# Questions about the calculations of PMF using 'fix smd'

Dear all,

i have some questions about the calculations of PMF using 'fix smd'. As the description of manual, 'This fix computes a vector list of 7 quantities, the x-, y-, and z-component of the pulling force, the total force in direction of the pull, the equilibrium distance of the spring, the distance between the two reference points, and finally the accumulated PMF'. i don't understand the meaning of 'the equilibrium distance of the spring'. why is it different from the fixed point which was settled in tether style. i performed a simple system consisted of a sodion, a chloridion and 1000 water molecuels. i attached a spring between a point and the sodion by command 'fix smd', but i found the equilibrium distance of the spring changed all the way even when the distance between sodion and reference point beconme zero. how do i understand this results?

parts of my input and output are as followed.

**************************** input **********************************

# Fix

fix temp1 all nvt temp \{temp\} {temp} 50 drag 0.2

# Output

thermo 1000
restart 500000 restartPMF.*

compute keatom all ke/atom
compute peatom all pe/atom
variable keatom atom c_keatom
variable peatom atom c_peatom
dump imf all custom 5000 Coords_EDL.txt id type x y z vx vy vz v_keatom v_peatom

run 500000

variable distance index 5 6 7 8 9 10
label loop

# PMF

fix pmf Na smd cvel 20.0 -0.00005 tether 12 12 \${distance} 0

variable tt equal dt*step
variable dr equal f_pmf[6]

fix out all print 1000 "\{tt\} {dr}" file umbrella_\${distance}.pmf screen no

thermo_style custom step f_pmf[1] f_pmf[2] f_pmf[3] f_pmf[4] f_pmf[5] f_pmf[6] f_pmf[7]

