- Email: [email protected]
A theoretical investigation on electronic properties and stability of IrSix (x=1–6) clusters
Chemical Physics 286 (2003) 181–192 www.elsevier.com/locate/chemphys
A theoretical investigation on electronic properties and stability of IrSix (x ¼ 1–6) clusters Ju-Guang Han * National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, PR China Structural Research Laboratory and The Key Laboratory of Structural Biology, USTC of Chinese Academy of Sciences, Hefei 230029, PR China Received 11 January 2002
Abstract A series of computational investigations on IrSin (n ¼ 1–6) clusters is reported. For each unit, geometry optimizations are performed at the UB3LYP/LanL2DZ level, subsequently, electronic and bonding features of the resulting equilibrium structure are presented and discussed. The emphasis of this study is placed on the geometries, stabilities and electron properties of IrSin (n ¼ 1–6) systems and, more specifically, the impact of the their spins on the internal electron transfer between the Sin subsystem and the Ir atom. As a general trend for IrSin clusters with n > 1, we record a change of the natural charge from negative to positive on Ir atom in IrSi and IrSi2 clusters, charges transferring from Si to Ir in IrSin (n ¼ 3–6) clusters as the spin constraint on the system increases from S ¼ 1=2 to 5/2. This feature is shown to be associated with a pronounced drop in the stability of the IrSin (n 6¼ 3) clusters as one goes from the doublet to the sextet spin configurations. It should be mentioned that equilibrium geometries of IrSin (n ¼ 3–6) clusters and ground electron states of IrSi and IrSi3 clusters are obviously different from MSin (M ¼ Cr, Mo, W, Ag, n ¼ 1–6). Our theoretical results show that IrSi2 cluster is the most stable cluster of all IrSin clusters, which is in good agreement with experimental result available. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction There has been a great deal of interest in negative magnetoresistance in materials, specifically in various classes of materials, including the magnetic semiconductors such as Rex Si1x (Re ¼ Gd, Tb) family of compounds. Magneto-resistive materials
* Present address: Department of Chemistry and Biochemistry, Texas Technology University, Lubbock, TX 79409-1061, USA. Fax: +86-551-3603754. E-mail address: [email protected]
find potential application in magnetic devices such as read heads and sensors in storage media. Of particular interest is to calculate, synthesize, characterize and study the magnetic and transport properties of rare earth transition metal intermetallics. Examination of solid-state materials reveals a striking change in properties due to the substitution of various metals. The study of relationships between crystal structures and electronic and magnetic properties will enable us to gain insights into the nature of the bonding. Because transition metal (TM) doped silicon is a semiconducting cluster of great importance in microelectronic
0301-0104/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 9 3 3 - 3
182
J.-G. Han / Chemical Physics 286 (2003) 181–192
technology, experimentally and theoretically [1–8]. There is currently great of interest in utilizing small clusters as constituent elements to build up well-controlled nanostructures, surface or bulk of a material. This consideration provides a strong motivation for the study of mixed TM-silicon clusters. In particular, the clusters are so stable and can be used as a tunable building block for cluster-assemble material. Beck and Hiura [6,9] have pioneered the experimental investigation of small mixed transition metal–silicon clusters (MSin ; M ¼ Cr, Mo, W, Ir, Re, Hf, Ta; n 6 18) by mass spectrometry. Scherer et al. [17–19] have produced mixed transitional metal silicides by time-of-flight mass spectroscopy, and studied the electronic states of CuSi, AgSi [20] and AuSi dimmers by measuring their laser absorption spectra as well as by theoretical calculation using CASPT2 method [21]. In addition, the VSi and NbSi dimmers have been investigated by matrix-isolated ESP spectroscopy [22], and bond energies are reported [23–25], furthermore, a systematic investigation on ZrSi20 cage [4], NiSi [5], MSin (M ¼ V, Nb, Ta; n ¼ 1–6) clusters [26] is studied by density functional method. AuSin (n ¼ 1–3) clusters are studied [27] by relativistic density functional method as well as ab initio method. With the aim to simulate and to predict the structures and properties, the technically important clusters have attracted attentions theoretically [1–16]. After the work of a density functional theoretical study on MSi15 and MSi17 (M ¼ Cr, Mo and W) [10] clusters has been performed, moreover, the charge transfer mechanism and the equilibrium geometries of MSin (M ¼ Cr, Mo, W, Ag; n ¼ 1–6) [11,12,31] and CuSin clusters [13] have been explored by use of Gaussian 98 program [28], theoretical investigations on metcars [29] clusters are reported also. In the case of silver silicides, the previous gas phase work consists of measurements of the dissociation energy of AgSi diatom deduced in the mass spectrometric studies of Rickert et al. [30] as well as ab initio study on AgSin (n ¼ 1–5) clusters [31]. Furthermore, the experimental investigation on iridium silicides by mass analysis, which includes the first gas phase spectra for any iridium silicides as well as the first direct evident for the
existence of polyatomic iridium silicides, is carried out. The results of the iridium silicides (IrSin and IrSin H2n ), which provide the insight into the information mechanism and properties of these species, are presented [6]. Experimental results [6] indicate that the relative abundance of Si2 Ir is the biggest one of all IrSin (n ¼ 1–6) clusters, in the other word, IrSi2 is the most stable one. To achieve a deeper and systematical understanding of any class of clusters, it is important to investigate the evolution of cluster properties with the size of the system. The present work is intended to serve this purpose, as it contains comparison between various small IrSin species with n < 7, thereby containing a serious of computational studies on small Sin M units that was recently started with an analysis of Sin M (M ¼ Cr, Mo, W, Ag) clusters [10–12,15,31]. We also examine if the substitution of Ir atom upon/into silicon cluster deprives each clusters without any major rearrangement of the framework of Si clusters. The structures and electronic properties of Sin Ir (n ¼ 1–6) clusters have not been determined theoretically and there no systematic investigations within the same approach, the main objective of this studies, therefore, is to provide theoretical data for the geometries, stabilities and charge transfer of the iridium silicides. We will concentrate on doping or surface site of Ir atom. To compare with experimental results, to give a reasonable explanation of the experimental phenomenon and to reveal the electron properties, hence calculation studies of total energy, geometry, along with the theoretical value of natural population and natural electron configuration, are performed by the density functional method in this paper.
2. Computational details In the present calculations, the DFT method is unrestricted (U) B3LYP [32,33] exchange-correlation potential and an effective core potential LanL2DZ basis sets [34–36]. The exchange term of UB3LYP consists of hybrid Hartree–Fock and local spin density (LSD) exchange functions with
J.-G. Han / Chemical Physics 286 (2003) 181–192
BeckeÕs gradient correlation to LSD exchange [37]. The correlation term of UB3LYP consists of the VWN3 local correlation functional and LYP (Lee, Yang and Parr) correlation correction functional. The UB3LYP method gives an improvement over SCF-HF results. Its predictions are in qualitative agreement with experimental values. In general, the DFT method overestimates the energies, and it gives shorter bond lengths than the experimental results. However, the optimized structures predicted at the UB3LYP level are in good agreement with experimental values. LanL2DZ basis sets are become widely used in quantum chemistry, particularly in the investigation on compounds containing heavy elements (atoms) [12,15,31]. The LanL2DZ basis sets have been employed to calculate the equilibrium geometries and spectroscopic properties of small molecules or clusters. The standard LanL2DZ basis sets of ECP theory consistent not only within the first row transition metal, but also with the second and third row transition metals. The LanL2DZ basis sets do not degrade when going from second to third row transition metal of the periodic table [11,12,15,31]. On the other hand, it has been shown that the LanL2DZ basis sets are capable of generating results of very satisfactory quality for TM compounds [11,12,15,31]. This examination of equilibrium bond lengths and angles lead to deviations of typically 1–6%. Due to its reliance on pseudopotentials, our study has to be considered as preliminary and qualitative in nature. All density functional theory (DFT) computations (ab initio) are performed with the Gaussian 98 [28] program package. Geometries are optimized at the hybrid functional DFT-UB3LYP [32,33] levels, employing LanL2DZ (Stuttgart/ Dresden effective core potential) basis sets [34–36]. A systematic investigation of IrSin (n ¼ 1–6) clusters at the UB3LYP/LanL2DZ level will give a general conclusion. In our calculation for IrSin (n ¼ 1–6) clusters, as a test the Ir2 molecule is analyzed at the B3LYP/LanL2DZ level, the Ir–Ir ) of Ir2 cluster is obtained. bond length (2.2159 A No theoretical or experimental results are reported up to now. However, theoretical calculations on Sin clusters indicate that this method gives a reliable result [10–12]. For each stationary point of
183
cluster, the stability is examined by the harmonic vibrational frequencies.
3. Results and discussions Computational results of bond lengths (Ir–Si and Si–Si) and bond angles, together with total energy, are listed in Table 1. Natural populations as well as natural electron configuration of IrSin (n ¼ 1–6) clusters are listed in Table 2. Spin net populations of Ir atom in the most stable IrSin (n ¼ 1–6) clusters are listed at Table 3. The geometrical structures are displayed in Fig. 1. 3.1. Geometry and stability In an effort to understand the electronic structures of IrSin (n ¼ 1–6) clusters, geometries and total energies of IrSin (n ¼ 1–6) clusters have been calculated by the Density Functional method at the UB3LYP/LanL2DZ level, together with natural population and natural electron configuration. All calculations are performed under the constraint of doublet, quartet and sextet spin configurations, stabilities of the various of spin electron configurations are justified. Theoretical results indicate that the doping transition metal contributes to the stability of Sin clusters [4]. Theoretical results of IrSin (n ¼ 1–6) clusters have been compared with the computational results of MSin (M ¼ Cr, Mo, W, Ag; n ¼ 1–6) clusters [11,12,15,31] as well as experimental results available [6]. IrSi. IrSi cluster with C1 v point-group symmetry considering of spin electron configurations (S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2) are calculated, the Ir–Si bond lengths for IrSi cluster with spin S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2 are 2.1447, 2.3736 , respectively, which are shorter than and 2.3691 A 2.45 A of Ir–Si bond length in iridium silicon material [37,38]. The stability of IrSi cluster decreases as the spin multiplicities and total energies increase monotonically. IrSi with spin S ¼ 1=2 is the most stable geometry, the corresponding ground electronic state is 2 R. However, the most stable WSi and MoSi clusters are corresponding to higher triplet spin electron states, this feature is
184
J.-G. Han / Chemical Physics 286 (2003) 181–192
Table 1 Geometries and total energies of IrSin (n ¼ 1–6) clusters System
Symm.
