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CASPT2 calculations
Chemical Physics Letters 721 (2019) 111–116
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Research paper
The ground and excited low-lying states of VSi20/−/+ clusters from CASSCF/ CASPT2 calculations Minh Thao Nguyena,b, Quoc Tri Trana, Van Tan Trana, a b
T
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Theoretical and Physical Chemistry Division, Dong Thap University, 783-Pham Huu Lau, Ward 6, Cao Lanh City, Dong Thap, Viet Nam Department of Chemistry, University of Science, Vietnam National University – Ho Chi Minh City, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Viet Nam
H I GH L IG H T S
An active space of 17 orbitals is required to obtain reliable CASPT2 energies. The relative energies of CASPT2 are in agreement with that of the CCSD(T). Bond distances and relative energies of the electronic states are reported. The ground states of VSi20/−/+ clusters are computed to be 4B1, 5A1 , and 3B1. Electron affinity and ionization energy of VSi2 cluster are 1.08 and 7.07 eV. Several vertical detachment energies of the anionic ground state are calculated.
A R T I C LE I N FO
A B S T R A C T
Keywords: VSi20/−/+ clusters CASSCF/CASPT2 Electronic state Electron affinity Ionization energy Electron detachment energy
The geometric and electronic structures of the ground and excited low-lying states of VSi20/−/+ clusters were investigated by the CASSCF/CASPT2 method. The structural parameters, harmonic vibrational frequencies, relative energies, and atomic charges of the low-lying electronic states were presented and discussed. The ground states of VSi20/−/+ clusters were 4B1, 5A1, and 3B1, respectively. At the CASPT2 level, the electron affinity and ionization energy of the neutral clusters were evaluated to be 1.08 and 7.07 eV, respectively. The vertical detachment energies of the detachments of one electron from several orbitals of the anionic cluster were computed.
1. Introduction Silicon clusters have been extensively investigated because of their potential applications in microelectronic industry [1–8]. However, silicon clusters are known to be unstable because of their high reactivity to form dangling bonds on their surface [9]. In order to stabilize silicon clusters, transition metals are incorporated. By doping transition metals, a large amount of stable transition metal-silicon clusters are created [10–22]. In order to search for the stable transition metal-silicon clusters, vanadium-doped silicon clusters were investigated by both experimental and theoretical methods [11–14,16,23–26]. Because the stability of these clusters depends on their size and shape, the experimental and computational methods were carried out to probe the geometric and electronic structures. In particular, the photoelectron spectra of VSin− (n = 3–20), V2Sin− (n = 3–6), and V3Sin− (n = 3–14) clusters were recorded [10,16,23]. The geometric and electronic structures of these clusters were calculated by density functional theory
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and multiconfigurational methods [11–14,23]. The VSi2 moieties can be found in form of nanoparticles and crystals that are investigated because of their applications in heterogeneous catalysts and thermoelectric materials [27,28]. Study of geometric and electronic structures of VSi2 moieties may give important information for a clear understanding of the properties of bulk materials. Although several studies on vanadium-doped silicon clusters have been published, the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters remain poorly understood. To the best of our knowledge, there is still no investigation of the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters. In this study, the geometric and electronic structures of VSi20/−/+ clusters are calculated by the CASSCF/CASPT2 methods. This computational method has proved to be sufficient to calculate the geometric and electronic structures of the low-lying states of vanadium-doped silicon clusters as VSi0/−/+, VSi3−/0, and VSi4−/0 [11–13]. The accuracy of CASPT2 method is calibrated with density functional theory and ROHF/
Corresponding author. E-mail address: [email protected] (V.T. Tran).
https://doi.org/10.1016/j.cplett.2019.02.043 Received 17 December 2018; Received in revised form 18 February 2019; Accepted 19 February 2019 Available online 05 March 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
Chemical Physics Letters 721 (2019) 111–116
M.T. Nguyen, et al.
methods predict slightly different V-Si and Si-Si bond distances. The difference between NPA and Mulliken charges are small for the neutral and cationic clusters, while it becomes large for the anionic cluster. For the 15A1 of VSi2−, the NPA charges of V and Si are 0.339 and −0.669 e−, while the Mulliken charges of these atoms are −0.012 and −0.494 e−. In the following discussion, NPA charge is utilized because it is known to be much less basis set dependent than Mulliken Population. The relative energies of the low-lying states of VSi20/−/+ clusters are reported at the BP86, B3LYP, CCSD(T), and CASPT2 levels in Table 1. The CASPT2 relative energies with an active space of 12 and 17 orbitals are respectively denoted as CASPT2(I) and CASPT2(II). The CASPT2 relative energies slightly change with the active spaces. The strongest variation appears in the case of 15A1 and 15B1 of the anionic cluster. In particular, the 15A1 is 0.26 eV less stable than the 15B1 at the CASPT2(I) level, while the former state becomes 0.05 eV more stable than the latter state at the CASPT2(II) level. Because the double-shell 3d, 4d effects of V are only included in the active space of CASPT2(II), it can be said that the double-shell effects of V are important to obtain a sufficient relative energy order of the electronic states of VSi20/−/+ clusters. This result is also supported by the BP86 and B3LYP functional and CCSD(T) calculations in which the 15A1 is above the 15B1 by 0.11, 0.06, and 0.01 eV. For the other electronic states of VSi20/−/+ clusters, the relative energies of the CASPT2(II) correspond well with those of the CCSD(T). In the subsequent discussion, the CASPT2 results are used instead of the CCSD(T) because the CASPT2 can access all the relevant low-lying states of VSi20/−/+ clusters and because the CCSD(T) calculations for the excited states are difficult to converge. In contrast to the CASPT2 and CCSD(T), the relative energies of density functional theory depend on the functionals. This feature can be seen in the case of the 1 A1 of VSi2− in which the relative energies are evaluated to be 0.30 and 1.14 eV by the BP86 and B3LYP functionals. These relative energies differ from the values of 0.60 and 0.61 eV of the CCSD(T) and CASPT2. Overall, the above discussion shows that the CASSCF/CASPT2 method with an active space of 17 orbitals (CASPT2(II)) is sufficient to obtain reliable relative energies of the low-lying states of VSi20/−/+ clusters.
Fig. 1. The geometric structure of VSi20/−/+ clusters.
