Synthesis and characterization of fluorenone derivatives with electrical properties explored using density functional theory (DFT)

Abstract

This study provides thorough computational and experimental assessments of four types of novel synthesized thiosemicarbazones. The compounds were effectively synthesized using a condensation reaction between thiosemicarbazide and fluorenone, producing a remarkable range of 70–88%. Additional chemical structures were examined utilizing spectroscopic methods, including Fourier-transform infrared spectroscopy (FTIR), NMR spectroscopy, and ultraviolet-visible spectroscopy. The computational analyses utilized DFT using the M06/6-311G (d, p) technique. The electrical characteristics, including the stability of orbitals via energy exchange between a donor and acceptor, can be evaluated by natural bond orbital (NBO) analysis. The nonlinear optical (NLO) properties were analyzed to detect any prohibited energy gaps. FTIR and UV-visible data were computed using the identical M06/6–311G (d, p) level of theory. The NBO test has confirmed the occurrence of charge separation due to the efficient transfer of electrons from the donor to the acceptor unit over the π bridge. The molecular chemical softness and hardness are dependable indications of a molecule’s chemical stability. A significant magnitude of the absolute value of polarizability and hyper-polarizability indicates considerable dispersion of electric charge. The outcomes derived from Density Functional Theory (DFT) generally align well with experimental findings.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-80477-0.

Introduction

The Italian–German chemist Hugo Schiff produced a group of compounds that were named after his name as “Schiff base” and he was also awarded with noble prize. Generally, Schiff base is prepared by a condensation reaction between active carbonyl compound either aldehyde or ketone and primary amine compound. As a result, imine group is generated between them¹. Various applications of Schiff bases are found in diverse fields such as inorganic chemistry, analytical chemistry, organic chemistry, pharmaceuticals, dye industries, catalysis, food industry and biological fields and in medical² as antitumor³ anti-inflammatory⁴, anticonvulsant⁵, analgesic⁶, and many more. These bases formed diverse group of complexes with transition metals, main group elements, actinides and lanthanides. They formed stable complexes because they simply retain⁷. Fluorenone derivatives, another key focus of this study, are known for their significance in organic electronics and optoelectronic devices, including applications in organic semiconductors and light-emitting diodes⁸².

Thiosemicarbazones are considered as the derivatives of thiourea synthesized by condensation reaction between thiosemicarbazone or N substituted thiosemicarbazide and a ketone⁸. According to IUPAC for classifying organic compounds, the general formula for thiourea (byproduct) is shown as R1R2C=N-NHCS-NR3R4 and termed by the condensed Ketone’s name. The numbering for atoms presents in formula are following in which R3& R4 could be alkyl or aryl groups as show in Figs. 1 and 2.

Fig. 1.

Synthesis of Schiff base.

Fig. 2.

General structures of thiosemicarbazone.

Density functional theory (DFT) approaches provide promising insights to the chemical and biological systems and the results are usually found in good contract to that of experimental results⁹. In chemistry, physics and materials science, DFT is a computational quantum mechanical method utilized to examine the electronic construction, mainly the ground state of various body systems, in specific atoms, molecules and the summarized phases. DFT is among the unlimited methods existing in computational physics, condensed matter physics and computational chemistry¹⁰. As computational costs decrease and the accuracy of DFT improves, it becomes increasingly practical for the study of complex organic molecules, including those with potential industrial and biomedical applications⁸³. Costs of computational methods were low as compared to the traditional methods, such as replace only Hartree–Fock theory and its descendants that include electron relationship^11,12.

Non-linear optical substances are classified as high-tech materials due to their capacity to change the frequency and phase of laser light that interacts with them¹³. This is because the need for more effective and novel opto-electronic materials is growing daily in today’s hi-tech society. In essence, an alteration in propagation is shown, when the NLO resources are sufficiently exposed to powerful laser beam¹⁴. They are utilized in photonic methods, medical diagnostics, photovoltaic DSSCs, OLEDs (used for illumination), fluorescent sensors, as well as other applications¹⁵. Due to their potential for use in future united photonic skills such as signal processing, connectivity switching, optical power limiting, two-photon processing of fluorescence imaging, three-dimensional optical information storage, and optical communication, NLO materials is the subject of broad-spectrum investigate in both the fundamental and applied communities¹⁶. The fields of matter sciences, pharmaceutical, physiochemical, chemical equilibrium, atomic, molecular, solid-state physics, surface interaction, telecommunication biophysics, and others are further possible uses of NLO materials¹⁷.

For using ultra-fast technology, recently it becomes crucial towards shifting our consideration for starting the use of photons instead of electrons. In the modern day, photons are highly preferred for the conveyance of information¹⁸. As a result, extensive research has been done to create photon manipulating materials that are more effective. This has led to a rise in various attempts to model novel NLO materials¹⁹. Analyses of first-order, second-order, and third-order non-linear optical features, such as electro-optic and photo-refractive impacts, second-harmonic invention, etc., are included in the field of non-linear optics. Molecular dyes that exhibit NLO reactions, organic and inorganic semiconductors, polymer frameworks, and naturally occurring and artificial nanomaterials have all been the subject of extensive scientific research^20,21. Designing extreme performance NLO materials employing organic and inorganic methods is now a difficult and crucial topic for researchers. Since they enable anisotropic ion-exchange and offer waveguide topologies, inorganic supplies have been utilized in numerous viable NLO applications for the majority of the time²².

However, the ease of synthesis and lower dielectric constants of organic molecules have significantly diverted research focus away from inorganic systems over the past fifteen years²³. Due to their (i) ease of fabrication, (ii) lower production costs, (iii) high photoelectric coefficients, (iv) inherent rapid NLO response, (v) tunable absorption wavelength, and (vi) maximum second order and third order hyperpolarizabilities, organic NLO materials are favored above inorganic NLO materials^24,25. Organic conjugated materials’ NLO characteristics can be effectively improved by fundamental tuning along with fullerene acceptor doping²⁶. Organic molecules and acceptor units made of fullerene are linked to improve charge transference capacity. Since many years ago, fullerene derivatives with improved photo-induced electron transport and appropriate charge separation properties have been widely employed like electron acceptors²⁷. Unfortunately, fullerene acceptors have specific inherent cons, such as low accepting power, low visible light absorption, poor photo-stability, and a shortage of information about their molecular energy intensities²⁸. Researchers are now concentrating on non-fullerene (NF) chromophores instead of fullerene due to their transparency, versatility in modifying chemical structures and electron affinities, ease of tuning energy levels, effective light absorption, and simplicity in synthesis^29,30. Their opto-electric characteristics could clearly be tweaked on account of favorable results through structural alterations because they have demonstrated extraordinary stability.

