond are as follows: σ component (1.984e) was composed of 51.37% sp^1.63(C⁸) and 48.63% sp^1.43(C⁹), and π component (1.957e) was composed of 48.38% p(C⁸) and 51.62% p(C⁹). It is visible that occupancy of the π bond for C¹=C² is lower in comparison with the π bond for C⁸=C⁹. The absence of a difference between the lengths of single C³–C⁴ (1.539 Å) and C⁴–C⁵ (1.538 Å) bonds (Table S1) is confirmed by NBO analysis: a contribution of 49.88% sp^2.5(C³) and 50.12% sp^2.92(C⁴) characterized the σ C³–C⁴ orbital (1.967e) and values of 50.35% sp^2.89(C⁴) and 49.65% sp^2.49(C⁵) were calculated as contributions in the C⁴–C⁵ orbital (1.967e). These findings completely coincide with the difference between the lengths of single C²–C³ (1.501 Å) and C¹–C⁷ (1.502 Å) bonds.

Table 1.

Occupancy of NBOs and hybrids of S-(+)-carvone by the B3LYP method with 6-311++G(2d,2p) basis set.

Bond orbital	Occupancy	Hybrids^a	AO (%)^b
σ C¹–C²	1.980	sp^1.64(C¹) + sp^1.55(C²)	50.83% (C¹) + 49.17% (C²)
π C¹–C²	1.862	p(C¹) + p(C²)	52.34% (C¹) + 47.66% (C²)
σ C¹–C⁶	1.972	sp^2.36(C¹) + sp^1.85(C⁶)	51.48% (C¹) + 48.52% (C⁶)
σ C¹–C⁷	1.982	sp^2.09(C¹) + sp^2.35(C⁶)	51.30% (C¹) + 48.70% (C⁷)
σ C²–C³	1.978	sp^2.02(C²) + sp^2.53(C³)	49.25% (C²) + 50.75% (C³)
σ C³–C⁴	1.967	sp^2.53(C³) + sp^2.92(C⁴)	49.88% (C³) + 50.12% (C⁴)
σ C⁴–C⁵	1.967	sp^2.89(C⁴) + sp^2.49(C⁵)	50.35% (C⁴) + 49.65% (C⁵)
σ C⁴–C⁸	1.968	sp^2.50(C⁴) + sp^2.19(C⁸)	51.06% (C⁴) + 48.94% (C⁸)
σ C⁵–C⁶	1.981	sp^2.79(C⁵) + sp^1.92(C⁶)	51.51% (C⁵) + 48.49% (C⁶)
σ C⁶–O²⁴	1.995	sp^2.27(C⁶) + sp^1.33(O²⁴)	34.50% (C⁴) + 65.50% (O²⁴)
π C⁶–O²⁴	1.972	p(C⁶) + p(O²⁴)	32.54% (C⁴) + 67.46% (O²⁴)
LP(1) O²⁴	1.979	sp^0.75	–
LP(2) O²⁴	1.895	P	–
σ C⁸–C⁹	1.984	sp^1.63(C⁸) + sp^1.43(C⁹)	51.37% (C⁸) + 48.63% (C⁹)
π C⁸–C⁹	1.957	p(C⁸) + p(C⁹)	48.38% (C⁸) + 51.62% (C⁹)
σ C⁸–C¹⁰	1.979	sp^2.28 (C⁸) + sp^2.26(C¹⁰)	49.99% (C⁸) + 50.01% (C¹⁰)

NBO: natural bond orbital; AO: atomic orbital; LP: lone electron pair.

Hybrids on atoms.

Percentage contribution of AOs in NBO hybrid.

Electronic properties and chemical reactivity

The chemical reactivity of a given molecule depends on its electronic structure, that is why the MEP surface of the S-(+)-carvone was investigated (Figure 2).

Figure 2.

The total electron density mapped with electrostatic potential surface of S-(+)-carvone.

