A global potential energy surface for H2S X 4A and quasi classical trajectory study of the S 4S H2 X1 g reaction

Prévia do material em texto

Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=tmph20
Download by: [CAPES] Date: 30 November 2017, At: 07:09
Molecular Physics
An International Journal at the Interface Between Chemistry and
Physics
ISSN: 0026-8976 (Print) 1362-3028 (Online) Journal homepage: http://www.tandfonline.com/loi/tmph20
A global potential energy surface for H2S
+(X 4A′′)
and quasi-classical trajectory study of the S+(4S) +
H2(X
1Σ+g) reaction
Y. Z. Song, Y. Zhang, S. B. Gao, Q. T. Meng, C. K. Wang & M. Y. Ballester
To cite this article: Y. Z. Song, Y. Zhang, S. B. Gao, Q. T. Meng, C. K. Wang & M. Y.
Ballester (2018) A global potential energy surface for H2S+(X 4A′′) and quasi-classical
trajectory study of the S+(4S) + H2(X1Σ+g) reaction, Molecular Physics, 116:1, 129-141, DOI:
10.1080/00268976.2017.1369597
To link to this article: https://doi.org/10.1080/00268976.2017.1369597
View supplementary material 
Published online: 01 Sep 2017.
Submit your article to this journal 
Article views: 33
View related articles 
View Crossmark data
MOLECULAR PHYSICS, 
VOL. , NO. , –
https://doi.org/./..
RESEARCH ARTICLE
A global potential energy surface forH2S+(X 4A′′) and quasi-classical trajectory
study of the S+(4S) + H2(X1�+g ) reaction
Y. Z. Songa, Y. Zhanga, S. B. Gaoa, Q. T. Menga, C. K. Wanga and M. Y. Ballesterb
aSchool of Physics and Electronics, Shandong Normal University, Jinan, China; bDepartamento de Física, Universidade Federal de Juiz de
Fora-UFJF, Juiz de Fora, Brazil
ARTICLE HISTORY
Received  May 
Accepted  August 
KEYWORDS
Potential energy surface;
molecular dynamics; classical
trajectories
ABSTRACT
A novel global potential energy surface for H2S
+(X 4A′′) based on accurate ab initio calculations is pre-
sented. Energies are calculated at the multi-reference configuration interaction level with Davidson
correction using aug-cc-pVQZ basis set plus core-polarisation high-exponent d functions. A grid of
4552 points is used for the least-square fitting procedure in the frame of amany-body expansion. The
topographical features of the new potential energy surface are here discussed in detail. Such a sur-
face is then employed for dynamic studies of the S(4S) + H2(X 1�+g ) →SH+(X 3�−) + H(2S) reaction
using the quasi-classical trajectorymethod. State specific trajectories are calculated, for both ground
and ro-vibrationally excited initial states of H2(X
1�+g ). Corrections to the zero point energy leakage
of the classical calculations are also presented. Calculated reaction cross sections and rate constants
are here reported and compared with available literature.
1. Introduction
Reactions of atomic ions with hydrogen play an impor-
tant role in many interesting situations such as elec-
tric discharges, interstellar processes and planetary iono-
spheres [1–3]. Specially, the collision between a sulphur
cation with molecular hydrogen, has been devoted to a
large number of research work, mostly due to the possi-
ble role in the chemistry of interstellar clouds [4–6].
Related to H2S+, its emission spectrum between 4000
and 5000 A˚ was first observed by Horani et al. [7]
in a controlled electron excitation of H2S. However,
this emitter was not verified until photo-electron data
of H2S became available, which was later measured by
CONTACT M. Y. Ballester maikel.ballester@ufjf.edu.br
Supplemental material for this article can be accessed at https://doi.org/./...
Dixon and Duxbury [8]. By employing the optical and
photo-electron techniques, Duxbury et al. [9] studied
this radical in considerable detail. The structural data
of the electronic ground (X2B1) and excited (A2A1)
states were obtained from the vibronic structure of the
2A1 − 2B1 transition. By analysing a high-resolution
photo-electron spectrum of H2S, Delwiche et al. [10]
presented the ionisation energies and frequencies for
2B1, 2A1 and 2B2 states of H2S+ as well as the infor-
mation of S+ + H2 dissociation. By employing a mass-
analysed threshold ionisation, photo-fragment excitation
approach, Han et al. [11] investigated the A2A1 and X2B1
electronic states of H2S+ above the barrier to linearity.
©  Informa UK Limited, trading as Taylor & Francis Group
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
130 Y. Z. SONG ET AL.
More recently, Duxbury et al. observed the Renner–Teller
effect in the A2A1 and X2B1 electronic states of H2S+ [6].
Early ab initio calculations of the radical ion H2S+
were reported by Sakai et al. using unrestricted Hartree–
Fock method [12]. By varying the bond angle for fixed
bond lengths, the potential energy curves (PECs) for
all three 2B1, 2A1 and 2B2 states were calculated. Shih
et al. studied several number of excited states includ-
ing the first ionisation potentials by large-scale Config-
uration Interaction (CI) calculations [13]. Multireference
configuration interaction (MRCI) calculations were pre-
sented by Bruna et al. for the bending PECs and for sym-
metric and asymmetric stretching PECs near the equi-
librium geometry [14]. By using the coupled electron
pair electronic wave functions, Lahmar et al. calculated
the near-equilibrium potential energy surfaces (PESs)
for the two lowest doublet states, correspondingly X2B1
and A2A1 [15]. The PES of X2B1 state was then used to
generate the ro-vibrational energy levels up to 104cm−1.
The PESs for three lowest doublet states X2B1, A2A1
and B2B2 were obtained by Takeshita and Shida employ-
ing the CI calculations which include single and dou-
ble excitations from single reference configurations [16].
Using such obtained PESs, the equilibrium geometries,
ionisation energies, Franck–Condon factors and vibra-
tional frequencies were calculated. Hirst reported the
PESs for X2B1, A2A1, B2B2, 14A2 and 14B1 states of H2S+
by using ab initio calculation at MRCI/cc-pvQZ level of
theory [17]. By carefully examining the features of these
PESs, seams of intersection were characterised and the
conical intersection between the A2A1 and B2B2 states
was also located. Chang and Huang studied the photo-
dissociation from theA2A1 state using the complete active
space self-consistent-field (CASSCF) and multiconfigu-
ration second-order perturbation theory methods [18].
The experimental and theoretical works so far men-
tioned, were focused on the doublet states X2B1, A2A1
and B2B2 of the H2S+. Concerning the quartet state,
Stowe et al. examined the translational and electronic
energy dependence of the reaction S+(4S) + H2 and its
isotopic variants HD/D2 using guided-ion beam mass
spectrometry [5]. The reaction cross sections were mea-
sured covering translational energies from 0 − 13eV.