The delocalized distribution of electric charges in non-fullerene based organic materials’ π-bond systems enables these compounds to have quick response times, greater laser damage thresholds, and attractive NLO responses³¹. Extremely delocalized conjugated π-electronic materials have been developed as potential energy sources of very unique and reliable NLO responses. NLO characteristics are strongly influenced by a crucial phenomenon called intramolecular charge transfer (ICT). NLO molecules’ donor-π-conjugated-acceptor arrangement, which forms a “push-pull” model, can be used to understand the ICT process³². This “push-pull” paradigm, which uses π-conjugated linkers to excite electrons after electron-giving donor groups to electron-drawing acceptor groups, offers effective intramolecular charge transfer (ICT). The molecular characteristics of NLO chromophores depend on the “push-pull” effect’s strength as an act of electron-donating and accepting capacity. With delocalized π-conjugated system, they produce second-order and third-order NLO chromophore matter^33,34. A “push-pull” process that creates a D-π-A architecture of the NLO materials might be used to advance ICT. Immense challenges have been created to make organic NLO dyes that are extremely effective in accordance with this requirement. The proper structural alteration of π-conjugated channel, donor or acceptor substituents, which can enhance the asymmetric electronic distribution and raise the NLO activity of synthesized molecules, is necessary for constructing promising NLO materials^35,36.

There have been reports of several different framework types in the literature, including D − A, D − π − A, D–π–π–A, D–A–π–A, D–D– π –A, D– π –A- π –D, A − π − D − π − A, D − π − A − π − D, D − π − π–A, D − A − π − A and D–D–π–A and A– π –D– π –A where “A” denotes acceptor fraction, “π” denotes π-spacer, and “D” denotes donor moiety³⁷. To provide a suitable push-pull architecture and a decent NLO response, these designs make it easier for the donor, π-spacer, and acceptor units to communicate effectively with one another. As a result, the NLO response is increased by proper push-pull arrangements because they reduce charge recombination, affect charge separation, extend the penetration limit at greater wavelengths, amplify the unequal electronic allocation, and reduce the HOMO-LUMO band gap³⁸. However, there haven’t been many reports of NFAs with NLO answers. A literature review also found that the creation of fullerene free nonlinear optical mixtures emerged as per latest peer group in the field of matter sciences³⁹.

Here, a parent NFA molecule that has been π-conjugated and a few its derivatives that have been created through changing the stable design by means of several donor and acceptor varieties in order to improve NLO parameters are being discussed. Designed compounds are typically based on adjusting molecular units made up of donor-acceptor structures, prolonged conjugation, twisted -electron systems, and so forth. Due to their built-in push-pull processes, some eminent traditional organic materials have excellent intramolecular charge transfer (ICT) capabilities⁴⁰. The fundamental D − π-bridge − A structure within the molecule could be altered to improve the ICT properties, which are responsible for the divergence of molecular methods⁴¹. These structural alterations can be used to create a variety of beneficial purposes in optics and NLO. In organic compounds’ ability to successfully improve NLO responses is greatly influenced by heteroatoms. ICT from donor (D) to π-conjugated linker and acceptor is also linked to the initial hyperpolarizability (β_tot) that emerges from an NLO investigation (A)⁴².

For the chromophores mentioned above, computations using density functional theory (DFT) and time-dependent density functional theory (TD-DFT) were performed to analyze FMO, natural bonding orbital (NBO), global reactivity parameter (GRP), absorption spectra, density of states (DOS), transition density matrix (TDM), and NLO. The first hyperpolarizability (βtot) evolving through NLO estimation is also correlated by ICT that occurs from donor (D) to πconjugated linker and then to acceptor (A). Modified chemicals MFT1-CFT4 are supposed to have a significant influence on the NLO field. A–π–D–π–D configuration-based compounds fullerene free organic objects can be designed using the promising DFT-based findings, which also inspire experimental researchers to create these molecules with excellent NLO response capabilities⁴³.

The forthcoming research is expected to substantially aid both theoretical and applied researchers in the domain of NLO-based technology. We expect our research will assist experimental physicists and chemists in initiating the development of compounds with remarkable NLO properties.

Materials and methods

Preparation of material

Thiosemicarbazides are synthesised through the nucleophilic addition reaction of arylamines to carbon disulphide, utilising a base as a catalyst, resulting in potassium arylcarbamodithioates. These compounds subsequently react with methyl iodide to yield N-arylmethyldithiocarbamates, which are produced upon hydrazinolysis, as depicted in Fig. 3.

Fig. 3.

Synthetic scheme of thiosemicarbazide.

The synthesis of thiosemicarbazones (TSC) was conducted by adding equimolar solutions of substituted thiosemicarbazide to a stirred solution of ketone (9-fluorenone), utilising ethanol as a solvent and incorporating 2–3 drops of acetic acid as a catalyst. The reaction was completed after refluxing at a temperature of 80–100 °C for 5 to 6 h. Subsequently re-crystallized using ethanol. Verification of reaction completion with TLC as depicted in Fig. 4.

Fig. 4.

Synthetic scheme of thiosemicarbazones. R = 4-OCH3; R = 4-CH3; R = 3,4-dichloro; R = 2,4-dichloro.

By replacing R group with above, we obtained the following compounds as portrayed in Fig. 5;

Fig. 5.

Chem-Draw structures of all designed compounds. R = 4-OCH₃; R = 4-CH₃; R = 3,4-dichloro; R = 2,4-dichloro.

Computational procedure

The properties were calculated using density functional theory. Including natural bond orbital analysis, maximum occupied molecular orbital, lowest unoccupied molecular orbital, FT-IR, UV-Visible spectroscopy, nonlinear optical characteristics, and hyperpolarizability. Utilizing the Gaussian 09 software, recent work on the quantum chemical approach to chromophores, i.e., manufactured molecules (MFT1-CFT4) as portrayed in Fig. 6, was completed in the gaseous phase^1,77. By using M06² level theory in conjunction with 6-311G(d, p)³ basis set, all the synthesized compounds’ geometrical optimizations were taken out without any symmetry limitations. Furthermore, ICT and hyper-conjugative interfaces are determined using the NBO study. NBO 3.1 program estimates with the same level of theory and NBO study. Accordingly, utilizing the foundation set and level of theory, analyses for Electronic Structures (FMOs), Global Reactivity Parameters (GRP), Natural Population Analysis (NPA), Density of State (DOS), TDMx, and NLO were carried out.

Fig. 6.

NPA diagram of compound MFT1-CFT4.

A spectral analysis was conducted by using time-dependent DFT/M06/6-311G (d, p) methodology to determine vertical transitions and absorption characteristics for compounds MFT1-CFT4. For the investigation of MFT1-CFT4 molecules, vibrational analysis has experimental and theoretical approaches. The vibrational exploration were accompanied at M06 level of theory and 6-311G (d, p) basis set. Additionally, all of the synthesized chromophores’ oscillator strengths, excitation energies, and absorption amplitudes were estimated using TD-DFT utilizing M06/6-311G(d, p) level of theory. Avogadro⁴, Origin 8.0⁵, Chemcraft⁶, PyMOlyz 2.0⁷, Multiwfn 3.7⁸ and Gauss View 5.0 program⁹ were employed to determine results from resulting files. Equation (1)¹⁰ was utilized to evaluate dipole moment of all novels (MFT1-CFT4) with x, y, and z directions:

1

Six linear polarizability tensors are available in Gaussian output file i.e., α_xx, α_yy, α_zz, α_xy, α_yz, α_yx. Therefore, Eq. (2)¹¹ was used to estimate average linear polarizability <a>:

2

Additionally, first ten hyperpolarizability tensors i.e., β_xxx, β_xyy, β_xzz, β_yyy, β_xxy, β_yzz, β_zzz, β_xxz, β_yyz, β_xyz, together with x, y, and z directions, were produced using the Gaussian output files. The significance of first hyperpolarizability (β_tot) was computed by means of the provided Eq. (3)¹²:

3

Equation (4)¹³ was implemented to help determine the second hyperpolarizability < γ>:

4

where,

Results and discussion

Chemistry of compounds

Synthesis of Thiosemicarbazones (TSC) was occur by introducing equimolar solutions of substituted thiosemicarbazide to a stirred solution of ketone (9-flourenone), ethanol was used as a solvent and using 2–3 drops of acetic acid as a catalyst. After refluxing at 80°–100° temperature and 5–6 h was required for the completion of reaction. Conformation of reaction completion by TLC as shown in Fig. 7 .

