A New Ab Initio Potential Energy Surface for HCl-H2O, Diffusion Monte Carlo
Calculations of D0 and a Delocalized Zero-point Wavefunction
John S. Mancini and Joel M. Bowman*
Department of Chemistry and Cherry L. Emerson Center for Scientific Computation
Emory University, Atlanta, GA 30322
* Email address: jmbowma@emory.edu
Supplemental Material
Fitting Procedure
The data for fitting were obtained from geometries calculated using classical
direct-dynamic simulations, performed with density functional theory, B3LYP/ aug-ccpVTZ. These classical simulations began with a variety of different kinetic and potential
energies. Long-distance molecular configurations characterized by a HCl-H2O separation
greater than 5.5 Å were sampled by re-evaluating portions of the shorter-distance
geometries at increased intermolecular separation. The maximum Cl-O distance of the
fitted geometries was 12 Å. The surface fitting proceeded in the usual iterative fashion,
i.e., by 1) performing a preliminary fit, 2) testing the fit using classical trajectories and
DMC calculations of the ZPE and then 3) adding additional points in poorly described
areas and re-fitting. The process completes when the objectives are met. In the present
case, this is when the surface produces accurate properties of stationary points, yields
sensible classical trajectories up to around 15 000 cm-1 and dissociates smoothly with an
accurate description of the fragments.
Fitting Precision
A total of 44 637 configurations and energies were fit with a total RMS value of
24 cm-1. A plot of the energy as a function of the number of points and the respective
RMS fitting error is shown for a portion of the fitting data in Figure 1S. A separate set of
615 geometries ranging from 0 to 9000 cm-1 above the global minimum that were not
included in the fitting set was used to further test the surface. In the test set, the RMS of
geometries with energies greater than 3500 cm-1 increased as a function of the energy to a
maximum RMS of 80 cm-1 at 9000 cm-1. Given that the purpose of the surface is an
accurate description of the dissociation of the complex as well as a future goal of the IR
spectroscopy of experimentally relevant states, the present PES is adequate for these
purposes.
Diffusion Monte Carlo
DMC calculations were conducted in the standard way. In these calculations 30
000 “walkers” were equilibrated for 10 000 steps and propagated for 190 000 steps with a
step size of 2.5 imaginary atomic time units and an  of 2.5. The ZPE was determined by
performing 19 block averages of the trajectory and then taking the average of the 19
blocks to be the ZPE and the deviation in the blocks as the statistical uncertainty. The
value of the ZPE is within 3 cm-1 of simulations using a 5.0 imaginary atomic time unit
step size, thus assuring minimal systematic errors are present with the smaller step size.
Table 1S. Geometry (Å and degrees) of indicated configuration from ab initio
calculations and the potential energy surface for the global minimum, transition state and
dissociated monomers.
global minimum
saddle point
monomers
ab initio
PES
ab initio
PES
ab initio
PES
RHCl
1.292
1.292
1.289
1.289
1.277
1.277
ROH
0.960
0.960
0.959
0.959
0.959
0.956
θ1
105.15 105.12 105.64 105.67 104.44 104.45
θ2
135.63 135.87
180.0
179.93
-
-
θ3
177.96 177.43
180.0
180.0
-
-
R
1.902
1.916
1.917
-
-
1.903
Table 2S. Harmonic Frequencies (cm-1) for HCl35-H2O from ab initio calculations and the
PES for the global minimum, transition state and dissociated monomers.
global minimum
ab initio
PES
145
149
2.62
167
169
190
saddle point
% diff ab initio
monomers
PES
% diff
ab initio
PES
% diff
152i
161i
5.92
-
-
-
1.25
146
142
2.89
-
-
-
196
3.60
150
152
1.60
-
-
-
452
458
1.29
386
391
1.20
-
-
-
559
562
0.67
512
512
0.01
-
-
-
1647
1649
0.13
1644
1646
0.08
1650
1641
0.57
2800
2800
0.01
2841
2848
0.25
2994
2991
0.10
3826
3827
0.02
3838
3842
0.10
3835
3836
0.03
3940
3934
0.14
3948
3951
0.07
3944
3954
0.25
Figure 1S. Energy as a function of the number of points and the respective RMS fitting
error for a portion of the fitting data.
Figure 2S. Relaxed 1-D potential along the dissociation coordinate of the dimer
demonstrating smooth dissociation of the surface.