Low-lying states of FeSin −/0/+ (n = 1-2) clusters from DMRG-CASPT2 calculations

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The electronic states of FeSin −/0/+ (n = 1-2) clusters have been investigated with DFT, CASPT2, and DMRGCASPT2 methods. By using relatively large active spaces, the DMRG-CASPT2 method is found to provide highly accurate relative energies for the various relevant electronic states. Leading configurations, bond distances, harmonic vibrational frequencies, and relative energies for the low-lying states of the title clusters are reported.

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Nội dung Text: Low-lying states of FeSin −/0/+ (n = 1-2) clusters from DMRG-CASPT2 calculations

Cite this paper: Vietnam J. Chem., 2023, 61(1), 43-51 Research article DOI: 10.1002/vjch.202200057 Low-lying states of FeSin−/0/+ (n = 1-2) clusters from DMRG-CASPT2 calculations Tran Van Tan1, Tran Quoc Tri1, Phan Trung Cang1, Nguyen Thi Hong Hanh1, Ho Sy Linh1, Nguyen Phu Tan1, Marc F.A. Hendrickx2* 1 Theoretical and Physical Chemistry Division, Dong Thap University, 783-Pham Huu Lau, Ward 6, Cao Lanh City, Dong Thap 81000, Viet Nam 2 Quantum chemistry and Physical Chemistry Division, Chemistry Department, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Heverlee-Leuven, Belgium Submitted April 7, 2022; Revised August 26, 2022; Accepted September 14, 2022 Abstract The electronic states of FeSin−/0/+ (n = 1-2) clusters have been investigated with DFT, CASPT2, and DMRG- CASPT2 methods. By using relatively large active spaces, the DMRG-CASPT2 method is found to provide highly accurate relative energies for the various relevant electronic states. Leading configurations, bond distances, harmonic vibrational frequencies, and relative energies for the low-lying states of the title clusters are reported. Electron detachment energies for the ground states of the anionic and neutral clusters were estimated at the DMRG-CASPT2 level. Franck-Condon factor simulations were performed for transitions from the anionic ground state to the neutral ground state and from the neutral ground state to the cationic ground state with the purpose to produce the vibrational progressions. Keywords. DMRG-CASPT2, detachment energy, relative energy, Franck-Condon factors, vibrational frequency. 1. INTRODUCTION investigated by the CASSCF and MRSDCI methods.[13] The ground state of the neutral cluster The structures and properties of many transition was predicted to be a 3Δ, with a 5Π at 0.36 eV. Bond metal-doped silicon clusters were studied by distances, vibrational frequencies, electron affinities, experimental and quantum chemical methods in the ionization potentials, dissociation energies, and search for stable structures that can be used as dipole moments of FeSi−/0/+ have been evaluated building blocks for nanomaterials.[1-9] Regarding with the B3LYP functional.[14] In the same work, iron-doped silicon clusters, the geometry, stability, ground states of FeSi−/0/+ were determined as 2Δ, 3Σ−, and electronic properties of FeSin−/0/+ (n = 1-8) and 4Σ−. In a subsequent ccCA study, the ground clusters were studied with the B3LYP functional and states of FeSi−/0/+ were calculated as 6Σ+, 3Σ−, and the 6-311+G* basis set.