Spin
R1 /R
IrSi
C1 v
IrSi2
C2 v
IrSi3
Cs
IrSi3
C2 v
IrSi3 IrSi3 (a) IrSi3 (a) IrSi4
C3 v Cs C2 v C3 v
IrSi4
C2 v
IrSi4 IrSi4 (a) IrSi5
C2 C3 v Cs
IrSi5 (a)
Cs
1/2 3/2 5/2 1/2 3/2 5/2 7/2 9/2 1/2 3/2 5/2 1/2 3/2 5/2 3/2 1/2 1/2 1/2 5/2 1/2 3/2 5/2 1/2 1/2 1/2 3/2 5/2 1/2
IrSi5 (b) IrSi5
Cs C2 v
IrSi6
C2 v
IrSi6
Cs
2.1447 2.2736 2.3691 2.2157 2.3402 2.4187 2.3914 2.8142 2.3606 2.3701 2.3710 2.3154 2.333 2.3734 2.2486 2.2226/2.352 2.1764 2.3498 2.3259 2.2386/2.2693 2.2508/2.3314 2.3385/2.3317 2.2528/2.2539 2.2437 2.3387/2.3389 2.3286/2.3144 2.3620 2.3075/2.3438/ 2.7881 2.253/2.330 2.2730/2.2988 2.2737/2.3660 2.3753/2.4980 2.3649/2.4497 2.2344./2.3461
1/2 1/2 3/2 3/2 5/2 1/2
R2
2.5761 2.6801 2.5824 2.4358 2.3911 4.6436 3.5062 3.6977 2.3841 3.2472 3.8280 3.4317 4.1399 3.7454
R3
R4
80.0254 62.5062 63.4663 105.9232 62.8172 75.2632 68.8461 66.1018 122.6537 85.6309 2.9572 102.4572 2.4085 2.5110 2.8385 3.7330 3.7179 4.0471 2.4559
3.7584 3.8045 4.6957 4.6734 3.9202
Si(1)MSi(2)
3.7622 3.7572 3.6310 3.5971 –
2.393 2.3841 2.3660 2.5091 2.4962 2.5222
Eb )108.4830181 )108.4550918 )108.3879006 )112.3805311 )112.3693827 )112.2633977 )112.1984103 )112.088595 )116.2503846 )116.2524719 )116.1801496 )116.2165918 )116.2209555 )116.1877653 )116.2600452 )116.2601663 )116.1763741 )120.1201885 )120.0930863 )120.1546745 )120.0985427 )120.0727834 )120.1547853 )119.9808507 )124.0209159 )123.997351 )123.9462694 )124.0239887
TS TS
TS TS
TS
)124.0555413 )124.0256331 )124.011207 )127.8397971 )127.8463522 )127.9225415
R1 /R represent the Ir–Si(1)/Ir–Si(3) bond lengths, R2 , R3 and R4 represent Si(1)–Si(2), Si(1)–Si(3) and Si(5)–Si(4), respectively.
different from MoSi and WSi clusters [11,12]. The charges transferring from Si to Ir in IrSi cluster with spin S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2 are )0.4121, )0.0180 and 0.2265, respectively, therefore, the charges transformation in IrSi cluster is obviously influenced by the spin electron configuration of cluster, it is different from the WSi and MoSi clusters [11,12]. IrSi2 . Considering of the case investigated, IrSi2 cluster with spin doublet, quartet and sextet structures is optimized at the UB3LYP/LanL2DZ level under the constraint of well-defined C2 v point-group symmetry. This computation is fol-
lowed by a vibrational frequency analysis. Based upon the findings of geometries and bond angles of IrSi2 clusters with spin doublet, quartet and sextet structures, the evident results of bond lengths and bond angles correlate with the spin of these clusters. As spin goes from S ¼ 1=2 to 5/2, the bond monolength increases from 2.2157 to 2.4187 A tonically, which is associated with the variation of the bond angle \SiIrSi from 80.0254°, 62.5062° to 63.4663°. We find an electronic ground state of 2 B1 character for IrSi2 with doublet spin configuration and a value of 1.1158 eV for Egap , which is much smaller than that of CrSi2 cluster [15], the opti-
J.-G. Han / Chemical Physics 286 (2003) 181–192
185
Table 2 Natural populations and natural electron configurations of IrSin (n ¼ 1–6) clusters System
Symm.
Spin
Atom
Natural population
Natural electron configuration
IrSi
C1 v
1/2
Ir Si Ir Si Ir Si Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1–2) Si(3) Ir Si(1–2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1–3) Ir Si(1) Si(2, 3) Ir Si(1) Si(2–3) Ir Si(1–3) Si(4) Ir Si(1–3) Si(4) Ir Si(1–2) Si(3–4) Ir Si(1–2) Si(3–4)
)0.4121 0.4121 )0.0180 0.0180 0.2265 )0.2265 )0.5367 0.2684 )0.0798 0.0399 0.2263 )0.1132 0.2499 )0.1249 0.6311 )0.3156 )0.3642 0.1793 0.0056 )0.3360 0.1120 0.1120 )0.0601 0.0389 )0.0177 )0.4314 0.2532 )0.0750 )0.0292 0.0621 )0.0950 )0.1879 0.0574 0.0731 )0.6208 0.2069 )0.4972 0.4309 0.0332 )0.1609 0.0023 0.0793 )0.4566 0.2785 )0.3788 )0.5572 0.2058 )0.0602 )0.8515 0.1986 0.2271 )0.7826 0.2150 0.1763
½core6s0:83 5d8:58 6p0:01 ½core3s1:92 3p1:66 ½core6s0:90 5d8:07 6p0:05 ½core3s1:94 3p2:03 4p0:01 ½core6s0:80 5d7:93 6p0:05 ½core3s1:67 3p2:55 4p0:01 ½core6s0:95 5d8:56 6p0:04 ½core3s1:87 3p1:85 4p0:01 ½core6s0:84 5d8:20 6p0:05 ½core3s1:81 3p2:14 4p0:01 ½core6s0:85 5d7:85 6p0:07 6d0:01 ½core3s1:74 3p2:36 4p0:01 ½core6s0:77 5d7:94 6p0:05 ½core3s1:68 3p2:44 ½core6s1:09 5d7:16 6p0:11 7s0:01 ½core3s1:76 3p2:55 ½core6s0:71 5d8:61 6p0:05 6d0:01 ½core3s1:82 3p1:99 4p0:01 ½core3s1:77 3p2:22 4p0:01 ½core6s0:72 5d8:57 6p0:05 6d0:01 ½core3s1:80 3p2:08 4p0:01 ½core3s1:80 3p2:08 4p0:01 ½core6s0:93 5d8:08 6p0:04 7s0:01 6d0:01 ½core3s1:74 3p2:22 4p0:01 ½core3s1:80 3p2:22 ½core6s0:72 5d8:67 6p0:05 6d0:01 ½core3s1:79 3p1:94 4p0:01 ½core3s1:68 3p2:39 4p0:01 ½core6s0:79 5d8:21 6p0:04 ½core3s1:71 3p2:22 4p0:01 ½core3s1:70 3p2:39 4p0:01 ½core6s0:74 5d8:38 6p0:07 6d0:01 ½core3s1:88 3p2:05 ½core3s1:88 3p2:04 4p0:01 ½core6s0:84 5d8:72 6p0:06 7s0:01 7p0:01 ½core3s1:89 3p1:89 4p0:01 ½core6s0:79 5d8:67 6p0:05 6d0:01 ½core3s1:90 3p1:66 ½core3s1:79 3p2:17 4p0:01 ½core6s0:98 5d8:19 6p0:01 ½core3s1:39 3p2:60 4p0:01 ½core3s1:68 3p2:23 ½core6s0:81 5d8:56 6p0:09 7s0:01 6d0:01 ½core3s1:82 3p1:89 4p0:01 ½core3s1:65 3p2:72 4p0:01 ½core6s0:77 5d8:70 6p0:09 7s0:01 6d0:01 ½core3s1:86 3p1:92 ½core3s1:83 3p2:22 4p0:01 ½core6s0:85 5d8:94 6p0:07 6d0:01 ½core3s1:86 3p1:93 ½core3s1:88 3p1:88 ½core6s0:83 5d8:89 6p0:06 6d0:01 ½core3s1:85 3p1:93 4p0:01 ½core3s1:85 3p1:97
3/2 5/2 IrSi2
C2 v
1/2 3/2 5/2 7/2 9/2
IrSi3
Cs
1/2
3/2
5/2
IrSi3
C2 v
1/2
3/2
5/2
IrSi3
C3 v
3/2
IrSi3 (a)
Cs
1/2
IrSi3
C2 v
1/2
IrSi4
C3 v
1/2
5/2
IrSi4
C2 v
1/2
3/2
186
J.-G. Han / Chemical Physics 286 (2003) 181–192
Table 2 (continued) System
Symm.
Spin
Atom
Natural population
Natural electron configuration
5/2
Ir Si(1–2) Si(3–4) Ir Si(1–4) Ir Si(1) Si(2–4) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1) Si(2) Si(3) Si(4) Si(5) Ir Si(1,2) Si(3,4) Si(5) Ir Si(1–2) Si(3–4) Si(5) Ir Si(1–2) Si(3–4) Si(5) Ir Si(1–2) Si(3–4) Si(5–6) Ir Si(1–2) Si(3–4) Si(5–6) Ir Si(1) Si(2) Si(3–4) Si(5) Si(6)
)0.8123 0.2114 0.1948 )0.8549 0.2137 0.1521 )0.3690 0.0723 )0.3883 0.2947 0.0650 )0.1952 )0.0709 )0.3271 0.2253 0.0876 )0.3295 0.1183 )0.3015 0.1527 0.1569 )0.2880 0.1172 )0.3773 )0.0053 0.1571 0.3089 )0.1695 0.0861 )0.78598 0.3398 0.1234 )0.1405 )0.7961 0.3385 0.1326 )0.1461 )0.7750 0.3088 0.1488 )0.1404 )0.4115 0.2211 0.1385 )0.1538 )0.5601 0.3183 0.1436 )0.1818 )0.8218 0.4168 0.1670 0.2562 )0.1935 )0.0808
½core6s0:87 5d8:90 6p0:04 6d0:01 ½core3s1:86 3p1:92 ½core3s1:80 3p1:99 ½core6s0:85 5d8:94 6p0:07 6d0:01 ½core3s1:87 3p1:91 ½core6s0:65 5d8:20 6p0:01 ½core3s1:40 3p2:96 4p0:01 ½core3s1:85 3p2:07 ½core6s0:69 5d8:61 6p0:10 6d0:01 ½core3s1:79 3p1:91 4p0:01 ½core3s1:70 3p2:22 4p0:01 ½core3s1:58 3p2:60 4p0:01 ½core3s1:62 3p2:44 4p0:01 ½core6s0:72 5d8:53 6p0:09 6d0:01 ½core3s1:79 3p1:98 4p0:01 ½core3s1:77 3p2:11 4p0:01 ½core3s1:59 3p2:72 4p0:01 ½core3s1:64 3p2:26 4p0:01 ½core6s0:69 5d8:52 6p0:09 6d0:01 ½core3s1:76 3p2:08 4p0:01 ½core3s1:73 3p2:10 4p0:01 ½core3s1:56 3p2:71 4p0:01 ½core3s1:66 3p2:22 ½core6s0:67 5d8:62 6p0:09 6d0:01 ½core3s1:69 3p2:30 4p0:01 ½core3s1:76 3p2:07 4p0:01 ½core3s1:77 3p1:91 4p0:01 ½core3s1:59 3p2:57 4p0:01 ½core3s1:72 3p2:18 4p0:01 ½core6s0:79 5d8:90 6p0:09 6d0:01 ½core3s1:87 3p1:78 ½core3s1:74 3p2:13 4p0:01 ½core3s1:68 3p2:45 4p0:01 ½core6s0:83 5d8:89 6p0:07 6d0:01 ½core3s1:88 3p1:77 ½core3s1:72 3p2:14 4p0:01 ½core3s1:68 3p2:45 4p0:01 ½core6s0:79 5d8:90 6p0:08 6d0:01 ½core3s1:87 3p1:81 ½core3s1:75 3p2:09 4p0:01 ½core3s1:60 3p2:53 4p0:01 ½core6s0:55 5d8:74 6p0:12 7s0:01 6d0:02 ½core3s1:68 3p2:09 4p0:01 ½core3s1:62 3p2:23 4p0:01 ½core3s1:53 3p2:62 4p0:01 ½core6s0:72 5d8:72 6p0:11 7s0:01 6d0:02 ½core3s1:73 3p1:94 4p0:01 ½core3s1:58 3p2:27 4p0:01 ½core3s1:61 3p2:57 4p0:01 ½core6s0:81 5d8:91 6p0:10 6d0:02 ½core3s1:86 3p1:71 ½core3s1:70 3p2:12 4p0:01 ½core3s1:80 3p1:94 4p0:01 ½core3s1:60 3p2:58 4p0:01 ½core3s1:60 3p2:47 4p0:01
IrSi4
C2
1/2
IrSi4 (a)
C3 v
1/2
IrSi5
Cs
1/2
3/2
5/2
IrSi5 (a)
Cs
1/2
IrSi5(b)
Cs
1/2
IrSi5
C2 v
1/2
3/2
IrSi6
C2 v
3/2
5/2
IrSi6
Cs
1/2
J.-G. Han / Chemical Physics 286 (2003) 181–192
187
Table 3 Natural spin population of Ir of the stable IrSin (n ¼ 1–6) clusters Cluster
Symm.
