Ab initio structural and spectroscopic study of HPSx and HSPx (x = 0,+1,1) in the gasphaseSaida Ben Yaghlane, C. Eric Cotton, Joseph S. Francisco, Roberto Linguerri, and Majdi Hochlaf Citation: The Journal of Chemical Physics 139, 174313 (2013); doi: 10.1063/1.4827520 View online: http://dx.doi.org/10.1063/1.4827520 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/17?ver=pdfcov Published by the AIP Publishing

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THE JOURNAL OF CHEMICAL PHYSICS 139, 174313 (2013)

Ab initio structural and spectroscopic study of HPSx and HSPx

(x = 0,+1,−1) in the gas phaseSaida Ben Yaghlane,1 C. Eric Cotton,2 Joseph S. Francisco,2,a) Roberto Linguerri,3

and Majdi Hochlaf3,a)

1Laboratoire de Spectroscopie Atomique, Moléculaire et Applications – LSAMA, Université de Tunis,Tunis, Tunisia2Department of Chemistry and Department of Earth and Atmospheric Science, Purdue University,West Lafayette, Indiana 49707, USA3Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est,5 bd Descartes, 77454 Marne-la-Vallée, France

(Received 4 September 2013; accepted 16 October 2013; published online 6 November 2013)

Accurate ab initio computations of structural and spectroscopic parameters for the HPS/HSPmolecules and corresponding cations and anions have been performed. For the electronic struc-ture computations, standard and explicitly correlated coupled cluster techniques in conjunction withlarge basis sets have been adopted. In particular, we present equilibrium geometries, rotational con-stants, harmonic vibrational frequencies, adiabatic ionization energies, electron affinities, and, forthe neutral species, singlet-triplet relative energies. Besides, the full-dimensional potential energysurfaces (PESs) for HPSx and HSPx (x = −1,0,1) systems have been generated at the standardcoupled cluster level with a basis set of augmented quintuple-zeta quality. By applying perturba-tion theory to the calculated PESs, an extended set of spectroscopic constants, including τ , first-order centrifugal distortion and anharmonic vibrational constants has been obtained. In addition,the potentials have been used in a variational approach to deduce the whole pattern of vibrationallevels up to 4000 cm−1 above the minima of the corresponding PESs. © 2013 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4827520]

I. INTRODUCTION

Current states of the most advanced ab initio methodsand computational power allow for very accurate descriptionof spectroscopic properties and reaction dynamics of smallmolecules in gas phase. This is particularly important forastrochemistry, where computational studies to the limit ofexperimental accuracy are beneficial for the detection andcharacterization of new molecular species, for instance, in theinterstellar medium (ISM).

Among the simplest triatomics are hydrides of diatomics,and many of the triatomic molecular species currently iden-tified in the ISM are monohydrides. This includes HCO+,1

HOC+,2 HCS+,3 HCN,4 HNC,5 HCO,6 NNH+,7 HCP,8 andHNO.9 To date, unlike the isovalent PO,10 PS is not identi-fied in the ISM, but it is proposed as a component in the at-mosphere of gas giants as brown and other low-mass dwarfstars.11–13 Likewise, PS based neutral or charged monohy-drides are not detected so far in the ISM, so a computationalstudy of these species is of astrochemical interest.

Both the precursor diatomics and triatomic monohy-drides have been widely studied both theoretically andexperimentally. Experimental data for PS and PS+ arereported in the literature14–16 as well as high-level ab initiocomputational work17 on PS, PS+, and PS−. Laboratorystudies on the isovalent neutral HPS and HSP species include

a)Authors to whom correspondence should be addressed. Electronic ad-dresses: francisc@purdue.edu and hochlaf@univ-mlv.fr. Telephone: +33 160 95 73 19. Fax: +33 1 60 95 73 20.

the neutralization–reionization mass spectrometry study byWong et al.18 and an experimental investigation by Halfenet al.19 reporting the pure rotational spectrum of HPS in theground electronic state, the deduced rotational constants,and the semi-experimental and CCSD(T)/cc-pwCVQZcalculated geometrical parameters. Recently, Clouthier andco-workers20 presented the laser induced fluorescence andsingle vibronic level emission spectra of HPS, after anelectrical discharge was applied through a gas current ofhydrogen sulfide and phosphine precursors in argon. Thespectrum is composed of a rich structure from which thefundamentals for the bending and PS stretching modes ofthe S0 and S1 electronic states were deduced. Theoretically,previous works consist of first principles investigations ofthe ground electronic states21–23 and a recent high-levelcomputational study using configuration interaction andcoupled cluster methods paired with Pople basis sets,24

where the energy barrier for the HPS to HSP interconver-sion was estimated. For the HPS−/HSP− radical anions25

and for the HPS+/HSP+ radical cations,21, 23, 26 theoreticaldata exist also from low-level computational approaches.In these works, the ground state geometry of the neutraland charged species is shown to be bent, in agreementwith the simple Walsh rules for HXY triatomics having11, 12, and 13 valence electrons. For instance in HPS,according to Walsh diagrams, the energy of the 13a′ orbitalcorrelating to the 4π orbital at linearity sharply increaseswith the bond angle. Since the ground state electron con-figuration of HPS is (11a′)2(12a′)2(3a′′)2(13a′)2(4a′′)0,

0021-9606/2013/139(17)/174313/12/$30.00 © 2013 AIP Publishing LLC139, 174313-1

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174313-2 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

the molecule is bent at equilibrium. Whereas, thepromotion of one electron from the HOMO to the LUMOresults in a (11a′)2(12a′)2(3a′′)2(13a′)1(4a′′)1 electron config-uration. Again, since the energy of the 4a′′ molecular orbitalcorrelating to the 4π orbital at linearity is practically invariantwith the bond angle, the molecule should remain bent even inthe lowest excited singlet or triplet states. Similar conclusionsapply to HSP.

