Quantum Chemical Investigation of (E)-2-(2-hydroxy-5- methoxybenzylidene)hydrazinecarbothioamide and its N-methyl Variant by Using DFT Methods

doi:10.21203/rs.3.rs-3881706/v1

Geometry optimization for 2-(2-hydroxy-5-methoxybenzylidene)hydrazinecarbothioamide (HMHC) and 2-(2-hydroxy-5methoxybenzylidene)-N-methylhydrazinecarbothioamide (HMNHC) was attempted using DFT/B3LYP/6-311 + + G(d,p) formalism. The computations identified the existence of both intra-molecular and bifurcated intra-molecular hydrogen bonds in both the molecules. Time-dependent density functional theory (TD-DFT) was employed to simulate Ultra-Violet spectra for both HMHC and HMNHC in order to substantiate experimental spectra in a solution of dimethyl formamide. For the two compounds under investigation, specific global reactivity descriptors were estimated with the help of frontier molecular orbital (FMO) analysis to understand the origin of UV-Vis spectra. Nonlinear optical (NLO) profile, for each of the two molecules, was computed, with in the frame work of the DFT/B3LYP/6-311 + + G(d,p) formalism to determine their utility for NLO applications. NBO analysis of hyper conjugate interactions made it possible to interpret the molecules NLO behavior in terms of intramolecular charge transfer (ICT). The reactive sites around the molecules were identified using Fukui function investigations and Molecular Electrostatic Potential (MEP).

Thiosemicarbazones

DFT

UV-Visible spectra

FMO

NBO

NLO

Bifurcated hydrogen bond and intra-molecular hydrogen bond exist in both HMHC and HMNHC molecules
The two compounds undergo UV-Visible transitions, of the type n→π* and π→ π*
The molecules are highly stable and reactive.
HMHC and HMNHC have potential applications as NLO materials.
The area around oxygen atoms of the hydroxyl moiety and methoxy groups is the best location for an electrophilic assault.

Heterocyclic thiosemicarbazones are a class of thiourea derivatives that have been the subject of extensive research because of their wide range of biological activities, widespread industrial use, and analytical sensitivity to different metal ions. Since 1956, when Brockman et al [1]. discovered the antitumoral property of 2-formylpyridine thiosemicarbazone derivatives, they have been used in biological applications. This inspired intense research investigations involving, numerous thiosemicarbazone derivatives for development of antibacterial, antiviral, antifungal, antioxidant, anti-inflammatory, and antiproliferative medicines [2–5]. Additionally, the effectiveness of this class of drugs against trypanosomiasis, coccidiosis, psoriasis, leprosy, psoriatic arthritis, and tuberculosis has been investigated [6, 7]. Herpes simplex virus (HSV) infection was selectively inhibited by several thiosemicarbazones both in vitro and in vivo. Impact of thiosemicarbazones on the human immunodeficiency viruses (HIV) has been documented [8]. It was found out that the biological activity of the thiosemicarbazones made from 2-formylpyridine and 2-acetylpyridine was increased by the presence of a bulky substitution at the N-terminal nitrogen atom [9–11]. Further, anticancer properties of thiosemicarbazones were attributed to their ability to inhibit ribonucleotide reductase, the enzyme that catalyzes the rate-limiting stage of DNA synthesis [12, 13]. The 3-aminopyridine-2-carboxaldehyde thiosemicarbazone (triapine) [14] and Di-2-pyridylketone 4-cyclohexyl-4-methyl-3-thiosemicarbazone [15], were subjects of extensive research to demonstrate their utility as medicine. The possible biological activity of the thiosemicarbazones is expected to be caused by the donor atoms of nitrogen and sulfur present in the compound [16]. Synthesis, and crystal structure, along with antioxidant, non-haemolysis and anti-inflammatory properties of 2-(2-hydroxy-5-methoxybenzylidene)hydrazinecarbothioamide (HMHC) and 2-(2-hydroxy-5-methoxybenzylidene)-N-methylhydrazinecarbothioamide (HMNHC) are available [17]. Hence we undertook this theoretical work with regard to their equilibrium geometry, UV-Visible spectra, frontier molecular orbital (FMO) characteristics, non-linear optical (NLO) behaviour, electrostatic potential surface (MESP) and natural bond orbital (NBO) properties. The purpose was: to demonstrate how far the theoretical parameters evaluated for HMHC and HMNHC agree with their corresponding available experimental counterparts [17–19].

All results presented in this article were accomplished by using Gaussian 09W/DFT program suit [21]. Important components that were used together for calculations consisted of (a) Becke’s three-parameter hybrid exchange functional B3;[22] (b) Lee-Young-Parr gradient corrected correlation functional[23] and (c) the split valence basis set, 6-311 + + G(d, p) expanded by including d-polarization functions on heavy atoms (carbon, oxygen, sulfur) and p-polarization functions on hydrogen atoms to achieve better description for polar bonds [24–26]. This is indicated as DFT/B3LYP/6-311 + + G(d,p) formalism. In order to start geometry optimization, one needs the initial structure of the molecule of interest. Fortunately, X-ray structure is available¹⁷ for HMHC and HMNHC. They were taken as the initial structure for geometry optimization. This was subjected to a rigorous geometry optimization by making simultaneous relaxation of all structural parameters. This procedure gave a non-planar structure of C₁ symmetry for both HMHC and HMNHC. The authenticity of optimized structure was ascertained by the absence of imaginary frequencies. By using time-dependent density functional theory (TD-DFT), electronic absorption spectra of HMHC and HMNHC were simulated, in a solution of dimethyl formamide (DMF) which was used as a solvent to record UV-Vis spectra of both the compounds, by earlier workers [17]. Effect of the solvent was addressed by means of polarizable continuum model, employing an updated version of integrated equation formalism (IEF-PCM) [27]. This is a part of Gaussian 09 program suit.

