Theoretical spectroscopic investigations of HNS(q) and HSN(q) (q = 0, +1, -1) in the gas phase.

Theoretical spectroscopic investigations of HNSq and HSNq (q = 0, +1, −1) in the gas phase S. Ben Yaghlane, N.-E. Jaidane, C. E. Cotton, J. S. Francisco, M. M. Al Mogren, R. Linguerri, and M. Hochlaf Citation: The Journal of Chemical Physics 140, 244309 (2014); doi: 10.1063/1.4883915 View online: http://dx.doi.org/10.1063/1.4883915 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Ab initio structural and spectroscopic study of HPSx and HSPx (x = 0,+1,−1) in the gas phase J. Chem. Phys. 139, 174313 (2013); 10.1063/1.4827520 Properties of the B+-H2 and B+-D2 complexes: A theoretical and spectroscopic study J. Chem. Phys. 137, 124312 (2012); 10.1063/1.4754131 Accurate theoretical study of PSq (q = 0,+1,−1) in the gas phase J. Chem. Phys. 136, 244309 (2012); 10.1063/1.4730303 Theoretical study of the spectroscopically relevant parameters for the detection of HNPq and HPNq (q = 0, +1, −1) in the gas phase J. Chem. Phys. 136, 244311 (2012); 10.1063/1.4730299 A theoretical and computational study of the anion, neutral, and cation Cu ( H 2 O ) complexes J. Chem. Phys. 121, 5688 (2004); 10.1063/1.1782191

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THE JOURNAL OF CHEMICAL PHYSICS 140, 244309 (2014)

Theoretical spectroscopic investigations of HNSq and HSNq (q = 0, +1, −1) in the gas phase S. Ben Yaghlane,1,a) N.-E. Jaidane,1 C. E. Cotton,2 J. S. Francisco,2 M. M. Al Mogren,3 R. Linguerri,4,a) and M. Hochlaf4 1

Laboratoire de Spectroscopie Atomique, Moléculaire et Applications - LSAMA, Université de Tunis El Manar, Tunis, Tunisia 2 Department of Chemistry and Department of Earth and Atmospheric Science, Purdue University, West Lafayette, Indiana 49707, USA 3 Chemistry Department, Faculty of Science, King Saud University, PO Box 2455, Riyadh 11451, Kingdom of Saudi Arabia 4 Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France

(Received 7 April 2014; accepted 5 June 2014; published online 26 June 2014) We performed accurate ab initio investigations of the geometric parameters and the vibrational structure of neutral HNS/HSN triatomics and their singly charged anions and cations. We used standard and explicitly correlated coupled cluster approaches in connection with large basis sets. At the highest levels of description, we show that results nicely approach those obtained at the complete basis set limit. Moreover, we generated the three-dimensional potential energy surfaces (3D PESs) for these molecular entities at the coupled cluster level with singles and doubles and a perturbative treatment of triple excitations, along with a basis set of augmented quintuple-zeta quality (aug-cc-pV5Z). A full set of spectroscopic constants are deduced from these potentials by applying perturbation theory. In addition, these 3D PESs are incorporated into variational treatment of the nuclear motions. The pattern of the lowest vibrational levels and corresponding wavefunctions, up to around 4000 cm−1 above the corresponding potential energy minimum, is presented for the first time. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4883915] I. INTRODUCTION

The interstellar medium (ISM) is characterized by an astonishingly rich chemistry. Since the first detection of CH radical in the late 1930s,1 more than 180 neutral/charged molecular species have been observed in space, of which around 20% are diatomics including sulfur containing diatomic molecules (e.g., CS, NS, HS, HS+ , SO, SO+ , and SiS). The NS radical, that is closely related to the molecular systems investigated here, is abundant in these media, as it was identified in the Galactic center cloud Sgr B2,2 in regions of massive star formation,3 in cold dark clouds4 and in the coma of HaleBopp comet.5 It is generally accepted that a key mechanism for the formation of NS in interstellar clouds involves the electron capture and subsequent decomposition of protonated NS, leading to neutral NS and hydrogen. However, up-to-date gas phase ion-molecule models fail in the accurate determination of abundances of NS in dark clouds,4, 6, 7 where the calculated fractional abundances differ by several orders of magnitude, ranging from ∼10−14 to ∼10−10 . The mechanisms of formation of the precursor HNS+ include for example the reaction of NH2 + with sulfur atoms. Several theoretical investigations of structural, energetic, and spectroscopic properties of neutral HNS/HSN and relative mono-cations and anions exist in the literature.8–20 For HNS and HSN, previous works showed that these systems a) Authors to whom correspondence should be addressed. Electronic

addresses: [email protected] and [email protected]

0021-9606/2014/140(24)/244309/11/$30.00

possess a closed-shell 1 A ground state with two close-lying (one triplet and one open-shell singlet) states.10, 20 In HNS, ˜ 1 A states are bent components of a Renner˜ 1 A and A the X Teller pair correlating to a 1 state at linearity, leading to a small vertical excitation energy in ground-state HNS of around 1 eV.11 The lowest excited triplet state (ã3 A ) lies at around 0.3 eV above the ground state.11, 21 This confers to the molecule partial biradical character and explains its strong re˜ 2 A and activity. In HNS+ the two lowest electronic states (X 2 ˜ A A ) are the components of a bent-linear Renner-Teller pair, correlating to a 2 state at linear configurations. Since the barrier to linearity is calculated here to be only ∼0.30 eV,14 the rovibronic coupling for this system cannot be neglected even in the low-energy levels. The vibrational spectra of neutral and positively charged HNS/HSN have already been investigated at different levels of theory,15,11,10, 14, 22 by use of both force field and variational approaches. Particularly, the works by Mehlhorn et al., Ben Yaghlane et al. and Gersdorf solved variationally the rotational-vibrational structure. For the anions (HNS− and HSN− ), theoretical investigations are limited to a study by Gersdorf,22 who calculated potential and dipole moment surfaces at the Complete Active Space Self-Consistent Field (CASSCF) level to simulate the rovibrational spectra, and to a density functional (B3LYP/cep31G*) study by Mawhinney and Goddard,19 in which energies, structures and harmonic vibrational frequencies were deduced and compared to the multiconfigurational results by Gersdorf.

