Figure 5.3 (page 198):

Contour representation of the potential-energy surface.

Code for Figure 5.3

Text of the GNU GPL.

main.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

initdata ();

an1 = 0;
en1 = 3;

an2 = 0;
en2 = 3;

n1 = 301;
n2 = 301;

step1 = (en1 - an1) / (n1 - 1);
step2 = (en2 - an2) / (n2 - 1);

d3table = zeros (n2, 3*n1);
table = zeros (n1, n2);

idx = [1,2,3];
for p1 = 1:n1
  r1 = (p1-1)*step1 + an1;
  for p2 = 1:n2
    r2 = (p2-1)*step2 + an2;
    tmp = Vau (r1, r2);
    d3table(p2,idx) = [r1, r2, tmp];
    table(p1,p2) = tmp;
  end
  idx += 3;
end

[fid, errmsg] = fopen ('hfc.dat', 'w');

for p2 = 1:n2
  fprintf (fid,'%f %f %f\n', d3table(p2,:));
  fprintf (fid,'\n');
end

fclose (fid);

x = d3table(1,1:3:end)';
y = d3table(:,2);
z = d3table(:,3:3:end);

levels = [3000, 1000, 200, -20, -40, -60, -80, -90.5, -92, -95, -100, -110, -120];

c = contourc (x, y, z, levels);

[fid, errmsg] = fopen ('hfc-contours.dat', 'w');

idx = 1;
nel = numel (c);

while (idx <= nel)
  fprintf (fid, '# contour level %f\n', c(idx));
  idx = idx + 1;
  len = c(idx);
  fprintf (fid, '%f %f\n', c(idx+1:idx+2*len));
  fprintf (fid, '\n');
  idx = idx + 2 * len + 1;
end

fclose (fid);

initdata.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

function initdata ()

  global D1 D3 B1 B3 r10 r30 R_1 C Si A

  D1 = [129.3; 94.8; 129.3];
  B1 = [2.316; 2.047; 2.316];
  r10 = [0.931; 0.753; 0.931];
  D3 = [51.83; 34.56; 51.83];
  B3 = [2.229; 1.522; 2.229];
  r30 = [0.931; 0.753; 0.931];
  R_1 = [1.217; 0.443; 1.217];
  C = [1174.9; 388.8; 1174.9];
  Si = [3.090; 1.929; 3.090];
  A = [1.315; 0.762; 1.315];

inittrace.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

function [s, V, d3trace, num] = inittrace (en1, en2)

  global D1 D3 B1 B3 r10 r30 R_1 C Si A

  R1sar = 1.29781;
  R2sar = 0.80363;
  numr = 30;

  R1r = linspace (R1sar, en1, numr)';

  opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
  [tsolver, R2r] = ode15s (@rder, R1r, R2sar, opts);

  R1sal = 1.297;
  R2sal = 0.80363;
  numl = 1000;

  R2l = linspace (R2sal, en2, numl)';

  opts  =  odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
  [tsolver, R1l] = ode15s (@lder, R2l, R1sal, opts);

  R1rn = zeros (numr, 1);
  R2rn = zeros (numr, 1);
  num = numl+numr;

  for i = 1:numr
    R1rn(i) = R1r(numr+1-i);
    R2rn(i) = R2r(numr+1-i);
  end

  R1 = [R1rn; R1l];
  R2 = [R2rn; R2l];
  trtable = [R1, R2];

  s = zeros (num, 1);
  V = zeros (num, 1);
  D = zeros (num, 1);

  s(1) = 0;
  V(1) = Vau (R1(1), R2(1));
  D(1) = 1;

  for i = 2:num
    D(i) = i;
    s(i) = sqrt ((R1(i)-R1(i-1))^2 + (R2(i)-R2(i-1))^2) + s(i-1);
    V(i) = Vau (R1(i), R2(i));
  end

  pot = [s, V, R1, R2, D];

  for i = 1:num
    j = i*3-2;
    d3trace(j) = R1(i);
    d3trace(j+1) = R2(i);
    d3trace(j+2) = V(i);
  end

  d3trace = d3trace';