Frontier molecular orbital (FMO) parameters, comprising of orbital energy gap (ΔE = E_HOMO-E_LUMO), ionization potential (I=-E_HOMO), electron affinity (A=-E_LUMO), global chemical softness (S = 1/(2η)), electronegativity (χ=(1 + A)/2), chemical potential(µ=-(I + A)/2), global electrophilicity index (ω = µ2/2η), and maximum charge transfer index (ΔNmax=-µ/η) [28–31], were calculated for both HMHC and HMNHC. Here HOMO and LUMO are the frontier molecular orbitals, known as highest occupied molecular orbital and the lowest unoccupied molecular orbital, respectively. Further, E_HOMO and E_LUMO are the energies of HOMO and LUMO orbitals, respectively. Non-linear optical behavior of a substance is defined by µ_t and its components, α_t and its components, ∆α and β_t, where µ_t, α_t, ∆α and β_t are its total dipole moment, total molecular polarizability, anisotropy of polarizability, and total first-order hyperpolarizability, respectively. All these parameters were computed for both molecules HMHC and HMNHC, using required equations, and employing DFT theory in combination with Buckingham’s formalism based on finite field approach [29].

The main structural aspect of HMHC and HMNHC is the π-electron delocalization between the mequinol ring and side chain in which lone pairs of two oxygen atoms, three nitrogen atoms, and one sulfur atom are also involved. This characteristic needs to be quantified, which requires understanding of second order interactions between occupied orbitals of one subsystem and empty orbitals of another subsystem. Therefore, an estimate of donor-acceptor interactions was made, based on second order perturbation analysis of Fock matrices in NBO basis for both HMHC and HMNHC, employing NBO 3.1 computer program suit [32], which is available with the Gaussian 09/DFT software suit. The exact equation for molecular electrostatic potential V(r) at a point positioned at r, due to the nucleus A with charge Z_A situated near R_A and electron charge density function ρ(rˈ) located at rˈ is given by [28, 33].

\(V(\mathbf{r})=\sum\limits_{A} {\frac{{{Z_A}}}{{|{\mathbf{R}_A} - \mathbf{r}|}}} - \int {\frac{{\rho (\mathbf{r}^{\prime})dr^{\prime}}}{{|\mathbf{r}^{\prime} - \mathbf{r}|}}}\)

where, Z_A, r, R_A and rˈ are taken with respect to an arbitrary origin.

In the above mentioned expression, the negative interaction energy is caused by the interaction of electrons with a positive test charge at ‘r’ as indicated by the second term on the right side of the expression, whereas the positive interaction energy arises due to interaction of the nuclei of the molecule with the same positive test charge used above at ‘r’ as indicated by the first term on the right hand side of the expression. Molecular electrostatic potential surfaces and associated electron density for HMHC and HMNHC were calculated by mapping MESP onto iso-electron density surfaces, at the level of DFT/B3LYP/6-311 + + G (d, p) formalism.

3.1 Optimized molecular geometry and bifurcated intra-molecular hydrogen bond

Equilibrium molecular geometry of the two molecules under investigation is decided by two forces, that oppose each other:

(i) Conjugation between the π-electron cloud of the mequinol ring and lone pairs on the three nitrogen atoms (N14, N15, and N19) along with lone pair electrons on the two oxygen atoms (O10 and O22) and lone pair electron on the sulfur atom tend to give coplanar structure to the molecule, which is further strengthened by the bifurcated intra-molecular hydrogen bond between N14 and (H11, H20) atoms, and intra-molecular hydrogen bonds between O22 and H8; and O10 and H9;

(ii) The steric repulsion effects in each of the molecules, that tend to stabilize the molecule in non-planar conformation, so as to minimize the steric effect. Primary source of this effect is the steric forces between pairs of hydrogen atoms (H7, H13) (H11, H20) and (H13, H16) along with that between (H16, S18). The most stable geometry of the molecules is dictated by the equilibrium between the above mentioned two opposing factors. The relative strength of the effects gets reflected in the dihedral angles associated with flexible bonds (C1-O10, C4-O22, O22-C23, C2-C12, N14-N15, N15-C17 and C17-N19). This delicate balance is significantly affected by two theoretical factors:

(i) Amount of correlation energy incorporated into computations, by theoretical method, and

(ii) The size of the basis set utilized for the computations.

Iterative method was implemented to solve self-consistent field equations, so as to obtain optimized molecular structure for both HMHC and HMNHC. The resulting structures are depicted in Fig.1. Optimized geometry structure data comprising of bond lengths, bond angles and torsional angles are collected in Table 1. Bifurcated intra-molecular hydrogen bond parameters are presented in Table 2.

Table 1. Experimental and DFT/B3LYP/6-311 ++ G(d,p) optimized geometry parameters of HMHC and HMNHC.

