DFT calculations as an efficient tool for prediction of Raman and infra-red spectra and activities of newly synthesized cathinones

3.1 Molecular geometry

The optimized structures of the title compounds along with numbering of atoms are shown in Figure 1.

Figure 1

Optimized structures obtained after DFT calculations of a) 3-FMC; b) 4-FMC; c) buphedrone; d) butylone; e) ethylone; f) MDPV; g) metcathinone; h) methylone; i) 4-MMC.

The global minimum energy obtained by the DFT structure optimization procedure for the investigated compounds is summarised in Table 1. All the calculated vibrational wavenumbers using the optimized geometry were found to be positive for the title compounds. The bond lengths, bond angles and the optimized parameters calculated using the DFT method are shown in the Supplementary material (Tables A1-A9).

In 3-FMC, the bond lengths of C1-C6, C3-C4, C5-C6, C6-C8, C8-C10, C10-C11 were found to be elongated to 1.407 Å, 1.401 Å, 1.409 Å, 1.493 Å, 1.529 Å, 1.562 Å, respectively compared to their default values of 1.39 Å. In the structurally similar 4-FMC, the bond lengths of C1-C6, C5-C6, C6-C8, C8-C10, and C10-C11 were found to be elongated to 1.409 Å, 1.410 Å, 1.489 Å, 1.541 Å, 1.538 Å, respectively, compared to their default values of 1.39 Å. In both cases, C10-H18 and C13-H24 were found to be elongated to 1.1 Å (3-FMC, 4-FMC) and 1.106 Å (3-FMC) and 1.104 Å (4-FMC) compared to their default values of 1.08 Å (3-FMC) and 1.09 Å (4-FMC). This elongation may be due to their proximity to the electronegative oxygen, fluorine and nitrogen atoms [19, 20]. It also indicates the extensive charge delocalization that takes place within the molecule.

In 4-MMC, the bond lengths of C3-C7, C6-C8, C8-C9, and C9-C10 were found to be elongated to 1.506 Å, 1.515 Å, 1.553 Å and 1.524 Å, respectively, compared to their default value of 1.39 Å. Similarly, the bond lengths of C9-H21, C10-H23, and C12-H26 were found to be elongated to 1.097 Å, 1.097 Å and 1.096 Å, respectively, compared to their default value of 1.08 Å. This elongation may be due to their proximity to the electronegative oxygen (O13) and nitrogen (N11) atoms [19, 20] indicating the extensive charge delocalization inside the molecule.

In buphedrone, the bond lengths of C6-C7, C7-C9, C9-C10, and C10-C11 were found to be elongated to 1.518 Å, 1.549 Å, 1.538 Å and 1.52 Å, respectively, compared to their default value of 1.39 Å. The bond lengths of C10-H20, C10-H21, and C13-H26 were found to be elongated to 1.098 Å, 1.099 Å and 1.096 Å, respectively, compared to their default value of 1.08 Å. Our assumption is that the phenomenon is caused by the presence of electronegative oxygen (O8) and nitrogen (N12) atoms [19, 20], which causes the delocalization inside the molecule.

In butylone, the bond lengths of C1-C6, C4-C5, C6-C7, C7-C9, C9-C13, and C13-C14 were found to be elongated to 1.419 Å, 1.401 Å, 1.411 Å, 1.487 Å, 1.545 Å, 1.551 Å and 1.536 Å, respectively, compared to their default value of 1.39 Å. The elongation is observed inside the bonds C13-H24, C14-H26, C16-H30, and C16-H31 as well (1.099 Å, 1.097 Å, 1.105 Å and 1.096 Å, respectively); the default value is 1.08 Å. Electronegative oxygen (O8) and nitrogen (N12) atoms are causes of this elongation and the delocalization of charges inside the molecule [19, 20].