In such a work, one-dimensional PESs (reaction paths)
for the 4A′′ and 2A′′ states were also calculated and used
to locate stationary points. Recently, Zanchet et al. [19]
performed studies on the ground quartet (X4A′′) state of
H2S+. There, ab initio calculations were carried out at the
MRCI level of theory [20,21], including theDavidson cor-
rection [MRCI(Q)] [22], using the correlation-consistent
Dunning’s basis sets cc-pVQZ [23,24]. In that work [19],
around 3200 ab initio points were calculated for the X4A′′
state. Ab initio energies covering the range from the
minimum up to 96.85kcalmol−1 above the dissociation
channel S+(4S) + H2(X1�+g ), were fitted to an
analytic function developed by Aguado et al. [25–
27]. The overall root-mean-square error of the fitted PES
is 0.42 kcalmol−1. The so obtained PES of H2S+(X4A′′)
was then used for dynamic studies of the reaction
S+(4S) + H2(X1�+g ) → SH+(X 3�−) + H(2S), using
the quasi-classical trajectory (QCT) method.The reac-
tion rate constants, over a wide range of temperatures
(10–4000 K,) were also calculated for the ground and
vibrationally excited states of H2. Results showed that
such a reaction is endothermic for H2(v = 0, 1) while
it becomes exothermic for v � 2 [19]. More recently,
Zanchet et al. [28] reported a quantum and quasi-
classical study of title system using such a previous
reported PES [19]. In [28], the authors discussed the
role of H2 internal energy in reactive collisions with S+
and presented a comparison with the experimental cross
section.
The existing global PESs of H2S+(X4A′′), to the best
of our knowledge, are due to Hirst [17] and Zanchet
et al. [19], both based on the ab initio energies cal-
culated using the MRCI/cc-pvQZ (VQZ) level of the-
ory. However, for molecules containing the second-row
atoms, as discussed before [29,30], the calculations using
the standard correlation consistent basis sets will cause
errors in the dissociation energies. Thus, the aim of
this work is to construct a new and accurate PES for
H2S+(X4A′′) using aug-cc-pVQZ (AVQZ) basis set plus
core-polarisation high-exponent d functions AVQdZ as
recommended elsewhere [29–32]. Such a PES will then
be used for quasi-classical dynamic calculations.
The paper is organised as follows. Section 2 sum-
marises the ab initio calculations employed in the present
work. Section 3 describes the analytic representation
of the H2S+(X 4A′′) PES. The main topographical fea-
tures of the novel PES are discussed in Section 4,
while the molecular dynamics calculations for S+(4S) +
H2(X 1�+g ) reaction are reported in Section 5. The con-
cluding remarks are gathered in the last section.
2. Ab initio calculations
Ab initio calculations were carried out at the
MRCI(Q) [20,21] level using the full valence
CASSCF [33] wave function as reference. All calculations
were performed with the Molpro 2012 package [34]. In
the ab initio calculation, the Cs point group has been
adopted. AVQdZ basis set of Dunning [30] was used for
the S atom and AVQZ for the H atoms. In the CASSCF
calculations, the active space consists of six molecular
orbitals (MOs) for H2S+(X 4A′′), which correspond to
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 131
fiveA′ and oneA′′ symmetryMOs, totalling 181 (116A′ +
65A′′) configuration state functions. A grid of 4552 ab ini-
tio points was chosen to map the H2S+(X 4A′′) PES. The
grid was defined for the S − H2 channel as 0.6 ≤ RH2 (A˚)
�4.2, 0.1 ≤ rS−H2 (A˚) ≤ 7.5 and 0.0 ≤ γ (deg) ≤ 90;
While, 0.8 � RSH (A˚) �2.3, 0.1 � rH-SH (A˚) �7.5 and
0.0 ≤ γ (deg) ≤ 180 were defined for H − SH interac-
tions. As usual, R, r and γ are the atom–diatom Jacobi
coordinates for both dissociation channels.
3. Potential energy surface of H2S+(X 4A′′)
The global PES for the H2S+(X 4A′′) can be represented
through a many-body expansion (MBE) scheme [35–
37], which is written as the following analytic functional
form:
VABC(R) =
∑
A
V (1)A +
∑
AB
V (2)AB (RAB)
+V (3)ABC(RAB,RAC,RBC), (1)
where V (1)A (A = S+,Ha,Hb) represents the atomic
energy in their corresponding electronic states, V (2)AB
(AB = SH+a , SH+b ,HH) the diatomic term and V (3)ABC the
triatomic term.
The H2S+(X 4A′′) has the following dissociation
scheme:
H2S+(X 4A′′) →
⎧⎨⎩
H2(X 1�+g ) + S+(4S)
SH+(X 3�−) + H(2S)
S+(4S) + H(2S) + H(2S),
(2)
where S+ ion and two H atoms are all in their ground
states, which correspond to 4S and 2S, respectively. Since
the zero energy is set to the three-atom dissociation limit,
the atomic energies V (1)A (A = S+,Ha,Hb) in Equation–
(1) then equal zero.
The analytic expression of the diatomic terms (V (2)AB )
corresponding to SH+(X 3�−) and H2(X 1�+g ) is also
written as a sum of the short and long-range energy con-
tributions, which is then expressed as [25–27]
V (2)AB (RAB)=V (2)short(RAB) +V (2)long(RAB), (3)
where
V (2)short(RAB)=
a0
RAB
e−β
(2)
1 RAB, (4)
and
V (2)long(RAB)=
n∑
i=1
ai
(
RAB e−β
(2)
2 RAB
)i
, (5)
where RAB represents the diatomic internuclear
distances. The parameters a0, ai, β1 and β2 are obtained
by non-linear fitting of the calculated ab initio points. All
the parameters for diatomic PECs of SH+(X 3�−) and
H2(X 1�+g ) are gathered in Table 1 of the supplementary
material.
The three-body term (V (3)ABC) is written as the Mth-
order polynomial [25–27]
V (3)ABC(R¯)
=
{∑M
j,k,l=0Cjkl ρ
i
ABρ
j
ACρ
k
BC (k = l)∑M
j,k,l=0Cjkl ρ
i
AB(ρ
j
ACρ
k
BC + ρ jBCρkAC) (k �= l),
(6)
where R¯ = (RAB,RBC,RAC), ρAB=RAB e−β(3)ABRAB , which
also holds for the expressions of ρAC and ρBC. The coeffi-
cients Cjkl and β(3)AB are the linear and non-linear param-
eters to be determined in the fitting procedure. The two
expressions of Equation (6) are used to ensure the sym-
metric permutation of the two H atoms. The constraints
j + k + l � j � k � l and j + k + l � M are imposed to
warrant that the three-body term goes to zero for all dis-
sociation limits and when at least one of the internuclear
distances is zero. In the present work, we chooseM= 10,
which results in 140 linear coefficients Cjkl and two non-
linear parameters (i.e. β(3)SH and β
(3)
HH) to be determined
by fitting ab initio energies after subtracting of the two-
body energy contributions. The root-mean-squared devi-
ation (rmsd) of the final H2S+(X 4A′′) PES with respect to
all the fitted ab initio energies is collected in Table 1. As
shown in Table 1, a total of 4552 points are used in the
non-linear least-square fitting procedure, which cover an
Table . Root-mean-squaredeviations (in
eV) of HS+(X A′′) PES.