Fig. 7.

Synthesis of thiosemicarbazone. R = 4-CH₃; R = 4-OCH₃; R = 2,4-dichloro; R = 3,4-dichloro.

Structures of synthesized novel thiosemicarbazone analyzed by IR, UV-Visible¹, H-NMR and C¹³ NMR spectroscopy. All synthesized compounds soluble in these solvents like ethanol, ethyl acetate, diethyl ether and di-chloromethane.

Physical data

The IR spectral data of compound showed important absorption bands in functional group region (Table 1). The infrared spectrum of compound MFT1 as portrayed in Fig. 8 showed significant band of (NH) at, 3343 cm^− 1. IR is typically qualitative, but it can be improved for quantitative work by calibrating peak areas or intensities to track concentration or structural changes⁷⁸. The absorption band at 1244 cm^− 1 that was corresponding to(C=S). The absorption band at 1725 cm^− 1 corresponded to (C = O) vanished and absorption bands at 1518 cm^− 1 were detected which confirmed to azomethine linkage (C=N). For complex spectra with overlapping peaks, deconvolution methods can help in separating these peaks for more accurate interpretation⁷⁹.

Table 1.

Physical data of all designed compounds.

Compound	Substituent R	Color	M.P °C	Yield
MFT1	CH3	Yellow	155	82
MFT2	OCH3	Yellow	157	85
CFT3	2,4-dichloro	Yellow	172	72
CFT4	3,4-dichloro	Yellow	188	88

Fig. 8.

Chem–Draw structures of all designed compounds.

The¹H–NMR spectrum signals of compound MFT1 showed absorption signal as multiplet at 6.890–7.352 ppm for first phenyl ring. Three protons of 2nd phenyl ring showed a downfield multiplet at 7.412–8.066 ppm. N-NH proton exhibited downfield singlet at 10.99 ppm. CH₂-N showed an up-field doublet signal at 4.870 ppm. Three protons of -CH₃ exhibited singlet peak at 2.267 ppm. One proton of NH-CH₂ showed triplet signal at 9.480 ppm. Use advanced NMR methods like COSY, HSQC, and NOESY for detailed structural insights. These techniques provide information on proton-proton couplings (COSY) or proton-carbon interactions (HSQC)⁸⁰.

The¹³C NMR of compound MFT1 the C=S appeared at 179 ppm. The signal showed at 158.34 ppm for C=N. The signal showed at 55 ppm for CH₂-NH. The CH₃ appeared at 20.74 ppm.

The IR spectral data of compound showed important absorption bands in functional group region. The infrared spectrum of compound MFT2 as portrayed in Fig. 8 showed significant band of (NH) at, 3352 cm^− 1. The absorption band at 1244.6 cm^− 1 corresponding to (C=S). The absorption bands at 1522.6 cm^− 1 were detected which confirmed to azomethine linkage (C=N). The¹H–NMR spectrum signals of compound MFT1 showed absorption signal as multiplet at 6.890–8.066 ppm phenyl rings. N-NH proton exhibited downfield singlet at 10.97 ppm. CH₂-N showed an up-field doublet signal at 4.837 ppm. Three protons of OCH₃ exhibited singlet peak at 55.10 ppm. One proton of NH-CH₂ showed triplet signal at 9.443 ppm. The¹³C NMR of compound MFT1 the C=S appeared at 179.27 ppm. The signal showed at 158.34 ppm for C=N. The signal showed at 46.54 ppm for CH₂-NH. The OCH₃ appeared at 55.10 ppm. The IR spectral data of compound showed important absorption bands in functional group region. The infrared spectrum of compound CFT3 as portrayed in Fig. 8 showed significant band of (NH) at, 3356.5 cm^− 1. The absorption band at 1284.1 cm^− 1 corresponding to (C=S). The absorption bands at 1522 cm^− 1 were detected which confirmed to azomethine linkage (C=N).

The¹H–NMR spectrum signals of compound CFT3 showed absorption signal as multiplet at 7.279–8.101 ppm phenyl rings. N-NH proton exhibited downfield singlet at 11.263 ppm. CH₂-N showed an up-field doublet signal at 4.940 ppm. One proton of NH-CH₂ showed triplet signal at 9.54 ppm. The¹³C NMR of compound CFT3 the C=S appeared at 180.28 ppm. The signal showed at 146.61 ppm for C=N. The signal showed at 44 ppm for CH₂-NH. The IR spectral data of compound showed important absorption bands in functional group region. The infrared spectrum of compound CFT4 as portrayed in Fig. 8 showed significant band of (NH) at, 3363.9 cm^− 1. The absorption band at 1187 cm^− 1 that were corresponding to (C=S). The absorption bands at 1515.2 cm^− 1 were detected which confirmed to azomethine linkage (C=N). The¹H–NMR spectrum signals of compound CFT4 showed absorption signal as multiplet at 7.279–8.101 ppm phenyl rings. N-NH proton exhibited downfield singlet at 11.132 ppm. CH₂-N showed an up-field doublet signal at 4.890 ppm. One proton of NH-CH₂ showed triplet signal at 9.568 ppm. The¹³C NMR of compound MFT1 the C=S appeared at 179.81 ppm. The signal showed at 146.38 ppm for C=N. The signal showed at 46 ppm for CH₂-NH.

Computational study

Vibrational analysis

For the investigation of MFT1-CFT4 molecules as indicated in Tables 2, 3, 4 and 5. Vibrational analysis has experimental and theoretical approaches. The vibrational investigation accompanied by M06 level of theory at the basis set 6-311G(d, p). By using different vibration of molecule at different frequencies and experimental results are also given in the below mentioned tables.

Table 2.

Calculated vibrational frequencies of compound MFT1.

DFTF.	Exp. F.	Intensities	Vibrations
3586	3343	37	(N-H)
3585			(N-H)
3183	2916	8	s(C-HBen)
3177		23	s(C-HBen)
3170		12	as(C-HBen)
3158		5	s (C-HBen)
3102		1	as(C-H)
3008		33	s(C-H)
1650		44
1554	1518	225	s+as(C = C-C=CBen)+(C-H)+(N-H)
1473	1483	206	)
1337		77
1317		21
1280	1244	190	ρ+(C-H)+ρ(N-H)
1211		146	(C=S)+ρ(N-H)++ρ(C-H) +(C=N)
1178		41	ρ + w + δ(C-H)+ρ(N-H)+(C=S)
1117		2	δ + ρ(C-HBen)+(CH3)
103		9	(C=N)+δ + ρ(C-HBen)+(N-N)
940		11	)
973		10	(C-CH3) + w + δ + ρ(C-HBen)+s+as(C = C-C=CBen)
1047		4	(C-CH3) + w(C-HBen)
809		16	w(C-HBen)
741	725	105	(C-H)+ γ(C-HBen)+(C-NH)
5		100	(C-HBen)++γ(N-H)++γ(C-NH)

Table 3.