CCSD(T) results. The leading configurations, structural parameters, harmonic vibrational frequencies, atomic charges, and relative energies of the low-lying states of VSi20/−/+ clusters will be reported. The vertical detachment energies of the removals of one electron from different orbitals of the anionic cluster will be calculated to predict the main features of the anion photoelectron spectrum. 2. Computational methods The geometries of the ground and excited low-lying states of VSi20/ clusters were optimized with density functional theory, ROHF/ CCSD(T), and CASSCF/CASPT2 methods. It has been known from the literature that MSi2 clusters have cyclic geometry with C2v symmetry as presented in Fig. 1 [15,29]. Therefore, this geometry was used as the initial structure for the geometry optimizations of the low-lying states of VSi20/−/+ clusters. In density functional calculations, the BP86 [30,31] and B3LYP [30,32,33] functionals were used with def2-QZVP basis sets [34]. Vibrational frequency calculations were carried out with the BP86 functional to ensure that the optimized structures correspond to minima on potential energy surfaces. In the ROHF/CCSD(T) and CASSCF/CASPT2 calculations, the aug-cc-pwCVTZ-DK and aug-ccpVTZ-DK basis sets were utilized for V and Si [35,36]; the scalar relativistic effects were covered by using the second-order Douglas-Kroll Hamiltonian [37–39]; and the 3 s, 3p of V and 3 s of Si were correlated. To reduce the memories for storing two-electron integrals, Cholesky decomposition with an accuracy of 10−6 a.u. was employed for the CASSCF/CASPT2 calculations. To prevent the intruder states, an imaginary shift of 0.1 was applied to the CASPT2. Density functional and ROHF/CCSD(T) calculations were carried out with NWCHEM 6.6 [40], and the CASSCF/CASPT2 calculations were performed with MOLCAS@ UU 8.0 [41]. Natural population analysis (NPA) was performed with JANPA 2.0.2 [42] based on CASSCF wave functions to estimate atomic charges of VSi20/−/+ clusters. The active space orbitals for CASSCF/CASPT2 calculations can be selected based on the valence orbitals of V and Si [11–13,43]. For VSi20/−/+ clusters, the active space was chosen to include the 3d, 4s orbitals of V and the 3p orbitals of Si. This approach results in an active space of 12 orbitals in which 9, 10, or 8 electrons are distributed. This active space was utilized to optimize the geometries and to calculate the harmonic vibrational frequencies of the electronic states. In order to include the double-shell effects of V, the 4d orbitals of V were added to form an active space of 17 orbitals. This active space was employed for single-point calculations to improve the energies of the electronic states. −/+
3.2. VSi2 The leading configurations, bond distances, vibrational frequencies, relative energies, and atomic charges of the low-lying states of VSi2 cluster are shown in Table 1. The ground state of VSi2 is determined to be 4B1. The V-Si and Si-Si distances of the ground state are computed to be 2.302 and 2.242 Å by the CASPT2 numerical gradient optimization. The potential energy surface of 4B1 is constructed by stretching the VSi2 and Si-Si distances at the CASPT2 level. From the potential energy surface as displayed in Fig. 2, the V-Si and Si-Si distances of 4B1 are determined to be 2.304 and 2.237 Å. It can be seen that the V-Si and SiSi distances as obtained from numerical gradient optimization and potential energy surface in good agreement together. The NPA charges of V and Si atoms are 0.438 and −0.219 e−. The positive charge of V and negative charges of Si atoms are explained by the fact that the electronegativity of Si (1.90) is larger than that of V (1.63). In order to obtain the leading configuration of the 4B1 ground state, the CASSCF molecular orbitals and electron occupation numbers of this state are plotted. As displayed in Fig. 3, the 4B1 has a leading configuration of 12a1213a1114a1015a10 4b125b108b212a21 with a reference weight of 42%. The molecular orbitals of the 4B1 also show strong linear combination between the 3d of V and the 3p of Si2 ligand. The 15a1 is predominantly 4s orbital of V, the 13a1 and 2a2 are nearly non-bonding with the main contribution from the 3d of V. The 11a1, 12a1, 4b1, and 8b2 are bonding orbitals between 3d of V and 3p of Si2 ligand, while the 14a1, 5b1, 9b2, 10b2, and 3a2 are anti-bonding orbitals. The 16a1, 17a1, 6b1, 11b2, and 4a2 are mainly 4d orbitals of V. In addition to the 4B1 ground state, the low-lying excited states of VSi2 are reported in Table 1. Starting from the 4B1 ground state, the first excited 2A2 state with CASPT2 relative energy of 0.49 eV can be
3. Results and discussion 3.1. Computational results The computational results for the low-lying states of the VSi20/−/+ clusters are presented in Table 1. For the low-lying states of VSi20/−/+, the positive vibrational frequencies as computed with the CASPT2 and BP86 functional imply that the optimized structures correspond to minima on potential energy surfaces. The CASPT2, BP86, and CCSD(T) 112
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Table 1 The leading configurations, bond distances, vibrational frequencies, relative energies (REs), and NPA charges of the low-lying states of VSi20/−/+ clusters. (a) The bond distances are calculated at the CASPT2, BP86 functional, and CCSD(T) levels. (b) The vibrational frequencies are evaluated by the CASPT2 and BP86 functional. (c) The CASPT2 relative energies are reported with an active space of 12 orbitals (CASPT2(I)) and of 17 orbitals (CASPT2(II)). (d) The numbers in parentheses are Mulliken atomic charges. State
VSi2 4 B1
Leading configuration
…12a1213a1114a1015a10 4b125b108b212a21 (42%)
2
…12a1213a1014a1015a10 4b125b108b222a21 (63%)
2
…12a1213a1114a1015a10 4b125b108b222a20 (67%)
4
A1
…12a1213a1014a1015a10 4b125b118b212a21 (74%)
14A2
…12a1213a1114a1015a10 4b125b118b212a20 (64%)
4
…12a1213a1114a1115a10 4b125b108b212a20 (67%)
2
B2
…12a1213a1014a1015a10 4b125b108b212a22 (65%)
24A2
…12a1213a1114a1115a10 4b125b108b202a21 (70%)
A2
A1
B2
VSi2− 15A1
…12a1213a1114a1015a10 4b125b118b212a21 (45%)
15B1
…12a1213a1114a1115a10 4b125b108b212a21 (59%)
3
…12a1213a1114a1015a10 4b125b108b222a21 (58%) …12a1213a1114a1015a11 4b125b108b212a21 (52%) …12a1213a1214a1015a10 4b125b108b212a21 (28%) …12a1213a1014a1115a10 4b125b118b212a21 (77%) …12a1213a1114a1115a10 4b125b118b212a20 (67%)