Energy(eV) Na rmsd N> rmsdb
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
.  . 
a Number of points in the indicated energy
range.
b Number of points with an energy deviation
larger than the rmsd.
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
132 Y. Z. SONG ET AL.
10-1
100
101
102
103
0.0 0.5 1.0 1.5 2.0
E/
eV
R/Å
-5
-4
-3
-2
-1
0
1
2
 H2(X 1∑+g)
E/
eV
-5.0
-2.5
0.0
2.5
5.0
0 1 2 3 4 5 6 7
er
ro
r/1
0−
4 e
V
R/Å
10-1
100
101
102
103
0.0 0.5 1.0 1.5 2.0
E/
eV
R/
-4
-3
-2
-1
0
1
2
 H+(X ∑ )
E/
eV
-10
-5
0
5
10
0 1 2 3 4 5 6 7
e
/1
eV
R/
(a) (b)
Figure . Potential energy curves of SH+(X �−) and H2(X
1�+g ). The circles indicate the MRCI(Q)/AVQdZ energies.
energy range up to 20.0eV above the H2S+(X 4A′′) global
minimum, showing high accuracy with the rmsd being
0.0277eV. All the coefficients of the three-body term are
gathered in Table 2 of the supplementary material.
4. Features of H2S+(X 4A′′) potential energy
surface
Displayed in Figure 1 are the H2(X 1�+g ) and
SH+(X 3�−) PECs. As shown in Figure 1, the two
PECs fit accurately the calculated ab initio energies,
showing also smooth behaviour both in short- and
long-range regions. From the SH+(X 3�−) PEC, the
equilibrium internuclear distance is Re = 1.3633 A˚ and
the dissociation energy De = 3.6803 eV, which com-
pares well with the experimental results Re = 1.3638 A˚
and De = 3.6999 eV [38]. The equilibrium internuclear
distance from H2(X1�+g ) PEC is Re = 0.7420 A˚ and
the dissociation energy De = 4.7325 eV, which are in
good agreement with the corresponding experimental
results [39]: Re = 0.7414 A˚ and De = 4.7399 eV, respec-
tively. The correspondingtheoretical results obtained by
Zanchet et al. [19] are Re = 1.3680 A˚ andDe = 3.6699 eV
for SH+(X 3�−), and Re = 0.7441 A˚ and De = 4.7299 eV
for H2(X1�+g ), respectively. Clearly, the equilibrium
diatomic internuclear distances and dissociation energies
obtained in the present work compare better with the
experimental values than those from the PES of Zanchet
et al. [19]. This is likely attributed to the different basis
set we used, which may produce different values, mostly
in the asymptotic dissociation channels. Notice here that
in the fitting, noad hoc parameters were introduced to
reproduce the experimental or other theoretical values.
Only data from our ab initio calculations was used.
Table 2 gathered the characteristics (geometries, ener-
gies and vibrational frequencies) of themajor interest sta-
tionary points for H2S+(X 4A′′) PES. For completeness,
properties from two stationary points from our ab initio
calculations are reported. At this point, it is worth men-
tioning that the ab initio geometry optimisation proce-
dures failed in finding all other structures collected in
Table 2, only Min2 and TS2 were successfully optimised.
The rather flat shape of the PES around such stationary
points difficults the geometry optmization in molecular
structure calculations.
Further, it must be remarked that in the paper intro-
ducing the H2S+ PES by Zanchet et al., no ab initio fea-
tures were reported for the three-body system. Topo-
graphical features are displayed in Figures 2 and 3. Specif-
ically, panel (a) of Figure 2 shows the contour plot for
bonds stretching in collinear [S − H − H]+ configura-
tions. From this figure, the notable feature is the existence
of C�v transition state (TS1) located at R1 = 0.746 A˚,
R2 = 2.921 A˚ and R3 = 3.667 A˚, see Table 2, where R1
is the HH interatomic distance, while R2 and R3 are the
two SH ones. Figure 2(b) displays the contour plot for
T-shaped insertion of S+ into H2 diatom. Visible from
such a figure are the stationary points corresponding to
the shallowC2v minimum (Min1),C�v minimum (Min2),
D�v and C2v transition state (TS2 and TS3) and C2v sad-
dle points (SP1 and SP2), see also Table 2. For the C2v
Min1, the geometry structure from the present PES com-
pares well with the result of Zanchet et al. Such a struc-
ture lies −0.1001eV relative to the S(4S) + H2(X1�+g )
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 133
Table . Attributes of stationary points on the HS+(X A′′) PES.
Method RH-H(A˚) RH−S+ (A˚) RH−S+ (A˚) E
a �Eb ω
c(cm−) ω
c(cm−) ω
c(cm−)
Cv Min
New PESd . . . −. −. . . .
Zanchet PESe . . . −.
H − S · · ·H C�v Min
New PESd . . . −. . . . .
Ab initio . . . −. . . . .
S · · ·H − H C�v TS
New PESd . . . −. −. . .i .
H − S − H D�v TS
New PESd . . . −. . . . .i
Ab initio . . . −. . . . .i
Zanchet PESe . . . .
Cv TS
New PESd . . . −. . . . .i
Cv SP
New PESd . . . −. . . .i .i
Cv SP
New PESd . . . −. . . .i .i
a Energies are relative to the S+(S) + H(S) + H(S) dissociation limit (in eV).
b Energies are relative to the S+(4S) + H2(X1�+g ) asymptote (in eV).
c Harmonic vibrational frequencies (in cm−1) for the symmetric (ω), bending (ω) and anti-symmetric (ω) motions.
d This work. The PES is obtained at MRCI(Q)/AVQdZ.
e Ref. []. The PES is obtained at MRCI(Q)/VQZ.
asymptote. Comparing with the result of Zanchet et al.,
the present PES predicts a slightly lowerwell depth, which
may due to the fact that the ab initio energies are cal-
culated using a larger basis set, AVQdZ. The D�v lin-
ear transition state (TS1) obtained from the present PES
locates at R1 = 3.077 A˚ and R2 = R3 = 1.538 A˚, with
the difference from the result of Zanchet et al. being
0.003 A˚ and 0.002 A˚, respectively. Moreover, the energy
of this D�v TS1 is 1.4071 eV, which differs by 0.0234 eV
from the result of Zanchet et al. Also shown in this fig-
ure are the C2v transition state (TS3) and saddle points
(SP1 and SP2). As shown in Figure 2(c), there exist two
equivalent C�v minimums (Min2) which are connected
by the D�v linear transition state (TS1). The C�v mini-
mum (Min2) is found to have a geometry R1 = 4.4534 A˚,
R2 = 1.366 A˚ and R3 = 3.088 A˚, and the energy 1.010eV
relative to the S(4S) + H2(X1�+g ) asymptote. The con-
tour plot for H atom attacking SH+ perpendicularly is
displayed in Figure 2(d). As depicted in the figure, there
exists a C2v transition state (TS3) when H atom attacks
SH+ perpendicularly. Panel (a) of Figure 3 displays the
contour plot for S+ atom moving around the HH diatom
with its internuclear distance being fixed at its equilib-
rium geometry RHH = 0.742 A˚, which lies along the
x-axis with the centre of the bond fixed at the origin.
