Globally Accurate Potential Energy Surface for HCS(A2Aâ²â²) by

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Globally Accurate Potential Energy Surface for HCS(AA ##) by Extrapolation to Complete Basis Set Limit Lu-Lu Zhang, Yu-Zhi Song, Shou-Bao Gao, and Qing-Tian Meng J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02131 • Publication Date (Web): 16 Apr 2018 Downloaded from http://pubs.acs.org on April 16, 2018

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The Journal of Physical Chemistry

(Submitted to J. Phys. Chem. A.)

Globally Accurate Potential Energy Surface for HCS(A2A′′) by Extrapolation to Complete Basis Set Limit Lu Lu Zhang, Yu Zhi Song, Shou Bao Gao, and Qing Tian Meng∗ School of Physics and Electronics, Shandong Normal University, Jinan 250358, China ABSTRACT: A global potential energy surface (PES) representation of the C(3 P) + SH(X 2 Π) → H(2 S) + CS(a 3 Π) system is developed by fitting a wealth of accurate ab initio energies calculated at the multireference configuration interaction level using aug-cc-pVQZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical features of the present PES are examined in detail and found to be in good agreement with previous calculations available in the literature. By utilizing the PES of HCS(A2 A′′ ), the corresponding reaction is investigated using quasi-classical trajectory (QCT) method in the collision energy range of 0.08 - 1.0 eV. The minimum energy paths (MEPs) calculated based on the present PES indicate that the titled reaction is exothermic, with the exothermicity being ∼ 0.204 eV. The calculation for the capture time indicates that at lower collision energy, the reaction is mainly governed by the indirect mechanism, while for higher collision energy, the direct mechanism and indirect mechanisms coexist with the latter being the dominant contributor.

1. INTRODUCTION The hydrogen, carbon, and sulfur are among the nine most abundant atoms in our universe. As the simplest neutral molecules containing these three atoms, the thioformyl (HCS) and isothioformyl (HSC) not only are the fundamental reaction intermediate in combustion processes,1 but also play an important role in molecular formation processes ∗

Corresponding author: [email protected].

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at interstellar clouds.2 Kaiser and co-workers1, 3, 4 demonstrated that HCS and HSC can be formed in the plume chemistry of Shoemaker-Levy 9 fragments during impacting into Jupiter. After carrying out the crossed molecular beams experiments and ab initio calculations, they found that in the shocked jovian atmosphere, HCS could further decompose to H and CS, and CS could react with SH and OH to yield the observed CS, and COS. In 1983, the equilibrium geometries for the 2 A′′ electronic states of HCS were firstly predicted by Goddard5 using the single-double configuration interaction (SDCI) method with a double-zeta basis. The predicted equilibrium structures from the CI calculations are: RCS = 2.941 a0 , RCH = 2.015 a0 , and αHCS = 180o . Stoecklin et al.6–8 investigated two analytic models of the lowest PES of the SH(X 2 Π) + C(3 P ) → H(2 S) + CS(X 1 Σ+ ) reaction using the MNDO/CI method, and found that three transition states connect the HCS to HSC and ground-state products. Senekowitsch et al.9 calculated the threedimensional multiconfiguration self-consistent field (MCSCF) CI potential energy, electric dipole and electronic transition moment functions for the X 2 A′ and A2 A′′ electronic states of the HCS. They also reported that in linear geometry the two lowest X 2 A′ and A2 A′′ states become degenerate components of the 2 Π state and exhibit a strong Renner–Teller coupling effect. The calculated equilibrium geometries for HCS(2 A′′ ) are: RCH = 2.009 a0 , RCS = 2.943 a0 , and αHCS =180o . In 1993, the transient species HCS was identified as the reactive intermediate in hydrogen abstraction reaction of methyl mercaptane (CH2 SH) by means of photoionization mass spectroscopy.10 HCS, HSC, and the corresponding cationic species were also investigated by Curtiss et al.,11 who performed a theoretical study of the organo-sulfur systems CSHn (n = 0 − 4) and CSn (n = 0 − 5). The dissociation and ionization energies, as well as enthalpies of formation were calculated. Habara et al.12–15 detected microwave transition of the HCS, HSC, H13 CS and HS13 C in the X 2 A′ ground electronic state. Ochsenfeld et al.16 calculated the structural data, dipole moments, rotational constants, vibrational frequencies, and zero-point energies of X 2 A′ using coupled cluster (CC) theory. In the same year, Chen et al.17 presented the hyperfine structure of the HCS and the isovalent HCO, HSiS and HSiO using the density functional theory (DFT) and multi-reference single and double excitation configuration interaction (MRS-

