Journal of Molecular Structure (Theochem) 589–590 (2002) 103–109 www.elsevier.com/locate/theochem
Structure and stability of SinCm2n clusters Zhenyi Jianga,b, Xiaohong Xub, Haishun Wub,*, Fuqiang Zhangb, Zhihao Jina a
School of Material Science and Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China b Institute of Material Chemistry, Shanxi Teachers University, Linfen 041004, People’s Republic of China Received 17 January 2002; accepted 3 April 2002
Abstract In this paper, both ab initio and density functional theory methods have been used to predict geometries, electronic states and energies of SinCm2n ðn ¼ 1; 2; m ¼ 3 – 16Þ: Harmonic frequencies for these clusters are given in order to aid in the characterization of the ground states. These results show that SiCm21 ðm ¼ 3 – 9Þ clusters form linear structure and SiCm21 ðm ¼ 10 – 16Þ isomers form ring structure. Si2Cm22 ðm ¼ 4 – 16Þ clusters have linear structure except ring isomer of Si2C12 molecule. Si atom favor to bond at end in linear isomers. However, C atom themselves favor to bond in the cyclic isomers. The stability of the SinCm2n ðn ¼ 1; 2; m ¼ 3 – 16Þ clusters with odd m are greater than that with even m. q 2002 Elsevier Science B.V. All rights reserved. Keywords: SinCm2n clusters; DFT theory; Geometric configuration; Ground state; Stability
1. Introduction Silicon carbide (SiC) has become one of the most promising semiconductors for high-power, high-frequency and high-temperature applications [1,2]. Those have aroused universal attention of physicists, researchers of materials and chemist. Under the vacuum condition, the sputtering Si reacts with C to prepare the new-type SiC nanofilm by using magnetron reactive sputtering (MRS) technique [3,4]. It is easy for MRS technique to form precursor intermediate complexes, and a series of SinCm [5,6] clusters had already been observed. Froudakis [7] obtained the forms of SinCm ðn ¼ 2; 3; n þ m ¼ 6Þ with MP2/6-31gp method; Nakajima [8] studied the electronic structure of Sin Cm2 ðn þ m ¼ 3 – 6Þ using the second-order Moller Plesset (MP2) * Corresponding author. Tel.: þ86-357-205-1010; fax: þ 86-357205-100. E-mail address:
[email protected] (H. Wu).
theory; Gordon [9] calculated structure of the linear SiC4 and SiC6 at CCSD/cc-pVDZ level. Recently Ding [10,11] studied the geometric structure and vibration spectra of SiC7, SiC9 clusters with B3LYP/cc-pVDZ method using the GAUSSIAN 94/DFT program suite. Since the properties of clusters are unique, it is expected that cluster assembled materials can have uncommon properties. Studies on the electronic and geometric structures of clusters are necessary. In this work, we performed density functional calculations at the standard B3LYP/6-311gp level using the GAUSSIAN 98 program [12]. To our knowledge, this is the first time to study the ground state geometries of SinCm2n ðn ¼ 1; 2; m ¼ 11 – 16Þ clusters.
2. Computational methods Molecular
0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 2 5 1 - 8
ground
state
geometries
were
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Fig. 1. Sketch figures of chain and ring geometries. (a) Chain SiCm21 ðm ¼ 3 – 9Þ; (b) ring SiCm21 ðm ¼ 10 – 16Þ; (c) chain Si2Cm22 ðm ¼ 4 – 13; 15 – 16Þ; (d) ring Si2Cm22 ðm ¼ 14Þ:
optimized. The HF/STO-3G, HF/6-31gp, B3LYP/631gp and B3LYP/6-311gp level have been used in this investigation. On the basis of final optimized results (at the B3LYP/6-311g p level), we calculated vibrational spectra and thermodynamic properties at the B3LYP/6-311gp level. All calculations were carried out using the GAUSSIAN 98 program on a SGI/O2 workstation.
