Fitting a pair potential with a user defined function

This example demonstrates the (ab)use of the embedded atom method (EAM) potential. A pair potential of the generalized Morse form is fitted to the lattice constant, bulk modulus, and cohesive energy of copper in the face-centered cubic (FCC) crystal structure. The example also illustrates the use of XML Inclusions. Note that the final potential is not particularly good, which is unsurprising given the fact that a pair potential form is being used with a limited number of parameters.

Location

examples/fitting_pair_potential

Input files

  • main.xml: main input file

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
    <?xml version="1.0" encoding="iso-8859-1"?>
<job>

  <name>Fitting an EAM potential for copper</name>
  
  <verbosity>medium</verbosity>
  
  <fitting>
    <BFGS conv-threshold="1e-5" max-iter="200" />
  </fitting>
  
  <atom-types>
    <species>Cu</species>
  </atom-types>
  
  <potentials>
    <xi:include href="potential.xml"
		xmlns:xi="http://www.w3.org/2003/XInclude" />
  </potentials>
  
  <structures>
    <xi:include href="structures.xml"
		xmlns:xi="http://www.w3.org/2003/XInclude" />
  </structures>

</job>

  • potential.xml: initial parameter set (included in main input file via XML Inclusions)

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
    <eam id='Cu pair potential' species-a='*' species-b='*'>

  <export-functions>Cu_potential</export-functions>

  <mapping>
    <pair-interaction species-a='*' species-b='*' function='V' />
  </mapping>

  <functions>

    <user-function id='V'>
      <input-var>r</input-var>
      <expression>
	D0 / (S-1) * exp(-beta * sqrt(2.0 * S) * (r-r0) )
	- S * D0 / (S-1) * exp(-beta * sqrt(2.0 / S) * (r-r0) )
      </expression>
      <derivative>
	- beta * ( sqrt(2 * S) * D0 / (S - 1)
	* exp(-beta * sqrt(2 * S) * (r - r0) )
        - sqrt(2 / S) * S * D0 / (S - 1)
	* exp(- beta * sqrt(2/S) * (r - r0) ) )
      </derivative>
      <param name='D0'>0.2</param>
      <param name='beta'>1.5</param>
      <param name='r0'>2.63</param>
      <param name='S'>1.84</param>
      <fit-dof>
	<D0/>
	<r0/>
	<beta/>
      </fit-dof>
      <screening>
	<user-function id='cutoff function'>
	  <cutoff>5.5</cutoff>
	  <input-var>r</input-var>
	  <expression>
	    1 - 1/(1 + ((r - cutoff) / h)^4)
	  </expression>
	  <derivative>
	    4 * h^4 * (r - cutoff)^3 / ((h^4 + (r - cutoff)^4)^2)
	  </derivative>
	  <param name='h'>0.5</param>
	</user-function>
      </screening>
    </user-function>

  </functions>

</eam>

  • structures.xml: input structures (included in main input file via XML Inclusions)

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
    <group>

  <fcc-lattice id="FCC">
    <atom-type>Cu</atom-type>
    <lattice-parameter>3.615</lattice-parameter>
    <properties>
      <lattice-parameter fit='true' target='3.615' relative-weight='4'/>
      <atomic-energy fit='true' target='-3.540' relative-weight='4'/>
      <bulk-modulus fit='true' target='138'/>
      <C11 target='170.0'/>
      <C12 target='122.5'/>
      <C44 target= '75.8'/>
    </properties>
  </fcc-lattice>

</group>

Output (files)

  • Cu_potential.V.table: pair potential suitable for plotting

      1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
    # 1st col: index
# 2nd col: x
# 3rd col: y
# 4th col: derivative