[10] Ground state structures of 4 − [11] Σ . From these results it can be concluded that FeSin−/0/+ (n = 1-8) clusters were found to change the B3LYP and ccCA methods propose different from planar to three-dimensional for n > 3. The ground states for the FeSi− cluster. For the larger electronic structures and properties of FeSin−/0/+ (n = FeSi2−/0/+ clusters, the B3LYP functional results 1-6) clusters were recently explored using ccCA revealed 4B1, 5B2, and 2A1 ground states with cyclic theory.[11] The structures, relative stabilities, electron geometries, respectively.[10] More recently, ccCA affinities, and charge transfer of these clusters were calculations proposed 4B1, 1A1, and 2A1 ground reported. The PBE functional was applied to explore states.[11] Therefore, for the neutral cluster there the shape- and size-specific aspects of the dipole appears to be a discrepancy, the B3LYP functional moments and polarizabilities of FeSin (n = 1-14) predicts a quintet ground state, while the ccCA clusters.[12] It was shown that the polarizabilities of method favors a singlet. silicon clusters increase by the doping with iron To calculate the relative energies of the atoms. electronic states of FeSin−/0/+ (n = 1-2) clusters, it is Regarding the smaller title FeSin−/0/+ (n = 1-2) recommended to employ multiconfigurational clusters, the low-lying states of FeSi were methods such as CASSCF/CASPT2 and DMRG- 43 Wiley Online Library © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Marc F.A. Hendrickx et al. SCF/DMRG-CASPT2. The DMRG-CASPT2 CASPT2 and DMRG-CASPT2 calculations method with the ability to extend the active space to were carried out with OpenMolcas[25] and more than 20 orbitals is expected to produce reliable CHEMPS2 package[26], respectively. The cc- relative energies for closely lying electronic states of pwCVQZ-DK and cc-pVQZ-DK basis sets were transition metal compounds.[15–20] This method has utilized for Fe and Si, respectively.[27,28] The already been successfully applied to study the maximum number of renormalized states (m) in the electronic states of several small transition metal- DMRG calculations was set to 1500.[21,23,24] BP86 doped silicon and germanium clusters.[21–24] In this and B3LYP exchange-correlation functionals in work, DMRG-CASPT2 calculations were carried combination with the def2-QZVP basis sets were out to compute the relative energies of the electronic applied to optimize the geometries and to calculate states of FeSin−/0/+ (n = 1-2) clusters. The the harmonic vibrational frequencies of the computational results can serve as a reference for the electronic states. All these calculations were carried future experiment research of iron-doped silicon out with NWCHEM 7.0.2.[29] clusters. The CASSCF and DMRG-SCF methods were employed to construct starting wave functions for 2. COMPUTATIONAL DETAILS the subsequent CASPT2 and DMRG-CASPT2 calculations. For FeSi−/0/+, the CASSCF active space The structures and symmetries of the studied clusters includes 13, 12, and 11 electrons distributed among are displayed in figure 1. The diatomic FeSi−0/+ 15 orbitals. These 15 orbitals are predominantly 3d clusters possess C∞v symmetry, but the calculations were performed in the C2v point-group as only and 4s of Fe, 3s and 3p of Si, and 5 virtual 4d Abelian groups are implemented in the software orbitals of Fe. The DMRG-SCF active space with 28 employed to perform the CASPT2 and DMRG- orbitals was obtained by adding 13 virtual orbitals to CASPT2 calculations. The cyclic isomers of the CASSCF active space. These 13 virtual orbitals FeSi2−/0/+ clusters have C2v symmetry. are complicated in nature and have large contributions from many orbitals of Fe