Copyright © 2004–2016 by A. Miyoshi
BEx1D - Quick start: step-2
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BEx1D - Quick start: step-2

  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

This sample problem treats the anharmonic wagging vibration of an H...O–H moiety in the transition state of hydrogen abstraction reaction from benzene (C6H6) by OH radical. (Fig. QS2-1)

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 xy 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
The potential energy curve derived by bx1fitPlls well fits the input points as shown in Fig. QS2-3.

Fig. QS2-3. Potential energy curve.
bx1VIBsol input:  wagOHbenTSabs.inp
  1. The first line is a title line copied from wagOHbenTSabs.fit:
    # CH-OH wag of OH + benzene H abstraction TS (mass weighted coordinate)
  2. Also, following nine non-blank lines are copy of continue block contents:
    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
    In this example, number of basis functions (numBasis) is 501, meaning that the harmonic oscillator basis functions (so-called Hermite-Gaussian functions) for quantum number 0 to 500 are used as the expansion basis.   The next key, rotConst (or equivalently, hbar2/2m), sets the rotational constant ( = 2 / 2I ) or 2 / 2m.   The exponent parameter, α, of the Hermite-Gaussian basis is set by the hoFreq, the harmonic oscillator frequency, input.
    Next three lines are comment, though the second line shows an example of output key input.   This key controls the output of bex1VIBsol.
    The last three lines specifies a list of temperatures at which the partition functions are calculated.
  3. The final part of the input is the potential function input:
    potPars{           ! potential parameters
      0   -1.0306367
      2   1287.7844
      4   2074.6208
      6   -1249.2067
      8   530.98393
      10   -121.79626
      12   11.063236
    }
    Each line in the block specifies the order ni and coefficient ai for the power series term, aixni.
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
numbereigenValuew
050.340893(1/1)
1156.5024(1/1)
2268.75298(1/1)
3385.86919(1/1)
4507.03996(1/1)
5631.67864(1/1)
6759.33796(1/1)
7889.66457(1/1)
81022.3721(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/TTQ
33.3333333001.882205
30.303033302.0603718
27.7777783602.2366488
25.6410263902.4112197
23.8095244202.5842349
.........

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