Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived

Nobel Kouakou N’guessan; Mamadou Koné Guy Richard; Ouattara Wawohinlin Patrice; Dembélé Georges Stéphane; Kafoumba Bamba; Nahossé Ziao

doi:doi:10.11648/j.mc.20241202.12

Research Article |

Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived

Nobel Kouakou N’guessan, Mamadou Koné Guy Richard, Ouattara Wawohinlin Patrice, Dembélé Georges Stéphane^*, Kafoumba Bamba, Nahossé Ziao

Published in Modern Chemistry (Volume 12, Issue 2)

Received: 18 July 2024 Accepted: 26 August 2024 Published: 11 September 2024

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Abstract

The performance of an organic solar cell is strongly influenced by the structure of the photosensitizer. In this work, the open-circuit voltage (V_OC) and conversion efficiency (η) of a series of coumarin dyes are quantitatively related to the structure of nine coumarin derivatives. The Quantitative Structure Property Relationship (QSPR) is performed using the statistical method of multiple linear regression. In addition, descriptors determined from the ground state at the Cam_B3lyp/6-31G(d, p) level of theory and from the 2D structure of the molecules are mathematically related to the photovoltaic properties. These VOC and η models are accredited with very good statistical indicators (R² = 0.906 and 0.918; Q_cv²= 0.845 and 0.849; S= 0.045 and 0.112; F = 14.524 and 16.846). These statistical indicators confirm the robustness and performance of the models developed. The results show that Voc improves with decreasing surface tension (ts) and increasing number of cycles (cycle). As for the conversion efficiency of light radiation into electrical energy, it is optimal when the light harvesting efficiency (LHE_th) and the excited state lifetime (τ_th) are high. In conclusion, these models have good predictive capabilities and can be used to predict and explain the open-circuit voltage and efficiency of coumarin derivatives that belong to the same field of application.

Published in	Modern Chemistry (Volume 12, Issue 2)
DOI	10.11648/j.mc.20241202.12
Page(s)	33-46
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Solar Cell, Coumarin, DFT, QSPR

1. Introduction

Dye-Sensitized Solar Cells (DSSCs) are a solar cell technology using organic dyes to absorb light and generate electricity

[1-5]

. DSSCs are promising alternative to traditional silicon solar cells because they are less expensive to produce and can be made from abundant materials

[6, 7]

. The dyes used in DSSCs are generally organic compounds that exhibit light absorption properties in the visible range (figure 1).

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Figure 1. Different constituents and functioning principle of a DSSC

[7]

DSSCs are composed of several layers

[7]

. Dye layer, usually based on organic dyes such as coumarins, is adsorbed onto a layer of porous semiconductor material, called electrode material. When sunlight hits dye and it is excited, it releases electrons. These electrons are then captured by electrode material. Subsequently, holes left by the electrons are filled by electrons from a liquid electrolyte or solid material in the opposite layer of DSSC. Dye behaves like an electron pump.

There are several types of dyes, including ruthenium-based dyes, phosphine derivatives and coumarin derivatives

[7]

Coumarin-derived photosensitizers

[8]

. are synthetic and natural organic compounds found in the plant kingdom

[9]

. The dye C343 is the basic motif for the development of coumarin-derived photosensitizers

[10, 11]

. Coumarin dyes offer several advantages for use in DSSCs. They have good light absorption capacity in the visible spectrum, enabling them to convert efficiently solar energy into electricity. In addition, coumarins can be synthesized with a wide variety of molecular structures, enabling researchers to modify their light absorption properties and facilitate electron transfer. Coumarins are chemical compounds with a characteristic structure called a coumarin core. The addition of specific functional groups enhances light absorption, while the use of special molecular structures facilitates electron transfer. Our study focuses on coumarin photosensitizers. This class of solar cell dyes is based on the π-conjugated donor-acceptor (D-π-A) structure)

[12-14]

. The donor is coumarin, which contains an amino group in its structure. The acceptor is cyano acrylic acid. In these compounds, the spacer is a π-conjugated system. It consists of thiophene or methine substituents

[15]

Coumarin-based DSSCs show promising results, with solar-to-electricity conversion efficiencies up to more than 10%. However, it should be noted that coumarin-based DSSCs are not yet widely commercialized and challenges remain to improve their long-term stability. Therefore, in order to improve the performance of these systems, it is important to understand the origin of their photovoltaic properties. The overall objective of this study is to establish a quantitative structure- photovoltaic property relationship (QSPR) for a series of nine coumarin derivatives. The QSPR methodology used in this work consists of establishing a mathematical property function whose variables are molecular descriptors

[16]

2. Material and Methods

2.1. Material and Method of Calcul

The molecular descriptors used in the models are obtained from the 2D structure of the dyes and the ground state molecule. The 2D and 3D descriptors are determined using Chemsketch and Gaussian 09 Rev A.02 software, respectively

[17]

. The minimum energy state is obtained after optimization and frequency calculation. In this study, the density functional theory (DFT) method

[11, 5, 18]

at Cam-B3LYP/6-31G(d,p) is employed for geometry optimization and frequency calculation. In addition to DFT, time-dependent DFT (TD-DFT)

[5]

is used to simulate excited states. This calculation is performed at the TD-Cam-B3LYP/6-31G(d,p) level.