Atoms with numbering				HMHC Molecule			HMNHC Molecule
Atoms with numbering				Bond Length (in Å)	Bond Angle ( in °)	Dihedral Angle ( in ° )	Bond Length (in Å)	Bond Angle ( in °)	Dihedral Angle ( in °)
C1	-				-	-	-	-	-
C2	C1			1.410 (1.388)	-	-	1.409 (1.391)	-	-
C3	C2	C1		1.414 (1.401)	119.19 (119.42)	-	1.414 (1.410)	119.11 (118.80)	-
C4	C3	C2	C1	1.386 (1.377)	120.82 (120.50)	-0.35 (-0.641)	1.386 (1.372)	120.85 (120.76)	-0.33 (-0.20)
C5	C4	C3	C2	1.404 (1.382)	119.22 (119.15)	0.21 (1.161)	1.404 (1.384)	119.25 (119.41)	0.19 (0.06)
C6	C5	C4	C3	1.382 (1.372)	120.66 (121.17)	0.06 (0.790)	1.382 (1.370)	120.61 (120.64)	0.05 (0.70)
H7	C3	C2	C1	1.082 0.930	118.19 (119.78)	179.77 (179.30)	1.082 (0.930)	118.20 (119.59)	179.77 (179.73)
H8	C5	C4	C3	1.083 (0.930)	118.49 (119.43)	179.95 (179.24)	1.083 (0.930)	118.52 (119.68)	179.97 (179.30)
H9	C6	C5	C4	1.083 (0.930)	120.89 (119.95)	179.78 (179.86)	1.083 (0.930)	120.89 (119.72)	179.82 (178.47)
O10	C1	C6	C5	1.354 (1.365)	118.05 (117.92)	179.84 (179.58)	1.355 (1.368)	118.06 (118.06)	179.84 (179.40)
H11	O10	C1	C6	0.975 (0.820)	107.81 (109.49)	-178.37 (-179.63)	0.975 (0.819)	107.72 (109.41)	178.53 (171.70)
C12	C2	C1	O10	1.449 (1.450)	122.53	0.05 (0.272)	1.450 (1.444)	122.64 (122.24)	-0.004 (-2.70)
H13	C12	C2	C1	1.094 (0.930)	116.71 (118.59)	-176.31 (-178.89)	1.094 (0.930)	116.65 (118.13)	176.54 (177.57)
N14	C12	C2	C1	1.292 (1.279)	123.34	3.46 (1.123)	1.292 (1.284)	123.511 (121.40)	-3.20 (-2.44)
N15	N14	C12	C2	1.361 (1.380)	117.50 (115.03)	-178.56 (-178.88)	1.359 (1.381)	117.58 (114.61)	178.50 (173.32)
H16	N15	N14	C12	1.015 (0.860)	120.73 (119.43)	-5.03 (-2.97)	1.015 (0.859)	120.73 (119.34)	-4.33 (-4.88)
C17	N15	N14	C12	1.370 (1.339)	123.49 (121.10)	-176.25 (-176.99)	1.377 (1.358)	123.75 (121.41)	176.32 (175.08)
S18	C17	N15	N14	1.674 (1.687)	119.78 (118.81)	-177.67 (-173.98)	1.677 (1.676)	118.97 (117.19)	177.73 (166.30)
N19	C17	N15	N14	1.348 (1.313)	115.99 (118.89)	1.89 (7.24)	1.344 (1.319)	115.84 (117.46)	-2.37 (-13.28)
H20	N19	C17	N15	1.007 (0.860)	121.54 (120.01)	8.21 (0.01)	1.008 (0.860)	117.61 (117.79)	-3.19 (-0.46)
H21	N19	C17	N15	1.005	117.58 (119.99)	176.22 (19.99)	-	-	-
C21	N19	C17	N15	-	-	-	1.455 (1.446)	123.62 (124.32)	179.83 (179.59)
O22	C4	C3	C2	1.367 (1.373)	125.06	-179.82 (-179.17)	1.367 (1.366)	125.04 124.35()	179.82 (179.08)
C23	O22	C4	C3	1.419 (1.419)	118.35	0.33 (0.120)	1.419 (1.414)	118.36 (118.21)	-0.14 (-0.46)
H24	C23	O22	C4	1.096 (0.960)	111.44	-61.60 (-61.78)	1.096 (0.960)	111.43	-61.11 (-59.58)
H25	C23	O22	C4	1.088 (0.960)	105.93	179.69 (178.25)	1.088 (0.960)	105.93	-179.83 (-179.6)
H26	C23	O22	C4	1.095 (0.960)	111.41	60.98 (1.60)	1.096 (0.960)	111.45	61.46 (60.40)
H27	C21	N19	C17	-	-	-	1.091 (0.960)	110.73 (109.45)	59.06 (53.188)
H28	C21	N19	C17	-	-	-	1.090 (0.960)	107.97 (109.48)	178.80 (173.89)
H29	C21	N19	C17	-	-	-	1.092 (0.960)	111.07 (109.46)	61.19 (66.17)

-: Not applicable

a: Value in braces corresponds to experiment (Ref. 17)

Table 2. Bifurcated intramolecular hydrogen bond geometry (bond lengths in Å, bond angles in degrees) for HMHC and HMNHC.

Molecule	D─H•••A	D─H^a	H•••A^a	D•••A^a	D─H•••A^a
HMHC	O10─H11•••N14	0.976 (0.820)	1.844 (1.963)	2.704 (2.680)	145.37 (145.45)
	N19─H20•••N14	1.007 (0.860)	2.373 (2.358)	2.714 (2.691)	98.65 (103.40)
HMNHC	O10─H11•••N14	0.976 (0.819)	1.848 (1.998)	2.710 (2.711)	145.63 (145.11)
	N19─H20•••N14	1.008 (0.860)	2.301 (2.330)	2.721 (2.699)	103.57 (106.19)

a: Value in braces corresponds to the experiment (Ref. 17)

Comparison of these values with corresponding X-ray values, for both HMHC and HMNHC showed good agreement (see Table 1). For example, for HMHC, as per the present computations, average bond length for mequinol intra-ring C-C bond is 1.399 Å; the average value of C-H bond length associated with the mequinol unit is 1.082 Å; and mequinol C-OH, C2-C12 and C-OCH3 bonds measure 1.354 Å, 1.450 Å, and 1.367 Å, respectively. The agreement with their corresponding X-ray values[17] at 1.384 Å, 0.93 Å, 1.36 Å, 1.450 Å, and 1.373 Å is good except for C-H bond length as expected (electron cloud around each hydrogen atom is not dense enough to scatter the X-rays effectively, as it arises from a single electron associated with an hydrogen atom). Further, existence of OH moiety and methoxy group in mequinol ring of both the molecules are likely to influence the values of bond angles ∠C5C6C1, ∠C6C1C2, and ∠C1C2C3, along with those for ∠C2C3C4, ∠C3C4C5 and ∠C4C5C6. Their corresponding calculated values at 120.71° (120.71°), 119.37° (119.46°), 119.20° (119.11°); and 120.82° (120.85°), 119.23° (119.25°), and 120.66° (120.61°) for HMHC (value in braces corresponds to HMNHC), exhibit good agreement with their corresponding X-ray values [17], near 120.05° (120.68°), 119.68° (119.69°), 119.42° (118.80°); and 120.50° (120.76°), 119.15° (119.41°), 121.17° (120.64°) for both the molecules. Our DFT computations recognised the existence of intra-molecular, hydrogen bond between O10•••H9, and O22•••H8, along with the presence of bifurcated intra-molecular hydrogen bond involving H11, H20 atoms with N14 atom (O10-H11•••N14 and N19-H20•••N14) in both the molecules HMHC and HMNHC. Corresponding parameters related to intra-molecular and bifurcated intra-molecular hydrogen bonds for both the molecules investigated, agree well with their X-ray values, as shown in Table 2.