 0 0.2 351.883 -1010.26
 1 0.2265 326.086 -937.589
 2 0.253 302.146 -870.092
 3 0.2795 279.929 -807.407
 4 0.306 259.314 -749.191
 5 0.3325 240.185 -695.129
 6 0.359 222.438 -644.924
 7 0.3855 205.972 -598.304
 8 0.412 190.698 -555.014
 9 0.4385 176.529 -514.818
 10 0.465 163.387 -477.496
 11 0.4915 151.199 -442.844
 12 0.518 139.895 -410.673
 13 0.5445 129.413 -380.805
 14 0.571 119.693 -353.078
 15 0.5975 110.682 -327.339
 16 0.624 102.328 -303.447
 17 0.6505 94.584 -281.27
 18 0.677 87.4065 -260.687
 19 0.7035 80.7545 -241.583
 20 0.73 74.5904 -223.854
 21 0.7565 68.879 -207.401
 22 0.783 63.5877 -192.134
 23 0.8095 58.6862 -177.968
 24 0.836 54.1463 -164.824
 25 0.8625 49.9421 -152.63
 26 0.889 46.0492 -141.317
 27 0.9155 42.445 -130.823
 28 0.942 39.1088 -121.09
 29 0.9685 36.0211 -112.062
 30 0.995 33.1638 -103.689
 31 1.0215 30.5202 -95.9247
 32 1.048 28.0748 -88.7252
 33 1.0745 25.8131 -82.0501
 34 1.101 23.7218 -75.8617
 35 1.1275 21.7884 -70.1251
 36 1.154 20.0015 -64.8079
 37 1.1805 18.3502 -59.8799
 38 1.207 16.8247 -55.3131
 39 1.2335 15.4156 -51.0816
 40 1.26 14.1146 -47.1612
 41 1.2865 12.9135 -43.5294
 42 1.313 11.8052 -40.1656
 43 1.3395 10.7826 -37.0502
 44 1.366 9.83946 -34.1654
 45 1.3925 8.96992 -31.4946
 46 1.419 8.16849 -29.0221
 47 1.4455 7.43012 -26.7337
 48 1.472 6.7501 -24.616
 49 1.4985 6.12408 -22.6565
 50 1.525 5.54801 -20.8439
 51 1.5515 5.01815 -19.1673
 52 1.578 4.53103 -17.617
 53 1.6045 4.08342 -16.1837
 54 1.631 3.67233 -14.8588
 55 1.6575 3.29501 -13.6344
 56 1.684 2.94889 -12.5032
 57 1.7105 2.63158 -11.4583
 58 1.737 2.34089 -10.4934
 59 1.7635 2.07478 -9.60258
 60 1.79 1.83135 -8.78043
 61 1.8165 1.60885 -8.02186
 62 1.843 1.40567 -7.32217
 63 1.8695 1.2203 -6.67701
 64 1.896 1.05134 -6.08232
 65 1.9225 0.897522 -5.53437
 66 1.949 0.757641 -5.02966
 67 1.9755 0.630597 -4.56497
 68 2.002 0.515371 -4.13731
 69 2.0285 0.411018 -3.7439
 70 2.055 0.316664 -3.38217
 71 2.0815 0.231504 -3.04973
 72 2.108 0.15479 -2.74437
 73 2.1345 0.0858312 -2.46405
 74 2.161 0.0239908 -2.20685
 75 2.1875 -0.0313208 -1.97103
 76 2.214 -0.0806481 -1.75495
 77 2.2405 -0.124494 -1.55709
 78 2.267 -0.163322 -1.37605
 79 2.2935 -0.197562 -1.21055
 80 2.32 -0.227608 -1.05937
 81 2.3465 -0.253825 -0.921399
 82 2.373 -0.27655 -0.795614
 83 2.3995 -0.296092 -0.681058
 84 2.426 -0.312737 -0.576848
 85 2.4525 -0.326749 -0.482165
 86 2.479 -0.338369 -0.396255
 87 2.5055 -0.347822 -0.318416
 88 2.532 -0.355311 -0.248003
 89 2.5585 -0.361026 -0.184415
 90 2.585 -0.36514 -0.127101
 91 2.6115 -0.367813 -0.0755472
 92 2.638 -0.369191 -0.0292818
 93 2.6645 -0.369408 0.0121324
 94 2.691 -0.368587 0.0490992
 95 2.7175 -0.366842 0.0819914
 96 2.744 -0.364275 0.111153
 97 2.7705 -0.360981 0.136903
 98 2.797 -0.357046 0.159533
 99 2.8235 -0.352551 0.179315
 100 2.85 -0.347566 0.196497
 101 2.8765 -0.342157 0.211311
 102 2.903 -0.336385 0.223967
 103 2.9295 -0.330304 0.234662
 104 2.956 -0.323964 0.243576
 105 2.9825 -0.317409 0.250873