The experimental database consists of nine molecules whose photovoltaic properties in derived solar cells have been determined under the same conditions

[12]

. Compound C343 is the reference. These compounds absorb in the visible region. The introduction of methine (-CH=CH-) groups linked to cyano (-CN) and carboxyl (-COOH) in the structure increases the extent of conjugation. Figure 2 shows the structures of the compounds studied.

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Figure 2. Structures of the coumarin derivatives studied.

Moreover, the introduction of thiophene not only increases conjugation but also stabilizes and performs photovoltaic without affecting absorption properties. Table 1 displays the photovoltaic property values of the coumarin dye solar cells studied.

Table 1. Absorption wavelengths of the coumarin derivatives studied and performance of the corresponding DSSCs)

[12]

Colorant	$λ_{\max}^{abs}$ (nm)	J_sc (mA cm^-2)	V_OC (V)	ff	η(%)
C343	442	4.100	0.410	0.560	0.900
NKX-2311	504	15.200	0.550	0.620	5.200
NKX-2388	493	12.900	0.500	0.640	4.100
NKX-2398	451	11.100	0.510	0.600	3.400
NKX-2586	506	15.100	0.470	0.500	3.500
NKX-2593	510	14.700	0.670	0.730	7.200
NKX-2677	511	14.300	0.730	0.740	7.700
NKX-2753	492	16.100	0.600	0.690	6.700
NKX-2807	566	14.300	0.510	0.730	5.300

These molecules are divided in two groups where six molecules form our training set and three molecules are used for validation.

Experimental properties can be mathematically related to theoretical descriptors. However, if the order of the property under investigation varies from one molecule to another, then the inverse of the base-10 logarithm of the property shall be used.

2.2. Data Analysis Methods

The aim of these methods is to analyze the structural data in order to identify the factors that determine the measured activity.

Some are linear, such as Simple Linear Regression (SLR), Multiple Linear Regression (MLR)

[19]

and Partial Least Squares (PLS)

[20]

. Others are non-linear, such as decision trees

[21]

, neural networks

[22]

, and genetic algorithms

[23]

. These methods are available in software such as Excel

[24]

. Origin Microcal, Minitab, XLSAT

[25]

Statistica, SPSS, to cite only those.

The statistical analysis method used in our study is the Multiple Linear Regression (MLR) method available in XLSAT

[25]

The selection of the best models is based on certain statistical indicators. These include the coefficient of determination R (and its square R²), the standard deviation S, and the Fischer coefficient F. The statistical quality of a model is determined by these three criteria

[26]

. They allow us to assess the accuracy of the values calculated on the test set and describe the internal predictive ability of the model. The coefficient of cross-determination

Q_{CV}^{2}

estimates the external predictive ability of the model. R², S and F refer to the fit between calculated and experimental values: they describe the predictive capacity within the limits of the model and allow us to estimate the accuracy of the values calculated on the training set

[26]

. The cross-validation correlation coefficient

Q_{CV}^{2}

provides information about the predictive power of the model. This predictive power is called "internal" because it is calculated from the structures used to build the model.

The coefficient of determination R²provides an assessment of the dispersion of theoretical values around experimental values.The quality of the model is best when the points are close to the line of best fit

[27]

. The fit of the points to this line can be assessed by the correlation coefficient:

R^{2} = 1 - \frac{\sum {(y_{i, \exp} - {\hat{y}}_{i, th é o})}^{2}}{\sum {(y_{i, \exp} - {\overset{̅}{y}}_{i, \exp})}^{2}}

(1)

Where:

𝑦_{𝑖, 𝑒𝑥}: Experimental value of the photovoltaic property

𝑦_{𝑖, 𝑡ℎé}: Theoretical value of the photovoltaic property

𝑦_{𝑖, 𝑒𝑥}: Average value of the experimental values of the photovoltaic property

The closer the R² value is to 1, the more the theoretical and experimental values are correlated. Furthermore, the variance

σ^{2}

is determined by relationship 2:

σ^{2} = s^{2} = \frac{\sum {(y_{i, \exp} - y_{i, th é o})}^{2}}{n - k - 1}

(2)

Where k is the number of independent variables (descriptors), n is the number of molecules in the test or training set and n-k-1 is the degree of freedom.

The standard deviation S:

S = \sqrt{\frac{\sum {(y_{i, \exp} - y_{i, th é o})}^{2}}{n - k - 1}}

(3)

The Fisher F index is used to measure the level of statistical significance of the model, i.e. the quality of the choice of descriptors making up the model.

F = \frac{\sum {(y_{i, th é o} - y_{i, \exp})}^{2}}{\sum {(y_{i, \exp} - y_{i, th é o})}^{2}} * \frac{n - k - 1}{k}

(4)

The coefficient of determination for cross-validation

Q_{CV}^{2}

is calculated using the following relationship:

Q_{cv}^{2} = \frac{\sum {(y_{i, th é o} - {\overset{̅}{y}}_{i, \exp})}^{2} - \sum {(y_{i, th é o} - y_{i, \exp})}^{2}}{\sum {(y_{i, th é o} - {\overset{̅}{y}}_{i, \exp})}^{2}}

(5)

For Eriksson and al.

