Quantum chemical studies on the molecular structure, spectroscopic and electronic properties of (6-Methoxy-2-oxo-2H-chromen-4-yl)-methyl pyrrolidine-1-carbodithioate

The atomic numbering scheme for the title crystal [18] and the theoretical geometric structure of the title compound are shown in Fig. 1. The crystal structure of the title compound is triclinic and space group is P-1. The crystal structure parameters are a = 6.7223 (2)Å, b = 8.0369 (2)Å, c = 15.4101 (5)Å, α = 75.320 (2)°, β = 88.482 (1)°, γ = 78.842 (1)° and V = 789.93 (4)ų [18].

The optimized bond lengths, bond angles and torsion angles of the title compound have been obtained using the HF and DFT/B3LYP methods with the 6-311++G(d,p) basis set. Theoretical and experimental geometric parameters are listed in Table 1. When the X-ray structure of the title compound is compared with its optimized counterparts (Fig. 2), slight conformational discrepancies are observed between them. The title crystal is not planar. The dihedral angle between the 2H-chromene (O4/C8–C16) ring and pyrrolidine (N6/C18–C22) ring is 75.24 (16)° for X-ray [18], whereas the dihedral angle has been calculated as 67.65° for B3LYP and 70.00° for HF. The orientation of the both the rings is defined by the torsion angles C22–N6–C18–S1 (178.00°), N6–C18–S1–C17 (–170.98°), C18–S1–C17–C14 (103.72°) and S1–C17–C14–C15 (–99.35°) which have been calculated as 178.48°, –176.56°, 105.99° and –104.04° for B3LYP, and 178.56°, –174.45°, 98.78° and –107.40° for HF, respectively. In the title compound, the bond lengths and angles are within normal ranges and they are comparable with those of related compounds [24–26].

It is well known that DFT-optimized bond lengths are usually longer and more accurate than HF due to the inclusion of electron correlation [27]. On the other hand, according to calculated results, the HF method correlates better for the bond distance compared with the DFT/B3LYP method (Table 1). The maximum difference of bond lengths between the experimental and the predicted values has been found at C20–C21 bond with the difference being 0.061 Å for B3LYP method, and with a value 0.053 Å for HF method. The root mean square error (RMSE) is obtained as 0.018 Å for HF and 0.021 Å for B3LYP, indicating that the bond lengths predicted by the HF method show a good correlation with the experimental values. For bond angles, the opposite trend was observed. As can be seen from Table 1, both the biggest difference and the RMSE for the bond angles calculated by the B3LYP method are smaller than those predicted by HF. A global comparing of the structures obtained by the theoretical calculations has been done by superimposing the molecular skeleton with that obtained from X-ray diffraction [28], giving a RMSE of 0.247 Å for B3LYP and 0.324 Å for HF method (Fig. 2). As a result, the B3LYP calculation well reproduces the the 3-D geometry of the title compound.

In order to define the preferential position of pyrrolidine and chrome rings, a preliminary search of low energy structures was performed using B3LYP/6-311++G(d,p) computations as a function of the selected degrees of torsional freedom T(S1–C18–N6–C19) and T(S1–C17–C14–C15). The respective values of the selected degrees of torsional freedom, T(S1–C18–N6–C19) and T(S1–C17–C14–C15), are –0.81° and –99.34° in X-ray structure [18], whereas the corresponding values in DFT optimized geometry are –1.35° and –104.04°. Molecular energy profiles with respect to rotations about the selected torsion angles are presented in Fig. 3.

As can be seen from the Fig. 3, the low energy domains for T(S1–C18–N6–C19) are located at 0° and 180°, while they are located at –100° and 120° for T(S1–C17–C14–C15). Energy difference between the most favorable and unfavorable conformers, which arises from rotational potential barrier calculated with respect to the two selected torsion angles, is 0.036 Hartree for T(S1–C18–N6–C19) and 0.14 Hartree for T(S1–C17–C14–C15), when both selected degrees of torsional freedom are considered. It must be remarked that the selected torsion angles in the crystal structure of the title compound are close to the value in the global energy minimum.