 106 3.009 -0.31068 0.256706
 107 3.0355 -0.303815 0.261216
 108 3.062 -0.296847 0.26453
 109 3.0885 -0.289805 0.266769
 110 3.115 -0.282716 0.26804
 111 3.1415 -0.275606 0.268443
 112 3.168 -0.268496 0.26807
 113 3.1945 -0.261405 0.267005
 114 3.221 -0.25435 0.265324
 115 3.2475 -0.247347 0.263098
 116 3.274 -0.24041 0.260391
 117 3.3005 -0.23355 0.257263
 118 3.327 -0.226778 0.253766
 119 3.3535 -0.220103 0.249951
 120 3.38 -0.213533 0.245861
 121 3.4065 -0.207075 0.241537
 122 3.433 -0.200734 0.237017
 123 3.4595 -0.194514 0.232334
 124 3.486 -0.188421 0.227518
 125 3.5125 -0.182457 0.222597
 126 3.539 -0.176624 0.217597
 127 3.5655 -0.170925 0.212539
 128 3.592 -0.16536 0.207445
 129 3.6185 -0.15993 0.202332
 130 3.645 -0.154636 0.197217
 131 3.6715 -0.149478 0.192115
 132 3.698 -0.144454 0.187038
 133 3.7245 -0.139564 0.182
 134 3.751 -0.134808 0.17701
 135 3.7775 -0.130182 0.172077
 136 3.804 -0.125687 0.167209
 137 3.8305 -0.12132 0.162415
 138 3.857 -0.117078 0.1577
 139 3.8835 -0.112961 0.15307
 140 3.91 -0.108965 0.148529
 141 3.9365 -0.105088 0.144083
 142 3.963 -0.101327 0.139734
 143 3.9895 -0.097681 0.135485
 144 4.016 -0.0941458 0.13134
 145 4.0425 -0.0907191 0.1273
 146 4.069 -0.087398 0.123368
 147 4.0955 -0.0841796 0.119545
 148 4.122 -0.0810611 0.115833
 149 4.1485 -0.0780395 0.112234
 150 4.175 -0.0751117 0.108748
 151 4.2015 -0.0722748 0.105376
 152 4.228 -0.0695258 0.102121
 153 4.2545 -0.0668614 0.0989824
 154 4.281 -0.0642786 0.0959629
 155 4.3075 -0.0617743 0.0930638
 156 4.334 -0.0593452 0.0902867
 157 4.3605 -0.056988 0.087634
 158 4.387 -0.0546995 0.0851082
 159 4.4135 -0.0524761 0.0827123
 160 4.44 -0.0503145 0.0804497
 161 4.4665 -0.0482111 0.0783247
 162 4.493 -0.0461621 0.0763419
 163 4.5195 -0.0441636 0.0745067
 164 4.546 -0.0422118 0.0728251
 165 4.5725 -0.0403025 0.071304
 166 4.599 -0.0384313 0.0699504
 167 4.6255 -0.0365936 0.0687717
 168 4.652 -0.0347847 0.0677754
 169 4.6785 -0.0329998 0.0669678
 170 4.705 -0.0312337 0.0663537
 171 4.7315 -0.0294814 0.0659344
 172 4.758 -0.0277375 0.0657062
 173 4.7845 -0.0259973 0.0656571
 174 4.811 -0.0242563 0.0657639
 175 4.8375 -0.0225108 0.0659872
 176 4.864 -0.0207585 0.0662667
 177 4.8905 -0.0189989 0.0665164
 178 4.917 -0.0172344 0.0666205
 179 4.9435 -0.0154706 0.0664326
 180 4.97 -0.0137176 0.0657803
 181 4.9965 -0.01199 0.0644776
 182 5.023 -0.0103076 0.0623473
 183 5.0495 -0.00869415 0.0592528
 184 5.076 -0.00717626 0.055134
 185 5.1025 -0.00578071 0.0500387
 186 5.129 -0.00453137 0.0441373
 187 5.1555 -0.00344608 0.0377116
 188 5.182 -0.00253416 0.031116
 189 5.2085 -0.00179515 0.0247206
 190 5.235 -0.00121929 0.0188515
 191 5.2615 -0.000789239 0.0137466
 192 5.288 -0.000482796 0.00953506
 193 5.3145 -0.000275746 0.0062417
 194 5.341 -0.000144375 0.00380814
 195 5.3675 -6.73101e-05 0.00212131
 196 5.394 -2.65902e-05 0.00104062
 197 5.4205 -8.10173e-06 0.000419336
 198 5.447 -1.53971e-06 0.000118464
 199 5.4735 -9.2548e-08 1.41062e-05
 200 5.5 -0 0