[28]

the performance of a mathematical model is characterised by a value of

Q_{CV}^{2}

> 0.5 for a satisfactory model. The model is said to be excellent if

Q_{CV}^{2}

> 0.9. According to them, given a test set, a model will perform well if the acceptance criterion

R^{2} - Q_{cv}^{2} < 0, 3

is met.

2.3. Interpretation and Validation of a QSPR Model

2.3.1. Internal Validation

The influence of compounds in the training set on the model is estimated by internal validation methods. Internal validation of a QSPR model is performed using LOO (Leave-One Out) or LMO (Leave-Many Out) cross-validation, which is quantified by the coefficient

Q_{CV}^{2}

. In this process, a certain number k of molecules are extracted from the initial set of N molecules, and a new model is built with the remaining (N-k) molecules using the selected descriptors (only the regression constants change). This process is then repeated to remove and predict the values of all the molecules in the training set. Depending on the number of molecules removed at each iteration, this refers to Leave-One-Out (LOO) or Leave-Many-Out (LMO), as one or more molecules are removed

[29]

2.3.2. Randomization

To ensure the reliability of a RQSP/RQSA model, randomization tests

[30]

are one of the most widely used techniques. The randomization test is used to assert that the good correlations between the descriptors and the activity or property presented by the RQSA/ RQSP model are not due to chance. To do this, the observations are disordered, for example ten times, by randomly changing the activity column, but the descriptor columns remain unchanged. The result is ten models with specific statistical characteristics. If the randomization of observations leads to reliable predictive models, then the predictive abilities of the constructed RQSA/ RQSP model are not due to chance correlations

[28, 31]

2.3.3. External Validation

External validation tests the reliability and predictive power of the QSAR/QSAR model. The model is applied to a set of molecules not used in its development to determine the correlation between calculated and experimental activities. The higher the correlation, the better the model's ability to predict activities for molecules outside the training set

[32]

. The set of molecules used in this framework is called the validation set. This validation is characterized by the parameters R² (test)

Q_{CV}^{2}

(test). Model validation can be performed by calculating the cross-validation regression coefficient

Q_{CV}^{2}

and the quotient (or ratio) of the theoretical activity to the experimental activity.

This ratio is calculated using the validation set. The model is considered to perform well if

Q_{CV}^{2}

or the ratio is close to one.

Other criteria can be used to check the predictive power of RQSP/RQSA models. They are known as "external validation criteria" or "Tropsha criteria"

[33]

External validation criteria (test series)

R_{Test}^{2} > 0, 7

(Criteria 1)

Q_{Cv Test}^{2} > 0, 6

(Criteria 2)

|R_{Test}^{2} - R_{0}^{2}| \leq 0, 3

(Criteria 3)

\frac{|R_{Test}^{2} - R_{0}^{2}|}{R_{Test}^{2}} < 0, 1

0, 85 \leq k \leq 1, 15

(Criteria 4)

\frac{|R_{Test}^{2} - {R'}_{0}^{2}|}{R_{Test}^{2}} < 0, 1

0, 85 \leq k' \leq 1, 15

(Criteria 5)

With

R^{2} :

Correlation coefficient for molecules in the test series.

R_{0}^{2}

: Correlation coefficient between predicted and experimental values for the test series.

R_{0}^{' 2}

: Correlation coefficient between experimental and predicted values for the test series.

k: is the constant of the correlation line (at the origin) (predicted values vs. experimental values).

k': is the constant of the correlation line (at the origin) (experimental values versus predicted values).

2.4. Photovoltaic Properties Studied

2.4.1. Light Harvesting Efficiency (LHE)

The electron injection efficiency can be approximated theoretically by calculating the light harvesting efficiency (LHE)

[34]

of the dyes. This value must be as high as possible to maximize the induced photocurrent. The LHE is determined by the following expression:

LHE = 1 – 10^-A= 1 – 10^-f(6)

A (or f) is the oscillator strength of the electronic transition of greatest absorbance.

2.4.2. Conversion Efficiency

The conversion efficiency of a system can be calculated from the short-circuit current density (J_SC), the open-circuit voltage (V_OC), the form factor (ff) and the light intensity I_S:

η = \frac{J_{SC} V_{OC} ff}{I_{S}}

(7)

In addition to the properties of the semiconductor and the redox mediator, the photo-physical and electrochemical properties of the photosensitizer will be largely responsible for the cell's performance. Indeed, its oxidation potential will determine the maximum Voc and the absorption properties will determine the short-circuit current

[35]

From this expression, J_SC and I_S cannot be calculated theoretically. The open-circuit voltage (V_OC) is a function of the dye's LUMO energy and the TiO₂ conduction band energy

[36]

by the following expression:

V_OC=

\frac{1}{e}

(E_LUMO- E_CB)(8)

A higher LUMO value results in a higher VOC value.

2.4.3. Excited STATE Lifetime τ

The excited state lifetime is an important factor in the evaluation of the charge transfer efficiency of the dye. A dye with a long excited state lifetime will have an easy electron transfer. The excited state lifetime is calculated by the following formula

[37]

τ = \frac{1, 499}{f E^{2}}

(9)

E and f represent the transition energy and transition oscillator strength respectively.