3.2. Non linear optical (NLO) properties

When an electromagnetic radiation interacts with a NLO material, there is a change in the propagation parameters like frequency, amplitude, and phase, creating new fields [34,35]. If these changes are note-worthy, then NLO material could be useful for nonlinear optical applications such as optical logic, optical memory, optical switching and frequency shifting [36, 37]. NLO utility of a given compound is decided by the value of its first- order hyper polarizability. Therefore, density functional theory has been commonly used to explore organic NLO materials [38-41]. Table. 3 consists of all the values of the NLO parameters for both the molecules HMHC and HMNHC.

It is a normal practice to compare total dipole moment (μ_t) and mean first-order hyperpolarizability (β_t) of a new compound with those of Urea, which are 1.3732 Debye and 372.8×10^-33 cm⁵/esu, respectively, to examine NLO behaviour. For HMHC, the values of μ_tand β_tare: 1.684 Debye and 1114.785×10^-33 cm⁵/esu, respectively, whereas the corresponding values are 1.395 Debye and 1071.073×10^-33 cm⁵/esu, for HMNHC. Thus, µ_t and β_t for HMHC are 1.22 and 2.99 times higher in comparison with that of Urea. In the case of HMNHC, µ_t and β_t are 1.01 and 2.87 times greater than the corresponding figures for Urea. Hence, HMHC and HMNHC are most suitable for NLO applications. It should be noted that the nonlinear optical activity originates from intra molecular charge transfer (ICT), which is connected to electron association via the π - conjugated network of electrons [42]. Hyper polarizability is helpful to understand the charge delocalization in the molecule. Maximum charge delocalization takes place along β_xxy direction in HMHC and HMNHC.

Table 3. Values of dipole moment, µ_t(in Debye); polarizability, α_tin 1.4818 × 10^-25cm³; and first order hyperpolarizability, β_t(in 8.641 × 10^-33cm⁵/e.s.u) of HMHC and HMNHC molecules.

Type of component	Value with B3LYP/6-311++G(d,p)
Type of component	HMHC	HMNHC
µ_x	-1.644	1.382
µ_y	-0.292	-0.028
µ_z	0.216	0.192
µ_t	1.684	1.395
a_xx	326.425	337.070
a_xy	-18.608	19.862
a_yy	174.093	191.870
a_xz	-1.112	1.569
a_yz	2.114	1.377
a_zz	91.932	101.809
α_t	197.483	210.250
∆α	206.085	205.599
β_xxx	-1100.922	1012.072
β_xxy	500.456	479.616
β_xyy	-59.382	154.603
β_yyy	-184.985	-200.774
β_xxz	65.766	51.658
β_xyz	-18.053	33.142
β_yyz	-11.254	-4.139
β_xzz	77.117	-115.535
β_yzz	-58.234	-78.834
β_zzz	2.771	0.419
β_t	1114.785	1071.073

3.3. Frontier molecular orbitals (FMO)

FMOs i.e. HOMO (highest occupied molecular orbital) considered as electron donor and LUMO (lowest unoccupied molecular orbital) treated as an electron acceptor are known for their vital role in quantum chemistry for proper understanding and correct interpretation of various electronic and electrical parameters, UV-Visible absorption bands, Chemical reactivity and charge transfer at molecular level [28, 42, 43-50].

3.3.1. UV-Visible spectra

Usefulness of UV-Visible absorption spectra is popular for quantitative analysis of organic solutions. But the process is beset by unavoidable presence of impurities in an organic synthesis, which takes place in the solution phase. There are several methods to address this problem:

Segregation of different impurities in the solution,
Synthesizing the impurities individually, and
Simulating UV-Visible spectra theoretically.

The first two methods are not only financially taxing but also need considerable time. This paved the way for development of theoretical methods, that strived to achieve the common goal of simulating UV-Visible spectra. A succinct review of these methods along with DFT was made by Parrish et al [51], while presenting their own method involving extension of variational quantum eigensolver approach for calculating electronic transitions. As time-dependent density functional theory (TD-DFT) is known to provide UV-Visible spectra with acceptable accuracy [28, 52], we employed the same in the present calculations. Another compelling reason for our choice is that it conforms to the overall aim of these investigations.

Simulation of UV-Visible spectra is a three-step process [53, 54].These steps are:

Generation of ground state geometry,
Analytical computation of vibrational wavenumbers in order to ensure the absence of imaginary frequencies, a mandatory condition, to ascertain that the structure correlates with a local minimum, and
Calculation of vertical transitions to valence excited states.

The first two steps are implemented with the help of DFT, whereas in the final step TD-DFT is employed.

Quantum chemical methods outlined above provide us with a line spectrum for the UV-Visible transitions, whereas its experimental counterpart appears with a broad shape caused by line-broadening effects (natural line width, Doppler effect, Pressure broadening and thermal excitement), that are inherent to a chemical system of present kind. This underlines the need for modifying each computed line to assume a Gaussian shape [55, 56]. To this end, we adopted an integrated approach due to Bremond et al [57], to calculate UV-Visible transitions, using electronic transitions generated by TD-DFT as input. This process broadens each line spectrum into a Gaussian function by making independent optimization using a convenient value for full width at half maximum (FWHM). This approach results in an improved concurrence of recorded spectra with their corresponding computed spectra [37]. However, it should be kept in mind that perfect agreement between the observed and simulated UV-Visible spectra is impossible to achieve, as it is beyond the scope of theoretical methods currently available to account for line-broadening effects in their totality.