In the present theoretical investigation, we employ high-level electronic structure theoretical methodologies to get ac-curate equilibrium geometrical parameters and rotational con-stants for the HPS and HSP neutral and charged species. Wededuce then the ionization energies and electron affinities ofHPS and HSP. The harmonic vibrational frequencies are com-puted at various levels of theory for the neutral moleculesin their lowest singlet (S0) and triplet states (T1) and for thepositive/negative ions in their ground doublet states. Our val-ues are compared to the experimental data, when available.In addition, we generated the ground state 3D potential en-ergy hypersurfaces (PESs) for the species under investigationat the coupled cluster level in connection with a large basisset augmented by diffuse atomic functions. Afterwards, thesePESs were incorporated into a variational treatment of thenuclear motions to get the vibrational spectra. We used alsothese PESs and second order perturbation theory to obtainan exhaustive panel of spectroscopic parameters. This workrepresents the first theoretical investigation of the vibrationalstructure of the HPS/HSP system going beyond the simpleharmonic picture, and it should help considerably in the de-tection of these molecules in the laboratory and in the ISM.

II. COMPUTATIONAL METHODS

A. Electronic structure calculations

Geometry optimizations and harmonic frequency calcu-lations were performed with the MOLPRO27 suite of ab initioprograms in its 2012.1 version. Bond orders are obtained fromNatural Resonance Theory28 calculations performed with theNBO 5.929 package as implemented in the GAUSSIAN 0930

suite of programs. In the geometry optimizations and har-monic frequencies calculations, the default options and algo-rithms set by MOLPRO and by GAUSSIAN 09 were used.

Inspection of the electronic wavefunctions of the molec-ular systems under investigation shows that they are dom-inantly described by a single determinant. Hence, for thepresent study, we used coupled cluster approaches. For closedshell systems, the coupled cluster approach in the singlesand doubles approximation with a perturbative treatment ofthe triple excitations31, 32 (CCSD(T)) and the explicitly cor-related coupled cluster technique33–36 (CCSD(T)-F12), in theF12b approximation, hereafter indicated simply as CCSD(T)-F12, have been used throughout. For open-shell systems, thepartially spin restricted versions of the above theories37–39

have been used instead. A large panel of basis sets has beenadopted with the CCSD(T) method. This includes the aug-cc-pV(X+d)Z (X = D,T,Q,5,6) and aug-cc-pV5Z sets,40–42

where the former has additional tight-d functions added tosecond row atoms and the latter has been chosen for the

generation of the PESs. For the explicitly correlated coupledcluster computations, the cc-pVXZ-F12 (X = T,Q) sets,43 inconnection with the corresponding resolutions of the identityand density fitting functions44 have been employed. It is wellestablished in the literature45–47 that the explicitly correlatedcoupled cluster procedure in both the F12a or F12b formula-tions with the cc-pVTZ-F12 basis set leads to relative ener-gies and spectroscopic parameters of a quality comparable tostandard coupled cluster with the aug-cc-pV5Z set, but witha large reduction of computational effort, both in terms ofCPU time and disk space. The coupled cluster methodologiesadopted here in conjunction with the above basis sets allow todescribe the correlation effects due to valence electrons, thatis, those giving the most important contributions to the for-mation of the chemical bonds. Small contributions from coreelectrons were not considered in this study.

B. Generation of the three dimensional potentialenergy surfaces and nuclear motion treatments

The 3D-PESs for the HPS, HPS−, HPS+, HSP, HSP−,and HSP+ species in their lowest electronic states have beenmapped in the set of internal coordinates, that is, R(PS) (R1)and R(HX, X = P or S) (R2) bond lengths and HXY bondangle (θ ). Calculations were done at different nuclear ge-ometries around the ground state equilibrium structure andthe internal coordinate space was chosen to cover an energyrange of around 10 000 cm−1 above each minimum. Then,the calculated energies were fitted, according to a linear leastsquare procedure, to the following analytical form, where allthe points contribute with equal weights,

V(R1, R2, θ ) =∑

ijk

cijkQi1Qj

2Qk3, (1)

with Qu = (Ru−Ru,ref) for u = 1 and 2, and Q3 = θ−θ ref (0◦

≤ θ ≤ 180◦), where coordinates R1,ref, R2,ref, and θ ref refer tothe equilibrium geometry of the considered electronic state.

The maximum degree of the polynomial expansion V(R1,R2, θ ) was fixed by the relation i + j + k ≤ 4. The cijk coeffi-cients were optimized in the least square procedure. The rootmean square of the fits was less than 1 cm−1.

The resulting PESs were used to compute the quarticforce fields in internal coordinates. After subsequent transfor-mation by the l-tensor algebra to quartic force fields in dimen-sionless normal coordinates with the SURFIT package,48, 49 aset of spectroscopic constants have been obtained by apply-ing second order perturbation theory. In addition, these 3D-PESs have been used in conjunction with the RVIB3 pro-gram by Carter and Handy50, 51 to obtain the variationallycalculated vibrational levels and wavefunctions. In the vari-ational approach, we accounted fully for anharmonicity ef-fects, rotational-vibrational, and electronic angular momentacouplings. The accuracy of the calculated vibrational levelsis mainly influenced by the numerical approximations intro-duced in the variational treatment, since the quality of the ana-lytical representations of the PESs should be high. We expectthat the energies of the calculated vibrational levels will notdiffer from experimental data by more than 10 cm−1, as it wasalready shown in similar studies on triatomic compounds,52–54

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174313-3 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

TABLE I. Geometric properties and harmonic vibrational frequencies of HPS, HPS+, and HPS−.

Method Basis set r(PH) r(PS) θ (HPS) HP str. SP str. HPS ben.