Calculated vibrational frequencies of compound MFT2.

DFT F.	Exp. F.	Intensities	Vibrations
3585	3352	3	(N-H)
3583		76	(N-H)
3178	2900	8	s(C-HBen)
3170		17	)
3168		15	as(C-HBen)
3159		8	)
3044		444	as(C-H)OCH3
3036		36	s(C-H)
2975		58	(C-H)OCH3
1675		67
1550	1522	223
1472	1470	203	(C=N)+(N-H)+(C-H)+s+as(C = C-C=CBen)+ w(C-H)OCH3
1335		61
1298	1284	252	3
1209		133	(C=S)+ρ(N-H)+ρ(C-H) +(C=N)
1103		133	ρ + w + δ(C-H)+ρ(N-H)+(C=S)
973		12	δ + ρ(C-HBen)+(N-H)+(C=N)
845		43	(O-CH3) + w (C-HBen)
738	725	87	(C-H)+γ(C-HBen)+(C-NH)
530		97	(C-HBen)++γ(N-H)++γ(C-NH)+γC-H(OCH3)+(C=S)

Table 4.

Calculated vibrational frequencies of compound CFT3.

DFT F.	Exp. F.	Intensities	Vibrations
3557	3356	20	(N-H)
3548		78	(N-H)
3176	2900	28	s(C-HBen)
3169		23	as(C-HBen)
3152		6	as(C-HBen)
3006		40	s(C-H)
1685		79	(N-H)+(C=N)+(C-H)+ s+as (C-CBen)+ δ(C-H)
1647		46	)
1559	1522	757
1467	1457	273	(C=N)+(N-H)+(C-H)+s+as(C = C-C=CBen)(C=S)
1339		73	(C=S)+δ + w(C-H)+(C-N)+δ + w(C-HBen)+(C-Cl)
1271	1244	91	)
1211		197	ρ(C-HBen)+ρ(N-H)+ρ(C-H)+(C=N)
1154		133	ρ + w+(C-H)+ρ(N-H)+(C=S)+(C=N)+ +w(C = C-HBen)+(C-Cl)
1099		65	+ρ(C-HBen)+(N-H)+(C=N)
873		56	)
735	721	83	)
548		55	(C-HBen)++γ(N-H)++γ(C-NH)+

Table 5.

Calculated vibrational frequencies of compound CFT4.

DFT F.	Exp. F.	Intensities	Vibrations
3584	3363	49	(N-H)
3583		71	(N-H)
3178	3066	21	s(C-HBen)
3168		13	as(C-HBen)
3139		6	as(C-HBen)
3041		31	s(C-H)
1650		52	(N-H)+(C=N)+(C-H)+ s+as (C-CBen)+ δ(C-H)
1647		46	(C-HBen)Cl)+s+as(C = C-C=CBen)
1547	1515	240
1500	1489	54	)
1471	1466	207	(C=S)+δ + w(C-H)+(C-N)+δ + w(C-HBen)+(C-HBen)
1333	1304	68	)
1282		194
1211		128	ρ + w+(C-H)+ρ(N-H)+(C=S)+(C=N)+ +w(C = C-HBen)+(C-Cl)
1128		28	ρ(C-HBen)+(N-H)+(C=N)
1036		28	)
735	721	90	)
527		101	(C-HBen)++γ(N-H)++γ(C-NH)+

Frequencies are given in cm^− 1, γ = out plane bending, , _s = symmetrical stretching, _{as =} asymmetrical stretching, w = wagging, ρ = rocking,

Fourier transform infrared spectroscopy (FT-IR)

In this work, FTIR absorption bands at 3183, 3178, 3176, and 3178 cm^− 1 (CFT) are attributable to symmetric stretching vibrations in MFT1-CFT4. Furthermore, experimental vibrational bands of C-H were discovered at 2916, 2900, 2900, and 3066 cm^− 1 in MFT1-CFT4 as portrayed in Fig. 9. It was due to the intrinsic nature of C–H stretching vibrations in different carbon environments sp³ and sp² hybridized carbons⁴⁴. Peaks at 2910.6 cm⁻¹ and 2849.5 cm⁻¹ are generally attributed to C-H stretching vibrations of alkanes⁴⁵. The peaks show an abundance of methyl (CH₃) and methylene (CH₂) groups due to their characteristic stretching vibrations⁴⁶. Aromatic compounds, including the fluorenylidene group, exhibit C-H bending out-of-plane vibrations in the 950–800 cm⁻¹ area⁴⁷.

Fig. 9.

Experimental vibrational frequencies of compound MFT1-CFT4.

In the results of our study, the strong bands are situated at 1473, 1472, 1467, and 1500 cm^− 1 (DFT) for MFT1-CFT4 as portrayed in Fig. 9, which are in close alignment with the measured values of 1610, 1620, 1617, and 1618 cm^− 1 due to several factors. These include the application of scaling factors to DFT-calculated frequencies, environmental effects such as intermolecular interactions and solvent influences, mode coupling, and differences in instrumentation calibration⁴⁸. The fingerprint zone, located between 1000 and 1500 cm⁻¹, is unique to each molecule and might contain bending or stretching vibrations⁴⁹. The peaks are caused by bending vibrations of methylene (CH₂) and methyl (CH₃) groups, which are abundant in aliphatic hydrocarbons⁴⁶.

In our research, the broad peaks are situated at 3586 and 3585, 3585 and 3583, 3557 and 3548, and 3584 and 3583 cm^− 1 (DFT) in MFT1-CFT4 as portrayed in Fig. 9. The broadening arises due to hydrogen bonding, vibrational coupling, anharmonicity, solvent interactions, and instrumental resolution. These factors collectively explain the observed broad peaks and their specific frequencies⁵⁰. This large peak at 3356.6 cm⁻¹ indicates an O-H stretching vibration, which is usually linked with alcohols or phenols. The broadness of this peak indicates hydrogen bonding, which is typical of hydroxyl groups in compounds such as alcohols or carboxylic acids⁵¹. Furthermore, in MFT1-CFT4 as portrayed in Fig. 3, N-H vibrational bands have been seen at 3352, 3356, 3343, and 3383 cm^− 1. Thiosemicarbazides include NH groups, which produce strong, wide absorption bands resulting from hydrogen bonding⁵².

The C=S absorption frequencies vary from 1500 to 1200 cm^− 1. The estimated C=S vibrational modes at 1337, 1298, 1271, and 1333 cm^− 1 correspond to the measured absorption bands of 1244, 1284, 1244, and 1304 cm^− 1 for MFT1-CFT4 as portrayed in Fig. 9, respectively. Thiosemicarbazides feature a unique C=S group that absorbs in this area⁵³.