Spin
a
b
c
IrSi
C1 v
IrSi2
C2 v
IrSi3
Cs
IrSi3 (a) IrSi4
C3 v C2 v C2 v C3 v
IrSi4 (a) IrSi5
C2 C3 v Cs
1/2 3/2 5/2 1/2 3/2 5/2 1/2 3/2 5/2 3/2 3/2 1/2 1/2 5/2 1/2 1/2 3/2 5/2 1/2 1/2 3/2 1/2 3/2 5/2
)0.7140 )1.0773 )1.1513 )0.4164 )0.8162 )0.9411 )0.3374 )0.3842 )0.9675 )0.4701 )0.7777 0.3187 )0.4340 )0.6326 )0.3996 )0.8741 )0.5566 )0.5874 )0.3623 )0.3736 )0.3237 )0.4002 )0.3634 )0.5382
0.3020 1.0593 1.3778 )0.1204 0.7364 1.1674 )0.0268 0.0887 0.9075 )0.1566 0.7485 )0.4795 )0.0226 0.0754 )0.4552 1.0262 0.2295 0.2860 )0.0150 )0.4225 )0.4513 )0.4216 )0.0481 )0.0219
1.0160 2.1366 2.5291 0.2960 1.5526 2.1085 0.3106 0.4727 1.8750 0.3135 1.5262 0.7982 0.4114 0.7080 0.0566 1.9003 0.7861 0.8374 0.3473 0.0489 0.1276 0.0214 0.3153 0.5163
IrSi5 (a)
Cs C2 v
IrSi6
Cs C2 v
Fig. 1. Structures of IrSin (n ¼ 1–6) clusters.
188
J.-G. Han / Chemical Physics 286 (2003) 181–192
mized structures turn out to thermodynamically stable. Ir–Si bond length and bond angle (\SiIrSi) of IrSi2 cluster (S ¼ 1=2) at the UB3LYP/ and 80.0254°, reLanL2DZ level are 2.2157 A spectively. One may note that the Ir–Si bond lengths in IrSi2 (S ¼ 1=2) cluster are longer than the respective bond length in IrSi2 (spin from S ¼ 3=2 to 9/2), in MoSi2 cluster (spin singlet) [11] and in CrSi2 cluster [15]. Based upon theoretical results of IrSi2 cluster with various of spin electron configurations (from S ¼ 1=2 to 9/2), one finds that total energy of IrSi2 cluster increases and the stability of IrSi2 cluster decreases as the increase of spin from S ¼ 1=2 to 9/ 2 monotonically. Therefore, IrSi2 cluster with spin S ¼ 1=2 is the most stable structure, the corresponding electron state is 2 B1 . IrSi3 . IrSi3 clusters with Cs, C3 v and C2 v pointgroup symmetries considering of different spin configurations are taken into accounts, all of them are selected as candidates for the ground-state configuration. Theoretical results show that IrSi3 ðaÞðC2 vÞ (Fig. 1) with spin doublet configuration is the only stable structure, Ir atom in IrSi3 ðaÞðC2 vÞ interacts with one Si atom with Ir– . Geometry optimiSi(1) bond length of 2.1764 A zations on IrSi3 ðC3 v and C2 vÞ clusters indicate only IrSi3 (C3 v and C2 v) clusters with spin quartet configuration are the thermodynamically stable. Moreover, the LUMO of IrSi3 (C3 v, S ¼ 3=2) consists of a degenerate (E) molecular orbital. Therefore, neither the spin doublet nor the spin sextet are expected to be stable in C3 v geometry as their system will contain incompletely filled degenerate molecular orbital, subject the species to Jahn–Teller distortion. IrSi3 cluster with C2 v symmetry is optimized, it should be mentioned that the IrSi3 (C2 v) clusters with spin S ¼ 1=2 and S ¼ 5=2 have an imaginary frequency, respectively, which are corresponding to the transition states. After the relaxation of the geometry of IrSi3 with C2 v symmetry, the thermodynamically stable IrSi3 clusters with Cs point-group symmetry are achieved with spin doublet, quartet and sextet electron configurations. The Ir–Si bond lengths in IrSi3 (Cs) clusters increase as the decrease of bond angle Si(1)IrSi(2) monotonically, however, IrSi3 (Cs) cluster with spin quartet electron con-
figuration is more stable than IrSi3 (Cs) with doublet and sextet spin electron configurations. The stable geometries and spin electron configurations of IrSi3 (Cs, C2 v, C3 v) clusters are obviously different from those of MSi3 (M ¼ Cr, Mo, W and Ag) clusters [11,12,15,31]. Total energy of IrSi3 (C3 v) cluster with spin quartet configuration is higher by about 0.2083, 1.0754 and 2.30179 eV than those of IrSi3 (Cs) and IrSi3 (C2 v) clusters with spin quartet configurations and IrSi3 ðaÞðC2 vÞ with spin doublet configuration due to the Ir atom in IrSi3 ðC3 vÞ interacts with three Si atoms simultaneously and with the equal bond lengths, therefore, IrSi3 (C3 v) cluster (Table 1) with spin quartet electron configuration is more stable than IrSi3 ðC2 vÞ, IrSi3 ðaÞðC2 vÞ and IrSi3 (Cs) clusters. Furthermore, the spin quartet electron configuration of IrSi3 with C3 v point-group symmetry is the most stable structure, which is selected as the ground state, the corresponding electron state is 4 A1 . IrSi3 ðC3 v, S ¼ 3=2) cluster is the only most stable MSin (n > 1) clusters with higher spin configuration up to now. The striking feature is different from those of MSi3 (M ¼ Cr, Mo, W, Ag) [11,12,15,31] clusters. IrSi4 . Based upon theoretical results of IrSi3 clusters, IrSi4 clusters with C3 v and C2 v pointgroup symmetries considering of spin multiplicities are carried out at the UB3LYP/LanL2DZ level. Frequency analysis on IrSi4 ðC3 vÞ with spin S ¼ 3=2 and IrSi4 ðC2 vÞ with spin doublet and sextet electron configurations, however, reveals that these structures have a saddle point with one imaginary frequency, respectively. It is noted that geometries of IrSi4 ðC3 vÞ clusters with spin doublet and sextet electron configurations are proved to be stable, the Ir atom interacts directly with three Si atoms simultaneously with equal bond lengths. IrSi4 ðC2 vÞ cluster with spin quartet electron configuration turns out to be a stable structure, after relaxation of IrSi4 (C2 v, S ¼ 1=2), the stable IrSi4 (C2 , S ¼ 1=2) cluster is obtained. Ir atom in IrSi4 (C2 v, S ¼ 3=2; C2 , S ¼ 1=2) interacts directly with four Si atoms simultaneously with Si(1)–Ir and Ir–Si(3) bond lengths. The structures of IrSi4 cluster with C2 v and C2 symmetries are captioned at Fig. 1, it is noted that the Ir atom is doped into Si4 cluster, a small deviation on Ir–Si bond lengths
J.-G. Han / Chemical Physics 286 (2003) 181–192
in IrSi4 (C2 ) with S ¼ 1=2 and IrSi4 ðC2 vÞ with S ¼ 3=2, respectively, is found, however, the geometry structures of IrSi4 (C2 v, C2 Þ clusters are obviously different from those of MSi4 (M ¼ Cr, Mo, W, Ag) clusters [11,12,15,31], Ir atom interacts with four Si atoms simultaneously in IrSi4 ðC2 vÞ cluster with non-equal Ir–Si(1) and Ir– Si(3) bond lengths. For IrSi4 (a)(C3 v, S ¼ 1=2) cluster, it is the only stable geometry, Ir interacts only with Si(1), the Ir–Si(1) bond length of 2.2437 . A Based upon the theoretical results of geometric parameters and total energies as well as the analysis on IrSi4 cluster with doublet, quartet and sextet spin configurations above, one finds that total energies for the stable IrSi4 clusters increase as the spin increasing from doublet, quartet to sextet, on the contrary, the stability decreases with the increasing of spin from S ¼ 1=2 to 5/2, IrSi4 ðC3 v, S ¼ 1=2) cluster is turned out to be higher in energy by 0.95 eV than IrSi4 (C2 , S ¼ 1=2) cluster, therefore, the most stable IrSi4 (C2 ) cluster is doublet spin configuration, which is corresponding to the ground state, the ground electron state is 2 A. In the other word, the Si4 cluster with endohedral Ir atom trapping into Si4 cluster is more stable than with Ir atom absorbing on surface of Si4 cluster, this discovery exemplifies the prediction of the large MSi15 (M ¼ Cr, Mo, W) clusters [10]. On ground of the findings of stability of cluster, the doping Ir atom into Si4 cluster brings out the stability of IrSi4 cluster. IrSi5 . Guided by theoretical results of the MoSi5 [11], WSi5 [12] and CrSi5 [15] clusters with C2 v point-group symmetry, IrSi5 clusters with Cs and C2 v point-group symmetries as the most likely candidates for the ground state geometry are considered and investigated. However, IrSi5 ðC2 vÞ cluster apparently bears some similarity to the C2 v point-group symmetry identified for the group of clusters discussed in the previous section (IrSi4 ; C2 v symmetry), specifically, this geometry can be seen as a Si4 structure face capped by Si atom and doped a Ir into the Si5 cluster, also the Ir atom interacts with four silicon atoms simultaneously. IrSi5 ðC2 v, S ¼ 1=2) cluster is optimized at the UB3LYP/LanL2DZ level, the distances of for Ir–Si(1) and Ir–Si(3) bond 2.273 and 2.2988 A
189
(R2 and R3 ) and 2.3841 A lengths as well as 3.76 A (R4 ) for Si–Si bond lengths, respectively, are obtained. After a relaxation on Si atoms, IrSi5 (Cs, S ¼ 1=2) cluster is yielded, frequency analysis, however, reveals that IrSi5 (Cs, S ¼ 1=2) cluster has an imaginary frequency, which is corresponding to a transition state. After relaxation on Ir and Si atoms along the coordination of the imaginary vibrational mode is performed on IrSi5 (Cs, S ¼ 1=2) cluster, a stable IrSi5 (a)(Cs) cluster is obtained. Hence, the two stable doublet spin configurations for IrSi5 (S ¼ 1=2) clusters with C2 v and Cs point-group symmetries are obtained. Geometry optimization and frequency on IrSi5 ðC2 v, Cs; S ¼ 3=2) clusters are carried out and reveals that these structures correspond to the stable ones. Ir–Si bond lengths for IrSi5 (Cs, , which S ¼ 3=2) cluster are 2.3286 and 2.3184 A are smaller than those of IrSi5 cluster (S ¼ 1=2) with C2 v and Cs point-group symmetries, respectively. IrSi5 clusters (S ¼ 5=2) with C2 v and Cs pointgroup symmetries taking into consideration of sextet spin configuration are performed at the UB3LYP/LanL2DZ level. Geometry optimization on IrSi5 ðC2 v, S ¼ 5=2) cluster finds an imaginary frequency, which is corresponding to a transition state. After a relaxation on geometry, a stable IrSi5 (Cs, S ¼ 5=2) cluster is obtained, Ir–Si bond , length in IrSi5 ðCs ; S ¼ 5=2Þ cluster is 2.3620 A which is longer than those of the stable IrSi5 (S ¼ 1=2 and S ¼ 3=2) clusters. Geometries of IrSi5 ðC2 vÞ clusters are also different from MSi5 (M ¼ Cr, Mo, W, Ag, Cu) clusters [11,12,15,31], however, it is obviously demonstrated my theoretical prediction on MSi15 (M ¼ Cr, Mo, W) [10] and ReSix (x ¼ 12; 20) clusters. According to theoretical results of total energies of IrSi5 clusters with doublet, quartet and sextet spin configurations, one finds that the total energy increases as the spin goes from S ¼ 1=2 to 5/2. This feature is shown to be associated with a pronounced drop in the stability of the cluster as spin goes from doublet, quartet to sextet spin configuration. It should be noted that total energy of IrSi5 (a) clusters (S ¼ 1=2) with Cs point-group symmetries is higher by about 0.045 eV than that of IrSi5 (C2 v; S ¼ 1=2) cluster, therefore, IrSi5
190
J.-G. Han / Chemical Physics 286 (2003) 181–192
