Upload
michael-hayes
View
213
Download
1
Embed Size (px)
Citation preview
Chemical Physics 308 (2005) 259–266
www.elsevier.com/locate/chemphys
An improved potential energy surface for the FþH2 reaction
Michael Hayes a, Magnus Gustafsson a, Alexander M. Mebel b, Rex T. Skodje a,*
a Department of Chemistry and Biochemistry, University of Colorado, Campus Box 215, Boulder, CO 80309-0215, USAb Department of Chemistry and Biochemistry, Florida International University, Miami, FL 33199, USA
Received 1 October 2003; accepted 25 May 2004
Available online
Abstract
A new ground state potential energy surface has been developed for the FþH2 reaction. Using the UCCSD(T) method, ab initio
calculations were performed for 786 geometries located mainly in the exit channel of the reaction. The new data was used to correct
exit channel errors that have become apparent in the potential energy surface of Stark and Werner [J. Chem. Phys. 104 (1996) 6515].
While the entrance channel and saddlepoint properties of the Stark–Werner surface are unchanged on the new potential, the exit
channel behavior is more satisfactory. The exothermicity on the new surface is much closer to the experimental value. The new
surface also greatly diminishes the exit channel van der Waals well that was too pronounced on the Stark–Werner surface. Several
preliminary dynamical scattering calculations were carried out using the new surface for total angular momentum equal to zero for
FþH2 and FþHD. It is found that gross features of the reaction dynamics are quite similar to those predicted by the Stark–
Werner surface, in particular the reactive resonance for FþHD and FþH2 survive. However, the most of the exit channel van der
Waals resonances disappear on the new surface. It is predicted that the differential cross-sections at low collision energy for the
FþH2 reaction may be drastically modified from the predictions based on the Stark–Werner surface.
� 2004 Published by Elsevier B.V.
1. Introduction
The reaction dynamics of FþH2 and its isotopomers
has been extensively studied over many years [1–10]. The
repeated study of this prototype system illustrates the
iterative process generally required to bring theory into
quantitative agreement with experiment, and to fully
comprehend the underlying reaction dynamics [11,12].
Much of the current interest [13–23] in this system has
generated by the recent observation of a clear resonancesignature in the FþHD ! HFþD reaction [24–28]. It
has become clear that the unambiguous identification of
a resonance signature required a combined theoretical–
experimental effort. In particular, accurate dynamical
simulations were necessary to establish that distinctive
behavior observed in experiment could, in fact, be traced
to the influence of a resonance state existing on an
accurate potential energy surface (PES). For Fþ
* Corresponding author. Tel.: +1-303-492-8194; fax: +1-303-492-
5194.
E-mail address: [email protected] (R.T. Skodje).
0301-0104/$ - see front matter � 2004 Published by Elsevier B.V.
doi:10.1016/j.chemphys.2004.05.028
HD ! HFþD, it was found that the robust resonance
step observed in the excitation function was reproducedusing accurate scattering simulations [29] that employed
the Stark–Werner PES (SW-PES) [30]. Furthermore, the
characteristics of the step were traced back to a reso-
nance state at the collision energy EC ¼ 0:52 kcal/mol
with a lifetime of 109 fs using the spectral quantization
method [31] that also employed the SW-PES.
While the gross features of the reaction dynamics for
the FþHD and FþH2 systems were theoretically re-produced using the SW-PES [7,24,25,15], it was also
clear that there were a number of quantitative errors in
the predictions. For the differential cross-section (DCS)
in FþHD ! HFþD, the predicted degree of forward–
backward peaking at EC > 1 kcal/mol was substantially
different from experiment. Furthermore, the product
branching [28] into the FþHD ! DþHFðv0 ¼ 3Þchannel was seriously underestimated by theory. Evencertain features of the resonance step itself computed
from theory are slightly different from experiment.
Namely, the predicted step position is roughly 0.1 kcal/
mol too high in position and the predicted step height is
260 M. Hayes et al. / Chemical Physics 308 (2005) 259–266
about a factor 2 too high [24]. For the FþH2(para)
reaction, the calculated excitation function [15] shows
some noticeable quantitative differences with experiment
[28]. It is unlikely that the source of the discrepancy
between theory and experiment will be found in thedynamical simulation since the computation of the S-
matrix is apparently converged. Furthermore, although
the spin–orbit excited state Fð2P1=2Þ, designated as F�, isknown to be present in the beam source for the experi-
ment, it does not appear to play a very large role in the
observed scattering cross-sections [28], nor do theoreti-
cal calculations suggest that it can account for the dis-
crepencies [10,22]. The dominant cause of the observeddifferences, instead, is likely errors in the SW-PES for
the ground state of the reaction.