and Si. For FeSi2−/0/+, the active space includes the 3d and 4s of Fe, 3s and 3p of Si, and 9 virtual 4p, 4d, 5s orbitals of Fe. This approach resulted in an active space of 17, 16, and 15 electrons in 23 orbitals for FeSi2−/0/+. Scalar relativistic effects were included by employing the second-order Douglas-Kroll Hamiltonian. The pertubation calculations additionally correlate electrons in the 2s, 2p orbitals of Si and 3s, 3p orbitals of Fe. The default IPEA shift of 0.25 and an imaginary shift of 0.1 were Figure 1: The geometries and symmetries of employed in the pertubation calculations. FeSi−/0/+ and cyclic FeSi2−/0/+ isomers 3. RESULTS AND DISCUSSION For the electronic states of diatomic FeSi−0/+ clusters, single-point CASPT2 calculations were performed for several bond distances around their 3.1. FeSi−/0/+ minima with the purpose to construct the corresponding potential energies profiles. Bond Leading configurations, bond distances, harmonic distances, harmonic vibrational frequencies, and vibrational frequencies, and relative energies of the relative energies of the electronic states were electronic states of FeSi−/0/+ are collected in table 1. obtained by fitting the potential energy profiles to a The leading configurations of the electronic states fourth-degree polynomial energy curve. To improve obtained from the CASSCF calculations show that the energies of the electronic states, the single-point most of the states have strong multireference DMRG-CASPT2 calculations were carried out at the character with reference weights around 50 %. For minima of the potential energy profiles. For the low- several excited states, the relative DMRG-CASPT2 lying electronic states of the FeSi2−/0/+ clusters, energies differ slightly from those obtained by single-point DMRG-CASPT2 calculations were CASPT2. Harmonic vibrational frequencies of all performed at the geometries optimized with the low-lying electronic states are in the range of 289 to BP86 functional. 517 cm-1. © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 44
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Low-lying states of FeSin−/0/+ … Table 1: Leading configurations, bond lengths, harmonic vibrational frequencies, and relative energies of the low-lying electronic states of FeSi−/0/+ Fe-Si Frequency Relative energy (eV) State Leading configuration -1 (Å) (cm ) CASPT2 DMRG-CASPT2 FeSi− 2 Δ (2A2) 9σ210σ211σ24π45π01δ3 (45 %) 2.114 400 0.00 0.00 4 Π (4B1) 9σ210σ211σ24π45π11δ2 (56%) 2.094 434 0.11 0.15 4 − 4 2 2 2 3 1 3 Σ ( A1) 9σ 10σ 11σ 4π 5π 1δ (51 %) 2.261 361 0.47 0.27 6 Π (6B1) 9σ210σ211σ24π35π21δ2 (67 %) 2.213 422 0.65 0.38 2 2 2 2 2 4 1 2 Π ( B1) 9σ 10σ 11σ 4π 5π 1δ (35 %) 2.176 375 0.51 0.46 6 + 6 Σ ( A1) 9σ210σ211σ14π45π21δ2 (76 %) 2.118 420 0.41 0.53 FeSi 3 − 3 Σ ( A2) 9σ210σ211σ24π45π01δ2 (49 %) 2.110 492 0.00 0.00 3 Δ (3A1) 9σ210σ211σ14π45π01δ3 (49 %) 2.095 517 0.28 0.31 5 5 2 2 1 4 1 2 Π ( B1) 9σ 10σ 11σ 4π 5π 1δ (67 %) 2.130 339 0.68 0.50 5 Δ (5A2) 9σ210σ211σ24π35π11δ2 (59 %) 2.214 391 0.86 0.60 + FeSi 4 − 4 Σ ( A2) 9σ210σ211σ14π45π01δ2 (67 %) 2.162 401 0.00 0.00 4 Π (14B1) 9σ210σ211σ24π35π01δ2 (49 %) 2.291 289 0.73 0.52 2 2 2 2 0 4 0 3 Δ ( A2) 9σ 10σ 11σ 4π 5π 1δ (50 %) 2.080 440 0.71 0.71 4 Δ (4A1) 9σ210σ111σ14π45π01δ3 (51 %) 2.153 397 1.10 1.05 CASPT2 and DMRG-CASPT2 levels agree that the doublet state is the anionic ground state, with the quartet 0.11 and 0.15 eV higher in energy. The molecular orbitals of the 2Δ state in figure 2 show that the