3. Results and discussion 3.1. Geometry The ground state geometric sketch figures of SinCm2n optimized by B3LYP method are shown in Fig. 1. Geometric parameters for all SiCm21 ðm ¼ 3 – 16Þ and Si2Cm22 ðm ¼ 4 – 16Þ clusters are listed in
Fig. 2. logðBeÞ as a function of logðmÞ; (O) Si2Cm22; (†) SiCm21.
Tables 1 and 2, respectively. SiCm21 ðm ¼ 3 – 9Þ are linear clusters and have C1v symmetry. Si2Cm22 ðm ¼ 4 – 13; 15 – 16Þ are linear clusters and have D1h symmetry except Si2Cm22 ðm ¼ 8 – 10Þ which have C1v symmetry. Their Si atoms favor to bond at ends of C linear chain. The chains with even m are triplet states whereas the ones with odd m are singlet ground states. SiCm21 ðm ¼ 10 – 16Þ are planar cyclic molecules and have Cs symmetry except SiC11 which is spatial isomer with Cs symmetry. Si2C12 are also cyclic planar molecules and have D2h symmetry. Their C atoms themselves favor to form ring structure. The symmetry of SiC9, SiC11, SiC13, SiC14 and SiC15 are very similar to C2v point group, so we reported their bond lengths according to C2v point group. Bond lengths of Si2C6, Si2C7 and Si2C8 are reported as D1h symmetry (not C1v ) from the same reason. In order to
Fig. 3. Dipole moments as a function of m; (O): Si2Cm22 (†): SiCm21.
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Table 1 Bond length L (nm) and symmetry parameters of SiCm21 clusters m
Type
L
3(1S )
Si–C2 C2– C3 Si–C2 C2– C3 C3– C4 Si–C2 C2– C3 C3– C4 C4– C5 Si–C2 C2– C3 C3– C4 C4– C5 C5– C6 Si–C2 C2– C3 C3– C4 C4– C5 C5– C6 C6– C7 Si–C2 C2– C3 C3– C4 C4– C5 C5– C6 C6– C7 C7– C8 Si–C2 C2– C3 C3– C4 C4– C5 C5– C6 C6– C7 C7– C8
0.1697 0.1282 0.1733 0.1287 0.1308 0.1699 0.1272 0.1298 0.1278 0.1726 0.1279 0.1282 0.1287 0.1295 0.1704 0.1274 0.1289 0.1262 0.1296 0.1280 0.1722 0.1277 0.1284 0.1276 0.1274 0.1291 0.1291 0.1706 0.1275 0.1288 0.1264 0.1287 0.1263 0.1297
4(3S )
5(1S )
6(3S )
7(1S )
8(3S )
1
9( S )
m
10(1A0 )
11(1A0 )
12(1A0 )
13(1A0 )
Type
L
C8–C9 Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C10– C2 Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C6–C7 C7–C8 C8–C9 C9–C10 C10– C11 C11– C2 C11– Si Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C6–C7 C12– C2 Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C6–C7 C7–C8 C8–C9
0.1280 0.1825 0.1328 0.1278 0.1300 0.1302 0.1475 0.1822 0.1361 0.1240 0.1336 0.1256 0.1326 0.1269 0.1307 0.1260 0.1332 0.1457 0.1849 0.1843 0.1375 0.1237 0.1342 0.1264 0.1331 0.1409 0.1843 0.1395 0.1223 0.1359 0.1226 0.1366 0.1226 0.1367
compare with Ref. [11], we performed single point energy calculation and geometric optimization for SiC9 with parameters in Ref. [11]. Its single point calculation does not converge. The energy of optimized geometry is 11.77 kJ mol21 more than that of Cs structure we reported, so SiC9 is a planar cyclic molecule with Cs symmetry. In Figs. 2 and 3, the behaviors for the calculated equilibrium rotational constant and the dipole moment with increasing values of m were given. The rotational constant logðBeÞ of SiCm21 ðm ¼ 3 – 9Þ go as 22:74 logðmÞ; which behave similarly to those of pure carbon chains [11]. The one of three rotational constant logðBeÞ of SiCm21 ðm ¼ 10 – 16Þ increase