(C2 v; S ¼ 1=2) cluster is more stable than IrSi5 (a)(Cs, S ¼ 1=2) cluster. IrSi5 ðC2 v; S ¼ 1=2Þ cluster is selected as the ground state configuration, the electronic state is 2 B2 . IrSi6 . Guided by our results of the IrSi5 and MSi5 (M ¼ Cr, Mo, W, Ag) [11,12,15,31] species, we based our geometry optimization of IrSi6 on the IrSi5 (C2 v, Cs, S ¼ 1=2) equilibrium geometry, replacing the Si5 by Si6 . The resulting geometry of C2 v symmetry distorts into the Cs structure displayed in Fig. 1. It is worth noting that the deformed Si6 cluster of IrSi6 (S ¼ 3=2) turns into a regular cluster as the S ¼ 3=2 spin condition is imposed on the system, corresponding to C2 v as the symmetry of IrSi6 (S ¼ 3=2). Whereas, for the spin doublet, the interaction between the Ir atom and the Si6 subsystem fragments turns into the subgroups (Si(1), Si(2)), (Si(3), Si(4)) and (Si(5), Si(6)), which relates to strongly direct bonding in (Si(1), Si(2)) and (Si(3), Si(4)) subsystems. In the spin sextet configuration, Ir interacts directly with four Si atoms simultaneously and with unequal strengths of Ir–Si(1) and Ir–Si(3). The distorted IrSi6 (Cs, S ¼ 1=2) cluster obtained, which is captioned at Fig. 1, turns out to be stable. The geometries of IrSi6 may be interpreted as deformed substitutional structures, derivable from the Oh ground state of Si7 through replacement of one Si atom by Ir. No stable structures were found in case of apical replacement. The hypothesis underlying these investigations, i.e., the avoidance of endohedral sites for a metal impurity in small Sin clusters, can be put to the test in the context of IrSi6 by considering a central Ir atom embedded into an octahedral Si6 network. However, they are corresponding to the saddle points with more than one imaginary frequencies. Total energy on IrSi6 (Cs, S ¼ 1=2) is lower in energy than the others, therefore, IrSi6 (Cs, S ¼ 1=2) is the most stable structure, the corresponding ground state is 2 0 A. 3.2. Population analysis and magnetism Charges localized in Ir or Si atoms are smaller in quantity than the values delocalized in Ir–Si(1) bond, furthermore, charges delocalized in Ir–Si(1) bond in IrSin are larger than those delocalized in
Si–Si bonds. Therefore, charges localized on Ir and Si atoms and charges delocalized Ir–Si(1) bond as well as Si–Si bonds in IrSin contribute to the stability of chemical bonding of IrSin (n ¼ 1–6) clusters. Charge of Ir–Si bond is shifted out of Si–Si bonds to Ir–Si(1) in IrSin (n ¼ 2–5) clusters. Moreover, the discovery of covalent bond participates strongly in the stabilization of IrSin (n ¼ 1–6) clusters. Therefore, Charge-transfer mechanism in IrSin (n ¼ 1–6) clusters is similar to those of MSin (M ¼ Cr, Mo, W; n ¼ 1–6; 15) [10– 12,15] clusters. The contribution of delocalized charges to stability on MSi15 (M ¼ Cr, Mo, W) [10] is discussed in detail. We conclude from our computation of natural atomic net populations that charges of Ir in the more stable IrSin (n ¼ 1–6) are negative, which are the same as Cr, Mo, and W in MSin (M ¼ Cr, Mo, W; n ¼ 1–6; 15) [10–12,15] clusters. On the basis of natural electron configuration (Table 2), one finds that the charges transfer from Si atoms and 6s orbitals of Ir to 5d orbitals of Ir in IrSin (n ¼ 1–6) clusters, more than 7.8 electrons occupy the 5d subshell of Ir in IrSin , the 5d orbitals of Ir atom in IrSin (n ¼ 1–6) do not behave as a core orbitals but take an active role in the bonding, which are different from Cu in CuSin clusters and Ag in AgSin clusters [31], in the other word, the 5d orbitals of Ir atom in the most stable IrSin clusters acting as an acceptor have a trend to pull out the charges from 6s of Ir and Si atoms (near Ir atoms). The charge transfer phenomenon as described here is the same as the ones that found in some of MSin (M ¼ Cr, Mo; n ¼ 1–6; 15) [10–12] clusters, furthermore, the charges transferring from Si to Ir atom correlate sensitively with the spin multiplicity. However, the charges transfer from 6s of Ir and 3s of Si(2), Si(3) and Si(4) to 3p of Si(1) and 5d of Ir in IrSi4 ðaÞðC3 v, S ¼ 1=2), generally, the charges transfer from Si(2), Si(3), Si(4) and Ir to Si(1) atom, this trend is different from the other IrSin clusters. As the magnet is in proportional to the c, where c ¼ ja bj (Table 3), we can find that the magnet of transition metal Ir for the most stable IrSin clusters are also controlled by the spin multiplicity, generally, the contribution of TM to magnet increases as the spin S ¼ 1=2–3/2.
J.-G. Han / Chemical Physics 286 (2003) 181–192
3.3. Fragmentation energies A systematic investigation on MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters finds that the hybrid density functional method (UB3LYP) in conjunction with LanL2DZ basis sets yields reasonable and accurate results [11,12]. The exchange-correlation energies are considered completely by the UB3LYP method during the calculation of IrSin (n ¼ 1–6) clusters. In a further series of investigations, we evaluate IrSin (n ¼ 1–6) fragmentation energies, defined according to the formula Dðn; n 1Þ ¼ Eb ðIrSin1 Þ þ Eb ðSiÞ Eb ðIrSin Þ as the change in total energy upon removing one Si atom from the cluster, where in each case the IrSin (n ¼ 1–6) structures are compared. Our findings are 4.8990, 4.3602, 4.7745, 4.1247 and 4.8868 eV for D(2, 1), D(3, 2), D(4, 3), D(5, 4) and D(6, 5), respectively, at the UB3LYP/LanL2DZ level. The remarkable values of D(6,5) and D(2,1) are found. Our results indicate that D(2,1) is larger than D(6,5), or, in other words, IrSi2 cluster is more stable than IrSi6 cluster with respect to the removing one silicon atom, it is in good agreement with experimental result [6]. According to our theoretical results of total energies (Eb ) for IrSin (n ¼ 1–6) clusters (Table 2), a general trend of stability is found, which is different from those of MSin (M ¼ Cr, Mo, W, Ag) (n ¼ 1–6) clusters [11,12,15,31] clusters and previous results for Gen (n ¼ 2–6) as part of Gen F (n ¼ 2–6) clusters [7]. Theoretical results also indicate that IrSin (n ¼ 1–6) clusters are not characterized by the same Sin (n ¼ 1–6) framework structures as MSin (M ¼ Cr, Mo, W, Cu, Ag; n ¼ 1–6) [11,12,15,31].
191
the stabilities of IrSin (n ¼ 1–6) clusters are investigated, along with fragmentation energies of IrSin (n ¼ 1–6) clusters upon removal of a Si atom. Theoretical results show that the stability of IrSin decreases as the spin increases from S ¼ 1=2 to 5/2 besides IrSi3 cluster with S ¼ 3=2, this feature, which is in good agreement with theoretical results of MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters, is shown to be associated with a pronounced drop in the stability of the cluster as one goes from doublet, quartet to sextet spin configurations. Natural population and natural electron configurations are calculated. Ir in IrSin cluster acts as acceptor and Sin in IrSin acts as donor. Theoretical results indicate that the geometry structures of Sin are deformed after Ir dopes in Sin clusters, furthermore, geometries of IrSin (n ¼ 1–6) clusters are obviously different from MSin (Cr, Mo, W; n ¼ 1–6) clusters, which demonstrate the prediction in MSi15 (M ¼ Cr, Mo, W), additionally, the Ir atom doping into Sin clusters does contribution to the stability of Sin clusters. The contribution of Ir in IrSin clusters to magnetism is also discussed. IrSi3 (C3 v, S ¼ 3=2) cluster is the only most stable MSin (n > 1) clusters with higher spin configuration up to now.
Acknowledgements This work is supported by National Natural Science Foundation of China (20173055), National foundation from Department of Science and Technology (P.R. China) (970211006) and Structural Research Laboratory of USTC of Chinese Academy of Sciences, P.R. China (2001B10).
References 4. Conclusions Geometry optimizations and population analyses are performed for IrSin (n ¼ 1–6) clusters at the UB3LYP/LanL2DZ level, maintaining pointgroup symmetry. Chemical bonding mechanisms and equilibrium geometries of IrSin (n ¼ 1–6) clusters are identified and compared with MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters. Additionally,
[1] [2] [3] [4] [5] [6] [7] [8]
H.F. Jarrold, Science 1085 (1991) 251. E. Kaxiras, Phys. Rev. Lett. 64 (1990) 551. K.M. Ho et al., Nature 392 (1998) 582. K. Jackson, B. Nellermoe, Chem. Phys. Lett. 254 (1996) 249. I. Shim, K.A. Gingerich, Z. Phys. D 16 (1990) 141. H. Hiura, T. Miyazaki, T. Kanayama, Phys. Rev. Lett. 86 (2001) 1733. J.G. Han, Chem. Phys. Lett. 324 (2000) 143. L. Turker, J. Mol. Str. (Theochem.) 548 (2001) 185.
192
J.-G. Han / Chemical Physics 286 (2003) 181–192
[9] S.M. Beck, J. Chem. Phys. 90 (1989) 6306. [10] J.G. Han, Y.Y. Shi, Chem. Phys. 266 (2001) 33. [11] J.G. Han, F. Hagelberg, J. Mol. Str. (Theochem.) 549 (2001) 168. [12] J.G. Han, C. Xiao, F. Hagelberg, Structural Chemistry 13 (2002) 173. [13] C. Xiao, F. Hagelberg, J. Mol. Struct. (Theochem.) 529 (2000) 241. [14] J.G. Han, W.M. Pang, Y.Y. Shi, Chem. Phys. 257 (2000) 21. [15] J.G. Han, F. Hagelberg, Chem. Phys. 263 (2001) 255. [16] Z. Chen, H. Jiao, A. Hirsch, W. Thiel, J. Org. Chem. 66 (2001) 3380. [17] J.J. Scherer, J.B. Paul, C.P. Collier, R.J. Saykally, J. Chem. Phys. 102 (1995) 5190. [18] J.J. Scherer, J.B. Paul, C.P. Collier, R.J. Saykally, J. Chem. Phys. 103 (1995) 113. [19] J.J. Scherer, J.B. Paul, C.P. Collier, A. OÕKeefe, R.J. Saykally, J. Chem. Phys. 103 (1995) 9187. [20] J. Budinavicius, L. Pranevicoius, S. Tamulevicius, Phys. Status. Solidi A 114 (1989) K25. [21] P. Turski, Chem. Phys. Lett. 315 (1999) 115. [22] Y.M. Harrick, W. Weltner Jr., J. Chem. Phys. 94 (1991) 3371.
[23] J.E. Kingcade Jr., K.A. Gringerick, J. Chem. Soc. Faraday Trans. 285 (1989) 195. [24] K.A. Gringerick, J. Chem. Phys. 50 (1969) 5426. [25] A.V. de Auwera-Mahieu, N.S. Melntyre, J. Drowert, Chem. Phys. Lett. 4 (1969) 198. [26] J.G. Han (in preparation). [27] J.G. Han (in preparation). [28] M.J. Frisch et al., Gaussian 98, Gaussian, Pittsburgh, PA, 1998. [29] R.D. Johnson, M.S. Vries, J. Salem, D.S. Bethune, C.S. Yannoni, Nature 355 (1992) 239. [30] G. Rickert, P. Lamparter, S. Steeb, Z. Met. 72 (1981) 765. [31] P.F. Zhang, J.G. Han, Q.R. Pu, Chem. Phys. (to be submitted). [32] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [33] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 27 (1988) 785. [34] N.C. Handy, H.F. Schaefer III, J. Chem. Phys. 81 (1984) 5031. [35] W.R. Wadt, P.J. Hay, J. Chem. Phys. 82 (1985) 284. [36] A. Nicklass, M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys. 102 (1995) 8942. [37] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [38] R. Mishra, R.D. Hoffmann, R. Pottgen, Z. Anorg. Allg. Chem. 627 (2001) 1787.