In ethylone, the bond lengths of C6-C7, C7-C9, C9-C13, and C15-C16 were found to be elongated to 1.518 Å, 1.548 Å, 1.529 Å and 1.522 Å, respectively, compared to their default value of 1.39 Å. Similarly, the bond lengths of C11-H21, C11-H22, C13-H24, C13-H25, and C15-H28 were found to be elongated to 1.096 Å, 1.096 Å, 1.096 Å, 1.096 Å and 1.097 Å, respectively from their default value of 1.08 Å. This fact may be due to their proximity to the electronegative oxygen (O8, O10, O12) and nitrogen (N15) atoms [19, 20].

The bond lengths of C1-C6, C4-C5, C5-C6, C6-C7, C7-C9, C9-C10, C10-C19, C16-C17, C17-C18, and C19-C20 in MDPV, were found to be elongated to 1.419 Å, 1.401 Å, 1.412 Å, 1.492 Å, 1.543 Å, 1.546 Å, 1.540 Å, 1.555 Å, 1.534 Å, 1.552 Å and 1.537 Å, respectively (the default value is 1.39 Å). The bond lengths of C9-H24, C10-H26, C15-H30, C16-H32, C19-H37, and C19-H38 were found to be elongated to 1.108 Å, 1.097 Å, 1.108 Å, 1.110 Å, 1.1 Å and 1.099 Å, respectively (the default value is 1.08 Å). The explanation for the elongation and the delocalization can be the presence of electronegative oxygen (O8, O12, O14) and nitrogen (N11) atoms [19, 20]. Regarding Metcathinone, the bond lengths of C1-C6, C2-C3, C3-C4, C5-C6, C6-C7, C7-C9, and C9-C10 were found to be elongated to 1.409 Å, 1.402 Å, 1.4 Å, 1.408 Å, 1.49 Å, 1.541 Å and 1.537 Å, respectively (default value is 1.39 Å). Similarly, the bond lengths of C9-H18, C12-H24, and C12-H25 were found to be elongated to 1.099 Å, 1.104 Å and 1.097 Å, respectively (default value is 1.08 Å). Similarly to previously investigated compounds, electronegative oxygen (O8) and nitrogen (N11) atoms are causes of the observed elongations and delocalisations [19, 20].

The bond lengths of C1-C6, C4-C5, C5-C6, C6-C7, C7-C9, and C9-C10 in the last investigated cathinone here, Methylone, were found to be elongated to 1.419 Å, 1.401 Å, 1.409 Å, 1.486 Å, 1.531 Å and 1.561 Å, respectively (the default value is 1.39 Å). The bond lengths of C9-H19, C10-H20, and C12-H26 were found to be elongated as well (1.099 Å, 1.095 Å and 1.098 Å, respectively) from the default value of 1.08 Å, which can be the consequence of the presence of electronegative oxygen (O8) and nitrogen (N11) atoms [19, 20].

3.2 Molecular vibrations and simulated spectra

The well-known excellent performance of density functional theory for the estimation of vibrational spectra of organic compounds can also be observed for the studied compounds. The unscaled B3LYP/6–31G vibrational wavenumbers are generally somewhat larger than the experimental values. This phenomenon is due to the over-estimation of the basis set and methodology used. However, the use of selective scaling is necessary to obtain reliable information on the vibrational properties. The calculated wavenumbers were scaled using a scale factor [21, 22]. The scaling procedure results in overcoming the anharmonicity and over-estimation. The calculated vibrational wavenumbers, IR intensities, Raman activities along with their assignments for all the title molecules are shown in Tables A10-A18. As shown by the data presented in Table 2 and Tables A10-A18 the theoretical results compare well to the experimental values.

3.3 Frontier Molecular Orbital Analysis

The excitation energy of a molecule can be calculated by finding the energy difference between the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO), and it is an excellent indicator of electronic transition absorption in the molecular systems [31, 32]. These molecular orbitals provide insight into the reactivity nature and the physical and structural properties of molecules. The positive and negative phase was represented in red and green color. The HOMO, LUMO energies and the energy gap for the investigated compounds were calculated using B3LYP/6-31G method. Owing to the HOMO–LUMO orbital interaction, LP-LP, and LP-bond pair type interactions were observed to be predominant in the investigated compounds according to the molecular orbital theory. The calculated HOMO, LUMO energies, and the energy gap are shown in Table 3.