Although the SW-PES is accurate to about 150 cm�1,
it is widely appreciated that it has some deficiencies. The
spin–orbit coupling is expected somewhat increase the
barrier height. The surface of Hartke, Stark, and Wer-
ner [32] (HSW-PES) does in fact predict an increase in
the barrier height by about 0.4 kcal/mol. Unfortunately,the dynamical predictions of the HSW-PES are clearly
in worse agreement with experiment than the SW-PES,
and the threshold of excitation function for
FþHD ! HFþD (and DF+H) is much closer to the
predictions based on the SW-PES [24]. While the SW-
PES seems adequate for the entrance channel and the
barrier region (perhaps fortuitously), there are serious
problems in the exit channel. The exothermicity of thereaction is in disagreement with the known thermo-
chemistry by about 0.4 kcal/mol. This seemingly small
discrepancy can have serious dynamical consequences
due to its effect on the energetic thresholds of the reac-
tion, in particular the important FþHD ! HFðv0 ¼3Þ þD channel which opens at a collision energy of
EC ¼ 1:2 kcal/mol. Furthermore, Takayanagi and
Kurosaki [33] have raised suspicions concerning thepredicted van der Waals well of the SW-PES in the
H� � �HF channel. Using an estimate based on CCSD(T)/
aug-cc-pVTZ, these authors concluded that the vdW-
well was probably much less pronounced than predicted
by the SW-PES. The exit channel vdW-resonance states,
studied extensively by Manolopoulos and coworkers
and others [21,34,35], can have a profound effect on the
observed reaction dynamics. In particular, Chao andSkodje [13,15] obtained a highly structured DCS for the
FþH2 reaction in the energy range EC ¼ 0:3–0.9 kcal/
mol that was caused by the interfering contributions of a
reactive resonance (analogous to the EC ¼ 0:5 kcal/mol
resonance in FþHD) and an exit channel vdW-reso-
nance. The qualitative shape of the DCS would be en-
tirely different should the vdW-resonance disappear.
Motivated by these considerations, we have con-structed an improved PES that eliminates some of the
more serious deficiencies of the SW-PES. Ab initio cal-
culations employing the UCCSD(T) method and MRCI
with an active space of (722/1) were carried out in the exit
channel of the reaction and are discussed in Section 2.
The new data were used to generate a correction term to
the SW-PES in Section 3 that modifies the SW-PES only
in the exit channel region of configuration space. TheJ ¼ 0 dynamics for the FþH2 and FþHD reactions on
the new surface are compared to the previous SW-PES
results in Section 4. Section 5 is a brief conclusion.
2. Ab initio calculations of the FþH2 fiFHþH
potential energy surface for the exit channel
Comparison to experimental results suggests that the
Stark–Werner potential energy surface [30] well de-
scribes the entrance channel of the FþH2 ! FHþH
reaction and the vicinity of the saddle point. On the
other hand, the reaction exothermicity (excluding the
zero point energies) on the SW-PES is 31.3 kcal/mol,
which underestimates the experimental value of 31.73
kcal/mol. Another problem with the exit channel on theSW-PES, as noted above, is that it shows (apparently,
because of deficiencies of the analytical fit) an existence
of unphysical barrier between the FH� � �H van der
Waals complex and the FH+H products at large H–H
distances. This feature of the SW-PES is expected to
lead to an over estimation of the dynamical influence of
the FH–H vdW-complex in the full reaction dynamics.
These observations suggest that the SW-PES can beimproved for the exit channel. Stark and Werner used in
their calculations the internally contracted multirefer-
ence configuration interaction method with single and
double excitations and with Davidson’s correction for
quadruple excitations [36,37], MRCI+Q, with the (622/
2) active space, where the notation (nmm/kll) denotes a
space with n and m occupied r and p orbitals, respec-
tively, and the lowest kr and lp orbitals are closed-shell(inactive) in the reference wavefunction.
In our calculations, we employed the MRCI+Q
method with a larger (722/1) active space as well the
unrestricted coupled cluster method with single and
double excitations and perturbative treatment of triple
excitations, UCCSD(T) [38–40]. The basis sets used in
the calculations, Dunning’s augmented correlation-
consistent basis sets of quadruple, quintuple, and sex-tuple zeta quality [41], avqz, av5z, av6z, respectively,
were comparable with or larger than the basis sets em-
ployed by Stark and Werner. Table 1 shows the exo-
thermicity of the FþH2 ! HFþH reaction calculated
at the MRCI+Q(722/1) and UCCSD(T) level with var-
ious basis sets, with and without spin–orbit correction.
