Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2, 1830-1838 2025 Publisher: Learning Gate DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate © 2025 by the authors; licensee Learning Gate History: Received: 20 December 2024; Revised: 28 January 2025; Accepted: 28 January 2025; Published: 20 February 2025 * Correspondence: ghufran.hassan@utq.edu.iq Theoretical investigation of the impact of zinc ion in the center of trimer porphyrins on the electrical and thermoelectric properties Ghofran Zamel Hassan1*, Mohammed Deia Noori2 1,2Department of Physics, College of Sciences, University of Thi-Qar, Thi-Qar, Iraq; ghufran.hassan@utq.edu.iq (G.Z.H.). Abstract: Thermoelectrics as a way to use waste heat is essential in many electronic applications. In this work, the effect of the appearance of zinc ions in the center of trimer porphyrins on the electronic and thermoelectric properties of zinc porphyrin trimer molecular junctions was investigated theoretically using a combination of density functional theory (DFT) methods. Our results show that all electronic and thermoelectric properties have been affected by the appearance of zinc ions in the center of porphyrin trimer units. However, the findings indicate that the presence of a zinc metal ion in the center of the porphyrin trimers with one, two, or three zinc ions significantly affects their electronic and thermal conductance, particularly in the vicinity of the Fermi energy. Keywords: Molecular junctions, Thermoelectrics, Zinc ions. 1. Introduction The performance of thermoelectric materials has been greatly improved by recent developments, allowing for effective waste heat recovery and the production of renewable energy. This helps to meet the pressing need for sustainable energy solutions and reduce greenhouse gas emissions in line with efforts to mitigate climate change [1]. The concept of generating a voltage disparity due to a temperature gradient, known as the Seebeck effect, was initially introduced during the early 19th century[2]. Nowadays, a significant focus has been on enhancing this phenomenon's effectiveness by examining the variables governing thermoelectrical properties, specifically molecular materials and devices. The thermoelectric figure of merit (ZT) is the primary metric for evaluating thermoelectrical materials' effectiveness. It is computed using the formula ZT = S2GT/κ, where S represents the Seebeck coefficient, G denotes the electrical conductance, T signifies the temperature, and κ stands for the electronic thermal conductivity. This equation allows researchers to quantitatively assess the efficiency of thermoelectrical materials by considering their unique properties, such as the Seebeck coefficient, electrical conductance, temperature, and electronic thermal conductivity. Using the ZT value, scientists can compare and contrast different materials and determine their potential for thermoelectrical applications. This metric comprehensively evaluates a material's thermoelectric performance, enabling researchers to make informed decisions regarding developing and optimizing thermoelectrical materials[3-9]. However, a large number of theoretical and experimental investigations have been conducted to produce and manipulate electronic molecules [4, 10-12]. They have been adjusted for future applications in molecular wires and other nanoelectronics circuits [13], biological systems[14, 15], quantum dots [16, 17], electrodes [18, 19] and switches [20, 21]. Porphyrins are characterized by their highly conjugated structure, rigid planar geometry, and remarkable chemical stability, which enable them to form metalloporphyrins through the coordination of metal ions within their macrocyclic framework [22-24]. Of the metalloporphyrin families, zinc 1831 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate porphyrin is one of the most well-known and prevalent. Their complexes' intriguing photochemical and photophysical properties have recently drawn increased attention[25-34]. Specifically, zinc porphyrin derivatives are important because of their distinct structural characteristics and possible uses in a number of industries, such as spintronics, thermoelectric materials, and catalysis [35]. Our previous studies have been done to investigate the thermoelectric characteristics of zinc porphyrins connected to gold electrodes with