ADDITION/CORRECTION pubs.acs.org/JPCA
Correction to “Diffusion Monte Carlo Approaches for Evaluating Rotationally Excited states of Symmetric Top Molecules: Application to H3O+ and D3O+” [The Journal of Physical Chemistry A 2009, 113, 12706–12714. DOI: 10.1021/ jp905098k]. Andrew S. Petit, and Anne B. McCoy* We were missing the factor of 2 in the numerator of the exponent in eq 10 of this paper, and the equation in the manuscript is the equation that was used in the calculations. The corrected equation is
Precross
2meff ðτÞ dðτ þ δτÞ dðτÞ ¼ exp δτ
ð10Þ
We have repeated all of the calculations. In cases where the differences between the experimental and calculated energies were smaller than the uncertainty of the DMC simulations, this difference remains smaller than our statistical uncertainty. In cases where the difference between the experimental and calculated energies was larger than the uncertainties of the DMC simulations, this correction to the recrossing term has improved the agreement between experiment and theory substantially. Some representative comparisons are provided in Table A. Corrected versions of the original Tables 15 and Figures 1, 2, and 5 are also provided. Table A. Effect of the Correction to Precross on Deviation of Representative Calculated Rotational Energies from the Experimental Values1,2 statea
original Precross (cm1)b
corrected Precross (cm1)b
|1,1,0æH + |1,1,0æH |1,0,0æH |10,10,0æH + |10,10,0æH |10,0,0æH |1,1,0æD + |1,1,0æD |1,0,0æD |10,10,0æD + |10,10,0æD |10,0,0æD
0.63 ( 3.27 0.23 ( 2.78 0.62 ( 2.60 25.35 ( 2.06 24.61 ( 2.08 149.12 ( 5.12 0.31 ( 2.42 0.54 ( 2.80 0.63 ( 2.21 7.59 ( 1.79 8.12 ( 1.77 61.84 ( 2.87
2.47 ( 3.34 1.45 ( 3.17 0.93 ( 3.62 0.13 ( 2.13 0.61 ( 2.15 84.86 ( 2.52 1.19 ( 2.26 1.43 ( 3.06 1.03 ( 2.32 0.88 ( 1.80 0.54 ( 1.83 38.98 ( 2.22
a b States are identified as |J,K,MæH/D +/ . Reported error bars are combined 99% confidence intervals of the ground and rotationally excited states.
Table 1. Comparison between DMC and RVIB43 Energies (cm1) for J = 0 and J = 1 States H3O+
D3O+
state
DMCa,b
RVIB4b
DMCa,b
RVIB4b
|0,0,0æ |1,1,0æ+ |1,1,0æ |1,0,0æ
7452.51 ( 1.98 19.85 ( 3.34 18.84 ( 3.17 23.43 ( 3.62
7451 17.4 17.4 22.3
5474.62 ( 1.70 10.01 ( 2.26 10.26 ( 3.06 12.38 ( 2.32
5474 8.9 8.9 11.3
a Reported error bars are combined 99% confidence intervals of ground and rotationally excited states. b Excited state energies reported relative to ground state values.
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dx.doi.org/10.1021/jp2064886 | J. Phys. Chem. A 2011, 115, 9325–9327
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ADDITION/CORRECTION
Table 2. Comparison between DMC, Experimental,1,2 and Rigid Rotor Fit Energies (cm1) for States of H3O+ and D3O+ with J = 1 to J = 2 H3O+
D3O+
state
Ecalca,b
Ecalc Eexptc
Ecalc Efitd,e
Ecalca,b
Ecalc Eexptc
Ecalc Efitd,e
|1,1,0æ+ |1,1,0æ |1,0,0æ |2,2,0æ+ |2,2,0æ |2,1,0æ+ |2,1,0æ |2,0,0æ
19.85 ( 3.34 18.84 ( 3.17 23.43 ( 3.62 48.37 ( 2.81 47.14 ( 2.41 62.89 ( 2.48 62.61 ( 2.77 69.72 ( 3.42
2.47 ( 3.34 1.45 ( 3.17 0.93 ( 3.62 1.34 ( 2.81 0.12 ( 2.41 0.52 ( 2.48 0.24 ( 2.77 2.24 ( 3.42
1.44 ( 3.87 0.42 ( 3.72 0.21 ( 4.17 0.56 ( 3.87 0.66 ( 3.72 0.59 ( 4.46 0.87 ( 4.63 1.01 ( 5.41
10.01 ( 2.26 10.26 ( 3.06 12.38 ( 2.32 25.13 ( 2.33 24.38 ( 2.07 33.15 ( 2.29 32.39 ( 2.10 35.45 ( 2.73
1.19 ( 2.26 1.43 ( 3.06 1.03 ( 2.32 1.19 ( 2.33 0.44 ( 2.07 1.63 ( 2.29 0.87 ( 2.10 1.41 ( 2.73
0.37 ( 2.03 0.61 ( 2.89 0.08 ( 2.13 0.26 ( 2.03 0.48 ( 2.89 0.32 ( 2.61 0.43 ( 2.44 0.02 ( 3.16
a DMC energies reported relative to ground state values given in Table 1. b Reported error bars are combined 99% confidence intervals of ground and rotationally excited states. c DMC energies relative to experiment. d Rigid rotor fit based on calculated J = 0 to J = 2 DMC energies. e Reported error bars are combined 99% confidence intervals of DMC and rigid rotor fit.