A2 5
2 B1 3
B1
25A1 5
A2
5
…12a1213a1114a1115a11 4b125b108b212a20 (66%)
1
…12a1213a1014a1015a10 4b125b108b222a22 (60%)
3
…12a1213a1114a1115a10 4b125b108b222a20 (58%)
3
…12a1213a1114a1115a11 4b125b108b212a20 (39%)
B2
A1
A1
B2
VSi2+ B1
3
…12a1213a1014a1015a10 4b125b108b212a21 (63%)
3
…12a1213a1114a1015a10 4b125b108b212a20 (61%)
3
…12a1213a1114a1015a10 4b125b108b202a21 (54%) …12a1213a1114a1015a10 4b115b108b212a21 (77%)
B2
A2
5
A1
15B1
…12a1113a1114a1015a10 4b125b108b212a21 (78%)
R1, R2(a) (Å)
Frequency(b) (cm−1)
NPA charge(d) (e−) (V, Si, Si)
RE(c) (eV) BP86
B3LYP
CCSD(T)
CASPT2(I)
CASPT2(II)
2.302, 2.337, 2.335, 2.280, 2.254, 2.285, 2.314, 2.290, 2.297, 2.398, 2.380, 2.389, 2.398, 2.420, 2.417, 2.415, 2.447, 2.440, 2.265, 2.232, 2.241, 2.447,
2.242; 2.227; 2.224 2.329; 2.328; 2.332 2.291; 2.295; 2.308 2.168; 2.203; 2.205 2.187; 2.184; 2.191 2.215; 2.232; 2.222 2.341; 2.321; 2.373 2.198
325, 342, 509 (297, 324, 498)
0.00
0.00
0.00
0.00
0.00
0.438, −0.219, −0.219 (0.530, −0.265, −0.265)
343, 322, 473 (340, 334, 480)
0.57
0.77
0.44
0.45
0.49
0.480, −0.240, −0.240 (0.594, −0.297, −0.297)
168, 366, 477 (317, 361, 476)
0.69
0.79
0.54
0.48
0.55
0.572, −0.286, −0.286 (0.502, −0.251, −0.251)
237, 350, 570 (257, 310, 508)
0.64
0.40
0.45
0.40
0.56
0.689, −0.345, −0.345 (0.620, −0.310, −0.310)
257, 336, 518 (224, 311, 520)
0.83
0.53
0.57
0.62
0.59
0.746, −0.373, −0.373 (0.548, −0.274, −0.274)
254, 300, 493 (291, 332, 516)
1.03
0.69
0.77
0.81
0.80
0.500, −0.250, −0.250 (0.560, −0.280, −0.280)
367, 312, 548 (356, 305, 490)
1.00
1.26
0.82
0.85
0.93
0.340, −0.170, −0.170 (0.556, −0.278, −0.278)
0.76
0.94
0.762, −0.381, −0.381 (0.526, −0.263, −0.263)
2.449, 2.406, 2.437, 2.375, 2.413, 2.440, 2.292, 2.286, 2.430,
2.193; 2.220; 2.206 2.222; 2.243; 2.204 2.379; 2.346 2.198
213, 229, 507 (268, 286, 495)
0.00
0.00
0.00
0.00
0.00
0.339, −0.669, −0.669 (−0.012, −0.494, −0.494)
247, 286, 514 (268, 294, 488)
0.11
0.06
0.01
−0.26
0.05
0.196, −0.598, −0.598 (−0.066, −0.467, −0.467)
360, 314, 467 (350, 317, 459) 326, 252, 473
0.01
0.22
−0.22
0.12
0.06
0.27
0.29
0.39
0.42
0.46
0.050, −0.525, −0.525 (0.044, −0.522, −0.522) 0.246, −0.623, −0.623 (−0.076, −0.462, −0.462) 0.260, −0.630, −0.630 (−0.098, −0.451, −0.451) 0.350, −0.675, −0.675 (−0.014, −0.493, −0.493) 0.460, −0.730, −0.730 (−0.030, −0.485, −0.485)
2.513, 2.183 2.474, 2.194 2.482, 2.542, 2.571, 2.539, 2.561, 2.563, 2.265, 2.264, 2.315, 2.355, 2.353, 2.343, 2.518,
2.175; 2.185; 2.168 2.184; 2.197; 2.184 2.366; 2.346; 2.276 2.329; 2.280; 2.315 2.185
2.346, 2.329, 2.327, 2.379, 2.388, 2.340, 2.367, 2.419, 2.398, 2.443, 2.434, 2.396, 2.461, 2.473,
2.246; 2.256; 2.243 2.224; 2.225; 2.210 2.321; 2.180 2.355; 2.343; 2.322 2.236; 2.179; 2.181
68, 332, 550 0.63
0.33
0.34
0.63
0.48
166, 296, 641 (138, 256, 523)
1.10
0.74
0.54
0.23
0.49
0.540, −0.770, −0.770 (−0.048, −0.476, −0.476)
329, 325, 452 (357, 318, 479)
0.30
1.14
0.60
0.09
0.61
−0.084, −0.458, −0.458 (−0.140, −0.430, −0.430)
(278, 325, 416)
0.98
0.97
0.74
0.23
0.74
0.274, −0.637, −0.637 (−0.052, −0.474, −0.474)
0.51
0.76
0.358, −0.679, −0.679 (−0.050, −0.475, −0.475)
(176, 266, 521)
286, 294, 495 (280, 306, 469)
0.00
0.00
0.00
0.00
0.00
0.836, 0.082, 0.082 (0.916, 0.042, 0.042)
316, 295, 553 (222, 311, 481)
0.27
0.12
0.14
0.22
0.05
0.950, 0.025, 0.025 (0.890, 0.055, 0.055)
196, 320, 423 (321, 329, 539) 251, 288, 465 (288, 296, 464)
0.60
0.42
0.60
0.49
0.53
0.37
0.52
1.15
0.61
0.822, 0.089, 0.089 (0.870, 0.065, 0.065) 0.964, 0.018, 0.018 (0.804, 0.098, 0.098)
311, 283, 442 (257, 293, 507)
0.52
0.33
0.48
0.66
0.65
0.892, 0.054, 0.054 (0.886, 0.057, 0.057)
(continued on next page) 113
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Table 1 (continued) State
Leading configuration
1
A1
…12a1213a1014a1015a10 4b125b108b222a20 (52%)
25B1
…12a1113a1014a1115a10 4b125b108b212a21 (68%) …12a1113a1114a1115a10 4b125b108b212a20 (63%)
5
B2
R1, R2(a) (Å)
Frequency(b) (cm−1)
2.349; 2.362; 2.385 2.276
320, 323, 453 (318, 328, 470)
2.506, 2.191; 2.575, 2.194; 2.542, 2.187
229, 317, 524 (257, 293, 508)
2.304, 2.261, 2.330, 2.415,
NPA charge(d) (e−) (V, Si, Si)
RE(c) (eV) BP86
B3LYP
CCSD(T)
CASPT2(I)
CASPT2(II)
1.08
1.56
0.94
0.89
0.77
0.722, 0.139, 0.139 (0.908, 0.046, 0.046)
0.89
0.86
1.01
0.86
0.890, 0.055, 0.055 (0.874, 0.063, 0.063) 1.072, −0.036, −0.036 (0.902, 0.049, 0.049)
257, 284, 529 1.03
0.62
0.81
Fig. 2. Potential energy surface of the 4B1 of VSi2 cluster as calculated at the CASPT2 level by stretching the Si-Si and V-Si2 distances.
obtained by transferring one electron from the 13a1 to 8b2 orbital. Because the 13a1 is mainly non-bonding orbital of V and the 8b2 is bonding orbital between 3d of V and 3p of Si2 ligand, the V–Si bond distance reduces from 2.302 to 2.280 Å in the transition from the 4B1 to the 2A2. Moreover, the 2A1, 4A1, 14A2, 4B2, 2B2, and 24A2 are above the 4 B1 by 0.55, 0.56, 0.59, 0.80, 0.93, and 0.94 eV. 3.3. VSi2− The CASPT2 relative energies of the electronic states of VSi2− cluster as shown in Table 1 suggest that the 15A1 is the anionic ground state. The V-Si and Si-Si distances of the 15A1 are 2.449 and 2.193 Å. The NPA charges of V and Si in the 15A1 are estimated to be 0.339 and −0.669 e−. Also, a leading configuration of 12a1213a1114a1015a10 4b125b118b212a21 with a reference weight of 45% is proposed for the 15A1. The 15B1 is nearly degenerate to the anionic 15A1 ground state with relative energies of 0.05 eV because the 15B1 is obtained from the 15A1 by moving one electron from an anti-bonding 5b1 orbital to an anti-bonding 14a1 orbital. The excited 3A2, 25B1, 3B1, 25A1, 5A2, 5B2, 1 A1, 3A1, and 3B2 states are 0.12, 0.27, 0.39, 0.46, 0.48, 0.49, 0.61, 0.74, and 0.76 eV less stable than the ground state 15A1, respectively. It can be seen that as compared to the 4B1 ground state of the neutral cluster, the 15A1 ground state of the anionic cluster has larger V-Si distance and smaller Si-Si distance. Particularly, the V-Si distance increases from 2.302 to 2.449 Å, while the Si-Si distance decreases from 2.242 to 2.193 Å in the transition from the 4B1 to the 15A1. This feature can be explained by the structural relaxations during the attachment of one electron to the 5b1 orbital in the transition from the 4B1 to the 15A1.
Fig. 3. The natural molecular orbitals and electron occupation numbers of the 4 B1 of VSi2 cluster as obtained from the CASSCF calculations.