promising results[10-12, 35-38]. These significant results increase the appeal of zinc porphyrins for molecular-scale thermoelectric devices. Therefore, we believe that more adjustments and changes in zinc porphyrins configurations can impact the thermoelectric properties of zinc porphyrins. Thus, in this work we have introduced a comprehensive investigation of transport properties, electrical and thermoelectric properties of six zinc porphyrin trimers as shown in Fig. 1. The aim of this investigation is to enhance our knowledge and understand how the presence of a zinc atom in the center of porphyrin trimer units impact charge transport, electronic properties, and thermoelectric performance. These factors are critical for advancing the development of molecular-scale devices and applications in nanotechnology [39]. Figure 1. Schematic illustration of the molecular structure junctions investigated consists of the zinc porphyrin trimers: free-based porphyrin trimer (Tr1), porphyrin trimer with one zinc ion in the edge unit of porphyrin trimer (Tr2), porphyrin trimer with one zinc ion in the middle unit of porphyrin trimer (Tr3), porphyrin trimer with two zinc ions in the terminal units of porphyrin trimer (Tr4), porphyrin trimer with two zinc ions in middle and terminal units of porphyrin trimer (Tr5), porphyrin trimer with three zinc ions in all units of porphyrin trimer (Tr6). 1832 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate 2. Methods Density Functional Theory (DFT) is a quantum computational technique that employs complex algorithms to achieve geometrical structure in a variety of molecular systems using quantum physics and quantum chemistry. DFT is used to compute the electronic characteristics of systems with several molecules, where the wave function determines the electron density [40]. All molecular structures of the porphyrin trimers that are shown in Fig.2 were optimized. Using the generalized gradient functional approximation (GGA-PBE), a double-polarized basis set (DZP) for exchange and correlation [41, 42], norm-conserving pseudopotentials, the density functional theory (DFT) package SIESTA code [43], and a real space grid defined with an energy cutoff of 200 Rydberg, the optimization was carried out. Next, we integrate the GOLLUM quantum transport code with the mean-field Hamiltonian H. The transmission coefficient, Tel(E), is found by combining the mean-field Hamiltonian H with the GOLLUM quantum transport code [44]. To calculate electrical conductance, the Landauer formula was employed. Additionally, a thermoelectric material's ability to convert heat into electricity is described by the Seebeck coefficient. Over a large range of Fermi energies, we calculate the thermopower S energies by using the equation S= −𝛥𝑉/𝛥𝑇 = − 1 𝑒𝑇 𝐿1 𝐿0 (1) where ΔT is established between them ΔV is the voltage difference generated between the two ends of the junction when temperature difference, e is the electron charge and Ln can be calculated as 𝐿𝑛 = ∫ (𝐸 − 𝐸𝐹)𝑛𝑇(𝐸) ( 𝜕𝑓(𝐸,𝑇) 𝜕𝐸 ) ∞ −∞ 𝑑𝐸 (2) where 𝑓(𝐸, 𝑇) is the Fermi distribution function defined as 𝑓(𝐸, 𝑇) = [𝑒(𝐸−𝐸𝐹)/𝐾𝐵𝑇 + 1]−1 where KB is Boltzmann’s constant. From Equation (1) it can also be obtained G and K: G =G0 L0 (3) where (G0 =2𝑒2 ℎ⁄ ) is the quantum of conductance, K=1 ℎ𝑇⁄ (𝐿2 − 𝐿1 2 𝐿0⁄ ) (4) This leads to the final evaluation of the figure of merit values (ZT). 3. Results and Discussion To investigate the impact of the presence zinc metal ions in the different centers of the units of porphyrin trimer on the electronic and thermoelectric properties, as shown in Fig. 1. The calculations starting by computing the key quantity which is transmission coefficient T(E) for all configurations that shown in Fig.1. Fig. 2 shows the essential change in transmission coefficient T(E) when moving from free-based porphyrin trimer Tr1 to zinc porphyrin trimer Tr6, passing through Tr2, Tr3, Tr4, and Tr5. Fig.2 reveals that the transmission coefficient T(E) is strongly affected by the presence of a zinc ion in the center porphyrin trimer. The gradual appearance of zinc ions in the center of porphyrin trimer units leads to shifting peaks on the both side of around Fermi energy (comparing black line with green line). 