In this study, harmonic vibrational frequencies were calculated using the DFT/B3LYP and HF methods with the 6-311++G(d,p) basis set. Using the Gauss-View molecular visualisation program, the vibrational band assignments were made. In order to facilitate assignment of the observed peaks, the vibrational frequencies have been analyzed and the calculation for the title compound have been compared with the experimental results. The vibrational frequencies in the region 4000 cm⁻¹ to 600 cm⁻¹ are given in Table 2. The IR spectra contain some characteristic bands of the stretching vibrations of the C–H, C–H₂, C–H₃, C=O, C–O, C–N, C=S and C–S groups.

GIAO ¹H and ¹³C chemical shift values were calculated using B3LYP and HF methods with the 6-311++G(d,p) basis set in gas phase and the calculated results are given in Table 3. To investigate the solvent effect on the chemical shift values of the compound, based on B3LYP and HF method and IEF-PCM model, two solvents (ε = 46.7, DMSO; ε = 24.55, ethanol) were selected and the calculated values were also listed in Table 3. Relative chemical shifts were estimated by using the TMS shielding calculated in advance at the same theoretical level as the reference. Calculated ¹H isotropic chemical shielding for TMS at the HF(gas), B3LYP(gas), HF(ethanol), B3LYP(ethanol), HF(DMSO) and B3LYP(DMSO) are 32.44 ppm, 31.97 ppm, 32.43 ppm, 31.96 ppm, 32.43 ppm and 31.96 ppm, respectively. Also, calculated ¹³C isotropic chemical shielding for TMS at the HF (gas), B3LYP (gas), HF (ethanol), B3LYP (ethanol), HF (DMSO) and B3LYP (DMSO) are 196.11 ppm, 184.06 ppm, 196.58 ppm, 184.54 ppm, 196.59 ppm and 184.66 ppm, respectively.

We have calculated ¹H chemical shift values (with respect to TMS) of 1.89 ppm to 7.37 ppm at the B3LYP (gas) and 1.73 ppm to 7.81 ppm at HF (gas) level. Besides, they were calculated to be 2.00 ppm to 7.48 ppm at the B3LYP (ethanol),1.71 ppm to 7.80 ppm at the HF (ethanol), 2.00 ppm to 7.49 ppm at the B3LYP (DMSO) and 1.71 ppm to 7.80 ppm at the HF (DMSO). In (S)-2-Oxopyrrolidin-1-yl Butanamide [61], CH₂ protons of the pyrrolidine ring are observed in the region of 2.47 ppm to 4.50 ppm. In our study, CH₂ protons of the pyrrolidine ring are found in the region of 1.89 ppm to 4.30 ppm at all the B3LYP levels and 1.73 ppm to 3.88 ppm at all the HF levels. In the 3-(1-((methoxycarbonyl)oxy)imino)ethyl)-2H-chromen-2-one, the chemical schift values of chromene ring protons were observed at 7.28 ppm to 8.08 ppm experimentally, and at 7.05 ppm to 7.91 ppm for the HF/6-311++G(d,p) level and 7.26 ppm to 8.41 ppm for the B3LYP/6-311++G(d,p) level [62]. In the present work, the chromene ring protons have been calculated at 6.80 ppm to 7.87 ppm for B3LYP and at 6.73 ppm to 7.81 ppm for HF levels in gas and solution phase.

The ¹³ C NMR chemical shift values (with respect to TMS) have been calculated to be 28.69 ppm to 205.44 ppm for B3LYP (gas), 24.57 ppm to 226.88 ppm for HF (gas), 29.23 ppm to 206.75 ppm for B3LYP (ethanol), 25.04 ppm to 227.35 ppm for HF (ethanol), 29.35 ppm to 206.97 ppm for B3LYP (DMSO) and 25.05 ppm to 227.36 ppm for HF (DMSO). The chromene ring carbons give peaks at 100 ppm to 200 ppm for all methods. These peaks have been observed at 113 ppm to 177 ppm in 7-Acetoxy-4-(bromomethyl)coumarin [63]. As seen from Table 3, ¹H and ¹³C NMR spectra were a little affected by the change in polarity of the solvent. ¹H and ¹³C chemical shift results of the title compound in gas phase are generally closer to the solvent phase. The calculated ¹H and ¹³C chemical shift values of the title compound are in a good agreement with those of related chromene and pyrrolidine derivatives [64, 65].

