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

Abstract Initially made for medical treatment for Parkinsonism, obesity, and depression, cathinones have become illegal drugs for the “recreational use”. The mechanism of action of synthetic cathinones consists of the inhibition of monoamine transporters. DFT (Density Functional Theory) calculations on the selected cathinones (3-FMC, 4-FMC, 4-MMC, Buphedrone, Butylone, Ethylone, MDPV, Methcathinone, and Methylone) were performed using B3LYP level of the Gaussian 09 program suite. The unscaled B3LYP/6–31G vibrational wavenumbers are in general larger than the experimental values, so the use of selective scaling was necessary. The calculated spectra of selected cathinones are in good correlation with the experimental spectra which demonstrates that DFT is a good tool for the prediction of spectra of newly synthesized and insufficiently experimentally characterised cathinones. Also, HOMO-LUMO (Highest Occupied Molecular Orbital-Lowest Unoccupied Molecular Orbital) analysis shows that 3-FMC possesses the minimum energy gap of 3.386 eV, and the molecule 4-FMC possesses the maximum energy gap of 4.205 eV among the investigated cathinones. It indicates that 3-FMC would be highly reactive among all the cathinones under investigation.


Introduction
The illegal drugs problem has reached an epidemic level with the increased number of registered users and deaths caused by overdoses, with the causes of this phenomenon being numerous.
Considering the potency of cathinones to inhibit dopamine, noradrenaline, and serotonin re-uptake and the ability to liberate these compounds, Simmler et al. [5] classified synthetic cathinones into three groups on the basis of in vitro experiments: 1. Cathinones which act like MDMA and cocaine are "cocaine-MDMA-mixed cathinones". The mechanism of action of this subgroup of cathinones involves non-selective inhibition of monoamine re-uptake. Representatives of this group are mephedrone, methylone, ethylone, and butylone (similar action to cocaine), and naphyrone (similar action to MDMA) [5,[7][8][9][10][11]]. 2. Cathinones which act like methamphetamine ("methamphetamine-like cathinones"). Their mechanism of action involves the preferential re-uptake inhibition of catecholamines and liberation of dopamine. Methcathinone, flephedrone, and clephedrone (4-chloromethcathinone) belong to this group [5,7]. 3. Synthetic cathinones with structures based on pyrovalerone (pyrovalerone-cathinones). The representatives of this group are MDPV and MDPBP, very potent and selective inhibitors of the catecholamine re-uptake demonstrating no neurotransmitter liberating effect [5,7]. The aim of this study was to perform numerous calculations in order to predict spectra and properties of selected cathinones.

Materials and Methods
The selected molecules were treated quantum mechanically by applying DFT method using the Gaussian 09 program suite [12] at the Becke-3-Lee-Yang-Par (B3LYP) level [13,14] combined with the standard 6-31G basis set. During the optimization procedure all the parameters were set in order to obtain a stable structure with minimum energy. The global minimum energy of the title compound was determined from the structure optimization procedure. The Natural bonding orbital (NBO) analysis was performed using the NBO 5.1 program [15] as implemented in the Gaussian 09 package at DFT/ B3LYP level. The hyperconjugation and the interaction energy within the molecule were obtained from the second-order perturbation approach [16][17][18].
Ethical approval: The conducted research is not related to either human or animal use.

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

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.

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.

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.

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.

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.

Conclusions
The use of DFT calculations has been shown to be a useful method for predicting vibrational and infra-red spectra of selected cathinones, particularly using the appropriate scaling. Therefore, this method can be used to predict the spectra of newly synthesized and not fully characterised cathinones which would be useful in forensics.