UV-visible analysis

Employing TD-DFT at M06/6-311G (d, p) for four unstable states, the observed spectrum characteristics of designed compounds have been estimated in order to understand impact of various substituents on the end covered acceptor moiety⁵⁴. The UV-visible analysis takes into account a number of variables, including the absorption wavelength (λ_max), transition energy (E_gap), oscillator strength (f_os), and the qualities of the compounds’ six smallest singlet-singlet transitions⁵⁷. The polarity of a solvent can influences the absorption or emission wavelength of a molecule, causing a shift toward longer wavelengths. Solvatochromism, is commonly used to study solvent-solute interactions and electronic transitions in spectroscopy⁸¹. The computed values for absorption wavelength (λ_max), change in energy (E_gap), oscillator strength (f_os), and transition natures are shown in Table 6 while other transition values are compiled in Table S1–S4. The calculated observed spectrum gives a broader peak; which is slightly deviated from the observed experimental results _max value.

Table 6.

Wave length, excitation energy and oscillator strength of investigated compound MFT1-CFT4.

Comp.	DFT (nm)	E (eV)	f	MO contributions
MFT1	421.815	2.9393	0.1334	H-1→L(29%), H→L(60%),H-7→L(2%), H-4→L(3%), H-3→L(3%)
MFT2	422.735	2.9329	0.1381	H-1→L(86%), H-7→L(2%), H-4→L(5%), H-2→L(4%)
CFT3	382.749	3.2393	0.1541	H-2→L(66%), H→L(32%)
CFT4	421.542	2.9412	0.1221	H-1→LUMO(22%), HOMO→LUMO(68%), H-7→LUMO(3%), H-3→LUMO(4%)

MO molecular orbital, H HOMO, L LUMO, f oscillator strength.

The UV-Visible spectral study of MFT1-CFT4 were done by CFT approach M06/6-311 + G(d, p). The recorded and computed absorbance, oscillator strength and transition assignment are shown in Table 6. The calculated observed spectrum gives a broader peak; which is slightly deviated from the observed experimental results λ_max value. The theoretically calculated main transition with maximum absorption values for MFT1-CFT4 are at 421.815, 422.735, 382.749 and 421.542 nm respectively, with oscillator strength of 0.1334, 0.1381, 0.1541 and 0.1221 and explain transitions with major and minor contributions of H-1→L (29%), H→L(60%),H-7→L (2%), H-4→L (3%), H-3→L (3%) for MFT1, H-1→L (86%), H-7→L (2%), H-4→L (5%), H-2→L (4%) for MFT2, H-2→L (66%), H→L (32%) for CFT3, H-1→LUMO (22%), HOMO→LUMO (68%)H-7→LUMO (3%), H-3→LUMO (4%) for CFT4, respectively. While the experimental absorption wavelengths are observed at 349, 361, 367 and 360 nm for MFT1-CFT4. The maximum wavelengths of molecules are increased with the following order: MFT3 < MFT4 < CFT1 < CFT2.

Natural bond orbital analysis

Analysis of natural bond orbitals (NBOs) is categorized as an effective method for providing insightful information about the intermolecular interactions between bonds and a strong basis for analyzing charge transfer among full and unoccupied orbitals⁵⁷. The exploration of electronic charge delocalization, hyper-conjugation, and electron density transfer (EDT) from donor to acceptor state with D–π–A structural design is one of the most crucial parts of NBO study⁵⁵.

NBO analysis has been considered as useful tool in computational chemistry. This can be ascribed to the evaluation of interactions between bonds, the transmission of charges between predictions of occupied orbitals, the dispersal of charges and the explanation of hyper conjugative relationships⁵⁸. The NBO approach also helps to evaluate the density transmission in donor acceptor arrangements from the donor to the acceptor⁵⁹. NBO analysis for the molecules MFT1-CFT4 performed on the assumption of all these key features as indicated in Table 7.

Table 7.

Natural bonding orbital (NBO) analysis of compound MFT1-CFT4 by using M06 level of theory at 6-311G(d, p).

Comp.	Donor (i)	Type	Acceptor (j)	Type	E(2) [kcal/mol]	E(j)_E(i) [a.u.]	F(i, j) [a.u.]
	C25-S26		C25-S26		5.88	0.24	0.038
	C6-H10		C1-C6		0.59	1.10	0.023
	C11-N22		C3-C4		102.35	0.02	0.073
	C11-N22		C12-C14		6.39	0.40	0.048
	N27-H28		C25-S26		5.54	0.95	0.065
MFT1	N23-H24		C11-N22		0.99	0.67	0.024
	N23	LP(1)	C25-S26		46.09	0.27	0.105
	N27	LP(1)	C29-C32		5.71	0.72	0.062
	N23	LP(1)	C11-N22		7.69	0.34	0.046
	S26	LP(2)	N23-C25		12.67	0.62	0.080
	S26	LP(2)	C25-N27		12.21	0.68	0.083
	C25-S26		C25-S26		5.88	0.24	0.038
	C6-H10		C1-C6		0.59	1.10	0.023
	C15-C17		C12-C14		23.93	0.30	0.076
	C1-C2		C13-C19		14.09	0.31	0.059
MFT2	N23	LP(1)	C25-S26		46.11	0.27	0.106
	N22	LP(1)	C11-C12		13.72	0.88	0.099
	N23	LP(1)	C11-N22		7.44	0.34	0.045
	S26	LP(2)	N23-C25		12.60	0.62	0.080
	S26	LP(2)	C25-N27		12.16	0.68	0.082
	N27-H28		C25-S26		5.96	0.96	0.068
	C6-H10		C1-C6		0.63	1.11	0.024
	C32-C33		C34-C37		23.13	0.29	0.073
	C13-C19		C1-C2		14.43	0.31	0.060
CFT3	N22	LP(1)	C11-C12		13.02	0.88	0.096
	N27	LP(1)	C25-S26		85.06	0.22	0.128
	N23	LP(1)	C11-N22		33.45	0.32	0.094
	S26	LP(2)	C25-N27		12.61	0.68	0.084
	Cl41	LP(3)	C34-C37		14.38	0.34	0.067
	C25-S26		C25-S26		5.90	0.24	0.038
	C6-H10		C1-C6		0.59	1.10	0.023
	C15-C17		C12-C14		24.08	0.30	0.076
	C1-C2		C13-C19		14.08	0.31	0.059
	N27-C29		C32-C40		2.00	0.80	0.039
CFT4	C25-S26		N22-N23		4.46	1.02	0.060
	C25-S26		C25-N27		1.74	1.18	0.041
	N27	LP(1)	C25-S26		73.38	0.23	0.121
	N23	LP(1)	C11-N22		6.76	0.34	0.043
	S26	LP(2)	N23-C25		12.61	0.63	0.081
	Cl42	LP(3)	C36-C37		15.46	0.32	0.070