run 20000000

next distance
jump PMF.txt loop

**************************** output **********************************

1200000 0.13417532 30.700681 -9.4321626 25.607361 -1.5501597 0.055726054 0.47532881
1201000 -15.688088 24.977646 -12.650066 19.658404 -1.5751597 0.029563946 0.42852453
1202000 14.443435 14.159703 25.511252 -5.6944718 -1.6001597 0.0276967 0.40492915
1203000 32.040956 7.9020835 6.8185608 9.5854276 -1.6251597 0.0597678 0.4226642
1204000 14.648126 4.3649454 -32.002901 30.59232 -1.6501597 0.12314335 0.45480282
1205000 12.507502 -13.149821 29.77001 -25.998444 -1.6751597 0.06814449 0.57874057
1206000 15.786123 -25.533626 18.694686 -24.398648 -1.7001597 0.068098218 0.6386023
1207000 -16.852911 26.469172 -17.257484 23.587299 -1.7251597 0.06543676 0.67385721
1208000 -4.7378556 -28.617036 -21.09795 -3.3602056 -1.7501597 0.043259801 0.59605446
1209000 33.37086 13.594044 0.31301224 18.219727 -1.7751597 0.026607737 0.66400911
1210000 31.412028 -10.961146 15.669513 -8.5558729 -1.8001597 0.038612083 0.69759557
1211000 -30.329692 15.189929 -15.68248 11.4648 -1.8251597 0.043397058 0.58171062
1212000 8.3996008 -19.64518 -31.344057 13.615387 -1.8501597 0.046531005 0.5125111
1213000 6.1506241 14.333962 35.600073 -15.519173 -1.8751597 0.068224418 0.48269767
1214000 25.060313 -4.422504 29.857568 -16.927485 -1.9001597 0.061403097 0.3982099
1215000 -37.374639 -4.1679274 9.1759458 -20.674443 -1.9251597 0.010345369 0.26652083
1216000 39.250566 -0.033441331 6.0389416 7.5382366 -1.9501597 0.035486686 0.25996775
1217000 -10.802206 -28.336728 25.845472 -39.464913 -1.9751597 0.017129271 0.25750954
1218000 -20.810114 30.423469 16.343266 0.14195844 -2.0001597 0.01589521 0.21038167
1219000 31.900824 7.5041209 -24.886051 32.549445 -2.0251597 0.032345511 0.10327074
1220000 6.3982917 3.3899763 40.976071 -26.033885 -2.0501597 0.030411195 0.0047946973
1221000 -0.45777128 18.884295 -37.924724 39.141634 -2.0751597 0.043302751 -0.015287922
1222000 -11.673335 36.23271 -18.816847 32.243671 -2.1001597 0.023040876 -0.029084163
1223000 -0.17742581 -0.093296259 43.832441 -32.252599 -2.1251597 0.066510261 -0.014104472
1224000 23.861642 -13.644029 34.156336 -26.047628 -2.1501597 0.042006271 -0.082837428
1225000 1.9110994 -33.165935 -29.078026 1.758673 -2.1751597 0.032331676 -0.13064592
1226000 -21.53909 1.6985325 -39.940765 23.741967 -2.2001597 0.070373014 -0.017977476
1227000 26.629805 27.284504 24.286458 6.8982712 -2.2251597 0.035077 0.078509951
1228000 18.822748 -0.57282741 -41.582886 35.892517 -2.2501597 0.032276531 -0.052239653
1229000 -22.211626 -31.937166 -24.878443 -7.9412757 -2.2751597 0.033693922 -0.098504441
1230000 22.253375 31.554015 -26.088831 45.094887 -2.3001597 0.029830803 -0.10598032
1231000 -7.1942597 -45.142745 12.837365 -39.033644 -2.3251597 0.048903424 -0.12391378
1232000 36.345853 24.125318 -21.287316 41.364987 -2.3501597 0.076901493 -0.10283411
1233000 -30.856034 -11.085017 -35.142517 9.6124612 -2.3751597 0.027972109 -0.050777393
1234000 -38.023696 -2.1388402 29.79669 -34.760954 -2.4001597 0.017621967 -0.070726487
1235000 19.041604 -17.845974 42.193672 -35.96588 -2.4251597 0.055473802 0.0018911764
1236000 -44.731781 -21.770119 9.9386531 -34.173439 -2.4501597 0.086421609 -0.035909388
1237000 23.541974 43.690107 6.7786642 28.7595 -2.4751597 0.029361404 0.0077498643
1238000 -22.928845 -35.191724 29.40581 -49.943285 -2.5001597 0.063500935 -0.015473611
1239000 17.673288 -46.650352 -11.603936 -14.432639 -2.5251597 0.035749814 -0.052101871
1240000 -9.23024 -9.1648916 49.84862 -44.939614 -2.5501597 0.025752284 -0.046722777
1241000 -40.297931 14.147665 29.529847 -25.366165 -2.5751597 0.021060392 -0.054443076
1242000 -0.15938496 51.588486 9.8000903 24.103784 -2.6001597 0.025431463 -0.011525974
1243000 -40.585809 -16.352846 -30.978289 0.38741336 -2.6251597 0.055479925 -0.061028054
1244000 -0.4663386 -42.837445 -32.803417 -2.1108036 -2.6501597 0.04770162 -0.0058045938
1245000 11.435002 -49.087685 19.788361 -40.837934 -2.6751597 0.032234589 -0.061819793
1246000 24.587054 -20.50685 44.766764 -37.775572 -2.7001597 0.051736166 -0.10240746
1247000 49.674587 -21.155324 12.402429 -6.7756286 -2.7251597 0.044762696 -0.014715679
1248000 -47.173129 -19.454738 21.987324 -42.347599 -2.7501597 0.028009172 -0.050166734
1249000 20.614678 -7.6361301 -51.963508 39.760947 -2.7751597 0.045982813 -0.030641212
1250000 -24.433513 -46.012527 -21.687003 -19.510498 -2.8001597 0.021423075 0.086271002
1251000 14.152487 -44.592528 32.943571 -46.923877 -2.8251597 0.035837772 0.040920808
1252000 -24.699322 -29.878511 42.851559 -57.115917 -2.8501597 0.039085824 -0.061859103
1253000 -43.581252 20.596049 33.251772 -25.18087 -2.8751597 0.052835221 -0.074881316
1254000 12.56603 -55.683397 17.349537 -42.710902 -2.9001597 0.082964481 -0.063338232
1255000 58.207872 -3.8902885 -8.0754307 21.334594 -2.9251597 0.019565348 -0.033000762