3. Results and Discussion

3.1. Molecular Descriptors and QSAR Models Obtained

A QSPR model is built from a database of experimental data, but most importantly from molecular descriptors. A large number of descriptors are available. In the case of this study, the 2D and 3D descriptors used (Table 1) are determined using Chemsketch and Gaussian 09 software, respectively

[17]

. The 3D descriptors are obtained from the geometry of the ground state. This minimum energy state is obtained after geometry optimization and frequency calculation using the DFT method at the Cam-B3LYP/6-31G(d,p) level. Table 2 shows the descriptors used in the QSPR model and the values of the photovoltaic properties determined experimentally. The photovoltaic properties, the open circuit voltage V_OC and the conversion efficiency η, are the subject of the study.

Table 2. Molecular descriptors used in the QSPR models.

CODE	Descriptors				Photovoltac property
Colorant	ts	cycle	LHEth	τth	pɳexp	Vocexp
C343	73.900	4	0.832	0.049	0.046	0.410
NKX-2388	64.300	4	0.888	0.136	-0.613	0.500
NKX-2586	61.900	4	0.992	0.078	-0.544	0.470
NKX-2677	74.200	6	0.98	0.107	-0.886	0.730
NKX-2753	59.000	5	0.986	0.085	-0.826	0.600
NKX-2807	73.000	5	0.985	0.09	-0.724	0.510
NKX-2311	62.900	4	0.972	0.095	-0.716	0.550
NKX-2398	58.500	4	0.806	0.155	-0.531	0.510
NKX-2593	68.200	5	0.986	0.096	-0.857	0.670

The interdependence of both descriptors is elucidated by a correlation matrix analysis (Table 2). The descriptors used in a QSPR model must be independent of each other. This non-dependence is verified for a cross-correlation coefficient a_ij less than 0.7. Examination of Table 3 shows that all a_ij coefficients are less than 0.7. Hence, the descriptors used in the different models are independent of each other.

Table 3. Cross Correlation Coefficients for Descriptors Used in QSPR Models.

Variables	LHE_th	τ_th	ts	cycle
LHE_th	1	0.188	-0.305	0.566
τ_th	0.188	1	-0.189	0.216
ts	-0.305	-0.189	1	0.345
cycle	0.566	0.216	0.345	1

Using linear regression, the descriptors are mathematically related to the photovoltaic property: this is called a QSPR model. The number of descriptors involved in a model must be equal to 1/5 of the number of molecules in the series studied. In our study, the models obtained are a function of two descriptors corresponding to 1/5 of the nine molecules of the coumarin series studied.

For the purposes of this study, this experimental database is divided into two parts. A first set of six molecules constitutes the learning set, while the remaining three molecules constitute the validation set. The validation set for the QSPR conversion efficiency model consists of the compounds NKX-2593, NKX-2677 and NKX-2807, while the validation set for the QSPR open circuit voltage V_OC model consists of the molecules NKX-2311, NKX-2398 and NKX-2593.

The best QSPR model obtained for open circuit voltage is a function of the 2D descriptor surface tension (ts) and the number of cycles contained in the coumarin derivative structure (cycle). The equation for this QSPR open circuit voltage model is:

Voc_exp= 0.19124 – 0.00455*ts + 0.14001*cycle(10)

The negative surface voltage coefficient indicates that an increase in the value of this parameter reduces the open-circuit voltage. However, increasing the number of cycles will increase the open-circuit voltage of the photovoltaic cell.

The relative contribution of the descriptors to open-circuit voltage prediction (Figure 3) is also studied.

Examination of the contributions shows that the conversion efficiency of a solar cell is closely related to its light-harvesting efficiency and the lifetime of the excited state of the photosensitizer. Examination of this equation shows that pɳ_exp increases as LH_Eth and τ_th decrease. In other words, the conversion efficiency ɳexp increases as LHE_th and τ_th increase. Light-harvesting efficiency is the key to maximizing electricity production from solar energy. Solar panels are designed to capture sunlight and convert it to electricity. The efficiency of solar panels depends on factors such as the quality of the materials used, the panel design, and the ability to absorb sunlight efficiently over a wide range of wavelengths. Thus, improving light-harvesting efficiency is a constant goal to optimize the performance of optical devices and maximize energy yields. The excited state lifetime of a photosensitizer, also known as the excitation lifetime, refers to the amount of time the photosensitizer remains in an excited state after absorbing light. This parameter is important in fields such as photobiology, photochemistry, and photodynamics. The longer the excitation lifetime, the greater the chance that the chromophore will transfer its electron to the semiconductor, such as titanium dioxide.

Furthermore, in this model, the light harvesting efficiency (LHE_th) is the primary descriptor in predicting the conversion yield of coumarin derivatives. This is clarified by analyzing the contribution of each descriptor (Figure 4). The number of aromatic rings is the main descriptor. Thus, an increase in the number of cycles, and therefore in the extent of conjugation, improves open-circuit voltage. In fact, in cycles, electrons do not belong to the atoms but to the cycle, which increases their mobility.

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Figure 3. Contribution of the various descriptors used in the model.