Simulated UV-Visible spectral parameters obtained in a solution of Dimethyl-formamide (DMF) for HMHC and HMNHC, according to the quantum chemical methods outlined in the preceding paragraphs (see section 2, to account for solvent effects), are shown in Figures 2 (a) and 2(b), respectively. They are compared with their experimental counterparts taken from reference 17 in Table 4.

Table 4. Experimental and theoretical (DFT/B3LYP/6-311++G(d,p) formalism) electronic absorption parameters for HMHC and HMNHC molecules.

Compound	Absorption Maximum λ_max (nm)		Oscillator Strengths (f)	Majorcontribution (≥10%)	Transition
Compound	Expt^a.	Cal.	Oscillator Strengths (f)	Majorcontribution (≥10%)	Transition
HMHC	329	332.02	0.3885	H→L (97%)	n→π*
HMHC	260	263.98	0.4926	H-1→L (41%), H-2→L (55%)	π→π*
HMNHC	337	340.87	0.4075	H→L (97%)	n→π*
HMNHC	270	273.45	0.4771	H-1→L (92%)	π→π*

H: HOMO; L: LUMO

a: from reference [17]

TD-DFT/B3LYP//6-311++G(d,p) computations predict two electronic transitions at λ_max=332 and 264 nm, with their oscillator strengths f=0.3885 and 0. 4926, for HMHC. These are in good agreement with experimental electronic transitions at λ_max= 329 and 260 nm, reported by Subhashree et al. [17], for HMHC. In the same way, for HMNHC, on the basis of computations we expect two electronic absorption bands near λ_max= 341 and 273 nm, with corresponding oscillator strengths f = 0.4075 and 0.4771, respectively. These values also agree well with their experimental counterparts around λ_max= 337 and 270 nm. TD-DFT computations for HMHC confirm that the first of the above-mentioned experimental band originates mainly from H→L (97%) transition, identifiable with n→π* transition, whereas the latter band has its origin in the transitions that start from (H-1) and (H-2) and end on (L), i.e., (H-1) →L (41%) and (H-2) →L (55%), atributable to π→π* transition (see table 4). Similar observations can be made with regard to HMNHC from the data available in Table 4.

3.3.2. Chemical reactivity

Table 5 contains the frontier molecular orbital parameters calculated using the DFT/B3LYP/6-311++G(d, p) method, for HMHC and HMNHC, using formulae given in section 2.

The energy gap (E_g), is computed near 1.998, and 2.036 eV, for HMHC and HMNHC, respectively, which is small. Small value of energy gap is characteristic of conjugated systems. This implies high chemical reactivity as it is energetically easy to transfer electrons to high-lying LUMO by exciting electrons from low-lying HOMO. This causes accumulation of electrons in LUMO, with subsequent polarization of the molecules. Hence, a molecule with a small frontier orbital gap is easily polarizable, usually exhibits high chemical reactivity and low kinetic stability [58-60].Both the molecules HMHC and HMNHC are stable under normal conditions, because they have negative chemical potential (µ) [61].

Table 5. Frontier molecular orbital parameters of HMHC and HMNHC molecules

Frontier molecular orbital parameter	Value (eV)
Frontier molecular orbital parameter	HMHC (This work)	HMNHC (This work)
HOMO energy	-7.537	-7.560
LUMO energy	-5.539	-5.524
Frontier molecular orbital energy gap	1.998	2.036
Ionization energy (I)	7.537	7.560
Electron affinity (A)	5.539	5.524
Global hardness (η)	0.999	1.018
Global softness (S)	0.500	0.491
Chemical potential (µ)	-6.538	-6.542
Electronegativity (χ)	6.538	6.542
Global electrophilicity power (ω)	21.373	21.020

3.4 Natural Bond Orbital (NBO) properties

NBO investigations identify inherent Lewis structure of the wave function (ψ), characterize conjugative charge transfer, and indicate the existence of inter- and intra-molecular hydrogen bonds, and show interactions between the bonds. In order to provide a convincing explanation for the above mentioned chemical processes, the NBO orbitals are selected in such a way that they have the most significant feasible amount of electron density (ED).

The stabilizing energy E(2) may be obtained from the expression:

In the above expression, is the population of the donor orbital, and are the energies of the i^th and j^th orbitals, respectively, and is the Fock matrix element in the NBO basis. Strong interaction between electron donors and acceptors, which envelops the structure in conjugation, implies significant value of stabilizing energy , that binds the entire structure in conjugation. Required computations are made with the help of NBO programme version 3.1 [32],which is a part of the Gaussian 09 software suit at the DFT/B3LYP/6-311++G(d,p) level of theory.

Table 6. Second-order perturbation theory analysis of FOCK matrix in NBO basis corresponding to the intra-molecular bonds of HMHC by DFT/B3LYP/6-311++G(d,p) method.

NBO(i)	Type	ED/e	NBO(j)	Type	ED/e	E(2)^a (kcal/mol)	E(j)-E(i)^b (a.u)	F(i,j)^c (a.u)
C1-C2	π	1.61434	C3-C4	π*	0.36844	19.24	0.29	0.066
			C5-C6	π*	0.30655	16.26	0.29	0.063
			C12-N14	π*	0.25821	22.80	0.24	0.069
	π	1.70950	C1-C2	π*	0.44157	16.96	0.29	0.065
	π	1.70950	C5-C6	π*	0.30655	17.73	0.30	0.065
C5-C6	π	1.71703	C1-C2	π*	0.44157	20.79	0.28	0.071
C5-C6	π	1.71703	C3-C4	π*	0.36844	18.40	0.28	0.066
LP(2)O10	-	1.84408	C1-C2	π*	0.44157	31.48	0.34	0.099
LP(1)N14	-	1.89533	O10-H11	σ*	0.04076	13.72	0.85	0.098
LP(1)N15	-	1.66097	C12-N14	π*	0.00909	28.36	0.27	0.079
LP(1)N15	-	1.66097	C17-S18	σ*	0.47684	53.01	0.24	0.105
LP(2)S18	-	1.87812	N15-C17	σ*	0.05876	11.45	0.62	0.076
LP(2)S18	-	1.87812	C17-N19	σ*	0.05040	11.70	0.65	0.079
LP(1)N19	-	1.72744	C17-S18	σ*	0.47684	62.08	0.23	0.113
LP(2)O22	-	1.85128	C3-C4	π*	0.36844	29.21	0.34	0.094

^a: E(2) means energy of hyper conjugative interaction (stabilization energy).