The electron density of conjugated double as well as single bond of the benzene ring has clearly demonstrated a strong delocalization of the electrons inside ring. Because it stems from the continuous overlap of p-orbitals, uniform electron distribution, molecular orbital theory, spectroscopic evidence, quantum chemical calculations, and characteristic chemical reactivity⁶⁰. This delocalization is a hallmark of aromatic stability and contributes to benzene’s unique chemical properties⁶². The analysis of the various donors and acceptors indicate that there are only two types of donors and , and two types of acceptors and *. Bonding nature in compound MFT1 as indicated in Table 7 was also explored by NBO calculations. The transitions takes place in investigated compound are (C₁₁-N₂₂)→*(C₃-C₄) with 102.35 kcal/mol, (C₃₄-C₃₇)→*(C₃₅-C₃₉) with 23.56 kcal/mol, (C₃₄-C₃₇)→*(C₃₂-C₃₃) with 22.34 kcal/mol and (C₁₂-C₁₄)→*(C₁₃-C₁₉) with 23.31 kcal/mol. The transition from (C₂₅-S₂₆)(C₂₅S₂₆) is 5.88 kcal/mol and (C₆-H₁₀)(C₁C₆) is 0.59 kcal/mol is the lowest stabilization energy among all. This least energy is due to the weak interaction between the electron donor and acceptor. In case of the resonance, the transition as LP(1) (N₂₇) → *(C₂₅-S₂₆) produces 75.93 kcal/mol which is enormous energy value. While a least value 5.71 kcal/mol which is produced by LP(1)(N₂₇) → *(C₂₉-C₃₂). The lone pair acceptor and donor orbital interaction as LP(1)(N₂₂) →*(C₁₁-C₁₂) with 13.72 kcal/mol, LP(1)(N₂₃) →*(C₂₅-S₂₆) with 46.09 kcal/mol, LP(1)(N₂₃) →*(C₁₁-N₂₂) with 7.69 kcal/mol, LP(2)(S₂₆) →*(N₂₃-C₂₅) with 12.67 kcal/mol.

In compound MFT2 as indicated in Table 7, the hyper conjugative interactions of the donor-acceptor transitions for the π type bonding orbitals to π* type anti-bonding orbitals are: π(C₁₂-C₁₄) →π*(C₁₃-C₁₉), π(C₁-C₂)→π*(C₅-C₆), π(C₅-C₆)→π*(C₃-C₄), and π(C₁-C₂)→π*(C₁₃-C₁₉) grant stabilization energies as 23.29, 23.10, 22.54 and 14.09 kcal/mol are noticed more prominent respectively. The σ→σ* interactions in compound MFT2 originated from weak donor (σ) to acceptor (σ*) interaction resulted in lesser values of stabilization energy E⁽²⁾.The interactions as →* are obtained from (C₃-H₄)→* (C₂-C₃) with 5.78 kcal/mol, and (C₂₅-S₂₆)→*(C₂₅-S₂₆) with 5.88 kcal/mol. In addition, the resonance interaction excitations were obtained from LP(1)(N₂₇) →σ*(C₂₅-S₂₆), LP(1)(N₂₃)→π*(C₁₁-N₂₂), and LP(1)(N₂₃) →σ*(C₂₅-S₂₆) with values of energy are 76.11, 7.44 and 46.11 kcal/mol respectively.

In compound CFT3 as indicated in Table 7, the hyper conjugative interactions of the donor-acceptor transitions for the π type bonding orbitals to π* type anti-bonding orbitals are: π(C₃₂-C₃₃) →π*(C₃₄-C₃₇), π(C₁₃-C₁₉)→π*(C₁₅-C₁₇), π(C₁₅-C₁₇)→π*(C₁₂-C₁₄), π(C₁-C₂)→π*(C₁₃-C₁₉) grant stabilization energies as 23.13, 23.00, 22.74 and 14.93 kcal/mol are noticed more prominent respectively. The σ→σ* interactions in compound CFT3 originated from weak donor (σ) to acceptor (σ*) interaction resulted in lesser values of stabilization energy E⁽²⁾.The interactions as →* are obtained from (C₁-C₂)→* (C₂-C₃) with 5.49 kcal/mol, and (N₂₇-H₂₈)→*(C₂₅-S₂₆) with 5.96 kcal/mol. In addition, the resonance interaction excitations were obtained from LP(1)(N₂₃) → π*(C₂₅-S₂₆), LP(1)(N₂₇)→π*(C₂₅-S₂₆), and LP(1)(N₂₂) →σ*(C₁₁-C₁₂) with values of energy are 59.52, 85.06 and 13.02 kcal/mol respectively.

In this study, the observation of greater E² value indicates that, there was an intensive interaction of Lewis, non-Lewis orbitals and conjugation were occurred in the molecule. The highest intermolecular hyper conjugative interaction for Compound CFT4 as indicated in Table 7 are(C₁₅-C₁₇)→*(C₁₂-C₁₄) with 24.08 kcal/mol causing stabilization of the system. These intermolecular charge transfers can induce large non-linearity of the molecule. The other hyper conjugative transition are (C₃-C₄)→*(C₁-C₂) with 23.03 kcal/mol,(C₁₂-C₁₄)→*(C₁₃-C₁₉) with 23.17 kcal/mol,(C₁₃-C₁₉)→*(C₁₅-C₁₇) with 22.79 kcal/mol,(C₁-C₂)→*(C₁₃-C₁₉) with 14.08 kcal/mol. The stabilization energy because of the donor, acceptor interaction can be characterized using second-order perturbation theory in the NBO analysis.

Moreover, additional donor, acceptor interactions found are the reason for stability in the dimmer of the Schiff base and the stabilization energies have been determined to be 5.90, 5.74, 5.80 and 0.59 kcal/mol because of the (C₂₅-S₂₆)(C₂₅-S₂₆),(C₃₆-C₄₀)(C₃₆C₃₇), (C₃-C₄)(C₂C₃) and(C₆-H₁₀)(C₁C₆) respectively. The most important interaction energy, related to the resonance in the molecule, the least energy is due to the strong interaction between the electron donor and acceptor. In case of the resonance, the transition as LP(3)(Cl₄₂) →*(C₃₆-C₃₇), LP(1)(N₂₃)(C₂₅-S₂₆), LP(1)(N₂₇)(C₂₅-S₂₆) and LP(2)(S₂₆)(C₂₅-N₂₇) produces 15.46, 48.08, 73.38 and 12.31 kcal/mol. While the other transitions of compound MFT1-CFT4 are shown in Table S5-S8. Based on the NBO study, we can conclude that the strong intra-molecular hyper conjugation interactions and intermolecular hydrogen bonding are responsible for the more stable dimmer conformation in the gas and solvent phases, which also exist in the solid-state structure.

Frontier molecular orbitals (FMOs) analysis

The frontier molecular orbital (FMOs) theory utilized as an effective tool to determine the chemical stability, optical and electronic properties^62,63. The ability to accept electron is determined by calculating LUMO values whereas electron donating property is calculated by HOMO. The HOMO/LUMO analysis shows a dynamic role to conclude UV-Vis and of reaction mechanism. The HOMO-LUMO energy gap is used as a key role to determine the parameters for calculation of chemical reactivity and dynamic stability of molecules^64,65. The compounds having high value of HOMO-LUMO band gap are considered as chemically stable. Due to the high energy barrier for electron excitation and reducing reactivity⁶⁶. The compounds with greater degree of softness are considered with less stability and displayed with low HOMO-LUMO energy. Furthermore, molecules with fewer HOMO/LUMO energy band typically display high polarizability and consequences harvests favorable NLO response³⁸. The Energy of frontier molecular orbitals of MFT1-CFT4 compounds were determined at M06 level of theory at 6-311G (d, p) level of theory the E_LUMO and E_HOMO are organized in Table 8.