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DCI) methods. Voronin18 reported a global analytical PES corresponding to the lowest adiabatic X 2 A′ state of HCS using a grid of 1357 energy points calculated at the MRCI level in conjunction with the aug-cc-pVT Z basis set. By employing the PES, the main stationary points of the X 2 A′ surface were also evaluated. Puzzarini19 also studied the isomer pair HCS/HSC by means of a highly accurate level of theory. They used the CC method in conjunction with correlation consistent basis sets ranging in size from quadruple to sextuple zeta for all the species to investigate the near-equilibrium PES. Mitrushchenkov et al.20 calculated spin-orbit constants, dipole moments and carbon-sulphur distances for HCn S (n = 1 − 12) in the 2 Π electronic ground state using the Hartree Fock (HF), complete active space self-consistent field (CASSCF) and MRCI methods with different basis sets. Recently, our group reported an accurate global adiabatic PES for the ground state of HCS, building which both aug-cc-pVQZ (AVQZ) and aug-cc-pV5Z (AV5Z) atomic basis sets have been employed.21 In order to improve the accuracy of PES, such obtained ab initio energies are then extrapolated to the complete basis set. The cited above shows that most of the works are mainly on the ground state (X 2 A′ ) PES or the equilibrium structures of the excited state(A2 A′′ ). To our knowledge, no global full dimensional PES has so far been reported for the A2 A′′ state of HCS. Such scarcity of electronic structure calculations on the three-dimensional configuration space of A2 A′′ state has prompted us to model a global PES for the titled species. The major goal of the present work is to built an accurate global adiabatic PES for the excited state of HCS based on many-body expansion (MBE) scheme with both AVQZ and AV5Z atomic basis sets. In order to improve the accuracy of PES, such calculated ab initio energies are subsequently extrapolated to complete basis set (CBS) limit. Based on the new adiabatic PES, the reaction dynamics of C(3 P ) + SH(X 2 Π) → H(2 S) + CS(a 3 Π) reaction is investigated using quasi-classical trajectory (QCT) method. The paper is organized as follows. Section 2 provides a description of the ab initio calculations, CBS extrapolation scheme, analytical PES function using MBE, as well as the QCT method. The main topographical features of the PES and the reaction dynamics are examined in Sec. 3, and some conclusions are gathered in Sec. 4.

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2. METHOD 2.1. Ab Initio Calculations and Extrapolation to CBS Limit All electronic structure calculations are carried out at the MRCI level22, 23 including the Davidson correction [MRCI(Q)],24 taking the full valence CASSCF25 wave function as the reference. It is worth noting that the H and C atoms are calculated using AVQZ and AV5Z basis sets and S atom is determined using AVQdZ and AV5dZ basis sets of Dunning26, 27 with MOLPRO 2012 package.28 A grid of 6209 ab initio points are chosen to map the PES over the H - CS, C - SH, and S-CH regions shown in Table 1. In quantum chemistry, calculations of molecular properties are all performed by using a finite set of basis functions, which may inevitably lead to the basis-set superposition error (BSSE). As the atoms of interacting molecules (or of different parts of the same molecule) approach one another, their basis functions overlap. Each monomer “borrows”functions from other nearby components, effectively increasing its basis set and improving the calculation of derived properties such as energy. If the total energy is minimized as a function of the system geometry, the short-range energies from the mixed basis sets must be compared with the long-range energies from the unmixed sets, and this mismatch introduces an error. However, as discussed by Varandas,29 the BSSE can be corrected by extrapolating the ab initio to the CBS limit, which suggests that a dual-level approach is referred to as uniform singlet- and triplet-pair extrapolation (USTE) protocol.30 The MRCI(Q) energy is treated as usual in split form by writing30–33 CAS dc EX (R) = EX (R) + EX (R),

(1)

where the subscript X indicates that the energy is calculated in the AVXZ basis, and the superscript dc and CAS stand for the dynamical correlation energy and complete-active space energy, respectively. Note that all extrapolations are carried pointwise, and hence the vector R of the nuclear geometrical coordinates will be omitted for simplicity. X = (Q, 5) is adopted in the present work, which is denoted as USTE(Q, 5). The CAS energies, which lack a dynamical correlation, are extrapolated to the CBS limit by employing the two-point extrapolation scheme proposed by Karton and Martin34

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and validated by Varandas30 for extrapolations of the CASSCF energy CAS CAS EX = E∞ + B/X α ,

(2)

CAS where α is a predefined constant. Being a two-parameter protocol (E∞ ,B), a minimum

of two raw energies will be required for the extrapolation. Specifically, Eq. (2) will be calibrated from the CAS/AV(Q, 5)Z energy pairs, using a value of α = 5.34 which has been found optimal when extrapolating HF energies to the CBS limit. The USTE method30, 35 has been successfully applied to extrapolate the dc energies, with its formalism being written as dc dc EX = E∞ +

A3 A5 + , 3 (X + α) (X + α)5

(3)

and here, (5/4)

A5 = A5 (0) + cA3

,

(4)

with A5 (0) = 0.0037685459, c = −1.17847713 and α = −3/8 as the universal-type padc rameters.30, 35 Thus, Eq. (3) can be reduced into a (E∞ , A3 ) two-parameter rule, which

is actually used for the practical procedure of the extrapolation. The extrapolation of the ab initio energies to CBS limit utilizing USTE protocol30 has been used to model the other PESs, such as S2 ,36, 37 NH2 .38, 39 2.2. Analytical potential energy surface function The analytical potential energy surface function (APES) for the HCS(A2 A′′ ) can be represented by MBE ,40–43 which is as follows: VABC =

∑

(1)

VA +

∑

A

(2)

(3)

VAB (RAB ) + VABC (RAB , RAC , RBC ),

(5)

AB (1)

in which the one-body term (VA ) is the energy of the separated atoms in their corre∑ (1) sponding electronic state, usually A VA = 0 for all the atoms in their ground states, (2)

the two-body term (VAB ) corresponds to the diatomics potential energy curves (PECs), (3)

including the nuclear repulsions, and the three-body term (VABC ) takes into account the interactions between three atoms.