HPS+

CCSD(T) aug-cc-pV(D+d)Z 1.4480 1.9580 95.4 2253 675 573aug-cc-pV(T+d)Z 1.4373 1.9350 96.1 2248 680 551aug-cc-pV(Q+d)Z 1.4367 1.9231 96.8 2252 692 542aug-cc-pV(5+d)Z 1.4368 1.9194 97.0 2249 695 539aug-cc-pV(6+d)Z 1.4367 1.9178 97.1

aug-cc-pV5Z a 1.4359 1.9208 96.6 2257 692 563CCSD(T)-F12 cc-pVTZ-F12 1.4370 1.9183 97.1 2247 701 543

cc-pVQZ-F12 1.4369 1.9172 97.2 2247 697 534

HPS–singletCCSD(T) aug-cc-pV(D+d)Z 1.4467 1.9672 101.3 2261 654 893

aug-cc-pV(T+d)Z 1.4349 1.9465 101.6 2266 673 899aug-cc-pV(Q+d)Z 1.4338 1.9373 101.8 2277 684 904aug-cc-pV(5+d)Z 1.4336 1.9345 101.8 2275 687 905aug-cc-pV(6+d)Z 1.4335 1.9333 101.8

aug-cc-pV5Z a 1.4335 1.9347 102.1 2273 686 909CCSD(T)-F12 cc-pVTZ-F12 1.4338 1.9336 101.9 2275 688 905

cc-pVQZ-F12 1.4335 1.9331 101.8 2276 689 906Expt. 1.4321b 1.9287b 101.8b 673c 885c

HPS–tripletCCSD(T) aug-cc-pV(D+d)Z 1.4354 2.0503 95.3 2334 491 626

aug-cc-pV(T+d)Z 1.4240 2.0244 95.9 2336 494 621aug-cc-pV(Q+d)Z 1.4226 2.0105 96.8 2346 488 625aug-cc-pV(5+d)Z 1.4224 2.0065 96.9 2345 486 626aug-cc-pV(6+d)Z 1.4222 2.0046 97.0

CCSD(T)-F12 cc-pVTZ-F12 1.4226 2.0054 96.9 2344 485 626cc-pVQZ-F12 1.4222 2.0039 97.1 2345 484 628

HPS−

CCSD(T) aug-cc-pV(D+d)Z 1.4544 2.0717 101.2 2176 543 828aug-cc-pV(T+d)Z 1.4422 2.0489 101.4 2183 561 836aug-cc-pV(Q+d)Z 1.4407 2.0386 101.6 2196 571 842aug-cc-pV(5+d)Z 1.4405 2.0357 101.6 2195 573 843aug-cc-pV(6+d)Z 1.4403 2.0343 101.6

aug-cc-pV5Za 1.4404 2.0338 101.9 2196 578 848CCSD(T)-F12 cc-pVTZ-F12 1.4406 2.0344 101.6 2195 574 844

cc-pVQZ-F12 1.4404 2.0336 101.6 2195 577 845

aFrom our 3D PESs.bReference 19.cReference 20.

where a direct comparison between theory and experimentcould be done.

III. RESULTS AND DISCUSSION

At the CCSD(T)/6-311++G(3df,3pd) level of theory,Viana and Pimentel24 computed isomerization barriers of49.8 kcal mol−1 and 22.3 kcal mol−1 for HPS to HSP in thesinglet potential and for the HSP to HPS in the triplet po-tential. These isomerization barriers are rather high, so eachisomeric form could be treated separately. Preliminary com-putations for the ionic species show that this is also the casefor the corresponding cations and anions.

A. Equilibrium structures

The calculated equilibrium structures for HPS, HPS+,HPS− and for HSP, HSP+, HSP− in their lowest electronic

states are reported in Tables I and II, respectively. For theneutral species data for the lowest triplet states are shown aswell. The calculated structural parameters refer in each caseto the structure at equilibrium. Values of bond lengths andbond angles in Tables I and II show convergence as the sizeof the basis set increases: this can be seen in particular go-ing from the aug-cc-pV(D+d)Z to the aug-cc-pV(6+d)Z sets.As expected, the CCSD(T)-F12/cc-pVQZ-F12 data are veryclose to the CCSD(T)/aug-cc-pV(6+d)Z ones, and we con-sider the latter values as best estimates of the investigated pa-rameters. In the following, we will quote the CCSD(T)/aug-cc-pV(6+d)Z ones.

The HPS molecule has a singlet ground electronic state,with PH and PS bond lengths of 1.4335 Å and 1.9333 Å, re-spectively (cf. Table I). The bond angle is calculated to be101.8◦. These predictions are in excellent agreement with theempirically determined geometric structure from the pure ro-tational spectrum by Halfen et al.,19 that give 1.4321 and

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174313-4 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

TABLE II. Geometric properties and harmonic vibrational frequencies of HSP, HSP+, and HSP−.

Method Basis set r(SH) r(PS) θ (HSP) HS str. SP str. HSP ben.

HSP+

CCSD(T) aug-cc-pV(D+d)Z 1.3709 2.0016 98.0 2546 601 756aug-cc-pV(T+d)Z 1.3600 1.9791 98.0 2553 624 760aug-cc-pV(Q+d)Z 1.3600 1.9686 98.2 2552 634 755aug-cc-pV(5+d)Z 1.3599 1.9654 98.3 2550 636 765aug-cc-pV(6+d)Z 1.3599 1.9640 98.3

aug-cc-pV5Za 1.3595 1.9651 98.6 2557 632 762CCSD(T)-F12 cc-pVTZ-F12 1.3603 1.9645 98.3 2549 636 755

cc-pVQZ-F12 1.3600 1.9639 98.3 2550 638 755

HSP–singletCCSD(T) aug-cc-pV(D+d)Z 1.3749 2.0047 105.9 2442 580 870

aug-cc-pV(T+d)Z 1.3622 1.9845 105.8 2468 597 879aug-cc-pV(Q+d)Z 1.3622 1.9742 106.1 2467 607 884aug-cc-pV(5+d)Z 1.3622 1.9710 106.1 2465 609 888aug-cc-pV(6+d)Z 1.3623 1.9695 106.1

