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  • Gupta Clusters

      The Gupta family of potentials can be used to model a variety of metals.

      Global optimization has been performed on the following Gupta clusters

      Points files for each minimum are accessible from the Tables.

      The work described on the above pages can be found in the following papers:

      • J.P.K. Doye, Phys. Rev. B 68, 195418 (2003)

      • Identifying structural patterns in `disordered' metal clusters         J.P.K. Doye, Comp. Mater. Sci. 35, 227-231 (2006).
        Lead clusters: different potentials, different structures
      • E.G. Noya, J.P.K. Doye, D.J. Wales and A. Aguado, Eur. Phys. J. D, accepted
        Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

      If you can improve on any of the results given in these pages email us, and I will update the database.

      Zinc Clusters: Table of Global Minima

      Global minima for clusters interacting with zinc Gupta potential up to N=125. For each minimum the energy and point group are given.

      Click on a label to access the points file for the structure in Cartesian coordinates.

      Alternatively, click here to access a tar file containing all the points.

      N PG Energy   N PG Energy   N PG Energy
      3 D3h -3.751296   34 C3 -45.125218   65 C1 -86.749702   96 C2v -128.501419
      4 Td -5.099346   35 Cs -46.472931   66 C1 -88.097872   97 Cs -129.836679
      5 D3h -6.422287   36 D2h -47.814946   67 C1 -89.426800   98 C2v -131.170669
      6 Oh -7.765873   37 C1 -49.144718   68 C1 -90.782264   99 Cs -132.525475
      7 D5h -9.088519   38 Cs -50.499983   69 C1 -92.135925   100 C2v -133.883827
      8 D2d -10.409083   39 C2v -51.846864   70 C1 -93.473840   101 Cs -135.219057
      9 C2v -11.733002   40 Cs -53.182148   71 Cs -94.828826   102 C1 -136.566429
      10 C3v -13.055156   41 Cs -54.521834   72 Cs -96.168254   103 C1 -137.902829
      11 C2 -14.379679   42 D4 -55.874358   73 Cs -97.513085   104 C1 -139.255744
      12 C2 -15.706971   43 C4 -57.213737   74 Cs -98.853247   105 C1 -140.593303
      13 Cs -17.032142   44 Cs -58.554345   75 C2v -100.203580   106 C1 -141.928489
      14 C6v -18.369312   45 C2v -59.895318   76 C1 -101.545341   107 C1 -143.279843
      15 Cs -19.697479   46 Cs -61.227348   77 Cs -102.900278   108 C1 -144.635048
      16 Cs -21.042019   47 Cs -62.580198   78 C1 -104.238674   109 C1 -145.978993
      17 C2v -22.395676   48 Cs -63.916581   79 C2v -105.595357   110 C1 -147.337545
      18 C4v -23.735972   49 C2v -65.269233   80 C2v -106.927940   111 C2 -148.697585
      19 D4d -25.067563   50 Cs -66.601903   81 Cs -108.284296   112 C1 -150.033337
      20 C2v -26.395373   51 C1 -67.938575   82 Cs -109.625208   113 C1 -151.385243
      21 Cs -27.715028   52 C2v -69.281361   83 Cs -110.976689   114 C1 -152.720206
      22 C2v -29.042499   53 C1 -70.622509   84 Cs -112.322650   115 C2 -154.071651
      23 C1 -30.386460   54 C1 -71.969642   85 C1 -113.668080   116 C1 -155.420956
      24 C2 -31.728122   55 C1 -73.310032   86 C2v -115.021815   117 C1 -156.762711
      25 C2 -33.075590   56 C1 -74.649595   87 C2v -116.375101   118 C1 -158.109816
      26 C2 -34.412179   57 C1 -75.992628   88 C2v -117.726908   119 C1 -159.451202
      27 C2 -35.744950   58 C1 -77.336947   89 Cs -119.057698   120 C2v -160.812498
      28 D6d -37.076416   59 C1 -78.672227   90 Cs -120.405576   121 C1 -162.152965
      29 C2 -38.410947   60 C1 -80.019432   91 C2v -121.767147   122 C1 -163.502185
      30 C1 -39.768212   61 C2 -81.363067   92 C2v -123.118340   123 C2v -164.859277
      31 C1 -41.107234   62 C1 -82.708058   93 Cs -124.451825   124 C1 -166.196591
      32 C1 -42.444864   63 C1 -84.061400   94 Cs -125.796431   125 C1 -167.548063
      33 C1 -43.776617   64 C2 -85.419385   95 Cs -127.142167
       