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For the HCS(A2 A′′ ) PES, it follows the dissociation scheme as    CS(a 3 Π) + H(2 S)      CH(X 2 Π) + S(3 P ) 2 ′′ HCS(A A ) → .  2 3  SH(X Π) + C( P )      H(2 S) + S(3 P ) + C(3 P )

(6)

(1)

Since H(2 S), C(3 P ) and S(3 P ) are all in their ground states, the value of VA can be set to zero. (2)

The term VAB involves CS(a 3 Π), CH(X 2 Π) and SH(X 2 Π), with their analytical expression being represented by the formalism developed by Aguado and Paniagua,44, 45 and can be expressed as a sum of two terms corresponding to the short- and long-range potentials, (2)

(2)

(2)

VAB = Vshort + Vlong ,

(7)

where (2)

Vshort =

a0 −β1(2) RAB , e RAB

(8)

which warrants the diatomic potentials tending to infinite value when RAB → 0, and the long-range potentials with the following expression (2) Vlong =

n ∑

)i ( (2) ai RAB e−β2 RAB

(9)

i=1

tending to zero as RAB → ∞. The linear parameters ai (i = 1, 2, · · · , 9) and the nonlinear parameters βi (i = 1, 2) in Eqs. (8) and (9) are obtained by fitting the ab initio potential energies of the diatoms. Here, we employ the accurate potential energy curves of CH(X 2 Π) reported in Ref .21, CS(a 3 Π), and SH(X 2 Π) from present least-squares fit to MRCI(Q) energies calculated using AVQZ (AVQdZ) and AV5Z (AV5dZ) basis sets, and extrapolated to the CBS limit. The values of parameters used to model the diatomic potentials are gathered in Table S1 of Supporting Information (SI). Since the potential curve of CH(X 2 Π) has been examined in detail elsewhere,21 only the CS(a 3 Π), and SH(X 2 Π) energy curves are shown in Figure 1. As seen, the modeled PECs can accurately mimic the

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ab initio energies showing smooth and accurate behavior both in short and long regions, with the maximum error being smaller than 0.002 eV. (3)

The three-body term (VABC ) of the global potential Eq. (5) can be written as M thorder polynomial44, 45 (3)

VABC (RAB , RBC , RAC ) =

M ∑

Cjkl ρjAB ρkAC ρlBC ,

(10)

j,k,l=0 (3)

where ρAB = RAB e−βAB RAB , Cjkl and βAB are the linear and nonlinear parameters to be (3)

determined in the fitting procedure. The constraints j+k+l ̸= j ̸= k ̸= l and j+k+l ≤ M are used to warrant that the three-body term becomes zero at all dissociation limits and at least one of the internuclear distances is zero. M equals 10 in the present work, which results in a complete set of parameters to be determined amounted to a total number of (3)

(3)

(3)

255 for linear coefficients Cjkl and 3 for nonlinear parameters (i.e., βCH , βSH and βCS ). The 255 linear coefficients and three nonlinear parameters of HCS(A2 A′′ ) PES are gathered in Table S2 of SI. The root mean squared deviation (rmsd) values of the final PES with respect to all the fitted ab initio energies are gathered in Table 2, in which a total of 6209 points have been used for the calibration procedure, thus covering a range up to 31.5 eV above the HCS global minimum. This table shows that the final PES is able to fit the region of major chemical interest with a high accuracy (rmsd= 0.0367 eV), including the global minimum and transition states for the C + SH dissociation process. 2.3. Reaction Dynamics. To study the dynamics of titled reactions, the QCT method46–50 is also applied here. In this method, the relative motion is described according to classical mechanics (through numerical integration of Hamilton′ s differential equations) and the pseudo-quantization of rovibrational states is performed using well known procedures. The accuracy of the numerical integration of Hamilton′ s differential equations is checked by analyzing the conservation of total energy and total angular momentum for each trajectory. In present work, for each reaction, a batch of 10 0000 trajectories are run, with the integration step size in the trajectories chosen to be 0.1 fs, while the initial distance (ρ0 ) from the C atom to the center of mass of SH is 37.8 a0 . In the present calculation, we chose the 0.08, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9