CCSD(T)-F12 cc-pVTZ-F12 1.3632 1.9693 106.2 2458 611 889cc-pVQZ-F12 1.3624 1.9694 106.2 2464 611 888

HSP–tripletCCSD(T) aug-cc-pV(D+d)Z 1.3552 2.1288 96.2 2659 483 722

aug-cc-pV(T+d)Z 1.3442 2.1000 96.2 2667 506 727aug-cc-pV(Q+d)Z 1.3437 2.0876 96.5 2671 514 728aug-cc-pV(5+d)Z 1.3436 2.0840 96.5 2669 517 729aug-cc-pV(6+d)Z 1.3437 2.0823 96.6

aug-cc-pV5Za 1.3431 2.0842 96.7 2675 515 732CCSD(T)-F12 cc-pVTZ-F12 1.3441 2.0836 96.4 2667 516 728

cc-pVQZ-F12 1.3440 2.0817 96.6 2667 519 729

HSP−

CCSD(T) aug-cc-pV(D+d)Z 1.3675 2.1596 104.8 2474 418 768aug-cc-pV(T+d)Z 1.3560 2.1283 105.0 2486 441 800aug-cc-pV(Q+d)Z 1.3563 2.1134 105.3 2482 451 791aug-cc-pV(5+d)Z 1.3563 2.1091 105.4 2479 455 794aug-cc-pV(6+d)Z 1.3564 2.1070 105.4

aug-cc-pV5Za 1.3562 2.1087 105.9 2479 448 797CCSD(T)-F12 cc-pVTZ-F12 1.3566 2.1077 105.5 2477 454 797

cc-pVQZ-F12 1.3564 2.1069 105.5 2479 456 796

aFrom our 3D PESs.

1.9287 Å for PH and PS bond lengths and 101.8◦ for thebond angle. Equilibrium rotational constants for this speciesat various levels of theory are given in Table III. They arecalculated to be 266 090 MHz for Ae, 8346 MHz for Be, and8093 MHz for Ce constants. This is compared to the experi-mentally determined values of 264 001, 8379, and 8111 MHz,respectively.19 This represents no more than 0.7% absolute er-ror. For the lowest triplet state, our calculations show a slightcontraction of the PH bond (1.4222 Å) and relaxation of thePS bond (2.0046 Å) with respect to the singlet. This is in ac-cord with the promotion of one electron from the 13a′ molec-ular orbital (MO) to the 4a′′ MO, with the latter being es-sentially the antibonding combination of the 3p orbitals ofsulfur and phosphorous. The bond angle is predicted to be97.0◦. The rotational constants Ae, Be, and Ce are calculatedto be 261 565, 7803, and 7577 MHz, respectively. Similar datafor HPS+ and HPS− are reported in Table I. Both speciesin the doublet ground state are bent, with the anion possess-ing the largest bond lengths (R(PH) = 1.4403 Å and R(PS)= 2.0343 Å). Corresponding equilibrium rotational constants

are equally shown in Table III. These data are predictive innature.

Table II reports equilibrium geometries for HSP, HSP+,and HSP− at various levels of theory. For HSP, data relativeto the lowest-lying singlet and triplet electronic states are con-sidered. As in the other isomer, none of these states are linearat equilibrium and the bond angle in the triplet state (96.6◦) isfound to be smaller than in the singlet (106.1◦). Bond lengthsin the singlet state are 1.3623 Å for R(SH) and 1.9695 Å forR(SP). Corresponding values for the triplet state are 1.3437 Åand 2.0823 Å. Again, a relaxation of the sulfur-phosphorousbond length in the triplet is seen. The equilibrium rotationalconstants Ae, Be, and Ce are 306 485, 8027, and 7822 MHzfor the singlet state, and 291 769, 7249, and 7073 MHz forthe triplet state. Table II lists also the data for the cationic andanionic HSP systems in their most stable doublet electronicstates. In both cases bent equilibrium geometries are found,with a slight lengthening of the R(SP) bond length in the an-ion (+0.143 Å). Bond angles are found to be 98.3◦ in HSP+

and 105.4◦ in HSP−. These results should be helpful in the

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174313-5 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

TABLE III. Equilibrium rotational constants (MHz) for neutral and charged HPS and HSP.

Ae Be Ce Ae Be Ce

Method Basis set HPS+ HSP+

CCSD(T) aug-cc-pV(D+d)Z 250 434 8189 7930 282 653 7833 7621aug-cc-pV(T+d)Z 255 011 8379 8113 287 079 8012 7794aug-cc-pV(Q+d)Z 256 189 8477 8205 287 581 8095 7874aug-cc-pV(5+d)Z 256 414 8508 8234 287 661 8121 7899aug-cc-pV(6+d)Z 256 561 8521 8247 287 695 8132 7909

aug-cc-pV5Z a 256 202 8508 8235 288 550 8129 7906CCSD(T)-F12 cc-pVTZ-F12 256 452 8517 8243 287 488 8128 7905CCSD(T)-F12 cc-pVQZ-F12 256 662 8526 8252 287 686 8133 7910

HPS–singlet HSP–singletCCSD(T) aug-cc-pV(D+d)Z 260 217 8066 7824 300 003 7751 7556

aug-cc-pV(T+d)Z 265 138 8236 7987 305 381 7910 7710aug-cc-pV(Q+d)Z 265 880 8312 8060 306 203 7991 7787aug-cc-pV(5+d)Z 266 020 8336 8083 306 402 8016 7811aug-cc-pV(6+d)Z 266 090 8346 8093 306 485 8027 7822

aug-cc-pV5Za 266 792 8340 8087CCSD(T)-F12 VTZ-F12 266 074 8343 8089 306 360 8028 7823CCSD(T)-F12 VQZ-F12 266 133 8348 8094 306 624 8028 7823