  • The final properties (as well as parameters) are written to standard output.

      1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
    This is program version 0.1.6
Reading job file main.xml
-------------------------------------------------------
Parsing input file(s)
-------------------------------------------------------
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.2
   elemental EAM potential[EAM].V[user-function].beta: 1.5
   elemental EAM potential[EAM].V[user-function].r0: 2.63
-------------------------------------------------------
-------------------------------------------------------
Number of properties being fitted: 3
-------------------------------------------------------
  iter= 1 residual= 14077.2 grad= 142826
  iter= 2 residual= 467034 grad= 2.33932e+06
  iter= 3 residual= 1463.38 grad= 27202.1
  iter= 4 residual= 1463.38 grad= 27202.1
  iter= 5 residual= 914.83 grad= 11131.5
  iter= 6 residual= 914.83 grad= 11131.5
  iter= 7 residual= 695.498 grad= 12252
  iter= 8 residual= 96.1781 grad= 9763.98
  iter= 9 residual= 96.1781 grad= 9763.98
  iter= 10 residual= 16.3463 grad= 3264.58
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.421798
   elemental EAM potential[EAM].V[user-function].beta: 1.5293
   elemental EAM potential[EAM].V[user-function].r0: 2.76538
-------------------------------------------------------
  iter= 11 residual= 16.3463 grad= 3264.58
  iter= 12 residual= 17.2543 grad= 3555.34
  iter= 13 residual= 7.98951 grad= 1445.09
  iter= 14 residual= 7.98951 grad= 1445.09
  iter= 15 residual= 8.90514 grad= 2132.15
  iter= 16 residual= 7.56993 grad= 1323.44
  iter= 17 residual= 7.56993 grad= 1323.44
  iter= 18 residual= 10.5635 grad= 2330.62
  iter= 19 residual= 6.97667 grad= 898.806
  iter= 20 residual= 6.97667 grad= 898.806
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.424874
   elemental EAM potential[EAM].V[user-function].beta: 1.52458
   elemental EAM potential[EAM].V[user-function].r0: 2.76091
-------------------------------------------------------
  iter= 21 residual= 7.0202 grad= 537.2
  iter= 22 residual= 6.97784 grad= 1497.81
  iter= 23 residual= 6.97561 grad= 987.668
  iter= 24 residual= 6.97797 grad= 1786.67
  iter= 25 residual= 6.97688 grad= 373.522
  iter= 26 residual= 6.97569 grad= 1531.91
  iter= 27 residual= 6.97569 grad= 1531.91
  iter= 28 residual= 114.257 grad= 10793.4
  iter= 29 residual= 7.12217 grad= 1337.44
  iter= 30 residual= 6.97273 grad= 538.562
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.424779
   elemental EAM potential[EAM].V[user-function].beta: 1.52381
   elemental EAM potential[EAM].V[user-function].r0: 2.76096
-------------------------------------------------------
  iter= 31 residual= 6.97273 grad= 538.562
  iter= 32 residual= 6.81371 grad= 264.436
  iter= 33 residual= 6.81371 grad= 264.436
  iter= 34 residual= 6.79466 grad= 601.69
  iter= 35 residual= 6.79466 grad= 601.69
  iter= 36 residual= 7.8179 grad= 875.562
  iter= 37 residual= 6.80111 grad= 473.237
  iter= 38 residual= 6.7948 grad= 901.646
  iter= 39 residual= 6.79405 grad= 400.6