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Experimental data on thionitrosyl hydride are very limited. They mainly consist of a mass spectrometric study by Nguyen et al.15 No rovibrational spectra for the neutral or charged species have been measured so far. Nevertheless and since potential detection of title molecules in outer space needs accurate spectroscopic parameters, the purpose of the present work is to fully characterize the geometrical parameters and the rovibronic structure of neutral and singly charged HNS and HSN by means of modern ab initio computations. This includes the accurate calculations of the equilibrium geometries of HSN, HNS, HSN±1 , and HNS±1 in the low energy region, which improves on the existing theoretical data in the literature. Particular emphasis is placed on the effects of size and quality of the employed basis sets, which is crucial for a realistic description of the related rotational and vibrational spectra, as it is explained in Sec. II. II. BENCHMARKS AND COMPUTATIONAL DETAILS A. Electronic structure computations

Calculations of optimized energies, geometrical parameters, and harmonic vibrational frequencies were carried out

with the Gaussian 0923 and MOLPRO24 (2012.1 version) suites of ab initio programs. The optimizations were performed in the Cs point group and using the default options and algorithms set by the respective codes. Since the electronic wavefunctions of the molecular systems concerned in this study are reasonably well described by a single determinant close to equilibrium (maximum T1 diagnostic is less than 0.02 and no large double excitation amplitudes are computed), the coupled cluster approach has been used throughout. For closed shell systems, the standard coupled cluster technique in the singles and doubles approximation with a perturbative treatment of triple excitations25, 26 (CCSD(T)) and the explicitly correlated coupled cluster method27, 28 (CCSD(T)-F12), in the F12b approximation (denoted hereafter as CCSD(T)-F12) have been used throughout. For open-shell systems, the partially spinrestricted versions of these theories29–32 were used whenever appropriate. The selected basis sets include the aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6) and aug-cc-pV5Z Dunning and co-workers’ basis sets33–38 where the former has additional tight-d functions added to sulfur, to improve the

TABLE I. Geometric parameters at equilibrium (distances in angstrom and angles in degrees) and harmonic vibrational frequencies of HNS+ , HNS, and HNS− . CBS is for Complete Basis Set (see text). Species ˜ 2 A ) HNS+ (X

Method

Basis set

r(NH)

r(NS)

θ (HNS)

HN str.

SN str.

HNS bend

CCSD(T)

aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z CBS cc-pVTZ-F12 cc-pVQZ-F12

1.0406 1.0304 1.0288 1.0286 1.0286 1.0275 1.0289 1.0287

1.5036 1.4843 1.4777 1.4756 1.4746 1.4741 1.4752 1.4743

129.7 132.6 133.4 133.5 133.6 133.8 133.5 133.6

3348 3387 3399 3398

1224 1269 1284 1290

791 743 744 740

3396 3397

1290 1293

742 739


1.0393 1.0287 1.0265 1.0265 1.0265 1.0253 1.0287 1.0265

1.6020 1.5824 1.5716 1.5729 1.5721 1.5716 1.5824 1.5716

108.2 108.7 108.9 108.9 108.9 108.9 108.7 108.9

3292 3338 3351 3351

984 1021 1040 1038

1228 1223 1222 1222

3350 3351

1039 1040

1223 1222


1.0256 1.0151 1.0130 1.0130 1.0130 1.0120 1.0132 1.0130

1.5766 1.5539 1.5434 1.5444 1.5434 1.5426 1.5444 1.5434

123.0 124.8 125.7 125.6 125.7 125.7 125.5 125.7

3499 3542 3553 3555

1050 1097 1115 1116

791 775 754 768

3554 3553

1113 1115

778 754

aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z CBS aug-cc-pV5Z cc-pVTZ-F12 cc-pVQZ-F12

1.0384 1.0270 1.0251 1.0247 1.0247 1.0236 1.0243 1.0247 1.0246

1.7105 1.6838 1.6757 1.6728 1.6718 1.6707 1.6658 1.6729 1.6720

104.6 104.9 105.1 105.1 105.2 105.2 105.3 105.1 105.1

3253 3306 3323 3322

771 808 821 821

1165 1174 1196 1182

3324 3321 3320

830 825 824

1182 1181 1171

CCSD(T)-F12 ˜ 1 A ) HNS (X

CCSD(T)

CCSD(T)-F12 HNS (ã3 A )

CCSD(T)

CCSD(T)-F12 ˜ 2 A ) HNS− (X

CCSD(T)

CCSD(T)-F12


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TABLE II. Geometric parameters at equilibrium (distances in angstrom and angles in degrees) and harmonic vibrational frequencies of HSN+ , HSN, and HSN− . CBS is Complete Basis Set (see text). Species ˜ 2 A ) HSN+ (X

Method

Basis set

r(SH)

r(SN)

θ (HSN)

HS str.

SN str.