The molecular orbital analysis for the investigated compounds based on their optimized geometry indicates that the frontier molecular orbitals are mainly composed of p type-atomic orbitals. An electronic system with larger HOMO-LUMO gap should be less reactive than one with a smaller gap. Moreover, the HOMO–LUMO energy gap clearly explains the eventual charge transfer taking place within the molecule.

The power of an electronegative atom in a compound to attract an electron towards it was introduced by Pauling. The parameters such as hardness (ɳ), ionization potential (I), electronegativity (χ), chemical potential (μ), electron affinity (A), global softness (σ) and global electrophilicity (ω) are defined as follows:

The ionization energy (IE) can be expressed through HOMO orbital energies, and electron affinity (EA) can be expressed through LUMO orbital energies. The hardness (ɳ) corresponds to the gap between HOMO and LUMO orbital energies. The hardness has been associated with the stability of the chemical system. All the calculated values of quantum chemical parameters of the investigated molecules using the B3LYP method with 6-31G basis set are summarised in Table 3.

From the results in Table 3 it is clear that for the molecules investigated 3-FMC has the minimum energy gap of 3.386 eV and 4-FMC has the maximum energy gap of 4.205 eV. These facts further indicate that 3-FMC would be highly reactive among all the cathinones under investigation.

3.4 Mulliken Population Analysis

The Mulliken population analysis [33, 34] of the title compounds was performed at DFT-B3LYP/6-31G level to obtain the values of the atomic charges and the results are shown in Table 4.

All calculated values indicate the extensive charge delocalization in the investigated molecules [19, 20]. The positive charges are localized over the hydrogen atoms.

3.5 Natural Bond Orbital (NBO) Analysis

The intramolecular interactions, delocalization of electrons and stabilization energy of the investigated compounds was performed with NBO analysis using the NBO 5.1 program [15] implemented in the Gaussian 09W package at the DFT-B3LYP/6-31G level. The energy arising from hyperconjugative interactions was deduced from the second-order perturbation approach [17]. The large values of E⁽²⁾ indicate the tendency of an electron to donate, and therefore, the greater extent of conjugation within the system.

The strength of the delocalization interaction can be estimated by the second-order energy lowering E⁽²⁾,

Where E⁽²⁾is the stabilization energy, q_i is the donor orbital occupancy, E_i and E_j are the diagonal elements and F(i,j) is the off diagonal NBO Fock matrix element reported [35].

The most predominant electron donor-acceptor interactions are shown in Tables A19-A27 for the investigated compounds.

In 3-FMC, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and fluorine atoms to bond pairs. A strong hyperconjugative interaction was observed due to п* (C2-C3)--- п* (C4-C5), п* (C8-O9)--- п* (C10-C11), п(C1-C6)--- п*(C2-C3), LP3 (F7)--- п* (C2-C3) and LP2 (O9)--- п* (C6-C8), and values were found to be 159.50 kcal/mol, 97.88 kcal/mol, 22.11 kcal/mol, 17.40 kcal/mol and 17.09 kcal/mol, respectively, which also leads to the stability of the molecule. Although quite similar to 3-FMC, in 4-FMC, the electron transfer was predominantly observed only from the bond pair to bond pairs. A strong hyperconjugative interaction was observed due to п (C1-C6)--- п* (C2-C3), п (C1-C6)--- п* (C4-C5), σ (C1-C2)--- σ* (C2-C3), σ (C1-C2)--- σ* (C6-C8) and σ (C1-C6)--- σ* (C5-C6), and values were found to be 19.27 kcal/mol, 22.11 kcal/mol, 3.97 kcal/mol, 3.37 kcal/mol and 3.82 kcal/mol, respectively.

The electron transfer in 4-MMC was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction was observed due to π (C₁- C₂)--- π* (C₃-C₄), π (C₁-C₂)--- π* (C₅-C₆), π* (C₇-O₈)--- π* (C₅-C₆), LP (2) O₈--- σ* (C₆-C₇) and LP (2) O₈--- σ* (C₇-C₉). Values were found to be 21.90 kcal/mol, 19.15 kcal/mol, 73.73 kcal/mol, 16.53 kcal/mol and 17.25 kcal/mol, respectively.