As can be seen in Fig. 3, the 5b1 is an anti-bonding orbital between the 3d of V and the π bonding orbital of Si2 ligand. Therefore, the attachment of one electron to this orbital would result in an increase of V-Si and a decrease of Si-Si distance. The attachment of one electron to the covalent anti-bonding 5b1 orbital is the reason why NPA charges of V and Si atoms mutually reduce from 0.438 and −0.219 e− to 0.339 and −0.669 e− in the transition from the 4B1 to the 15A1. The electron affinity of the neutral cluster is calculated for the transition from the 4B1 to the 15A1 in which one electron is added to the 5b1 orbital. Because the 5b1 is an anti-bonding orbital, the electron affinity of the neutral cluster is predicted to be small. Indeed, the CASPT2 and CCSD(T) calculations provide electron affinities of 1.08 114
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presented in Table 2. The initial state for electron detachments is 15A1 because this quintet state is the ground state of the anionic cluster. Also, because of the electronic selection rules, only one-electron detachment processes are allowed in the anion photoelectron spectroscopy. Therefore, our calculations focus on the one-electron detachment processes. VDEs of the transitions from the 15A1 to the 14B1, 14A1, 14A2, and 24B2 are 1.09, 1.58, 1.67, and 2.45 eV. In these transitions, one electron is respectively detached from the singly occupied 5b1, 13a1, 2a2, and 8b2 orbitals of 15A1. VDEs of the transitions to 26B1, 46A1, and 66A1 are 2.51, 2.94, and 3.66 eV. In the transitions to these sextet states, one electron is removed from the doubly occupied 4b1, 12a1, and 11a1 orbitals of 15A1. From the calculated VDEs of VSi2−, it can be predicted that the photoelectron spectrum could have five bands at 1.09, 1.58, 2.45, 2.94, and 3.66 eV. The bands at 1.67 eV could overlap with the band at 1.58 eV because their VDEs are almost the same. In a similar way, the band at 2.51 eV could join the band at 2.45 eV. Also, the first band at 1.09 eV could be composed of vibrational progressions because there are large structural relaxations during the transition from the 15A1 to 14B1. Because of the detachment of one electron from the anti-bonding 5b1 orbital in the transition from 15A1 to 14B1, the V-Si bond reduces from 2.449 to 2.302 Å, while the Si-Si bond increases from 2.193 to 2.242 Å.
and 1.17 eV for the neutral cluster. The computed electron affinities of VSi2 are smaller than that of VSi (1.46 eV) and VSi3 (1.96 eV) [11,13]. This result can be understood because the electron attachment happens at an anti-bonding orbital in VSi2 cluster, while it occurs at bonding orbitals in VSi and VSi3 clusters. 3.4. VSi2+ The computational results for VSi2+ cluster as presented in Table 1 show that the 3B1 state is the ground state. This triplet state has a leading configuration of 12a1213a1014a1015a10 4b125b108b212a21 with a reference weight of 63%. The 3B1 has V-Si and Si-Si bond distances of 2.346 and 2.246 Å. The NPA charges of V and Si atoms are 0.836 and 0.082 e−. At the CASPT2 level, the 3B2 is nearly degenerate to the 3B1. The 3B2 can be obtained from the 3B1 by moving one electron from 2a2 to 13a1 orbital. Because 2a2 and 13a1 are prominently non-bonding 3d orbitals of V, the energy difference between 3B2 and 3B1 are expected to be small. Indeed, the 3B2 is less stable than the 3B1 by only 0.05 eV as computed at the CASPT2 level. In addition to the 3B2, the 3A2, 5A1, 15B1, 1A1, 25B1 and 5B2 are above the 3B1 by 0.49, 0.61, 0.65, 0.77, 0.86, and 0.86 eV as evaluated at the CASPT2 level. The 3B1 ground state of VSi2+ is obtained from the 4B1 of VSi2 by ionization of one electron from the 13a1 orbital. Because the 13a1 is a nearly non-bonding orbital with the main contribution of the 3d of V, the ionization of one electron from this orbital does not cause large structural relaxations. Indeed, in the transition from 4B1 of VSi2 to 3B1 of VSi2+, the V-Si and Si-Si slightly change from 2.302 and 2.242 Å to 2.346 and 2.246 Å as estimated at the CASPT2 level. The ionization energy of the transition from the 4B1 of VSi2 to the 3B1 of VSi2+ is computed to be 7.07 and 7.08 eV by the CASPT2 and CCSD(T) methods.
4. Conclusion Density functional theory, ROHF/CCSD(T), and CASSCF/CASPT2 methods were employed to investigate the geometric and electronic structures of the ground and excited states of VSi20/−/+ clusters. It was found that the CASSCF/CASPT2 method with an active space of 17 orbitals was able to provide comparable relative energies of the lowlying states to the ROHF/CCSD(T) method. The leading configurations, bond distances, vibrational frequencies, relative energies, and atomic charges of the low-lying electronic states were reported. The ground state of VSi2 cluster was determined to be 4B1. The leading configuration of the 4B1 neutral ground state was 12a1213a1114a1015a10 4b125b108b212a21. The V-Si and Si-Si bond distances of the 4B1 were 2.302 and 2.242 Å. The NPA charges of V and Si in the 4B1 were evaluated to be 0.438 and −0.219 e−. The ground states of VSi2− and VSi2+ were 15A1 and 3B1, respectively. The electron affinity and ionization energy of the neutral cluster were estimated to be 1.08 and 7.07 eV at the CASPT2 level. The V-Si distance increased in the attachment of one electron to the neutral cluster because the attachment happened at the anti-bonding 5b1 orbital. In the ionization of one electron from the mainly non-bonding 13a1 orbital of the neutral cluster, the V-Si slightly increased, while the Si-Si bond remained
3.5. Vertical detachment energies of VSi2− Vertical detachment energies (VDEs) are the energies required to detach electrons from different orbitals of clusters. VDEs are usually measured by anion photoelectron spectroscopy in order to probe the geometric and electronic structures of both anionic and neutral clusters. Although several anion photoelectron spectra of vanadium-doped silicon clusters have been reported and interpreted, it is quite surprising that the photoelectron spectrum of VSi2− is still not known [12,13,16,23]. In order to get insight into the geometric and electronic structures of VSi2−/0 clusters, the VDEs of the anionic cluster are computed by the CASPT2 method. The computational results are important to interpret the anion photoelectron spectrum that can be published in the near future. The VDEs of VSi2− cluster as computed by the CASPT2 method are
Table 2 Vertical detachment energies (VDEs) of the removal of one electron from the 15A1 of VSi2− cluster to form several electronic states of the neutral cluster as computed at the CASPT2 level. State
Leading configuration
Orbital
VDE (eV)
5b1 13a1 2a2
1.09 1.58 1.67 1.77 2.45 2.50 2.51 2.59 2.62 2.94 3.34 3.66
−
VSi2 15A1
11a1212a1213a1114a1015a104b125b118b219b202a213a20
VSi2 14B1 14A1 14A2 14B2 24B2 16A1 26B1 26A1 36A1 46A1 56A1 66A1
11a1212a1213a1114a1015a104b125b108b219b202a213a20 11a1212a1213a1014a1015a104b125b118b219b202a213a20 11a1212a1213a1114a1015a104b125b118b219b202a203a20 11a1212a1213a1114a1115a104b125b108b219b202a203a20 11a1212a1213a1114a1015a104b125b118b209b202a213a20 11a1212a1213a1114a1115a104b115b108b219b202a213a20 11a1212a1213a1114a1015a104b115b118b219b202a213a20 11a1112a1213a1014a1115a104b125b118b219b202a213a20 11a1112a1213a1114a1015a104b125b118b219b202a213a20 11a1212a1113a1114a1015a104b125b118b219b202a213a20 11a1212a1113a1014a1115a104b125b118b219b202a213a20 11a1112a1213a1114a1115a104b125b108b219b212a203a20
115
8b2 4b1
12a1 11a1
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unchanged. The VDEs of the detachments of one electron from the 5b1, 13a1, 2a2, 8b2, 4b1, 12a1, and 11a1 orbitals of 15A1 were 1.09, 1.58, 1.67, 2.45, 2.51, 2.94, and 3.66 eV as evaluated at the CASPT2 level. The computational results provide new insights into the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters.