bonding orbitals 9σ (predominantly silicon) and 4π (predominantly silicon) are fully occupied. The remaining doubly occupied orbitals 10σ, 11σ, and the 1δ level, which is triply occupied, are all nonbonding orbitals on iron. Quite reasonably the 5π level is unoccupied in the anionic ground state. The lowest excited 4Π state can be obtained from the 2Δ by transferring an electron from the 1δ level to the 5π level. Bond distances of these doublet and quartet states are evaluated to be 2.114 and 2.094 Å. Other low-lying excited states of the anionic cluster could be identified as 4Σ−, 6Π, 2Π, and 6Σ+ with DMRG- CASPT2 relative energies in the range from 0.27 to 0.53 eV. For the neutral cluster, the ground state is 3 − Figure 2: The molecular orbitals of the leading Σ with a bond distance of 2.110 Å. The 3Δ, 5Π, and 5 configurations of the 2Δ state of FeSi− obtained from Δ states were identified as the lowest excited states the DMRG-SCF calculation with relative energies in the region from 0.31 to 0.60 eV. Regarding the cationic cluster, the ground state Regarding the anionic cluster, it is found that is the 4Σ− state with a bond length of 2.162 Å. The the 2Δ state is positioned closely to the 4Π state. Both lower excited states of the cationic cluster are © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 45
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Marc F.A. Hendrickx et al. determined as 4Π, 2Δ, and 4Δ with relative energies the transitions from the anionic 2Δ to the neutral 3Σ−, 3 from 0.52 to 1.05 eV. Δ, and 3Φ states have VDEs of 1.09, 1.35, and 2.63 Ground states of FeSi−/0/+ were reported in eV. Also, the results show that the ADE of the previous calculations at several levels of theory. The transition to the neutral 3Σ− ground state is 1.07 eV, ground state of the anionic cluster was specified as indicating that there is not much structural change 6 Σ by a ccCA study[11] or as 2Δ by using the B3LYP accompanying this electron detachment. Indeed, at functional.[10,14] Our DMRG-CASPT2 calculations the CASPT2 level, the bond distance of the doublet with an active space as large as 28 orbitals point to state is 2.114 Å, while that of the triplet state is the 2Δ as the anionic ground state. Regarding the 2.110 Å. This marginally geometric change for this neutral and cationic cluster, our DMRG-CASPT2 transition results in just one peak in the Franck- results are in agreement with the previous B3LYP Condon factor simulation (figure 3a). On the other calculations in which the ground states are specified hand, the ADE and VDE of the transition from 3Σ− as 3Σ− and 4Σ−.[11,14] However, for the neutral cluster, to 4Σ− within the FeSi0/+ are 6.97 and 7.00 eV. In this the DMRG-CASPT2 result differs from that of a transition, the bond distance elongates slightly from MRSDCI study in which the 3Δ was mentioned as 2.110 Å in the triplet to 2.162 Å in the quartet. Due the ground state.[10] to this somewhat larger structural relaxation, this Mulliken atomic charges for iron and silicon in transition exhibits a vibrational progression of just the ground states are -0.4658 and -0.5342, +0.1004 two observable peaks with a frequency of 401 cm-1 and -0.1004, and +0.6204 and +0.3796 for the in the Franck-Condon factor simulation (figure 3b). anionic, neutral and cationic clusters, respectively. This nonexistent progression (2Δ to 3Σ− for FeSi-/0) For all three cases the slightly more negative and small progression (3Σ− to 4Σ− for FeSi0/+) are