The corresponding contour plot for the H atom moving
around a fixed SH+ diatom with the bond length fixed at
the corresponding equilibrium geometry RSH = 1.363 A˚
is shown in Figure 3(b). The two plots clearly reveal a
smooth behaviour both at short- and long-range regions,
warranting good performance of the present PES.
Figure 4 shows theminimumenergy paths (MEPs) cal-
culated on the present H2S+(X 4A′′) PES for the S+(4S) +
H2(X 1�+g ) → SH+(X 3�−) + H(2S) reaction as a func-
tion of RH2 − RSH+ . Panel (a) of Figure 4 displays the
MEP for the perpendicular configuration, �SHH= 90o,
while the equivalent MEP for a collinear approach,
�SHH= 180o is depicted in panel (b). In the minimisa-
tion of the potential energy for both the perpendicular
and collinear configuration, the �SHH angles are main-
tained fixed at 90o and 180o, respectively. At large negative
values of the reaction coordinates, the RH2 approaches
the corresponding equilibrium geometry for the reactant
channel, while the large positive values correspond to SH
approaching the equilibrium geometry for the product
channel. These two plots of MEPs represent the potential
energy of H2S+(X 4A′′) as a function of a suitable reac-
tion coordinate defined as RHH − RSH+ , where RSH+ and
RHH are the SH+ and HH internuclear distances, respec-
tively. As shown in Figure 4(a), there exists a large barrier
of about 2.06 eV, when S+ approachesH2 perpendicularly,
located at rSH+ = 1.624 A˚ and rHH = 1.410 A˚. As can be
seen from the MEP for the collinear approach depicted
in Figure 4(b), there is no barrier along the reaction path,
whereas the reaction shows the endothermic feature by
about 1.05 eV,which is still∼1.0 eV lower than the barrier
appearing in the perpendicular MEP. These characteris-
tics appearing in the PES will definitely influence the pro-
cess of dynamics for S(4S) + H2(X 1�+g ) reaction, which
favours the reaction through linear configurations. Also
significant from this figure is the slightly attractive char-
acter of the potential in the van der Waals region while
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
134 Y. Z. SONG ET AL.
1
2
3
4
5
6
0 1 2 3 4 5 6
R
2/Å
R1/Å
5
5
6 6
6 6
7
7 7
8
8
8
8
9
9
9 9
10 10
10 10 10
11
11 11 11
11 11
12
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
17
18
18
19
19
19
20
20 20
20 20
[S H H]+
R2 R1
0
1
2
3
4
5
6
0 1 2 3 4 5 6
y/
Å
x/Å
2
2
3 3
4
4
5
5
5
66
7
7
7
8
8
9
9
10
10
11
11
11
11
12
12
13
13
13
13
14
14
14
14
14
14
15
15
15
15
16
16
16
16
16
17
17
17
17
17
18
18
18
18
18
18
19
19 19
19
19
20
20 20
20
20
21
21
21
21
21
22
22
22
22
23
23
24
24
2425
25
26
26
27
27
27
28
28
29
29
30
30
30
31
31
32
32
H H
S+
x
y
1
2
3
4
5
6
1 2 3 4 5 6
R
3/Å
R2/Å
1
1
2
2
22
3
3
3 3 3
4
4
4 4 4
5
5
5 5 5
6
6
6
7
7
7
7
7
7
8
8
8 8
8
8
8
9 9
9
9 9
10
10
10 10 10
11
11
11
11
11
11
12
12 12
12
12 12
13
13 13
14
14
14 14
14
14
14
15
15 15
16
16 16
16
16
16 16
17
17
17
17
17
18
18
18 1819 19 19
20
20
20
21
21
21
22
22 2223 23
24
24
24
25
25
25
26
26 26
[H S H]+
R2 R3
1
2
3
4
5
6
1 2 3 4 5 6
y/
Å
x/Å
1
1
1
2
2
2
22
2
3
3
3
33
3 3
4
4
44
4
5
5
5
5
6
6
6
6
6 6
7
7
7
7
7
8
8
8
88
9
9
9
9
9
9
10 10
10
10
10
11
11 11 11
12
12
12
12
12
12
13
1313
13
13
1414
14
15
15 15
15
15
15
16
16
16
16
S H
H
x
y
(a) (b)
(c) (d)
Figure . (a) Contour plot for bond stretching in [S − H − H]+ linear configuration. (b) Contour plot for T-shaped insertion of S+ intoH2
diatom. (c) Contour plot for bond stretching in [H − S − H]+ linear configuration. (d) Contour plot for H atom attacking SH+ perpendic-
ularly. Contours are equally spaced by . eV, starting from−. eV for panel (a),−. eV for panel (b),−. eV for panel (c) and
−. eV for panel (d).
the PES from Zanchet et al. shows repulsive behaviour in
such a region (see Figure 1 fromRef. [19]). Again, this dif-
ference must be related to the larger basis set used here,
which is expected to more accurately describe the long-
range interaction region.
5. Dynamical calculations
Using the PES of H2S+(X 4A′′) presented here, molecular
dynamic studies were then carried out. The reaction cross
section and rate constant for the S+(4S) + H2(X 1�+g )→
SH+(X 3�−) + H(2S) reaction were investigated. For
such a goal, the QCT method [40–42] was used.
Trajectories were obtained using the MERCURY
program [43], accommodated to the PES.
From the PES and of interest for dynamical studies
is the predicted reaction enthalpy: �H00 =1.052eV.
This value compares well with the corresponding
ones reported in literature by Zanchet et al., �H00 =
1.059eV [19], Dibeler et al., �H00 =0.91eV [44] and
Prest et al., �H00 =0.93eV [45].