A theoretical investigation on electronic properties and stability of IrSix (x ¼ 1–6) clusters Ju-Guang Han * National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, PR China Structural Research Laboratory and The Key Laboratory of Structural Biology, USTC of Chinese Academy of Sciences, Hefei 230029, PR China Received 11 January 2002
Abstract A series of computational investigations on IrSin (n ¼ 1–6) clusters is reported. For each unit, geometry optimizations are performed at the UB3LYP/LanL2DZ level, subsequently, electronic and bonding features of the resulting equilibrium structure are presented and discussed. The emphasis of this study is placed on the geometries, stabilities and electron properties of IrSin (n ¼ 1–6) systems and, more specifically, the impact of the their spins on the internal electron transfer between the Sin subsystem and the Ir atom. As a general trend for IrSin clusters with n > 1, we record a change of the natural charge from negative to positive on Ir atom in IrSi and IrSi2 clusters, charges transferring from Si to Ir in IrSin (n ¼ 3–6) clusters as the spin constraint on the system increases from S ¼ 1=2 to 5/2. This feature is shown to be associated with a pronounced drop in the stability of the IrSin (n 6¼ 3) clusters as one goes from the doublet to the sextet spin configurations. It should be mentioned that equilibrium geometries of IrSin (n ¼ 3–6) clusters and ground electron states of IrSi and IrSi3 clusters are obviously different from MSin (M ¼ Cr, Mo, W, Ag, n ¼ 1–6). Our theoretical results show that IrSi2 cluster is the most stable cluster of all IrSin clusters, which is in good agreement with experimental result available. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction There has been a great deal of interest in negative magnetoresistance in materials, specifically in various classes of materials, including the magnetic semiconductors such as Rex Si1x (Re ¼ Gd, Tb) family of compounds. Magneto-resistive materials
* Present address: Department of Chemistry and Biochemistry, Texas Technology University, Lubbock, TX 79409-1061, USA. Fax: +86-551-3603754. E-mail address: [email protected]
find potential application in magnetic devices such as read heads and sensors in storage media. Of particular interest is to calculate, synthesize, characterize and study the magnetic and transport properties of rare earth transition metal intermetallics. Examination of solid-state materials reveals a striking change in properties due to the substitution of various metals. The study of relationships between crystal structures and electronic and magnetic properties will enable us to gain insights into the nature of the bonding. Because transition metal (TM) doped silicon is a semiconducting cluster of great importance in microelectronic
0301-0104/03/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 ( 0 2 ) 0 0 9 3 3 - 3
182
J.-G. Han / Chemical Physics 286 (2003) 181–192
technology, experimentally and theoretically [1–8]. There is currently great of interest in utilizing small clusters as constituent elements to build up well-controlled nanostructures, surface or bulk of a material. This consideration provides a strong motivation for the study of mixed TM-silicon clusters. In particular, the clusters are so stable and can be used as a tunable building block for cluster-assemble material. Beck and Hiura [6,9] have pioneered the experimental investigation of small mixed transition metal–silicon clusters (MSin ; M ¼ Cr, Mo, W, Ir, Re, Hf, Ta; n 6 18) by mass spectrometry. Scherer et al. [17–19] have produced mixed transitional metal silicides by time-of-flight mass spectroscopy, and studied the electronic states of CuSi, AgSi [20] and AuSi dimmers by measuring their laser absorption spectra as well as by theoretical calculation using CASPT2 method [21]. In addition, the VSi and NbSi dimmers have been investigated by matrix-isolated ESP spectroscopy [22], and bond energies are reported [23–25], furthermore, a systematic investigation on ZrSi20 cage [4], NiSi [5], MSin (M ¼ V, Nb, Ta; n ¼ 1–6) clusters [26] is studied by density functional method. AuSin (n ¼ 1–3) clusters are studied [27] by relativistic density functional method as well as ab initio method. With the aim to simulate and to predict the structures and properties, the technically important clusters have attracted attentions theoretically [1–16]. After the work of a density functional theoretical study on MSi15 and MSi17 (M ¼ Cr, Mo and W) [10] clusters has been performed, moreover, the charge transfer mechanism and the equilibrium geometries of MSin (M ¼ Cr, Mo, W, Ag; n ¼ 1–6) [11,12,31] and CuSin clusters [13] have been explored by use of Gaussian 98 program [28], theoretical investigations on metcars [29] clusters are reported also. In the case of silver silicides, the previous gas phase work consists of measurements of the dissociation energy of AgSi diatom deduced in the mass spectrometric studies of Rickert et al. [30] as well as ab initio study on AgSin (n ¼ 1–5) clusters [31]. Furthermore, the experimental investigation on iridium silicides by mass analysis, which includes the first gas phase spectra for any iridium silicides as well as the first direct evident for the
existence of polyatomic iridium silicides, is carried out. The results of the iridium silicides (IrSin and IrSin H2n ), which provide the insight into the information mechanism and properties of these species, are presented [6]. Experimental results [6] indicate that the relative abundance of Si2 Ir is the biggest one of all IrSin (n ¼ 1–6) clusters, in the other word, IrSi2 is the most stable one. To achieve a deeper and systematical understanding of any class of clusters, it is important to investigate the evolution of cluster properties with the size of the system. The present work is intended to serve this purpose, as it contains comparison between various small IrSin species with n < 7, thereby containing a serious of computational studies on small Sin M units that was recently started with an analysis of Sin M (M ¼ Cr, Mo, W, Ag) clusters [10–12,15,31]. We also examine if the substitution of Ir atom upon/into silicon cluster deprives each clusters without any major rearrangement of the framework of Si clusters. The structures and electronic properties of Sin Ir (n ¼ 1–6) clusters have not been determined theoretically and there no systematic investigations within the same approach, the main objective of this studies, therefore, is to provide theoretical data for the geometries, stabilities and charge transfer of the iridium silicides. We will concentrate on doping or surface site of Ir atom. To compare with experimental results, to give a reasonable explanation of the experimental phenomenon and to reveal the electron properties, hence calculation studies of total energy, geometry, along with the theoretical value of natural population and natural electron configuration, are performed by the density functional method in this paper.
2. Computational details In the present calculations, the DFT method is unrestricted (U) B3LYP [32,33] exchange-correlation potential and an effective core potential LanL2DZ basis sets [34–36]. The exchange term of UB3LYP consists of hybrid Hartree–Fock and local spin density (LSD) exchange functions with
J.-G. Han / Chemical Physics 286 (2003) 181–192
BeckeÕs gradient correlation to LSD exchange [37]. The correlation term of UB3LYP consists of the VWN3 local correlation functional and LYP (Lee, Yang and Parr) correlation correction functional. The UB3LYP method gives an improvement over SCF-HF results. Its predictions are in qualitative agreement with experimental values. In general, the DFT method overestimates the energies, and it gives shorter bond lengths than the experimental results. However, the optimized structures predicted at the UB3LYP level are in good agreement with experimental values. LanL2DZ basis sets are become widely used in quantum chemistry, particularly in the investigation on compounds containing heavy elements (atoms) [12,15,31]. The LanL2DZ basis sets have been employed to calculate the equilibrium geometries and spectroscopic properties of small molecules or clusters. The standard LanL2DZ basis sets of ECP theory consistent not only within the first row transition metal, but also with the second and third row transition metals. The LanL2DZ basis sets do not degrade when going from second to third row transition metal of the periodic table [11,12,15,31]. On the other hand, it has been shown that the LanL2DZ basis sets are capable of generating results of very satisfactory quality for TM compounds [11,12,15,31]. This examination of equilibrium bond lengths and angles lead to deviations of typically 1–6%. Due to its reliance on pseudopotentials, our study has to be considered as preliminary and qualitative in nature. All density functional theory (DFT) computations (ab initio) are performed with the Gaussian 98 [28] program package. Geometries are optimized at the hybrid functional DFT-UB3LYP [32,33] levels, employing LanL2DZ (Stuttgart/ Dresden effective core potential) basis sets [34–36]. A systematic investigation of IrSin (n ¼ 1–6) clusters at the UB3LYP/LanL2DZ level will give a general conclusion. In our calculation for IrSin (n ¼ 1–6) clusters, as a test the Ir2 molecule is analyzed at the B3LYP/LanL2DZ level, the Ir–Ir ) of Ir2 cluster is obtained. bond length (2.2159 A No theoretical or experimental results are reported up to now. However, theoretical calculations on Sin clusters indicate that this method gives a reliable result [10–12]. For each stationary point of
183
cluster, the stability is examined by the harmonic vibrational frequencies.
3. Results and discussions Computational results of bond lengths (Ir–Si and Si–Si) and bond angles, together with total energy, are listed in Table 1. Natural populations as well as natural electron configuration of IrSin (n ¼ 1–6) clusters are listed in Table 2. Spin net populations of Ir atom in the most stable IrSin (n ¼ 1–6) clusters are listed at Table 3. The geometrical structures are displayed in Fig. 1. 3.1. Geometry and stability In an effort to understand the electronic structures of IrSin (n ¼ 1–6) clusters, geometries and total energies of IrSin (n ¼ 1–6) clusters have been calculated by the Density Functional method at the UB3LYP/LanL2DZ level, together with natural population and natural electron configuration. All calculations are performed under the constraint of doublet, quartet and sextet spin configurations, stabilities of the various of spin electron configurations are justified. Theoretical results indicate that the doping transition metal contributes to the stability of Sin clusters [4]. Theoretical results of IrSin (n ¼ 1–6) clusters have been compared with the computational results of MSin (M ¼ Cr, Mo, W, Ag; n ¼ 1–6) clusters [11,12,15,31] as well as experimental results available [6]. IrSi. IrSi cluster with C1 v point-group symmetry considering of spin electron configurations (S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2) are calculated, the Ir–Si bond lengths for IrSi cluster with spin S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2 are 2.1447, 2.3736 , respectively, which are shorter than and 2.3691 A 2.45 A of Ir–Si bond length in iridium silicon material [37,38]. The stability of IrSi cluster decreases as the spin multiplicities and total energies increase monotonically. IrSi with spin S ¼ 1=2 is the most stable geometry, the corresponding ground electronic state is 2 R. However, the most stable WSi and MoSi clusters are corresponding to higher triplet spin electron states, this feature is
184
J.-G. Han / Chemical Physics 286 (2003) 181–192
Table 1 Geometries and total energies of IrSin (n ¼ 1–6) clusters System
Symm.
Spin
R1 /R
IrSi
C1 v
IrSi2
C2 v
IrSi3
Cs
IrSi3
C2 v
IrSi3 IrSi3 (a) IrSi3 (a) IrSi4
C3 v Cs C2 v C3 v
IrSi4
C2 v
IrSi4 IrSi4 (a) IrSi5
C2 C3 v Cs
IrSi5 (a)
Cs
1/2 3/2 5/2 1/2 3/2 5/2 7/2 9/2 1/2 3/2 5/2 1/2 3/2 5/2 3/2 1/2 1/2 1/2 5/2 1/2 3/2 5/2 1/2 1/2 1/2 3/2 5/2 1/2
IrSi5 (b) IrSi5
Cs C2 v
IrSi6
C2 v
IrSi6
Cs
2.1447 2.2736 2.3691 2.2157 2.3402 2.4187 2.3914 2.8142 2.3606 2.3701 2.3710 2.3154 2.333 2.3734 2.2486 2.2226/2.352 2.1764 2.3498 2.3259 2.2386/2.2693 2.2508/2.3314 2.3385/2.3317 2.2528/2.2539 2.2437 2.3387/2.3389 2.3286/2.3144 2.3620 2.3075/2.3438/ 2.7881 2.253/2.330 2.2730/2.2988 2.2737/2.3660 2.3753/2.4980 2.3649/2.4497 2.2344./2.3461
1/2 1/2 3/2 3/2 5/2 1/2
R2
2.5761 2.6801 2.5824 2.4358 2.3911 4.6436 3.5062 3.6977 2.3841 3.2472 3.8280 3.4317 4.1399 3.7454
R3
R4
80.0254 62.5062 63.4663 105.9232 62.8172 75.2632 68.8461 66.1018 122.6537 85.6309 2.9572 102.4572 2.4085 2.5110 2.8385 3.7330 3.7179 4.0471 2.4559
3.7584 3.8045 4.6957 4.6734 3.9202
Si(1)MSi(2)
3.7622 3.7572 3.6310 3.5971 –
2.393 2.3841 2.3660 2.5091 2.4962 2.5222
Eb )108.4830181 )108.4550918 )108.3879006 )112.3805311 )112.3693827 )112.2633977 )112.1984103 )112.088595 )116.2503846 )116.2524719 )116.1801496 )116.2165918 )116.2209555 )116.1877653 )116.2600452 )116.2601663 )116.1763741 )120.1201885 )120.0930863 )120.1546745 )120.0985427 )120.0727834 )120.1547853 )119.9808507 )124.0209159 )123.997351 )123.9462694 )124.0239887
TS TS
TS TS
TS
)124.0555413 )124.0256331 )124.011207 )127.8397971 )127.8463522 )127.9225415
R1 /R represent the Ir–Si(1)/Ir–Si(3) bond lengths, R2 , R3 and R4 represent Si(1)–Si(2), Si(1)–Si(3) and Si(5)–Si(4), respectively.