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Declaration of interests The authors declared that there is no conflict of interest. Acknowledgment This research is supported by Dong Thap University, Vietnam under Grant No. SPD2018.01.15. The authors are grateful to Prof. Dr. Tho Thanh Bui for fruitful discussion. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
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Research paper
The ground and excited low-lying states of VSi20/−/+ clusters from CASSCF/ CASPT2 calculations Minh Thao Nguyena,b, Quoc Tri Trana, Van Tan Trana, a b
T
⁎
Theoretical and Physical Chemistry Division, Dong Thap University, 783-Pham Huu Lau, Ward 6, Cao Lanh City, Dong Thap, Viet Nam Department of Chemistry, University of Science, Vietnam National University – Ho Chi Minh City, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, Viet Nam
H I GH L IG H T S
An active space of 17 orbitals is required to obtain reliable CASPT2 energies. The relative energies of CASPT2 are in agreement with that of the CCSD(T). Bond distances and relative energies of the electronic states are reported. The ground states of VSi20/−/+ clusters are computed to be 4B1, 5A1 , and 3B1. Electron affinity and ionization energy of VSi2 cluster are 1.08 and 7.07 eV. Several vertical detachment energies of the anionic ground state are calculated.
A R T I C LE I N FO
A B S T R A C T
Keywords: VSi20/−/+ clusters CASSCF/CASPT2 Electronic state Electron affinity Ionization energy Electron detachment energy
The geometric and electronic structures of the ground and excited low-lying states of VSi20/−/+ clusters were investigated by the CASSCF/CASPT2 method. The structural parameters, harmonic vibrational frequencies, relative energies, and atomic charges of the low-lying electronic states were presented and discussed. The ground states of VSi20/−/+ clusters were 4B1, 5A1, and 3B1, respectively. At the CASPT2 level, the electron affinity and ionization energy of the neutral clusters were evaluated to be 1.08 and 7.07 eV, respectively. The vertical detachment energies of the detachments of one electron from several orbitals of the anionic cluster were computed.
1. Introduction Silicon clusters have been extensively investigated because of their potential applications in microelectronic industry [1–8]. However, silicon clusters are known to be unstable because of their high reactivity to form dangling bonds on their surface [9]. In order to stabilize silicon clusters, transition metals are incorporated. By doping transition metals, a large amount of stable transition metal-silicon clusters are created [10–22]. In order to search for the stable transition metal-silicon clusters, vanadium-doped silicon clusters were investigated by both experimental and theoretical methods [11–14,16,23–26]. Because the stability of these clusters depends on their size and shape, the experimental and computational methods were carried out to probe the geometric and electronic structures. In particular, the photoelectron spectra of VSin− (n = 3–20), V2Sin− (n = 3–6), and V3Sin− (n = 3–14) clusters were recorded [10,16,23]. The geometric and electronic structures of these clusters were calculated by density functional theory
⁎
and multiconfigurational methods [11–14,23]. The VSi2 moieties can be found in form of nanoparticles and crystals that are investigated because of their applications in heterogeneous catalysts and thermoelectric materials [27,28]. Study of geometric and electronic structures of VSi2 moieties may give important information for a clear understanding of the properties of bulk materials. Although several studies on vanadium-doped silicon clusters have been published, the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters remain poorly understood. To the best of our knowledge, there is still no investigation of the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters. In this study, the geometric and electronic structures of VSi20/−/+ clusters are calculated by the CASSCF/CASPT2 methods. This computational method has proved to be sufficient to calculate the geometric and electronic structures of the low-lying states of vanadium-doped silicon clusters as VSi0/−/+, VSi3−/0, and VSi4−/0 [11–13]. The accuracy of CASPT2 method is calibrated with density functional theory and ROHF/
Corresponding author. E-mail address: [email protected] (V.T. Tran).
https://doi.org/10.1016/j.cplett.2019.02.043 Received 17 December 2018; Received in revised form 18 February 2019; Accepted 19 February 2019 Available online 05 March 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.
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methods predict slightly different V-Si and Si-Si bond distances. The difference between NPA and Mulliken charges are small for the neutral and cationic clusters, while it becomes large for the anionic cluster. For the 15A1 of VSi2−, the NPA charges of V and Si are 0.339 and −0.669 e−, while the Mulliken charges of these atoms are −0.012 and −0.494 e−. In the following discussion, NPA charge is utilized because it is known to be much less basis set dependent than Mulliken Population. The relative energies of the low-lying states of VSi20/−/+ clusters are reported at the BP86, B3LYP, CCSD(T), and CASPT2 levels in Table 1. The CASPT2 relative energies with an active space of 12 and 17 orbitals are respectively denoted as CASPT2(I) and CASPT2(II). The CASPT2 relative energies slightly change with the active spaces. The strongest variation appears in the case of 15A1 and 15B1 of the anionic cluster. In particular, the 15A1 is 0.26 eV less stable than the 15B1 at the CASPT2(I) level, while the former state becomes 0.05 eV more stable than the latter state at the CASPT2(II) level. Because the double-shell 3d, 4d effects of V are only included in the active space of CASPT2(II), it can be said that the double-shell effects of V are important to obtain a sufficient relative energy order of the electronic states of VSi20/−/+ clusters. This result is also supported by the BP86 and B3LYP functional and CCSD(T) calculations in which the 15A1 is above the 15B1 by 0.11, 0.06, and 0.01 eV. For the other electronic states of VSi20/−/+ clusters, the relative energies of the CASPT2(II) correspond well with those of the CCSD(T). In the subsequent discussion, the CASPT2 results are used instead of the CCSD(T) because the CASPT2 can access all the relevant low-lying states of VSi20/−/+ clusters and because the CCSD(T) calculations for the excited states are difficult to converge. In contrast to the CASPT2 and CCSD(T), the relative energies of density functional theory depend on the functionals. This feature can be seen in the case of the 1 A1 of VSi2− in which the relative energies are evaluated to be 0.30 and 1.14 eV by the BP86 and B3LYP functionals. These relative energies differ from the values of 0.60 and 0.61 eV of the CCSD(T) and CASPT2. Overall, the above discussion shows that the CASSCF/CASPT2 method with an active space of 17 orbitals (CASPT2(II)) is sufficient to obtain reliable relative energies of the low-lying states of VSi20/−/+ clusters.
Fig. 1. The geometric structure of VSi20/−/+ clusters.