      Cadmium Clusters: Table of Global Minima

      Global minima for clusters interacting with cadmium Gupta potential up to N=125. For each minimum the energy and point group are given.

      Click on a label to access the points file for the structure in Cartesian coordinates.

      Alternatively, click here to access a tar file containing all the points.

       
      N PG Energy   N PG Energy   N PG Energy
      3 D3h -3.391649   34 C1 -39.318659   65 C1 -75.330653   96 Cs -111.382493
      4 Td -4.556244   35 C1 -40.483344   66 C1 -76.493660   97 Cs -112.543725
      5 D3h -5.710992   36 D2h -41.646892   67 C1 -77.650700   98 Cs -113.703547
      6 Oh -6.873544   37 Cs -42.803277   68 C1 -78.815370   99 Cs -114.863226
      7 D5h -8.028455   38 D2d -43.967614   69 C1 -79.982620   100 Cs -116.029828
      8 D2d -9.182587   39 C2v -45.132103   70 C1 -81.143066   101 Cs -117.191782
      9 C2v -10.337961   40 Cs -46.291870   71 C1 -82.302019   102 C1 -118.354639
      10 D4d -11.492834   41 C2v -47.451405   72 C1 -83.462242   103 C1 -119.516811
      11 C2 -12.648250   42 D4 -48.613389   73 Cs -84.623790   104 C1 -120.682922
      12 C2 -13.804680   43 C4 -49.774701   74 Cs -85.787478   105 C1 -121.841138
      13 Cs -14.960307   44 Cs -50.937992   75 C1 -86.948788   106 C1 -123.000416
      14 D6d -16.116921   45 C2v -52.100346   76 C1 -88.112746   107 C1 -124.164675
      15 D3 -17.276238   46 Cs -53.258607   77 Cs -89.279311   108 C1 -125.323742
      16 Cs -18.434583   47 Cs -54.421794   78 C1 -90.441924   109 C1 -126.488046
      17 C2v -19.600675   48 Cs -55.581917   79 C2v -91.609644   110 C1 -127.654226
      18 C2v -20.764865   49 C2v -56.746239   80 Cs -92.767096   111 C2 -128.824065
      19 C2v -21.923540   50 Cs -57.905181   81 Cs -93.931045   112 C1 -129.985671
      20 C2v -23.080283   51 C1 -59.063265   82 C1 -95.092765   113 C1 -131.150549
      21 C1 -24.234793   52 C1 -60.223182   83 Cs -96.259818   114 C1 -132.311215
      22 C1 -25.390380   53 C1 -61.383718   84 C1 -97.415006   115 C2 -133.475490
      23 C1 -26.552108   54 C1 -62.547483   85 C1 -98.582433   116 C1 -134.637941
      24 C1 -27.710728   55 Cs -63.711040   86 C1 -99.742283   117 C1 -135.800525
      25 C2 -28.875894   56 C2 -64.871474   87 C2v -100.912912   118 C1 -136.963187
      26 C2 -30.036716   57 C1 -66.031560   88 C2v -102.077956   119 C1 -138.125231
      27 C1 -31.194825   58 C1 -67.193590   89 Cs -103.236780   120 C1 -139.285228
      28 C2 -32.354453   59 C1 -68.352805   90 C1 -104.397182   121 C2 -140.450672
      29 C1 -33.511796   60 C1 -69.515486   91 C2v -105.565322   122 C1 -141.614397
      30 C2 -34.677431   61 C2 -70.678373   92 C2v -106.733237   123 C2v -142.780180
      31 C1 -35.838691   62 C2 -71.838429   93 Cs -107.892659   124 C1 -143.938617
      32 C1 -36.999668   63 C1 -73.002649   94 Cs -109.048698   125 C1 -145.100610
      33 C1 -38.157466   64 C2 -74.172601   95 Cs -110.214298
       

      Lead Clusters: Table of Global Minima

      Global minima for clusters interacting with a zinc Gupta potential up to N=150. For each minimum the energy and point group are given.