Table 8.

Calculated energies (E) and energy gap (ΔE) for MFT1-CFT4.

Comp.	MFT1		MFT2		CFT3		CFT4
MO(S)	E ( eV )	E	E ( eV )	E	E ( eV )	E	E ( eV )	E
HOMO	− 5.983	3.539	− 5.957	3.543	− 6.251	3.949	− 6.182	3.597
LUMO	− 2.444		− 2.414		− 2.302		− 2.585
HOMO-1	− 6.145	4.906	− 6.117	4.91	− 6.284	5.034	− 6.338	4.968
LUMO + 1	− 1.239		− 1.207		− 1.250		− 1.370
HOMO-2	− 6.731	6.330	− 6.462	6.13	− 6.745	5.714	− 6.867	5.933
LUMO + 2	− 0.401		− 0.332		− 1.031		− 0.934

The energies and the pictorial illustration of HOMO, LUMO, HOMO-1 and LUMO^+ 1, HOMO^− 2 and LUMO^+ 2 from biological activity of the compounds just because by influencing a compound’s reactivity and interaction with biological targets. The HOMO-LUMO gap determines the compound’s chemical stability and reactivity, with smaller gaps suggesting greater activity in biological systems through electron transfer⁸⁴. The relatively high value of, ΔE_HOMO–LUMO shows that the title compound presents high chemical stability and it has low reactivity. The energy difference between the HOMO and LUMO orbitals for the compound MFT1-CFT4 found as 3.539, 3.543, 3.949 and 3.597 eV respectively, as indicated in Table 8. The energy difference between the HOMO-1 and LUMO + 1orbitals for the compound MFT1-CFT4 found as 4.906, 4.91, 5.034 and 4.968 eV respectively. The energy difference between the HOMO-2 and LUMO + 2 orbitals for the compound MFT1-CFT4 found as 6.330, 6.13, 5.714 and 5.933 eV respectively. Table 8 shows that CFT3 contains highest energy gap value as 3.949 eV, while MFT1 contains least energy gap as 3.539 eV which represents the effective intra-molecular charge transfer (ICT) communication. Overall order of energy gap is achieved: CFT3 > CFT4 > MFT2 > MFT1.

In compound MFT1 as indicated in Fig. 10, the charge density of HOMO is placed on 4-methylthiosemicarbazide and charge density of LUMO on 1-(9 H-fluoren-9-ylidene)-4-methylthiosemicarbazide. In compound MFT2 as indicated in Fig. 10, charge density of HOMO on 4-methylthiosemicarbazide and charge density of LUMO placed on 1-(9 H-fluoren-9-ylidene)-4-methylthiosemicarbazide. In compound CFT3 and CFT4 as indicated in Fig. 10, charge density HOMO positioned on 4-methylthiosemicarbazide and LUMO positioned on 4-(2,4-dichlorobenzyl) thiosemicarbazide.

Fig. 10.

Frontier molecular orbitals structure of MFT1-CFT4.

Global reactivity parameters

It is important to consider HOMO energy (E_HOMO), LUMO energy (E_LUMO) and HOMOLUMO energy gap (E_gap = E_LUMO − E_HOMO) when assessing global reactivity parameters of compounds under investigation, such as global softness (σ), global electrophilicity (ω), global hardness (η), electronegativity (X), chemical potential (µ), electron affinity (EA) and ionization potential (IP). Energy requisite to remove an electron from HOMO is shown by ionization potential, while energy necessary to add an electron to LUMO is indicated by electron affinity⁶⁷. However, using the following Eqs. (5–11), it was possible to calculate these parameters for the compounds MFT1-CFT4 using Koopman’s theorem and their findings are shown in Table 2. Energy band gap of FMOs (E_gap = E_LUMO-E_HOMO) can be used to define global reactivity, and subsequent equations are used to estimate GRPs.

5

6

The following Equations have been employed to determine chemical potential (µ), electronegativity (X) and chemical hardness;

7

8

9

10

Parr et al. presented an electrophilicity index (x) and it could be defined by Eq. (11).

11

Chemical reactivity of atoms and molecules is represented by ionization energy. High stability and chemical softness are indicated by high ionization energy, whereas more reactivity of the atoms and molecules is indicated by low ionization energy. The findings of IP demonstrate a direct correlation with the electron-donating capacity, which is determined from HOMOs, while the values of EA are calculated from LUMOs, which represent the electron-accepting nature of compounds⁶⁸. The energy band gap and chemical hardness are precisely related to each other and in reverse related to overall softness and reactivity of molecule⁶⁹. Greater HOMOLUMO energy gap (E_gap) are believed to render materials less reactive, higher kinetically stable, and resistant to electronic modifications, which makes them harder molecules. On the contrary, molecules that are smoother and have a lower HOMOLUMO energy gap are highly unstable, softer, and more reactive⁷⁰. Soft molecules with a lower energy gap are thought to be superior aspirants for qualitative NLO response estimate. Because it can be ascribed to the higher polarizability and increased electron mobility, which enhance their response to external electric fields⁷¹. The smaller energy gap facilitates stronger nonlinear interactions and efficient charge transfer, resulting in a more dynamic and substantial NLO response⁷².

In wide context, the electron-donating and electron-acceptance capabilities are differentiated by ionization potential and the values of electron affinity, respectively. As indicated in Table 9 all the studied compounds, compound CFT3 showed maximum ionization potential value as 6.251eV while compound MFT2 showed minimum ionization potential 5.957eV.

Table 9.

Global reactivity factors of compounds (MFT1-CFT4).

Compounds	I	E	X	η	ω	σ
MFT1	5.983	2.444	4.2135	1.7695	5.016553	0.282566
MFT2	5.957	2.414	4.1855	1.7715	4.944513	0.282247
CFT3	6.251	2.302	4.2765	1.9745	4.63116	0.253229
CFT4	6.182	2.585	4.3835	1.7985	5.341972	0.278009

Ionization potential (I), electron affinity (E), electronegativity (X), global hardness (η), chemical potential (µ), global electrophilicity (ω) and global softness (σ).

This increases in the order of the ionization potential of compounds by MFT2 < MFT < CFT4 < CFT3. Compound CFT3 has lowest electron affinity value (2.302eV) and compound CFT4 has the highest electron affinity value (2.585eV) among all the studied compounds as indicated in Table 9. The global hardness (η) is greater than the global softness (σ) for all compounds which states that they have been a large band gap and least reactivity. The molecules are more chemically stable with less chemical reactivity and higher hardness if the energy gap value is greater. The chemical hardness was 1.7695, 1.7715, 1.9745 and 1.7985 for MFT1-CFT4 compounds, as indicated in Table 9. Molecules (MFT1-CFT4) may be soft, unstable, and more reactive, according to these findings. These compounds have excellent NLO characteristics and are highly polarizable [G10].