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and 1.0 eV as the collision energies, and the corresponding collision parameters bmax are 4.52, 4.25, 3.33, 2.99, 2.80, 2.69, 2.58, 2.50, 2.47, 2.43 and 2.40, respectively. And in this calculation, bmax for each trajectory at a given collision energy can be obtained by systematically increasing the value of impact parameter, b, until no reaction trajectory is found. In order to get more information on the nature of the collision mechanism, the capture time τcap which is the time that the three atoms spend close together without a possible assignment to any of the three collision channels, is calculated. The use of this property will facilitate characterizing the mechanism corresponding to each trajectory, and make it possible to establish a clear cut differentiation between direct collisions and trajectories where an intermediate complex is formed. A careful examination of trajectories for a given reaction indicates that the time of strong interaction generally occurs when the initial, ′ Rcm , and final, Rcm , center-of-mass atom-diatom distances are less than two distance ′ parameters Rint and Rint which define the strong interaction region. The values of these

parameters depend on the reaction and are determined by following the time evolution of the interatomic distances and potential energy for a significant number of trajectories. Here we use the QCT method to calculate the τcap defined by51, 52 τcap = ttot −

′ ∆Rcm ∆Rcm − , vr vr′

(11)

′ ′ = R0′ − Rint where ttot is the total duration of the trajectory, △Rcm = R0 − Rint , △Rcm ,

R0 and R0′ are the initial and final value of the atom–diatom distance, vr and vr′ are the initial and final relative velocities, respectively. The values of Rint (= 3.781a0 ) and ′ (= 3.781a0 ) have been determined by examining the time evolution of the interatomic Rint

distances of hundreds of trajectories. These choices are reasonable from the perspective of the PES features.

3. RESULTS AND DISCUSSION 3.1. Characteristics of the potential energy surface. Figure 2(a)-(c) illustrates

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the major topographical features of the HCS(A2 A′′ ) PES with collinear configuration. The visible from these plots is its major stationary points including global minim, four transition states (TS3, TS4, TS5, TS7) and one saddle point (SP2). Clearly, the variation of the contours is quite smooth in the whole configuration space. Most notable in Figure 2(a) is the global minimum (GM), which locates at R1 = 4.918 a0 , R2 = 2.908 a0 and R3 = 2.010 a0 (R1 is the SH interatomic separation, R2 the CS interatomic separation, and R3 the CH interatomic separation) with the angle being fixed at its equilibrium (̸ α = 180o ), and the well depth being −0.3487 Eh relative to the H(2 S) + S(3 P ) + C(3 P ) asymptote. The linear (A2 A′′ ) symmetry state lies 0.346 eV above the ground state(X 2 A′ ), which is 0.07 eV smaller than that of Goddard.5 For convenience of discussion, the properties of all stationary points are collected in Table 3, including the internuclear distances, energies and vibrational frequencies. The differences of the global minimum for the first excited state CBS HCS PES with that of Ref. 9 are 0.035 a0 , 0.035 a0 , and 0.001 a0 , while the harmonic frequencies of GM are ωbend = 607.36 cm−1 , ωCH = 3951.62 cm−1 and ωCS = 1073.60 cm−1 . A closer observation reveals in Figure 2(a) that the S(3 P ) + CH(X 2 Π) asymptote is higher than the H(2 S) + CS(a 3 Π) asymptote, and both are above the global minimum. The other collinear configurations are shown in Figure 2(b) and (c). From Figure 2(b), we can find that there exists no barrier toward the dissociation of HCS(A2 A′′ ) into C(3 P ) + SH(X 2 Π) at this configuration, and there is a transition state (TS3) connecting the H(2 S) + CS(a 3 Π) asymptote. It is interesting to notice that the energy of the H(2 S) + CS(a 3 Π) asymptote is lower than that of the C(3 P ) + SH(X 2 Π) asymptote, which indicates that the C(3 P )+SH(X 2 Π) → H(2 S)+CS(a 3 Π) reaction is an exothermic one with a transition state in the product channel. The notable feature in panel(c) is that there are one second-order saddle point (SP2) and two transition states (TS4 and TS7) at this configuration. In order to illustrate the other stationary points on the new PES, the contour graphs are plotted in Figure 3, which are presented as a function of three sets of internal coordinates (RCH and ̸ HCS with a fixed C-S distance, RCS and ̸ HSC with a fixed S-H distance and RCS and ̸ HCS with a fixed C-H distance). From Figure 3 (a), two deep minima (GM

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and LM) corresponding to the stable HCS and HSC intremediates and the isomerization transition state (TS6) connecting these two minima are clearly seen. The barrier height of TS6 is calculated to be 0.351 eV and 2.950 eV above the LM and GM, respectively. It is interesting to notice that the energy level of the SCH ↔ CSH transition state for the A2 A′′ state is lower than the H(2 S) + CS(a 3 Π) asymptotic energy level. The contour plots in Figure 3 (a) also show the existence of an entrance barrier for the H addition pathway to the CS molecule (or an exit barrier for the HCS/HSC → H+CS dissociation). In another words, the saddle point (SP1) connects the GM/LM with the H(2 S)+CS(a 3 Π) asymptote. From the result presented in Figure 3 (b), it is seen that C atom can be added to SH to form the HSC intermediate without a barrier on the surface. Similarly, S atom is added to CH to form HCS without a barrier for the states, too, which can be seen in Figure 3 (c). To better view all major topographical features of the APES, we display a relaxed triangular plot53 in Figure 4 which utilizes scaled hyperspherical coordinates (β ∗ = β/Q and γ ∗ = γ/Q), where the Q, β and γ are defined as 