the (anionic and neutral cluster) or less positive result of a one-electron detachment out of the (cationic) atomic charge of silicon when compared nonbonding 1δ and 11σ orbitals, respectively. to iron is in complete agreement with a slightly higher Pauling electronegativity of silicon (1.90) 3.2. FeSi2−/0/+ when compared to that of iron (1.83). Leading configurations, bond distances, vibrational Table 2: Adiabatic and vertical detachment energies frequencies, and relative energies of the electronic (ADEs and VDEs) of the anionic and neutral states of the cyclic isomers of FeSi2−/0/+ are shown clusters computed at the DMRG-CASPT2 level in table 3. The results show that for several low- lying states, the BP86 and B3LYP functionals ADE VDE provide different relative energy orders. For the Cluster Transition Orbital (eV) (eV) anionic cluster, at the BP86 level, the 4B2 is above FeSi−/0 2 Δ → 3Σ− 1δ 1.07 1.09 the 4B1 by 0.17 eV, while according to the B3LYP 2 calculations, the 4B2 is below the 4B1 by 0.03 eV. Δ → 3Δ 11σ 1.35 This problem also occurs for the 5B2 and 3B1 of the 2 Δ → 3Φ 4π 2.63 neutral cluster and the 2A1 and 4B2 of the cationic 0/+ 3 − 4 − cluster. In these cases, the DMRG-CASPT2 FeSi Σ → Σ 11σ 6.97 7.00 calculations with an active space of up to 23 FeSi2−/0 4 B1 → 5B2 2a2 1.70 1.77 orbitals could provide more trustworthy relative 4 3 energies for these electronic states. B1 → B1 14a1 1.83 Regarding the FeSi2− cluster, the DMRG- 4 B1 → 3A1 5b1 1.86 CASPT2 results show a 4B1 ground state. The 4B2 is 4 B1 → 5A2 8b2 2.15 above the ground state by only 0.19 eV. The other low-lying excited states 4A2, 2A1, and 2B1 are higher in 4 5 B1 → B1 12a1 2.72 energy by at least 0.50 eV. For the neutral cluster, the 5 FeSi20/+ 5 B2 → 4B2 14a1 7.05 7.10 B2 is the ground state and the 3B1 is higher by 0.10 eV. The 3B2, 3A2, 5A2, 1A1, 5A1, and 5B1 are in the range from 0.30 to 0.86 eV. The ground state of the Electron detachment energies of the anionic and cationic cluster is identified as 2A1, while the 4B2, 2A2, neutral clusters as estimated at the DMRG-CASPT2 and 4A2 are 0.13, 0.31, and 0.73 eV less stable. In a level are presented in table 2. Several possible one- previous B3LYP study, the ground states of FeSi2−/0/+ electron detachment processes are specified for are respectively 4B1, 5B2, and 2A1.[10] Recent ccCA transitions from the anionic ground state to the calculations on the other hand, the ground states of neutral ground and its excited states. In particular, FeSi2−/0/+ are specified as 4B1, 1A1, and 2A1.[11] Our © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 46
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Low-lying states of FeSin−/0/+ … DMRG-CASPT2 results in table 3 provide similar ground states as the previous B3LYP study.[10] (c) 4B1 → 5B2 (cyclic FeSi2−/0) (d) 5B2 → 4B2 (cyclic FeSi20/+) (a) 2Δ → 3Σ− (FeSi−/0) (b) 3Σ− → 4Σ− (FeSi0/+) Figure 3: The Franck-Condon factor simulations for the transition 2Δ → 3Σ− within FeSi−/0 (a), 3Σ− → 4Σ− within FeSi0/+ (b), 4B1 → 5B2 within cyclic FeSi2−/0 (c), and 5B2 → 4B2 within cyclic FeSi20/+ (d) The molecular orbitals and electron occupation is evaluated to be 1.70 eV. The Franck-Condon numbers of the anionic 4B1 ground state are factor simulation for this transition is presented in displayed in figure 4. The predominantly 3d and 4s figure 3c and exhibits a vibrational progression of orbitals of Fe appear as 13a1, 14a1, 15a1, 5b1, 8b2, five peaks. The frequency