As one can see, the UCCSD(T) values with the spin–
orbit correction ()0.38 kcal/mol in experiment [42])eventually approach the experimental result for DHr as
the basis set increases from avqz to av5z and av6z.
Without the spin–orbit correction, the agreement with
Table 1
Exothermicity of the FþH2 ! FHþH reaction (Hr) and FH� � �H complex formation energy (in kcal/mol) calculated at the MRCI+Q(722/1) and
UCCSD(T) levels of theory with the avqz, av5z, and av6z basis sets
Method UCCSD(T) MRCI+Q(722/1)
Basis set avqz av5z av6z avqz av5z
DHra 31.76 (31.38) 31.86 (31.48) 31.93 (31.55) 32.13 (31.75) 32.24 (31.86)
Complex formation 0.32 0.31 0.30 0.29 0.27
Zero-point energies are excluded.aNumbers in parentheses show DHr values taking into account the spin–orbit correction, )0.38 kcal/mol.
M. Hayes et al. / Chemical Physics 308 (2005) 259–266 261
experiment worsens and the best value, 31.76 kcal/mol,
is obtained with the avqz basis set. At the MRCI+
Q(722/1) level, the most accurate DHr, 31.75 kcal/mol, isobtained with the spin–orbit correction and the avqz
basis set. However, if the spin–orbit correction is not
taken into account, the MRCI values overestimate the
experimental exothermicity by 0.4–0.5 kcal/mol. Both
UCCSD(T) and MRCI calculations with all three basis
sets show an existence of a FH� � �H van der Waals
complex at the H� � �H distance of about 4.35 bohr. At all
five levels of theory, the complex formation energy fromFH and H is in the narrow margins of 0.27–0.32 kcal/
mol (see Table 1) and the complex decomposes to
FH+H without an exit barrier, i.e. the PES for the exit
channel is smooth and does not show any artificial
‘‘bumps’’. The state-to-state energetics for various im-
portant processes are given in Table 2.
Obviously, MRCI+Q(722/1) calculations with spin–
orbit corrections represent the best choice to describethe entire FþH2 PES. However, for our purposes in
this study, we opted for the UCCSD(T)/avqz level of
theory without spin–orbit corrections. This rather eco-
nomic method accurately reproduces the reaction exo-
thermicity (although due to a fortuitous compensation
of errors) and properly describes the van der Waals
complex in the exit channel. In our calculations, we used
the grid points in terms of Jacobi coordinates R, r, anda, where R is the distance of the hydrogen atom to the
center of mass of the FH molecule, r is the FH bond
distance, and a is the angle between R and r. The fol-
lowing points were computed: (i) far region – R ¼ð7:1; 7:6; 8:5; 10:0; 12:0Þ bohr, r ¼ ð1:35; 1:45; 1:6; 1:735;1:85; 2:1; 2:4Þ bohr, a ¼ ð0; 30; 60; 90; 135; 180Þ degree;
(ii) van der Waals region – R ¼ ð4:8; 5:1; 5:4; 5:8;6:2; 6:6Þ, r ¼ ð1:35; 1:45; 1:6; 1:735; 1:85; 2:1; 2:4; 2:7Þ,a ¼ ð0; 30; 60; 90; 120; 150; 180Þ; and TS-product region
Table 2
State-to-state energetics for the FþH2 and FþHD reactions on the
SW-PES and the SWMHS-PES expressed in kcal/mol
Transition SW-PES SWMHS-PES
FþH2ð0; 0Þ ! HFð0; 0Þ þH )31.66 )32.13FþH2ð0; 0Þ ! HFð3; 0Þ þH 0.81 0.37
FþHDð0; 0Þ ! HFð0; 0Þ þD )30.84 )31.31FþHDð0; 0Þ ! HFð3; 0Þ þD 1.64 1.19
– R ¼ ð3:5; 3:75; 4:0; 4:25; 4:5Þ, r ¼ ð1:4; 1:6; 1:735; 1:9;2:1; 2:3; 2:5; 2:75Þ, a ¼ ð0; 30; 60; 90; 135; 180Þ; in total –
786 grid points.In the vicinity of the transition state, the UCCSD(T)
energies are inferior with respect to the MRCI energies
obtained by Stark and Werner (SW-PES). This state-
ment is supported by the fact that the potential energy
curve for the H–F bond rupture in FH calculated at the
UCCSD(T) level is non-parallel to the most accurate
curve obtained using the full configuration interaction
(FCI) method. According to the results of Dutta andSherill [43], significant deviations between the
UCCSD(T) and FCI relative energies of FH are found
for bond distances between 1.3 and 3.0 �A and the largest
error is 3.8 kcal/mol for r ¼ 2:0 �A. They concluded that
the nonparallelity errors of UCCSD(T) with respect to
FCI can reach 3–4 kcal/mol. Therefore, the UCCSD(T)
results in our calculations are expected to be less trust-
worthy than the SW-PES when the H–F bond distanceis 40% longer than its equilibrium value (0.918 �A) or
larger. Based on this, we introduced a weight function in
the fitting process to obtain our analytical fit of PES,
which emphasizes the UCCSD(T) results near the
equilibrium H–F bond length.