The theoretical calculations showed that the MEP of S-(+)-carvone varies from −0.054 to +0.017 a.u. The electron-rich and electron-deficient sites of the molecule are represented by different colors. The red color corresponds to the regions localized the most negative charge, whereas the blue color denotes the most positive ones. The molecular electron density surface is used to identify the electrophilic and nucleophilic reactive sites and to study interactions between molecules and ions or solvents and biological properties of molecules.^31,32 The negative potential region in the studied molecule is found around the polar oxygen atom, which shows high activity of this site. The positive regions are localized on the hydrogen atoms, which can be considered as possible sites for nucleophilic attack.

In addition, the atomic charges of the neutral, cationic and anionic species of S-(+)-carvone were established by NBO using the B3LYP method with 6-311++G(2d,2p) basis set and are presented in Table 2.

Table 2.

NPA atomic charges and bond orders in S-(+)-carvone.

Atom	NPA charges	Bond	Bond order
C¹	−0.120	C¹–C²	1.727
C²	−0.099	C²–C³	1.098
C³	−0.411	C³–C⁴	1.009
C⁴	−0.232	C⁴–C⁵	1.012
C⁵	−0.458	C⁵–C⁶	1.041
C⁶	0.557	C⁶–C¹	1.082
C⁷	−0.589	C¹–C⁷	1.101
C⁸	0.001	C⁴–C⁸	1.030
C⁹	−0.377	C⁸–C⁹	1.875
C¹⁰	−0.602	C⁸–C¹⁰	1.096
H¹¹	0.214	C⁶–O²⁴	2.525
H¹²	0.211	C²–H²⁵	0.865
H¹³	0.201	C³–H¹¹	0.855
H¹⁴	0.217	C³–H¹²	0.838
H¹⁵	0.228	C⁴–H¹³	0.808
H¹⁶	0.199	C⁵–H¹⁴	0.833
H¹⁷	0.220	C⁵–H¹⁵	0.848
H¹⁸	0.218	C⁷–H¹⁶	0.903
H¹⁹	0.187	C⁷–H¹⁷	0.893
H²⁰	0.188	C⁷–H¹⁸	0.894
H²¹	0.203	C⁹–H¹⁹	0.918
H²²	0.208	C⁹–H²⁰	0.912
H²³	0.210	C¹⁰–H²¹	0.891
O²⁴	−0.568	C¹⁰–H²²	0.891
H²⁵	0.192	C¹⁰–H²³	0.899

NPA, natural population analysis.

It is visible that the most positive charge of +0.557 was detected on the carbon atom (C⁶) linked with the oxygen one, followed by the charge value of +0.228 located on the H¹⁵ atom. These data propose that the nucleophilic reactivity of the titled molecule depends in a greater extent on the C⁶ atom rather than H¹⁵ one. The calculated NPA charges showed that a significant amount of negative charge is located on the carbon atoms C¹⁰ (−0.602), followed by the negative charge of −0.589 on the carbon atom C⁷ and −0.568 on the oxygen atom O²⁴, which assumed the existence of a charge compensation effect between the oxygen atom and C⁶ one. The latter was confirmed by means of MEP surface analysis, where it is clearly exposed that O²⁴ is located in the area with most negative charge. Hence, we state that the electrophilic reactivity of S-(+)-carvone depends mainly on the oxygen atom.

The carbon atoms 1 and 8 have a similar bonding environment, but NBO gives different charges, −0.120 and +0.001, respectively. The latter is linked with lowest amount of electron density (+0.557) on the carbon 6 atom bonded to the oxygen (electronegative atom). According to the NPA analysis (Table 2), values of +0.557, −0.099, and −0.589 were calculated as charges located on the C⁶, C², and C⁷ atoms, respectively. On the contrary, the C⁴, C⁹, and C¹⁰ atoms were characterized with charges of −0.232, −0.377, and −0.602, respectively. Consequently, a stronger charge compensation effect between C⁴, C⁹, C¹⁰, and C⁸ atoms with respect to those between C⁶, C², C⁷, and C¹ was assumed. As a result, a positive charge exists on the C⁸ atom.