1833 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate Figure 2. The electronic transmission coefficients as a function of energy for all the porphyrin trimers structures are shown in Figure 1. The corresponding room temperature electrical conductance versus energy is presented in Fig. 3. As expected, and reflected in the transmission coefficient in Fig. 2, the electrical conductance decreased with the appearance of zinc ions in the center of porphyrin trimer units. Fig. 3 shows that moving from a free-based porphyrin trimer (black line Tr1) to a zinc porphyrin trimer with three zinc ions in the center of the porphyrin (green line Tr6) leads to a noticeable decrease in electrical conductance around Fermi energy. E-EF(eV) T (E ) -1 -0.5 0 0.5 1 1x10-8 1x10-7 1x10-6 1x10-5 1x10-4 1x10-3 1x10-2 1x10-1 1x100 1x101 Tr1 Tr2 Tr3 Tr4 Tr5 Tr6 1834 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate Figure 3. The electrical conductance (G) as a function of energy for all the ethynyl and phenyl-linked porphyrin trimers molecular structures are presented in Figure 1. Figure 4. The electronic thermal conductivity κ as a function of energy for all the porphyrin trimers structures are presented in Figure 1. E-EF(eV) G /G o -0.6 -0.4 -0.2 0 0.2 0.4 0.6 1x10-6 1x10-5 1x10-4 1x10-3 1x10-2 1x10-1 Tr1 Tr2 Tr3 Tr4 Tr5 Tr6 1835 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate The electronic thermal conductivity of these junctions is shown in Fig.4. This figure shows that the electronic thermal conductivity of free-based porphyrin trimer Tr1 is higher than other structures Tr2, Tr3, Tr4, Tr5, and Tr6. This means that the electronic thermal conductance also decreased with the appearance of zinc ion in porphyrin trimer units. Figure 5. The Seebeck coefficient S (thermopower) for all the porphyrin trimers molecular structures are presented in Figure 1. Figure 5 shows the Seebeck coefficient S over a range of Fermi energies at room temperature for each porphyrin trimers' molecular structures. Fig. 5 demonstrates that both the magnitude and sign of S are sensitive to the appearance of zinc ions at the center of the porphyrin trimers. Structure Tr6 porphyrin with three zinc and Tr5 with two zinc atoms has the highest values, (green line and pink line) around Fermi energy. Figure of merit ZT is the crucial factor that establishes the thermoelectric efficiency. ZT, is inversely proportional to the thermal conductance κ and proportional to the electric conductance G and the square of the Seebeck coefficient S. for all the porphyrin trimers molecular structures, Fig. 6 shows the thermoelectric figure of merit ZT over a range of Fermi energies at room temperature for all the porphyrin trimers molecular structures are shown in Figure 1. Due to the highest value of the Seebeck coefficient S and the low value of electronic thermal conductance κ, Fig. 6 shows that the highest thermoelectric figure of merit ZT value is achieved at Tr1 and Tr4 around EF=0eV but outside this window of energy (-0.1 to 0.1) almost all structures have a good value of ZT. 1836 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 2: 1830-1838, 2025 DOI: 10.55214/25768484.v9i2.4936 © 2025 by the authors; licensee Learning Gate Figure 6. The electronic figure of merit ZT for all the porphyrin trimers molecular structures are presented in Figure 1. 4. Conclusion This work has explored the potential of porphyrin trimer structures for high efficiency thermoelectricity. Our calculations perfectly focused on the correlation between the presence of zinc metal ions in the center of the porphyrin trimer units and electronic and thermoelectric properties. The result demonstrates that in the in all zinc porphyrin trimers, all electrical and thermoelectric properties transmission coefficient, electrical conductance G, thermal conductivity K, thermopower S, and figure of merit ZT have been affected by the appearance of zinc ion in the center of porphyrin trimers. The result demonstrates that the electrical and thermal conductance are decrease by the presence of a zinc metal ion in the center of these trimers. where a noticeable drop in electrical and thermal conductance occurs when a zinc atom appears. Moreover, the thermopower of structures has a noticeable change particularly in the vicinity of Fermi energy leading to varied in ZT values. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. This study followed all ethical practices during writing. 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