      Click on a label to access the points file for the structure in Cartesian coordinates.

      Alternatively, click here to access a tar file containing all the points.

      N PG Energy   N PG Energy   N PG Energy
      3 D3h -4.231623   40 D2 -73.262766   77 C2v -144.258747   114 Cs -215.807472
      4 Td -6.099714   41 C1 -75.112816   78 Cs -146.128629   115 Cs -217.749269
      5 D3h -7.886887   42 Cs -77.023173   79 Oh -148.146432   116 C3v -219.694133
      6 Oh -9.755691   43 C2v -78.931871   80 C4v -150.013008   117 Cs -221.691036
      7 D5h -11.556399   44 C2 -80.861958   81 C2v -151.930037   118 Cs -223.559459
      8 D2d -13.327553   45 C1 -82.746570   82 C2v -153.841784   119 Cs -225.523689
      9 C2v -15.144569   46 C3 -84.666164   83 C2v -155.720227   120 Cs -227.470026
      10 C3v -16.964625   47 C1 -86.561578   84 Cs -157.668905   121 C2v -229.493351
      11 C2v -18.763846   48 C1 -88.486884   85 Cs -159.543391   122 C2v -231.398205
      12 C5v -20.578513   49 C1 -90.376393   86 C3v -161.564185   123 C2v -233.325446
      13 Ih -22.582269   50 D3h -92.296124   87 Cs -163.431365   124 C2v -235.254926
      14 C6v -24.314590   51 Cs -94.162526   88 Cs -165.391034   125 C3v -237.188016
      15 D6d -26.251716   52 C2v -96.110032   89 Cs -167.258681   126 Cs -239.203573
      16 C2v -28.118745   53 C3v -98.050794   90 Cs -169.211406   127 Cs -241.071732
      17 C2v -29.970808   54 Ih -100.007540   91 C2v -171.177663   128 Cs -243.041253
      18 Cs -31.807535   55 Ih -101.835280   92 Cs -173.043249   129 Cs -244.983046
      19 Cs -33.630069   56 D2h -103.745751   93 C1 -174.999552   130 C2v -247.006258
      20 Cs -35.455114   57 C2v -105.662759   94 Cs -176.951443   131 C2v -248.910730
      21 C6v -37.331154   58 C1 -107.560437   95 C2v -178.892736   132 Cs -250.839600
      22 Cs -39.259153   59 C2v -109.458501   96 Cs -180.777213   133 Cs -252.753620
      23 C2 -41.158169   60 C2v -111.406643   97 Cs -182.761992   134 C1 -254.691944
      24 Cs -43.011299   61 C3v -113.381653   98 Cs -184.740639   135 Cs -256.715113
      25 C1 -44.836233   62 Cs -115.247146   99 Cs -186.654481   136 C4v -258.635983
      26 Cs -46.711166   63 Cs -117.178015   100 C5v -188.605832   137 Cs -260.551431
      27 Cs -48.618276   64 C2v -119.187860   101 D5h -190.629737   138 Cs -262.495627
      28 C1 -50.525086   65 C2v -121.058816   102 D2h -192.543687   139 C2v -264.518644
      29 C2 -52.420240   66 Cs -122.990751   103 C2v -194.458602   140 Oh -266.440716
      30 C3v -54.337045   67 C2v -124.922594   104 C2v -196.367268   141 C2v -268.353333
      31 C3 -56.148062   68 C3v -126.812603   105 C2v -198.306531   142 Cs -270.260176
      32 D2d -58.061383   69 C1 -128.726858   106 Cs -200.237783   143 C3v -272.223375
      33 C1 -59.923961   70 Cs -130.690514   107 Cs -202.155252   144 Cs -274.213617
      34 C2 -61.841131   71 C2v -132.710251   108 Cs -204.178302   145 C5v -276.170441
      35 C2v -63.721030   72 Cs -134.580108   109 Cs -206.044130   146 D5h -278.193661
      36 C2 -65.627949   73 Cs -136.507283   110 Cs -208.009245   147 Cs -280.051292
      37 C2v -67.555415   74 C5v -138.466765   111 Cs -209.955620   148 C2v -282.029242
      38 Oh -69.488671   75 D5h -140.489863   112 C2v -211.979029   149 Cs -283.886484
      39 C4v -71.356501   76 C2v -142.358601   113 C2v -213.884008   150 C2v -285.864042
       