In addition to open-circuit voltage, the conversion efficiency η of light radiation into electrical energy is related to descriptors. The conversion efficiency η is a key parameter for assessing the efficiency of converting light energy into electrical energy. Using the multilinear regression method, the opposite of the logarithm to base ten (pɳ_exp = -log(ɳ_exp)) is mathematically related to descriptors. Table 2 shows the values of the descriptors and the photovoltaic property under study.

The equation of the QSPR-pɳ_exp model is as follows:

pɳ_exp= 3.13044-3.35340*LHE_th-6.02687*τ_th(11)

The conversion efficiency of a solar cell is closely related to its light-harvesting efficiency and the lifetime of the excited state of the photosensitizer. Examination of this equation shows that pɳexp increases as LHEth and τth decrease. In other words, the conversion efficiency ɳexp increases as LHEth and τth increase. Light-harvesting efficiency is the key to maximizing electricity production from solar energy. Solar panels are designed to capture sunlight and convert it to electricity. The efficiency of solar panels depends on factors such as the quality of the materials used, the panel design, and the ability to absorb sunlight efficiently over a wide range of wavelengths. Thus, improving light-harvesting efficiency is a constant goal to optimize the performance of optical devices and maximize energy yields. The excited state lifetime of a photosensitizer, also known as the excitation lifetime, refers to the amount of time the photosensitizer remains in an excited state after absorbing light. This parameter is important in fields such as photobiology, photochemistry, and photodynamics. The longer the excitation lifetime, the greater the chance that the chromophore will transfer its electron to the semiconductor, such as titanium dioxide.

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Figure 4. Contribution of descriptors in the QSPR-pɳ_exp model.

3.2. Internal and External Validation of the QSPR Models

3.2.1. Internal Validation and Significance of the Models

The statistical indicators for the QSPR-VOC and QSPR-ɳ_exp models are shown in Table 4.

Table 4. Statistical indicators.

QSPR model	Voc	ɳ_exp
Indicators statistical	Value
Number of compounds N	9
Correlation coefficient of the regression line R²	0.906	0.918
Prediction correlation coefficient $Q_{cv}^{2}$	0.845	0.849
Standard Deviation	0.045	0.112
Validation of Fischer F	14.524	16.846
Confidence level α	95%

Statistical analysis was used to determine the significance of the model. The values of the statistical indicators determined are summarized in Table 4.

The values of the statistical indicators listed in this table reflect a good correlation of the property with surface tension and the number of cycles in the different molecules. The correlation coefficient 𝑅² indicates that 90.64% of the molecular descriptors were taken into account in establishing the model. Moreover, the standard deviation of 0.045 reflects the consistency of the method used. The significance of the model is given by the Fischer coefficient F= 14.524: this high value reflects a strong relationship between the photovoltaic property and the descriptors used in the model. Also, the value of the Q_CV² cross-validation coefficient of determination is 0.845. This value (greater than 0.5 and close to 0.9) indicates that the model is highly satisfactory. The acceptability of this model is proven by calculating the absolute value of the difference between 𝑅² and Q_CV². This difference (0.062), which is less than 0.3, testifies the model's acceptability.

As for the QSPR-ɳ_exp model, molecular descriptors (LHE et τ) are taken into account at 91.82%, with a standard deviation of 0.112. This model is significant with a Fischer coefficient (F= 16.846) above the Fischer threshold. This indicator shows a strong relationship between conversion yield and the descriptors. This model is acceptable and very satisfactory with a cross-validation correlation coefficient Q_CV² = 0.849 ˃ 0.5 and

|R^{2} - Q_{cv}^{2}| = 0, 069 < 0, 3

Internal validation is achieved by calculating Roy's parameter. This key parameter of the randomization test is obtained after ten (10) iterations. The randomization test is performed only on the compounds in the test set, as the model is based on these. We have limited ourselves to ten iterations. The randomized coefficients of determination (R²_r) for each iteration are given in the following Table 5:

Table 5. Randomized coefficients of determination (R²_r).

QSPR-V_OC model
Iterations	1	2	3	4	5	6	7	8	9	10
$R_{r}^{2}$	0,841	0,842	0,535	0,012	0,092	0,027	0,027	0,101	0,101	0,101
QSPR- ɳ_exp model
Iterations	1	2	3	4	5	6	7	8	9	10
$R_{r}^{2}$	0,852	0,804	0,840	0,321	0,276	0,711	0,790	0,472	0,461	0,251

Roy's parameter (R²_p =0.679 and 0.506) is lower than the model's R² coefficient (0.911), so we can confirm that the pattern established is not due to chance.

3.2.2. External Validation of QSPR Models

External validation is carried out using the ratio (Theoretical property/Experimental property) and the Trophsa criteria. The Voc_th/Voc_exp ratio is determined for all nine molecules. The values are shown in Table 6.

The values of the Vocth/Vocexp ratio of the validation set, which tend towards unity (Table 6.), reflect the good correlation between the theoretical and experimental open-circuit voltage of coumarin molecules.

The model can therefore be used to predict the properties of other coumarin molecules. These observations are confirmed by the regression line corresponding to the QSPR-Voc model (Figure 5). The blue points correspond to the test set and the red points correspond to the validation set. In addition to the Voc_th/Voc_exp ratio, Tropsha criteria are used for external model validation. The Tropsha criteria are listed in Table 7.