  ## this seems to be unused.
  ## for a = 1:3
  ##   for i = 1:num
  ##    j = i*3-2;
  ##    d3sptrace(a,j) = R1(i)+(a-2)*0.1;
  ##    d3sptrace(a,j+1) = R2(i);
  ##    d3sptrace(a,j+2) = -100+(a-2);
  ##   end
  ## end

lder.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

function retval = lder (r2, r1)

  global D1 D3 B1 B3 r10 r30 R_1 C Si A

  r3 = r1+r2;
  r(1) = r1;
  r(2) = r2;
  r(3) = r3;

  for x = 1:3
   E1(x) = D1(x)*(exp(-2*B1(x)*(r(x)-r10(x)))-2*exp(-B1(x)*(r(x)-r10(x))));
   E3(x,1) = D3(x)*(exp(-2*B3(x)*(r(x)-r30(x)))+2*exp(-B3(x)*(r(x)-r30(x))));
   E3(x,2) = C(x)*(r(x)+A(x))*exp(-Si(x)*r(x));
    if(r(x) <= R_1(x))
     y = 1;
     else 
     y = 2;
    end
   Q(x) = (E1(x)+E3(x,y))/2;
   J(x) = (E1(x)-E3(x,y))/2;
  end

  %dQ(a,b) means dQ(a)/dr(b)
  for i = 1:3
     dE1(i,i) = -2*B1(i)*D1(i)*(exp(-2*B1(i)*(r(i)-r10(i)))-exp(-B1(i)*(r(i)-r10(i))));
   if(r(i) <= R_1(i))
     dE3(i,i) = -2*B3(i)*D3(i)*(exp(-2*B3(i)*(r(i)-r30(i)))+exp(-B3(i)*(r(i)-r30(i))));
   else
     dE3(i,i) = C(i)*exp(-Si(i)*r(i))*(1-Si(i)*(r(i)+A(i)));
   end
  end
  dE1(1,2) = 0;
  dE3(1,2) = 0;
  dE1(2,1) = 0;
  dE3(2,1) = 0;
  dE1(3,1) = dE1(3,3);
  dE3(3,1) = dE3(3,3);
  dE1(3,2) = dE1(3,3);
  dE3(3,2) = dE3(3,3);
  dE1(1,3) = 1000;
  dE3(1,3) = 1000;
  dE1(2,3) = 1000;
  dE3(2,3) = 1000;
  dE1(3,3) = 1000;
  dE3(3,3) = 1000;
  for i = 1:3
   for j = 1:3
    dQ(i,j) = (dE1(i,j)+dE3(i,j))/2;
    dJ(i,j) = (dE1(i,j)-dE3(i,j))/2;
   end
  end

  dV(1) = dQ(1,1)+dQ(3,1)-0.5/sqrt(0.5*((J(1)-J(2))*(J(1)-J(2))+(J(2)-J(3))*(J(2)-J(3))+(J(1)-J(3))*(J(1)-J(3))))*(J(1)*(2*dJ(1,1)-dJ(3,1))+J(2)*(-dJ(1,1)-dJ(3,1))+J(3)*(2*dJ(3,1)-dJ(1,1)));

  dV(2) = dQ(2,2)+dQ(3,2)-0.5/sqrt(0.5*((J(1)-J(2))*(J(1)-J(2))+(J(2)-J(3))*(J(2)-J(3))+(J(1)-J(3))*(J(1)-J(3))))*(J(1)*(-dJ(2,2)-dJ(3,2))+J(2)*(2*dJ(2,2)-dJ(3,2))+J(3)*(2*dJ(3,2)-dJ(2,2)));

  retval = dV(1)/dV(2);

rder.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

function retval = rder (r1, r2)

  global D1 D3 B1 B3 r10 r30 R_1 C Si A

  retval = 1 / lder (r2, r1, D1, D3, B1, B3, r10, r30, R_1, C, Si, A);

Matlab dynamically-linked MEX functions (C language)

Vau.c

/*

Copyright (C) 2001, James B. Rawlings and John G. Ekerdt

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; see the file COPYING.  If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.

*/

#include 

#include 

void
mexFunction (int nlhs, mxArray* plhs[], int nrhs, const mxArray* prhs[])
{
  int nargin = nrhs;

  if (nargin == 2)
    {
      double r1 = mxGetScalar (prhs[0]);
      double r2 = mxGetScalar (prhs[1]);

      mxArray *mx_D1 = mexGetVariable ("global", "D1");
      mxArray *mx_D3 = mexGetVariable ("global", "D3");
      mxArray *mx_B1 = mexGetVariable ("global", "B1");
      mxArray *mx_B3 = mexGetVariable ("global", "B3");
      mxArray *mx_r10 = mexGetVariable ("global", "r10");
      mxArray *mx_r30 = mexGetVariable ("global", "r30");
      mxArray *mx_R_1 = mexGetVariable ("global", "R_1");
      mxArray *mx_C = mexGetVariable ("global", "C");
      mxArray *mx_Si = mexGetVariable ("global", "Si");
      mxArray *mx_A = mexGetVariable ("global", "A");