A useful method for investigating the chemical reactivity of a given molecule is the analysis of the FMOs.³³ The FMOs and their negative (green) and positive (red) regions obtained by the B3LYP method with 6-311++G(2d,2p) basis set for the S-(+)-carvone are shown in Figure 3(a) and (b), respectively.

Figure 3.

Frontier molecular orbitals of S-(+)-carvone: HOMO (a) and LUMO (b).

The HOMO is with the contribution: ψ_HOMO = 16.8% 3p_x (O²⁴) + 12.1% 4p_x (O²⁴) + 8.8% 2p_x (O²⁴) − 8.4% 3p_y (O²⁴) − 6.4% 4p_y (O²⁴) + 5.1% 3p_x (C⁵). The electron donor capability of O²⁴ confirmed the results from the MEP surface and NPA charge analyses that the electrophilic reactivity of the S-(+)-carvone is primarily influenced by the oxygen atom. The LUMO is with the contribution: ψ_LUMO = −11.4% 3p_z (C²) + 11.0% 3p_z (C⁶) − 10.3% 4p_z (C²) + 8.8% 4p_z (C⁶) − 8.3% 3p_z (O²⁴) − 5.9% 5p_z (C²). It is clear that the nucleophilic reactivity of the S-(+)-carvone depends on the carbon atoms (C² and C⁶). The frontier orbital gap value was used to characterize the chemical reactivity and the kinetic stability of the titled compound.³⁴ Molecules with a high chemical reactivity and low kinetic stability are with a small frontier orbital gap. In this work, the values obtained for HOMO and LUMO orbitals were −6.813 and −1.648 eV, respectively. The values of global hardness $(η = Δ E_{LUMO - HOMO} / 2)$ and global softness $(S = 1 / η)$ are an indication for the polarizability and reactivity of a given compound.^35–39 Calculations show that the values of 2.2583 and 0.387 eV characterize $η$ and $S$ , respectively, in the case of S-(+)-carvone. Therefore, the title compound was denoted as a highly polarizable and reactive material. It was confirmed from MEP analysis (Figure 2) and from calculations of its electronegativity $(χ = - (E_{HOMO} + E_{LUMO}) / 2)$ , chemical potential (μ = −χ), and electrophilicity index $(ω = μ^{2} / 2 η),$ the values of 4.231, −4.231, and 3.465 eV were obtained, respectively.

The local reactivity descriptors such as Fukui function and local softness are related to the selectivity of the specific site in a molecule, whereas chemical potential, hardness, and softness are the global properties related to the chemical reactivity. The Fukui’s indices provide information about the molecule’s tendency to lose or receive an electron and predicting which atom in the molecule would be more susceptible to an electrophilic or nucleophilic attack.^20,40 The condensed reactivity parameters for the title compound were calculated by NPA. Morell et al.³⁵ proposed new dual descriptors for chemical reactivity: Δf_k and Δs_k. They are defined as follows

Δ f_{k} = (f_{k}^{+} - f_{k}^{-})

(9)

Δ s_{k} = S (f_{k}^{+} - f_{k}^{-}) = (s_{k}^{+} - s_{k}^{-})

(10)

If ∆f_k (Δs_k) is positive, then the site is electrophilic (atom k), and if ∆f_k (Δs_k) is negative, then the site is nucleophilic. For the titled compound, O²⁴ acts as an electrophilic site and it is prone to nucleophilic attack, whereas C⁶, C², C¹, and all the hydrogen atoms are nucleophilic sites and are prone to electrophilic attack. The condensed Fukui functions and local softness and dual descriptors for S-(+)-carvone are given in Table 3.

Table 3.

The condensed Fukui functions, local softness, and dual descriptors (Δf_k, Δs_k) for S-(+)-carvone.