Table 6. Experimental and theoretical open-circuit voltage values of the QSPR-Voc model.

Colorants	Voc_exp	Voc_th	Voc_th/Voc_exp
Training set
C343	0.410	0.415	1.013
NKX-2388	0.500	0.459	0.918
NKX-2586	0.470	0.470	1.000
NKX-2677	0.730	0.694	0.951
NKX-2753	0.600	0.623	1.038
NKX-2807	0.510	0.559	1.097
Validation set
NKX-2311	0.550	0.465	0.846
NKX-2398	0.510	0.485	0.951
NKX-2593	0.670	0.581	0.867

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Figure 5. Model linear regression line QSPR-Voc.

Table 7. Tropsha Criteria.

Tropsha criteria	$R_{Test}^{2}$	$Q_{cv Test}^{2}$	$\|R_{Test}^{2} - R_{0}^{2}\|$	$\frac{\|R_{Test}^{2} - R_{0}^{2}\|}{R_{Test}^{2}}$	$\frac{\|R_{Test}^{2} - R_{0}^{' 2}\|}{R_{Test}^{2}}$	k	k’
QSPR-Voc model	0.845	0.845	0	0	0.007	1.131	0.886
QSPR-ɳ model	0.849	0.849	0	0	0.172	0.916	1.088

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Figure 6. Model linear regression line QSPR-pɳ.

All values satisfy the Tropsha criteria, so these models are acceptable for predicting the photovoltaic properties of coumarins.

External validation of this QSPR-n_exp model is performed using the pn_th/pn_exp ratio and Tropsha criteria. The pn_th/pn_exp ratio values reported in the table are close to unity. These values indicate the good correlation between theoretical and experimental conversion efficiencies. This is illustrated by the model's regression line (figure 6). This model therefore offers a better prediction of the conversion yields of the coumarin derivatives in the validation set.

Table 8. pn_th/pn_exp ratio values.

Colorants	pɳ exp	pɳ_th	pn_th/pn_exp
Training set
C343	0.046	0.045	0.986
NKX-2311	-0.716	-0.702	0.980
NKX-2388	-0.613	-0.667	1.089
NKX-2398	-0.532	-0.507	0.953
NKX-2586	-0.544	-0.666	1.225
NKX-2753	-0.826	-0.688	0.833
Validation set
NKX-2593	-0.857	-0.755	0.880
NKX-2677	-0.887	-0.801	0.903
NKX-2807	-0.724	-0.715	0.987

With respect to the Tropsha criteria listed in Table 8, examination of this table shows that all five Tropsha criteria are met. Therefore, this model is acceptable for predicting the photovoltaic properties of coumarins that belong to the same field of application.

3.3. Scope of Applicability

A QSPR model can be used to determine the property value for systems belonging to the same family. However, this prediction is only possible if the system belongs to the same applicability domain. This applicability domain is obtained by determining the threshold lever from the standardized residuals. Analysis of this graph indicates that a molecule belongs to the same applicability domain if the value of its lever is less than 1 (hthreshold =1).

A QSPR model cannot be considered universal because it is developed on a limited number of compounds that do not cover the entire chemical space. For this reason, the predicted property of a compound that is chemically dissimilar to the training set cannot be considered reliable. The applicability domain defines the range in which a compound can be predicted with confidence. It therefore corresponds to the region of chemical space that includes compounds from the training set and similar, nearby compounds in the same space. This region is defined by a threshold lever. For the QSPR model, the threshold lever is one (Figures 7 and 8). Thus, the prediction of the conversion yield of a coumarin derivative using this model is reliable only if the compound has a leverage value less than unity.

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Figure 7. Domain of application of QSPR-Voc model.

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Figure 8. Scope of application of the QSPR-conversion efficiency model.

4. Conclusion

In this work, the photovoltaic properties of a series of nine coumarin derivatives are related to molecular descriptors using QPSR methodology. The photovoltaic properties studied are open circuit voltage and conversion efficiency. Molecular descriptors are related to these photovoltaic properties using multiple linear regression. The best QSPR model obtained for the open-circuit voltage is a function of the surface tension (ts) and the number of aromatic rings in the coumarin derivative structure. As for the light conversion efficiency, the best QSPR model obtained depends on the light harvesting efficiency (LHE_th) and the excited state lifetime (τ_th). Furthermore, the open-circuit voltage is strongly influenced by the aromatic ring number, while the conversion efficiency is closely related to the light collection efficiency. These V_OC and η models are accredited with very good statistical indicators

R^{2}

= 0.906 – 0.918;

Q_{cv}^{2}

= 0.845 – 0.849; S= 0.045 – 0.112; F=14.524 – 16.846, highlighting their acceptability and performance in predicting open-circuit voltage characteristics and conversion efficiency (V_OC and ɳ). These models are not arbitrary. All five Tropsha criteria are met, demonstrating the predictive effectiveness of the established models. The significance of these two QSPR models through validity tests and ranges of applicability will play an important role in understanding the relationship between the selected descriptors and the photovoltaic properties of coumarin derivatives. This study could help us to design new photovoltaic compounds of coumarin derivatives with improved properties.

