Computational studies of the thermodynamic properties,and global and reactivity descriptors of fluorescein dye derivatives in acetonitrile using density functional theory

Abstract

This work reports density functional theory calculations of the optimized geometries, molecular reactivity, energy gap, and thermodynamic properties of molecular dyes fluorescein (FS), fluorescein attached with methoxy (FSO), fluorescein attached with amine (FSA), fluorescein attached with methane (FSM), fluorescein attached with ethene (FSE), and fluorescein attached with thiophene (FST) using the hybrid functional B3LYP and 6-311G basis sets. When donating groups are attached to the molecular dye, the bond lengths are slightly decreased which is important for easy transfer of electron from donating to the accepting group. For all dyes, highest occupied molecular orbital/lowest occupied molecular orbital analysis results in positive outcomes upon electron injection to semiconductors and subsequent dye regeneration by the electrolyte. The ionization potential increases with increasing conjugation; therefore, the molecular dye attached to thiophene has the highest ionization potential. Meanwhile, a donating group with increased conjugation results in low electron affinity.

Introduction

Fluorescein (FS) is a metal-free organic dye which is a dark orange/red powder and is slightly soluble in water and alcohol. The molecular formula of FS [2-(3-hydroxy-6-oxo-6H-xanthen-9-yl) benzoic acid] is C₂₀H₁₂O₅, its molar mass is 332.31 g mol⁻¹, its density is 1.602 g/mL, and its melting point is 314–316 °C. Generally, FS is a xanthene dye, with the central carbon bonded to a benzoic acid. ¹

FS has absorption spectra in water and alcohol from 380 to 512 nm, and emits from 510 to 517 nm. ² It has high molar absorptivity at the wavelength of an argon laser (488 nm). It has a large fluorescence quantum yield and high photostability, making it a very useful and sensitive fluorescent label. Commercially, many derivatives of FS are available such as fluorescein isothiocyanate and fluorescein succinimidyl ester. ³ FS in an aqueous solution occurs in cationic, neutral, anionic, and dianionic forms as displayed in Figure 1.

Figure 1.

Different forms of fluorescein molecules.

When FS combines in acetonitrile solution, the absorption occurs at 460 nm, while emission occurs in the wavelength range of 500–540 nm. ⁴ FS has many applications such as in forensics and in serology to detect latent bloodstains. It is also used as a diagnostic tool in the field of ophthalmology and optometry. Topical FS is used in the diagnosis of corneal abrasions, corneal ulcers, and herpetic corneal infection. ⁵

Density functional theory (DFT) is an important method for the prediction of the thermodynamic properties and chemical reactivity of molecules. ⁶ Therefore, through applying the DFT method, several reactivity descriptors of FS derivatives can be discussed such as hardness, global softness, chemical potential, electronegativity, electrophilicity, electrofugality, nucleofugality, and other parameters of chemical reactivity.

Computational methods

The molecular structures were optimized in both gas and solvent phases by DFT using the B3LYP/6-311G basis sets. ⁷ All calculations were carried out using the Gaussian 09 software program.^8,9 From these calculations, the optimized geometry and frequencies were also obtained. The calculations have been widely used to study different mechanism such as the reaction mechanism of the molecules. The visual representation of the densities of the highest occupied molecular orbitals (HOMOs) and the lowest occupied molecular orbitals (LUMOs) of all the studied molecules was accomplished with the Gaussian View 05 program. ¹⁰

Theoretical background

DFT is an important method for studying the theoretical chemical reactivity mechanisms of molecules.^6,11 According to Koopmans’ theory, the ionization potential (IP) and electron affinity (EA) are the eigenvalues of HOMO and LUMO energy levels.^11,12 Therefore, the IP and EA can be calculated through the following relations, respectively ¹³

$$\mathrm{IP}=-E_{\mathrm{HOMO}}\mathrm{and}\mathrm{EA}=-E_{\mathrm{LUMO}}$$

(1)