Expt.b 264 001 8379 8111

HPS–triplet HSP–tripletCCSD(T) aug-cc-pV(D+d)Z 254 743 7472 7259 286 400 6938 6774

aug-cc-pV(T+d)Z 259 496 7660 7440 291 451 7241 7065aug-cc-pV(Q+d)Z 261 071 7760 7536 291 689 7253 7077aug-cc-pV(5+d)Z 261 390 7790 7564 291 732 7237 7062aug-cc-pV(6+d)Z 261 565 7803 7577 291 769 7249 7073

aug-cc-pV5Za 292 331 7241 7066CCSD(T)-F12 cc-pVTZ-F12 261 236 7799 7573 291 451 7241 7065CCSD(T)-F12 cc-pVQZ-F12 261 680 7808 7582 291 689 7253 7077

HPS− HSP−

CCSD(T) aug-cc-pV(D+d)Z 257 057 7278 7077 299 413 6694 6548aug-cc-pV(T+d)Z 261 857 7439 7234 305 048 6891 6739aug-cc-pV(Q+d)Z 262 726 7513 7304 306 057 6986 6830aug-cc-pV(5+d)Z 262 881 7534 7324 306 300 7014 6857aug-cc-pV(6+d)Z 262 989 7544 7334 306 393 7027 6896

aug-cc-pV5Za 263 650 7554 7343 307 952 7020 6863CCSD(T)-F12 cc-pVTZ-F12 262 880 7544 7333 306 701 7022 6865CCSD(T)-F12 cc-pVQZ-F12 262 958 7549 7339 306 764 7027 6869

aFrom our 3D PESs.bReference 19.

experimental characterization of these species from mi-crowave studies whenever measured.

B. Energetics: Ionization energiesand electron affinities

Energetic properties, including adiabatic ionization ener-gies, electron affinities, and singlet-triplet energy differenceof HPS/HSP are characterized at different levels of accuracy(cf. Tables S1 and S2 of the supplementary material).55 Re-sults are shown in Table IV. In addition, extrapolations of theCCSD(T) values at the CBS limit are presented. We used Pe-terson et al.’s56 equation in conjunction with a least squareprocedure

En = ECBS + A exp[−(n − 1)] + Bexp[−(n − 1)2], (2)

with n being the zeta level of the basis set and A, B fitting pa-rameters, to extrapolate the single point energies of the neu-

tral and charged species. In the fit, only the CCSD(T)/aug-cc-pV(X+d)Z energies with X = T,Q,5,6 have been used.

At all levels of theory employed in this research, wefound that mono-charged positive and negative ions possess aground electronic state of doublet spin multiplicity. Moreover,Table IV reports the singlet-triplet energy differences calcu-lated for HPS and HSP. In the CBS limit, and including thezero-point energy (ZPE) correction within the harmonic ap-proximation, these are 26.2 kcal mol−1 for HPS and −4.6 kcalmol−1 for HSP, where a negative value means that the tripletstate has lower energy than the singlet. For neutral HPS, theground state possesses a X̃1A′ ground state, whereas neutralHSP has a X̃3A′′ ground state. This is in good agreement withViana and Pimentel’s findings.24

The adiabatic ionization energies (AIE) in Table IV arecalculated as differences at 0 K between the energies of thecationic and corresponding neutral forms, at the appropriateoptimized equilibrium geometries. Analogously, the adiabatic

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174313-6 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

TABLE IV. Corrected singlet triplet energy differences (�E), adiabatic ion-ization energies (IE), and electron affinities (EA) for HPS and HSP neutralspecies (kcal mol−1).

Method Basis set �Ea IEa EAa

HPSCCSD(T) aug-cc-pV(D+d)Z 24.2 208.4 −32.9

aug-cc-pV(T+d)Z 25.1 212.9 −35.4aug-cc-pV(Q+d)Z 25.8 214.3 −36.2aug-cc-pV(5+d)Z 26.0 214.8 −36.4aug-cc-pV(6+d)Z 26.1 215.0 −36.4

CBS 26.2 215.1 −37.0CCSD(T)-F12 cc-pVTZ-F12 26.1 214.4 −35.5CCSD(T)-F12 cc-pVQZ-F12 26.1 215.0 −36.2

HSPb

CCSD(T) aug-cc-pV(D+d)Z −8.6 187.8 −25.3aug-cc-pV(T+d)Z −6.0 190.8 −29.8aug-cc-pV(Q+d)Z −5.0 191.3 −31.2aug-cc-pV(5+d)Z −4.7 191.5 −31.6aug-cc-pV(6+d)Z −4.6 191.5 −31.8

CBS −4.6 192.4 −31.8CCSD(T)-F12 cc-pVTZ-F12 −9.2 195.6 −26.1CCSD(T)-F12 cc-pVQZ-F12 −7.7 194.6 −28.3

aCorrected for ZPE.bNegative �E indicates triplet is lower energy.

TABLE V. HXY bond order from natural resonance theory.

Total bond order

Species R(HX) R(XY)

HPS+ 0.95 2.17HPS singlet 0.97 2.02HPS triplet 0.98 1.54HPS− 0.98 1.52HSP+ 0.99 2.55HSP singlet 0.97 2.03HSP triplet 0.99 1.95HSP− 0.97 1.53

electron affinities (AEA) at 0 K are evaluated as differencesbetween the anionic and corresponding neutral forms. TheZPE correction deduced from the harmonic approximationhas been applied in each case. At the CBS limit, the AIE forHPS and HSP are 215.1 and 192.4 kcal mol−1, respectively.We compute AEA(HPS) = −37.0 and AEA(HSP) = −31.8kcal mol−1. It is worth noting that while in HPS the CCSD(T)-F12/cc-pVQZ-F12 values in Table IV are almost at the CBSconverged limit, with differences in energy of no more than0.8 kcal mol−1, in HSP larger differences are observed,

HPS- - HPS HSP- -HSP

HPS+ - HPS HSP+ - HSP

HP

S

HS

P

HP

S

HS

P

FIG. 1. Contour plots of the difference of electron densities, calculated at the full valence CASSCF/aug-cc-pVQZ level where the internal coordinates in theion and the neutral are fixed to their values computed at the CCSD(T)-F12 /VQZ-F12 equilibrium geometry of the ion. The first contour is drawn for 0.025e/bohr3 with steps of 0.025 e/bohr3. The blue (red) lines correspond to region where the density in the ion is higher (lower) than in the neutral.