different from MoSi and WSi clusters [11,12]. The charges transferring from Si to Ir in IrSi cluster with spin S ¼ 1=2, S ¼ 3=2 and S ¼ 5=2 are )0.4121, )0.0180 and 0.2265, respectively, therefore, the charges transformation in IrSi cluster is obviously influenced by the spin electron configuration of cluster, it is different from the WSi and MoSi clusters [11,12]. IrSi2 . Considering of the case investigated, IrSi2 cluster with spin doublet, quartet and sextet structures is optimized at the UB3LYP/LanL2DZ level under the constraint of well-defined C2 v point-group symmetry. This computation is fol-
lowed by a vibrational frequency analysis. Based upon the findings of geometries and bond angles of IrSi2 clusters with spin doublet, quartet and sextet structures, the evident results of bond lengths and bond angles correlate with the spin of these clusters. As spin goes from S ¼ 1=2 to 5/2, the bond monolength increases from 2.2157 to 2.4187 A tonically, which is associated with the variation of the bond angle \SiIrSi from 80.0254°, 62.5062° to 63.4663°. We find an electronic ground state of 2 B1 character for IrSi2 with doublet spin configuration and a value of 1.1158 eV for Egap , which is much smaller than that of CrSi2 cluster [15], the opti-
J.-G. Han / Chemical Physics 286 (2003) 181–192
185
Table 2 Natural populations and natural electron configurations of IrSin (n ¼ 1–6) clusters System
Symm.
Spin
Atom
Natural population
Natural electron configuration
IrSi
C1 v
1/2
Ir Si Ir Si Ir Si Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Ir Si(1, 2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1–2) Si(3) Ir Si(1–2) Si(3) Ir Si(1, 2) Si(3) Ir Si(1–3) Ir Si(1) Si(2, 3) Ir Si(1) Si(2–3) Ir Si(1–3) Si(4) Ir Si(1–3) Si(4) Ir Si(1–2) Si(3–4) Ir Si(1–2) Si(3–4)
)0.4121 0.4121 )0.0180 0.0180 0.2265 )0.2265 )0.5367 0.2684 )0.0798 0.0399 0.2263 )0.1132 0.2499 )0.1249 0.6311 )0.3156 )0.3642 0.1793 0.0056 )0.3360 0.1120 0.1120 )0.0601 0.0389 )0.0177 )0.4314 0.2532 )0.0750 )0.0292 0.0621 )0.0950 )0.1879 0.0574 0.0731 )0.6208 0.2069 )0.4972 0.4309 0.0332 )0.1609 0.0023 0.0793 )0.4566 0.2785 )0.3788 )0.5572 0.2058 )0.0602 )0.8515 0.1986 0.2271 )0.7826 0.2150 0.1763
½core6s0:83 5d8:58 6p0:01 ½core3s1:92 3p1:66 ½core6s0:90 5d8:07 6p0:05 ½core3s1:94 3p2:03 4p0:01 ½core6s0:80 5d7:93 6p0:05 ½core3s1:67 3p2:55 4p0:01 ½core6s0:95 5d8:56 6p0:04 ½core3s1:87 3p1:85 4p0:01 ½core6s0:84 5d8:20 6p0:05 ½core3s1:81 3p2:14 4p0:01 ½core6s0:85 5d7:85 6p0:07 6d0:01 ½core3s1:74 3p2:36 4p0:01 ½core6s0:77 5d7:94 6p0:05 ½core3s1:68 3p2:44 ½core6s1:09 5d7:16 6p0:11 7s0:01 ½core3s1:76 3p2:55 ½core6s0:71 5d8:61 6p0:05 6d0:01 ½core3s1:82 3p1:99 4p0:01 ½core3s1:77 3p2:22 4p0:01 ½core6s0:72 5d8:57 6p0:05 6d0:01 ½core3s1:80 3p2:08 4p0:01 ½core3s1:80 3p2:08 4p0:01 ½core6s0:93 5d8:08 6p0:04 7s0:01 6d0:01 ½core3s1:74 3p2:22 4p0:01 ½core3s1:80 3p2:22 ½core6s0:72 5d8:67 6p0:05 6d0:01 ½core3s1:79 3p1:94 4p0:01 ½core3s1:68 3p2:39 4p0:01 ½core6s0:79 5d8:21 6p0:04 ½core3s1:71 3p2:22 4p0:01 ½core3s1:70 3p2:39 4p0:01 ½core6s0:74 5d8:38 6p0:07 6d0:01 ½core3s1:88 3p2:05 ½core3s1:88 3p2:04 4p0:01 ½core6s0:84 5d8:72 6p0:06 7s0:01 7p0:01 ½core3s1:89 3p1:89 4p0:01 ½core6s0:79 5d8:67 6p0:05 6d0:01 ½core3s1:90 3p1:66 ½core3s1:79 3p2:17 4p0:01 ½core6s0:98 5d8:19 6p0:01 ½core3s1:39 3p2:60 4p0:01 ½core3s1:68 3p2:23 ½core6s0:81 5d8:56 6p0:09 7s0:01 6d0:01 ½core3s1:82 3p1:89 4p0:01 ½core3s1:65 3p2:72 4p0:01 ½core6s0:77 5d8:70 6p0:09 7s0:01 6d0:01 ½core3s1:86 3p1:92 ½core3s1:83 3p2:22 4p0:01 ½core6s0:85 5d8:94 6p0:07 6d0:01 ½core3s1:86 3p1:93 ½core3s1:88 3p1:88 ½core6s0:83 5d8:89 6p0:06 6d0:01 ½core3s1:85 3p1:93 4p0:01 ½core3s1:85 3p1:97
3/2 5/2 IrSi2
C2 v
1/2 3/2 5/2 7/2 9/2
IrSi3
Cs
1/2
3/2
5/2
IrSi3
C2 v
1/2
3/2
5/2
IrSi3
C3 v
3/2
IrSi3 (a)
Cs
1/2
IrSi3
C2 v
1/2
IrSi4
C3 v
1/2
5/2
IrSi4
C2 v
1/2
3/2
186
J.-G. Han / Chemical Physics 286 (2003) 181–192
Table 2 (continued) System
Symm.
Spin
Atom
Natural population
Natural electron configuration
5/2
Ir Si(1–2) Si(3–4) Ir Si(1–4) Ir Si(1) Si(2–4) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1–2) Si(3) Si(4) Si(5) Ir Si(1) Si(2) Si(3) Si(4) Si(5) Ir Si(1,2) Si(3,4) Si(5) Ir Si(1–2) Si(3–4) Si(5) Ir Si(1–2) Si(3–4) Si(5) Ir Si(1–2) Si(3–4) Si(5–6) Ir Si(1–2) Si(3–4) Si(5–6) Ir Si(1) Si(2) Si(3–4) Si(5) Si(6)
)0.8123 0.2114 0.1948 )0.8549 0.2137 0.1521 )0.3690 0.0723 )0.3883 0.2947 0.0650 )0.1952 )0.0709 )0.3271 0.2253 0.0876 )0.3295 0.1183 )0.3015 0.1527 0.1569 )0.2880 0.1172 )0.3773 )0.0053 0.1571 0.3089 )0.1695 0.0861 )0.78598 0.3398 0.1234 )0.1405 )0.7961 0.3385 0.1326 )0.1461 )0.7750 0.3088 0.1488 )0.1404 )0.4115 0.2211 0.1385 )0.1538 )0.5601 0.3183 0.1436 )0.1818 )0.8218 0.4168 0.1670 0.2562 )0.1935 )0.0808
½core6s0:87 5d8:90 6p0:04 6d0:01 ½core3s1:86 3p1:92 ½core3s1:80 3p1:99 ½core6s0:85 5d8:94 6p0:07 6d0:01 ½core3s1:87 3p1:91 ½core6s0:65 5d8:20 6p0:01 ½core3s1:40 3p2:96 4p0:01 ½core3s1:85 3p2:07 ½core6s0:69 5d8:61 6p0:10 6d0:01 ½core3s1:79 3p1:91 4p0:01 ½core3s1:70 3p2:22 4p0:01 ½core3s1:58 3p2:60 4p0:01 ½core3s1:62 3p2:44 4p0:01 ½core6s0:72 5d8:53 6p0:09 6d0:01 ½core3s1:79 3p1:98 4p0:01 ½core3s1:77 3p2:11 4p0:01 ½core3s1:59 3p2:72 4p0:01 ½core3s1:64 3p2:26 4p0:01 ½core6s0:69 5d8:52 6p0:09 6d0:01 ½core3s1:76 3p2:08 4p0:01 ½core3s1:73 3p2:10 4p0:01 ½core3s1:56 3p2:71 4p0:01 ½core3s1:66 3p2:22 ½core6s0:67 5d8:62 6p0:09 6d0:01 ½core3s1:69 3p2:30 4p0:01 ½core3s1:76 3p2:07 4p0:01 ½core3s1:77 3p1:91 4p0:01 ½core3s1:59 3p2:57 4p0:01 ½core3s1:72 3p2:18 4p0:01 ½core6s0:79 5d8:90 6p0:09 6d0:01 ½core3s1:87 3p1:78 ½core3s1:74 3p2:13 4p0:01 ½core3s1:68 3p2:45 4p0:01 ½core6s0:83 5d8:89 6p0:07 6d0:01 ½core3s1:88 3p1:77 ½core3s1:72 3p2:14 4p0:01 ½core3s1:68 3p2:45 4p0:01 ½core6s0:79 5d8:90 6p0:08 6d0:01 ½core3s1:87 3p1:81 ½core3s1:75 3p2:09 4p0:01 ½core3s1:60 3p2:53 4p0:01 ½core6s0:55 5d8:74 6p0:12 7s0:01 6d0:02 ½core3s1:68 3p2:09 4p0:01 ½core3s1:62 3p2:23 4p0:01 ½core3s1:53 3p2:62 4p0:01 ½core6s0:72 5d8:72 6p0:11 7s0:01 6d0:02 ½core3s1:73 3p1:94 4p0:01 ½core3s1:58 3p2:27 4p0:01 ½core3s1:61 3p2:57 4p0:01 ½core6s0:81 5d8:91 6p0:10 6d0:02 ½core3s1:86 3p1:71 ½core3s1:70 3p2:12 4p0:01 ½core3s1:80 3p1:94 4p0:01 ½core3s1:60 3p2:58 4p0:01 ½core3s1:60 3p2:47 4p0:01
IrSi4
C2
1/2
IrSi4 (a)
C3 v
1/2
IrSi5
Cs
1/2
3/2
5/2
IrSi5 (a)
Cs
1/2
IrSi5(b)
Cs
1/2
IrSi5
C2 v
1/2
3/2
IrSi6
C2 v
3/2
5/2
IrSi6
Cs
1/2
J.-G. Han / Chemical Physics 286 (2003) 181–192
187
Table 3 Natural spin population of Ir of the stable IrSin (n ¼ 1–6) clusters Cluster
Symm.