Atom	$f_{k}^{+}$	$f_{k}^{-}$	$f_{k}^{o}$	∆ $f_{k}$	$s_{k}^{+}$	$s_{k}^{-}$	$s_{k}^{o}$	∆ $s_{k}$
C¹	−0.0490	−0.0110	−0.0300	−0.0380	−0.0190	−0.0043	−0.0116	−0.0147
C²	−0.2240	−0.0800	−0.1520	−0.1440	−0.0867	−0.0310	−0.0588	−0.0557
C³	0.0200	0.0120	0.0160	0.0080	0.0077	0.0046	0.0062	0.0031
C⁴	−0.0100	0.0110	0.0005	−0.0210	−0.0039	0.0043	0.0002	−0.0081
C⁵	0.0220	−0.0320	−0.0050	0.0540	0.0085	−0.0124	−0.0019	0.0209
C⁶	−0.1630	−0.0130	−0.0880	−0.1500	−0.0631	−0.0050	−0.0341	−0.0581
C⁷	0.0030	0.0050	0.0040	−0.0020	0.0012	0.0019	0.0015	−0.0008
C⁸	0.0110	−0.0870	−0.0380	0.0980	0.0043	−0.0337	−0.0147	0.0379
C⁹	−0.0910	−0.1790	−0.1350	0.0880	−0.0352	−0.0693	−0.0522	0.0341
C¹⁰	−0.0040	0.0200	0.0080	−0.0240	−0.0015	0.0077	0.0031	−0.0093
H¹¹	−0.0380	−0.0260	−0.0320	−0.0120	−0.0147	−0.0101	−0.0124	−0.0046
H¹²	−0.0420	−0.0270	−0.0345	−0.0150	−0.0163	−0.0104	−0.0134	−0.0058
H¹³	−0.0130	−0.0200	−0.0165	0.0070	−0.0050	−0.0077	−0.0064	0.0027
H¹⁴	−0.0440	−0.0360	−0.0400	−0.0080	−0.0170	−0.0139	−0.0155	−0.0031
H¹⁵	−0.0290	−0.0250	−0.0270	−0.0040	−0.0112	−0.0097	−0.0104	−0.0015
H¹⁶	−0.0260	−0.0280	−0.0270	0.0020	−0.0101	−0.0108	−0.0104	0.0008
H¹⁷	−0.0280	−0.0150	−0.0215	−0.0130	−0.0108	−0.0058	−0.0083	−0.0050
H¹⁸	−0.0220	−0.0160	−0.0190	−0.0060	−0.0085	−0.0062	−0.0074	−0.0023
H¹⁹	−0.0190	−0.0240	−0.0215	0.0050	−0.0074	−0.0093	−0.0083	0.0019
H²⁰	−0.0060	−0.0140	−0.0100	0.0080	−0.0023	−0.0054	−0.0039	0.0031
H²¹	−0.0050	−0.0300	−0.0175	0.0250	−0.0019	−0.0116	−0.0068	0.0097
H²²	−0.0230	−0.0250	−0.0240	0.0020	−0.0089	−0.0097	−0.0093	0.0008
H²³	−0.0230	−0.0240	−0.0235	0.0010	−0.0089	−0.0093	−0.0091	0.0004
O²⁴	−0.1580	−0.3010	−0.2295	0.1430	−0.0611	−0.1165	−0.0888	0.0553
H²⁵	−0.0370	−0.0350	−0.0360	−0.0020	−0.0143	−0.0135	−0.0139	−0.0008

For studying intramolecular bonding, charge transfer, and conjugative interactions, NBO analysis was provided. When there is more intensive interaction between electron donors (occupied (lone pair) orbitals) and electron acceptors (unoccupied (antibonding) orbitals), the second-order stabilization energy (E⁽²⁾) value is larger, it corresponds to a stable donor–acceptor interaction. These interactions and their E⁽²⁾ values for carvone are presented in Table 4.

Table 4.

Second-order perturbation theory analysis of Fock matrix in NBO basis.