HSN bend

CCSD(T)


1.3916 1.3828 1.3829 1.3831 1.3832 1.3833 1.3841 1.3837

1.5632 1.5416 1.5333 1.5304 1.5294 1.5290 1.5295 1.5286

97.8 98.2 98.5 98.5 98.6 98.6 98.6 98.6

2377 2365 2364 2358

996 1042 1059 1064

825 828 829 823

2355 2355

1067 1069

833 829


1.4247 1.4091 1.4076 1.4073 1.4074 1.4056 1.4088 1.4077

1.5243 1.5055 1.4991 1.4967 1.4957 1.4953 1.4954 1.4950

109.9 109.9 109.9 109.9 109.9 109.9 110.0 110.0

2082 2126 2138 2140

1125 1161 1174 1179

1002 1024 1032 1033

2132 2138

1182 1183

1034 1034


1.3598 1.3503 1.3501 1.3500 1.3501 1.3500 1.3506 1.3502

1.6768 1.6457 1.6352 1.6316 1.6302 1.6293 1.6305 1.6293

96.8 97.4 97.8 97.9 97.9 97.9 97.8 97.9

2611 2604 2605 2603

734 765 775 778

850 866 873 876

2599 2601

779 781

877 879


1.4528 1.4359 1.4345 1.4341 1.4340 1.4336 1.4362 1.4346

1.6124 1.5850 1.5763 1.5730 1.5717 1.5709 1.5711 1.5707

111.5 111.5 111.6 111.6 111.6 111.6 111.8 111.8

1765 1817 1831 1833

801 850 867 873

916 942 951 953

1822 1831

876 877

954 954

CCSD(T)-F12 ˜ 1 A ) HSN (X

CCSD(T)

CCSD(T)-F12 HSN (ã3 A )

CCSD(T)

CCSD(T)-F12 ˜ 2 A ) HSN− (X

CCSD(T)

CCSD(T)-F12

accuracy of the calculated geometries and vibrational frequencies. For the explicitly correlated coupled cluster computations, the cc-pVXZ-F12 (X = T, Q) basis sets of Peterson et al.,39 in connection with the corresponding resolutions of the identity and density fitting functions40 have been employed. It has been widely documented in the literature41, 42 that the explicitly correlated coupled cluster method in both its F12a or F12b versions, in conjunction with the cc-pVTZF12 basis set, leads to relative energies and spectroscopic constants of a quality comparable to standard coupled cluster with the aug-cc-pV5Z set, but at a considerable reduction in computational cost (both CPU time and disk space). The selected coupled cluster methodologies and basis sets allow for the description of correlation effects linked to valence electrons only. Since they are expected to be small, core correlation effects were not addressed in this study. B. Basis set size effect

To assess the influence of basis set size on the calculated bond lengths and bond angles, the structures of HNSq and HSNq (q = 0, +1, −1) were systematically optimized using

the standard CCSD(T) technique using the aug-cc-pV(X+d)Z basis sets, where X = D, T, Q, 5, 6 (cf. Table I for HNSq and Table II for HSNq ). The results were extrapolated to complete basis set (CBS) limit, by means of the two-parameter equation A = B + C/X343 where X = 2,3, . . . ,6. Tables I and II report also data obtained at the CCSD(T)-F12/cc-pVXZ-F12 (X = T, Q) levels. For the neutral species, both the lowest singlet and triplet electronic states were considered. From these tables we deduce that results obtained with doubleor triple-zeta quality basis sets, with the standard coupled cluster procedure, are generally still far from complete basis set convergence. Nevertheless, satisfactory agreement with the CBS geometrical parameters and the related sets of rotational constants is reached after addition of higher angular momentum functions. For instance, when using aug-ccpV(X+d)Z basis sets, the mean absolute deviations from CBS limits in the bond lengths of neutral and charged HNS/HSN are of 0.0248, 0.0073, and 0.0081 for X = D, T, and Q, respectively, while deviations in the bond angles are 1.6◦ , 0.5◦ , and 0.1◦ , in the same order. Bond angles present always negative deviations from the corresponding CBS values. As expected, results obtained using (R)CCSD(T)-F12/cc-pVTZF12 are close to those obtained using the costly (R)CCSD(T)/


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aug-cc-pV(5+d)Z level. A similar trend is found when comparing (R)CCSD(T)-F12/cc-pVQZ-F12 to (R)CCSD(T)/augcc-pV(6+d)Z. Tables I and II list the harmonic vibrational constants, at different levels of theory, obtained by simple normal mode analysis. They consist in the HN/HS (ω1 ) and SN (ω3 ) stretches and the bending (ω2 ). Similar to the equilibrium geometries, inspection of the standard coupled cluster results reveals that the convergence of the calculated frequencies requires at least basis sets of quadruple-zeta quality. For example, the mean absolute differences between the HN stretching frequencies of HNS+ , HNS (singlet and triplet), and HNS− calculated at the CCSD(T)/aug-cc-pV(X+d)Z and CCSD(T)/aug-cc-pV((X−1)+d)Z levels are 45.3, 13.3, and 1.0 cm−1 for X = T, Q, 5, respectively. A similar trend is found for the other modes of HNS0,±1 and for all modes of HSN0,±1 as well. As expected, frequencies calculated at the (R)CCSD(T)-F12/cc-pVTZ-F12 level are very similar to those calculated at the CCSD(T)/aug-cc-pV(5+d)Z level (cf. Tables I and II).

C. Generation of the three-dimensional potential energy surfaces

The spectroscopic parameters calculated at the (R)CCSD(T)/aug-cc-pV5Z level differ only slightly with those obtained at the (R)CCSD(T)/aug-cc-pV(5+d)Z level (see Ref. 44 and Tables I and II). Therefore, the addition of tight-d functions to describe sulfur within the molecular species under investigation is not that crucial and can be omitted, whereas an appreciable gain of computational cost is noticed. Accordingly, we chose the (R)CCSD(T)/aug-ccpV5Z method for the generation of the fully dimensional PESs for all molecular entities considered in this study in their respective ground electronic states. Additionally, the ground state barriers to linearity are quite large for all species except HNS+ . For a description of their low-energy vibrational spectra, the corresponding electronic component can be treated separately without considering the upper excited states and the Renner-Teller and spin-orbit effects if any. For HNS+ , this however is not possible. The surfaces were mapped in the set of three internal coordinates, i.e., R(NS) (R1 ) and R(HX, X = N or S) (R2 ) bond TABLE III. Bond orders from natural resonance theory. X and Y refer to N or S.