It should be also noted that although the UCCSD(T)
method may offer a better description of the PES in the
exit channel, it would be impossible to use this particularapproach to calculate the set of three global PESs for the
entire reaction, since two of the surfaces have the same
symmetry (A0) and the UCCSD(T) method in its present
realization cannot be applied for calculations of excited
electronic states. Furthermore, we do not expect that
any single reference method can improve the barrier
height (even if the spin–orbit correction is taken into
account) as compared to most accurate MRCI calcula-tions since the wavefunction in the vicinity of the tran-
sition state intrinsically has a multireference character.
3. Potential fitting
Since the SW-PES is apparently accurate in the en-
trance channel and the saddlepoint regions of configu-ration space, we have parameterized the new PES,
referred to as the SWMHS-PES, as
SWMHS-PES
3 6 9 12RH-FH [a0]
1.6
1.7
1.8
1.9
-32
-31
-30
-29
r FH [
a 0]
SW-PES
3 6 9 12RH-FH [a0]
1.6
1.7
1.8
1.9
-32.5
-31.5
-30.5
-29.5
r FH [
a 0]
(b)
(a)
Fig. 1. Contour diagrams of the SW-PES (a) and the SWMHS-PES
(b). The potentials (in kcal/mol) are plotted in the collinear space for
the HF+H exit channel.
262 M. Hayes et al. / Chemical Physics 308 (2005) 259–266
VSWMHS ¼ VSW þ DV : ð3:1ÞThe SW-PES, VSW, is augmented by a small correction
term DV that contributes only in the channels FHþH0
and FH0 þH. Thus the correction term, DV , is fit to thenew ab initio data points minus the SW-PES prediction
at that geometry. For most relevant geometries in the
exit channel we find that DV is less than 1 kcal/mol in
magnitude. The correction term also serves to implicitly
reduce the fitting errors that are suspected to exist in the
SW-PES itself.
The difference between the new ab initio points and
the SW-PES prediction is represented using a polyno-mial expansion of the form
f ðrHH0 ; rFH; rFH0 Þ ¼XM
i¼1
XN
j<k
cijkqiHH0 ðqj
FHqkFH0 þ qk
FHqjFH0 Þ
ð3:2Þwith qAB ¼ rABe
�aABrAB . This expression is symmetric
with respect to the two FH-bond lengths. Based on an
optimization in the collinear space, that factors aFH and
aFH0 are chosen to be 2.8 a�10 , while the aHH0 factor is set
to 1.0 a�10 . The expansion is taken to M ¼ 4 and N ¼ 5
to give a total of 105 parameters cijk that enter the ex-
pression in a linear fashion. To restrict the contributionof the correction term to exit channel, we multiply the
function f times switching functions to obtain
DV ðrHH0 ; rFH; rFH0 Þ ¼ u � v w � f ðrHH0 ; rFH; rFH0 Þ�
þ t�:
ð3:3Þ
Using the common form for a switching function
kðxÞ ¼ 1
2½tan hðxÞ þ 1� ð3:4Þ
we define
u ¼ 1� k 5ðrFHð � 10ÞÞk 5ðrFH0�
� 10Þ�; ð3:5Þ
v ¼ k 5ðrFHð � 1ÞÞk 5ðrFH0�
� 1Þ�
� k 5ðrHH0�
� 2:5Þ�k rHH0rFHrFH0�
� 15�; ð3:6Þ
w ¼ kð � 0:4ðrFH � 10ÞÞk�� 0:4ðrFH0 � 10Þ
�ð3:7Þ
t ¼ �7:505 � 10�4 k 4ðrFHð�
� 10ÞÞ þ k 4ðrFH0�
� 10��;
ð3:8Þ
where all quantities have been expressed in atomic units.
The coefficients cijk, defined in Eq. (3.2), are fit to the ab
initio data using a linear least squares procedure. Sincethe quantum chemistry calculations are known to ex-
hibit increasing error as the FH-bond distance increases
in the exit channel, the least-squares weighting factors
were chosen to fall off with distance from the equilib-
rium HF-bond distance, i.e. jrFH � 1:735 a0j. The dom-
inant contribution to the fitting comes from points
within 0.2 a0 of the reaction path. The average error
between the analytical expression and the new ab initio
data is less than 0.1 kcal/mol for the points used in the
fitting.