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

HPS HPS+ HPS− HSP HSP+ HSP−

τAAAA −2.67 × 10−3 −2.59 × 10−3 −2.76 × 10−3 −2.53 × 10−3 −2.75 × 10−3 −4.357 × 10−3

τBBBB −7.2 × 10−7 −8.2 × 10−7 −7.6 × 10−7 −8.3 × 10−7 −7.7 × 10−7 −9.8 × 10−7

τCCCC −6.4 × 10−7 −7.3 × 10−7 −6.8 × 10−7 −7.6 × 10−7 −6.9 × 10−7 −9.0 × 10−7

τAABB −1.40 × 10−6 −2.65 × 10−6 −1.3 × 10−7 −1.58 × 10−6 −7.6 × 10−7 −4.47 × 10−6

τBBCC −6.8 × 10−7 −7.8 × 10−7 −7.1 × 10−6 −7.9 × 10−7 −7.3 × 10−7 −9.4 × 10−7

τCCAA −3.78 × 10−6 −5.16 × 10−6 −2.27 × 10−6 −2.98 × 10−6 −2.79 × 10−6 −6.44 × 10−6

τABAB −1.27 × 10−5 −3.11 × 10−5 −1.19 × 10−5 −1.68 × 10−5 −1.94 × 10−5 −1.479 × 10−5

DJ 1.070 × 10−7 1.943 × 10−7 1.788 × 10−7 1.989 × 10−7 1.829 × 10−7 2.349 × 10−7

DJK 7.335 × 10−6 1.711 × 10−5 6.229 × 10−6 9.177 × 10−6 1.022 × 10−5 9.653 × 10−6

DK 6.622 × 10−4 6.314 × 10−4 6.854 × 10−4 6.248 × 10−4 6.792 × 10−4 1.079 × 10−3

δJ 4.924 × 10−9 5.820 × 10−9 4.929 × 10−9 4.694 × 10−9 4.905 × 10−9 4.946 × 10−9

R5 −1.444 × 10−6 −3.728 × 10−6 −1.360 × 10−6 −2.018 × 10−6 −2.296 × 10−6 −1.723 × 10−6

R6 −7.309 × 10−11 −8.942 × 10−11 −6.148 × 10−11 −4.187 × 10−11 −5.852 × 10−11 −4.347 × 10−11

ω1 2273 2257 2197 2675 2557 2479ω2 909 692 849 732 762 797ω3 686 563 578 515 632 448x11 −64.94 −71.42 −72.82 −71.19 −75.26 −112.77x12 −18.039 −31.10 −15.83 −16.88 −16.88 −8.011x13 −37.67 −25.77 2.54 −1.08 −2.11 3.225x21 −18.039 −31.10 −15.83 −16.88 −16.88 −8.011x22 −4.60 −3.04 −4.368 −4.57 −5.25 −7.28x23 −4.843 0.71 −3.844 −0.44 0.026 −3.764x31 −37.67 −25.77 2.539 −1.08 −2.11 3.225x32 −4.843 0.71 −3.844 −0.44 0.026 −3.764x33 −3.941 −7.93 −3.002 −2.76 −2.80 −3.332ν1

a 2263.9 2238.6 2156.4 2595.4 2533.1 2425.8ν2

a 894.1 674.0 836.0 720.1 762.3 786.5ν3

a 655.9 551.3 573.3 510.4 658.3 446.0αA

1 0.301 0.333 3.178 × 10−1 3.218 × 10−1 3.252 × 10−1 3.152 × 10−1

αA2 −0.150 −7.57 × 10−3 −1.588 × 10−1 −2.334 × 10−1 −2.095 × 10−1 −2.185 × 10−1

αA3 2.337 × 10−2 −0.247 5.070 × 10−3 −1.893 × 10−3 −1.548 × 10−2 2.315 × 10−2

αB1 9.763 × 10−4 7.798 × 10−4 −6.083 × 10−4 −3.514 × 10−4 −5.732 × 10−4 −2.406 × 10−3

αB2 1.68 × 10−4 1.422 × 10−3 2.486 × 10−4 −1.524 × 10−4 −2.171 × 10−4 8.606 × 10−4

αB3 1.657 × 10−3 −9.905 × 10−4 1.545 × 10−3 1.567 × 10−3 1.497 × 10−3 1.943 × 10−3

αC1 1.148 × 10−3 1.055 × 10−3 −3.650 × 10−4 −1.595 × 10−4 −3.181 × 10−4 −2.161 × 10−3

αC2 7.161 × 10−4 1.432 × 10−3 7.297 × 10−4 3.243 × 10−4 2.931 × 10−4 1.253 × 10−3

αC3 1.660 × 10−3 −1.690 × 10−4 1.527 × 10−3 1.559 × 10−3 1.5713 × 10−3 1.947 × 10−3

aComputed variationally.

especially in the AEA, where a difference of 3.5 kcal mol−1

is found. There are no known measurements or computationalestimates of the AIE or AEA for HPS or HSP to comparewith.

