Having succeeded to run BEx1D tools, let us investigate the sample input and ouput files in detail in the next three steps.

Sample problem 1: wagOHbenTSabs

Fig. QS2-1. "Wagging" vibraion of H-abstraction TS of OH + benzene.

bx1fitPlls input:  wagOHbenTSabs.fit

1. The first line beginning with '#' is a title line:

   # CH-OH wag of OH + benzene H abstraction TS (mass weighted coordinate)

2. Next non-blank line is an output option control;

   outputOption powerSeries

   which tells bx1fitPlls to generate input file for bx1VIBsol named 'wagOHbenTSabs.inp'.   Note that bx1VIBsol only accept power series potential and the regression function defined in the following block must be a power series.
3. The first block input beginning with 'optFuncs';

   optFuncs{
     const
     pow   2
     pow   4
     pow   6
     pow   8
     pow  10
     pow  12
   }

   defines the regression function.   The key 'const' stands for a constant term, and 'pow n' means xⁿ.   Thus, this example is a polynomial;  y = a₀ + a₁x² + a₂x⁴ + a₃x⁶ + a₄x⁸ + a₅x¹⁰.
4. Next block is a x–y data table;

   xyTable{
     0.           0.
     0.175395353  40.11886525
     0.354069718  189.0859545
     0.538962708  521.7658202
     0.73251983   1134.26377
     0.936579205  2136.432343
     1.152654481  3654.297605
     1.382347157  5833.785823
     1.627451293  8827.658145
     1.889951279  12732.18273
   }

   where each line in the block beginning with 'xyTable{' terminating by '}' contains one datum point, in the order of x (coordinate) and y (potential energy).   As shown in Fig. QS2-2, the potential energy curve is anharmonic.
   
   Fig. QS2-2. Input potential energy points.
5. The last block is a 'continue' block:

   continue{
    numBasis  501     ! number of basis functions
    rotConst  1.89349 ! rotational constant [cm-1]
    hoFreq    73.3072 ! harmonic oscillator frequency [cm-1]
    !
    ! output vector   ! (and/or function)
    !
     tempRange 300 570 30
     tempRange 600 950 50
     tempRange 1000 2000 100
   }

   Any line in this block is merely copied to the bx1VIBsol input, 'wagOHbenTSabs.inp'.   Although bx1fitPlls neither reads nor checks the contents of this block, they must be proper input for bx1VIBsol.

bx1fitPlls console output

1.   When bx1fitPlls is invoked as;
   bx1fitPlls wagOHbenTSabs
   only the essential output, the coefficients for the potential function are stored in 'wagOHbenTSabs.inp'.   Other diagnostic messages and related statistics are printed to the console.
2. The first output is a regression function:

   ===== results of linear least squares regression =====
   Function:
    y = a0 + a1 * x^2 + a2 * x^4 + a3 * x^6 + a4 * x^8 + a5 * x^10 + a6 * x^12

   The parameters to be optimized are numbered consecutively, a0, a1, a2, ..., as they appear in the optFuncs block.
3. The following block;

    Optimum parameters (+-) standard deviations (relative)
     a0 = -1.0306367e+000 (+-)  1.3167189e+000 ( 127.76 %)
     a1 =  1.2877844e+003 (+-)  2.0212666e+001 (   1.57 %)
     a2 =  2.0746208e+003 (+-)  7.4216348e+001 (   3.58 %)
     a3 = -1.2492067e+003 (+-)  1.0363676e+002 (   8.30 %)
     a4 =  5.3098393e+002 (+-)  6.5249151e+001 (  12.29 %)
     a5 = -1.2179626e+002 (+-)  1.8647156e+001 (  15.31 %)
     a6 =  1.1063236e+001 (+-)  1.9588634e+000 (  17.71 %)

   show the optimum parameters and their estimated errors.
4. And the last block shows the correlation coefficients between parameters as:

    Parameter correlation coefficients
               a0       a1       a2       a3       a4       a5
     a1  -0.68038
     a2   0.53582 -0.95926
     a3  -0.46231  0.90454 -0.98652
     a4   0.41867 -0.85999  0.96386 -0.99420
     a5  -0.39058  0.82631 -0.94249  0.98355 -0.99721
     a6   0.37162 -0.80129  0.92476 -0.97281  0.99186 -0.99858

Fig. QS2-3. Potential energy curve.

bx1VIBsol output

For this example, bx1VIBsol creates two output files, namely, 'wagOHbenTSabs_eigen_values.csv' (eigen values) and 'wagOHbenTSabs_part_funcs.csv' (partition functions). Optionally, by setting the output key in the input, 'wagOHbenTSabs_eigen_vectors00.csv' (eigen vectors) and 'wagOHbenTSabs_eigen_funcs00.csv' (eigen functions) will be also created.

Eigen value output

Fig. QS2-4. Calculated eigen values
(horizontal dotted lines)

First few rows of the eigen value output is shown in Table QS2-1 and in Fig. QS2-4.

Table QS2-1. Eigenvalues

number	eigenValue	w
0	50.340893	(1/1)
1	156.5024	(1/1)
2	268.75298	(1/1)
3	385.86919	(1/1)
4	507.03996	(1/1)
5	631.67864	(1/1)
6	759.33796	(1/1)
7	889.66457	(1/1)
8	1022.3721	(1/1)
...	...	...

Partition function output

First few rows of the partition function output is shown in Table QS2-2.

Table QS2-2. Partition function

10000/T	T	Q
33.333333	300	1.882205
30.30303	330	2.0603718
27.777778	360	2.2366488
25.641026	390	2.4112197
23.809524	420	2.5842349
...	...	...