Equation (1) is the basic equation for calculating different global chemical reactivity descriptors of the molecules like electronegativity (χ), chemical potential (µ), electrophilicity (ω), hardness (η), and softness (S). ¹¹ The chemical potential and the hardness of the molecules are defined as the second derivatives of the energy with respect to the number of electrons (N). Equations (2) and (3) display the relationships

$$\eta =\frac{1}{2}\left(\frac{{\partial }^2}{\partial N^2}\right)\mathrm{and}\mu =\frac{\partial E}{\partial N}$$

(2)

where E is the electronic energy, and N is the number of electrons

$$S=\frac{1}{\eta }\mathrm{and}\chi =-\mu =\frac{\partial E}{\partial N}$$

(3)

Using Koopmans’ theory for closed-shell molecules, the electronegativity (χ), chemical potential (µ), and global hardness (η) can be expressed as ¹⁴

$$\chi =\frac{I+A}{2}$$

(4)

Also, the chemical potential (µ) can be defined as

$$\mu \approx \frac{1}{2}\left(\mathrm{IP}+\mathrm{EA}\right)\approx \frac{1}{2}\left({\epsilon }_{\mathrm{HOMO}}-{\epsilon }_{\mathrm{LUMO}}\right)$$

(5)

But the hardness (η) of the molecules is expressed as

$$\eta \approx \frac{1}{2}\left(\mathrm{IP}-\mathrm{EA}\right)\approx \frac{1}{2}\left({\epsilon }_{\mathrm{LUMO}}-{\epsilon }_{\mathrm{HOMO}}\right)$$

(6)

where I and A are the IP and the EA, respectively.

As part of the calculations the eletrophilicity of the molecule can also be discussed. It is a descriptor of the reactivity that allows a quantitative classification of the global electrophilic nature of a molecule within a relative scale. In 2005, Parr et al. proposed that electrophilicity index as a measure of energy lowering due to the maximum of electron flow between the donor and acceptor. Therefore, the electrophilicity index can be defined through the following relation ¹⁵

$$\omega =\frac{{\mu }^2}{2\eta }$$

(7)

where ω is the electrophilicity index, η is the hardness, and µ is the chemical potential.

The maximum amount of electron charge transfer (ΔN_max), which can be accepted by the electrophile, is evaluated from the following equation

$$\Delta N_{\max }=-\frac{\mu }{\eta }$$

(8)

From equation (8), the maximum amount of electron transfer from the nucleophile to the electrophile can be evaluated for each studied molecule.

Finally, the nucleofugality (ΔE_n) and the electrofugality (ΔE_e) of the molecules can be discussed with respect to the nucleophilic and electrophilic capabilities of the leaving group in the molecules.^11,16 A good electrofuge with a high electrofugality will simultaneously dissociate from a substrate and donate an electron, leaving behind an electrophile. Conversely, a good nucleofuge with a high nucleofugality will readily accept an electron from a system, leaving behind a nucleophile. ¹⁷ Therefore, equations (9) and (10) express how the nucleofugality and the electrofugality can be calculated, respectively

$$\Delta E_n=\mathrm{EA}+\omega =\frac{{\left(\mu +\eta \right)}^2}{2\eta }$$

(9)

$$\Delta E_e=\mathrm{IP}+\omega =\frac{{\left(\mu -\eta \right)}^2}{2\eta }$$

(10)

Results and discussion

Molecular geometry

All molecules were fully optimized by DFT using B3LYP with the 6-311G basis set. The optimization of the molecules was performed in the gaseous phase as well as in the solvent phase. Figure 2 shows the optimized structures of the studied molecules.

Figure 2.

The optimized structures of the molecules calculated at the B3LYP/6-311G level.

After optimization, the bond lengths and bond angles were obtained (Table 1). Generally, the bond lengths of the studied molecules slightly decrease after the attachment of an electron-donating group. The decreasing of the bond length helps intramolecular charge transfer from the electron donor to the electron-accepting group. In fluorescein attached with amine (FSA), the C17–C18 bond length increased from 1.3966 to 1.4158 Å and that of other derivatives slightly increased as shown in Figure 3. Also, the C23–O25 bond length in FSA slightly increased in from 1.3735 to 1.3832 Å.

Table 1.

The bond lengths of the fluorescein derivatives determined.