Abbreviations

DSSC	Dye-Sensitized Solar Cells
QSPR	Quantitative Structure- Property Relationship
DFT	Density Functional Theory
TD-DFT	Time-Dependent DFT
SLR	Simple Linear Regression
MLR	Multiple Linear Regression
PLS	Partial Least Squares
LOO	Leave-One Out
LMO	Leave-Many Out
V_OC	Open-Circuit Voltage

Author Contributions

Nobel Kouakou N’guessan: Conceptualization, Formal Analysis, Methodology

Mamadou Koné Guy Richard: Formal Analysis, Methodology, Writing – original draft

Ouattara Wawohinlin Patrice: Formal Analysis, Methodology

Dembélé Georges Stéphane: Methodology, Software, Validation, Writing – original draft

Kafoumba Bamba: Formal Analysis, Supervision, Writing – original draft

Nahossé Ziao: Formal Analysis, Methodology, Supervision, Writing – original draft

Conflicts of Interest

The authors declare no conflicts of interest.

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N’guessan, N. K., Richard, M. K. G., Patrice, O. W., Stéphane, D. G., Bamba, K., et al. (2024). Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Modern Chemistry, 12(2), 33-46. https://doi.org/10.11648/j.mc.20241202.12

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N’guessan, N. K.; Richard, M. K. G.; Patrice, O. W.; Stéphane, D. G.; Bamba, K., et al. Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Mod. Chem. 2024, 12(2), 33-46. doi: 10.11648/j.mc.20241202.12

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AMA Style

N’guessan NK, Richard MKG, Patrice OW, Stéphane DG, Bamba K, et al. Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Mod Chem. 2024;12(2):33-46. doi: 10.11648/j.mc.20241202.12

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@article{10.11648/j.mc.20241202.12,
  author = {Nobel Kouakou N’guessan and Mamadou Koné Guy Richard and Ouattara Wawohinlin Patrice and Dembélé Georges Stéphane and Kafoumba Bamba and Nahossé Ziao},
  title = {Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived
},
  journal = {Modern Chemistry},
  volume = {12},
  number = {2},
  pages = {33-46},
  doi = {10.11648/j.mc.20241202.12},
  url = {https://doi.org/10.11648/j.mc.20241202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mc.20241202.12},
  abstract = {The performance of an organic solar cell is strongly influenced by the structure of the photosensitizer. In this work, the open-circuit voltage (VOC) and conversion efficiency (η) of a series of coumarin dyes are quantitatively related to the structure of nine coumarin derivatives. The Quantitative Structure Property Relationship (QSPR) is performed using the statistical method of multiple linear regression. In addition, descriptors determined from the ground state at the Cam_B3lyp/6-31G(d, p) level of theory and from the 2D structure of the molecules are mathematically related to the photovoltaic properties. These VOC and η models are accredited with very good statistical indicators (R2 = 0.906 and 0.918; Qcv2= 0.845 and 0.849; S= 0.045 and 0.112; F = 14.524 and 16.846). These statistical indicators confirm the robustness and performance of the models developed. The results show that Voc improves with decreasing surface tension (ts) and increasing number of cycles (cycle). As for the conversion efficiency of light radiation into electrical energy, it is optimal when the light harvesting efficiency (LHEth) and the excited state lifetime (τth) are high. In conclusion, these models have good predictive capabilities and can be used to predict and explain the open-circuit voltage and efficiency of coumarin derivatives that belong to the same field of application.
},
 year = {2024}
}

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TY  - JOUR
T1  - Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived

AU  - Nobel Kouakou N’guessan
AU  - Mamadou Koné Guy Richard
AU  - Ouattara Wawohinlin Patrice
AU  - Dembélé Georges Stéphane
AU  - Kafoumba Bamba
AU  - Nahossé Ziao
Y1  - 2024/09/11
PY  - 2024
N1  - https://doi.org/10.11648/j.mc.20241202.12
DO  - 10.11648/j.mc.20241202.12
T2  - Modern Chemistry
JF  - Modern Chemistry
JO  - Modern Chemistry
SP  - 33
EP  - 46
PB  - Science Publishing Group
SN  - 2329-180X
UR  - https://doi.org/10.11648/j.mc.20241202.12
AB  - The performance of an organic solar cell is strongly influenced by the structure of the photosensitizer. In this work, the open-circuit voltage (VOC) and conversion efficiency (η) of a series of coumarin dyes are quantitatively related to the structure of nine coumarin derivatives. The Quantitative Structure Property Relationship (QSPR) is performed using the statistical method of multiple linear regression. In addition, descriptors determined from the ground state at the Cam_B3lyp/6-31G(d, p) level of theory and from the 2D structure of the molecules are mathematically related to the photovoltaic properties. These VOC and η models are accredited with very good statistical indicators (R2 = 0.906 and 0.918; Qcv2= 0.845 and 0.849; S= 0.045 and 0.112; F = 14.524 and 16.846). These statistical indicators confirm the robustness and performance of the models developed. The results show that Voc improves with decreasing surface tension (ts) and increasing number of cycles (cycle). As for the conversion efficiency of light radiation into electrical energy, it is optimal when the light harvesting efficiency (LHEth) and the excited state lifetime (τth) are high. In conclusion, these models have good predictive capabilities and can be used to predict and explain the open-circuit voltage and efficiency of coumarin derivatives that belong to the same field of application.