m
14(1A0 )
15(1A1)
16(3A00 )
Type
L
C9 –C10 C10–C11 C11–C12 C12–C13 C13–C2 C13–Si Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 C7 –C8 C14–C2 Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 C7 –C8 C8 –C9 C15–C2 Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 C7 –C8 C8 –C9 C16–C2
0.1225 0.1360 0.1223 0.1396 0.1379 0.1842 0.1836 0.1335 0.1259 0.1300 0.1275 0.1292 0.1288 0.1433 0.1839 0.1354 0.1239 0.1323 0.1244 0.1324 0.1245 0.1326 0.1423 0.1844 0.1371 0.1234 0.1331 0.1246 0.1318 0.1266 0.1298 0.1399
with 22:65 logðmÞ: Their slopes are close on the whole in Fig. 2. The rotational constant logðBeÞ of linear Si2Cm22 go as 22:49 logðmÞ: The slopes of dipole moment (De ) of SiCm21 ðm ¼ 3 – 9Þ with increasing values of m are about 0.8, and the line with even m is nearly parallel to the line with odd. The De of SiCm21 ðm ¼ 10 – 16Þ increase gently with increasing values of m. De of SiC11 molecule is differ from others because of its non-planar structure. 3.2. Vibrational spectrum analysis A vibrational frequency calculation is important to predicting molecular stability. To determine the
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Table 2 Bond length L (nm) and symmetry parameters of Si2Cm22 clusters m
Type
L
4(3Sg)
Si–C C –C Si–C C –C Si–C2 C2 –C3 C3 –C4 Si1–C2 C2 –C3 C3 –C4 Si–C2 C2 –C3 C3 –C4 C4 –C5 Si–C2 C2 –C3 C3 –C4 C4 –C5 Si–C2 C2 –C3
0.1742 0.1276 0.1691 0.1288 0.1727 0.1274 0.1294 0.1696 0.1284 0.1279 0.1721 0.1277 0.1289 0.1268 0.1699 0.1283 0.1280 0.1275 0.1717 0.1277
5(1Sg) 3
6( Sg)
7(1Sg)
8(3Sg)
9(1Sg)
10(3Sg)
m
11(1Sg)
12(3Sg)
13(1Sg)
Type
L
m
Type
L
C3 –C4 C4 –C5 C5 –C6 Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7 Si–C2 C2 –C3 C3 –C4 C4 –C5 C5 –C6 C6 –C7
0.1287 0.1270 0.1284 0.1701 0.1282 0.1282 0.1274 0.1277 0.1716 0.1278 0.1287 0.1271 0.1283 0.1272 0.1703 0.1281 0.1282 0.1273 0.1278 0.1276
14(1Ag)
Si–C2 C2–C3 C3–C4 C4–C5 C2–C14 Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C6–C7 C7–C8 Si–C2 C2–C3 C3–C4 C4–C5 C5–C6 C6–C7 C7–C8 C8–C9
0.1839 0.1396 0.1220 0.1359 0.1385 0.1704 0.1280 0.1283 0.1273 0.1279 0.1275 0.1277 0.1713 0.1278 0.1286 0.1271 0.1282 0.1273 0.1281 0.1273
ground state of clusters, we tried at least three different initial configurations with low total energies and then calculated vibrational frequencies for these clusters. We reported the lowest vibrational frequencies and the highest infrared spectra intensity of the ground states for each cluster in Tables 3 and 4. It can be clearly seen that they are actually equilibrium states without imaginary frequencies. The highest Table 3 Vibrational frequencies of SiCm m 3 4 5 6 7 8 9
21
n (cm ) 46.6 1925.8 150.6 1985.9 97.3 2183.0 83.8 1960.1 63.2 2215.3 52.6 2123.4 41.8 2049.6
21
I (km mol ) 0.6 648.0 1.8 152.5 0.2 2586.9 1.2 479.3 0.5 4766.0 0.8 1717.5 0.5 6282.9
m 10 11 12 13 14 14 16
21
n (cm ) 117.7 1956.7 91.5 2043.7 56.5 1933.9 67.0 495.4 74.2 1979.0 59.0 857.7 49.9 864.3
21
15(1Sg)