C. Bonding in cationic, neutral, and anionicHPS and HSP

In order to provide quantitative bond orders, a naturalbond order calculation is performed on neutral and chargedHPS and HSP. Table V reports the results. In all calculations,the bond involving hydrogen is predicted to have a bond or-der of approximately 1.0. Indeed, the range for all calculatedbond orders for bonds to hydrogen atoms is 0.91-0.99. For theHPS series, the bond orders are predicted to be 2.17, 2.02, and1.52 for the 11, 12, and 13 electron systems. For HSP, the cal-culated bond orders are 2.55, 1.95, and 1.53. Upon electronic

excitation from the singlet state to the triplet state, there is adecrease of the bond orders in both HPS and HSP.

For rationalization, Figure 1 presents the CASSCF elec-tronic density difference maps calculated as the electronicdensity differences between ions and the correspondingneutrals. We performed these calculations at the equilibriumstructures of the ionic species. These densities were drawnwith the MOLDEN program.57 Blue contour lines representregions with more electron density in the ions than in theneutrals and the red ones those with lower densities. Thisfigure shows that removal of one electron in HPS results ina loss of electron density mainly localized in the HP bondregion, while the addition of one electron occurs on the Satom center. This is in good agreement with the evolutionof the bond lengths from HPS+, to HPS and to HPS− (cf.Table I). Indeed, the R(HP) distance increases slightly goingfrom the neutral to the positively charged molecule, whereasthe PS bond slightly decreases upon ionization. The HPS−

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TABLE VII. Variationally computed rovibrational levels of H31P32S/H32S31P species in their electronic group states up to ∼4000 cm−1 and their tentativeassignment. We used our (R)CCSD(T)/aug cc-pV5Z 3D-PESs. The asterisk denotes anharmonic resonances. See text for more details.

HPS HPS+ HPS− HSP HSP+ HSP−

(v1,v2,v3) Energy (v1,v2,v3) Energy (v1,v2,v3) Energy (v1,v2,v3) Energy (v1,v2,v3) Energy (v1,v2,v3) Energy

(0,0,0) 0.0 (0,0,0) 0.0 (0,0,0) 0.0 (0,0,0) 0.0 (0,0,0) 0.0 (0,0,0) 0.0(0,0,1) 655.9 (0,1,0) * 551.3 (0,0,1) 573.3 (0,0,1) 510.4 (0,0,1) * 628.3 (0,0,1) 446.0(0,1,0) 894.1 (0,0,1) * 674.0 (0,1,0) 836.0 (0,1,0) 720.1 (0,1,0) * 762.6 (0,1,0) 786.5(0,0,2) 1305.0 (0,2,0) * 1110.5 (0,0,2) 1144.4 (0,0,2) 1018.1 (0,0,2) * 1253.6 (0,0,2) 893.3(0,1,1) 1544.3 (0,1,1) * 1235.0 (0,1,1) 1405.9 (0,1,1) 1230.5 (0,1,1) * 1394.7 (0,1,1) 1230.9(0,2,0) 1785.9 (0,0,2) * 1345.4 (0,2,0) 1671.4 (0.2,0) 1439.9 (0,2,0) * 1544.6 (0,0,3) * 1347.9(0,0,3) 1950.5 (0,2,1) * 1680.5 (0,0,3) 1716.5 (0,0,3) 1525.8 (0,0,3) * 1878.3 (0,2,0) 1571.4(0,1,2) 2187.5 (0,3,0) * 1809.3 (0,1,2) 1973.9 (0,1,2) 1738.4 (0,1,2) * 2023.6 (0,1,2) * 1678.2(1,0,0) 2263.9 (0,0,3) * 1919.4 (1,0,0) 2156.4 (0,2,1) 1950.2 (0,2,1) * 2179.3 (0,0,4) * 1814.7(0,2,1) 2430.3 (0,1,2) * 2017.7 (0,2,1) 2238.5 (0,0,4) 2036.1 (0,3,0) * 2360.5 (0,2,1) * 2015.1(0,0,4) 2595.8 (1,0,0) 2238.6 (0,0,4) 2293.0 (0,3,0) 2164.6 (0,0,4) * 2505.1 (0,1,3) * 2134.4(0,3,0) 2679.2 (0,2,2) * 2258.5 (0,3,0) 2510.5 (0,1,3) * 2246.3 (1,0,0) 2522.2 (0,0,5) * 2297.0(0,1,3) 2827.0 (0,3,1) * 2394.7 (0,1,3) 2543.4 (0,2,2) * 2458.1 (0,1,3) * 2651.7 (0,3,0) * 2359.9(1,0,1) 2877.7 (0,0,4) * 2509.9 (1,0,1) 2731.8 (0,0,5) * 2551.6 (0,2,2) * 2810.4 (1,0,0) 2425.8(0,2,2) * 3067.5 (0,4,0) * 2609.4 (0,2,2) 2804.1 (1,0,0) 2595.4 (0,3,1) * 2995.4 (0,2,2) * 2463.4(1,1,0) 3152.0 (0,2,2) * 2697.5 (0,0,5) 2877.9 (0,3,1) 2674.5 (0,0,5) * 3136.8 (0,1,4) * 2603.7(0,0,5) 3244.2 (0,1,1) * 2765.2 (1,0,1) 2986.8 (0,1,4) * 2757.1 (1,0,1) * 3150.5 (0,0,6) * 2798.8(0,3,1) 3317.6 (0,2,3) * 2842.2 (0,3,1) 3075.2 (0,4,0) 2898.8 (0,4,0) 3216.9 (0,3,1) * 2803.8(0,1,4) * 3466.3 (1,0,1) * 2887.7 (0,1,4) * 3118.4 (0,2,3) * 2966.1 (1,1,0) * 3280.0 (1,0,1) 2877.1(0,1,4) * 3466.3 (0,4,1) * 2986.9 (1,0,2) 3306.5 (0,0,6) * 3074.5 (0,1,4) * 3282.0 (0,2,3) * 2921.9(1,0,2) 3485.0 (0,3,2) * 3109.2 (0,4,0) 3356.7 (1,0,1) 3104.9 (0,2,3) * 3440.5 (0,1,5) * 3089.8(0,4,0) 3577.0 (0,0,5) * 3214.4 (0,2,3) 3371.7 (0,3,2) * 3182.0 (0,3,2) * 3626.5 (0,4,0) * 3159.8(0,2,3) * 3700.9 (1,0,2) * 3297.5 (0,0,6) 3471.7 (0,1,5) * 3274.2 (1,0,2) * 3775.1 (1,1,0) * 3247.1(1,1,1) 3760.5 (0,5,0) * 3308.9 (1,1,1) 3558.4 (1,1,0) 3309.2 (0,0,6) * 3776.3 (0,3,2) * 3253.7(0,0,6) 3896.6 (0,4,1) * 3397.3 (0,3,2) * 3639.0 (0,4,1) 3407.8 (0,4,1) 3851.3 (0,0,7) * 3316.4(0,3,2) * 3948.8 (1,0,2) * 3422.5 (0,1,5) * 3707.5 (0,2,4) * 3477.3 (1,1,1) * 3851.2 (1,0,2) 3328.4