VL  - 12
IS  - 2
ER  -

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Author Information

Nobel Kouakou N’guessan

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Mamadou Koné Guy Richard

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Ouattara Wawohinlin Patrice

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Dembélé Georges Stéphane

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Kafoumba Bamba

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Nahossé Ziao

Thermodynamics and Physical Chemistry of the Environment Laboratory, Unit of Formation and Recherche Sciences Fondamentales et Appliquée, University of Nangui Abrogoua, Abidjan, Ivory Cost

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Plain Text BibTeX RIS

APA Style

N’guessan, N. K., Richard, M. K. G., Patrice, O. W., Stéphane, D. G., Bamba, K., et al. (2024). Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Modern Chemistry, 12(2), 33-46. https://doi.org/10.11648/j.mc.20241202.12

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ACS Style

N’guessan, N. K.; Richard, M. K. G.; Patrice, O. W.; Stéphane, D. G.; Bamba, K., et al. Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Mod. Chem. 2024, 12(2), 33-46. doi: 10.11648/j.mc.20241202.12

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AMA Style

N’guessan NK, Richard MKG, Patrice OW, Stéphane DG, Bamba K, et al. Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived. Mod Chem. 2024;12(2):33-46. doi: 10.11648/j.mc.20241202.12

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@article{10.11648/j.mc.20241202.12,
  author = {Nobel Kouakou N’guessan and Mamadou Koné Guy Richard and Ouattara Wawohinlin Patrice and Dembélé Georges Stéphane and Kafoumba Bamba and Nahossé Ziao},
  title = {Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived
},
  journal = {Modern Chemistry},
  volume = {12},
  number = {2},
  pages = {33-46},
  doi = {10.11648/j.mc.20241202.12},
  url = {https://doi.org/10.11648/j.mc.20241202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mc.20241202.12},
  abstract = {The performance of an organic solar cell is strongly influenced by the structure of the photosensitizer. In this work, the open-circuit voltage (VOC) and conversion efficiency (η) of a series of coumarin dyes are quantitatively related to the structure of nine coumarin derivatives. The Quantitative Structure Property Relationship (QSPR) is performed using the statistical method of multiple linear regression. In addition, descriptors determined from the ground state at the Cam_B3lyp/6-31G(d, p) level of theory and from the 2D structure of the molecules are mathematically related to the photovoltaic properties. These VOC and η models are accredited with very good statistical indicators (R2 = 0.906 and 0.918; Qcv2= 0.845 and 0.849; S= 0.045 and 0.112; F = 14.524 and 16.846). These statistical indicators confirm the robustness and performance of the models developed. The results show that Voc improves with decreasing surface tension (ts) and increasing number of cycles (cycle). As for the conversion efficiency of light radiation into electrical energy, it is optimal when the light harvesting efficiency (LHEth) and the excited state lifetime (τth) are high. In conclusion, these models have good predictive capabilities and can be used to predict and explain the open-circuit voltage and efficiency of coumarin derivatives that belong to the same field of application.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Quantitative Structure Photovoltaic Properties Relationship of Coumarin Dyes Derived

AU  - Nobel Kouakou N’guessan
AU  - Mamadou Koné Guy Richard
AU  - Ouattara Wawohinlin Patrice
AU  - Dembélé Georges Stéphane
AU  - Kafoumba Bamba
AU  - Nahossé Ziao
Y1  - 2024/09/11
PY  - 2024
N1  - https://doi.org/10.11648/j.mc.20241202.12
DO  - 10.11648/j.mc.20241202.12
T2  - Modern Chemistry
JF  - Modern Chemistry
JO  - Modern Chemistry
SP  - 33
EP  - 46
PB  - Science Publishing Group
SN  - 2329-180X
UR  - https://doi.org/10.11648/j.mc.20241202.12
AB  - The performance of an organic solar cell is strongly influenced by the structure of the photosensitizer. In this work, the open-circuit voltage (VOC) and conversion efficiency (η) of a series of coumarin dyes are quantitatively related to the structure of nine coumarin derivatives. The Quantitative Structure Property Relationship (QSPR) is performed using the statistical method of multiple linear regression. In addition, descriptors determined from the ground state at the Cam_B3lyp/6-31G(d, p) level of theory and from the 2D structure of the molecules are mathematically related to the photovoltaic properties. These VOC and η models are accredited with very good statistical indicators (R2 = 0.906 and 0.918; Qcv2= 0.845 and 0.849; S= 0.045 and 0.112; F = 14.524 and 16.846). These statistical indicators confirm the robustness and performance of the models developed. The results show that Voc improves with decreasing surface tension (ts) and increasing number of cycles (cycle). As for the conversion efficiency of light radiation into electrical energy, it is optimal when the light harvesting efficiency (LHEth) and the excited state lifetime (τth) are high. In conclusion, these models have good predictive capabilities and can be used to predict and explain the open-circuit voltage and efficiency of coumarin derivatives that belong to the same field of application.

VL  - 12
IS  - 2
ER  -

Copy | Download