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: skodje@spot.colorado.edu (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.

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