FS		FSA		FSE		FSM		FSO		FST
Bond value (Å)		Bond value (Å)		Bond value (Å)		Bond value (Å)		Bond value (Å)		Bond value (Å)
C1–C2	1.5141	C1–C2	1.514	C1–C2	1.5139	C1–C2	1.5141	C1–C2	1.5138	C1–C2	1.5139
C1–C6	1.3555	C1–C6	1.3558	C1–C6	1.3555	C1–C6	1.3556	C1–C6	1.3555	C1–C6	1.3554
C1–O7	1.3693	C1–O7	1.369	C1–O7	1.3692	C1–O7	1.3691	C1–O7	1.3692	C1–O7	1.3694
C2–C3	1.502	C2–C3	1.502	C2–C3	1.5021	C2–C3	1.502	C2–C3	1.5021	C2–C3	1.5024
C2–C10	1.5354	C2–C10	1.5347	C2–C10	1.5352	C2–C10	1.5349	C2–C10	1.5348	C2–C10	1.5349
C2–H26	1.104	C2–H27	1.1039	C2–H28	1.104	C2–H27	1.104	C2–H28	1.104	C2–H31	1.1043
C3–C4	1.3409	C3–C4	1.3411	C3–C4	1.341	C3–C4	1.341	C3–C4	1.341	C3–C4	1.341
C3–H27	1.0807	C3–H28	1.0806	C3–H29	1.0807	C3–C28	1.0807	C3–H29	1.0807	C3–H32	1.0808
C4–C5	1.4752	C4–C5	1.475	C4–C5	1.4752	C4–C5	1.4752	C4–C5	1.4752	C4–C5	1.4752
C4–H28	1.0813	C4–H29	1.0814	C4–H30	1.0813	C4–H29	1.0814	C4–H30	1.0813	C4–H33	1.0813
C5–C6	1.448	C5–C6	1.4478	C5–C6	1.4479	C5–C6	1.448	C5–C6	1.448	C5–C6	1.448
C5–O21	1.267	C5–O21	1.2674	C5–O21	1.2671	C5–O21	1.2672	C5–O21	1.267	C5–O21	1.2671
C6–H29	1.0801	C6–H30	1.0802	C6–H31	1.0802	C6–H30	1.0802	C6–H31	1.0802	C6–H34	1.0801
O7–C8	1.5339	O7–C8	1.5353	O7–C8	1.534	O7–C8	1.535	O7–C8	1.5339	O7–C8	1.5324
C8–C9	1.5154	C8–C9	1.515	C8–C9	1.5155	C8–C9	1.5151	O8–C9	1.5155	C8–C9	1.5153
C8–C11	1.4857	C8–C11	1.4853	C8–C11	1.4856	C8–C11	1.4853	C8–C11	1.4856	C8–C11	1.4858
C8–H30	1.096	C8–H31	1.096	C8–H32	1.096	C8–H31	1.0959	C8–H32	1.0961	C8–H35	1.0961
C9–C10	1.3566	C9–C10	1.3568	C9–C10	1.3566	C9–C10	1.3568	C9–C10	1.3564	C9–C10	1.3563
C9–C14	1.4544	C9–C14	1.4541	C9–C14	1.4544	C9–C14	1.4543	C9–C14	1.4543	C9–C14	1.4544
C10–C15	1.4926	C10–C15	1.4931	C10–C15	1.4931	C10–C15	1.4927	C10–C15	1.493	C10–C15	1.4931
C11–C12	1.348	C11–C12	1.3481	C11–C12	1.348	C11–C12	1.3481	C11–C12	1.348	C11–12	1.3478
C11–H31	1.0813	C11–H32	1.0812	C11–H33	1.0812	C11–H32	1.0812	C11–H33	1.0813	C11–H36	1.0812
C12–C13	1.456	C12–C13	1.4558	C12–C13	1.456	C12–C13	1.4559	C12–C13	1.4561	C12–C13	1.4562