lengths and HXY bond angle (θ ). More than 35 total energies for non-equivalent nuclear configurations uniformly spread around the energy minimum were computed. The internal coordinate space was selected to cover an energy range of around 10000 cm−1 above the corresponding minima. Then, the calculated energies were fitted with the following polynomial expansion in the internal coordinates j cijk Qi1 Q2 Qk3 , (1) V(R1 , R2 , θ ) = ijk

where Qp = (Rp − Rp,ref ) for p = 1 and 2, and Q3 = θ − θ ref (0o ≤ θ ≤ 180o ), and coordinates R1,ref , R2,ref , θ ref refer to the equilibrium geometry of the considered electronic state. The cijk parameters were adjusted according to a least square procedure, where equal weights were assigned to the calculated energies. The maximum degree of the polynomial expansion was fixed by the constraint i + j + k ≤ 4. The root mean square of the fits was typically less than 1 cm−1 . Later on, the resulting 3D-PESs were derived as quartic force fields in internal coordinates. After transformation by l-tensor algebra to quartic force fields in dimensionless normal coordinates with the SURFIT package,45, 46 a set of spectroscopic constants have been obtained by applying second order perturbation theory. Finally, the three-dimensional PESs have been employed in the RVIB3 code by Handy and Carter,47, 48 to deduce the variationally calculated vibrational levels and wavefunctions for these species. We refer to Refs. 47 and 48 for further details on this variational treatment. We expect that the main source of possible inaccuracies in the calculated levels will stem mainly from the PES’s. TABLE IV. Corrected singlet-triplet energy differences (E), adiabatic ionization energies (IE), electron affinities (EA), and HNS to HSN isomerization energies (Eisom ) for neutral HNS and HSN species (in kcal mol−1 ). Method

CCSD(T)

CCSD(T)-F12 CCSD(T)-F12 CCSD(T)

Total bond order Species HNS+ HNS singlet HNS triplet HNS− HSN+ HSN singlet HSN triplet HSN−

r(HX)

r(XY)

0.99 0.99 0.99 0.99 0.97 0.94 0.98 0.91

2.51 2.01 2.00 1.51 2.04 2.06 1.52 1.58

CCSD(T)-F12 CCSD(T)-F12

Basis set

Ea

IEa

EAa,b

Eisom a,c

HNS aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z CBS VTZ-F12 VQZ-F12

5.5 5.0 5.1 5.1 5.2 5.1 5.2 5.1

202.9 205.8 215.1 207.0 207.1 207.7 206.7 207.1

− 27.5 − 29.4 − 30.2 − 30.4 − 30.5 − 30.6 − 29.6 − 30.3

21.1 20.4 19.9 19.6 19.5 19.5 19.4 19.5

HSNd aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z CBS VTZ-F12 VQZ-F12

4.1 7.4 8.5 9.0 9.2 9.3 9.2 9.3

211.9 218.2 220.0 220.6 220.9 221.9 220.5 221.0

− 21.8 − 23.4 − 24.1 − 24.2 − 24.3 − 24.5 − 23.2 − 23.9

a

Corrected for ZPE. Electron affinity is calculated as the energy of the anion minus the energy of the neutral molecule. c Positive Eisom means that HNS is more stable than HSN. d Positive E indicates singlet is lower in energy. b


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Nevertheless, we expect our calculated levels to differ no more than 10 cm−1 from experimental values, as it was already pointed out in other studies on triatomic molecular species using similar methodologies, where experimental data were available for comparison.49–51

III. RESULTS A. Equilibrium geometries

In the following, we will describe briefly the equilibrium structures of HNS0,±1 /HSN0,±1 obtained with the CBS extrapolation of the CCSD(T)/aug-cc-pV(X+d)Z results of Tables I and II. We confirm that ground state HNS has 1 A symmetry with NH and NS bond lengths of 1.0253 Å and 1.5716 Å, respectively (cf. Table I). The bond angle is calculated 108.9◦ , that is slightly larger than in the isovalent HPS molecule (101.8◦ , see Ref. 52). For the lowest triplet state, contractions of the NH bond (1.0120 Å) and of the NS bond (1.5426 Å) with respect to the singlet are seen. The bond angle is predicted to be 125.7◦ , which is substantially larger than in the singlet. Similar data for HNS+ and HNS− are reported in Table I. Both species in the doublet ground state are bent,

with the anion possessing the largest NS bond length (1.6707 vs. 1.4741 Å). When going from HNS+ to neutral (singlet) HNS and to HNS− , the NH bond length does not change significantly, whereas a slight increase of around 0.1 Å is seen in the NS bond length. This is because the added electrons are localized mainly on orbitals with antibonding character in the NS region, composed essentially of the 2p and 3p orbitals of nitrogen and sulfur. Bond angles in HNS+ and HNS− are 133.8◦ and 105.2◦ , respectively. Table II reports equivalent data for HSN, HSN+ , and HSN− . Neutral HSN has a ground state of 1 A symmetry with SH and NS bond lengths of 1.4056 and 1.4953 Å, respectively, and a bond angle of 109.9◦ . In the close-lying triplet state, the SH bond length is shorter than in the singlet by around 0.056 Å (1.3500 Å), while a larger SN bond length is found (1.6293 Å). A smaller bond angle in the triplet compared to the singlet is also found (97.9◦ ). Ground state HSN+ and HSN− are both doublets. The anion possesses larger bond lengths (∼0.05 Å) and bond angle (13◦ ). When comparing the two pairs HSN+ /HSN− and HNS+ /HNS− , the NS bond length is systematically larger in the anion than in the cation, but this effect is less pronounced in the HSN+ /HSN− couple. In contrast, the bond angle in HNS+ /HNS− is larger in

