Spin-Orbit Coupling Effect on the Electrophilicity Index, Chemical Potential, Hardness and Softness of Neutral Gold Clusters: A Relativistic Ab-initio Study

Mahnaz Jabbarzadeh Sani

Abstract


Electrophilicity index (𝜔) is related to the energy lowering associated with a maximum amount of electron flow between a donor and an acceptor and possesses adequate information regarding structure, stability, reactivity and interactions. Chemical potential (μ) measures charge transfer from a system to another having a lower value of μ, while chemical hardness (η) is a measure of characterizing relative stability of clusters. The main purpose of the present research work is to examine the Spin-Orbit Coupling (SOC) effect on the behavior of the electrophilicity index, chemical potential, hardness and softness of neutral gold clusters Aun (n=2-6). Using the second-order Douglas-Kroll-Hess Hamiltonian, geometries are optimized at the DKH2-B3P86/DZP-DKH level of theory. Spin-orbit coupling energies are computed using the fourth-order Douglas-Kroll-Hess Hamiltonian, generalized Hartree-Fock method and all-electron relativistic double-ζ level basis set. Then, spin-orbit coupling (SOC) corrections to the electrophilicity index, chemical potential, hardness and softness are calculated. It is revealed that spin-orbit correction to the vertical chemical hardness has important effect on Au3 and Au6, i.e. SOC decreases (increases) the hardness of gold trimer (hexamer). Due to the relationship between hardness and softness, σ = , inclusion of spin-orbit coupling increases (decreases) the softness of Au3 (Au6) and thus destabilizes (stabilizes) it. Spin-orbit coupling (SOC) also has more important effect on the chemical potential of Au3 by decreasing its value. It is found that spin-orbit coupling has considerable effect on the electrophilicity index of gold trimer and greatly increases its value. Furthermore, SOC increases the maximal charge acceptance of Au3 more and thus destabilizes it more. As a result, spin-orbit coupling effect appears to be important in calculating the electrophilicity index of the gold trimer.

 

Doi: 10.28991/HIJ-2021-02-01-05

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Keywords


Density Functional Theory; Douglas-Kroll-Hess; Electronic Properties; Gold Clusters; Spin-orbit Coupling.

References


Liu, W., Zhang, Z., Zhang, Z. M., Hao, P., Ding, K. & Li, Z. (2019). Integrated phenotypic screening and activity-based protein profiling to reveal potential therapy targets of pancreatic cancer. Chem. Commun., 55, 1596-1599. doi:10.1039/C8CC08753A.

Kurdekar, A. D., Chunduri, L. A. A., Manohar, C. S., Haleyurgirisetty, M. K., Hewlett, I. K. & Venkataramaniah, K. (2018). Streptavidin-conjugated gold nanoclusters as ultrasensitive fluorescent sensors for early diagnosis of HIV infection. Sci. Adv., 4, eaar6280. doi:10.1126/sciadv.aar6280.

Kaur, N., Aditya, R. N., Singh, A. & Kuo, T. R. (2018). Biomedical Applications for Gold Nanoclusters: Recent Developments and Future Perspectives. Nanoscale Res. Lett., 13, 302. doi:10.1186/s11671-018-2725-9.

Liu, M., Tang, F., Yang, Z., Z. Xu, J. & Yang, X. (2019). Recent Progress on Gold-Nanocluster-Based Fluorescent Probe for Environmental Analysis and Biological Sensing. J. Anal. Methods Chem., 2019, 1-10. doi:10.1155/2019/1095148.

Xu, D. D., Zheng, B., Song, C. Y., Lin, Y., Pang, D. W. & Tang, H. W. (2019). Metal-enhanced fluorescence of gold nanoclusters as a sensing platform for multi-component detection. Sens. Actuators B Chem., 282, 650-658. doi:10.1016/j.snb.2018.11.122.

Liu, L. & Corma, A. (2018). Metal Catalysts for Heterogeneous Catalysis: From Single Atoms to Nanoclusters and Nanoparticles. Chem. Rev., 118, 4981-5079. doi:10.1021/acs.chemrev.7b00776.