NBO analysis provides an efficient method for studying intra and intermolecular hydrogen bonding and interaction among bonds, and provides a convenient basis for investigating charge transfer or conjugative interaction in molecular systems. The energy of hyperconjugative interactions or the stabilization energy gives the interaction between donor groups and acceptor ones [66, 67]. More intensive interactions between electron donors and electron acceptors depend on larger E⁽²⁾ value, i.e., the more donating tendency from electron donors to electron acceptors the greater the extent of conjugation of the whole system [68]. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E⁽²⁾ is estimated by the following equation [69,70]: E(2) = − qi(Fij)2ε<!-- e -->j - ε<!-- e -->i $${E^{{\text{(2)}}}}{\text{ = - }}{q_i}\frac{{{{{\text{(}}Fij{\text{)}}}^{\text{2}}}}}{{{\text{ }}{\varepsilon _j}{\text{ - }}{\varepsilon _i}}}{\text{ }} $$ (1)

where q_i is the donor orbital occupancy, ε_i, ε_j are diagonal elements (orbital energies) and F_ij is the off-diagonal NBO Fock matrix element. In order to investigate the intramolecular interaction, the stabilization energies of the title compound were performed using the second-order perturbation theory. The results of second-order perturbation theory analysis of the Fock Matrix at B3LYP/6-311++G(d,p) level of theory are collected in Table 4. For the table, the stabilization energies larger than 13 kJ/mol have been chosen.

The NBO analysis has revealed that the intramolecular interactions which are formed by the orbital overlap between bonding (C–S), (C–O), (C–N), (C–C) and (C–H) anti-bonding orbital, result in intramolecular charge transfer causing stabilization of the compound. These interactions are observed as an increase in electron density (ED) in (C–S), (C–C) and (C–O) anti-bonding orbitals that weakens the respective bonds. The electron density of the five conjugated single bonds of pyrrolidine ring (~1.98 e) clearly demonstrates strong delocalization. Additionally, the ED of conjugated bond of 2H-chromene ring (~ 1.91 e) clearly shows strong delocalization inside the compound [59].

In the studied compound, strong intramolecular hyperconjugative interactions of π-electrons with the greater energy contributions from C8–C9 → C10–C11 (73.94 kJ/mol),C12–C13 (69.93 kJ/mol); C10–C11 → C8–C9 (74.48 kJ/mol), C12–C13 (71.68 kJ/mol); C14–C15 (42.21 kJ/mol); C12–C13 → C8–C9 (80.67 kJ/mol), C10–C11 (75.53 kJ/mol); C14–C15 → O5–C16 (91.54 kJ/mol), C10–C11 (43.76 kJ/mol) are observed for the chromene part of the compound. The hyperconjugative interactions of the σ → σ^* and σ → π^* transitions occur also from various bonds in the compound, such as the hyperconjugative interaction of the σ(C22–H22B) distribute to σ^* (C22–H22B); (C15–H15); (C10–C14)(C14–C17) and (C22–H22A) leading to stabilization of 33.27 kJ/mol, 46.94 kJ/mol, 61.61 kJ/mol, 118.16 kJ/mol and 269.02 kJ/mol, respectively. This enhanced bond further conjugate with antibonding orbital of π^* (C14–C15), which results in strong delocalization of 52.54 kJ/mol.

There is a very weak intramolecular C–H... S hydrogen bond exposed in the NBO analysis results shown in Table 4 caused by the interactions between the sulfur lone-pair LP(2) S2 and the antibonding orbital σ^*(C17–H17B). The lone pair of N6 donates its electrons to the σ-type antibonding orbital for (S2–C18). This interaction gives the strongest stabilization to the system of the title compound by 357.01 kJ/mol. In addition, the π^* (C8–C9) NBO conjugates with respective bonds of π^* (C10–C11) and π^* (C12–C13) resulting in an enormous stabilization of 532.95 kJ/mol and 830.56 kJ/mol, respectively.