The resulting SWMHS-PES is virtually identical to
the SW-PES in the entrance channel. The characteristicsof the bent saddlepoint and the collinearly constrained
saddlepoint are likewise identical to those predicted by
the SW-PES. The exit channel for the new surface does,
however, exhibit significant improvement over the SW-
PES. The reaction exothermicity on the SWMHS-PES is
31.80 kcal/mol compared to 31.32 kcal/mol on the SW-
PES. The suspicious exit channel vdW well is also
greatly reduced. In Fig. 1, we show a contour diagram ofthe SWMHS-PES for FþH2 in the Jacobi coordinates
ðRH–FH; rFHÞ in the collinear geometry along with that
for the SW-PES. The much greater influence of the
vdW-well is apparent for the SW-PES. In Fig. 2, a one-
dimensional plot of the SWMHS-PES, the SW-PES, and
the ab initio data is shown for the equilibrium distance,
rFH ¼ 1:735 a0, in the collinear exit channel. It is seen
that the two surfaces converge near the steep repulsivewall, but exhibit a difference of about 0.4 kcal/mol fur-
SWMHSSWrFH = 1.735 a0γ = 0˚
3 6 9 12RH-FH [a0 ]
-35
-30
-25
V [k
cal/m
ol]
Fig. 2. The SWHMS-PES (solid line) and the SW-PES (dashed line) in
the HF+H exit channel for the collinear geometry and rFH held fixed
at the asymptotic equilibrium value of 1.735 a0. The corresponding
new ab initio data points are plotted with circles.
F + HD → HF + D (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.4
0.8
1.2
1.6
2.0
NR
F + HD → HF + D (J=0)
SWMHS
SW
0.4
0.6
0.8
P R (
tot)
(a)
(b)
M. Hayes et al. / Chemical Physics 308 (2005) 259–266 263
ther out in the channel. The spurious barrier to the
vdW-well has disappeared on the SWMHS-PES.
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.2
F + HD → HF + D (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.2
0.4
0.6
PR (
v')
v' = 0
v' = 1
v' = 2
v' = 3
(c)
Fig. 3. Reaction probabilities for FþHD ! HFþD with J ¼ 0 cal-
culated with the SWMHS-PES (solid lines) and the SW-PES (dashed
lines). (a) Cumulative reaction probability is plotted versus collision
energy. (b) Total reaction probability from the FþHDðv ¼ 0; j ¼ 0Þinitial channel versus collision energy is plotted. (c) Vibrational
branching for FþHDð0; 0Þ ! HFðv0; j0 ¼ allÞ þD is plotted versus
collision energy.
4. Dynamical simulations
In order to assess the impact of the modifications tothe potential surface upon the reaction dynamics, we
have carried out preliminary scattering calculations
making use of the new SWMHS-PES. The dynamical
simulations were done using the ABC-program of Ma-
nolopoulos and co-workers [29], using the same con-
vergence parameters as reported previously [13,15]. In
this report, we focus on the J ¼ 0 dynamics for the
FþH2 ! HFþH and FþHD ! HFþD reactions.While the J ¼ 0 dynamics alone is insufficient to address
the disagreement between theory and experiment, it does
provide a basis for comparison to the predictions of the
SW-PES.
We consider first the FþHD reaction that has been
previously shown to exhibit a strong signature of reac-
tive resonance. In Fig. 3(a), we show the cumulative
reaction probability, NR, as a function of collision en-ergy in kcal/mol for SWMHS-PES (solid line) along
with the result for the SW-PES (dashed line). It is seen
that except for the fine details the two surfaces yield very
similar results. In particular, the strong resonance peak
[24] near EC ¼ 0:5 kcal/mol is seen to survive on the
SWMHS-PES. The width of the resonance, 0.14 kcal/
mol, is slightly decreased and the resonance energy shifts
downward to 0.48 kcal/mol (compared to 0.52 kcal/molon the SW-PES). The resonance peak height is reduced
by about 10% due to the decrease in resonant tunneling
as the resonance energy falls further below the barrier
height. The total reaction probability from the F+HD
ðv ¼ 0; j ¼ 0Þ initial channel is shown in Fig. 3(b). Again
the SWMHS-PES and SW-PES are in qualitative
agreement with a similar shift of the resonance peak. We
note that the modifications to the resonance peak are
in the correct direction to improve agreement with
264 M. Hayes et al. / Chemical Physics 308 (2005) 259–266
experiment. The vibrational branching of the J ¼ 0 re-
action versus collision energy is depicted in Fig. 3(c).