  iter= 40 residual= 6.7953 grad= 711.802
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.424077
   elemental EAM potential[EAM].V[user-function].beta: 1.52379
   elemental EAM potential[EAM].V[user-function].r0: 2.76089
-------------------------------------------------------
  iter= 41 residual= 6.79581 grad= 592.135
  iter= 42 residual= 6.79527 grad= 842.651
  iter= 43 residual= 6.79412 grad= 994.064
  iter= 44 residual= 6.79412 grad= 994.064
  iter= 45 residual= 6.7906 grad= 913.106
  iter= 46 residual= 6.7906 grad= 913.106
  iter= 47 residual= 6.76243 grad= 542.524
  iter= 48 residual= 6.76243 grad= 542.524
  iter= 49 residual= 6.82223 grad= 752.146
  iter= 50 residual= 6.76024 grad= 1402.08
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.42355
   elemental EAM potential[EAM].V[user-function].beta: 1.52278
   elemental EAM potential[EAM].V[user-function].r0: 2.76094
-------------------------------------------------------
  iter= 51 residual= 6.76223 grad= 1325.41
  iter= 52 residual= 6.76061 grad= 704.579
  iter= 53 residual= 6.76038 grad= 1078.16
  iter= 54 residual= 6.75934 grad= 930.737
  iter= 55 residual= 6.75934 grad= 930.737
  iter= 56 residual= 6.96147 grad= 1045.85
  iter= 57 residual= 6.7702 grad= 792.081
  iter= 58 residual= 6.76002 grad= 1230.7
  iter= 59 residual= 6.76052 grad= 1135.03
  iter= 60 residual= 6.76138 grad= 1151.42
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.423544
   elemental EAM potential[EAM].V[user-function].beta: 1.52277
   elemental EAM potential[EAM].V[user-function].r0: 2.76095
-------------------------------------------------------
  iter= 61 residual= 6.76134 grad= 842.388
  iter= 62 residual= 6.76055 grad= 552.923
  iter= 63 residual= 6.75985 grad= 859.367
  iter= 64 residual= 6.75845 grad= 969.45
  iter= 65 residual= 6.76031 grad= 1497
  iter= 66 residual= 6.75959 grad= 1022.64
  iter= 67 residual= 6.75952 grad= 460.327
  iter= 68 residual= 6.75952 grad= 460.327
-------------------------------------------------------
Potential parameters being optimized (#dof=3):
   elemental EAM potential[EAM].V[user-function].D0: 0.42355
   elemental EAM potential[EAM].V[user-function].beta: 1.52278
   elemental EAM potential[EAM].V[user-function].r0: 2.76094
-------------------------------------------------------
Fitting process complete.
-------------------------------------------------------
Computing structure properties
Structure 'FCC':
   total-energy: -3.53491 eV
   atomic-energy: -3.53491 eV/atom (target: -3.54 eV/atom) Abs. weight: 0.444444; Tolerance: 0.01; Weighted residual: 0.115302
   total-volume: 11.8546 A^3
   atomic-volume: 11.8546 A^3/atom
   bulk-modulus: 153.04 GPa (target: 138 GPa) Abs. weight: 0.111111; Tolerance: 2; Weighted residual: 6.28344
   C11: 201.423 GPa
   C12: 128.859 GPa
   C44: 128.857 GPa
   lattice-parameter: 3.6195 A (target: 3.615 A) Abs. weight: 0.444444; Tolerance: 0.005; Weighted residual: 0.360779 (relaxed) [0:]
-------------------------------------------------------
Writing EAM function tables to Cu_potential.*
-------------------------------------------------------