C12–O22	1.3899	C12–O22	1.3903	C12–O22	1.3898	C12–O22	1.39	C12–O22	1.3898	C12–O22	1.3899
C13–C14	1.3508	C13–C14	1.3511	C13–C14	1.3509	C13–C14	1.351	C13–C14	1.3508	C13–C14	1.3509
C13–H32	1.0799	C13–H33	1.0799	C13–H34	1.0799	C13–H33	1.0799	C13–H34	1.0799	C13–H37	1.0799
C14–H33	1.0803	C14–H34	1.0802	C14–H35	1.0803	C14–H34	1.0803	C14–H35	1.0803	C14–H38	1.0803
C15–C16	1.4032	C15–C16	1.3918	C15–C16	1.3971	C15–C16	1.4013	C15–C16	1.4015	C15–C16	1.3979
C15–C20	1.4176	C15–C20	1.4232	C15–C20	1.4196	C15–C20	1.4167	C15–C20	1.4162	C15–C20	1.4169
C16–C17	1.3965	C16–C17	1.4165	C16–C17	1.4085	C16–C17	1.4029	C16–C17	1.4003	C16–C17	1.4087
C16–H34	1.0806	C16–H35	1.0815	C16–H36	1.0802	C16–H35	1.0815	C16–H36	1.0784	C16–H39	1.0805
C17–C18	1.3966	C17–C18	1.4158	C17–C18	1.4069	C17–C18	1.4038	C17–C18	1.4029	C17–C18	1.4104
C17–H35	1.081	C17–N26	1.3653	C17–C26	1.4728	C17–C26	1.5085	C17–O26	1.3791	C17–C26	1.4602
C18–C19	1.3924	C18–C19	1.3812	C18–C19	1.3891	C18–C19	1.3896	C18–C19	1.3833	C18–C19	1.3864
C18–H36	1.0805	C18–H36	1.0815	C18–H37	1.0815	C18–H36	1.0817	C18–H37	1.0796	C18–H40	1.0797
C19–C20	1.4059	C19–C20	1.4122	C19–C20	1.4046	C19–C20	1.4062	C19–C20	1.411	C19–C20	1.4064
C19–H37	1.0786	C19–H37	1.0791	C19–H38	1.0787	C19–H37	1.0789	C19–H38	1.0785	C19–H41	1.0787
C20–C23	1.4761	C20–C23	1.4576	C20–C23	1.4725	C20–C23	1.4724	C20–C23	1.468	C20–C23	1.4719
O22–H38	0.9732	O22–H38	0.9733	O22–H39	0.9732	O22–H38	0.9733	O22–H39	0.9731	O22–H42	0.9733
C23–O24	1.2421	C23–O24	1.2485	C23–O24	1.243	C23–O24	1.2431	C2–O24	1.2444	C23–O24	1.243
C23–O25	1.3735	C23–O25	1.3832	C23–O25	1.3749	C23–O25	1.3752	C23–O25	1.3771	C23–O25	1.3748
C8–H30	0.9769	O25–H39	0.9763	O25–H40	0.9768	O25–H39	0.9768	O25–H40	0.9766	O25–H43	0.9768
		N26–H40	1.0044	C26–C27	1.3404	C26–H40	1.0904	O26–C27	1.4657	C26–S27	1.8307
		N26–H41	1.0044	C26–H41	1.0852	C26–H41	1.0895	C27–H41	1.0835	C26–C30	1.3724
				C27–H42	1.0814	C26–H42	1.0938	C27–H42	1.0895	S27–C28	1.8003
				C27–H43	1.0825			C27–H43	1.0895	C28–C29	1.3619
										C28–H44	1.075
										C29–C30	1.4315
										C29–H45	1.0794
										C30–H46	1.0796