^b: Energy difference between donor (i) and acceptor (j) NBO orbitals.

^c: F(i,j) is the Fock matrix element between i and j NBO orbitals.

Table 7. Second-order perturbation theory analysis of FOCK matrix in NBO basis corresponding to the intra-molecular bonds of HMNHC by DFT/B3LYP/6-311++G(d,p) method.

NBO(i)	Type	ED/e	NBO(j)	Type	ED/e	E(2)^a (kcal/mol)	E(j)-E(i)^b (a.u)	F(i,j)^c (a.u)
C1-C2	π	1.61513	C3-C4	π*	0.36986	19.24	0.28	0.066
			C5-C6	π*	0.30928	16.45	0.29	0.063
			C12-N14	π*	0.26092	22.49	0.24	0.068
	π	1.70927	C1-C2	π*	0.44124	17.00	0.29	0.065
	π	1.70927	C5-C6	π*	0.30928	17.69	0.30	0.065
C5-C6	π	1.71742	C1-C2	π*	0.44124	20.69	0.28	0.071
C5-C6	π	1.71742	C3-C4	π*	0.36986	18.47	0.28	0.066
LP(2)O10	-	1.84591	C1-C2	π*	0.44124	31.13	0.34	0.099
LP(1)N14	-	1.89342	O10-H11	σ*	0.04066	13.48	0.85	0.097
LP(1)N15	-	1.66792	C12-N14	π*	0.26092	29.58	0.26	0.080
LP(2)S18	-	1.84591	C17-S18	σ*	0.50675	58.71	0.23	0.108
	-		N15-C17	σ*	0.05692	11.33	0.61	0.075
	-		C17-N19	σ*	0.05695	12.03	0.67	0.081
LP(1)N19	-	1.67563	C17-S18	σ*	0.50675	80.32	0.20	0.120
LP(2)O25	-	1.85166	C3-C4	σ*	0.36986	29.12	0.34	0.094

^a: E(2) means energy of hyper conjugative interaction (stabilization energy).

^b: Energy difference between donor (i) and acceptor (j) NBO orbitals.

^c: F(i,j) is the Fock matrix element between i and j NBO orbitals.

The results of such analysis [28, 62,63] for both the molecules HMHC and HMNHC are displayed in Tables 6 and 7, respectively. They consist of only major contributions of energy values (contributions below 10% are not included).

Donor-acceptor interactions may be stabilized by the delocalization of electron density between empty non-bonding or Rydberg (non-Lewis NBO) orbitals and lone pair or bonding (i.e., Lewis-type) NBO orbitals. Intra-molecular hyper conjugative interactions occur when a bonding π-orbital and an anti-bonding π^*-orbital overlap. These interactions result in intra-molecular charge transfer (ICT), which stabilizes the system. As a result of these interactions, there is an increase of ED in mequinol C1-C2 and C5-C6 anti-bonding orbitals. This is reflected in the reduction of strength of corresponding bonds. The ED, for HMHC near the conjugated π-bonds of the mequinol ring is between 1.6143 and 1.7095, according to the values available in Table 7. Similarly, on the basis of values in the same Table, the corresponding values for π^*-anti-bonds for HMHC are in the range 0.2582-0.4415. This causes intense charge delocalization in the molecule generating total stabilization energy 170.07 kcal mol^-1from mequinol ring alone. According to NBO analysis, the interactions π (C1-C2)→ π^* (C3-C4, C5-C6 and C12-N14); π (C5-C6) → π^* (C1-C2, C3-C4); LP(2)O10 → π^* (C1-C2); LP(2)O22→ π^*(C3-C4) exhibit high stabilization energies in the range 16.26 – 31.48 kcal mol^-1.

Using the data presented in Table 7, similar results can be arrived at for HMNHC.

3.5 Molecular electrostatic Potential

Molecular electrostatic Potential (MESP) is a well established method for understanding molecular reactivity sites [64, 65]. The function of MESP also includes understanding the nature of biological recognition mechanisms. We know that, with the help of diffraction experiments [66], MESP can be determined experimentally for a given molecule just like any other real physical quantity. This is an essential attribute of MESP that sets it apart from other reactivity indices like atomic charges, which are just conceptual entities and hence have no direct relation to the physical world. MESP maps generated using the procedure stated to section 2 are available in Figure 3.

To identify the areas of the molecule with changing electron density, colour grading [67] technique is used. The colour scheme suggests that red denotes electron-rich region, blue indicates electron deficient area, Orange (light blue) colour is associated with slightly electron deficient region, yellow indicates a somewhat electron-rich region, and green indicates a neutral area [67]. Therefore, the colour grading from most negative region to the most positive area follows the order red˃yelow˃green˃orange˃blue.

It is evident from Fig.3 that the electron-rich area in HMHC and HMNHC is around oxygen atoms of the hydroxy and methoxy groups. Therefore oxygen atom is the most reactive site in mequinol ring. This is supported by the fact that these oxygen atoms participate in the formation of inter-molecular hydrogen bonds in both molecules. The sulfur atom, which is seen in figure as yellow region, is the next region in both the molecules that is prone to chemical attack by approaching species.

Three nitrogen atoms of the two molecules are places of negative potential whereas the hydrogen atoms correspond to areas of positive potential.