In order to investigate the electron population of each atom of the title compound, the natural population analysis (NPA) atomic charges of the compound were calculated using the DFT/B3LYP method with the 6-311++G(d,p) basis set. The obtained results are given in Table 5. NPA charge plot has been shown in Fig. 4. The NPA analysis shows that the carbon atoms attached to hydrogen atoms are negative, whereas the carbon atoms (C8, C11, C16) adjacent to the oxygen atoms of the chromene ring are positively charged. The oxygen atoms of chromene fragment and N6 atom of pyrrolidine ring have more negative atomic charges whereas all the hydrogen atoms have positive charges. The maximum positive atomic charge is obtained for C16 atom of carbonyl group when compared with all other atoms. This is due to the attachment of maximum negatively charged O5 atom.

The electronic absorption spectra of the title compound were computed using the TD-DFT method in the gas phase and the DMSO solvent (Fig. 5). The solvent effect was calculated using IEF-PCM method. For TD-DFT calculations, a theoretical absorption band was calculated at 242.43 nm (3.62 eV) with oscillator strength being 0.104. The other absorption peak was calculated at 231.21 nm (5.36 eV) with oscillator strength being 0.114. In addition to the calculations in gas phase, TD-DFT calculations of the title compound in DMSO solvent were performed at 352.01 nm (3.52 eV) with oscillator strength being 0.127 and at 233.41 nm (5.31 eV) with oscillator strength being 0.208. According to the investigations on the frontier molecular orbital (FMO) energy levels of the title compound, we can find that the corresponding electronic transfers happened between the HOMO–1 and LUMO, HOMO–3 and LUMO+1 orbitals, respectively.

The FMO plays an important role in the electric and optical properties, as well as in UV-Vis spectra and chemical reactions [71, 72]. Fig. 6 shows the distributions and energy levels of calculated at the B3LYP/6-311++G(d,p) level for the title molecule. As can be seen from Fig. 6, both for the HOMO and HOMO–1, the electrons are delocalized on the sulfur atoms of the pyrrolidine-1-carbodithioate. For the LUMO and LUMO+1, the electrons are mainly delocalized on the 2-oxo-2H-chromen ring, C14–C17 bond and S1 atom. The value of the energy separation between the HOMO and LUMO is 1.42 eV. Considering the chemical hardness, small HOMO–LUMO gap (ΔE_H−L) means a soft molecule and large ΔE_H−L means a hard molecule. One can also relate the stability of the molecule to hardness, which means that the molecule with the least ΔE_H−L is more reactive and less stable [73]. The η and S can be calculated using the HOMO and LUMO energy values for a molecule as follows: η = (E_LUMO−E_HO_MO)/2 and S = 1/2η [60], where E_LUMO and E_HOMO are LUMO and HOMO energies, respectively. The calculated values of η and S for the title compound are 0.71 eV and 0.70 eV⁻¹, respectively.

Molecular electrostatic potential (MEP) mapping is very useful for understanding the sites for electrophilic attack and nucleophilic reactions as well as hydrogen bonding interactions [74]. Red-electron rich or partially negative charge regions of MEP are related to electrophilic reactivity and the blue-electron deficient or partially positive charge regions of MEP are related to nucleophilic reactivity shown in Fig. 7. The MEP clearly indicates that the electron rich centres were found around the O3, O5 and S2 atoms. The negative V(r) values are −0.023 a.u. for O3 atom, −0.103 a.u. for O5 and −0.035 a.u. for S2 atom. Thus, it could be predicted that an electrophile would preferentially attack the title molecule at O5 atom. On the other hand, a maximum positive region is localized on the methyl nearby with a value of +0.069 a.u. indicating a possible site for nucleophilic attack. So, the MEP surfaces clearly indicate that positive potential sites are around methylene and methyl hydrogen atoms. These sites give information that the compound can have metallic bonding and intermolecular interactions [73].

Nonlinear optics (NLO) is at the forefront of current research because of its importance in providing the key functions of frequency shifting, optical switching, optical modulation, optical logic, and optical memory for emerging technologies in areas such as telecommunications, signal processing, and optical interconnections [75, 76].