Higaki, T., Li, Y., Zhao, S., Li, Q., Li, S., Du, X. S., Yang, S., Chai, J. & Jin, R. (2019). Atomically Tailored Gold Nanoclusters for Catalytic Application. Angew. Chem. Int. Ed., 58, 8291-8302. doi:10.1002/anie.201814156.

Kumar, B., Kawawaki, T., Shimizu, N., Imai, Y., Suzuki, D., Hossain, S., Nair, L. V. & Negishi, Y. (2020). Gold nanoclusters as electrocatalysts: size, ligands, heteroatom doping, and charge dependences. Nanoscale, 12, 9969-9979. doi:10.1039/D0NR00702A.

Jorge, F. E. & Santos, A. S. (2018). Structures Stabilities Reactivities and (Hyper) Polarizabilities of Small Gold Clusters. J. Braz. Chem. Soc., 29, 838-844. doi:10.21577/0103-5053.20170207.

Baek, H., Moon, J. & Kim, J. (2017). Benchmark Study of Density Functional Theory for Neutral Gold Clusters, Aun (n = 2–8). J. Phys. Chem. A, 121, 2410-2419. doi:10.1021/acs.jpca.6b11868.

Singh, N. B. & Sarkar, U. (2015). Geometry chemical reactivity and Raman spectra of gold clusters. Cogent Chem., 1, 1076713. doi:10.1080/23312009.2015.1076713.

Nhat, P. V., Si, N. T., Leszczynski, J. & Nguyen, M. T. (2017). Another look at structure of gold clusters Aun from perspective of phenomenological shell model. Chem. Phys., 493, 140-148. doi:10.1016/j.chemphys.2017.06.009.

Xiao, L. & Wang, L. (2004). From planar to three-dimensional structural transition in gold clusters and the spin-orbit coupling effect. Chem. Phys. Lett., 392, 452-455. doi:10.1016/j.cplett.2004.05.095.

Shi, Y. K., Li, Z. H. & Fan, K. N. (2010). Validation of Density Functional Methods for the Calculation of Small Gold Clusters. J. Phys. Chem. A, 114, 10297-10308. doi:10.1021/jp105428b.

Flores, M. A. & Menéndez-Proupin, E. (2016). Spin-orbit coupling effects in gold clusters: The case of Au13. J. Phys. Conf. Ser., 720, 012034. doi:10.1088/1742-6596/720/1/012034.

Rusakov, A. A., Rykova, E., Scuseria, G. E. & Zaitsevskii, A. (2007). Importance of spin-orbit effects on the isomerism profile of Au3: An ab initio study. J. Chem. Phys., 127, 164322. doi:10.1063/1.2795710.

Afshar, M. & Sargolzaei, M. (2013). Spin and orbital magnetism of coinage meta trimers (Cu3, Ag3, Au3): A relativistic density functional theory study. AIP Adv., 3, 112122. doi:10.1063/1.4834336.

Shayeghi, A., Pašteka, L. F., Götz, D. A., Schwerdtfeger, P. & Schäfer, R. (2018). Spin-orbit effects in optical spectra of gold-silver trimers. Phys. Chem. Chem. Phys., 20, 9108-9114. doi:10.1039/c8cp00672e.

Jiang, D. E., Kühn, M., Tang, Q. & Weigend, F. (2014). Superatomic Orbitals under Spin-Orbit Coupling. J. Phys. Chem. Lett., 5, 3286-3289. doi:10.1021/jz501745z.

Parr, R. G., Szentpály, L. v., & Liu, S. (1999). Electrophilicity Index. Journal of the American Chemical Society, 121(9), 1922–1924. doi:10.1021/ja983494x.

Chattaraj, P. K., Sarkar, U. & Roy, D. R. (2006). Electrophilicity Index. Chem. Rev., 106, 2065-2091. doi:10.1021/cr040109f.

