Donald L. Thompson's Theoretical Chemistry Group
Department of Chemistry, Schlundt Hall, University of Missouri - Columbia


Potential Energy Surface Fitting
  • We have developed two main schemes for automated fitting of potential energy surfaces.  The first is a global driver based on ranges of coordinates and energy.1,3,4  An illustrative one-dimensional example of how the automatic data point selection algorithm works is shown in Figure 1 below.  The second approach uses classical trajectories to explore configuration space.2
  • Figures 2-4 show recent results1 for our general 3-atom method.  Our IMLS-based method was used to produce wavenumber accurate fits to ab initio data for several three-atom systems.  A single input file specifies the molecule, the choice of coordinates and energy range, the choice of ab initio code and the accuracy target.  Running in parallel a usable PES is produced quickly in a fairly black box fashion.  The accuracy of spectroscopic calculations using the fitted PESs was confirmed by computing a set of 216 vibrational levels for the singlet methylene system.  The mean and maximum errors for all 216 levels below 20000 cm-1, were found to be 0.10 and 0.41 cm-1.
  • We are currently working on a series of benchmark level ab initio PESs.  Much of our current effort is directed at devising robust schemes for automated use of multi-reference ab initio methods such as dynamically-weighted state-averaged CASSCF and MRCI.
  • We are also working on fitting high-dimensional systems with multiple reaction channels.  These systems present challenges both from ab initio as well as PES fitting standpoints.  We are working on special coordinates with which to efficiently describe these systems.  The goal is to permit straightforward inclusion of special coordinates such as arbitrary vectors for polyspherical coordinates as well as combinations of Euler angles with other coordinates.
    •
a)b)
c)d)
Figure 1: Example of automatic surface generation scheme: 2nd (green) and 3rd (red) degree fits to Morse function (blue) using five-point seed grid (diamonds).  Peaks in squared difference surface (black) indicate locations for new data.  Frames (a) through (d) follow the addition of three automatically generated points, and the resulting convergence of the functions.  The energy and distance units are, respectively, kcal/mol and bohr.

                                 
Figure 2:  Convergence of IMLS automatic surface generation (HCN, Jacobi coordinates) to wavenumber accuracy. The Aces II electronic structure code was used to compute energies and analytic gradients using the CCSD(T) method and the aug-cc-pVTZ basis set. Test sets of 8000 randomly placed points were used to evaluate RMS (unfilled squares) and mean (unfilled triangles) estimated errors.  Test sets of 500 randomly placed ab initio points were used to evaluate RMS (filled squares) and mean (filled triangles) true errors.  True mean error is sub-wavenumber at 440 ab initio data points.

                                   
Figure 3:  As in Fig. 2 only for CH2 and for valence coordinates. The Molpro code was used to compute energies and gradients for the CASSCF (full valence) method using the aug-cc-pVDZ basis set. PES data files were outputted for vibrational calculations (Fig. 4) at estimated mean errors of A) 2.0 cm-1 (259 data points), B) 0.33 cm-1 (435 data points).

                       A)
                       B)
Figure 4:  Plot of absolute errors for 216 vibrational levels (below 20000 cm-1). Variational     vibrational calculations were performed using a DVR and fitted PESs with mean estimated errors of: A) 2.0 cm-1, B) 0.33 cm-1.  Exact levels were benchmarked by the same DVR calculation using ab initio calculations at all 22400 DVR points.  Mean and maximum errors for levels computed with surface B are 0.10 and 0.41 cm-1.
Figure 5: Automatic PES generation for HOOH (6-D) required only 1400 points with value and gradient to acheive 0.1 kcal/mol RMS accuracy over a 100 kcal energy range. Numbers in parentheses refer to the HDMR basis set described in ref 3.

1.      Dawes R, Wagner A.F, Thompson D.L.
Wavenumber accurate ab initio potential energy surfaces for spectroscopy and dynamics calculations: converged vibrational levels computed using an IMLS-based automated potential energy surface generator (Max Wolfsberg Festschrift, JPC A.).

2.      Dawes R, Passalacqua A, Sewell T.D., Wagner A.F, Minkoff M., Thompson D.L.
Interpolating moving least-squares methods for fitting potential energy surfaces: using classical trajectories to explore configuration space. (JCP A08.08.0250).

3.      Dawes R, Thompson D.L, Wagner A.F, Minkoff M.
Interpolating moving least-squares methods for fitting potential energy surfaces: a strategy for efficient optimal data point placement in high dimensions. J. Chem. Phys. 128:084107 (2008).

4.   Dawes R, Thompson D.L, Guo Y, Wagner A.F, Minkoff M.
      Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from             low-density ab initio data points. J. Chem. Phys. 126:184108 (2007).

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