 

Q 1 1 1    √ √     β = 0 3 − 3    2 −1 −1 γ

 R12

   2    R2  .   R32

(12)

As shown in Figure 4, all stationary points discussed above which correspond to the global minimum (GM), local minimum (LM), transition state and second-order saddle points are visible, and the transition state (TS6) connects the global minimum (GM) and local minimum (LM). All the linear configuration stationary points are on the edge of the circle, such as GM, TS3, TS4, TS7, and SP2. To assess the quality of the new HCS(A 2 A′′ ) PES used in our dynamic calculations, we calculate the low-lying energy levels using Lanczos algorithm. For comparison with other theoretical results, we do not attempt to include energy levels beyond 3500 cm−1 . The calculated vibrational levels (cm−1 ) of HCS(A 2 A′′ ) for total angular momentum J = 0 are given in Table 4, together with Senekowitsch results.9 The quantum numbers vCH ,

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vCS , and vbend denote the symmetric stretching, antisymmetric, and bending stretching modes, respectively. It is apparent from the table that the calculated energy levels are in good agreement with the theoretical data.9 For instance, the frequency of bending mode (0, 0, 1) is calculated to be 721.96 cm−1 , which differs from the theoretical value9 by 7.64 cm−1 . The comparison of the results from the present work with those from other theoretical data9 gives the deviations of them are 1.42 %, 2.11%, 8.63%, 4.05%, 1.30%, 1.66%, 0.97%, 2.90%, and 1.30%, respectively, which shows excellent agreement with those theoretical data. 3.2. Molecular reaction dynamics. The MEPs in different configurations (at a fixed ̸ CSH angle) calculated on the excited (A 2 A′′ ) state of HCS PES are displayed in Figure 5. These MEPs represent the potential energy of HCS as a function of a suitable reaction coordinate defined as RSH − RCS , where RSH and RCS are the SH and CS internuclear distances, respectively. As shown in Figure 5, RSH approaches the SH equilibrium distance when the values of the reaction coordinate are in large negative values, whereas large positive values of the reaction coordinate correspond to RCS approaching the CS equilibrium distance. It can be seen that there exists a deep well for C(3 P ) + SH(X 2 Π) → H(2 S) + CS(a 3 Π) reaction, with the calculated well depth of 3.076 eV at ̸ CSH = 90o relative to C(3 P ) + SH(X 2 Π). Moreover, the C(3 P ) + SH(X 2 Π) → H(2 S) + CS(a 3 Π) reaction is exoergic by ∼ 0.204 eV, while the exothermicity is ∼ 3.66 eV for the ground state.21 Note further that the MEPs on the PES presented have low potential barriers in H(2 S) + CS(a 3 Π) asymptote at ̸ CSH = 90o , which can be assigned to the saddle point (SP1) connecting the H(2 S) + CS(a 3 Π) asymptote. In order to shed further light on the reaction mechanism, capture time distributions of reactive classical trajectories have been produced and depicted in Figure 6. Note that contributions from all impact parameters between 0 and bmax have been taken into account in these results. As expected, the capture time decreases sharply with the increase of collision energies. For instance, the capture time at 0.1 eV is longer than that at 1.0 eV by more than one order of magnitude. In addition, in contrast to the broad capture time distributions for lower energies (≤ 0.3 eV), the capture time for the higher collision

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energy (> 0.3 eV) is narrowly distributed and characterized by a major peak followed by a long tail. For energies lower than or equal to 0.3 eV, most trajectories examined are found to be captured by the well long enough to form many (> 2) minima in the time evolutions of the interatomic distances. In fact, the probability is quite small at very short capture times for these energies as Figure 6 shows. The probabilities less than 0.13 ps are 0.00072 for 0.08 eV, 0.0059 for 0.1 eV, 0.025 for 0.2 eV and 0.059 for 0.3 eV. At higher energies, a considerable number of trajectories (denoted as Type-I trajectories hereafter) start to appear in which the time evolution of the C–S distance forms just one or two minima. The reason for the results may be that with the energy increasing and the trap-binding becoming small, when the centrifugal potential is approximately equal to the depth of the well, the direct reaction begins to appear. When the capture time is less than 0.13 ps, the sum of probability for distributions is bigger than 0.1 and smaller than 0.33, the reason of which may be due to the deep well in PES and existence of the complex state which plays a dominant role during the reaction. The Type-I trajectories come exclusively from the first major peak in each capture time distribution, and the type-II trajectories which form multiple minima are from the tails. The time denoted as τ0 = 0.13 ps serves as the boundary between the peaks and the tails or between type-I and type-II trajectories. Although there exists no well-established consensus with regard to when a reaction is considered to be direct or indirect, it is reasonable to regard type-I trajectories as direct and type-II as indirect. Assuming that features in Figure 6 lead us to conclude that at lower collision energy, the reaction is mainly governed by the indirect mechanism, for higher collision energy, the direct and indirect mechanisms coexist with the latter being the dominant contributor. The total QCT ICS is displayed in Figure 7. As expected for a barrierless PES, the value of ICS is very large at the low collision energies (≤ 0.3 eV), and rapidly decreases with the increase of relative translational energy, which is very similar to other exothermic reactions.54–57 To better understand the meaning of the ICS result, we divide the contributions to the ICS into two parts, one from Type-I trajectories which represents a direct event, and the other from type-II trajectories which represent an indirect event.