Spin
a
b
c
IrSi
C1 v
IrSi2
C2 v
IrSi3
Cs
IrSi3 (a) IrSi4
C3 v C2 v C2 v C3 v
IrSi4 (a) IrSi5
C2 C3 v Cs
1/2 3/2 5/2 1/2 3/2 5/2 1/2 3/2 5/2 3/2 3/2 1/2 1/2 5/2 1/2 1/2 3/2 5/2 1/2 1/2 3/2 1/2 3/2 5/2
)0.7140 )1.0773 )1.1513 )0.4164 )0.8162 )0.9411 )0.3374 )0.3842 )0.9675 )0.4701 )0.7777 0.3187 )0.4340 )0.6326 )0.3996 )0.8741 )0.5566 )0.5874 )0.3623 )0.3736 )0.3237 )0.4002 )0.3634 )0.5382
0.3020 1.0593 1.3778 )0.1204 0.7364 1.1674 )0.0268 0.0887 0.9075 )0.1566 0.7485 )0.4795 )0.0226 0.0754 )0.4552 1.0262 0.2295 0.2860 )0.0150 )0.4225 )0.4513 )0.4216 )0.0481 )0.0219
1.0160 2.1366 2.5291 0.2960 1.5526 2.1085 0.3106 0.4727 1.8750 0.3135 1.5262 0.7982 0.4114 0.7080 0.0566 1.9003 0.7861 0.8374 0.3473 0.0489 0.1276 0.0214 0.3153 0.5163
IrSi5 (a)
Cs C2 v
IrSi6
Cs C2 v
Fig. 1. Structures of IrSin (n ¼ 1–6) clusters.
188
J.-G. Han / Chemical Physics 286 (2003) 181–192
mized structures turn out to thermodynamically stable. Ir–Si bond length and bond angle (\SiIrSi) of IrSi2 cluster (S ¼ 1=2) at the UB3LYP/ and 80.0254°, reLanL2DZ level are 2.2157 A spectively. One may note that the Ir–Si bond lengths in IrSi2 (S ¼ 1=2) cluster are longer than the respective bond length in IrSi2 (spin from S ¼ 3=2 to 9/2), in MoSi2 cluster (spin singlet) [11] and in CrSi2 cluster [15]. Based upon theoretical results of IrSi2 cluster with various of spin electron configurations (from S ¼ 1=2 to 9/2), one finds that total energy of IrSi2 cluster increases and the stability of IrSi2 cluster decreases as the increase of spin from S ¼ 1=2 to 9/ 2 monotonically. Therefore, IrSi2 cluster with spin S ¼ 1=2 is the most stable structure, the corresponding electron state is 2 B1 . IrSi3 . IrSi3 clusters with Cs, C3 v and C2 v pointgroup symmetries considering of different spin configurations are taken into accounts, all of them are selected as candidates for the ground-state configuration. Theoretical results show that IrSi3 ðaÞðC2 vÞ (Fig. 1) with spin doublet configuration is the only stable structure, Ir atom in IrSi3 ðaÞðC2 vÞ interacts with one Si atom with Ir– . Geometry optimiSi(1) bond length of 2.1764 A zations on IrSi3 ðC3 v and C2 vÞ clusters indicate only IrSi3 (C3 v and C2 v) clusters with spin quartet configuration are the thermodynamically stable. Moreover, the LUMO of IrSi3 (C3 v, S ¼ 3=2) consists of a degenerate (E) molecular orbital. Therefore, neither the spin doublet nor the spin sextet are expected to be stable in C3 v geometry as their system will contain incompletely filled degenerate molecular orbital, subject the species to Jahn–Teller distortion. IrSi3 cluster with C2 v symmetry is optimized, it should be mentioned that the IrSi3 (C2 v) clusters with spin S ¼ 1=2 and S ¼ 5=2 have an imaginary frequency, respectively, which are corresponding to the transition states. After the relaxation of the geometry of IrSi3 with C2 v symmetry, the thermodynamically stable IrSi3 clusters with Cs point-group symmetry are achieved with spin doublet, quartet and sextet electron configurations. The Ir–Si bond lengths in IrSi3 (Cs) clusters increase as the decrease of bond angle Si(1)IrSi(2) monotonically, however, IrSi3 (Cs) cluster with spin quartet electron con-
figuration is more stable than IrSi3 (Cs) with doublet and sextet spin electron configurations. The stable geometries and spin electron configurations of IrSi3 (Cs, C2 v, C3 v) clusters are obviously different from those of MSi3 (M ¼ Cr, Mo, W and Ag) clusters [11,12,15,31]. Total energy of IrSi3 (C3 v) cluster with spin quartet configuration is higher by about 0.2083, 1.0754 and 2.30179 eV than those of IrSi3 (Cs) and IrSi3 (C2 v) clusters with spin quartet configurations and IrSi3 ðaÞðC2 vÞ with spin doublet configuration due to the Ir atom in IrSi3 ðC3 vÞ interacts with three Si atoms simultaneously and with the equal bond lengths, therefore, IrSi3 (C3 v) cluster (Table 1) with spin quartet electron configuration is more stable than IrSi3 ðC2 vÞ, IrSi3 ðaÞðC2 vÞ and IrSi3 (Cs) clusters. Furthermore, the spin quartet electron configuration of IrSi3 with C3 v point-group symmetry is the most stable structure, which is selected as the ground state, the corresponding electron state is 4 A1 . IrSi3 ðC3 v, S ¼ 3=2) cluster is the only most stable MSin (n > 1) clusters with higher spin configuration up to now. The striking feature is different from those of MSi3 (M ¼ Cr, Mo, W, Ag) [11,12,15,31] clusters. IrSi4 . Based upon theoretical results of IrSi3 clusters, IrSi4 clusters with C3 v and C2 v pointgroup symmetries considering of spin multiplicities are carried out at the UB3LYP/LanL2DZ level. Frequency analysis on IrSi4 ðC3 vÞ with spin S ¼ 3=2 and IrSi4 ðC2 vÞ with spin doublet and sextet electron configurations, however, reveals that these structures have a saddle point with one imaginary frequency, respectively. It is noted that geometries of IrSi4 ðC3 vÞ clusters with spin doublet and sextet electron configurations are proved to be stable, the Ir atom interacts directly with three Si atoms simultaneously with equal bond lengths. IrSi4 ðC2 vÞ cluster with spin quartet electron configuration turns out to be a stable structure, after relaxation of IrSi4 (C2 v, S ¼ 1=2), the stable IrSi4 (C2 , S ¼ 1=2) cluster is obtained. Ir atom in IrSi4 (C2 v, S ¼ 3=2; C2 , S ¼ 1=2) interacts directly with four Si atoms simultaneously with Si(1)–Ir and Ir–Si(3) bond lengths. The structures of IrSi4 cluster with C2 v and C2 symmetries are captioned at Fig. 1, it is noted that the Ir atom is doped into Si4 cluster, a small deviation on Ir–Si bond lengths
J.-G. Han / Chemical Physics 286 (2003) 181–192
in IrSi4 (C2 ) with S ¼ 1=2 and IrSi4 ðC2 vÞ with S ¼ 3=2, respectively, is found, however, the geometry structures of IrSi4 (C2 v, C2 Þ clusters are obviously different from those of MSi4 (M ¼ Cr, Mo, W, Ag) clusters [11,12,15,31], Ir atom interacts with four Si atoms simultaneously in IrSi4 ðC2 vÞ cluster with non-equal Ir–Si(1) and Ir– Si(3) bond lengths. For IrSi4 (a)(C3 v, S ¼ 1=2) cluster, it is the only stable geometry, Ir interacts only with Si(1), the Ir–Si(1) bond length of 2.2437 . A Based upon the theoretical results of geometric parameters and total energies as well as the analysis on IrSi4 cluster with doublet, quartet and sextet spin configurations above, one finds that total energies for the stable IrSi4 clusters increase as the spin increasing from doublet, quartet to sextet, on the contrary, the stability decreases with the increasing of spin from S ¼ 1=2 to 5/2, IrSi4 ðC3 v, S ¼ 1=2) cluster is turned out to be higher in energy by 0.95 eV than IrSi4 (C2 , S ¼ 1=2) cluster, therefore, the most stable IrSi4 (C2 ) cluster is doublet spin configuration, which is corresponding to the ground state, the ground electron state is 2 A. In the other word, the Si4 cluster with endohedral Ir atom trapping into Si4 cluster is more stable than with Ir atom absorbing on surface of Si4 cluster, this discovery exemplifies the prediction of the large MSi15 (M ¼ Cr, Mo, W) clusters [10]. On ground of the findings of stability of cluster, the doping Ir atom into Si4 cluster brings out the stability of IrSi4 cluster. IrSi5 . Guided by theoretical results of the MoSi5 [11], WSi5 [12] and CrSi5 [15] clusters with C2 v point-group symmetry, IrSi5 clusters with Cs and C2 v point-group symmetries as the most likely candidates for the ground state geometry are considered and investigated. However, IrSi5 ðC2 vÞ cluster apparently bears some similarity to the C2 v point-group symmetry identified for the group of clusters discussed in the previous section (IrSi4 ; C2 v symmetry), specifically, this geometry can be seen as a Si4 structure face capped by Si atom and doped a Ir into the Si5 cluster, also the Ir atom interacts with four silicon atoms simultaneously. IrSi5 ðC2 v, S ¼ 1=2) cluster is optimized at the UB3LYP/LanL2DZ level, the distances of for Ir–Si(1) and Ir–Si(3) bond 2.273 and 2.2988 A
189
(R2 and R3 ) and 2.3841 A lengths as well as 3.76 A (R4 ) for Si–Si bond lengths, respectively, are obtained. After a relaxation on Si atoms, IrSi5 (Cs, S ¼ 1=2) cluster is yielded, frequency analysis, however, reveals that IrSi5 (Cs, S ¼ 1=2) cluster has an imaginary frequency, which is corresponding to a transition state. After relaxation on Ir and Si atoms along the coordination of the imaginary vibrational mode is performed on IrSi5 (Cs, S ¼ 1=2) cluster, a stable IrSi5 (a)(Cs) cluster is obtained. Hence, the two stable doublet spin configurations for IrSi5 (S ¼ 1=2) clusters with C2 v and Cs point-group symmetries are obtained. Geometry optimization and frequency on IrSi5 ðC2 v, Cs; S ¼ 3=2) clusters are carried out and reveals that these structures correspond to the stable ones. Ir–Si bond lengths for IrSi5 (Cs, , which S ¼ 3=2) cluster are 2.3286 and 2.3184 A are smaller than those of IrSi5 cluster (S ¼ 1=2) with C2 v and Cs point-group symmetries, respectively. IrSi5 clusters (S ¼ 5=2) with C2 v and Cs pointgroup symmetries taking into consideration of sextet spin configuration are performed at the UB3LYP/LanL2DZ level. Geometry optimization on IrSi5 ðC2 v, S ¼ 5=2) cluster finds an imaginary frequency, which is corresponding to a transition state. After a relaxation on geometry, a stable IrSi5 (Cs, S ¼ 5=2) cluster is obtained, Ir–Si bond , length in IrSi5 ðCs ; S ¼ 5=2Þ cluster is 2.3620 A which is longer than those of the stable IrSi5 (S ¼ 1=2 and S ¼ 3=2) clusters. Geometries of IrSi5 ðC2 vÞ clusters are also different from MSi5 (M ¼ Cr, Mo, W, Ag, Cu) clusters [11,12,15,31], however, it is obviously demonstrated my theoretical prediction on MSi15 (M ¼ Cr, Mo, W) [10] and ReSix (x ¼ 12; 20) clusters. According to theoretical results of total energies of IrSi5 clusters with doublet, quartet and sextet spin configurations, one finds that the total energy increases as the spin goes from S ¼ 1=2 to 5/2. This feature is shown to be associated with a pronounced drop in the stability of the cluster as spin goes from doublet, quartet to sextet spin configuration. It should be noted that total energy of IrSi5 (a) clusters (S ¼ 1=2) with Cs point-group symmetries is higher by about 0.045 eV than that of IrSi5 (C2 v; S ¼ 1=2) cluster, therefore, IrSi5
190
J.-G. Han / Chemical Physics 286 (2003) 181–192