3.6 Fukui functions analyses

The Fukui functions provide quantitative data on the electrophilicity and nucleophilicity of each atom based on population of Mulliken charges. The electron density is a variable that is determined by the quantity of electrons present at a specific place. The electrons inside the molecule are added or subtracted in order to calculate the Fukui functions. In biological research, the local softness characteristics may be used to examine the protein-ligand bonding. [44,45, 68]. Tables 8 and 9 displays each atom of both the molecules HMHC and HMNHC along with the full Fukui functions and dual descriptor values. The order of positive calculated dual descriptor values for each atom in the case of HMHC,

N15>S18>H26>C4>O10>C17>C6>C23>H24>C1>C3>H11>H25>O22. The atom C12 has an electrophilic attack value of -0.102, it is the most detrimental site. The order accepting active sites can be organized as supervene:

C12>N14>C5>H13>C2>N19>H7>C21>H9>H8>H21>H16. For the second molecule that is HMNHC, the order of positive calculated dual descriptor values for each atom as follows,

N15>S18>O22>C4>O10>C17>C6>H27>H19>C1>H11>H20>C3>H23>H28>C21. The most determinantal site atom C12 and the value of its electrophilic attack is -0.106. The order of negative values of f(r) is C12>N14>C5>H13>C2>H7>H9>H8>N19>H29>H22>C23>H16.

Table 8. Condensed Fukui function, dual descriptor, and local softness of HMHC

Atom	Mulliken atomic charges			Fukui functions			dual desciptors	local softness
Atom	0, 1 (N)	N +1 (-1, 2)	N-1 (1,2)	f_r⁺	f_r^-	f_r⁰	Df	sr+ ƒ_r⁺	sr-ƒ_r^-	sr0 ƒ_r⁰
C1	-0.2794	-0.329737	-0.22104	-0.050	-0.058	-0.054	0.008	-0.011	-0.013	-0.012
C2	1.133	1.038187	1.209101	-0.095	-0.076	-0.085	-0.019	-0.021	-0.017	-0.019
C3	-0.2669	-0.301523	-0.22561	-0.035	-0.041	-0.038	0.007	-0.008	-0.009	-0.008
C4	-0.8491	-0.843732	-0.81838	0.005	-0.031	-0.013	0.036	0.001	-0.007	-0.003
C5	-0.0592	-0.090971	-0.07831	-0.032	0.019	-0.006	-0.051	-0.007	0.004	-0.001
C6	-0.2056	-0.166888	-0.22644	0.039	0.021	0.030	0.018	0.008	0.005	0.006
H7	0.10085	0.053236	0.139155	-0.048	-0.038	-0.043	-0.009	-0.010	-0.008	-0.009
H8	0.2026	0.140837	0.258051	-0.062	-0.055	-0.059	-0.006	-0.013	-0.012	-0.013
H9	0.19114	0.133537	0.2413	-0.058	-0.050	-0.054	-0.007	-0.013	-0.011	-0.012
O10	-0.2692	-0.319279	-0.1851	-0.050	-0.084	-0.067	0.034	-0.011	-0.018	-0.015
H11	0.37728	0.373655	0.386424	-0.004	-0.009	-0.006	0.006	-0.001	-0.002	-0.001
C12	-0.3731	-0.467459	-0.38078	-0.094	0.008	-0.043	-0.102	-0.021	0.002	-0.009
H13	0.18271	0.111502	0.22199	-0.071	-0.039	-0.055	-0.032	-0.016	-0.009	-0.012
N14	0.00156	-0.112405	0.032239	-0.114	-0.031	-0.072	-0.083	-0.025	-0.007	-0.016
N15	0.10665	0.158985	0.137639	0.052	-0.031	0.011	0.083	0.011	-0.007	0.002
H16	0.22912	0.189534	0.267069	-0.040	-0.038	-0.039	-0.002	-0.009	-0.008	-0.008
C17	0.05818	0.108845	0.038507	0.051	0.020	0.035	0.031	0.011	0.004	0.008
S18	-0.4757	-0.711199	-0.19095	-0.236	-0.285	-0.260	0.049	-0.051	-0.062	-0.057
N19	-0.3716	-0.406065	-0.35429	-0.035	-0.017	-0.026	-0.017	-0.008	-0.004	-0.006
H20	0.2711	0.263455	0.283876	-0.008	-0.013	-0.010	0.005	-0.002	-0.003	-0.002
H21	0.30429	0.264372	0.336305	-0.040	-0.032	-0.036	-0.008	-0.009	-0.007	-0.008
O22	-0.1649	-0.185372	-0.10255	-0.020	-0.062	-0.041	0.042	-0.004	-0.014	-0.009
C23	-0.3404	-0.332227	-0.35415	0.008	0.014	0.011	-0.006	0.002	0.003	0.002
H24	0.1563	0.140348	0.182353	-0.016	-0.026	-0.021	0.010	-0.003	-0.006	-0.005
H25	0.18327	0.148578	0.220914	-0.035	-0.038	-0.036	0.003	-0.008	-0.008	-0.008
H26	0.15695	0.141785	0.182677	-0.015	-0.026	-0.020	0.011	-0.003	-0.006	-0.004