In trajectories, the reactants were initially separated by
a distance of 15 A˚,making the interaction energy between
themnegligible. Initial conditionswere selected following
normal modes energy sampling [43]. The time step used
for numerical integrationwas of 1.0 × 10−16s, whichwar-
rants the conservation of the total energy to be better than
1 : 103. The maximum impact parameter, for each trans-
lational energy, was obtained by the usual procedure of
calculating sets of 1000 trajectories at fixed values of b,
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 135
0
1
2
3
4
5
6
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
y/
Å
x/Å
H H
1 2 33
44 55 6
6
6
77
7
8
8
8
8
9
9
9
1010
10
10
10
11
1111
11
11 11
11
12
12
12
12
12
12
13
13
13
13
13
13
13
13
14
14
14
14
14
14
14
1415
15
15
15
15
15 15
1516
16
16
16
16
16 16
16
17 17
17
17
17
17
17
171
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
34 4
4
4
4
4 4
4
4
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
10 10
10
10
10
10
10
10
11
11
11
11
11
11
11
11
11
12
12
12
12
12
12
12
12
12
13
13
13
13
13 13
13
13
0
1
2
3
4
5
6
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
y/
x/
H
1
1
1
2
2
2
3
3
4
4
4
5
5
6
6
7
7 7
8
8
9
9
10
10
11
11
12
1213
14
14
15 15
16
16
17 17
18
19
1920
20
21
22
22
23
24
25
25
26
27 27
28
29 29
30
31
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3 3
3
34
4
4
4
4
4
4 4
4
5
5
5
5
5
5 5
5
6
6
6
6
6
6
6
6
67
7
7
7
7
7
7
78
8
8
8
8
8
8
8
8
9
9
9
9
9
9 9
10
10
10
10
10
10
10
11
11
11
11
11
12
12
12
12
12
13
13
13
14
14
14
15
16
17
17
18
19
20
21222324
25
27
2830
(a)
(b)
Figure . (a) Contour plot of potential energy when S+ moves around H diatom fixed at its equilibrium geometry RHH = . A˚ and lying
along the x-axis with the centre of the bond fixed at the origin. Contours are equally spaced by . eV, starting at−. eV. Shown
in dash are contours equally spaced by . eV, starting at −. eV. (b) Same as (a), but for H atom moving around SH+ fixed at its
equilibrium geometry RSH+ = 1.363 A˚. Contours are equally spaced by . eV, starting at−. eV. Shown in dash are contours equally
spaced by−. eV, starting at−. eV.
which is then reduced until the reaction takes place [46].
This procedure allows to determine bmax with an error of
0.1 A˚.
The reactive cross section is given by [41]
σR(Etr; vH2 ) = πb2max
NR
NT
(7)
and the associated uncertainty is
�σR =
(
NT − NR
NTNR
)1/2
σR, (8)
where NR is the number of reactive trajectories in a total
of NT, NR/NT is the reaction probability(PR).
The calculations have covered translational energies
over the range 1.0 � Etr(eV) � 12.0, for five vibrational
states of H2(v, j), vH2 = 0, 1, 2, 3, 4; j = 0 and five
rotational states of H2(v, j), jH2 = 0, 1, 2, 3, 4; v = 0.
Batches of 100, 000 trajectories were run for each
translational and vibrational energy combination. Such
a number produces a reactive cross section with an
error of typically a few per cent. Selected trajectory
calculation results are summarised in Table 3, full
results are collected in Table 3 of the supplementary
material.
5.1. Corrections to zero point energy leakage
Classical calculations does not forbid molecular systems
to have vibrational energies below the lowest value given
by the quantum calculations. This is usually referred to
as zero-point energy (ZPE) leakage. It must be remarked
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
136 Y. Z. SONG ET AL.
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
V/
eV
H|
S+ + H
H 
+
[S−H]+
(a)
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
-5 -4 -3 -2 -1 0 1 2 3 4 5
V/
eV
RH2−RSH+/Å
S++H−H
[S−H]++H
(b)
Figure . Minimum energy path for the S(4S) + H2(X 1�+g ) →
SH+(X �−) + H(S) reaction as a function of RH2 − RSH+ . (a) Per-
pendicular configurationŜHH angle α = . (b) Collinear config-
uration ŜHH angle α = .
Table . Results of trajectory calculations for title reaction
with H(v = , j = ) . Each batch is of NT = , 
trajectories.
Etr bmax/ QCT IEQMT
(eV) (A˚) NR NT NR
. .  ,  
. .  ,  
. .  ,  
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
. . ,  ,  , 
that previousworks dealingwith title systemhave not dis-
cussed this deficiency [19,28].
Several methodologies have been proposed to deal
with such a problem [47–49]. In this work, we used
the Internal Energy Quantum Mechanical Thresh-
old (IEQMT) [50] method. According to this procedure,
only the trajectories for which the internal energy of each
product exceeds its corresponding ZPEs are considered
in the statistical analysis. However, when this method is
applied here, a large number of non-reactive trajectories
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10 12
σ
R
 /Å
2
Etr/eV
H2(v=0,j=0)+S
+
 ➞ H+ HS+
QCT
IEQMT
GB
Figure . Cross section for the reaction H(v = , j = ) + S+ → H
+ HS+ obtained in QCT calculations (squares), using IEQMT (stars)
and GB (circles) methodologies, see text.
must be disregarded, leading to higher reaction proba-
bilities than pure QCT calculations, see Table 3. Note,
in Table 3, that all reactive trajectories meet the require-
ments of IEQMT, i. e. HS+ is always produced with an
internal energy larger than its ZPE. Of course, these cor-
rected calculations might be producing spurious results
once a large number of trajectories are neglected, there-
fore, perturbing considerably the sampling of reactants
initial conditions. This is significant, mostly, for H2(v =
0) and translational energies below 5.0eV.
Another methodology to overcome such a ZPE issue
of the QCT calculations is the Gaussian weighted bin-
ning (GB) [48,51,52]. In GB, each trajectory is assigned
a statistical weight given by a Gaussian function, centred
on the nearest vibrational quantumnumber. As suggested
elsewhere [52,53], for the Gaussian function, we used a
full width at half maximum, FWHM = 0.1. The QCT–
GB cross section is then obtained as
σGBR (Etr; vH2, jH2 ) = πb2max
∑NR
i ωR,i∑NT
j ω j
(9)
wereωR, i is the Gaussian weight of the ith reactive trajec-
tory and ωj is the corresponding weight for the jth trajec-
tory.
Figure 5 displays the results obtained from pure
QCT calculations, using IEQMT methodology and
GB. Previous works have reported an improvement
in classical calculations when using GB, particularly
for low relative energy of the reactants [52,54]. How-
ever, in corrected results using GB, specifically for
high total energies (see also Figures of the supplemen-
tary material), there is a significant and unexpected
increase in reaction probability. This can be ratio-
nalised as follows. For reactants with energy content
around the total dissociation (H + H + S+) threshold,
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 137
Ethat = 4.57eV trajectories may lead to intermediate con-
figurations with very large H − H distance (RH-H >
5 A˚). These trajectories were referred to as roaming in the
work of Zanchet et al. [28]. In a roaming non-reactive tra-
jectory, the H2 diatom is temporally split into two atoms;
however, in the course of the trajectory, they recom-
bine again going back to a configuration in the reac-
tants channel. The so recombined hydrogen molecule is
very unlikely to have vibrational energy above its ZPE.
The larger the impact parameter of this atom–atom colli-
sion, the larger the rotational energy, thus, the lower the
vibrational energy. Roaming reactive trajectories are less
affected by this leakage for two reasons: the sulphur atom
is bigger than hydrogen (see Figure 1) and ZPE value for
HS+ is smaller than the corresponding for H2.