16(3Sg)
infrared spectra intensity of the ground states for SiC9 is consistence with experiment [11], so this is one of reasons that SiC9 is determined to be cyclic forms. 3.3. Energy and thermodynamical property The total energy, zero point energy, thermocapacity (Cv) and entropy (S 0) are listed in Tables 5 and 6. The zero point energy, Cv and S 0 are nearly in Table 4 Vibrational frequencies of Si2Cm
I (km mol ) 1.1 429.8 0.2 130.0 4.9 99.4 0.1 140.3 0.5 424.5 0.2 62.1 0.2 61.2
m
n (cm21)
I (km mol21)
4
123.9 901.7 84.5 2047.7 69.1 1865.1 53.2 2144.5 44.5 2071.8 36.3 1958.5 30.1
2.2 4.6 4.0 2511.0 1.0 119.2 1.6 5161.7 0.6 545.4 0.9 6082.4 0.5
5 6 7 8 9 10
m
11 12 13 14 15 16
n (cm21)
I (km mol21)
2138.5 25.3 2016.1 22.7 1999.6 18.8 1903.5 48.0 463.4 14.8 1903.7 13.5 1954.6
1153.5 0.6 16 663.0 0.3 2239.1 0.5 19 469.6 0.6 191.4 0.4 34 126.8 0.3 6297.3
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Table 5 Total energy, zero-point energy and Cv ; S for SiCm21 m
Symmetry
Total energy (a.u.)
Zero-point energy (kJ mol21)
Thermocapacity (J mol21 K21)
Entropy (J mol21 K21)
3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16
C1v C2v C1v C2v C1v C2v C1v C2v C1v C2v C1v C2v C1v C2v Cs C1v Cs C1v Cs C1v Cs C1v Cs C1v Cs C1v Cs C1v
365.5665 365.5642 403.6193 403.6065 441.7410 441.6945 479.8029 479.7635 517.9146 517.8775 555.9830 555.9511 594.0894 593.9892 632.1657 632.1621 670.2820 670.2649 708.3396 708.2168 746.4459 746.4409 784.5543 784.5189 822.6666 822.6173 860.7293 860.6970
16.851 16.310 29.998 28.647 45.637 41.477 56.846 55.383 74.239 69.697 85.757 82.959 104.817 91.909 114.619 117.098 127.941 126.141 137.698 139.392 153.901 156.645 164.819 164.019 179.337 181.169 184.808 190.061
40.11 35.91 53.89 45.47 66.73 63.99 82.04 73.63 92.54 82.49 106.96 99.80 116.08 104.42 121.12 129.72 137.58 150.75 152.55 162.99 171.60 174.07 181.22 192.75 198.91 204.43 216.03 221.35
265.67 257.12 274.58 264.71 291.49 298.16 320.90 311.17 334.07 318.45 363.77 353.30 376.27 354.92 368.40 405.91 389.17 427.41 419.80 450.70 445.37 469.05 450.42 501.34 469.32 515.49 509.13 547.75
proportion to increased m. Their average enhancement are 13.3 kJ mol21, 13.05 J mol21 K21 and 17.82 J mol21 K21 for SiCm21 molecules, respectively, and those are 13.46 kJ mol 21 , 21 21 and 19.31 J mol 21 K 21 for 13.44 J mol K Si2Cm22 molecules, respectively. Both Cv and S 0 of
ground state isomers are greater than those of substable state isomers for SiC m21 ðm ¼ 3 – 9Þ molecules except SiC4. However, both Cv and S 0 of ground state isomers are smaller than those of substable state isomers for SiCm21 ðm ¼ 10 – 16Þ molecules. The zero point energies of ground state isomers are greater than that of substable state isomers for Si2Cm22 molecules, which can be thought to be the ways for judging a ground state correctly. To test the stability of SinCm2n clusters further, The following energy variations of the two kinds of reactions are considered: 2ðSin Cðm2nÞ Þ ! ðSin Cðm2nÞþ1 Þ þ ðSin Cðm2nÞ21 Þ
Fig. 4. D2 Em as a function of m; (O): Si2Cm22 (†): SiCm21.