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As Figure 7 shows, the two contributors have drastically different energy dependencies. The type-II is very similar to the total ICS, i.e. the energy dependence is declining from a large value to near zero energy, which resembles very much a typical feature of complex forming reactions governed by the indirect mechanism. On the other hand the Type-I is monotonically increasing with the collision energy, a typical characteristics for reactions governed by the direct mechanism. These analyses support the arguments made in the previous section, i.e. the indirect mechanism is the dominant contributor no matter at the lower energy region or higher energy region, and at higher energy region, the indirect mechanism and direct mechanism are equally important.

Figure 8 presents the final state resolved ICSs at the collision energy of 0.08, 0.4 and 0.8 eV. In all cases the CS product is formed with a strong vibrational population inversion, with v ′ = 1 being the most populated vibrational state for 0.08, 0.4 and 0.8 eV. Moreover, the CS product is found to be highly excited in its vibrational degree of freedom and high vibration level of v ′ = 8 for 0.8 eV is observed. With the increasing of collision energy, the behavior of vibrational inversion becomes more obvious, which is consistent with the direct mechanism as proposed in previous sections, and the reaction proceeds through a relatively short-lived intermediate complex followed by a fast dissociation into the asymptotic channels. Similar to the product vibrational distribution, all the rotational distributions are also inverted, populating mostly in high rotational state. The ICS first increases with j ′ to a maximum value and then decreases to a small value. The shapes of the ICSs for each v ′ state are found to resemble to each other. The variation of the ICSs with increasing collision energy is displayed in two aspects. First, the range of j ′ is expanded, and its increasing is very evident. Second, the CS product is increasingly inclined to distribute in rotational hot states at higher collision energy. For example, the maximum value of the ICS for each v ′ state is located at an intermediate j ′ value at 0.08 eV. At 0.8 eV, the maximum value of the ICS for each v ′ state is located at a larger j ′ value.

13



4. CONCLUSIONS We report a globally accurate PES for the HCS(A 2 A′′ ) based on a wealth of ab initio energies calculated at MRCI(Q)/AVQZ and MRCI(Q)/AV5Z level of theory, which is expected to be reliable over the entire configuration space. Such raw energies are subsequently extrapolated to CBS limit and fitted to a single-sheeted MBE form, which shows that the properties of the major stationary points, including geometries, energies and vibrational frequencies are in good agreement with previous theoretical and available experimental results. Besides, we calculate the low-lying energy levels, which shows good agreement with previous high quality theoretical studies. The MEPs calculated based on the present PES indicate that the titled reaction is exothermic, with the exothermicity being ∼ 0.204 eV. The QCT calculation for the capture time on this PES indicates that at lower collision energy, the reaction is mainly governed by the indirect mechanism, while for higher collision energy, the direct mechanism and indirect mechanisms coexist with the latter being the dominant contributor. Because of the deep potential well and barrierless PES, the calculated cross sections show decreasing trends as the collision energy increases. Meanwhile, the inversion vibrational and rotational distributions reflected in the final state resolved ICSs are consistent with the direct reaction mechanism. The PES presented is not only recommended for the reaction dynamics studies of C(3 P )+SH(X 2 Π) → H(2 S) + CS(a 3 Π) reaction in more detail, but also can be used as a building block for constructing the PESs of larger sulfur/ carbon/ hydrogen containing systems.

ACKNOWLEDGMENTS This work was supported by National Natural Science Foundation of China (Grant No 11674198 and No 11304185), China Postdoctoral Science Foundation (Grant No 2014M561957).

14


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21



Table 1: The range of ab initio points chosen to map the PES of HCS(A 2 A′′ ) for three channels. parameter

value

H − CS region RCS 2.0-4.0 a0 rH−CS 0.6-15 a0 γ 0.0-180 deg C − SH region RSH 2.0-4.0 a0 rC−SH 0.6-15 a0 γ 0.0-180 deg S − CH region RCH 1.5-4.0 a0 rS−CH 0.6-15 a0 γ 0.0-180 deg

22


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Table 2: Root-mean-square deviations (in eV) of the PES. Energy

Na

rmsd

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 10.0 20.0 30.0 31.5

11 30 57 95 140 250 531 864 1147 1450 4750 5582 6208 6209

0.0062 0.0077 0.0102 0.0138 0.0172 0.0207 0.0216 0.0249 0.0286 0.0318 0.0361 0.0367 0.0367 0.0367

N >rmsd

b

5 10 12 30 45 74 168 255 285 335 1230 1470 1579 1579

a

Number of points in the indicated energy range.

b

Number of points with an energy deviation larger than the rmsd.