      Na Gupta Clusters: Table of Global Minima

      Global minima for clusters interacting with the Gupta Na potential up to N=379. For each minimum the energy and point group are given.

      Click on a label to access the points file for the structure in Cartesian coordinates.

      Alternatively, click here to access a tar file containing all the points.

      N PG Energy   N PG Energy   N PG Energy   N PG Energy   N PG Energy
      3 D3h -1.159644   79 C2v -69.712379   155 C1 -145.169142   231 Cs -222.477833   307 C2v -301.214554
      4 Td -1.838004   80 Cs -70.694899   156 Cs -146.160292   232 Cs -223.483769   308 C5v -302.213363
      5 D3h -2.512913   81 C2v -71.677502   157 C2v -147.159075   233 C1 -224.535592   309 Ih -303.212162
      6 Oh -3.268232   82 Cs -72.646022   158 C1 -148.135423   234 Cs -225.590256   310 Cs -304.210948
      7 D5h -3.980488   83 D3 -73.592774   159 C1 -149.134524   235 Cs -226.590223   311 C2v -305.298037
      8 D2d -4.718604   84 C1 -74.559063   160 Cs -150.157598   236 C5v -227.630112   312 Cs -306.305810
      9 D3h -5.469023   85 C3v -75.547480   161 Cs -151.166347   237 C5v -228.628637   313 Cs -307.315332
      10 C3v -6.250815   86 C3 -76.531024   162 Cs -152.189864   238 C1 -229.676198   314 Cs -308.323779
      11 C2v -7.047212   87 Cs -77.504794   163 Cs -153.207737   239 Cs -230.743517   315 C2v -309.331381
      12 C5v -7.931467   88 C3v -78.483387   164 Cs -154.256060   240 C1 -231.783043   316 Cs -310.330741
      13 Ih -8.888411   89 C3v -79.461398   165 Cs -155.311681   241 C5v -232.875884   317 C1 -311.349409
      14 C3v -9.603668   90 C1 -80.445707   166 C5v -156.396694   242 C5v -233.875906   318 C1 -312.384761
      15 D6d -10.438991   91 C1 -81.440750   167 Cs -157.396349   243 Cs -234.902291   319 C1 -313.418936
      16 D3h -11.236269   92 T -82.437176   168 Cs -158.395992   244 Cs -235.901904   320 Cs -314.506202
      17 Td -12.050330   93 C1 -83.350670   169 Cs -159.395572   245 Cs -236.928476   321 C1 -315.514278
      18 C5v -12.917979   94 C1 -84.334980   170 Cs -160.395078   246 C5 -237.968093   322 Cs -316.528853
      19 D5h -13.863720   95 C3 -85.320620   171 C5v -161.394563   247 C5 -238.967424   323 C1 -317.536891
      20 C2v -14.686968   96 Cs -86.277663   172 C5v -162.393691   248 C5 -239.966482   324 C1 -318.545487
      21 C2v -15.508373   97 C2v -87.271991   173 C5v -163.392487   249 Cs -240.979187   325 C1 -319.554139
      22 Cs -16.388969   98 Cs -88.265920   174 C1 -164.360255   250 C1 -241.979142   326 Cs -320.591492
      23 D3h -17.344617   99 C2v -89.260166   175 Cs -165.351025   251 C1 -242.994183   327 C1 -321.622151
      24 Cs -18.168084   100 C1 -90.231508   176 C1 -166.350654   252 C3v -244.053410   328 C5v -322.708863
      25 C1 -19.051823   101 D3 -91.225567   177 Cs -167.350203   253 C1 -245.097869   329 Cs -323.735327