Non-linear optical (NLO) properties

NLO materials and dyes are frequently used in intense laser communication technologies, including maximum data charges, electro-optic variation for information storing, enhanced optical signal managing, optical switches, communication technology, signal processing, harmonic production, and frequency socializing⁷³. Understanding the extent of optical response, molecular structure, and bandgap of a molecule related to its NLO characteristics is greatly simplified because it is attributed by the significant chemical computations involving the ideas of average polarizability or average polarizability response < α > and nonlinear responses or hyperpolarizabilities (β and γ)³⁴. Briefly, delocalization of π-electrons works in conjunction with improvement in hyperpolarizability values in MFT1-CFT4 compounds. The HOMO→LUMO energy band gap is reduced by this delocalization. According to the literature, HOMO→LUMO band gap has an essential impact on the polarizability of chromophores; in other words, minimum band gap, higher will be polarizability values, and vice versa⁷⁴.

Strength of optical response is strongly correlated with a molecule’s electronic characteristics, which are typically in accordance with < α>, β_tot and γ. Prior knowledge on the reaction of the investigated compounds to an external electric field is essential for understanding the link between structure and molecular properties. It will also be intriguing to see how the core π-conjugated linkers and acceptor parts affect the linear and non-linear response. The NLO assets of above-mentioned chromophores, together with dipole moment (µ_tot), average polarizability < α>, first (β_tot) and second hyperpolarizability (γ_tot), as shown in Tables 10 and 11, and their main supporting tensors are covered in part in Tables S9–S10.

Table 10.

Dipole polarizability and major contributing tensor (a.u) of the studied compounds.

Polarizability	αtotal	Dipole moment	Total
MFT1	283.92	MFT1	5.7997
MFT2	288.82	MFT2	5.1889
CFT3	325.81	CFT3	4.3482
CFT4	293.59	CFT4	6.2418

Table 11.

Computed first hyperpolarizabilities (β_tot) and major contributing tensor (a.u) of the studied compounds.

Polarizability	MFT1	MFT2	CFT3	CFT4
β total	1839.066259	841.3918399	1520.101786	859.3106031
	1.59E−29	7.27E−30	1.31E−29	7.42E−30

The nonlinear optical properties of compounds MFT1-CFT4 have not been studied before neither computationally nor experimentally for the NLO response. Mainly due to the presence of the electron withdrawing groups along with the heterocyclic ring major attention is attained by compounds (MFT1-CFT4).

The computed data for polarizability and hyperpolarizabilities of MFT1-CFT4 are presented in Tables 10 and 11. The findings of polarizability tensors along three coordinates (x, y and z axis) explore that x-axis contains larger and prominent values among all. Among MFT1-CFT4 show polarizability 347.89, 352.38, 400.25, 358.15 a.u respectively. The highest polarizability of CFT3 is 325.8149733 and MFT1 is 283.91683 (a.u.) the least. The highest value of αtotal MFT1 is seen because of highest x-axis contribution transition. The αtotal decreasing order is to be: CFT3 > CFT4 > MFT2 > MFT1. Values of dipole moment are in decreasing order: 325.81 > 293.59 > 288.82 > 283.92 a.u.

Data demonstrates that transition along x-axis which provided considerable contribution in the calculation of β_tot for all studied compounds. Highest β_tot value of MFT1 is achieved because of maximum contribution of transition along x-axis with positive value, whereas, MFT2 contained least value of β_tot as 841.39 (a.u). Consequently, the falling order in terms of βtot for studied compounds is acquired like MFT1 > CFT3 > CFT4 > MFT2.

Natural population analysis

Mulliken population analysis of molecule utilized to investigate the hydrogen bonding pathway. More electronegative atoms N, S and O, in the entitled compounds provide an asymmetrical electronic density distribution all across the molecules, as per Mulliken statistics. The M06 level of theory at 6-311 G (d, p) utilized to get the fundamental values of MFT1-CFT4 compounds as portrayed in Fig. 6. The compounds containing high negative charges on oxygen and nitrogen atoms and they impose a large negative charge on some carbon atoms. Due to the high electronegativity of oxygen and nitrogen withdraws electron density from adjacent carbons (inductive effect) and also the resonance structures can delocalize negative charges onto carbon atoms⁷⁵. The positive charges on H-atoms are because of the negative charges of carbon atoms.

Molecular electrostatic potential (MEP)

Molecular electrical potential map is also known as electrostatic potential energy map or molecular electrical potential surface. MEP is utilized to represent complete electron density in three dimensions. Herein, we performed molecular electrical potential analyses in order to understand the movement of charges in our studied compounds with the aid of Multiwfn with a version no. 3.7⁸⁵. Furthermore, the entire computations of this work were done with the help of Gaussian 09 software⁸⁶. MEP is well-known for its ability to assess numerous electrophilic and nucleophilic positions in the marked molecule. Because it visualizes charge distribution and highlights regions of high and low electron density and provides quantitative values that predict reactivity, identifying specific sites prone to chemical attacks⁷⁶. By following MEP design two different sections developed red for electronegative region and blue for electropositive region. The positive and negative regions exhibited attraction for electrophilic and nucleophilic attacks. A light color (white) represents non-polar region. Electrophilic potential is increased in this order: red < orange < yellow < green < blue. CFT calculations executed on the optimized geometry by using M06-6-311G(d, p) level of theory to determine the electric potential areas and physiochemical characteristics of the investigated molecules and a pictorial illustration of compound MFT1-CFT4 are presented in Fig. 11.

Fig. 11.

MEP diagrams of compound MFT1-CFT4 using Multiwfn - version no. 3.7⁸⁵ & Gaussian 09 software⁸⁶.

Conclusion

This study has revealed that thiosemicarbazones can be generated with a desirable yield ranging from 70 to 88%. Four thiosemicarbazones were created in this study by combining thiosemicarbazides with fluorenone. The structural characteristics were adjusted utilizing spectroscopic tools such as¹³C NMR, ¹H NMR, UV, and FTIR. Computational research was conducted by employing DFT at M06/6–311 G (d, p). The FTIR spectrum of these thiosemicarbazones was obtained and the vibrational assignments are found between the HOMO-1 and LUMO + 1orbitals for the compound MFT1-CFT4 as 4.906, 4.91, 5.034 and 4.968 eV respectively. Similarly, the HOMO-2 and LUMO + 2 orbitals for the compound MFT1-CFT4 found as 6.330, 6.13, 5.714 and 5.933 eV respectively. Structural change may result in the development of specific narrative and highly efficient thiosemicarbazones that are of interest in the fields of agriculture and medicine. In general, the results of Density Functional Theory (DFT) show a high level of agreement with the experimental data. The investigation of the compounds’ NLO characteristics has potential for their future employment in various scientific and domestic applications, including optical storage devices, optical transmission, light-emitting diodes, and health-related pharma-active substances.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

M.U.F, M.M, A.S. and M.A.R designed and conceived the study idea. M.U.F, completed the experiments. K.U, G.M., and R.I, analysed the data and performed visualizations and statistical data analysis. K.U, G.M., R.I, J.I, and M.R, reviewed and edited the manuscript. R.I, and M.R, reviewed the manuscript and provided funds. M.U.F, provided the resources and supervision. All authors made valuable revisions and edited the manuscript and approved the last version.

Data availability

All the raw data in this research can be obtained from the corresponding authors upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval and consent to participate

This study does not include human or animal subjects.

Statement on guidelines

All experimental studies and experimental materials involved in this research are in full compliance with relevant institutional, national and international guidelines and legislation.