Furthermore, from Table 3, it is verified that for
Etr� 5.0 eVmore than 75% of trajectories are considered
in IEQMT. Thus, for translational energies above such a
value, the statistical distribution of the reactants can be
considered as non-significantly perturbed.
Considering the above discussion, we found it appro-
priate to correct the ZPE leakage of the QCT calculations
using GB when the number of disregarded trajectories in
IEQMT is larger than 30%, and IEQMT for the remaining
cases. This combined correctionwill be heretofore named
as GB–IEQMT. Of course, to fully address this problem, a
comparison between the corrected results with quantum
dynamics calculations is desirable. Such a detailed study
is out of the goals of this work.
5.2. The role of reactants internal energy
Title reaction is an endoergic process. The role of
ro-vibrational energy content of H2 has already been
addressed by Zanchet et al. [28], using both quantum
and classical dynamics. In [28], the authors report a sig-
nificant increase in reactivity as vibrational or rotational
energy is deposited in H2. Besides, in such a work, a com-
parison between reactivity for similar internal energy dis-
tributed differently in the internal modes is presented.
Vibrational energy is reported as more efficient in rising
reactivity than rotational energy.
Figure 6 displays the state-specific excitation
functions obtained in this work after GB–IEQMT
correction. Figure 7 displays how the reaction cross
section is affected when H2 is initially excited, for six
different translational energies. From such figures, the
general behaviour is to get higher reaction cross section
as the internal energy of H2 is increased. This result was
expected also in the frame of Polanyi rule [55]. Also
from Figure 7, the role of initial ro-vibrational excitation
is more significant at lower translational energies. As
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12
σ
R
 /Å
2
Etr/eV
H2(v,j)+S
+
 ➞ H+ HS+
v=0,j=0
v=0, j=4
v=0,j=8
v=1, j=0
v=2,j=0
v=3, j=0
v=4,j=0
Figure . State-specific excitation functions. Values for the cross
sections correspond to GB–IEQMT corrected ones.
discussed in a previous work, at high values of transla-
tional energy, the collision time is not long enough as
to allow reorientation of the reactants while approach-
ing [56]. Further from Figures 6 and 7, it is possible to
verify that for H2(v = 0, j = 8) and H2(v = 1, j = 0) with
excitation energy of 0.76 and 0.77eV respectively, the
reaction cross section for the latter combination is larger
than for the former. Thus, we also verify that vibrational
energy is more efficient than the rotational counterpart
to promote reaction. This can be related to the presence
of a barrier (see Figure 4) for a perpendicular approach-
ing of S+ to H2 and the absence of a barrier for the
linear configuration. Increasing the internal energy of
H2 in the rotational degree will produce an oscillation
between the two cases displayed in Figure 4 as collision
partners approach. When there is no initial rotational
motion, the reactants tend to a linear orientation as
they approach each other, favouring then the reactive
channel.
The calculated reactive cross sections can then be
modelled by the following barrier-type excitation func-
tion [57,58]:
σR(Etr; vH2, jH2 ) = C(Etr − Ethtr )n exp[−m(Etr − Ethtr )]
(10)
where C, n and m are the least-squares parameters, Ethtr
is the translational energy threshold. As it has been pre-
viously remarked elsewhere [59], the value of Ethtr dic-
tates the slope of the calculated rate constant and is
hard to determine at the QCT level due to ZPE leak-
age.Following Ref. [59], we have then fixed its value
at the energy difference between products and reac-
tants once the zero-point energies are accounted for,
yielding Ethtr = 1.052, 0.536, 0.049 eV for vH2 = 0, 1, 2,
respectively. Table 4 collects the fitted coefficients for
these three vibrational states.
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
138 Y. Z. SONG ET AL.
Figure . Cross section for the reaction H(v, j) + S
+ → H + HS+ for different translational energies.
Table . Coefficients fitted from the calculated cross
section by Equation () to the function in Equa-
tion (). Units are such that the cross section comes
in A˚ when energy is in eV.
vH2
C m n
 . . .
 . . .
 . . .
0.0
0.5
1.0
1.5
2.0
2 4 6 8 10 12
σ
R
 
/Å
2
Etr/eV
H2(T=300K)+S
+
 ➞ H+ HS+
Stowe et al.
IEQMT
QCT
Figure . Thermally averaged cross section ( T = 300K) for the
reaction H2 + S+ → H + HS+ obtained in GB–IEQMT. For com-
parison, results from Stowe et al. Ref. [], are also presented.
Figure 8 displays the thermally averaged GB–IEQMT
cross section, obtained as
σR(Etr;T ) =
∑
j
Q j(T )σGB−IEQMTR (Etr; vH2 = 0, j)
(11)
where, Qj(T) is the H2 partition function for the j rota-
tional state, kB is the Boltzmann constant and T is the
temperature. The corresponding fitted function of these
values to the model in Equation (10) is shown. For com-
parison, the experimental values of the cross sections
from Stowe et al. [5] were also included in Figure 8. The
associated uncertainties of 20% they reported [5] are pre-
sented as well. Accordingly, we used T = 300K in Equa-
tion (11). For providing an estimate value of the error
of our results, we used averaged QCT results (without
ZPE corrections) as a reference, also included in Figure 8.
Thus, our recommended cross section is represented by
the filled region in the same figure. Notice further in
Figure 8, the unusual behaviour in the experimental cross
section. As discussed in [5], this issue is related to the
presence of excited sulphur cations in the ion beam.
Indeed, the data here reproduced corresponds to the S+
ions obtained from electron impact ionisation of CS2 at
electrons energyEe = 15.0 eV,which produces the lowest
relative population of excited sulphur ions [5]. Our results
predict larger reactivity than the corresponding from the
experiment, yet there is a reasonable agreement with such
results. Notice also the maximum in the cross section is
around 8eV for QCT and experimental values, while for
the corrected GB–IEQMT results, it is near 6eV.
Assuming aMaxwell–Boltzmann distribution over the
translational energy (Etr), the specific rate coefficient is
obtained as
k(T; vH2, jH2 ) = ge(T )
(
2
kBT
)3/2 ( 1
πμ
)1/2
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 139
10-14
10-13
10-12
10-11
10-10
10-9
 0.25 0.5 0.75 1
k(
T
)/
cm
3 
s-
1
1000/T(K)
H2(v)+S
+ ➞ H+ HS+
v=0
v=1
v=2
Figure . Rate constant for the reaction H(v = , , ) + S+ → H
+ HS+ obtained in QCT calculations. For comparison, QCT results
from Ref. [] are also displayed with squares (v= ), circles (v= )
and triangles (v= ).
×
∫ ∞
0
EtrσR(Etr; vH2 ) exp
(
− Etr
kBT
)
dEtr (12)
where T is the temperature, μ is the reactants reduced
mass and ge(T) is the electronic degeneracy factor [60,61].
Note that there is no spin-orbit splitting in the reactants.