of the progression of 321 and 2a2. The 11a1, 12a1, 4b1, 8b2, and 2a2 are fully cm-1 belongs to the symmetric SiFeSi bending mode occupied, while the 13a1, 14a1, and 5b1 are singly as calculated with the BP86 functional. The occupied. The one-electron detachment processes observation of this vibrational progression is the between the FeSi2−/0 clusters are proposed as the outcome of large geometric changes accompanying transitions from the 4B1 to 5B2, 3B1, 3A1, 5A2, and 5B1. this electron detachment process. Indeed, the BP86 In these transitions, one electron is respectively results show that the Fe-Si bond increases from detached from the 2a2, 14a1, 5b1, 8b2, and 12a1 2.196 to 2.253 Å, while the Si-Si bond decreases orbitals of the initial state. The VDEs of these from 2.319 to 2.271 Å, resulting in a noticeable transitions are estimated to be 1.77, 1.83, 1.86, 2.15, change in SiFeSi bond angle which reduces from and 2.72 eV at the DMRG-CASPT2 level (table 2). 63.7° to 60.5°. The transition from 5B2 to 4B2 within The ADE for the transition from the 4B1 to 5B2 the FeSi20/+ clusters has an ADE and VDE of 7.05 © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 47
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Marc F.A. Hendrickx et al. Table 3: Leading configurations, bond distances, harmonic vibrational frequencies, and relative energies of the low-lying electronic states of the cyclic FeSi2−/0/+ isomers. (a), (b) The bond distances and vibrational frequencies are obtained at the BP86 level Fe-Si, Si-Si(a) Frequency(b) Relative energy (eV) State Leading configuration (Å) (cm-1) BP86 B3LYP DMRG-CASPT2 FeSi2− 4 B1 11a1212a1213a1114a1115a10 2.196, 2.319 295, 332, 472 0.00 0.00 0.00 4b125b118b229b202a223a20 4 B2 11a1212a1213a1214a1115a10 2.256, 2.261 292, 309, 485 0.17 −0.03 0.19 4b125b118b229b202a213a20 4 A2 11a1212a1213a1114a1115a10 2.291, 2.256 325, 331, 509 0.64 0.33 0.50 4b125b128b229b202a213a20 2 A1 11a1212a1213a1214a1115a10 2.151, 2.402 273, 347, 432 0.77 1.16 0.80 4b125b108b229b202a223a20 2 B1 11a1212a1213a1214a1015a10 2.155, 2.305 302, 363, 488 0.50 0.82 0.93 4b125b118b229b202a223a20 FeSi2 5 B2 11a1212a1213a1114a1115a10 2.253, 2.271 274, 321, 482 0.00 0.00 0.00 4b125b118b229b202a213a20 3 B1 11a1212a1213a1114a1015a10 2.148, 2.272 309, 368, 494 −0.11 0.12 0.10 4b125b118b229b202a223a20 3 A1 11a1212a1213a1114a1115a10 2.178, 2.384 289, 331, 443 0.06 0.22 0.15 4b125b108b229b202a223a20 3 B2 11a1212a1213a1214a1015a10 2.213, 2.217 320, 320, 507 0.17 0.14 0.30 4b125b118b229b202a213a20 3 A2 11a1212a1213a1214a1115a10 2.236, 2.317 307, 314, 452 0.27 0.19 0.34 4b125b108b229b202a213a20 5 A2 11a1212a1213a1114a1115a10 2.275, 2.214 282, 306, 509 0.24 0.13 0.34 4b125b118b219b202a223a20 1 A1 11a1212a1213a1214a1015a10 2.111, 2.353 297, 387, 475 0.25 0.86 0.35 4b125b108b229b202a223a20 5 A1 11a1212a1213a1214a1115a10 2.325, 2.188 242, 309, 526 0.47 0.24 0.50 4b125b118b219b202a213a20 5 B1 11a1212a1113a1114a1115a10 2.315, 2.240 296, 318, 497 0.73 0.60 0.86 4b125b118b229b202a223a20 FeSi2+ 2 A1 11a1212a1213a1114a1015a10 2.140, 2.395 249, 361, 441 0.00 0.00 0.00 4b125b108b229b202a223a20 4 B2 11a1212a1213a1114a1015a10 2.249, 2.245 366, 402, 496 0.22 −0.06 0.13 4b125b118b229b202a213a20 2 A2 11a1212a1213a1214a1015a10 2.218, 2.300 293, 314, 440 0.33 0.01 0.31 4b125b108b229b202a213a20 4 A2 11a1212a1213a1114a1015a10 2.281, 2.194 259, 276, 496 0.67 0.26 0.73 4b125b118b219b202a223a20 © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 48
