- 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.
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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. |
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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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