FS: fluorescein; FSA: fluorescein attached with amine; FSE: fluorescein attached with ethane; FSM: fluorescein attached with methane; FSO: fluorescein attached with methoxy; FST: fluorescein attached with thiophene.

Figure 3.

Selected bond lengths of the studied dye molecules.

At the point of attachment between FS and the electron-donating groups, the bond length values increased as indicated in Figure 4. The bonds formed in the FS derivatives (FSA, fluorescein attached with ethene (FSE), fluorescein attached with methane (FSM), fluorescein attached with methoxy (FSO), and fluorescein attached with thiophene (FST)) after addition of the substituent group are C17–N26, C17–C26, C17–C26, C17–O26, and C17–C26 and their values are 1.3653, 1.4728, 1.5085, 1.3791, and 1.4602 Å, respectively. FSE and FSM have the same bonds, but their values are different because FSE contains π-bond after C26 and FSM has no π-bond after C26. Thus, increasing of the π-conjugate spacer slightly decreases the bond length.

Figure 4.

The bond lengths at the attachment point between the fluorescein and the donor group.

The HOMO/LUMO energies and energy gap (∆E_g)

The HOMO energy actually determines the ability of the molecule to donate an electron. In addition, the higher the value of the HOMO energy, the higher is the electron donation ability to the acceptor. But, the LUMO energy of the molecule indicates the ability to accept an electron. Therefore, the results show that the FSA and FST have the highest HOMO energies and that FSO has the lowest HOMO energy. This means that FST has higher ability to donate an electron, while FSA has the lowest ability to donate an electron. Table 2 displays the HOMO and LUMO energies, and the energy gap between the EA and the ionization energy of the studied molecules. The results indicate that FST has a low band gap (energy gap); this means that the ability to transfer an electron from the ground state to the excited state is very easy. If the energy gap is larger for the molecules, then the ability to transfer an electron from the HOMO to the LUMO will be lower.

Table 2.

The HOMO and LUMO energies, and the energy gap between ionization potential and electron affinity calculated at the DFT/6-311G level.

Dye	HOMO	LUMO	∆Eg
FS	−6.164	−2.248	3.916
FSA	−6.108	−2.091	4.017
FSE	−6.164	−2.42	3.744
FSM	−6.155	−2.204	3.951
FSO	−6.168	−2.179	3.989
FST	−6.171	−2.496	3.675

FS: fluorescein; FSA: fluorescein attached with amine; FSE: fluorescein attached with ethane; FSM: fluorescein attached with methane; FSO: fluorescein attached with methoxy; FST: fluorescein attached with thiophene.

Global molecular reactivity

IP and EA

The IP is the amount of energy required to remove an electron from a molecule, computed as the energy difference between the cation and the neutral molecule. It is negative value of the HOMO energy as displayed in equation (1). The lower the energy used to remove the electron from the molecule, the easier ionization of the molecule, but the higher the energy required to remove the electron, the more difficult the molecule is to ionize. Generally, the IP is affected by the size of the molecule, that is, the higher the molecular size, the lower the IP, and a smaller molecular leads to a higher IP. From the DFT results, it can be seen that the FST dye has a high IP and that the FSA dye has a low ionization (Table 3). The increasing order of IP for the studied dyes is FSA < FSM < FSE = FS < FSO < FST.

Table 3.

Calculated global quantities, ionization potential, electron affinity chemical potential, electronegativity, hardness, softness, and electrophilicity of the different dyes determined at the DFT/B3LYP/6-311G level.

Dye	I	A	χ	η	μ	S	μ 2	2η	Ω	ΔN	ΔEn	ΔEe
FS	6.164	2.248	7.288	1.958	−7.288	0.510725	53.11494	3.916	13.56357	3.722165	11.31557	19.72757
FSA	6.108	2.091	7.1535	2.0085	−7.1535	0.497884	51.17256	4.017	12.739	3.561613	10.648	18.847
FSE	6.164	2.42	7.374	1.872	−7.374	0.534188	54.37588	3.744	14.52347	3.939103	12.10347	20.68747
FSM	6.155	2.204	7.257	1.9755	−7.257	0.506201	52.66405	3.951	13.3293	3.6735	11.1253	19.4843
FSO	6.168	2.179	7.2575	1.9945	−7.2575	0.501379	52.67131	3.989	13.20414	3.638757	11.02514	19.37214
FST	6.171	2.496	7.419	1.8375	−7.419	0.544218	55.04156	3.675	14.9773	4.037551	12.4813	21.1483

FS: fluorescein; FSA: fluorescein attached with amine; FSE: fluorescein attached with ethane; FSM: fluorescein attached with methane; FSO: fluorescein attached with methoxy; FST: fluorescein attached with thiophene.