Table 3. Parameters from Rigid Rotor Fits of the DMC Dataa,b,c H3O+
D3O+
fit parameter J = 0 to J = 2 E0 B
all states
J = 0 to J = 2
all states
7453.61 ( 2.55 7451.22 ( 1.73 5475.33 ( 1.28 5474.50 ( 1.02 11.27 ( 0.65 11.88 ( 0.05 5.79 ( 0.32 5.99 ( 0.03
C
6.04 ( 0.87
6.09 ( 0.04
3.14 ( 0.43
3.11 ( 0.02
Average values of B and C from the DMC ground state are 10.975 ( 0.015 and 6.116 ( 0.004 cm1 for H3O+ and 5.587 ( 0.006 and 3.100 ( 0.001 cm1 for D3O+. b DMC data fit to Efit(J,K) = BJ(J + 1) (B C) K2 + E0. c Fit parameters are reported in cm1 and error bars are 99% confidence intervals. a
Table 4. Comparison between DMC, Experimental,1,2 and Rigid Rotor Fit Energies (cm1) for States of H3O+ and D3O+ with J = 6 and J = 10 H3O+ state
Ecalc Eexptc
Ecalca,b
D3O+ Ecalc Efitd,e
Ecalca,b
Ecalc Eexptc
Ecalc Efitd,e
|6,6,0æ+
289.27 ( 2.19
0.96 ( 2.19
3.08 ( 31.55
147.41 ( 1.88
0.11 ( 1.88
1.16 ( 15.84
|6,6,0æ
289.39 ( 2.19
1.08 ( 2.19
3.20 ( 31.55
147.52 ( 1.89
0.22 ( 1.89
1.05 ( 15.84
|6,0,0æ |10,10,0æ+
492.49 ( 2.74 726.62 ( 2.13
22.13 ( 2.74 0.13 ( 2.13
18.18 ( 27.31 8.72 ( 86.98
248.62 ( 2.15 370.22 ( 1.80
10.78 ( 2.15 0.88 ( 1.80
4.52 ( 13.73 2.61 ( 43.68
|10,10,0æ |10,0,0æ
727.35 ( 2.15
0.61 ( 2.15
9.45 ( 86.99
370.56 ( 1.83
0.54 ( 1.83
2.27 ( 43.69
1306.97 ( 2.52
84.86 ( 2.52
66.53 ( 71.23
659.78 ( 2.22
38.98 ( 2.22
21.61 ( 35.89
a
DMC energies reported relative to ground state values given in Table 1. b Reported error bars are combined 99% confidence intervals of ground and rotationally excited states. c DMC energies relative to experiment. d Rigid rotor fit based on calculated J = 0 to J = 2 DMC energies. e Reported error bars are combined 99% confidence intervals of DMC and rigid rotor fit.
Table 5. Average Bond Lengths and Bond Angles of the J = 0 and J = 10 States of H3O+ and D3O+ a,b H3O+ ÆrOHæ (Å)
ÆθHOHæ ()
ÆrODæ (Å)
ÆθDODæ ()
|0,0,0æ+
0.99536 ( 0.00026
113.062 ( 0.041
0.99070 ( 0.00020
112.584 ( 0.031
|10,10,10æ+
0.00094 ( 0.00027
0.316 ( 0.043
0.00049 ( 0.00021
0.159 ( 0.031
|10,10,0æ
0.00101 ( 0.00027
0.318 ( 0.043
0.00049 ( 0.00021
0.158 ( 0.032
|10,10,10æ
0.00230 ( 0.00029
0.222 ( 0.045
0.00107 ( 0.00022
0.109 ( 0.034
state
a
D3O+
Reported error bars are 99% confidence intervals. b Geometric parameters of J = 10 states reported relative to ground state. 9326
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ADDITION/CORRECTION
Figure 1. Average energy in each of the nodal regions of (a) the |10,10,0æ and (b) the |10,0,0æ states of H3O+. The error bars represent 99% confidence intervals.
Figure 2. Average energy of the nodal regions of the |10,0,0æ state of (white H3O+ bound to the left by θ = 0 (black circles) or θ = θnode circles) for different values of θnode. Error bars represent 99% confidence intervals and the lines are least-squares fits of the DMC data.
Figure 5. Plots of the projections of the DMC probability amplitude onto Γ for (a) H3O+ and (b) D3O+. Results for the |0,0,0æ (black solid line), |10,0,0æ (gray dashed line), and |10,10,0æ+ (blue dash-dot-dot line) states are reported.
’ REFERENCES (1) Tang, J.; Oka, T. J. Mol. Spectrosc. 1999, 196, 120–130. (2) Araki, M.; Ozeki, H.; Saito, S. Mol. Phys. 1999, 97, 177–183. (3) Huang, X.; Carter, S.; Bowman, J. M. J. Chem. Phys. 2003, 118, 5431–5441. DOI: 10.1021/jp2064886 Published on Web 07/28/2011 9327
dx.doi.org/10.1021/jp2064886 |J. Phys. Chem. A 2011, 115, 9325–9327