TABLE V. Equilibrium rotational constants (MHz) for neutral and charged H14 N32 S and H32 S14 N. Ae Method




CCSD(T)-F12 CCSD(T)-F12

Ce

Ae

HNS+

Basis set aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z cc-pVTZ-F12 cc-pVQZ-F12

905909 1017393 1048436 1051810 1057284 1050755 1055302

aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z VTZ-F12 VQZ-F12

570430 585731 589323 590106 590298 590136 590421

aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z cc-pVTZ-F12 cc-pVQZ-F12 aug-cc-pV(D+d)Z aug-cc-pV(T+d)Z aug-cc-pV(Q+d)Z aug-cc-pV(5+d)Z aug-cc-pV(6+d)Z cc-pVTZ-F12 cc-pVQZ-F12

Be

2022 2063 2078 2083 2085 2084 2086

Be

Ce

HSN+ 1977 2022 2037 2043 2045 2044 2046

274873 279177 279625 279656 279664 279296 279546

HNS-singlet 1862 1907 1923 1929 1931 1931 1932

1803 1847 1862 1868 1870 1869 1871

297448 304082 304915 305175 305209 304893 305286

HSN-singlet 2141 2195 2213 2220 2222 2223 2224

1997 2047 2063 2096 2072 2072 2073

772800 824273 843864 845461 848267 844098 847769

HNS-triplet 1871 1920 1934 1940 1942 1940 1942

1827 1876 1891 1896 1898 1896 1898

285963 291003 291681 291882 291913 291596 291898

HSN-triplet 1812 1880 1903 1912 1915 1914 1917

1704 1766 1787 1794 1797 1796 1798

545554 559854 563102 563805 564035 563608 563924

HNS− 1648 1699 1715 1721 1723 1721 1723

292500 299771 300807 301154 301256 301152 301598

HSN− 1911 1977 1998 2006 2009 2010 2011

1794 1854 1873 1881 1884 1884 1885

1599 1649 1664 1670 1672 1670 1671

2081 3138 2160 2168 2171 2170 2173

1934 1986 2005 2012 2014 2014 2016


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the cation than in the anion (by ∼29◦ ), whereas the opposite holds for HSN+ /HSN− (by ∼ −13◦ ). The comparison of both isomers (HNS and HSN) reveals that the r(SN) equilibrium distance is larger in HNS than in HSN by ∼0.08 Å, while the bond angles remain almost unchanged. Our findings are in good agreement with previous published data (see for instance Ref. 20). For rationalization, we performed a natural bond order calculation on neutral and charged HNS and HSN species. Bond orders are obtained from Natural Resonance Theory53–55 calculations performed with the NBO 5.956 package implemented in the Gaussian09 suite of programs. This allows determining a quantitative bond orders for them that are reported in Table III. This table shows that the bond involving hydrogen is predicted to have a bond order of approximately 1.0 for all species. In general, calculated bond orders for bonds between heavy atoms decreases as electrons are added from 11 valance

electrons to 13 valence electrons. For HNS, bond orders are computed 2.51, 2.01, and 1.51 for the 11, 12, and 13 valence electron system, respectively. HSN provides the exception as its predicted bond orders are 2.04, 2.06, and 1.58 for the 11, 12, and 13 valence electron system, respectively. Additionally, it is found that for HSN neutral there is a decrease in calculated bond order upon electronic excitation from the singlet state to the triplet state. HNS has no calculated bond order change upon electronic excitation. B. Energetics, ionization energies, and electron affinities

Calculations to determine adiabatic ionization energies (IE) and electron affinities are performed from energy calculations carried out at the CCSD(T)/aug-cc-pV(X+d)Z (X = D, T, Q, 5, 6) and CCSD(T)-F12b/VXZ-F12 (X = T, Q)

TABLE VI. Tau constants, first-order centrifugal distortion constants, harmonic and anharmonic vibrational constants for neutral and ionic HNS/HSN. Dimensional constants are in cm−1 . HNS

HNS+

HNS−

HSN

HSN+

HSN− SP−

τ AAAA τ BBBB τ CCCC τ AABB τ BBCC τ CCAA τ ABAB

−2.14 × 10−2 −3.86 × 10−6 −3.44 × 10−6 −1.06 × 10−5 −3.63 × 10−6 −3.14 × 10−5 −7.62 × 10−5

−7.96 × 10−1 −3.21 × 10−6 −2.92 × 10−6 −2.28 × 10−4 −3.01 × 10−6 −7.23 × 10−5 −2.30 × 10−4

−1.66 × 10−2 −4.38 × 10−6 −3.93 × 10−6 −2.45 × 10−5 −4.14 × 10−6 −3.78 × 10−5 −6.80 × 10−5

−5.01 × 10−3 −4.64 × 10−6 −3.49 × 10−6 −1.57 × 10−5 −3.96 × 10−6 −9.40 × 10−6 −7.16 × 10−5

−2.83 × 10−3 −5.34 × 10−6 −3.96 × 10−6 −8.67 × 10−6 −4.55 × 10−6 −7.19 × 10−6 −1.00 × 10−4

−6.34 × 10−3 5.87 × 10−6 −4.45 × 10−6 −2.66 × 10−5 −5.05 × 10−6 −1.33 × 10−6 −7.46 × 10−5