      double *D1 = mxGetPr (mx_D1);
      double *D3 = mxGetPr (mx_D3);
      double *B1 = mxGetPr (mx_B1);
      double *B3 = mxGetPr (mx_B3);
      double *r10 = mxGetPr (mx_r10);
      double *r30 = mxGetPr (mx_r30);
      double *R_1 = mxGetPr (mx_R_1);
      double *C = mxGetPr (mx_C);
      double *Si = mxGetPr (mx_Si);
      double *A = mxGetPr (mx_A);

      double r3 = r1 + r2;

      double r[3];

      double E1[3];
      double E3[3][2];
      double Q[3];
      double J[3];

      int i;

      double retval;

      r[0] = r1;
      r[1] = r2;
      r[2] = r3;

      for (i = 0; i < 3; i++)
	{
	  int j;

	  E1[i] = D1[i]*(exp(-2*B1[i]*(r[i]-r10[i]))-2*exp(-B1[i]*(r[i]-r10[i])));
	  E3[i][0] = D3[i]*(exp(-2*B3[i]*(r[i]-r30[i]))+2*exp(-B3[i]*(r[i]-r30[i])));
	  E3[i][1] = C[i]*(r[i]+A[i])*exp(-Si[i]*r[i]);

	  j = (r[i] > R_1[i]);

	  Q[i] = (E1[i] + E3[i][j]) / 2;
	  J[i] = (E1[i] - E3[i][j]) / 2;
	}

      retval = Q[0]+Q[1]+Q[2]-sqrt(0.5*((J[0]-J[1])*(J[0]-J[1])+(J[1]-J[2])*(J[1]-J[2])+(J[0]-J[2])*(J[0]-J[2])));

      plhs[0] = mxCreateDoubleScalar (retval);
    }
  else
    mexErrMsgTxt ("usage: Vau (r1, r2)");
}

Octave dynamically-linked functions (C++ language)

Vau.cc

/*

Copyright (C) 2001, James B. Rawlings and John G. Ekerdt

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; see the file COPYING.  If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.

*/

#include 
#include 

DEFUN_DLD (Vau, args, ,
  "")
{
  octave_value retval;

  int nargin = args.length ();

  if (nargin == 2)
    {
      double r1 = args(0).double_value ();
      double r2 = args(1).double_value ();

      if (! error_state)
	{
	  const ColumnVector D1 = get_global_value ("D1") . column_vector_value ();
	  const ColumnVector D3 = get_global_value ("D3") . column_vector_value ();
	  const ColumnVector B1 = get_global_value ("B1") . column_vector_value ();
	  const ColumnVector B3 = get_global_value ("B3") . column_vector_value ();
	  const ColumnVector r10 = get_global_value ("r10") . column_vector_value ();
	  const ColumnVector r30 = get_global_value ("r30") . column_vector_value ();
	  const ColumnVector R_1 = get_global_value ("R_1") . column_vector_value ();
	  const ColumnVector C = get_global_value ("C") . column_vector_value ();
	  const ColumnVector Si = get_global_value ("Si") . column_vector_value ();
	  const ColumnVector A = get_global_value ("A") . column_vector_value ();

	  if (! error_state)
	    {
	      double r3 = r1 + r2;

	      ColumnVector r (3);
	      r(0) = r1;
	      r(1) = r2;
	      r(2) = r3;

	      ColumnVector E1 (3, 0.0);
	      Matrix E3 (3, 2, 0.0);
	      ColumnVector Q (3, 0.0);
	      ColumnVector J (3, 0.0);

	      for (int i = 0; i < 3; i++)
		{
		  E1(i) = D1(i)*(exp(-2*B1(i)*(r(i)-r10(i)))-2*exp(-B1(i)*(r(i)-r10(i))));
		  E3(i,0) = D3(i)*(exp(-2*B3(i)*(r(i)-r30(i)))+2*exp(-B3(i)*(r(i)-r30(i))));
		  E3(i,1) = C(i)*(r(i)+A(i))*exp(-Si(i)*r(i));

		  int j = (r(i) > R_1(i));