Donor (i)	ED(i)/e	Acceptor (j)	ED(j)/e	E ⁽²⁾	E(j)− E(i)	F(i, j)
π C¹–C²	1.862	π* C⁶–O²⁴	0.144	20.97	0.30	0.070
σ C²–H²⁵	1.977	σ* C¹–C⁶	0.070	6.07	0.97	0.069
π C⁶–O²⁴	1.972	π* C¹–C²	0.089	5.75	0.42	0.044
π C⁸–C⁹	1.957	σ* C³–C⁴	0.024	3.29	0.64	0.041
π C⁸–C⁹	1.957	σ* C⁴–C⁵	0.023	2.89	0.64	0.039
LP(1) O²⁴	1.979	σ* C¹–C⁶	0.070	1.86	1.13	0.041
LP(1) O²⁴	1.979	σ* C⁵–C⁶	0.058	1.55	1.07	0.037
LP(2) O²⁴	1.895	σ* C¹–C⁶	0.070	19.27	0.71	0.105
LP(2) O²⁴	1.895	σ* C⁵–C⁶	0.058	20.18	0.65	0.104
π* C⁶–O²⁴	0.144	π* C¹–C²	0.089	29.60	0.03	0.073

NBO: natural bond orbital; LP: lone electron pair.

ED—electron delocalization (occupation number); E⁽²⁾—energy of hyperconjugative interactions (stabilization energy), kcal mol⁻¹; E(j)− E(i)—energy difference between donor and acceptor i and j NBO orbitals, a.u.; and F(i, j)—Fock matrix elements between i and j NBO orbitals, a.u.

Results showed (Table 3) a strong hyperconjugative interaction of the π electrons of C¹–C² to the π* C⁶–O²⁴ with a value of 20.97 kcal mol⁻¹ as stabilization energy, which decreases the occupied orbital population (1.862e) and increases the electron density of the acceptor orbital (0.144e). In the same way, slightly higher stabilization energy of 29.60 kcal mol⁻¹ was observed for the hyperconjugative interaction π* C⁶–O²⁴ → π* C¹–C². The values of 3.29 and 2.89 kcal mol⁻¹ were calculated as stabilization energies for the interactions π C⁸–C⁹ → σ* C³–C⁴ and π C⁸–C⁹ → σ* C⁴–C⁵, respectively. Comparing the stabilization energies, it is clear that the double bond C¹=C² is longer than the double bond C⁸=C⁹. The latter was in accordance with the bond order value (1.875) calculated for C⁸=C⁹, which is higher in comparison with bond order (1.727) for C¹=C². A considerable electron density distribution from the lone electron pair LP(2) O²⁴ to the antibonding σ* C⁵–C⁶ and σ* C¹–C⁶ orbitals was established. In detail, E⁽²⁾ values of 20.18 and 19.27 kcal mol⁻¹ characterized the LP(2) O²⁴ → σ* C⁵–C⁶ and LP(2) O²⁴ → σ* C¹–C⁶ interactions, respectively. This increases the electron density of the acceptor orbitals (0.058e and 0.070e) and weakens the nonbonding LP(2) O²⁴ (1.895e) orbital. The latter was in accordance with the order value of 1.082 calculated for the C¹–C⁶ bond, which is slightly higher in comparison with bond order of C⁵–C⁶ (1.041). Weaker stabilization energies were obtained for LP(1) O²⁴ → σ* C¹–C⁶ and LP(1) O²⁴ → σ* C⁵–C⁶ interactions (expressed with E⁽²⁾ of 1.86 and 1.55 kcal mol⁻¹, respectively).

Intermolecular interactions

The Hirshfeld surface and associated two-dimensional (2D) fingerprint plots were used to examine the interactions in the crystal structure of R-(−)-carvone.⁴¹ The Hirshfeld surface is not simply a function of the molecular geometry but is only defined within the crystal.²⁷ The Hirshfeld surface shows the result of the interaction between different atomic sizes and intermolecular contacts in the crystal.²⁸ The blue regions are longer than the van der Waal distance of the interacting atoms, whereas the red regions show the region of the molecule contacts that are shorter than the van der Waal’s distances, the white regions are those where the distances are comparable to the distances of Van der Waal’s. Hirshfeld surface of R-(−)-carvone mapped with $d_{n o r m}$ , shape index and curvedness is presented in Figure 4. The results obtained are as follows: $d_{n o r m}$ values vary from −0.258 to +1.351 Å, shape index ranges from −0.987 to +0.999 Å, and curvedness from −4.054 to +0.181 Å.