In Buphedrone, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen atoms to bond pairs. A strong hyperconjugative interaction was observed due to π* (C₈- O₁₃)--- π* (C₁-C₆), π (C₁-C₆)--- π* (C₄-C₅), π (C₁-C₆)--- π* (C₈- O₁₃), LP (2) O₁₃--- σ* (C₆-C₈) and LP (2) O₁₃--- σ* (C₈-C₉), and the values were 65.53 kcal/mol, 20.09 kcal/mol, 21.33 kcal/mol, 16.55 kcal/mol and 17.01 kcal/mol, respectively.

In Butylone, similarly to 4-MMC, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction appeared due to π (C₃-C₄)--- π* (C₅-C₆), π (C₅-C₆)--- π* (C₁-C₂), π (C₅-C₆)--- π* (C₇-O₈), LP (2) O₁₀--- π* (C₃-C₄) and LP (2) O₁₂--- π* (C₁-C₂), and values were found to be 21.41 kcal/mol, 21.38 kcal/mol, 22.06 kcal/mol, 26.68 kcal/mol and 24.92 kcal/mol, respectively.

In Ethylone, similarly to butylone and 4-MMC, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction appeared due to π^* (C1-C2)--- π^* (C5-C6), π^* (C3-C4)--- π^* (C5-C6), π (C3-C4)--- π^* (C5-C6), LP (2)(O12)--- π^* (C1-C2) and LP (2)(O10)--- s^* (C3-C4), and values were 228.68 kcal/mol, 229.07 kcal/mol, 20.93 kcal/mol, 25.00 kcal/mol and 26.65 kcal/mol, respectively.

In MDPV (similarly to ethylone, butylone and 4-MMC), the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction was noticed due to π (C₁-C₂)--- π* (C₃-C₄), π (C₃- C₄)--- π* (C₅-C₆), π (C₅-C₆)--- π* (C₁-C₂), LP (2) O₁₂--- π* (C₃-C₄) and LP (2) O₁₄--- π* (C₁-C₂). Values were found to be 21.12 kcal/mol, 21.02 kcal/mol, 21.44 kcal/mol, 26.57 kcal/mol and 24.74 kcal/mol, respectively.

In Methcathinone, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction was due to π (C₁-C₂)--- π* (C₃-C₄), π (C₃-C₄)--- π* (C₅-C₆), π (C₅-C₆)--- π* (C₁-C₂), LP (2) O₈--- π* (C₆-C₇) and LP (1) N₁₁--- σ* (C₉-C₁₀). The energies were found to be 22.07 kcal/mol, 22.30 kcal/mol, 20.55 kcal/mol, 16.38 kcal/mol and 8.48 kcal/mol, respectively.

In Methylone, the electron transfer was predominantly observed from the bond pair to bond pairs and lone pair of oxygen and nitrogen atoms to bond pairs. A strong hyperconjugative interaction was observed due to π (C₁- C₂)--- π* (C₃-C₄), π (C₃-C₄)--- π* (C₅-C₆), π (C₅-C₆)--- π* (C₁-C₂), LP (2) O₈--- σ* (C₆-C₇) and LP (2) O₁₃--- π* (C₃-C₄). The values were found to be 20.88 kcal/mol, 20.93 kcal/mol, 21.33 kcal/mol, 16.76 kcal/mol and 26.64 kcal/mol, respectively.

3.6 Thermodynamic Parameters

The thermodynamic parameters, namely, heat capacity, entropy, rotational constants, dipole moments, vibrational zero-point energies, of the molecules under investigation have also been computed at DFT-B3LYP level using 6-31G basis set and are presented in Table 5. The thermodynamic data provides useful information for further studies of the investigated compounds [36]. These standard thermodynamic functions can be used as reference thermodynamic values to calculate changes of entropies (ΔS_T), changes of enthalpies (ΔH_T) and changes of Gibbs free energies (ΔG_T) of the reaction. The dipole moment and its principal inertial axes are strongly dependent upon the conformation of the molecule.