DJ DJK DK δJ R5 R6

9.11 × 10−7 4.68 × 10−5 5.30 × 10−3 2.65 × 10−8 −8.21 × 10−6 −5.49 × 10−10

7.62 × 10−7 7.49 × 10−5 1.99 × 10−1 1.83 × 10−8 −1.00 × 10−5 −1.84 × 10−9

1.03 × 10−6 4.75 × 10−5 4.10 × 10−3 2.78 × 10−8 −7.65 × 10−6 −4.00 × 10−10

1.00 × 10−6 3.22 × 10−5 1.22 × 10−3 7.23 × 10−8 −7.34 × 10−6 −3.20 × 10−9

1.15 × 10−6 4.77 × 10−5 6.59 × 10−4 8.61 × 10−8 −1.15 × 10−5 −2.98 × 10−9

1.28 × 10−6 2.84 × 10−5 1.55 × 10−3 8.86 × 10−8 −7.53 × 10−6 −3.23 × 10−9

ω1 ω2 ω3

3358 1223 1038

3402 730 1305

3324 1182 830

2136 1033 1177

2367 835 1065

1844 953 866

x11 x12 x13 x21 x22 x23 x31 x32 x33

−105.33 −12.46 0.88 −12.46 −10.22 −6.20 0.88 −6.20 −7.27

−8.97 −1.04 −5.31 −1.04 −22.44 −3.03 −5.31 −3.03 −8.97

−113.73 −17.88 1.83 −17.88 −8.41 −8.76 1.83 −8.76 −6.63

−81.11 −5.28 5.66 −5.28 −11.72 −5.64 5.66 −5.64 −8.19

−72.21 −25.20 3.56 −25.20 −5.26 −2.10 −8.73 −2.10 −8.73

−123.51 −30.34 28.62 −30.34 0.03 −33.95 28.62 −33.95 −10.33

ν1a ν2a ν3a

3180 1193 1021

...b ...b ...b

3141 1153 816

2031 1005 1162

2241 811 1049

1657 923 845

α1A α2A α3A α1B α2B α3B α1C α2C α3C

0.800 −0.880 3.57 × 10−2 4.173 × 10−4 −4.57 × 10−4 5.31 × 10−3 1.059 × 10−3 1.165 × 10−3 5.530 × 10−3

0.86 2.77 −10.65 4.49 × 10−3 1.96 × 10−3 −4.21 × 10−4 4.60 × 10−3 2.85 × 10−3 1.09 × 10−3

8.125 × 10−1 −7.141 × 10−1 5.411 × 10−2 1.803 × 10−4 1.490 × 10−4 6.657 × 10−3 7.865 × 10−4 1.735 × 10−3 6.602 × 10−3

3.900 × 10−1 −2.073 × 10−2 −1.041 × 10−1 −1.745 × 10−3 5.214 × 10−3 6.182 × 10−4 −2.030 × 10−4 4.694 × 10−3 4.078 × 10−3

3.464 × 10−1 −2.15 × 10−3 5.27 × 10−1 −3.08 × 10−3 −2.67 ×10−3 6.80 × 10−3 −1.05 × 10−3 2.07 × 10−3 5.40 × 10−3

5.53 × 10−1 −2.15 × 10−1 −1.81 × 10−2 −5.51 × 10−3 9.09 × 10−4 6.76 × 10−3 −3.18 × 10−3 5.21 × 10−4 9.95 × 10−3

a b

Computed variationally. See text.


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levels of theory. We also extrapolated these values to the CBS limit using Peterson et al.’s57 equation in conjunction with a least square procedure (i.e., EX = ECBS + A exp[− (X – 1)] + B exp[− (X – 1)2 ], where EX are single point energies of the neutral and charged species to extrapolate, X is the zeta level of the basis set and A, B are fitting parameters). Table IV reports the corresponding results for the IE calculations and the results of the EA calculations. For instance, the calculated IE for HNS is 207.1 kcal mol−1 when corrected for ZPE at CCSD(T)/aug-cc-pV(6+d)Z and 207.1 kcal mol−1 when corrected for ZPE at CCSD(T)-F12b/VQZF12. The corresponding values for the HSN isomer are 220.9 kcal mol−1 and 221.0 kcal mol−1 , respectively. Concerning the EA, we compute a value of −30.5 kcal mol−1 for HNS when corrected for ZPE at CCSD(T)/aug-cc-pV(6+d)Z and −30.3 kcal mol−1 when corrected for ZPE at CCSD(T)F12b/VQZ-F12. These values for the HSN isomer are −24.3 kcal mol−1 and −23.9 kcal mol−1 , respectively. These predictions have implications for molecular stability. Since HSN is predicted to require the most energy for the ionization process and predicted to release the least amount of energy from electron capture, it is predicted that given similar chemical environments, HSN will be the least reactive. Finally, Table IV lists the relative energy between HNS and HSN (denoted there as Eisom ). Both CCSD(T)/CBS and CCSD(T)F12/VQZ-F12 provide a Eisom of 19.5 kcal mol−1 , in favor of HNS species. C. Spectroscopic parameters

We present in Tables I and II the harmonic vibrational frequencies for neutral and charged HNS and HSN computed using different combinations of theory/basis sets. Unfortunately, no experimental data concerning the IR spectra of these molecules are available in the literature for comparison. The following discussion focuses on results obtained TABLE VII. Anharmonic vibrational levels of ground state, HNS and HNS− obtained from variational calculations (see text for details on the adopted methodology). HNS−

HNS (v1 ,v2 ,v3 )

Energy (cm−1 )

(v1 ,v2 ,v3 )

Energy (cm−1 )

0.0 1021.5 1193.7 2030.2 2208.3 2367.0 3027.5 3180.0 3210.9 3373.5 3520.6

(0,0,0) (0,0,1) (0,1,0) (0,0,2) a (0,1,1)a (0,2,0) (0,0,3)a (0,1,2)a (0,2,1)a (1,0,0) (0,0,4)a (0,3,0)a (0,1,3)a (0,2,2)a (1,0,1)

0.0 816.0 1153.4 1624.9 1960.6 2290.1 2430.5 2761.1 3087.8 3141.6 3237.0 3410.0 3559.2 3879.6 3961.7

(0,0,0) (0,0,1) (0,1,0) (0,0,2) (0,1,1)a (0.2,0)a (0,0,3)a (1,0,0) (0,1,2)a (0,2,1)a (0,3,0)a

a

Anharmonic resonance.