Figure 4.

Hirshfeld surface for R-(−)-carvone mapped with $d_{n o r m}$ (a), shape index with areas of complementarity identified (paired circles) (b), and curvedness (c).

The mapping $d_{n o r m}$ showed the existence of a bright red area in the Hirshfeld surface due to a strong interaction between an oxygen atom (O¹) inside of the surface and a hydrogen atom (H³²) in the structure outside of the surface via O¹. . .H³² hydrogen bond (Figures 4(a) and 5). The presence of an identical hydrogen bond (H³². . .O¹) between hydrogen atom (H³²) in the structure inside of the surface and an oxygen atom (O¹) outside of the surface was detected. A value of 2.263 Å was observed as length of the aforementioned hydrogen bonds. It was established that a hydrogen bond appeared between molecule inside and outside of the surface expressed by H⁶¹. . .O¹ and O¹. . .H⁶¹ interactions with values of 2.513 Å. Very close contacts were detected between atoms: H⁹¹. . .H¹⁰³ and H¹⁰³. . .H⁹¹ inside and outside of the surface with values of 2.183 Å and between C⁹. . .H¹⁰³ and H¹⁰³. . .C⁹of 2.516 Å (Figure 5).

The complementarity between molecules in the crystal packing structure is a feature of Hirshfeld surface analysis namely Shape index.^42,43 The areas of intermolecular complementarity have an identical pattern but opposite colors. The blue patches represent convex regions which are indication for ring atoms of the molecule inside the surface, the red ones represent concave regions related to atoms of the π-stacked molecule above them (Figure 4(b)).

Figure 5.

Hirshfeld surface for R-(−)-carvone mapped with d_norm and neighboring molecules associated with close contacts are shown along with distances between the atoms involved.

The 2D fingerprint plots identify each type of intermolecular contact and enable the analysis of very small differences in these patterns and represent a new way of summarizing the major intermolecular contacts of an entire crystal structure.⁴⁴ Figure 6 shows the associated fingerprint plots of the four R-(−)-carvone molecules showing the contributions of different intermolecular interactions on the Hirshfeld surface.

Figure 6.

Two-dimensional fingerprint plots with d_norm view of the contacts in the R-(−)-carvone.

It is visible (Figure 6(b)) that the highest contribution of total Hirshfeld surface is attributed to H. . .H contacts with 76.6% and appear in the middle of the scattered points in the two-dimensional fingerprint map with a single broad peak at d_i = d_e = 1.2 Å. In detail, the spike characterized the O. . .H interactions with a contribution of 7.4%. The calculated distances between nearest atoms present inside (O) and outside (H) the surface were approximately equal to 1.28 and 0.95 Å, respectively. The H. . .O interactions with a contribution of 6.7% of the total surface were detected to form a spike with values of 0.95 and 1.28 Å as d_i and d_e, respectively (Figure 6(c)). It was stated that the presence of O. . .H/H. . .O interactions are a result of hydrogen bond formation, which ensures the stability of the crystal framework. The C. . .H/H. . .C interactions with contribution of 7.4% are other significant contacts for the investigated compound (Figure 6(d)). The C. . .H interactions were exhibited by a spike with d_i ≈ 1.5 Å and d_e ≈ 1.2 Å. These types of interactions involve 4% of the total surface in the bottom right region of the fingerprint plot. The H. . .C interactions represented by spike with d_i ≈ 1.3 Å and d_e ≈ 1.6 Å cover 3.4% of the total surface in the top left region of the fingerprint plot. Figure 6(e) shows that the C. . .O/O. . .C interactions $(d_{i} + d_{e} \approx 2.4)$ Å are 1.4% of the total surface with no important role in the stabilization of the structure. The contribution of C. . .C contacts (Figure 6(f)) represents 0.5% of the Hirshfeld surface with $d_{i} + d_{e} \approx 2.5$ Å.