The two surfaces are again seen to yield similar results.
Of course, for the SWMHS-PES the energetic threshold
for the HFðv0 ¼ 3Þ+D channel has shifted downward toEC ¼ 1:19 kcal/mol compared to 1.64 kcal/mol on the
SW-PES. However, for the J ¼ 0 dynamics the vibra-
tional branching into the v0 ¼ 3 state is quite low for
both surfaces.
The most dramatic difference between the dynamical
predictions of the two surfaces is the elimination of the
most of the narrow peaks for EC > 1 kcal/mol that were
due to vdW-states in the exit channel. Indeed, on theSWMHS-PES, only one such vdW-state survives at
EC ¼ 1:8 kcal/mol. The exit channel vdW-well on the
new surface is apparently too shallow to support the
progression of rotationally excited states observed for
the SW-PES.
The results for the J ¼ 0 reaction dynamics for the
case FþH2 are shown in Fig. 4. Again, the general
behavior of the reaction probabilities are similar for the
F + H2 → HF + H (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.4
0.8
1.2
1.6
2.0
NR
F + H2 → HF + H (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.2
0.4
0.6
0.8
1
PR (
tot)
(a)
(b)
Fig. 4. Reaction probabilities for FþH2 ! HFþH with J ¼ 0 calculated
(a) Cumulative reaction probability is plotted versus collision energy. (b) T
versus collision energy is plotted. (c, d) Vibrational branching for FþH2ð0;
two surfaces, although the differences are somewhat
greater than for the FþHD case. The cumulative re-
action probability and total reaction probability from
the ground state, Figs. 4(a) and (b) respectively, ob-
tained using the SWMHS-PES are much less structuredthan those obtained using the SW-PES. We note in
particular that the dramatic bimodal structure of NC
and PR (tot) near EC ¼ 0:5 kcal/mol obtained using the
SW-PES are replaced with a single peak on the
SWMHS-PES. In a previous work, Chao and Skodje
[13,15] argued that the bimodal feature of the SW-PES
dynamics was due to a transition state resonance at
EC ¼ 0:37 kcal/mol overlapping an H–FH vdW-state at0.62 kcal/mol. On the SWMHS-PES, the first (and ap-
parently only) vdW-state in the exit channel is shifted
much higher energy, EC ¼ 1:1 kcal/mol and does not
overlap the resonance peak. On the other hand, the
resonance peak at EC ¼ 0:4 kcal/mol is only slightly
perturbed by the modification to the potential. The vi-
brational branchings, FþH2 ! HFðv0Þ þH, shown in
Figs. 4(c) and (d), are significantly altered by the po-
(c)
(d)
F + H2 → HF + H (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.1
0.2
0.3
0.4
0.5
PR (
v')
P
R (
v')
v' = 0
v' = 3
F + H2 → HF + H (J=0)
SWMHS
SW
0.5 1.0 1.5 2.0 2.5 3.0Ec [kcal/mol]
0
0.2
0.4
0.6
0.8
v' = 1
v' = 2
with the SWMHS-PES (solid lines) and the SW-PES (dashed lines).
otal reaction probability from the FþH2ðv ¼ 0; j ¼ 0Þ initial channel0Þ ! HFðv0; j0 ¼ allÞ þH is plotted versus collision energy.
M. Hayes et al. / Chemical Physics 308 (2005) 259–266 265
tential change at low energies, EC < 1:5 kcal/mol. Again,
this behavior seems to trace to the disappearance of
most of the vdW-structure on the SWMHS-PES.
We note that the differences in reaction dynamics
incurred with the change in PES may be large enough toaffect the collision observables. For the FþH2 reaction,
the disappearance of most exit channel vdW-states is
likely to yield a qualitatively different DCS from that
predicted by the SW-PES at collision energies less than 1
kcal/mol. The FþHD reaction, while show less change
than the FþH2 case, may exhibit an observable differ-
ence in the vibrational branching due to the lowering of
the HFðv0 ¼ 3Þ+D energetic threshold on the SWMHS-PES. The J ¼ 0 dynamics does not provide a good test
in this regard, however, since the production of the
HFðv0 ¼ 3Þ product is expected to be greatest when
mediated through the reactive resonance which would
not become important until about J ¼ 15.