˜ 1 A ), at the CCSD(T)-F12/cc-pVQZ-F12 level. For HNS (X we calculated HN and NS stretching frequencies of 3351 and 1040 cm−1 , respectively. For comparison, the ωe of the NS diatomic is 1218.7 cm−1 .58 A bending frequency of 1222 cm−1 is computed. In HNS triplet, the HN stretching is very similar to what is found for the singlet, while a slightly larger frequency is obtained for the NS stretching. The vibrational bending mode is markedly smaller in the triplet (754 cm−1 ). ˜ 1 A ), we computed HS and NS stretching freFor HSN (X quencies of 2138 and 1183 cm−1 , respectively, and a bending frequency of 1034 cm−1 . Compared to the singlet, triplet HSN shows smaller frequencies for both SN stretching (781 cm−1 ) and HSN bending (879 cm−1 ). Ionization of HSN and HNS or their one-electron attachment lead to redshifted bending frequencies and, in the case of HSN, to redshifted SN stretching. The NH stretching does not change appreciably when going from HNS+ to HNS (singlet) and to HNS− , while a sharp decrease is seen in the SH stretching for HSN+ -HSN (singlet)HSN− . Interestingly, the frequency difference between the HS stretching of HSN triplet and HSN− is of 770 cm−1 , as reflected by the difference in the SH equilibrium bond length of 0.08 Å. To facilitate the comparison with the experimental data deduced from the rotational spectra, we give in Table V, at the various levels of theory adopted, the rotational constants of neutral HNS and HSN (in the singlet and triplet states) and of the relative mono-charged species. We recommend those obtained at the (R)CCSD(T)/aug-cc-pV(X+d)Z+CBS or (R)CCSD(T)-F12/VQZ-F12 values for the analysis of the TABLE VIII. Anharmonic vibrational levels of ground state HSN+ , HSN, and HSN− obtained from variational calculations (see text for details on the adopted methodology). HSN+

(v1 ,v2 ,v3 )

Energy (cm−1 )

(0,0,0) (0,1,0) (0,0,1) (0,2,0)a (0,1,1)a (0,0,2)a (1,0,0) (0,3,0)a (0,2,1)a (0,1,2)a (1,1,0) (0,0,3)a (0,4,0)a (1,0,1) (0,3,1)a (0,2,2)a (1,2,0)a (0,1,3)a (0,5,0)a

0.0 811.0 1049.1 1611.1 1858.6 2083.1 2241.3 2400.1 2656.9 2890.4 3028.2 3104.2 3177.8 3295.2 3444.3 3686.9 3803.9 3910.0 3944.0

a

HSN−

HSN

(v1 ,v2 ,v3 )

Energy (cm−1 )

(0,0,0) (0,1,0) (0,0,1) (0,2,0) a (1,0,0)a (0,1,1)a (0,0,2)a (1,1,0)a (0,3,0)a (0,2,1)a (1,0,1)a (0,1,2)a (0,0,3)a (1,2,0)a (2,0,0)a

0.0 1005.6 1162.5 1975.4 2031.7 2162.1 2310.6 2939.0 3031.5 3135.0 3194.0 3305.0 3446.1 3883.6 3963.7

(v1 ,v2 ,v3 )

Energy (cm−1 )

(0,0,0) (0,0,1)a (0,1,0)a (1,0,0)a (0,0,2)a (0,1,1)a (0,2,0)a (1,0,1)a (0,0,3)a (1,1,0)a (0,1,2)a (0,2,1)a (0,3,0)a (0,0,4)a (2,0,0)a (1,0,2)a (0,2,2)a (1,1,1)a (0,1,3)a (1,2,0)a (0,0,5)a

0.0 845.3 923.2 1656.8 1682.2 1761.9 1840.5 2481.6 2517.1 2548.5 2603.5 2669.6 2751.8 3288.5 3306.1 3341.4 3377.5 3432.3 3442.1 3509.5 3570.1

Anharmonic resonance.


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(0,0,3)

(0,1,2)

(0,2,1)

(0,3,0)

˜ 1 A ) vibrational wave functions of the (0,0,3), (0,1,2), (0,2,1), (0,3,0) levels along the SN stretching and bending coFIG. 1. Contour plots of the HNS (X ˜ 1 A ). The energies (in cm−1 ) of the levels are given in the upper corner of each 2D ordinates. The HN distance is fixed at the equilibrium value of HNS (X cut.

experimental spectra. From the 3D potential energy surfaces (3D PESs) for all species considered in this study, a set of spectroscopic parameters was also obtained following the approach described in Sec. II. They include τ and first-order centrifugal distortion constants, rovibrational (α i ) and anharmonic terms (xij ), and fundamental frequencies (ν i ). They are listed in Table VI. D. Variationally determined vibrational spectra

The pattern of the lowest vibrational levels and wavefunctions for ground state HNS0,− and HSN0,± has been obtained up to 4000 cm−1 above the minima of the respective 3D

PESs. Results are shown in Tables VII and VIII. A tentative assignment in terms of harmonic components contributing to each level, based on the inspection of the corresponding vibrational wavefunctions, is presented as well. In Table VII, v1 , v2 , v3 quantum numbers refer to HN stretching, HNS bending, and NS stretching modes, in the same order, while in Table VIII they refer to HS, HSN bending, and SN stretching. In these tables, an asterisk is placed to highlight vibrational levels that are anharmonic resonances, for which the (v1 , v2 , v3 ) symbol represents the dominant component within the resonant modes. From comparison of Tables VI–VIII, we see that the largest negative deviations from the harmonic values for the fundamental vibrational frequencies are found for the


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(0,2,0)

(1,0,0)

(0,1,1)

(1,1,0)

(0,3,0)

˜ 1 A ) vibrational wave functions of the (0,2,0), (1,0,0), (0,1,1), (1,1,0), (0,3,0) levels along the SN stretching and bending FIG. 2. Contour plots of the HSN (X ˜ 1 A ). The energies (in cm−1 ) of the levels are given in the upper corner of each coordinates. The HS distance is fixed at the equilibrium value of HSN (X 2D cut.