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Low-lying states of FeSin−/0/+ … and 7.10 eV. The corresponding Franck-Condon small structural changes. The BP86 functional factor simulation for this transition as displayed in proposes Fe-Si and Si-Si bonds of 2.253 and 2.271 figure 3d contains just one peak, confirming the Å for 5B2 and of 2.249 and 2.245 for 4B2. Figure 4: The molecular orbitals and occupation numbers of the 4B1 state of cyclic FeSi2− obtained from the DMRG-SCF calculation Atomic Mulliken charges for iron and silicon are 4. CONCLUSION −0.18 and −0.41, +0.24 and −0.12, and +0.50 and +0.25 for the anionic 4B1, neutral 5B2, and the The electronic states of FeSin−/0/+ (n = 1-2) are cationic 2A1 ground states, respectively. So, starting investigated with a combination of the DFT, from the neutral cluster the removal of an electron CASPT2, and DMRG-CASPT2 methods. The occurs predominantly from the Si2 moiety while the leading configurations, bond distances, vibrational addition of an extra electron takes place across the frequencies, and relative energies of all low-lying entire cluster, indicating large orbital relaxation electronic states are reported. For all ground states of processes. For all ground states of FeSi2−/0/+ the FeSin−/0/+ (n = 1-2), the atomic Mulliken charges of atomic charges on silicon atoms are more negative silicon are more negative or less positive than those or less positive than the corresponding charges on for iron. For FeSi−/0/+ clusters, the ground states are iron, reflecting ones again the higher electron predicted to be 2Δ, 3Σ−, and 4Σ−. The cyclic ground negativity of silicon. states of FeSi2−/0/+ are proposed as 4B1, 5B2, and 2A1. © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 49
25728288, 2023, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200057 by Readcube (Labtiva Inc.), Wiley Online Library on [02/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Vietnam Journal of Chemistry Marc F.A. Hendrickx et al. The lowest ADEs of FeSi−, FeSi2−, FeSi, and FeSi2 10. Y. Liu, G. L. Li, A. M. Gao, H. Y. Chen, D. Finlow, are 1.07, 1.70, 6.97, and 7.05 eV, respectively. The Q. S. Li. The structures and properties of VDEs for the transitions from the anionic 2Δ ground FeSin/FeSin+/FeSin− (n = 1~8) clusters, Eur. Phys. J. state to the neutral 3Σ−, 3Δ, and 3Φ states within the D, 2011, 64(1), 27. 11. J. Lu, Q. Lu, J. Yang. Probing the electronic FeSi−/0 clusters are 1.09, 1.35, and 2.63 eV. Within structures and properties of neutral and charged the cyclic FeSi2−/0 isomers, the VDEs of the FeSin(−1,0,+1) (n = 1-6) clusters using CcCA theory, J. transition from the anionic 4B1 ground states to the Mol. Model., 2020, 26(10), 283. neutral 5B2, 3B1, 3A1, 5A2, and 5B1 are 1.77, 1.83, 12. L. Ma, J. Wang, G. Wang. Site-specific analysis of 1.86, 2.15, and 2.72 eV. Vibrational progressions are dipole polarizabilities of heterogeneous systems: expected to be observed for the transitions 3Σ− → 4Σ− Iron-doped Sin (n = 1-14) clusters, J. Chem. Phys., within the FeSi0/+ and 4B1 → 5B2 within the cyclic 2013, 138(9), 094304. FeSi2−/0 isomers, while they are thought to be absent 13. M. Sekiya, K. Miwa, K. Tanaka, M. Yoshimine. for the transitions 4Π → 3Σ− within the FeSi−/0 and Theoretical study on lower electronic states of the 5 B2 → 4B2 within the cyclic FeSi20/+ isomer. All these FeSi molecule, Mol. Phys., 2003, 101(1-2), 99-104. 14. Z. J. Wu, Z. M. Su. 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