1256000 -14.738155 -49.334087 -31.582121 -11.311418 -2.9501597 0.070004269 0.039269472
1257000 -9.8427941 58.093806 -12.173001 41.210938 -2.9751597 0.033167494 0.044688798
1258000 22.099936 -53.011223 19.063282 -39.432706 -3.0001597 0.025590723 0.020501899
1259000 17.636006 -2.5575286 -58.640352 46.832449 -3.0251597 0.039282298 -0.027693372
1260000 48.452187 -9.3117786 -36.737312 36.079232 -3.0501597 0.025557805 -0.069455569
1261000 48.441561 25.225368 29.969321 8.1413753 -3.0751597 0.039774726 -0.13918782
1262000 37.667789 46.672998 -18.846976 53.676387 -3.1001597 0.043286843 -0.13629362
1263000 46.243779 20.924991 37.572375 -0.71740097 -3.1251597 0.032406189 -0.10077016
1264000 -43.36122 23.087317 39.928294 -28.496095 -3.1501597 0.015101609 -0.0094275271
1265000 24.377725 35.383702 48.717438 -6.7843426 -3.1751597 0.072814111 0.0046417155
1266000 -24.289301 58.884299 9.6269411 21.293685 -3.2001597 0.020893428 -0.055045234
1267000 -23.695952 5.1268696 60.753573 -48.671896 -3.2251597 0.045484346 -0.11620643
1268000 -57.206734 -29.821227 -12.209118 -26.633382 -3.2501597 0.032767452 -0.21305237
1269000 13.690558 52.677295 -37.623157 63.769706 -3.2751597 0.033124209 -0.21764684
1270000 -23.595241 56.707278 -25.743177 46.11959 -3.3001597 0.02971588 -0.2935223
1271000 48.919827 2.6552521 45.884018 -17.093388 -3.3251597 0.031032394 -0.28107684
1272000 38.543602 -44.054398 -33.205859 9.3583742 -3.3501597 0.014768095 -0.28509302
1273000 -61.981294 7.5851813 -26.714157 5.2683245 -3.3751597 0.020768002 -0.27194938
1274000 68.161552 -9.5284899 -2.523468 16.878125 -3.4001597 0.043394462 -0.20792782
1275000 -63.658591 21.712567 15.125827 -17.342569 -3.4251597 0.021835897 -0.15338336
1276000 61.416349 28.924668 -14.139999 46.695782 -3.4501597 0.0170486 -0.22399902
1277000 61.9628 -1.1497279 -32.668787 42.180121 -3.4751597 0.027707056 -0.21748011
1278000 17.653733 49.746927 47.004398 1.1436553 -3.5001597 0.033922656 -0.33500732
1279000 39.670433 -56.185072 -19.475274 -7.7350396 -3.5251597 0.049005738 -0.31025793
1280000 -41.655485 -39.363243 -42.35883 -5.5723089 -3.5501597 0.013190598 -0.28208805
1281000 31.697554 56.681006 31.738722 20.838928 -3.5751597 0.039010391 -0.35434888
1282000 19.151199 -13.130348 -69.088795 48.534153 -3.6001597 0.044188306 -0.25397795
1283000 48.650691 20.728339 -50.278403 64.317985 -3.6251597 0.023314184 -0.23383119
1284000 19.746008 -63.047476 -31.916256 -8.865745 -3.6501597 0.018494643 -0.33991213
1285000 45.751551 57.35126 10.89849 40.819938 -3.6751597 0.033351721 -0.22783228
1286000 46.1992 39.052703 44.098439 5.4956487 -3.7001597 0.04290953 -0.22586243
1287000 56.230508 34.484418 -36.568294 64.935844 -3.7251597 0.0459014 -0.15192022
1288000 49.515055 4.9089917 -57.395756 60.191151 -3.7501597 0.047927877 -0.12234541
1289000 -30.796059 30.472858 62.552488 -36.762271 -3.7751597 0.029404081 -0.15187534
1290000 -71.048689 -23.514928 -17.309158 -23.289898 -3.8001597 0.040592795 -0.14608343
1291000 -49.945508 -21.142518 -55.099461 12.307156 -3.8251597 0.040583372 -0.093702499
1292000 -33.161967 56.357838 41.578837 -6.380619 -3.8501597 0.024372253 -0.10007907
1293000 -33.834293 -10.403065 69.559117 -67.659107 -3.8751597 0.027253657 0.047696652
1294000 33.399951 25.895315 -66.785443 74.903725 -3.9001597 0.051579958 0.080040234
1295000 -74.761362 15.933973 -20.511605 1.8888254 -3.9251597 0.032098764 0.11626589
1296000 73.346073 -18.763673 26.692874 -8.572658 -3.9501597 0.06366382 0.18644606
1297000 -51.373385 18.556399 -59.205884 38.998391 -3.9751597 0.052551162 0.077229479
1298000 21.017735 -69.223371 37.603473 -63.206955 -4.0001597 0.076518804 0.014360973
1299000 57.381317 -11.840297 56.5028 -31.101612 -4.0251597 0.044685507 0.085946678
1300000 -18.236676 75.848093 -24.950225 58.802168 -4.0501597 0.044991487 0.12491612

Dear all,

i have some questions about the calculations of PMF using 'fix smd'. As the description of manual, 'This fix computes a vector list of 7 quantities, the x-, y-, and z-component of the pulling force, the total force in direction of the pull, the equilibrium distance of the spring, the distance between the two reference points, and finally the accumulated PMF'. i don't understand the meaning of 'the equilibrium distance of the spring'. why is it different from the fixed point which was settled in tether style.

because you are doing a *steered MD* at *constant velocity*. that
means your reference point is moving at a constant rate. please note,
that this fix also supports constant force mode, where the reference
distance changes at a varying rate. this "equilibrium distance" is the
distance that would happen, for an infinitely large force constant. in
reality, the distance between the tether point and the reference group
will fluctuate, so it is not useful for plotting. there is extensive
published literature on how to set up and interpret steered MD
calculation and how to estimate and minimize errors.

axel.