      26 Td -20.014727   102 Cs -92.170941   178 C1 -168.349327   254 C1 -246.126891   330 Cs -324.787324
      27 Cs -20.838122   103 C2v -93.155010   179 C1 -169.348307   255 Cs -247.184381   331 C1 -325.824411
      28 T -21.739771   104 D5 -94.156307   180 C1 -170.367811   256 Cs -248.206214   332 Cs -326.865471
      29 D3h -22.673854   105 C5 -95.155821   181 C2v -171.403037   257 C1 -249.263987   333 C1 -327.902825
      30 C2v -23.500157   106 D5 -96.155315   182 Cs -172.404983   258 Cs -250.321648   334 Cs -328.940187
      31 C1 -24.381282   107 C1 -97.151882   183 C1 -173.408969   259 C1 -251.342470   335 C1 -329.982985
      32 C2v -25.333450   108 C1 -98.148768   184 C1 -174.459475   260 C1 -252.401363   336 Cs -331.029448
      33 D3 -26.216596   109 C1 -99.146087   185 C1 -175.511656   261 C5v -253.495588   337 C1 -332.066615
      34 T -27.177692   110 C5 -100.144949   186 C2v -176.596719   262 C5v -254.605314   338 Cs -333.103679
      35 D3 -28.066153   111 C5 -101.144686   187 Cs -177.596524   263 Cs -255.628665   339 Cs -334.168348
      36 C2 -28.936290   112 C1 -102.135683   188 Cs -178.622993   264 Cs -256.708139   340 Cs -335.204506
      37 C3 -29.867486   113 C1 -103.127844   189 Cs -179.622808   265 Cs -257.793258   341 C1 -336.225049
      38 Th -30.813621   114 C1 -104.154049   190 C2v -180.648732   266 C1 -258.882308   342 C1 -337.278360
      39 C5 -31.732577   115 Ih -105.278713   191 Cs -181.648203   267 Ih -260.023721   343 C1 -338.336090
      40 Cs -32.612732   116 C5v -106.241158   192 C2v -182.647633   268 C5v -260.993126   344 Cs -339.423885
      41 C1 -33.536249   117 C2v -107.202779   193 Cs -183.646713   269 C2v -261.969150   345 Cs -340.442241
      42 D2 -34.452186   118 C3v -108.163440   194 C2v -184.645759   270 Cs -262.958822   346 C1 -341.488716
      43 C2 -35.374925   119 C2 -109.127146   195 Cs -185.644477   271 C2v -263.945734   347 Cs -342.556830
      44 C2v -36.292037   120 C1 -110.097895   196 C1 -186.660172   272 Cs -264.916503   348 C5v -343.645747
      45 C1 -37.204670   121 C2 -111.065958   197 Cs -187.689574   273 C2 -265.911936   349 Cs -344.645283
      46 C2v -38.179412   122 C1 -112.031554   198 Cs -188.707167   274 C1 -266.895916   350 Cs -345.644816
      47 C1 -39.094801   123 C2v -113.036508   199 C1 -189.757184   275 Cs -267.896955   351 Cs -346.650848
      48 Cs -40.061827   124 Cs -114.036009   200 Cs -190.808643   276 C3v -268.951598   352 C1 -347.682270
      49 C5v -41.053345   125 C2v -115.035361   201 C3v -191.893935   277 Cs -269.978850   353 Cs -348.717613
      50 Cs -42.042000   126 Cs -116.034602   202 Cs -192.893580   278 Cs -271.004379   354 Cs -349.749960
      51 C2v -43.033200   127 C1 -117.069215   203 Cs -193.920265   279 Cs -272.047936   355 Cs -350.838259
      52 C3v -44.024237   128 C3v -118.119727   204 C1 -194.919913   280 C1 -273.052237   356 Cs -351.846583