The dipole moment (μ), polarizability (α) and first hyperpolarizbility (β) values of the title molecule were computed at the B3LYP/6-311++G(d,p) level using the Gaussian 09W program package. Calculations of the polar properties (α and β) from the Gaussian output have been explained in detail previously [77], and DFT has been used extensively as an effective method to investigate organic NLO materials [78, 79].

The calculated values of μ, α and β are 9.007 Debye, 38.299 ų and 4.868 esu for the title compound. Urea is used as one of the prototypical molecules in the study of NLO properties of molecular systems. Therefore, it has been used frequently as a threshold value for comparative purposes [78]. The values of α and β of the title compound are greater than those of urea (the α and β of urea are 5.042 ų and 0.78 × 10⁻³⁰ esu obtained using the B3LYP/6-311++G(d,p) method) [22]. Theoretically, the β value of the title compound is of 6.24 times magnitude of urea. When we compare it with the similar compounds in the literature, the calculated value of β of the title compound is smaller than those of 9-methoxy-2H-furo3,2-gchromen-2-one (β = 5.2983 × 10⁻³⁰ esu calculated with B3LYP/6-311++G(d,p) method) [80] and 6-phenylazo-3-(p-tolyl)-2H-chromen-2-one (β = 34.528 × 10⁻³⁰ esu calculated with B3LYP/6-311++G(d,p) method) [81]. According to the magnitude of β , the title coumarin compound may be a potential applicant in the development of NLO materials.

The standard thermodynamic functions: entropy (Sm0 ${\text{S}}_{\text{m}}^{\text{0}}$ ), heat capacity (Cp,m0 ${\text{C}}_{{\text{p,m}}}^{\text{0}}$ ) and enthalpy (Hm0 ${\text{H}}_{\text{m}}^{\text{0}}$ ) were obtained on the basis of B3LYP/6-311++G(d,p) vibrational analysis and statistical thermodynamics and listed in Table 6. The Table shows that the Sm0 ${\text{S}}_{\text{m}}^{\text{0}}$ , Cp,m0 ${\text{C}}_{{\text{p,m}}}^{\text{0}}$ and Hm0 ${\text{H}}_{\text{m}}^{\text{0}}$ increase at any temperature from 200.00 K to 600.00 K, because the intensities of the molecular vibration increase with the increasing temperature.

The correlations equations between these thermodynamic properties and temperatures T are as follows: Cp,m0 = −<!-- - -->11.97047 + 1.36407T − 6.32498×<!-- ? -->10 − 4T2(R2 = 0.99978) $$\begin{array}{} {C}_{{p,m}}^{\text{0}}\;{\text{ = }}\; - {\text{11}}{\text{.97047 + 1}}{\text{.36407}}T{\text{ - 6}}{\text{.32498}}\; \times {\text{1}}{{\text{0}}^{{\text{ - 4}}}}{{T}^{\text{2}}} \\ \qquad\quad{\text{(}}{{R}^{\text{2}}}{\text{ = 0}}{\text{.99978)}} \ \end{array} $$ (2)

Sm0=290.75334 + 1.33432T−<!-- - -->2.92022×<!-- ? -->10 − 5T2(R2 = 1) $$\begin{array}{} S_m^{\text{0}} = \;{\text{290}}{\text{.75334 + 1}}{\text{.33432}}T - {\text{2}}{\text{.92022}}\; \times \;{\text{1}}{{\text{0}}^{{\text{ - 5}}}}{T^{\text{2}}}\\ \quad\quad{\text{(}}{R^{\text{2}}}{\text{ = 1)}} \end{array} $$ (3)Hm0= − 6.01208 + 0.08769T+4.33528×<!-- ? -->10 − 4T2(R2 = 0.99995) $$\begin{array}{} H_m^{\text{0}} = \;{\text{ - 6}}{\text{.01208 + 0}}{\text{.08769}}T + {\text{4}}{\text{.33528}} \times \;{\text{1}}{{\text{0}}^{{\text{ - 4}}}}{T^{\text{2}}} \\ \qquad{\text{(}}{R^{\text{2}}}{\text{ = 0}}{\text{.99995)}} \end{array} $$ (4)

These equations will be helpful for the further studies of the title compound [82, 83].