Other files

  • pairpotential_reference.table: the pair potential from the embedded atom method (EAM) potential presented in [MisMehPap01]

      1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
    # pair potential from Mishin's EAM potential (2001)
# 1st col: index
# 2nd col: x
# 3rd col: y
# 4th col: derivative

 0 0.2 8379.04 -50890.7
 1 0.226534 7132.66 -43259.4
 2 0.253068 6073.32 -36763.4
 3 0.279602 5173.15 -31235.8
 4 0.306136 4408.4 -26534.2
 5 0.33267 3758.81 -22536.8
 6 0.359204 3207.12 -19139.7
 7 0.385738 2738.59 -16254.1
 8 0.412272 2340.69 -13804.3
 9 0.438806 2002.75 -11725.5
 10 0.465339 1715.66 -9962.36
 11 0.491873 1471.69 -8467.78
 12 0.518407 1264.27 -7201.46
 13 0.544941 1087.81 -6129.04
 14 0.571475 937.564 -5221.19
 15 0.598009 809.501 -4452.93
 16 0.624543 700.211 -3802.92
 17 0.651077 606.803 -3253.01
 18 0.677611 526.833 -2787.73
 19 0.704145 458.233 -2393.93
 20 0.730679 399.259 -2060.4
 21 0.757213 348.443 -1777.64
 22 0.783747 304.546 -1537.59
 23 0.810281 266.529 -1333.42
 24 0.836815 233.519 -1159.35
 25 0.863349 204.782 -1010.5
 26 0.889883 179.707 -882.781
 27 0.916417 157.779 -772.746
 28 0.942951 138.568 -677.522
 29 0.969485 121.714 -594.718
 30 0.996018 106.915 -522.36
 31 1.02255 93.9159 -458.828
 32 1.04909 82.5 -402.806
 33 1.07562 72.4828 -353.239
 34 1.10215 63.7047 -309.297
 35 1.12869 56.0251 -270.339
 36 1.15522 49.3185 -235.892
 37 1.18176 43.4699 -205.62
 38 1.20829 38.3717 -179.307
 39 1.23482 33.922 -156.659
 40 1.26136 30.0302 -137.166
 41 1.28789 26.619 -120.37
 42 1.31443 23.6221 -105.876
 43 1.34096 20.983 -93.3484
 44 1.36749 18.6535 -82.4975
 45 1.39403 16.5924 -73.0768
 46 1.42056 14.7647 -64.8758
 47 1.4471 13.1404 -57.7145
 48 1.47363 11.694 -51.44
 49 1.50016 10.4039 -45.9222
 50 1.5267 9.25134 -41.0509
 51 1.55323 8.22051 -36.7331
 52 1.57977 7.29779 -32.8903
 53 1.6063 6.47147 -29.4572
 54 1.63283 5.73142 -26.3792
 55 1.65937 5.06884 -23.6115
 56 1.6859 4.476 -21.1174
 57 1.71244 3.94603 -18.8675
 58 1.73897 3.47279 -16.8385
 59 1.7655 3.05065 -15.0126
 60 1.79204 2.67442 -13.3767
 61 1.81857 2.33918 -11.9207
 62 1.8451 2.04038 -10.6273
 63 1.87164 1.77396 -9.47641
 64 1.89817 1.53638 -8.45024
 65 1.92471 1.32455 -7.53348
 66 1.95124 1.13575 -6.71283
 67 1.97777 0.967568 -5.97681
 68 2.00431 0.817908 -5.31549
 69 2.03084 0.684901 -4.72032
 70 2.05738 0.566891 -4.18395
 71 2.08391 0.462404 -3.70008
 72 2.11044 0.370119 -3.26335
 73 2.13698 0.288848 -2.86922
 74 2.16351 0.217513 -2.51385
 75 2.19005 0.155129 -2.19404
 76 2.21658 0.100789 -1.90717
 77 2.24311 0.0536478 -1.65107
