Figure 5.2 (page 197):

Potential-energy surface for the F, H_2 reaction.

Code for Figure 5.2

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 = 31;
n2 = 31;

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 ('hfs.dat', 'w');

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

fclose (fid);

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

%----------------------------
				%the following part is changed in hfc.m
				%and hfp.m
[fid, errmsg] = fopen ('hfts.dat', 'w');
for i = 1:num
  j = i*3-2;
  fprintf (fid, '%f %f %f\n', d3trace(j:j+2));
end
fclose (fid);
				%End of changed part
%----------------------------

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

hfs.dat

0.000000 0.000000 11062.280761
0.100000 0.000000 7482.672756
0.200000 0.000000 5120.253601
0.300000 0.000000 3136.255264
0.400000 0.000000 1947.570964
0.500000 0.000000 1247.339784
0.600000 0.000000 844.812714
0.700000 0.000000 621.871127
0.800000 0.000000 505.736652
0.900000 0.000000 451.861778
1.000000 0.000000 433.218057
1.100000 0.000000 433.601560
1.200000 0.000000 443.458503
1.300000 0.000000 457.179340
1.400000 0.000000 471.705987
1.500000 0.000000 485.546005
1.600000 0.000000 498.013824
1.700000 0.000000 508.865353
1.800000 0.000000 518.097117
1.900000 0.000000 525.827232
2.000000 0.000000 532.226416
2.100000 0.000000 537.479309
2.200000 0.000000 541.763940
2.300000 0.000000 545.241850
2.400000 0.000000 548.054323
2.500000 0.000000 550.321981
2.600000 0.000000 552.146095
2.700000 0.000000 553.610682
2.800000 0.000000 554.784831
2.900000 0.000000 555.724981
3.000000 0.000000 556.477005

0.000000 0.100000 8501.848708
0.100000 0.100000 5629.028591
0.200000 0.100000 3745.799166
0.300000 0.100000 2386.481091
0.400000 0.100000 1472.657471
0.500000 0.100000 925.406230
0.600000 0.100000 612.790604
0.700000 0.100000 442.872257
0.800000 0.100000 357.617391
0.900000 0.100000 321.287924
1.000000 0.100000 312.208064
1.100000 0.100000 317.437776
1.200000 0.100000 329.346099
1.300000 0.100000 343.583240
1.400000 0.100000 357.869371
1.500000 0.100000 371.108611
1.600000 0.100000 382.834372
1.700000 0.100000 392.924724
1.800000 0.100000 401.440226
1.900000 0.100000 408.528685
2.000000 0.100000 414.370743
2.100000 0.100000 419.150084
2.200000 0.100000 423.038235
2.300000 0.100000 426.187848
2.400000 0.100000 428.730728
2.500000 0.100000 430.778393
2.600000 0.100000 432.423860
2.700000 0.100000 433.743927
2.800000 0.100000 434.801512
2.900000 0.100000 435.647869
3.000000 0.100000 436.324566

0.000000 0.200000 6705.666472
0.100000 0.200000 4384.755409
0.200000 0.200000 2885.324952
0.300000 0.200000 1877.973087
0.400000 0.200000 1172.067315
0.500000 0.200000 721.550318
0.600000 0.200000 460.573849
0.700000 0.200000 319.748173
0.800000 0.200000 250.918381
0.900000 0.200000 223.647950
1.000000 0.200000 219.326327
1.100000 0.200000 226.736185
1.200000 0.200000 239.376271
1.300000 0.200000 253.647788
1.400000 0.200000 267.643322
1.500000 0.200000 280.438461
1.600000 0.200000 291.647351
1.700000 0.200000 301.170802
1.800000 0.200000 309.035667
1.900000 0.200000 315.261079
2.000000 0.200000 319.696446
2.100000 0.200000 322.098561
2.200000 0.200000 322.988946
2.300000 0.200000 323.274347
2.400000 0.200000 323.379718
2.500000 0.200000 323.436981
2.600000 0.200000 323.484437
2.700000 0.200000 323.531913
2.800000 0.200000 323.580501
2.900000 0.200000 323.628909
3.000000 0.200000 323.675551

0.000000 0.300000 5565.568859
0.100000 0.300000 3623.035098
0.200000 0.300000 2372.966542
0.300000 0.300000 1554.891650
0.400000 0.300000 985.943886
0.500000 0.300000 591.264670
0.600000 0.300000 354.620397
0.700000 0.300000 226.155855
0.800000 0.300000 163.121008
0.900000 0.300000 137.390842
1.000000 0.300000 131.111563
1.100000 0.300000 132.978357
1.200000 0.300000 135.955050
1.300000 0.300000 136.727599
1.400000 0.300000 135.412710
1.500000 0.300000 133.328824
1.600000 0.300000 131.314495
1.700000 0.300000 129.665065
1.800000 0.300000 128.418994
1.900000 0.300000 127.524241
2.000000 0.300000 126.907643
2.100000 0.300000 126.500218
2.200000 0.300000 126.244742
2.300000 0.300000 126.096559
2.400000 0.300000 126.022072
2.500000 0.300000 125.996640
2.600000 0.300000 126.002569
2.700000 0.300000 126.027412
2.800000 0.300000 126.062591
2.900000 0.300000 126.102349
3.000000 0.300000 126.142941

0.000000 0.400000 4872.390620
0.100000 0.400000 3171.539769
0.200000 0.400000 2075.353411
0.300000 0.400000 1363.181429
0.400000 0.400000 875.120450
0.500000 0.400000 501.851819
0.600000 0.400000 271.323506
0.700000 0.400000 145.649044
0.800000 0.400000 82.134195
0.900000 0.400000 52.560595
1.000000 0.400000 39.409299
1.100000 0.400000 32.788930
1.200000 0.400000 28.244540
1.300000 0.400000 24.413751
1.400000 0.400000 21.086398
1.500000 0.400000 18.341580
1.600000 0.400000 16.195799
1.700000 0.400000 14.587041
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