The enrichment ratio (E) was determined in order to confirm both the nature and contribution of the bonds established in R-(−)-carvone. The enrichment ratio is defined as the ratio between the proportion of actual contacts in the crystal and the theoretical proportion of random contacts, derived from the Hirshfeld surface analysis.⁴⁵ The E value is larger than one for a pair of elements with a higher propensity to form contacts. The E value is lower than one for pairs with a lower propensity to form contacts.⁴¹ It is visible from Table 5 that the 87.35% of the molecular surface is generated by H atoms, followed by the O atoms with surface contribution of 7.75%, while C atoms complement the total molecular surface with contribution of 4.90%.

Table 5.

Hirshfeld contact surfaces and enrichment ratios for R-(−)-carvone.

Atoms	H	O	C
Surface, %	87.35	7.75	4.90
H	1.00	1.04	0.86
O	–	0.0	1.84
C	–	–	2.08

The C. . .C and C. . .O interactions are the most enriched contacts ( $E_{C \cdot \cdot \cdot C}$ = 2.08; $E_{C \cdot \cdot \cdot O}$ = 1.84), which represents a major attraction in the R-(−)-carvone despite its small surface. These interactions (C. . .O) are probably a secondary effect due to (1) a proximity of the carbon atom via hydrogen bond C³–H³². . .O¹ and (2) of the carbon atom via hydrogen bond C⁶–H⁶¹. . .O¹ (Figure 5). The electrostatically unfavorable contacts C. . .H (0.86% of the total Hirshfeld surface) were poorly presented in the R-(−)-carvone structure with enrichment ratio values of 0.86. In addition, an enrichment ratio value of 1.00 showed that the H. . .H interactions possess a repulsive character rather than an attractive one.

A study of Hirshfeld surface carried out on R-(−)-carvone gives the following measurement: molecular volume, 236.88 Å³; surface area, 231.17 Å²; globularity, 0.801; and asphericity, 0.114.

Conclusion

Analyses on the molecular geometry, chemical bonds nature, electronic properties, and chemical activity of the carvone were described using theoretical calculations (expressed by MEP surface, FMO, and NBO analyses at the B3LYP/6-311++G(2d,2p) level). The MEP surface and FMO theory showed that the nucleophilic activity of the carvone was connected with the low electron density on the hydrogen atoms. In contrary, a large electronegative potential was detected on the oxygen atom. Using FMO analysis, values of −6.813 and −1.648 eV were related to HOMO and LUMO orbitals, respectively. As a result, the chemical hardness and softness, electronegativity, chemical potential, and electrophilicity index were calculated as 2.583, 0.387, 4.231, −4.231, and 3.465 eV, respectively. The intermolecular interactions were examined via Hirshfeld surface analysis. It was established that $d_{n o r m}$ values varied from −0.258 to +1.351 Å, the shape index ranged from −0.987 to +0.999 Å, and the curvedness from −4.054 to +0.181 Å. It was stated that the presence of O. . .H/H. . .O interactions are a result of hydrogen bond formation, which ensures the stability of the crystal framework.

The theoretical calculations will be used to interpret the difference in antimicrobial and antioxidant activity of essential oils containing the two forms of carvone, which are the subject of our next research.

Supplemental Material

Supplementary_information – Supplemental material for Electronic structure, reactivity, and Hirshfeld surface analysis of carvone

Supplemental material, Supplementary_information for Electronic structure, reactivity, and Hirshfeld surface analysis of carvone by Rumyana Yankova, Milen Dimov, Krasimira Dobreva and Albena Stoyanova in Journal of Chemical Research

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Rumyana Yankova

Supplemental material

Supplemental material for this article is available online.

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