Table 9. Condensed Fukui function, dual descriptor, and local softness of HMNHC

Atom	Mulliken atomic charges			Fukui functions			dual descriptors	local softness
Atom	0, 1 (N)	N +1 (-1, 2)	N-1 (1,2)	f_r⁺	f_r^-	f_r⁰	Df	sr+ ƒ_r⁺	sr-ƒ_r^-	sr0 ƒ_r⁰
C1	-0.3051	-0.35454	-0.24852	-0.049	-0.057	-0.053	0.007	-0.011	-0.012	-0.012
C2	1.16505	1.080102	1.235264	-0.085	-0.070	-0.078	-0.015	-0.019	-0.015	-0.017
C3	-0.2242	-0.261929	-0.18208	-0.038	-0.042	-0.040	0.004	-0.008	-0.009	-0.009
C4	-0.8323	-0.827185	-0.80118	0.005	-0.031	-0.013	0.036	0.001	-0.007	-0.003
C5	-0.0713	-0.102761	-0.09025	-0.031	0.019	-0.006	-0.050	-0.007	0.004	-0.001
C6	-0.2233	-0.185188	-0.24486	0.038	0.022	0.030	0.016	0.008	0.005	0.007
H7	0.09141	0.044515	0.128624	-0.047	-0.037	-0.042	-0.010	-0.010	-0.008	-0.009
H8	0.20153	0.139886	0.256635	-0.062	-0.055	-0.058	-0.007	-0.013	-0.012	-0.013
H9	0.18849	0.130876	0.238108	-0.058	-0.050	-0.054	-0.008	-0.013	-0.011	-0.012
O10	-0.267	-0.316248	-0.18499	-0.049	-0.082	-0.066	0.033	-0.011	-0.018	-0.014
H11	0.38832	0.383927	0.397456	-0.004	-0.009	-0.007	0.005	-0.001	-0.002	-0.001
C12	-0.4114	-0.51383	-0.41502	-0.102	0.004	-0.049	-0.106	-0.022	0.001	-0.011
H13	0.17954	0.107545	0.220572	-0.072	-0.041	-0.057	-0.031	-0.016	-0.009	-0.012
N14	0.03165	-0.081241	0.06134	-0.113	-0.030	-0.071	-0.083	-0.025	-0.006	-0.016
N15	0.11243	0.156754	0.150876	0.044	-0.038	0.003	0.083	0.010	-0.008	0.001
H16	0.24408	0.204903	0.281946	-0.039	-0.038	-0.039	-0.001	-0.009	-0.008	-0.008
C17	-0.0479	-0.018662	-0.05429	0.029	0.006	0.018	0.023	0.006	0.001	0.004
S18	-0.4128	-0.621359	-0.14736	-0.209	-0.265	-0.237	0.057	-0.045	-0.058	-0.052
N19	-0.2596	-0.266939	-0.25913	-0.007	0.000	-0.004	-0.007	-0.002	0.000	-0.001
H20	0.31752	0.313185	0.326984	-0.004	-0.009	-0.007	0.005	-0.001	-0.002	-0.002
C21	-0.3296	-0.320018	-0.3392	0.010	0.010	0.010	0.000	0.002	0.002	0.002
O22	-0.1657	-0.18597	-0.10542	-0.020	-0.060	-0.040	0.040	-0.004	-0.013	-0.009
C23	-0.3386	-0.33033	-0.35209	0.008	0.013	0.011	-0.005	0.002	0.003	0.002
H24	0.15675	0.141427	0.18187	-0.015	-0.025	-0.020	0.010	-0.003	-0.005	-0.004
H25	0.18314	0.148458	0.2202	-0.035	-0.037	-0.036	0.002	-0.008	-0.008	-0.008
H26	0.15623	0.140201	0.181598	-0.016	-0.025	-0.021	0.009	-0.003	-0.006	-0.005
H27	0.17755	0.15163	0.198372	-0.026	-0.021	-0.023	-0.005	-0.006	-0.005	-0.005
H28	0.11707	0.092585	0.144781	-0.024	-0.028	-0.026	0.003	-0.005	-0.006	-0.006
H29	0.17797	0.150206	0.199768	-0.028	-0.022	-0.025	-0.006	-0.006	-0.005	-0.005

Geometry optimization made for HMHC and HMNHC using DFT/B3LYP/6-311 + + G(d,p) method showed that the structure parameters so obtained were in reasonably, in good agreement not only with their corresponding X-ray values for both the molecules, but also with their corresponding counterparts in related molecules. The calculations indicated the existence of bifurcated intra-molecular hydrogen bond between (H11, H20) atoms and N14 atom (O10-H11•••N14 and N19-H20•••N14), in addition to the presence of intra-molecular hydrogen bond between O10•••H9 and O22•••H8 in the investigated molecules. Simulated electronic transitions, two each for HMHC and HMNHC, obtained employing Time-Dependent variant of DFT using above mentioned exchange correlation functional and basis set in a solution of dimethylformamide, along with IEF-PCM model, exhibited excellent coincidence with their corresponding experimental counterparts. This observation also concurs with that made for related systems. FMO analysis involving HOMO and LUMO orbitals led to the conclusion that their origin was in n→π* and π→π* transitions, which agree with that found for related compounds. Further, the value of energy gap (∆E), as provided by HOMO and LUMO values, being relatively small around 2 eV, which is also true for related molecules, suggested that both HMHC and HMNHC were highly reactive. Moreover, chemical potential (µ), being negative for both the molecules, emphasized that they were stable under normal conditions, as in the case of related systems. Comparison of NLO parameters µ_t and β_t with those of Urea, revealed that both the molecules could be employed gainfully for NLO applications. It is interesting to note that this is also true of related molecules. A deeper insight into NLO behavior of these molecules in terms of ICT was provided by analysing hyperconjugative interactions using NBO analysis. MESP analysis helped to locate most reactive sites in both the molecules, which were around the oxygen atoms of the hydroxyl and the methoxy groups. By using Fukui functions, we have determined the reactivity of a molecule to nucleophilic and electrophilic attacks. Thus, Fukui functions have proven to be valuable tools in predicting chemical reactivity. In the molecule HMHC, most positive atom is N15 and the most negative site C12, whereas in the case of HMNHC, the highest positive atom site is N15 and the highest negative atom is C12.

Acknowledgments

The first author (KSS) is grateful to the management of SR University, Warangal, India, for permitting him to undertake the reported investigations. The second author (LR) thanks the management of Malla Reddy Engineering College(A), Secundrabad-500100, Telangana, India for permitting him to undertake the reported investigations.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding Declaration in the manuscript

There was no funding sources.

Author Contribution

K. Srishailam: Original draft preparation L. Ravindranath: ConceptualizationGaddam. Ramesh: Methodology,D. Praveena: Drafting figuresSunil kumar V: Drafting tables Danikonda. Suresh Kumar: Investigation, and validationS. Muthu: Reviewing and editing manuscript G. Ramana Rao: Reviewing and editing manuscript

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No competing interests reported.

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Quantum Chemical Investigation of (E)-2-(2-hydroxy-5- methoxybenzylidene)hydrazinecarbothioamide and its N-methyl Variant by Using DFT Methods

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Abstract

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Highlights

1. Introduction

2. Computational techniques

3. Results and Discussion

4.Conclusions

Declarations

Author Contribution

References

Additional Declarations

Supplementary Files

Status:

Version 1