The EA is the energy released when an electron is added to a neutral molecule, and it is computed as the energy difference between the neutral form and the anion. This parameter is the negative value of the LUMO energy and is calculated as indicated in equation (1). In the studied molecules, FST has the highest EA and FSA has the lowest EA. The decreasing order of EA of the dye is FST > FSE > FS > FSM > FSO > FSA. Table 3 displays the values of each molecule.

Chemical hardness (η)

This is an important descriptor for understanding the behavior of a chemical system, because it measures the resistance to change in the electron distribution of nuclei and electrons, ¹⁸ and it is calculated as indicated in equation (6). It is an important global reactivity indicator for predicting the susceptibility to and the type of reactions a reagent undergoes. ¹⁷ Table 3 displays the chemical hardness of the FS dye derivatives. The results show that the dye with a large energy gap has a large value of chemical hardness and that with a low energy gap has a low chemical hardness. Therefore, from the studied molecules, FSA has a high value of chemical hardness, and FST has a low value of chemical hardness.

Chemical potential (µ)

The chemical potential is the negative of the Mulliken electronegativity. ¹⁹ It is an indicator for a chemical reaction to take place. This means that a reagent with a high electronic chemical potential is a good electron donor, whereas a reagent with small electronic chemical potential is a good electron acceptor. ¹⁷ From the results in Table 3, it can be seen that FSA has a high chemical potential (−7.1535), which is a good electron donor compared with other derivatives. While the FST dye has a small chemical potential (−7.419), it is a good electron acceptor. The chemical hardness and the chemical potential are considered as intrinsic properties of the molecules, and help to give an important guide for the prediction of the product in a chemical reaction. ¹⁹

Electrophilicity (ω)

Electrophilicity is the change in energy that occurs when a reagent is placed in contact with a perfect nucleophile. This descriptor measures the property of electron accepting by molecules. A molecule with good electrophilicity has low chemical potential and low chemical hardness. ¹⁹ Equation (7) helps calculate the electrophilicity of a molecule, and the values are displayed in Table 3. The results indicate that the FSA dye has good electrophilicity properties compared with the other dyes and FST has poor electrophilicity property.

Thermodynamic properties

The thermodynamic properties of the molecular dyes discussed in this study are entropy, dipole moment, heat capacity, and energy of the molecules. The DFT results show that the entropy, heat capacity, and dipole moment of the molecules increased as the conjugation increases. Therefore, FST has a larger dipole moment, heat capacity, entropy, and energy compared with the other molecules (Table 4).

Table 4.

The energies of the dyes enthalpies, free energies, entropies, and dipole moments calculated at the DFT B3LYP/6-311G level.

Dye	Enthalpies	Free energy (eV)	Energy (eV)	CV (eV)	S	Dipole (debye)
FS	−1146.281	−1146.351	197.187	79.213	147.066	9.8233
FSA	−1201.629	−1201.702	208.594	85.349	153.042	9.7597
FSE	−1223.645	−1223.721	219.337	88.045	159.683	9.5789
FSM	−1185.569	−1185.643	215.542	85.285	156.545	9.6031
FSO	−1260.766	−1260.842	218.993	88.765	159.663	8.2833
FST	−1698.029	−1698.112	229.366	96.744	172.411	10.681

FS: fluorescein; FSA: fluorescein attached with amine; FSE: fluorescein attached with ethane; FSM: fluorescein attached with methane; FSO: fluorescein attached with methoxy; FST: fluorescein attached with thiophene.

Conclusion

A donating group attached to a dye molecule results in decreasing of the bond length. A large energy gap results in a lowering of the transfer of electrons from the HOMO to the LUMO. For this case, a dye molecule will easily transfer an electron from the LUMO to a titanium dioxide (TiO₂) electrode. Therefore, it will easily produce electricity.

The molecular geometry was determined through this experiment, and the result indicates that electron donating usually increases the bond length. For the molecule with π-conjugated spacer, the bond length slightly decreases which results in easy transfer of electron. Not only the bond length but also the energy gap helps to determine electron transfer from ground to excited state of the molecule.

The tendency of atom to accept the electron was determined using electrophilicity in which the FSA is good for accepting electron while FST is poor in electron acceptor. Also the experiment was aimed to determine the free energy, heat capacity, enthalpy, and dipole moment of dye which is very important for searching the good dye.