我們使用了brownian-type分子動力學來分析研究合金金屬叢集的的溫度效應
這篇文章主要探討兩個議題:
其一 不同系綜在有限大系統下是否等價?
我們計算並比較Cv(比熱)和 δ(lindemann index)這兩個物理量分別在正則(本篇)和微正則(文獻)系綜的數值結果
,發現不同系綜存在著一些普適性的差異
其二 這兩個物理量再同一系綜預測溶化溫度上也出現不一致,我們試著用能量分布圖和rij來解釋背後機制,獲得非常令人滿意的結果

The brownian-type molecular dynamics has been
applied to study the effect of temperature on bimetallic clusters. Two specific issues are addressed. The first issue concerns the use of different ensembles in simulation of finite
systems. We make a semiquantitative comparison between the specific heat Cv and the root-mean-squared relative bond length fluctuation
parameter δ of bimetallic clusters obtained in the present canonical ensemble simulations and those by the microcanonical ensemble. Systematic
discongruity in the simulation results alludes to the inherent difference of the two ensembles for finite-sized systems. The second issue concerns the generally incomplete agreement in temperature dependences for Cv and δ. Here we make an analysis of the time evolution of the
instantaneous relative bond length fluctuation rij, where the ith and jth are two atoms judiciously selected from the cluster. We give temporal evidence that the permutational isomer transition between ij-atoms in the bimetallic cluster which contributes to δ is due to these two atoms transiting to a higher-lying isomer state and this temporal behavior
can be inferred from rij. The rij(t) therefore dictates the detail of the microscopic change in time and provides us with a means for understanding the incompatibility of δ and Cv

1 S. Chen, R.S. Ingram, M.J. Hostetler, J.J. Pietron, R.W. Murray, T. G. Schaaff, J.T. Khoury,
M. M. Alvarez and R.L. Whetten, Science 280, 2098 (1998).
2 N. Toshima and T. Yonezawa, New. J. Chem. 22, 1179 (1998).
3 J.D. Aiken III, D. John and R.G. Finke, J Mol. Catal. A: Chem. 145, 1 (1999).
4 H. Bonnemann and R.M. Richards, Eur. J. Inorg. Chem. 2001, 2455 (2001).
5 F. Favier, E. C. Walter, M. P. Zach, T. Benter and R.M. Penner, Science 293, 2227 (2001).
6 M.J. L´opez, P.A. Marcos, and J.A. Alonso, J. Chem. Phys. 104, 1056 (1996).
7 C. Rey, J. Garcia-Rodeja and L.J. Gallego, Phys. Rev. B 54, 2942 (1996).
8 J. Jellinek and E.B. Krissinel, Chem. Phys. Lett. 258, 283 (1996).
9 E.B. Krissinel and J. Jellinek, Chem. Phys. Lett. 272, 301 (1997); Int. J. Quamtum Chem. 62,
185 (1997).
10 A. F. Voter and S. P. Chen, in Characterization of Defects in Materials, edited by R.W. Siegal, J.
R. Weertman, and R. Sinclair, MRS Symposia Proceedings No. 82 (Materials Research Society,
Pittsburgh, 1987), p. 175.
11 R.P. Gupta, Phys. Rev. B 23, 6265 (1981).
12 F. Cleri and V. Rosato, Phys. Rev. B 48, 22 (1993).
13 M. Calleja, C. Rey, M. M. G. Alemany, L. J. Gallego, P. Ordej´on, D. S´achez-Portal, E. Artacho
and J. M. Soler, Phys. Rev. B 60, 2020 (1999).
14 E.F. Rexer, J. Jellinek, E.B. Krissinel, E.K. Parks and S.J. Riley, J. Chem. Phys. 117, 82
(2002).
15 J. Wang, G.H. Wang, X.S. Chen, W. Lu and J. Zhao, Phys. Rev B 66, 014419 (2002).
16 S. Darby, T.V. Mortimer-Jones, R.L. Johnston, and C. Roberts, J. Chem. Phys. 116, 1536
(2002).
17 R.A. Lordeiro, F.F. Guimar˜aes, J.C. Belchior, and R.L. Johnston, Int. J. Quantum Chem. 95,
112 (2003).
18 G. Rossi, A. Rapallo, C. Mottet, A. Fortunelli, F. Baletto, and R. Ferrando, Phys. Rev. Lett.
93, 105503 (2004).
19 A. Rapallo, G. Rossi, R. Ferrando, A. Fortunelli, B.C. Curley, L.D. Lloyd, G.M Tarbuck and
R.L. Jonnston, J. Chem. Phys. 122, 194308 (2005); J. Chem. Phys. 122, 194309 (2005).