CCSD(T) results. The leading configurations, structural parameters, harmonic vibrational frequencies, atomic charges, and relative energies of the low-lying states of VSi20/−/+ clusters will be reported. The vertical detachment energies of the removals of one electron from different orbitals of the anionic cluster will be calculated to predict the main features of the anion photoelectron spectrum. 2. Computational methods The geometries of the ground and excited low-lying states of VSi20/ clusters were optimized with density functional theory, ROHF/ CCSD(T), and CASSCF/CASPT2 methods. It has been known from the literature that MSi2 clusters have cyclic geometry with C2v symmetry as presented in Fig. 1 [15,29]. Therefore, this geometry was used as the initial structure for the geometry optimizations of the low-lying states of VSi20/−/+ clusters. In density functional calculations, the BP86 [30,31] and B3LYP [30,32,33] functionals were used with def2-QZVP basis sets [34]. Vibrational frequency calculations were carried out with the BP86 functional to ensure that the optimized structures correspond to minima on potential energy surfaces. In the ROHF/CCSD(T) and CASSCF/CASPT2 calculations, the aug-cc-pwCVTZ-DK and aug-ccpVTZ-DK basis sets were utilized for V and Si [35,36]; the scalar relativistic effects were covered by using the second-order Douglas-Kroll Hamiltonian [37–39]; and the 3 s, 3p of V and 3 s of Si were correlated. To reduce the memories for storing two-electron integrals, Cholesky decomposition with an accuracy of 10−6 a.u. was employed for the CASSCF/CASPT2 calculations. To prevent the intruder states, an imaginary shift of 0.1 was applied to the CASPT2. Density functional and ROHF/CCSD(T) calculations were carried out with NWCHEM 6.6 [40], and the CASSCF/CASPT2 calculations were performed with MOLCAS@ UU 8.0 [41]. Natural population analysis (NPA) was performed with JANPA 2.0.2 [42] based on CASSCF wave functions to estimate atomic charges of VSi20/−/+ clusters. The active space orbitals for CASSCF/CASPT2 calculations can be selected based on the valence orbitals of V and Si [11–13,43]. For VSi20/−/+ clusters, the active space was chosen to include the 3d, 4s orbitals of V and the 3p orbitals of Si. This approach results in an active space of 12 orbitals in which 9, 10, or 8 electrons are distributed. This active space was utilized to optimize the geometries and to calculate the harmonic vibrational frequencies of the electronic states. In order to include the double-shell effects of V, the 4d orbitals of V were added to form an active space of 17 orbitals. This active space was employed for single-point calculations to improve the energies of the electronic states. −/+
3.2. VSi2 The leading configurations, bond distances, vibrational frequencies, relative energies, and atomic charges of the low-lying states of VSi2 cluster are shown in Table 1. The ground state of VSi2 is determined to be 4B1. The V-Si and Si-Si distances of the ground state are computed to be 2.302 and 2.242 Å by the CASPT2 numerical gradient optimization. The potential energy surface of 4B1 is constructed by stretching the VSi2 and Si-Si distances at the CASPT2 level. From the potential energy surface as displayed in Fig. 2, the V-Si and Si-Si distances of 4B1 are determined to be 2.304 and 2.237 Å. It can be seen that the V-Si and SiSi distances as obtained from numerical gradient optimization and potential energy surface in good agreement together. The NPA charges of V and Si atoms are 0.438 and −0.219 e−. The positive charge of V and negative charges of Si atoms are explained by the fact that the electronegativity of Si (1.90) is larger than that of V (1.63). In order to obtain the leading configuration of the 4B1 ground state, the CASSCF molecular orbitals and electron occupation numbers of this state are plotted. As displayed in Fig. 3, the 4B1 has a leading configuration of 12a1213a1114a1015a10 4b125b108b212a21 with a reference weight of 42%. The molecular orbitals of the 4B1 also show strong linear combination between the 3d of V and the 3p of Si2 ligand. The 15a1 is predominantly 4s orbital of V, the 13a1 and 2a2 are nearly non-bonding with the main contribution from the 3d of V. The 11a1, 12a1, 4b1, and 8b2 are bonding orbitals between 3d of V and 3p of Si2 ligand, while the 14a1, 5b1, 9b2, 10b2, and 3a2 are anti-bonding orbitals. The 16a1, 17a1, 6b1, 11b2, and 4a2 are mainly 4d orbitals of V. In addition to the 4B1 ground state, the low-lying excited states of VSi2 are reported in Table 1. Starting from the 4B1 ground state, the first excited 2A2 state with CASPT2 relative energy of 0.49 eV can be
3. Results and discussion 3.1. Computational results The computational results for the low-lying states of the VSi20/−/+ clusters are presented in Table 1. For the low-lying states of VSi20/−/+, the positive vibrational frequencies as computed with the CASPT2 and BP86 functional imply that the optimized structures correspond to minima on potential energy surfaces. The CASPT2, BP86, and CCSD(T) 112
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Table 1 The leading configurations, bond distances, vibrational frequencies, relative energies (REs), and NPA charges of the low-lying states of VSi20/−/+ clusters. (a) The bond distances are calculated at the CASPT2, BP86 functional, and CCSD(T) levels. (b) The vibrational frequencies are evaluated by the CASPT2 and BP86 functional. (c) The CASPT2 relative energies are reported with an active space of 12 orbitals (CASPT2(I)) and of 17 orbitals (CASPT2(II)). (d) The numbers in parentheses are Mulliken atomic charges. State
VSi2 4 B1
Leading configuration
…12a1213a1114a1015a10 4b125b108b212a21 (42%)
2
…12a1213a1014a1015a10 4b125b108b222a21 (63%)
2
…12a1213a1114a1015a10 4b125b108b222a20 (67%)
4
A1
…12a1213a1014a1015a10 4b125b118b212a21 (74%)
14A2
…12a1213a1114a1015a10 4b125b118b212a20 (64%)
4
…12a1213a1114a1115a10 4b125b108b212a20 (67%)
2
B2
…12a1213a1014a1015a10 4b125b108b212a22 (65%)
24A2
…12a1213a1114a1115a10 4b125b108b202a21 (70%)
A2
A1
B2
VSi2− 15A1
…12a1213a1114a1015a10 4b125b118b212a21 (45%)
15B1
…12a1213a1114a1115a10 4b125b108b212a21 (59%)
3
…12a1213a1114a1015a10 4b125b108b222a21 (58%) …12a1213a1114a1015a11 4b125b108b212a21 (52%) …12a1213a1214a1015a10 4b125b108b212a21 (28%) …12a1213a1014a1115a10 4b125b118b212a21 (77%) …12a1213a1114a1115a10 4b125b118b212a20 (67%)