HN and HS stretching modes, where the average differences are of around −156 cm−1 . Smaller mean differences are calculated for the other modes, that is ∼ −16 for the SN stretching and ∼ −28 for the bending. In HNS, no strong anharmonic resonances are seen in the fundamental vibrational levels, while slightly interacting Fermi polyads, because of the rough closeness of the SN

stretching and HNS bending unperturbed frequencies (1038 and 1223 cm−1 , respectively), are found. For illustration we display in Figure 1 the (0,0,3), (0,1,2), (0,2,1), (0,3,0) series. Although, anharmonicity exists within the low-energy vibrational levels of the HNS− anion, it does not affect the fundamentals. No polyad structures are calculated for this system in the considered energy window.


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(0,0,1)

(0,1,0)

(0,0,2)

(1,0,0)

(0,1,1)

(0,2,0)

˜ 2 A ) vibrational wave functions of the (0,0,1), (0,1,0), (1,0,0), (0,0,2), (0,1,1), (0,2,0) levels along the SN stretching and FIG. 3. Contour plots of the HSN− (X bending coordinates. The HS distance is fixed at the equilibrium value of HSN− . The energies (in cm−1 ) of the levels are given in the upper corner of each 2D cut.

For neutral HSN molecule in the lowest singlet state, a strong Fermi resonance is found between the (1,0,0) fundamental vibration and the (0,2,0) overtone (see Figure 2). The corresponding energy levels are displaced from the unperturbed ones and only variationally computed frequencies (as those given here) are reliable and comparable to the recorded spectra. Another noticeable anharmonic resonance exists in the two levels at 2939 cm−1 and 3031 cm−1

between the (1,1,0) and (0,3,0) harmonic components (see Figure 2). In HSN+ , anharmonicity is caused by weak interaction of polyads involving combination modes and overtones with quanta of excitation on the bending and SN stretching modes. In HSN− , all vibrational fundamental levels are affected by mixing with the close lying unperturbed levels resulting in anharmonic resonances as illustrated in Figure 3. This is due to the closeness of the SN stretching and


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bending unperturbed frequencies (866 cm−1 and 953 cm−1 , respectively, Table VI), which are roughly half the value of the HS stretching frequency (1844 cm−1 ). Polyad structures are found also in higher levels. Again, for this anion, solely the full variationally computed spectrum can be directly compared to any measured one. IV. CONCLUSIONS

Using ab initio methodology, we examined the structural and energetic properties of gas phase HNSq and HSNq (q = 0, +1, −1) with specific emphasis on the equilibrium geometries, rotational constants, and harmonic frequencies. We also generated their 3D PESs close to equilibrium that were incorporated into perturbative and variational treatment of the nuclear motions. An ensemble of highly accurate theoretical data that should be close to the experimental values is provided. These molecular properties should facilitate the assignments of the microwave, IR and rotationally resolved photoelectron spectra and the photodetachment spectra of HNS and of HSN. They should also be useful in the identification of these molecular species in the ISM and related media. We recommend hence the anharmonic wavenumbers derived from variational computations for that purposes. ACKNOWLEDGMENTS

This study was undertaken while M.H. was a Visiting Professor at King Saud University. The support of the Visiting Professor Program at King Saud University is hereby gratefully acknowledged. 1 P.

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Panel 1: phase I investigations.

Si(1 1 0) corners in nanostructures.

Gas-Phase Thermal Tautomerization of Imidazole-Acetic Acid: Theoretical and Computational Investigations.

Geometries, stabilities and fragmental channels of neutral and charged sulfur clusters: Sn(Q) (n = 3-20, Q = 0, ±1).

Growth, structure and morphology of epitaxial Fe(0 0 1) films on GaAs(0 0 1)c(4 × 4).

Elaboration, Rietveld refinements and vibrational spectroscopic study of Na₁-xKxCaPb₃(PO₄)₃ lacunar apatites (0 ⩽ x ⩽ 1).

[1 + 1 = 0. Reprogramming of nociceptors].

Phonon dispersion of silicene on ZrB2(0 0 0 1).

Bistable Si dopants in the GaAs (1 1 0) surface.

Mixed micelles of sodium cholate and sodium dodecylsulphate 1:1 binary mixture at different temperatures--experimental and theoretical investigations.

Reflectance anisotropy of the anatase Tio2(0 0 1)-(4 × 1) surface.

Spectroscopic and structural investigations of iron(III) isothiocyanates. A comparative theoretical and experimental study.

Hydroxo-bridged dimers of oxo-centered ruthenium(III) triangle: synthesis and spectroscopic and theoretical investigations.

Adsorption and enhanced photocatalytic activity of the {0 0 0 1} faceted Sm-doped ZnIn2S4 microspheres.

On the chemistry of 1-pyrroline in solution and in the gas phase.

A theoretical benchmark study of the spectroscopic constants of the very heavy rare gas dimers.

Theoretical and numerical investigations of inverse patchy colloids in the fluid phase.

Cr(1 1 0) interface.

Constrained-geometry bisphosphazides derived from 1,8-diazidonaphthalene: synthesis, spectroscopic characteristics, structural features, and theoretical investigations.

The growth of ultra-thin zirconia films on Pd(3)Zr(0 0 0 1).

A first-principles investigation of the stabilities and electronic properties of SrZrO3 (1 1 0) (1 × 1) polar terminations.

Growth, reaction and nanowire formation of Fe on the ZnS(1 0 0) surface.

(0 0 1)SrTiO3 interface.

Ag(0 0 1): undulation of hexagonal oxide monolayers due to square lattice metal substrates.