20 F. Baletto, C. Mottet and R. Ferrando, Phys. Rev B 66, 155420 (2002); Phys. Rev. Lett. 90,
135504 (2003).
21 M.S. Bailey, N.T. Wilson, C. Roberts and R.L. Johnston, Eur. Phys. J. D 25, 41 (2003).
22 P.J. Hsu and S.K. Lai, J. Chem. Phys., to appear (2005).
23 G.E. Lopez and D.L. Freeman, J. Chem. Phys. 98, 1428 (1993).
24 S.P. Huang and P.B. Balbuena, J. Phys. Chem B 106, 7225 (2002).
25 Subramanian K.R.S. Sankaranarayanan, Venkat R. Bhethanabotla and Babu Joseph, Phys.
Rev. B 71, 195415 (2005).
26 K. Michaelian and I.L. Garz´on, Eur. J. D 34, 183 (2005).
27 S. K. Lai, W. D. Lin, K. L. Wu, W. H. Li and K. C. Lee, J. Chem. Phys. 121, 1487 (2004).
28 M. Bixon and J. Jortner, J. Chem. Phys. 91, 1631 (1989).
29 J.P. Hsu and S.K. Lai, J. Chem. Phys., in press (2005).
30 C.H. Chien, E. Blaisten-Barojas, and M.R. Pederson, J. Chem. Phys. 112, 2301 (2000).
31 M.J. L´opez and J. Jellinek, J. Chem. Phys. 110, 8899 (1999).
32 N.T. Wilson and R.L. Johnston, J. Mat. Chem. 12, 2913 (2002).
33 F. Belatto and R. Ferrado, Rev. Mod. Phys. 77, 371 (2005).
34 N. Ju and A. Bulgac, Phys. Rev. B 48, 2721 (1993); See also Ref. 42; W. G. Hoover, Molecular
Dynamics, Lecture Note in Physics (Springer, New York, 1986), Vol. 258.
35 . H. Sloan, D. Kusnezov, and A. Bulgac, in Computational Quantum Physics, edited by A. S.
Umar, V. E. Oberacker, M. R. Strayer, and C. Bottcher, AIP Conf. Proc. No. 260 (AIP, New
York, 1992), p. 23.
36 A. Bulgac and D. Kusnezov, Phys. Rev. A 42, 5045 (1990); Phys. Rev. Lett. 68, 1335 (1992);
Phys. Rev. B 45, 1988 (1992); D. Kusnezov, A. Bulgac, and W. Bauer, Ann. Phys. (N.Y.) 204,
155 (1990); D. Kusnezov and A. Bulgac, ibid. 214, 180 (1992).
37 A. Bulgac and D. Kusnezov, Phys. Lett. A 151, 122 (1990).
38 D. Liu and J. Nocedal, Math. Program. B 45, 503 (1989).
39 F. Calvo and F. Spiegelmann, J. Chem. Phys. 112, 2888 (2000).
40 Y.J. Lee, J.Y. Yaeng, E.K. Lee, B. Kim, S. Kim and K.K. Han, J. Comp. Chem. 21, 380 (2000).
41 S. Sawada and S. Sugano, Z. Phys. D 14, 247 (1989).
42 R. Werner, Eur. J. Phys. B, 43, 47 (2005).
43 E.G. Noya, J.P.K. Doye and F. Calvo, arXiv:cond-mat509334 v1, (2005).
44 G.A. Breaux, C.M. Neal, B. Cao and M.F. Jarrold, Phys. Rev. Lett. 94, 173401-1 (2005).
45 L.J. Gallego, M.J. Grimson and C. Rey, Phys. Rev. B 51, 5518 (1995).
46 C. Borgs and R. Kotecky, J. Stat. Phys. 79, 43 (1995).
47 S. Nose, J. Chem. Phys. 81, 511 (1984).
48 D.M. Deaven and K.M. Ho, Phys. Rev. Lett. 75, 288 (1995).
49 Y. Zeiri, Comp. Phys. Comm. 103, 28 (1997).
50 C. Roberts, R.L. Johnston, N.T. Wilson, Theor. Chem. Acc 104, 123 (2000).
51 L. Zhan, B. Piwowar, W.K. Liu, P.J. Hsu, S.K. Lai and Jeff Z.Y. Chen, J. Chem. Phys. 120,
5536 (2004).
52 S.K. Lai, P.J. Hsu, K.L. Wu, W.K. Liu and M. Iwamatsu, J. Chem. Phys. 117,10715 (2002).