ð1Þ
We define the energy variation in formula (1) as D2 Em ¼ Eðm2nÞþ1 þ Eðm2nÞ21 2 2Eðm2nÞ ; the second difference in energy for SinCm2n. Hence, we obtain the curves shown in Fig. 4 corresponding to the energy variations in formula (1) as m. The larger the
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Table 6 Total energy, zero-point energy and Cv ; S for Si2Cm22 m
Symmetry
Total energy (a.u.)
Zero-point energy (kJ mol21)
Thermocapacity (J mol21 K21)
Entropies (J mol21 K21)
4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16
D1h D2h D1h C2v D1h D2h D1h C2v C1v D2h C1v C2v C1v D2h D1h C2v D1h D2h D1h C2v D2h D1h D1h C2v D1h C2v
655.1026 655.1003 693.2174 693.1257 731.2851 731.1817 769.3928 769.3230 807.4644 807.4020 845.5683 845.4990 883.6431 883.5965 921.7442 921.7238 959.8214 959.8032 997.9206 997.8758 1036.0072 1035.9995 1074.0971 1074.0683 1112.1776 1112.1776
24.954 24.811 40.363 33.090 52.210 47.226 68.911 61.348 80.968 74.459 99.646 85.244 114.135 100.264 119.744 119.265 130.440 127.782 148.006 137.435 163.054 157.887 175.067 164.632 187.648 177.536
57.64 48.75 69.36 67.77 84.41 77.30 95.06 95.36 109.269 100.81 118.34 128.13 130.47 136.26 154.59 140.24 170.00 159.75 180.12 185.95 183.18 196.35 207.31 213.34 219.71 220.18
282.53 270.52 297.32 310.39 327.06 313.46 340.21 330.59 375.56 343.33 387.73 390.13 417.04 381.88 434.37 390.01 464.46 410.45 477.53 466.43 448.99 508.47 522.09 500.00 550.36 495.42
D2 Em is, the more stable the cluster corresponding to m is. Therefore, from Fig. 4, it is clear that the D2 Em is larger as odd m and low as even m, which indicates that those SinCm2n clusters corresponding to m are more stable, so that the ‘magical number’ regularity of SinCm2n is that the total atom number m should be odd. Therefore, it can be excellent to explain why SiC10, SiC14 in TOF mass spectra [5] are more stable.
Acknowledgments This work was supported by the Shanxi Provincial Youth Science Foundation, Backbone Teacher Plan Project of the Education Ministry of China and Shanxi Provincial Returnee Foundation.
References 4. Conclusions The structures of the SiCm21 ðm ¼ 3 – 9Þ and Si2Cm22 ðm ¼ 4 – 13; 15 – 16Þ are linear isomers, and their Si atoms favor to bond at ends of C linear chain. The SiCm21 ðm ¼ 10 – 16Þ and Si2C12 are cyclic isomers, and their C atoms themselves favor to form ring structure. The stability of the SinCm2n ðn ¼ 1; 2; m ¼ 3 – 16Þ clusters with odd m are greater than that with even m.
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