Frisch, M. J., Trucks, G. W., Schlegel, H. B., Scuseria, G. E., Robb, M. A., Cheeseman, J. R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G. A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H. P., Izmaylov, A. F., Bloino, J., Zheng, G., Sonnenberg, J. L., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery, J. A., Jr., Peralta, J. E., Ogliaro, F., Bearpark, M., Heyd, J. J., Brothers, E., Kudin, K. N., Staroverov, V. N., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A., Burant, J. C., Iyengar, S. S., Tomasi, J., Cossi, M., Rega, N., Millam, J. M., Klene, M., Knox, J. E., Cross, J. B., Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R. E., Yazyev, O., Austin, A. J., Cammi, R., Pomelli, C., Ochterski, J. W., Martin, R. L., Morokuma, K., Zakrzewski, V. G., Voth, G. A., Salvador, P., Dannenberg, J. J., Dapprich, S., Daniels, A. D., Farkas, O., Foresman, J. B., Ortiz, J. V., Cioslowski, J. & Fox, D. J. Gaussian 09, Gaussian, Inc., Wallingford, Revisions A.02 (2009) and D.01 (2013).

Dennington, R. D., Keith, T. A. & Millam, J. M. (2000-2008). GaussView, Version 5.0.9.

Neto, A. C. & Jorge, F. E. (2013). All-electron double zeta basis sets for the most fifth-row atoms: Application in DFT spectroscopic constant calculations. Chem. Phys. Lett., 582, 158-162. doi:10.1016/j.cplett.2013.07.045.

Douglas, M. & Kroll, N. M. (1974). Quantum Electrodynamical Corrections to the Fine Structure of Helium. Ann. Phys., 82, 89-155. doi:10.1016/0003-4916(74)90333-9.

Jansen, G., & Hess, B. A. (1989). Revision of the Douglas-Kroll transformation. Physical Review A, 39(11), 6016–6017. doi:10.1103/physreva.39.6016.

Nakajima, T. & Hirao, K. (2012). The Douglas-Kroll-Hess Approach. Chem. Rev., 112, 385-402. doi:10.1021/cr200040s.

Reiher, M. (2012) Relativistic Douglas-Kroll-Hess theory. WIREs Comput. Mol. Sci., 2, 139-149. doi:10.1002/wcms.67.

Reiher, M. & Wolf, A. (2015). Douglas–Kroll–Hess Theory, in: Reiher, M. & Wolf, A., Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science, Second Ed., WILEY-VCH, Germany, pp. 469-501. doi:10.1002/9783527667550.ch12.

Gruene, P., Butschke, B., Lyon, J. T., Rayner, D. M., & Fielicke, A. (2014). Far-IR Spectra of Small Neutral Gold Clusters in the Gas Phase. Zeitschrift für physikalische Chemie, 228(4-5), 337-350. doi:10.1515/zpch-2014-0480.

Hammes-Schiffer, S. & Andersen, H. C. (1993). The advantages of the general Hartree-Fock method for future computer simulation of materials. J. Chem. Phys., 99 (3), 1901-1913. doi:10.1063/1.465305.

Pearson, R. G. (1988). Absolute Electronegativity and Hardness: Application to Inorganic Chemistry. Inorg. Chem., 27, 734-740. doi:10.1021/ic00277a030.

Wesendrup, R., Hunt, T. & Schwerdtfeger, P. (2000). Relativistic coupled cluster calculations for neutral and singly charged Au3 Clusters. J. Chem. Phys., 112, 9356. doi:10.1063/1.481556.

Jorge, F. E., Ferreira, I. B., Soprani, D. D. & Gomes, T. (2016). Estimating the Impact of an All-Electron Basis Set and Scalar Relativistic Effects on the Structure, Stability, and Reactivity of Small Copper Clusters. J. Braz. Chem. Soc., 27, 127-135. doi:10.5935/0103-5053.20150261.

Glendening, E. D., Reed, A. E., Carpenter, J. E. & Weinhold. F. NBO Version 3.1.

Carvalho, F. S. & Braga, J. P. (2018). DFT Study of Small Gold Clusters, Aun(2≤n≤6): Stabilityand Charge Distribution Using M08-SO Functional. Brazilian Journal of Physics, 48, 390-397. doi:10.1007/s13538-018-0577-5.


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DOI: 10.28991/HIJ-2021-02-01-05

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