 78 2.26965 0.0129159 -1.42364
 79 2.29618 -0.0221292 -1.22194
 80 2.32272 -0.0521329 -1.04321
 81 2.34925 -0.0776711 -0.884964
 82 2.37578 -0.0992577 -0.745002
 83 2.40232 -0.117351 -0.621352
 84 2.42885 -0.13236 -0.512256
 85 2.45539 -0.14465 -0.416144
 86 2.48192 -0.154547 -0.331613
 87 2.50845 -0.16234 -0.257409
 88 2.53499 -0.168288 -0.192413
 89 2.56152 -0.172623 -0.13562
 90 2.58806 -0.17555 -0.0861355
 91 2.61459 -0.177252 -0.0431567
 92 2.64112 -0.177891 -0.00596593
 93 2.66766 -0.177614 0.0260791
 94 2.69419 -0.176548 0.0535531
 95 2.72073 -0.174808 0.0769705
 96 2.74726 -0.172495 0.0967917
 97 2.77379 -0.169699 0.113428
 98 2.80033 -0.1665 0.127249
 99 2.82686 -0.162968 0.138583
 100 2.85339 -0.159165 0.147726
 101 2.87993 -0.155146 0.154939
 102 2.90646 -0.150958 0.16046
 103 2.933 -0.146644 0.164498
 104 2.95953 -0.14224 0.167241
 105 2.98606 -0.137779 0.168855
 106 3.0126 -0.133288 0.169491
 107 3.03913 -0.128791 0.169281
 108 3.06567 -0.124311 0.168343
 109 3.0922 -0.119863 0.166782
 110 3.11873 -0.115465 0.164692
 111 3.14527 -0.111127 0.162156
 112 3.1718 -0.106863 0.159246
 113 3.19834 -0.102679 0.156029
 114 3.22487 -0.0985848 0.15256
 115 3.2514 -0.094585 0.148891
 116 3.27794 -0.0906848 0.145065
 117 3.30447 -0.0868878 0.141123
 118 3.33101 -0.0831965 0.137097
 119 3.35754 -0.0796128 0.133018
 120 3.38407 -0.0761377 0.128912
 121 3.41061 -0.0727717 0.124801
 122 3.43714 -0.0695146 0.120704
 123 3.46368 -0.0663659 0.116638
 124 3.49021 -0.0633245 0.112617
 125 3.51674 -0.0603891 0.108653
 126 3.54328 -0.0575579 0.104756
 127 3.56981 -0.0548292 0.100934
 128 3.59635 -0.0522008 0.0971953
 129 3.62288 -0.0496705 0.0935438
 130 3.64941 -0.0472358 0.0899845
 131 3.67595 -0.0448944 0.0865207
 132 3.70248 -0.0426435 0.0831548
 133 3.72902 -0.0404806 0.0798884
 134 3.75555 -0.0384031 0.0767224
 135 3.78208 -0.0364082 0.0736573
 136 3.80862 -0.0344934 0.0706928
 137 3.83515 -0.0326558 0.0678284
 138 3.86169 -0.030893 0.065063
 139 3.88822 -0.0292022 0.0623954
 140 3.91475 -0.0275809 0.0598239
 141 3.94129 -0.0260266 0.0573468
 142 3.96782 -0.0245369 0.054962
 143 3.99435 -0.0231091 0.0526673
 144 4.02089 -0.0217411 0.0504604
 145 4.04742 -0.0204306 0.0483389
 146 4.07396 -0.0191752 0.0463004
 147 4.10049 -0.0179728 0.0443422
 148 4.12702 -0.0168213 0.0424617
 149 4.15356 -0.0157188 0.0406563
 150 4.18009 -0.0146631 0.0389232
 151 4.20663 -0.0136526 0.0372598
 152 4.23316 -0.0126852 0.0356633
 153 4.25969 -0.0117594 0.0341309
 154 4.28623 -0.0108734 0.0326598
 155 4.31276 -0.0100257 0.0312471
 156 4.3393 -0.00921474 0.0298899