5. Conclusions
We have constructed a new ground state potential
energy surface for the FþH2 reaction that corrects
some of the deficiencies of the SW-PES. Ab Initio cal-
culations using the UCCSD(T) method were carried out
at 784 points in the exit channel arrangement. Using
these new calculations, a correction term to the SW-PES
was devised that improved the treatment of the reactionexothermicity and eliminated the spurious behavior as-
sociated with the H–HF vdW-complex. The influence of
the changes to the potential surface on the reaction
dynamics was assessed by examining the J ¼ 0 reactive
scattering. The gross features of the reaction dynamics
on the new SWMHS-PES were found to be similar to
those predicted on the SW-PES. In particular, the re-
active resonances for FþHD and FþH2 were found toremain intact on the new surface. However, most of the
vdW-states in the H–HF (and D–HF) exit channel
predicted by SW-PES were no longer supported on the
SWMHS-PES. For the FþH2 reaction in particular,
the disappearance of most of the vdW-states had a quite
profound influence on the reaction probabilities at low
energy. The results of Chao and Skodje [15] further
suggest that the differential cross-section for FþH2
should be significantly altered at low energy. If the DCS
is measured experimentally on a fine grid of energies for
EC < 1 kcal/mol, a rigorous test of the potential surface
should be possible.
The surface developed here is a hybrid obtaining by
combining quantum chemistry calculations carried out at
different levels that optimize distinct regions of configu-
ration space. The two set of result were merged along thesteep repulsive exothermic wall in the exit channel using
smooth switching functions that minimizes the inevitable
mismatch. Ultimately, of course, one expects that the
optimal treatment of the system will require a single high-
level calculation of all the relevant states including the
spin–orbit coupling. Until such calculations are avail-
able, however, the present surface provides a sensible
representation of the ground state reaction that is con-sistent with the experimental observations.
Acknowledgements
This work was supported by a grant from the Na-
tional Science Foundation. The authors are grateful to
Kopin Liu for useful discussions.
References
[1] J.H. Parker, G.C. Pimentel, J. Chem. Phys. 51 (1969) 91.
[2] G.C. Schatz, J.M. Bowman, A. Kuppermann, J. Chem. Phys. 63
(1975) 674.
[3] M.J. Redmon, R.E. Wyatt, Chem. Phys. Lett. 63 (1979) 209.
[4] D.M. Neumark, A.M. Wodke, G.N. Robinson, C.C. Hayden, R.
Shobatake, R.K. Sparks, T.P. Schafer, Y.T. Lee, J. Chem. Phys.
82 (1985) 3045.
[5] G.C. Lynch, R. Stechler, D.W. Schwenke, A.J.C. Varandas, D.G.
Truhlar, J. Chem. Phys. 94 (1991) 7136.
[6] M. Faubel, L. Rusin, S. Schlemmer, F. Sondermann, U. Tappe,
J.P. Toennies, J. Chem. Phys. 101 (1994) 2106.
[7] J.F. Castillo, D.E. Manolopoulos, K. Stark, H.J. Werner, J.
Chem. Phys. 104 (1996) 6531;
F.J. Aoiz, L. Banares, V. Herrero, K. Stark, H.J. Werner, Chem.
Phys. Lett. 254 (1996) 341.
[8] J.M. Launay, M. Le Dourneuf, Chem. Phys. Lett. 169 (1990) 473.
[9] D.H. Zhang, S.Y. Lee, M. Baer, J. Chem. Phys. 112 (2000) 9802.
[10] M.H. Alexander, D.M. Manolopoulos, H.J. Werner, J. Chem.
Phys. 113 (2000) 11084.
[11] K. Liu, Annu. Rev. Phys. Chem. 52 (2001) 139;
P. Casavecchia, Rep. Prog. Phys. 63 (2000) 355;
F. Fernandez-Alonso, R.N. Zare, Annu. Rev. Phys. Chem. 53
(2002) 67;
S.C. Althorpe, D.C. Clary, Annu. Rev. Phys. Chem. 54 (2003) 494.
[12] F.J. Aoiz, L. Banares, J.E. Castillo, M. Brouard, W. Denzer, C.
Vallance, P. Honvault, J.M. Launay, A.J. Dobbyn, P.J. Knowles,
Phys. Rev. Lett. 86 (2001) 1729;
S.C. Althorpe, F. Fernandez-Alonso, B.D. Bean, J.D. Ayers, A.E.
Pomerantz, R.N. Zare, E. Wrede, Nature 416 (2002) 67;
F. Fernandez-Alonso, B.D. Bean, R.N. Zare, F.J. Aoiz, L.
Banares, J.F. Castillo, J. Chem. Phys . 114 (2001) 4534;
S.A. Harich, D. Dai, C.C. Wang, X. Yang, S.D. Chao, R.T.
Skodje, Nature 419 (2002) 281;
S.D. Chao, S.A. Harich, D.X. Dai, C.C. Wang, X. Yang, R.T.