In turn, S+(4S) and the complexH2S+(X 4A′′) are quartets,
producing ge(T) = 1.
By substituting Equation (10) into Equation (12) and
integrating, one gets
k(T; vH2, jH2 ) = ge(T )C
(
8kBT
πμ
)1/2
× (kBT )
n exp(−Ethtr /kBT )
(1 + mkBT )n+2
×
[
�(n + 2) + �(n + 1) (1 + mkBT )E
th
tr
kBT
]
(13)
where � is the Gamma function.
Specific rate constants, for vH2 = 0, 1, 2, jH2 = 0 cal-
culated are presented in Figure 9, for temperature in the
range 1000 − 4000K. Points in Figure 9 represent the
results from QCT calculations of Zanchet et al. [19].
Good agreements are observed when comparing results
for v= 2. However, for v= 0, 1, differences between both
results are significant. Such a divergence can be related
not only to differences in PESs but also to different mod-
els used in obtaining the rate constants from computed
cross section. As noticed before [59], the calculated rate
constants strongly depend upon the value used for the
threshold energy (Ethtr ), mostly at low temperatures. Pre-
cisely at low temperatures, large differences between both
results are observed.
As discussed in previous paragraphs, the rate constant
significantly increases whenmolecular hydrogen is vibra-
tionally excited. The corresponding values obtained for
the averaged cross section presented in Figure 8 do not
differ from k(T, vH2 = 0) displayed in Figure 9. Note fur-
ther that, according to these results, HS+ is very unlikely
to be produced at low temperatures, in the absence of
vibrationally excitedH2. Specific rate constants presented
here as functions of temperature can be recommended for
kinetics models.
6. Conclusions
We have reported a new global accurate PES for
H2S+(X4A′′) by fitting the ab initio energies calculated at
MRCI(Q)/AVQdZ level of theory, which is expected to be
realistic over the entire configuration space. The proper-
ties of the major stationary points, including geometries,
energies and vibrational frequencies, have been charac-
terised on the current H2S+(X4A′′) PES. The topolog-
ical features of the current PES show a proper behav-
ior over the short and long-range interaction regions.
By examining the MEPs for both the perpendicular and
collinear approach of sulphur to H2 diatom, it can be
concluded that the S+(4S) + H2(X 1�+g ) is endothermic
and favours the collinear abstraction scheme. The present
PES has been subsequently employed to carry out the
QCT calculation of the reaction cross section and specific
rate constants of S+(4S) + H2(X 1�+g ) → SH+(X 3�−)
+ H(2S). Ro-vibrationally excited H2 was also studied.
A discussion on ZPE corrections to QCT was also pre-
sented. Results obtained here overestimate the reactiv-
ity when compared with previous experimental results.
Yet, the calculated cross section reasonably agrees with
the experimental values. Finally, the function presented
here can also be used, within the MBE formalism, in
the construction of PESs for larger polyatomic molecular
systems.
Acknowledgments
Financial Support from China Postdoctoral Science Foun-
dation [grant number 2014M561957]; National Natural Sci-
ence Foundation of China [grant number 11304185]; Natu-
ral Science Foundation of Shandong Province [grant number
ZR2014AM022]; Shandong Province Higher Educational Sci-
ence and Technology Program [grant number J15LJ03]; Post-
Doctoral Innovation Project of Shandong Province [grant num-
ber 201402013] and FAPEMIG, Brazil is acknowledged.
Disclosure statement
No potential conflict of interest was reported by the authors.
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
140 Y. Z. SONG ET AL.
Funding
China Postdoctoral Science Foundation [grant number
2014M561957]; National Natural Science Foundation of
China [grant number 11304185]; Natural Science Foundation
of Shandong Province [grant number ZR2014AM022]; Shan-
dong Province Higher Educational Science and Technology
Program [grant number J15LJ03]; Post-Doctoral Innovation
Project of Shandong Province [grant number 201402013].
References
[1] W.W. Duley and D.A. Williams, Interstellar Chemistry
(Academic, New York, 1984).
[2] C.Y. Ng, J. Phys. Chem. A 106(25),5953 (2002).
[3] R. Martínez, J. Millán, and M. González, J. Chem. Phys.
120(10), 4705 (2004).
[4] D. Smith, N.G. Adams, and W. Lindinger, J. Chem. Phys.
75(7), 3365 (1981).
[5] G.F. Stowe, R.H. Schultz, C.A.Wight, and P. Armentrout,
Int. J. Mass Spectrom. Ion Phys. 100, 177 (1990).
[6] G. Duxbury, C. Jungen, A. Alijah, J. Maier, and D. Klap-
stein, Mol. Phys. 112(23), 3072 (2014).
[7] M. Horani, S. Leach, and J. Rostas, C. R. Acad. Sci. (Paris)
22, 2196 (1959).
[8] R. Dixon, G. Duxbury, M. Horani, and J. Rostas, Mol.
Phys. 22(6), 977 (1971).
[9] G. Duxbury, M. Horani, and J. Rostas, Proc. R. Soc. A,
Math. Phys. Eng. Sci. 331(1584), 109 (1972).
[10] J. Delwiche and P. Natalis, Chem. Phys. Lett. 5(9), 564
(1970).
[11] S. Han, T.Y. Kang, and S.K. Kim, J. Chem. Phys. 132(12),
124304 (2010).
[12] H. Sakai, S. Yamabe, T. Yamabe, K. Fukui, and H. Kato,
Chem. Phys. Lett. 25(4), 541 (1974).
[13] S. Kuo Shih, S.D. Peyerimhoff, and R.J. Buenker, Chem.
Phys. 17(4), 391 (1976).
[14] P.J. Bruna, G. Hirsch, M. Peric´, S.D. Peyerimhoff, and R.J.
Buenker, Mol. Phys. 40(3), 521 (1980).
[15] S. Lahmar, Z.B. Lakhdar, G. Chambaud, and P. Rosmus,
J. Mol. Struct. Theochem. 333, 29 (1995).
[16] K. Takeshita and N. Shida, Chem. Phys. 210(3), 461
(1996).
[17] D.M. Hirst, J. Chem. Phys. 118(20), 9175 (2003).
[18] H.B. Chang and M.B. Huang, Theoret. Chim. Acta
122(3–4), 189 (2009).
[19] A. Zanchet, M. Agúndez, V.J. Herrero, A. Aguado, and O.
Roncero, Astrophys. J. 146(5), 125 (2013).
[20] H.J. Werner and P.J. Knowles, J. Chem. Phys. 89, 5803
(1988).
[21] H.J. Werner and P.J. Knowles, Chem. Phys. Lett. 145, 514
(1988).
[22] S.R. Langhoff and E.R. Davidson, Int. J. Quantum Chem.
8(1), 61 (1974).
[23] T.H. Dunning Jr, J. Chem. Phys. 90, 1007 (1989).
[24] R.A. Kendall, T.H. Dunning Jr, and R.J. Harrison, J.