23


ωCS

Table 3: Properties of stationary points on the fitted HCS(A 2 A′′ ) PES (harmonic frequencies in cm−1 ) ωCH

ωbend


E/Eh

1073.60 1191.5 — — 147.15

R3 /a0

3951.62 3454.8 — — 2324.59

964.48 990.02 41.13 i 480.65 626.70 787.72 54.32

R2 /a0

HCS Minimum -0.3487 607.36 — 735.6 — — — — -0.2532 2744.76

21.48i 112.18 3555.73 2411.59 3608.44 828.90i 2675.12

R1 /a0

Transition state (TS) -0.1347 154.20 -0.1353 360.80i -0.1465 36.27 -0.1421 445.42i -0.2152 892.25i -0.2403 3033.37 -0.1412 72.91i

Feature

HCS 2.117 2.139 9.499 2.427 5.710 2.408 6.088

155.99i 2699.19

2.010 2.009 2.015 1.987 3.766

9.019 6.132 2.958 5.026 3.161 3.110 8.622

HCS Second-order saddle (SP) 5.182 -0.1430 3198.38 485.42i 3.059 -0.1392 212.03i 86.36i

2.908 2.943 2.941 2.783 3.267

8.609 7.574 6.541 2.599 2.550 2.995 2.534

2.981 5.640

4.918 4.953 4.957 4.769 2.585

TS1 TS2 TS3 TS4 TS5 TS6 TS7

5.319 2.580

GM/CBS Theor.9 Theor.5 Theor.6 LM

SP1 SP2

24

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 34 The Journal of Physical Chemistry

Page 25 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4: Calculated vibrational energy levels (cm−1 )of HCS(A 2 A′′ ) for total angular momentum J = 0. vCH

vCS

vbend

0 0 0 0 0 0 0 0 0 1

0 1 0 1 0 2 1 0 2 0

1 0 2 1 3 0 2 4 1 0

This work Theor.9 721.96 1191.12 1476.91 1734.64 2083.31 2368.25 2653.57 2911.85 3147.90 3283.30

25


729.6 1174.2 1445.8 1898.5 2171.3 2337.5 2609.6 2883.5 3056.7 3326.0

102 101 100 10-1 10-2

6

HS(Χ2Π)

8

10

2

4

6

CS(a3Π)

8

10


-0.02

4

26

-0.06

-0.10

-0.14

2

R/a0 Figure 1: Potential energy curves of SH(X 2 Π) and CS(a 3 Π), and the differences between the fit and ab initio points.

-0.002

0.000

0.002

V/Eh error/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


27


0

GM

2

H

C

S

4

R2/a0

6

H R3

C

8

R2

S

10

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

2

4

6

8

0

2

C

TS5

S H

4

R1/a0

6

C

H

TS3

S

R1

S

8

R2

H

C

(b)

10

-0.20

-0.15

-0.10

-0.05

0.00

0

2

4

6

8

10

R3/a0

R2/a0

0

TS7

TS4

SP2

2

C

H

S

4

R1/a0

6

S R1

H

8

R3

(c)

C

10

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

−0.1429 Eh in panel (c). And energy curves of (d)-(f) are the minimum energy path for (a)-(c), respectively.

configurations. Contours are spaced by 0.006 Eh , starting from −0.3484 Eh in panel (a), −0.2298 Eh in panel (b), and

Figure 2: The contour plots and minimum energy path for the first excited state PES of the HCS system with collinear

0

2

4

6

8

10

C

0.00

H

C

(a)

S

H

10

S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R3/a0


34

(a)

3029 282726 25 21 18 16

23

90

10 10 16

GM TS5

LM1 TS6 SP1

23

13

150

3

23 18 17 14 12 9

120

H-C-S/deg

20 19

4

8 1 675 11 15 19 21 20

180

8

6

4

2 30

(b)

60

1615 14 13 9 33 2921 25 12 3 32 8 20 16 15 28 2417 14 9 19 13 21 23 31 27

0

1

18

10

2

15 14

7

9 4

6

LM TS4 TS5

5

18

7

150

11

17

180

5 67 10 11 18 30 26 29

10

SP2

120

3 8 11 12 12 16 20 15 17 1918 27 31 23 32 2824

90

H-S-C/deg

8

6

4

2 0

30

30

35 34 33 32 30 28 26 24 21

22

15

31

29

20 19 17 18 13 11 8 3

26

34 32 33

35

GM

28

24 21 16

150

180

2 5 6 7 12 14 10 18 17 23 19 28 35 34 332632 20

9

120

10 15 25 29 2722

16 13 12

90

H-C-S/deg

23 30

31

(c)

312722 25

60

from −0.3459 Eh with an optimized C-S bond distance in panel (a), starting from −0.2535 Eh with an optimized S-H bond


33

60

22 17 14 33 32 31 302928 27 25 26 34 35 36 23

24 36

32 31 30 24 29 24 34 28 22 27 33 33 32 26 32 31 31 25 30 22 34 35 21 29 28 21 27 25 26

30

R2/a0

distance in panel (b), and starting from −0.3527 Eh with an optimized C-H bond distance in panel (c).