(C2 v; S ¼ 1=2) cluster is more stable than IrSi5 (a)(Cs, S ¼ 1=2) cluster. IrSi5 ðC2 v; S ¼ 1=2Þ cluster is selected as the ground state configuration, the electronic state is 2 B2 . IrSi6 . Guided by our results of the IrSi5 and MSi5 (M ¼ Cr, Mo, W, Ag) [11,12,15,31] species, we based our geometry optimization of IrSi6 on the IrSi5 (C2 v, Cs, S ¼ 1=2) equilibrium geometry, replacing the Si5 by Si6 . The resulting geometry of C2 v symmetry distorts into the Cs structure displayed in Fig. 1. It is worth noting that the deformed Si6 cluster of IrSi6 (S ¼ 3=2) turns into a regular cluster as the S ¼ 3=2 spin condition is imposed on the system, corresponding to C2 v as the symmetry of IrSi6 (S ¼ 3=2). Whereas, for the spin doublet, the interaction between the Ir atom and the Si6 subsystem fragments turns into the subgroups (Si(1), Si(2)), (Si(3), Si(4)) and (Si(5), Si(6)), which relates to strongly direct bonding in (Si(1), Si(2)) and (Si(3), Si(4)) subsystems. In the spin sextet configuration, Ir interacts directly with four Si atoms simultaneously and with unequal strengths of Ir–Si(1) and Ir–Si(3). The distorted IrSi6 (Cs, S ¼ 1=2) cluster obtained, which is captioned at Fig. 1, turns out to be stable. The geometries of IrSi6 may be interpreted as deformed substitutional structures, derivable from the Oh ground state of Si7 through replacement of one Si atom by Ir. No stable structures were found in case of apical replacement. The hypothesis underlying these investigations, i.e., the avoidance of endohedral sites for a metal impurity in small Sin clusters, can be put to the test in the context of IrSi6 by considering a central Ir atom embedded into an octahedral Si6 network. However, they are corresponding to the saddle points with more than one imaginary frequencies. Total energy on IrSi6 (Cs, S ¼ 1=2) is lower in energy than the others, therefore, IrSi6 (Cs, S ¼ 1=2) is the most stable structure, the corresponding ground state is 2 0 A. 3.2. Population analysis and magnetism Charges localized in Ir or Si atoms are smaller in quantity than the values delocalized in Ir–Si(1) bond, furthermore, charges delocalized in Ir–Si(1) bond in IrSin are larger than those delocalized in
Si–Si bonds. Therefore, charges localized on Ir and Si atoms and charges delocalized Ir–Si(1) bond as well as Si–Si bonds in IrSin contribute to the stability of chemical bonding of IrSin (n ¼ 1–6) clusters. Charge of Ir–Si bond is shifted out of Si–Si bonds to Ir–Si(1) in IrSin (n ¼ 2–5) clusters. Moreover, the discovery of covalent bond participates strongly in the stabilization of IrSin (n ¼ 1–6) clusters. Therefore, Charge-transfer mechanism in IrSin (n ¼ 1–6) clusters is similar to those of MSin (M ¼ Cr, Mo, W; n ¼ 1–6; 15) [10– 12,15] clusters. The contribution of delocalized charges to stability on MSi15 (M ¼ Cr, Mo, W) [10] is discussed in detail. We conclude from our computation of natural atomic net populations that charges of Ir in the more stable IrSin (n ¼ 1–6) are negative, which are the same as Cr, Mo, and W in MSin (M ¼ Cr, Mo, W; n ¼ 1–6; 15) [10–12,15] clusters. On the basis of natural electron configuration (Table 2), one finds that the charges transfer from Si atoms and 6s orbitals of Ir to 5d orbitals of Ir in IrSin (n ¼ 1–6) clusters, more than 7.8 electrons occupy the 5d subshell of Ir in IrSin , the 5d orbitals of Ir atom in IrSin (n ¼ 1–6) do not behave as a core orbitals but take an active role in the bonding, which are different from Cu in CuSin clusters and Ag in AgSin clusters [31], in the other word, the 5d orbitals of Ir atom in the most stable IrSin clusters acting as an acceptor have a trend to pull out the charges from 6s of Ir and Si atoms (near Ir atoms). The charge transfer phenomenon as described here is the same as the ones that found in some of MSin (M ¼ Cr, Mo; n ¼ 1–6; 15) [10–12] clusters, furthermore, the charges transferring from Si to Ir atom correlate sensitively with the spin multiplicity. However, the charges transfer from 6s of Ir and 3s of Si(2), Si(3) and Si(4) to 3p of Si(1) and 5d of Ir in IrSi4 ðaÞðC3 v, S ¼ 1=2), generally, the charges transfer from Si(2), Si(3), Si(4) and Ir to Si(1) atom, this trend is different from the other IrSin clusters. As the magnet is in proportional to the c, where c ¼ ja bj (Table 3), we can find that the magnet of transition metal Ir for the most stable IrSin clusters are also controlled by the spin multiplicity, generally, the contribution of TM to magnet increases as the spin S ¼ 1=2–3/2.
J.-G. Han / Chemical Physics 286 (2003) 181–192
3.3. Fragmentation energies A systematic investigation on MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters finds that the hybrid density functional method (UB3LYP) in conjunction with LanL2DZ basis sets yields reasonable and accurate results [11,12]. The exchange-correlation energies are considered completely by the UB3LYP method during the calculation of IrSin (n ¼ 1–6) clusters. In a further series of investigations, we evaluate IrSin (n ¼ 1–6) fragmentation energies, defined according to the formula Dðn; n 1Þ ¼ Eb ðIrSin1 Þ þ Eb ðSiÞ Eb ðIrSin Þ as the change in total energy upon removing one Si atom from the cluster, where in each case the IrSin (n ¼ 1–6) structures are compared. Our findings are 4.8990, 4.3602, 4.7745, 4.1247 and 4.8868 eV for D(2, 1), D(3, 2), D(4, 3), D(5, 4) and D(6, 5), respectively, at the UB3LYP/LanL2DZ level. The remarkable values of D(6,5) and D(2,1) are found. Our results indicate that D(2,1) is larger than D(6,5), or, in other words, IrSi2 cluster is more stable than IrSi6 cluster with respect to the removing one silicon atom, it is in good agreement with experimental result [6]. According to our theoretical results of total energies (Eb ) for IrSin (n ¼ 1–6) clusters (Table 2), a general trend of stability is found, which is different from those of MSin (M ¼ Cr, Mo, W, Ag) (n ¼ 1–6) clusters [11,12,15,31] clusters and previous results for Gen (n ¼ 2–6) as part of Gen F (n ¼ 2–6) clusters [7]. Theoretical results also indicate that IrSin (n ¼ 1–6) clusters are not characterized by the same Sin (n ¼ 1–6) framework structures as MSin (M ¼ Cr, Mo, W, Cu, Ag; n ¼ 1–6) [11,12,15,31].
191
the stabilities of IrSin (n ¼ 1–6) clusters are investigated, along with fragmentation energies of IrSin (n ¼ 1–6) clusters upon removal of a Si atom. Theoretical results show that the stability of IrSin decreases as the spin increases from S ¼ 1=2 to 5/2 besides IrSi3 cluster with S ¼ 3=2, this feature, which is in good agreement with theoretical results of MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters, is shown to be associated with a pronounced drop in the stability of the cluster as one goes from doublet, quartet to sextet spin configurations. Natural population and natural electron configurations are calculated. Ir in IrSin cluster acts as acceptor and Sin in IrSin acts as donor. Theoretical results indicate that the geometry structures of Sin are deformed after Ir dopes in Sin clusters, furthermore, geometries of IrSin (n ¼ 1–6) clusters are obviously different from MSin (Cr, Mo, W; n ¼ 1–6) clusters, which demonstrate the prediction in MSi15 (M ¼ Cr, Mo, W), additionally, the Ir atom doping into Sin clusters does contribution to the stability of Sin clusters. The contribution of Ir in IrSin clusters to magnetism is also discussed. IrSi3 (C3 v, S ¼ 3=2) cluster is the only most stable MSin (n > 1) clusters with higher spin configuration up to now.
Acknowledgements This work is supported by National Natural Science Foundation of China (20173055), National foundation from Department of Science and Technology (P.R. China) (970211006) and Structural Research Laboratory of USTC of Chinese Academy of Sciences, P.R. China (2001B10).
References 4. Conclusions Geometry optimizations and population analyses are performed for IrSin (n ¼ 1–6) clusters at the UB3LYP/LanL2DZ level, maintaining pointgroup symmetry. Chemical bonding mechanisms and equilibrium geometries of IrSin (n ¼ 1–6) clusters are identified and compared with MSin (M ¼ Cr, Mo, W; n ¼ 1–6) clusters. Additionally,
[1] [2] [3] [4] [5] [6] [7] [8]
H.F. Jarrold, Science 1085 (1991) 251. E. Kaxiras, Phys. Rev. Lett. 64 (1990) 551. K.M. Ho et al., Nature 392 (1998) 582. K. Jackson, B. Nellermoe, Chem. Phys. Lett. 254 (1996) 249. I. Shim, K.A. Gingerich, Z. Phys. D 16 (1990) 141. H. Hiura, T. Miyazaki, T. Kanayama, Phys. Rev. Lett. 86 (2001) 1733. J.G. Han, Chem. Phys. Lett. 324 (2000) 143. L. Turker, J. Mol. Str. (Theochem.) 548 (2001) 185.
192
J.-G. Han / Chemical Physics 286 (2003) 181–192
[9] S.M. Beck, J. Chem. Phys. 90 (1989) 6306. [10] J.G. Han, Y.Y. Shi, Chem. Phys. 266 (2001) 33. [11] J.G. Han, F. Hagelberg, J. Mol. Str. (Theochem.) 549 (2001) 168. [12] J.G. Han, C. Xiao, F. Hagelberg, Structural Chemistry 13 (2002) 173. [13] C. Xiao, F. Hagelberg, J. Mol. Struct. (Theochem.) 529 (2000) 241. [14] J.G. Han, W.M. Pang, Y.Y. Shi, Chem. Phys. 257 (2000) 21. [15] J.G. Han, F. Hagelberg, Chem. Phys. 263 (2001) 255. [16] Z. Chen, H. Jiao, A. Hirsch, W. Thiel, J. Org. Chem. 66 (2001) 3380. [17] J.J. Scherer, J.B. Paul, C.P. Collier, R.J. Saykally, J. Chem. Phys. 102 (1995) 5190. [18] J.J. Scherer, J.B. Paul, C.P. Collier, R.J. Saykally, J. Chem. Phys. 103 (1995) 113. [19] J.J. Scherer, J.B. Paul, C.P. Collier, A. OÕKeefe, R.J. Saykally, J. Chem. Phys. 103 (1995) 9187. [20] J. Budinavicius, L. Pranevicoius, S. Tamulevicius, Phys. Status. Solidi A 114 (1989) K25. [21] P. Turski, Chem. Phys. Lett. 315 (1999) 115. [22] Y.M. Harrick, W. Weltner Jr., J. Chem. Phys. 94 (1991) 3371.
[23] J.E. Kingcade Jr., K.A. Gringerick, J. Chem. Soc. Faraday Trans. 285 (1989) 195. [24] K.A. Gringerick, J. Chem. Phys. 50 (1969) 5426. [25] A.V. de Auwera-Mahieu, N.S. Melntyre, J. Drowert, Chem. Phys. Lett. 4 (1969) 198. [26] J.G. Han (in preparation). [27] J.G. Han (in preparation). [28] M.J. Frisch et al., Gaussian 98, Gaussian, Pittsburgh, PA, 1998. [29] R.D. Johnson, M.S. Vries, J. Salem, D.S. Bethune, C.S. Yannoni, Nature 355 (1992) 239. [30] G. Rickert, P. Lamparter, S. Steeb, Z. Met. 72 (1981) 765. [31] P.F. Zhang, J.G. Han, Q.R. Pu, Chem. Phys. (to be submitted). [32] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [33] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 27 (1988) 785. [34] N.C. Handy, H.F. Schaefer III, J. Chem. Phys. 81 (1984) 5031. [35] W.R. Wadt, P.J. Hay, J. Chem. Phys. 82 (1985) 284. [36] A. Nicklass, M. Dolg, H. Stoll, H. Preuss, J. Chem. Phys. 102 (1995) 8942. [37] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [38] R. Mishra, R.D. Hoffmann, R. Pottgen, Z. Anorg. Allg. Chem. 627 (2001) 1787.