 157 4.36583 -0.00843906 0.0285852
 158 4.39236 -0.00769734 0.0273299
 159 4.4189 -0.00698831 0.0261208
 160 4.44543 -0.00631079 0.0249545
 161 4.47197 -0.00566369 0.0238273
 162 4.4985 -0.00504601 0.0227355
 163 4.52503 -0.00445689 0.0216748
 164 4.55157 -0.00389554 0.0206405
 165 4.5781 -0.00336135 0.0196277
 166 4.60464 -0.0028538 0.0186306
 167 4.63117 -0.00237258 0.0176427
 168 4.6577 -0.00191753 0.0166569
 169 4.68424 -0.00148869 0.015665
 170 4.71077 -0.00108635 0.0146581
 171 4.73731 -0.000711038 0.0136259
 172 4.76384 -0.00036357 0.0125576
 173 4.79037 -4.50522e-05 0.0114418
 174 4.81691 0.000243102 0.0102671
 175 4.84344 0.000499188 0.00902306
 176 4.86998 0.000721253 0.00770177
 177 4.89651 0.00090719 0.00629994
 178 4.92304 0.0010549 0.00482166
 179 4.94958 0.00116251 0.00328152
 180 4.97611 0.00122874 0.00170785
 181 5.00264 0.00125324 0.00014482
 182 5.02918 0.00123705 -0.00134747
 183 5.05571 0.00118299 -0.0026966
 184 5.08225 0.00109589 -0.00382582
 185 5.10878 0.000982528 -0.00466597
 186 5.13531 0.00085127 -0.00516907
 187 5.16185 0.000711345 -0.00531972
 188 5.18838 0.000571892 -0.00514044
 189 5.21492 0.000440972 -0.00468847
 190 5.24145 0.00032478 -0.00404508
 191 5.26798 0.0002272 -0.00330065
 192 5.29452 0.000149758 -0.00254022
 193 5.32105 9.19208e-05 -0.00183278
 194 5.34759 5.15999e-05 -0.00122598
 195 5.37412 2.57372e-05 -0.000745547
 196 5.40065 1.08566e-05 -0.00039786
 197 5.42719 3.52603e-06 -0.000173891
 198 5.45372 7.13171e-07 -5.31468e-05
 199 5.48026 4.55553e-08 -6.83139e-06
 200 5.50679 0 0

  • plot_pairpotential.py: a python script that plots a comparison between the pair potential fitted here and the pair potential from the EAM potential in [MisMehPap01]

     1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
    # creates: pairpotential.svg

import matplotlib.pyplot as plt
import numpy as np

x_ref,y_ref = np.loadtxt('pairpotential_reference.table',
                         usecols=(1,2), unpack=True)
x_fit,y_fit = np.loadtxt('Cu_potential.V.table',
                         usecols=(1,2), unpack=True)

plt.figure(figsize=(4, 3))
plt.xlabel(r'Pair distance (A)')
plt.ylabel(r'Pair potential (eV)')
plt.axis([1.8, 5.5, -0.5, 2])
plt.plot(x_ref, y_ref,
         color='cornflowerblue',
         linestyle='-',
         label='from EAM potential')
plt.plot(x_fit, y_fit,
         color='orange',
         linestyle='-',
         label='fitted potential')
plt.legend()
plt.savefig('pairpotential.svg', bbox_inches='tight')
../_images/pairpotential.svg

Pair interaction from a pure pair and an EAM potential [MisMehPap01].