		  Q(i) = (E1(i) + E3(i,j)) / 2;
		  J(i) = (E1(i) - E3(i,j)) / 2;
		}

	      retval = Q(0)+Q(1)+Q(2)-sqrt(0.5*((J(0)-J(1))*(J(0)-J(1))+(J(1)-J(2))*(J(1)-J(2))+(J(0)-J(2))*(J(0)-J(2))));
	    }
	  else
	    error ("Vau: error getting global values");
	}
      else
	error ("Vau: invalid arguments");
    }
  else
    print_usage ("Vau");

  return retval;
}

Data files

hfc-contours.dat

# contour level -120.000000
0.843983 3.000000
0.844262 2.990000
0.844546 2.980000
0.844834 2.970000
0.845127 2.960000
0.845424 2.950000
0.845725 2.940000
0.846031 2.930000
0.846341 2.920000
0.846656 2.910000
0.846976 2.900000
0.847301 2.890000
0.847630 2.880000
0.847964 2.870000
0.848304 2.860000
0.848648 2.850000
0.848997 2.840000
0.849352 2.830000
0.849711 2.820000
0.850000 2.812090
0.850089 2.810000
0.850523 2.800000
0.850964 2.790000
0.851411 2.780000
0.851864 2.770000
0.852324 2.760000
0.852791 2.750000
0.853264 2.740000
0.853744 2.730000
0.854231 2.720000
0.854726 2.710000
0.855227 2.700000
0.855736 2.690000
0.856251 2.680000
0.856775 2.670000
0.857305 2.660000
0.857843 2.650000
0.858389 2.640000
0.858943 2.630000
0.859504 2.620000
0.860000 2.611287
0.860087 2.610000
0.860776 2.600000
0.861474 2.590000
0.862181 2.580000
0.862899 2.570000
0.863627 2.560000
0.864364 2.550000
0.865112 2.540000
0.865870 2.530000
0.866639 2.520000
0.867418 2.510000
0.868207 2.500000
0.869008 2.490000
0.869819 2.480000
0.870000 2.477795
0.870782 2.470000
0.871799 2.460000
0.872829 2.450000
0.873873 2.440000
0.874930 2.430000
0.876002 2.420000
0.877088 2.410000
0.878188 2.400000
0.879302 2.390000
0.880000 2.383819
0.880543 2.380000
0.881983 2.370000
0.883442 2.360000
0.884919 2.350000
0.886415 2.340000
0.887930 2.330000
0.889464 2.320000
0.890000 2.316548
0.891343 2.310000
0.893419 2.300000
0.895521 2.290000
0.897647 2.280000
0.899799 2.270000
0.900000 2.269079
0.902823 2.260000
0.905969 2.250000
0.909150 2.240000
0.910000 2.237358
0.913942 2.230000
0.919355 2.220000
0.920000 2.218822
0.930000 2.211890
0.940000 2.215573
0.943249 2.220000
0.950000 2.229330
0.950289 2.230000
0.954541 2.240000
0.958735 2.250000
0.960000 2.253057
0.962089 2.260000
0.965058 2.270000
0.967988 2.280000
0.970000 2.286958
0.970702 2.290000
0.972979 2.300000
0.975227 2.310000
0.977446 2.320000
0.979636 2.330000
0.980000 2.331685
0.981514 2.340000
0.983311 2.350000
0.985085 2.360000
0.986835 2.370000
0.988563 2.380000
0.990000 2.388429
0.990234 2.390000
0.991703 2.400000
0.993152 2.410000
0.994583 2.420000
0.995994 2.430000
0.997387 2.440000
0.998762 2.450000
1.000000 2.459128
1.000106 2.460000
1.001304 2.470000
1.002485 2.480000
1.003652 2.490000
1.004802 2.500000
1.005937 2.510000
1.007057 2.520000
1.008162 2.530000
1.009252 2.540000
1.010000 2.546957
1.010298 2.550000
1.011265 2.560000
1.012219 2.570000
1.013160 2.580000
1.014088 2.590000
1.015004 2.600000
1.015907 2.610000
1.016797 2.620000
1.017675 2.630000
1.018541 2.640000
1.019396 2.650000
1.020000 2.657174
1.020220 2.660000
1.020988 2.670000
1.021746 2.680000
1.022493 2.690000
1.023230 2.700000
1.023956 2.710000
1.024672 2.720000
1.025378 2.730000
1.026074 2.740000
1.026761 2.750000
1.027437 2.760000
1.028104 2.770000
1.028762 2.780000
1.029410 2.790000
1.030000 2.799231
1.030046 2.800000
1.030635 2.810000
1.031216 2.820000
1.031788 2.830000
1.032353 2.840000
1.032909 2.850000
1.033457 2.860000
1.033997 2.870000
1.034530 2.880000
1.035054 2.890000
1.035572 2.900000
1.036081 2.910000
1.036583 2.920000
1.037078 2.930000
1.037566 2.940000
1.038046 2.950000
1.038520 2.960000
1.038987 2.970000
1.039446 2.980000
1.039899 2.990000
1.040000 2.992259
1.040326 3.000000

# contour level -110.000000
0.799234 3.000000
0.799382 2.990000
0.799532 2.980000
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