      53 C2v -45.015142   129 Cs -119.119204   205 Cs -195.946284   281 C1 -274.105529   357 C1 -352.861879
      54 C5v -46.008593   130 C5v -120.136159   206 Cs -196.945939   282 Cs -275.160064   358 C1 -353.870347
      55 Ih -47.004771   131 Cs -121.157626   207 C3v -197.971967   283 C1 -276.163362   359 C1 -354.869904
      56 C3v -47.842109   132 Cs -122.222701   208 Cs -198.971078   284 C1 -277.216009   360 C1 -355.872252
      57 C2v -48.724602   133 Cs -123.289634   209 Cs -199.970078   285 C3v -278.271572   361 Cs -356.940569
      58 C2 -49.599248   134 C1 -124.367897   210 C3v -200.968991   286 C2v -279.374444   362 Cs -358.029282
      59 C2v -50.552826   135 Ih -125.506010   211 Cs -201.967658   287 C2v -280.441986   363 C1 -359.037397
      60 Cs -51.544278   136 C5v -126.505380   212 C1 -202.984958   288 Cs -281.466409   364 C1 -360.070924
      61 Td -52.535993   137 D5d -127.504743   213 C2v -204.007998   289 C1 -282.536643   365 C1 -361.107626
      62 C2 -53.409482   138 C3v -128.504089   214 Cs -205.055430   290 C1 -283.608206   366 Cs -362.155166
      63 C1 -54.341339   139 C2v -129.503330   215 Cs -206.103880   291 C1 -284.693241   367 C1 -363.192039
      64 C1 -55.240001   140 Cs -130.502458   216 C2v -207.188824   292 C5v -285.830935   368 C1 -364.233187
      65 C2 -56.178877   141 C2 -131.501553   217 C1 -208.188642   293 C1 -286.854852   369 C2v -365.292560
      66 C2v -57.123389   142 Cs -132.500563   218 C1 -209.215265   294 C1 -287.925582   370 C1 -366.329379
      67 C1 -58.099835   143 C2v -133.499539   219 C1 -210.215082   295 C1 -288.997437   371 Cs -367.366212
      68 C1 -59.090688   144 C3v -134.498465   220 C2 -211.241598   296 C1 -290.082339   372 C1 -368.402982
      69 C5 -60.082573   145 D5d -135.497331   221 C1 -212.240959   297 Ih -291.223679   373 C3v -369.447482
      70 C5 -61.078013   146 C5v -136.496139   222 C1 -213.267139   298 C5v -292.222960   374 Cs -370.497622
      71 C5 -62.072403   147 Ih -137.494938   223 C1 -214.266485   299 D5d -293.222239   375 Cs -371.547688
      72 C2 -62.977542   148 Cs -138.362605   224 C2v -215.292531   300 C3v -294.221507   376 C3v -372.597681
      73 C1 -63.918515   149 Cs -139.307875   225 Cs -216.291524   301 C1 -295.220687   377 C1 -373.635352
      74 C2h -64.889830   150 C3v -140.293953   226 Cs -217.297423   302 Cs -296.219777   378 C1 -374.685345
      75 C1 -65.797202   151 Cs -141.229288   227 C1 -218.316685   303 C1 -297.218855   379 C1 -375.721583
      76 C1 -66.747888   152 C2v -142.205517   228 Cs -219.328040   304 Cs -298.217849
      77 C1 -67.730007   153 Cs -143.204435   229 Cs -220.375849   305 C2v -299.216831
      78 Cs -68.716377   154 C2v -144.203256   230 C1 -221.393072   306 C3v -300.215735

       
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