A2 5
2 B1 3
B1
25A1 5
A2
5
…12a1213a1114a1115a11 4b125b108b212a20 (66%)
1
…12a1213a1014a1015a10 4b125b108b222a22 (60%)
3
…12a1213a1114a1115a10 4b125b108b222a20 (58%)
3
…12a1213a1114a1115a11 4b125b108b212a20 (39%)
B2
A1
A1
B2
VSi2+ B1
3
…12a1213a1014a1015a10 4b125b108b212a21 (63%)
3
…12a1213a1114a1015a10 4b125b108b212a20 (61%)
3
…12a1213a1114a1015a10 4b125b108b202a21 (54%) …12a1213a1114a1015a10 4b115b108b212a21 (77%)
B2
A2
5
A1
15B1
…12a1113a1114a1015a10 4b125b108b212a21 (78%)
R1, R2(a) (Å)
Frequency(b) (cm−1)
NPA charge(d) (e−) (V, Si, Si)
RE(c) (eV) BP86
B3LYP
CCSD(T)
CASPT2(I)
CASPT2(II)
2.302, 2.337, 2.335, 2.280, 2.254, 2.285, 2.314, 2.290, 2.297, 2.398, 2.380, 2.389, 2.398, 2.420, 2.417, 2.415, 2.447, 2.440, 2.265, 2.232, 2.241, 2.447,
2.242; 2.227; 2.224 2.329; 2.328; 2.332 2.291; 2.295; 2.308 2.168; 2.203; 2.205 2.187; 2.184; 2.191 2.215; 2.232; 2.222 2.341; 2.321; 2.373 2.198
325, 342, 509 (297, 324, 498)
0.00
0.00
0.00
0.00
0.00
0.438, −0.219, −0.219 (0.530, −0.265, −0.265)
343, 322, 473 (340, 334, 480)
0.57
0.77
0.44
0.45
0.49
0.480, −0.240, −0.240 (0.594, −0.297, −0.297)
168, 366, 477 (317, 361, 476)
0.69
0.79
0.54
0.48
0.55
0.572, −0.286, −0.286 (0.502, −0.251, −0.251)
237, 350, 570 (257, 310, 508)
0.64
0.40
0.45
0.40
0.56
0.689, −0.345, −0.345 (0.620, −0.310, −0.310)
257, 336, 518 (224, 311, 520)
0.83
0.53
0.57
0.62
0.59
0.746, −0.373, −0.373 (0.548, −0.274, −0.274)
254, 300, 493 (291, 332, 516)
1.03
0.69
0.77
0.81
0.80
0.500, −0.250, −0.250 (0.560, −0.280, −0.280)
367, 312, 548 (356, 305, 490)
1.00
1.26
0.82
0.85
0.93
0.340, −0.170, −0.170 (0.556, −0.278, −0.278)
0.76
0.94
0.762, −0.381, −0.381 (0.526, −0.263, −0.263)
2.449, 2.406, 2.437, 2.375, 2.413, 2.440, 2.292, 2.286, 2.430,
2.193; 2.220; 2.206 2.222; 2.243; 2.204 2.379; 2.346 2.198
213, 229, 507 (268, 286, 495)
0.00
0.00
0.00
0.00
0.00
0.339, −0.669, −0.669 (−0.012, −0.494, −0.494)
247, 286, 514 (268, 294, 488)
0.11
0.06
0.01
−0.26
0.05
0.196, −0.598, −0.598 (−0.066, −0.467, −0.467)
360, 314, 467 (350, 317, 459) 326, 252, 473
0.01
0.22
−0.22
0.12
0.06
0.27
0.29
0.39
0.42
0.46
0.050, −0.525, −0.525 (0.044, −0.522, −0.522) 0.246, −0.623, −0.623 (−0.076, −0.462, −0.462) 0.260, −0.630, −0.630 (−0.098, −0.451, −0.451) 0.350, −0.675, −0.675 (−0.014, −0.493, −0.493) 0.460, −0.730, −0.730 (−0.030, −0.485, −0.485)
2.513, 2.183 2.474, 2.194 2.482, 2.542, 2.571, 2.539, 2.561, 2.563, 2.265, 2.264, 2.315, 2.355, 2.353, 2.343, 2.518,
2.175; 2.185; 2.168 2.184; 2.197; 2.184 2.366; 2.346; 2.276 2.329; 2.280; 2.315 2.185
2.346, 2.329, 2.327, 2.379, 2.388, 2.340, 2.367, 2.419, 2.398, 2.443, 2.434, 2.396, 2.461, 2.473,
2.246; 2.256; 2.243 2.224; 2.225; 2.210 2.321; 2.180 2.355; 2.343; 2.322 2.236; 2.179; 2.181
68, 332, 550 0.63
0.33
0.34
0.63
0.48
166, 296, 641 (138, 256, 523)
1.10
0.74
0.54
0.23
0.49
0.540, −0.770, −0.770 (−0.048, −0.476, −0.476)
329, 325, 452 (357, 318, 479)
0.30
1.14
0.60
0.09
0.61
−0.084, −0.458, −0.458 (−0.140, −0.430, −0.430)
(278, 325, 416)
0.98
0.97
0.74
0.23
0.74
0.274, −0.637, −0.637 (−0.052, −0.474, −0.474)
0.51
0.76
0.358, −0.679, −0.679 (−0.050, −0.475, −0.475)
(176, 266, 521)
286, 294, 495 (280, 306, 469)
0.00
0.00
0.00
0.00
0.00
0.836, 0.082, 0.082 (0.916, 0.042, 0.042)
316, 295, 553 (222, 311, 481)
0.27
0.12
0.14
0.22
0.05
0.950, 0.025, 0.025 (0.890, 0.055, 0.055)
196, 320, 423 (321, 329, 539) 251, 288, 465 (288, 296, 464)
0.60
0.42
0.60
0.49
0.53
0.37
0.52
1.15
0.61
0.822, 0.089, 0.089 (0.870, 0.065, 0.065) 0.964, 0.018, 0.018 (0.804, 0.098, 0.098)
311, 283, 442 (257, 293, 507)
0.52
0.33
0.48
0.66
0.65
0.892, 0.054, 0.054 (0.886, 0.057, 0.057)
(continued on next page) 113
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Table 1 (continued) State
Leading configuration
1
A1
…12a1213a1014a1015a10 4b125b108b222a20 (52%)
25B1
…12a1113a1014a1115a10 4b125b108b212a21 (68%) …12a1113a1114a1115a10 4b125b108b212a20 (63%)
5
B2
R1, R2(a) (Å)
Frequency(b) (cm−1)
2.349; 2.362; 2.385 2.276
320, 323, 453 (318, 328, 470)
2.506, 2.191; 2.575, 2.194; 2.542, 2.187
229, 317, 524 (257, 293, 508)
2.304, 2.261, 2.330, 2.415,
NPA charge(d) (e−) (V, Si, Si)
RE(c) (eV) BP86
B3LYP
CCSD(T)
CASPT2(I)
CASPT2(II)
1.08
1.56
0.94
0.89
0.77
0.722, 0.139, 0.139 (0.908, 0.046, 0.046)
0.89
0.86
1.01
0.86
0.890, 0.055, 0.055 (0.874, 0.063, 0.063) 1.072, −0.036, −0.036 (0.902, 0.049, 0.049)
257, 284, 529 1.03
0.62
0.81
Fig. 2. Potential energy surface of the 4B1 of VSi2 cluster as calculated at the CASPT2 level by stretching the Si-Si and V-Si2 distances.
obtained by transferring one electron from the 13a1 to 8b2 orbital. Because the 13a1 is mainly non-bonding orbital of V and the 8b2 is bonding orbital between 3d of V and 3p of Si2 ligand, the V–Si bond distance reduces from 2.302 to 2.280 Å in the transition from the 4B1 to the 2A2. Moreover, the 2A1, 4A1, 14A2, 4B2, 2B2, and 24A2 are above the 4 B1 by 0.55, 0.56, 0.59, 0.80, 0.93, and 0.94 eV. 3.3. VSi2− The CASPT2 relative energies of the electronic states of VSi2− cluster as shown in Table 1 suggest that the 15A1 is the anionic ground state. The V-Si and Si-Si distances of the 15A1 are 2.449 and 2.193 Å. The NPA charges of V and Si in the 15A1 are estimated to be 0.339 and −0.669 e−. Also, a leading configuration of 12a1213a1114a1015a10 4b125b118b212a21 with a reference weight of 45% is proposed for the 15A1. The 15B1 is nearly degenerate to the anionic 15A1 ground state with relative energies of 0.05 eV because the 15B1 is obtained from the 15A1 by moving one electron from an anti-bonding 5b1 orbital to an anti-bonding 14a1 orbital. The excited 3A2, 25B1, 3B1, 25A1, 5A2, 5B2, 1 A1, 3A1, and 3B2 states are 0.12, 0.27, 0.39, 0.46, 0.48, 0.49, 0.61, 0.74, and 0.76 eV less stable than the ground state 15A1, respectively. It can be seen that as compared to the 4B1 ground state of the neutral cluster, the 15A1 ground state of the anionic cluster has larger V-Si distance and smaller Si-Si distance. Particularly, the V-Si distance increases from 2.302 to 2.449 Å, while the Si-Si distance decreases from 2.242 to 2.193 Å in the transition from the 4B1 to the 15A1. This feature can be explained by the structural relaxations during the attachment of one electron to the 5b1 orbital in the transition from the 4B1 to the 15A1.
Fig. 3. The natural molecular orbitals and electron occupation numbers of the 4 B1 of VSi2 cluster as obtained from the CASSCF calculations.