Skodje, J. Chem. Phys. 117 (2002) 8341;
D. Dai, C.C. Wang, S.A. Harich, X. Yang, S.D. Chao, R.T.
Skodje, Science 300 (2003) 1730.
[13] S.D. Chao, R.T. Skodje, J. Chem. Phys. 119 (2003) 1462.
[14] T. Alferova, S. Andersson, N. Elander, S. Levin, E. Yarevsky,
Few Body Syst. 31 (2002) 177.
[15] S.D. Chao, R.T. Skodje, J. Chem. Phys. 113 (2000) 3487.
[16] S.C. Althorpe, Chem. Phys. Lett. 370 (2003) 443;
J. Phys. Chem. A 107 (2003) 7152.
[17] V. Aquilanti, S. Cavalli, D. De Fazio, A. Volpi, A. Aguilar, X.
Gimenez, J.M. Lucas, Chem. Phys. Lett. 371 (2003) 504;
Phys. Chem. Chem. Phys. 4 (2002) 401.
[18] T. Takayanagi, A. Wada, Chem. Phys. Lett. 348 (2001) 514.
266 M. Hayes et al. / Chemical Physics 308 (2005) 259–266
[19] M.H. Alexander, D.M. Manolopoulos, H.J. Werner, J. Chem.
Phys. 113 (2000) 11084.
[20] W.W. Harper, S.A. Nizkorodov, D.J. Nesbitt, J. Chem. Phys. 116
(2002) 5622.
[21] S.D. Chao, R.T. Skodje, Theor. Chem. Acc. 108 (2002) 273.
[22] T.X. Xie, Y. Zhang, M.Y. Zhao, K.L. Han, Phys. Chem. Chem.
Phys. 5 (2003) 2034.
[23] W.B. Zeimen, J. Klos, G.C. Groenenboom, A. van der Avoird, J.
Chem. Phys. 118 (2003) 7340.
[24] R.T. Skodje, D. Skouteris, D.E. Manolopoulos, S.-H. Lee, F.
Dong, K. Liu, J. Chem. Phys. 112 (2000) 4536.
[25] R.T. Skodje, D. Skouteris, D.E. Manolopoulos, S.-H. Lee, F.
Dong, K. Liu, Phys. Rev. Lett. 85 (2000) 1206.
[26] K. Liu, R.T. Skodje, D.E. Manolopoulos, Phys. Chem. Commun.
4 (2002) 27.
[27] S.H. Lee, F. Dong, K. Liu, J. Chem. Phys. 116 (2002) 7839.
[28] F. Dong, S.H. Lee, K. Liu, J. Chem. Phys. 113 (2000) 3633.
[29] D. Skouteris, J.F. Castillo, D.E. Manolopolous, Comput. Phys.
Commun. 113 (2000) 128.
[30] K. Stark, H.-J. Werner, J. Chem. Phys. 104 (1996) 6515.
[31] R. Sadeghi, R.T. Skodje, J. Chem. Phys. 102 (1995) 193;
R. Sadeghi, R.T. Skodje, J. Chem. Phys. 99 (1993) 5126;
R. Sadeghi, R.T. Skodje, Phys. Rev. A 52 (1995) 1996;
R.T. Skodje, R. Sadeghi, H. Koppel, J.L. Krause, J. Chem. Phys.
101 (1994) 1725.
[32] B. Hartke, H.J. Werner, Chem. Phys. Lett. 280 (1997) 430.
[33] T. Takayanagi, Y. Kurosaki, Phys. Chem. Chem. Phys. 1 (1999)
1099.
[34] D.E. Manolopoulos, J. Chem. Soc., Faraday Trans. 93 (1997) 973.
[35] J.F. Castillo, D.E. Manolopoulos, Faraday Discuss. 110 (1997)
119.
[36] H.-J. Werner, P.J. Knowles, J. Chem. Phys. 89 (1988) 5803.
[37] P.J. Knowles, H.-J. Werner, Chem. Phys. Lett. 145 (1988) 514.
[38] G.D. Purvis, R.J. Bartlett, J. Chem. Phys. 76 (1982) 1910.
[39] M. Rittby, R.J. Bartlett, J. Phys. Chem. 92 (1988) 3033.
[40] K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon,
Chem. Phys. Lett. 157 (1989) 479.
[41] T.H. Dunning Jr., J. Chem. Phys. 90 (1989) 1007.
[42] C. Moore, Natl. Bur. Stand. (US) Circular (1952) 467.
[43] A. Dutta, C.D. Sherrill, J. Chem. Phys. 118 (2003) 1610.