28

8

6

4

2 0

R2/a0

Figure 3: The contour maps for the first excited state PES of the HCS system. Contours are spaced by 0.006 Eh , starting

R3/a0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


29


-1.0

34 31

33 30

26

-0.5

31 33 40 41 44 46 48

26

24

β*

0.0

C+SH

39 43

35 36

0.5

47

44

50

1.0

TS7

TS6

TS5

TS4

TS3

TS2

TS1

SP2

SP1

LM

GM

state). Contours equally spaced by 0.004 Eh , starting at -0.3613 Eh .

visible (GM: global minimum, LM: local minimum, SPi (i=1,2): second-order saddle points, and TSi (i=1-7): transition

Figure 4: Relaxed triangular plot of new PES in hyperspherical coordinates. All stationary points discussed above are

-1.0

S 47

31 28 29 33 32 41

CH

4542

50 48

9 1815

25 45 1116 42 13 21 4947 19 33 2023 32 37 36 31 27 41 24 3843 35 26 44 39 48 40 30 34 41 38 46 31 35 43 44 40 34 30 29 39 35 32 30 30 39 50 2928 373632 46 38 28 29 27 43 34 48 27 46 38 35 37 36 25 40 27 25 42 45

28

S+

-0.5

0.0

0.5

1.0

H+ C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

γ*


1 0.5

C

S

H

−4

−2

0

RSH−RCS/a0

2

4

C

S

6

H

8


0

o

45 o 90 o 135 o 180

−6

30

−0.5 −1 −1.5 −2 −2.5 −3 −3.5 −8

RSH − RCS at the ̸ CSH angle 45o , 90o , 135o , and 180o .

Figure 5: Minimum energy path for the C(3 P ) + SH(X 2 Π) → H(2 S) + CS(a 3 Π) calculated on new PES as a function of

V/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


P(τ)

10

15

31

ACS Paragon Plus Environment 2

0.000

1

0

0

4

τcap(ps)

1

Ec = 0.7 eV

8

Ec = 0.2 eV

2

12

0.000

0.040

0.080

0.120

0.000

0.005

0.010

0.015

0

0

3

τcap(ps)

1

Ec = 0.8 eV

6

Ec = 0.3 eV

2

9

0.000

0.050

0.100

0.150

0.000

0.012

0.024

0.036

0

0

0.5 τcap(ps)

1

Ec = 0.9 eV

2

Ec = 0.4 eV

0.050

0.100

0.150

0.000 0

0.000 1.5 0

4

0.020

0.040

0.060

0.5

1

τcap(ps)

1

Ec = 1.0 eV

2

Ec = 0.5 eV

1.5

3

Figure 6: The capture time distributions calculated classically for some energies from 0.1 eV to 1.0 eV.

τcap(ps)

0.000

0.054

0.081

0.027

0

Ec = 0.6 eV

0.025

0.050

0.075

0.000

5

0.000

0.004

0.006

0.002

0

Ec = 0.1 eV

0.002

0.004

0.006

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

P(τ)



ICS/Å2

14

12

10

8

6

4

2

0 0 0.2 0.4 Ec

0.6 total ICS Direct Indirect

0.8 1

Figure 7: The total integral cross section with two different reaction mechanism.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 34

32


ICS/Å2

0

33


0

10

1

20

2

30 j′

v′

40

(d) Ec = 0.08 eV

3

4

50

v′=0 v′=1 v′=2

(a) Ec = 0.08 eV

60

5

0

0.000

0.010

0.020

0.030

0.040

0.0

0.3

0.6

0.9

1.2

1.5

0

10

1

20

2

30

3

40

v′

j′

50

60

(e) Ec = 0.4 eV

4

5

(b) Ec = 0.4 eV

70

v′=0 v′=1 v′=2 v′=3 v′=4

6

80

90

7

0

0.000

0.004

0.008

0.012

0.016

0.0

0.2

0.4

0.6

0.8

0

1

15

2

30

3

4

45

6

60

7

75

(f) Ec = 0.8 eV

j′

5 v′

(c) Ec = 0.8 eV

90

v′=0 v′=1 v′=2 v′=3 v′=4 v′=5

8

9

105

10

using the QCT method.

vibrational state manifold (v ′ ) at three energies (0.08 eV: left panel; 0.4 eV: middle panel; 0.8 eV: right panel) calculated

Figure 8: The final vibrational state distributions (upper panel) and rotational state distributions (lower panel) in a given

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ICS/Å2



(TOC Graphic)

HCS ACS Paragon Plus Environment

0.00

34

-0.05

-0.10

-0.15

-0.20

-0.25

-0.30

-0.35

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 34

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