As can be seen in Fig. 3, the 5b1 is an anti-bonding orbital between the 3d of V and the π bonding orbital of Si2 ligand. Therefore, the attachment of one electron to this orbital would result in an increase of V-Si and a decrease of Si-Si distance. The attachment of one electron to the covalent anti-bonding 5b1 orbital is the reason why NPA charges of V and Si atoms mutually reduce from 0.438 and −0.219 e− to 0.339 and −0.669 e− in the transition from the 4B1 to the 15A1. The electron affinity of the neutral cluster is calculated for the transition from the 4B1 to the 15A1 in which one electron is added to the 5b1 orbital. Because the 5b1 is an anti-bonding orbital, the electron affinity of the neutral cluster is predicted to be small. Indeed, the CASPT2 and CCSD(T) calculations provide electron affinities of 1.08 114
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presented in Table 2. The initial state for electron detachments is 15A1 because this quintet state is the ground state of the anionic cluster. Also, because of the electronic selection rules, only one-electron detachment processes are allowed in the anion photoelectron spectroscopy. Therefore, our calculations focus on the one-electron detachment processes. VDEs of the transitions from the 15A1 to the 14B1, 14A1, 14A2, and 24B2 are 1.09, 1.58, 1.67, and 2.45 eV. In these transitions, one electron is respectively detached from the singly occupied 5b1, 13a1, 2a2, and 8b2 orbitals of 15A1. VDEs of the transitions to 26B1, 46A1, and 66A1 are 2.51, 2.94, and 3.66 eV. In the transitions to these sextet states, one electron is removed from the doubly occupied 4b1, 12a1, and 11a1 orbitals of 15A1. From the calculated VDEs of VSi2−, it can be predicted that the photoelectron spectrum could have five bands at 1.09, 1.58, 2.45, 2.94, and 3.66 eV. The bands at 1.67 eV could overlap with the band at 1.58 eV because their VDEs are almost the same. In a similar way, the band at 2.51 eV could join the band at 2.45 eV. Also, the first band at 1.09 eV could be composed of vibrational progressions because there are large structural relaxations during the transition from the 15A1 to 14B1. Because of the detachment of one electron from the anti-bonding 5b1 orbital in the transition from 15A1 to 14B1, the V-Si bond reduces from 2.449 to 2.302 Å, while the Si-Si bond increases from 2.193 to 2.242 Å.
and 1.17 eV for the neutral cluster. The computed electron affinities of VSi2 are smaller than that of VSi (1.46 eV) and VSi3 (1.96 eV) [11,13]. This result can be understood because the electron attachment happens at an anti-bonding orbital in VSi2 cluster, while it occurs at bonding orbitals in VSi and VSi3 clusters. 3.4. VSi2+ The computational results for VSi2+ cluster as presented in Table 1 show that the 3B1 state is the ground state. This triplet state has a leading configuration of 12a1213a1014a1015a10 4b125b108b212a21 with a reference weight of 63%. The 3B1 has V-Si and Si-Si bond distances of 2.346 and 2.246 Å. The NPA charges of V and Si atoms are 0.836 and 0.082 e−. At the CASPT2 level, the 3B2 is nearly degenerate to the 3B1. The 3B2 can be obtained from the 3B1 by moving one electron from 2a2 to 13a1 orbital. Because 2a2 and 13a1 are prominently non-bonding 3d orbitals of V, the energy difference between 3B2 and 3B1 are expected to be small. Indeed, the 3B2 is less stable than the 3B1 by only 0.05 eV as computed at the CASPT2 level. In addition to the 3B2, the 3A2, 5A1, 15B1, 1A1, 25B1 and 5B2 are above the 3B1 by 0.49, 0.61, 0.65, 0.77, 0.86, and 0.86 eV as evaluated at the CASPT2 level. The 3B1 ground state of VSi2+ is obtained from the 4B1 of VSi2 by ionization of one electron from the 13a1 orbital. Because the 13a1 is a nearly non-bonding orbital with the main contribution of the 3d of V, the ionization of one electron from this orbital does not cause large structural relaxations. Indeed, in the transition from 4B1 of VSi2 to 3B1 of VSi2+, the V-Si and Si-Si slightly change from 2.302 and 2.242 Å to 2.346 and 2.246 Å as estimated at the CASPT2 level. The ionization energy of the transition from the 4B1 of VSi2 to the 3B1 of VSi2+ is computed to be 7.07 and 7.08 eV by the CASPT2 and CCSD(T) methods.
4. Conclusion Density functional theory, ROHF/CCSD(T), and CASSCF/CASPT2 methods were employed to investigate the geometric and electronic structures of the ground and excited states of VSi20/−/+ clusters. It was found that the CASSCF/CASPT2 method with an active space of 17 orbitals was able to provide comparable relative energies of the lowlying states to the ROHF/CCSD(T) method. The leading configurations, bond distances, vibrational frequencies, relative energies, and atomic charges of the low-lying electronic states were reported. The ground state of VSi2 cluster was determined to be 4B1. The leading configuration of the 4B1 neutral ground state was 12a1213a1114a1015a10 4b125b108b212a21. The V-Si and Si-Si bond distances of the 4B1 were 2.302 and 2.242 Å. The NPA charges of V and Si in the 4B1 were evaluated to be 0.438 and −0.219 e−. The ground states of VSi2− and VSi2+ were 15A1 and 3B1, respectively. The electron affinity and ionization energy of the neutral cluster were estimated to be 1.08 and 7.07 eV at the CASPT2 level. The V-Si distance increased in the attachment of one electron to the neutral cluster because the attachment happened at the anti-bonding 5b1 orbital. In the ionization of one electron from the mainly non-bonding 13a1 orbital of the neutral cluster, the V-Si slightly increased, while the Si-Si bond remained
3.5. Vertical detachment energies of VSi2− Vertical detachment energies (VDEs) are the energies required to detach electrons from different orbitals of clusters. VDEs are usually measured by anion photoelectron spectroscopy in order to probe the geometric and electronic structures of both anionic and neutral clusters. Although several anion photoelectron spectra of vanadium-doped silicon clusters have been reported and interpreted, it is quite surprising that the photoelectron spectrum of VSi2− is still not known [12,13,16,23]. In order to get insight into the geometric and electronic structures of VSi2−/0 clusters, the VDEs of the anionic cluster are computed by the CASPT2 method. The computational results are important to interpret the anion photoelectron spectrum that can be published in the near future. The VDEs of VSi2− cluster as computed by the CASPT2 method are
Table 2 Vertical detachment energies (VDEs) of the removal of one electron from the 15A1 of VSi2− cluster to form several electronic states of the neutral cluster as computed at the CASPT2 level. State
Leading configuration
Orbital
VDE (eV)
5b1 13a1 2a2
1.09 1.58 1.67 1.77 2.45 2.50 2.51 2.59 2.62 2.94 3.34 3.66
−
VSi2 15A1
11a1212a1213a1114a1015a104b125b118b219b202a213a20
VSi2 14B1 14A1 14A2 14B2 24B2 16A1 26B1 26A1 36A1 46A1 56A1 66A1
11a1212a1213a1114a1015a104b125b108b219b202a213a20 11a1212a1213a1014a1015a104b125b118b219b202a213a20 11a1212a1213a1114a1015a104b125b118b219b202a203a20 11a1212a1213a1114a1115a104b125b108b219b202a203a20 11a1212a1213a1114a1015a104b125b118b209b202a213a20 11a1212a1213a1114a1115a104b115b108b219b202a213a20 11a1212a1213a1114a1015a104b115b118b219b202a213a20 11a1112a1213a1014a1115a104b125b118b219b202a213a20 11a1112a1213a1114a1015a104b125b118b219b202a213a20 11a1212a1113a1114a1015a104b125b118b219b202a213a20 11a1212a1113a1014a1115a104b125b118b219b202a213a20 11a1112a1213a1114a1115a104b125b108b219b212a203a20
115
8b2 4b1
12a1 11a1
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unchanged. The VDEs of the detachments of one electron from the 5b1, 13a1, 2a2, 8b2, 4b1, 12a1, and 11a1 orbitals of 15A1 were 1.09, 1.58, 1.67, 2.45, 2.51, 2.94, and 3.66 eV as evaluated at the CASPT2 level. The computational results provide new insights into the geometric and electronic structures of the low-lying states of VSi20/−/+ clusters.
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Declaration of interests The authors declared that there is no conflict of interest. Acknowledgment This research is supported by Dong Thap University, Vietnam under Grant No. SPD2018.01.15. The authors are grateful to Prof. Dr. Tho Thanh Bui for fruitful discussion. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
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