Chem. Phys. 96, 6769 (1992).
[25] A. Aguado and M. Paniagua, J. Chem. Phys. 96, 1265
(1992).
[26] A. Aguado, C. Suárez, and M. Paniagua, J. Chem. Phys.
98, 308 (1993).
[27] A. Aguado, C. Tablero, and M. Paniagua, Comp. Phys.
Comm. 108(2–3), 259 (1998).
[28] A. Zanchet, O. Roncero, and N. Bulut, Phys. Chem.
Chem. Phys. 18, 11391 (2016).
[29] J.M.L. Martin and O. Uzan, Chem. Phys. Lett. 282, 16
(1998).
[30] T.H. Dunning Jr., K.A. Peterson, and A.K. Wilson, J.
Chem. Phys. 114, 9244 (2001).
[31] Y.Z. Song and A.J.C. Varandas, J. Chem. Phys. 130(13),
134317 (2009).
[32] Y.Z. Song and A.J.C. Varandas, J. Phys. Chem. A 115(21),
5274 (2011).
[33] P.J. Knowles and H.J. Werner, Chem. Phys. Lett. 115, 259
(1985).
[34] H.J. Werner, P.J. Knowles, G. Knizia, F.R. Manby, M.
Schützet, P. Celani, W. Gyorffy, D. Kats, T. Korona, R.
Lindh, A. Mitrushenkov, G. Rauhut, K. R. Shamasun-
dar, T.B. Adler, R.D. Amos, A. Bernhardsson, A. Bern-
ing, D.L. Cooper, M.J.O. Deegan, A.J. Dobbyn, F. Eckert,
E. Goll, C. Hampel, A. Hesselmann, G. Hetzer, T. Hre-
nar, G. Jansen, C. Koppl, Y. Liu, A.W. Lloyd, R.A. Mata,
A.J. May, S.J. McNicholas, W. Meyer, M.E. Mura, A.
Nicklab, D.P. O’Neill, P. Palmieri, D. Peng, K. Pfluger,
R. Pitzer, M. Reiher, T. Shiozaki, H. Stoll, A.J. Stone, R.
Tarroni, T. Thorsteinsson, M. Wang, MOLPRO, version
2012.1, a package of ab initio programsCardiff, UK, 2012.
<http://www.molpro.net>.
[35] S. Carter, I.M. Mills, and J.N. Murrell, J. Mol. Spectrosc.
81, 110 (1980).
[36] J.N.Murrell, S. Carter, S.C. Farantos, P.Huxley, andA.J.C.
Varandas, Molecular Potential Energy Functions (Wiley,
Chichester, 1984).
[37] A.J.C. Varandas and J.N.Murrell, FaradayDiscuss. Chem.
Soc. 62, 92 (1977).
[38] J. Rostas,M.Horani, J. Brion, D. Daumont, and J.Malicet,
Mol. Phys. 52(6), 1431 (1984).
[39] K.P. Huber and G. Herzberg, Molecular Spectra and
Molecular Structure IV. Constants of Diatomic Molecules
(Van Nostrand Reinhold, New York, 1979).
[40] M. Karplus, R. Porter, and R.D. Sharma, J. Chem. Phys.
40, 2033 (1964).
[41] M. Karplus, R. Porter, and R.D. Sharma, J. Chem. Phys.
43, 3259 (1965).
[42] M. Karplus and K.T. Tang, Discuss. Farad. Soc. 44, 56
(1967).
[43] W.L. Hase, W.L. Hase, R.J. Duchovic, X. Hu, A.
Komornik, K.F. Lim, D.-H. Lu, G.H. Peslherbe, K.N.
Swamy, S.R. van de Linde, A. J.C. Varandas, H.Wang, R.J.
Wolf, MERCURY: a general Monte-Carlo classical trajec-
tory computer program, QCPE#453. An updated version
of this code is VENUS96, QCPE Bull 1996, 16, 43.
[44] V. Dibeler and S. Liston. J. Chem. Phys. 49(2), 482 (1968).
[45] H. Prest, W. Tzeng, J. Brom, and C. NG, Int. J. Mass Spec-
trom. Ion Processes 50(3), 315 (1983).
[46] W.A.D. Pires, J.D. Garrido,M.A.C. Nascimento, andM.Y.
Ballester, Phys. Chem. Chem. Phys. 16(25), 12793 (2014).
[47] A.J.C. Varandas, Int. Rev. Phys. Chem. 19, 199 (2000).
[48] L. Bonnet and J. Rayez, Chem. Phys. Lett. 277(1–3), 183–
190 (1997).
[49] W. Arbelo-González, L. Bonnet, P. Larrégaray, J.C. Rayez,
and J. Rubayo-Soneira, Chem. Physics 399(0), 117
(2012).
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
MOLECULAR PHYSICS 141
[50] A.J.C. Varandas, J. Brandão, and M.R. Pastrana, J. Chem.
Phys. 96, 5137 (1992).
[51] L. Bonnet and J.C. Rayez, Chem. Phys. Lett. 397, 106
(2004).
[52] P. Halvick, T. Stoecklin, P. Larrégarray, and L. Bonnet,
Phys. Chem. Chem. Phys. 9, 582 (2007).
[53] L. Bañares, F.J. Aoiz, P.Honvault, and J.M. Launay, J. Phys.
Chem. A 108, 1616 (2004).
[54] M.L. González-Martínez, L. Bonnet, P. Larrégaray, and
J.C. Rayez, J. Chem. Phys. 126(4), 041102 (2007).
[55] J.C. Polanyi, Acc. Chem. Res. 5(5), 161 (1972).
[56] M.Y. Ballester, Y. Orozco-Gonzalez, J. De Dios Gar-
rido, and H.F. Dos Santos, J. Chem. Phys. 132, 044310
(2010).
[57] R.L. LeRoy, J. Phys. Chem. 73, 4338 (1969).
[58] M.Y. Ballester, P.J.S.B. Caridade, and A.J.C. Varandas,
Chem. Phys. Lett. 439, 301 (2007).
[59] A.J.C. Varandas, P.J.S.B. Caridade, J.Z.H. Zhang, Q. Cui,
and K.L. Han, J. Chem. Phys. 125, 064312 (2006).
[60] D.G. Truhlar, J. Chem. Phys. 56, 3189 (1972).
[61] J.T. Muckerman and M.D. Newton, J. Chem. Phys. 56,
3191 (1972).
D
ow
nl
oa
de
d 
by
 [C
AP
ES
] a
t 0
7:0
9 3
0 N
ov
em
be
r 2
01
7 
	Abstract
	1.Introduction
	2.Ab initio calculations
	3.Potential energy surface of H2S+(X4A’’)
	4.Features of H2S+(X4A’’)nullpotential energy surface
	5.Dynamical calculations
	5.1.Corrections to zero point energy leakage
	5.2.The role of reactants internal energy
	6.Conclusions
	Acknowledgments
	Disclosure statement
	Funding
	References