(0,2,4) * 3431.9 (1,0,2) 3818.5 (0,0,7) * 3606.1 (1,1,1) * 3918.8 (0,2,4) * 3394.4(1,1,1) * 3540.7 (1,0,3) 3880.9 (1,0,2) 3611.8 (0,1,6) * 3602.8(0,1,5) * 3584.9 (0,4,1) 3919.4 (0,5,0) 3646.1 (0,4,1) * 3603.2(0,0,6) * 3713.2 (0,2,4) * 3946.3 (0,3,3) * 3689.8 (1,1,1) * 3694.2(0,4,2) * 3823.4 (0,1,6) * 3799.7 (0,3,3) * 3714.3(1,1,2) * 3840.4 (1,1,1) 3819.1 (1,0,3) * 3785.0(0,1,5) * 3923.9 (0,4,2) * 3914.5 (0,0,8) * 3854.4(1,0,3) * 3970.4 (0,2,5) * 3819.1 (0,2,5) * 3886.2

(0,5,0) * 3974.7

← HPS + e− reaction is accompanied by an increase ofHP and PS distances. For HSP species, the added electronspans over all the molecule and ionization takes place mainlyfrom the sulfur lone pair. This results in HS increase forboth ionic species and a slight decrease of PS in HSP+ and alengthening of PS in HSP− (cf. Table II).

D. Spectroscopic parameters

The harmonic vibrational frequencies for neutral andcharged HPS and HSP are illustrated in Tables I and II fordifferent combinations of theory/basis sets. The accuracy ofour predictions could be checked directly only in the case ofHPS neutral, because no experimental data are available forthe other species. In the following, we focus the discussion onthe results obtained at the CCSD(T)-F12/cc-pVQZ-F12 level.For HPS (X̃1A′), we calculated HP and PS stretching fre-quencies of 2276 and 689 cm−1, respectively. The latter can

be compared to the experimental value for the PS diatomic of739.1 cm−1.58 The experimental value for the PS stretchingas measured by Clouthier and co-workers is 673 cm−1,20 thatis, 16 cm−1 below the calculated value. A bending frequencyof 906 cm−1 is found, which compares favorably with theexperimental value of 885 cm−1.20 For HSP (X̃3A′′), wecomputed HS and PS stretching frequencies of 2667 and519 cm−1, respectively. The latter value is significantly lowerthan what is found in diatomic PS. For both HPS and HSP,the analysis of the decomposition of normal modes in internalcoordinates reveals that the coupling between the two stretch-ing modes is minimal, whereas a slight coupling is foundbetween the PS stretching and the in-plane bending angle.

The larger vibrational frequency for the PS stretchingin HPS compared to HSP, blue-shifted of 170 cm−1, is re-flected by a corresponding contraction of the PS bond lengthof around 0.15 Å. Ionization of HPS leads to a sharp decreaseof 372 cm−1 in the bending frequency, while in HSP it leadsto a decrease of the HS stretching frequency (117 cm−1) and

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174313-9 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

(0,1,0) @ E = 551.3 (0,0,1) @ E = 674.0 (0,2,0) @ E = 1110.5

(0,1,1) @ E = 1235.0 (0,0,2) @ E = 1345.4

FIG. 2. Contour plots of the HPS+(X̃2A′) vibrational wave functions of the (0,1,0), (0,0,1), (0,2,0), (0,1,1), and (0,0,2) levels along the SN stretching and thebending coordinates. The HP distance is fixed at its equilibrium value for HPS+(X̃2A′).

to an increase of the PS stretching (119 cm−1) and HSP bend-ing (26 cm−1) frequencies. Attachment of one electron to HPSleads to red-shifted frequencies in all modes, with the largestchange observed for the PS stretching (112 cm−1). Apart fromthe bending mode, a similar behavior is seen in HSP− com-pared to HSP, where the largest decrease is found for the HSstretching mode (188 cm−1).

In the calculation of the CCSD(T) full-dimensional PESsfor the neutral and charged HPS/HSP systems, we selectedthe aug-cc-pV5Z basis set. This is due to the observa-tion that geometric parameters and harmonic vibrational fre-quencies calculated with this set and with the equivalentaug-cc-pV(5+d)Z one, that incorporates additional tight-dfunctions for second row elements, are almost identical. Thisenabled to save computational time in the generation of thepotential energy surfaces. The polynomial expressions inEq. (1) of the 3D PESs for all the molecular systems investi-gated here (cf. Tables S2–S8 of the supplementary material55)have been deduced as quartic force fields in internal coor-dinates and then transformed by l-tensor algebra into quar-tic force fields in dimensionless normal coordinates. Theseare used to determine a set of spectroscopic parameters,including τ and first-order centrifugal distortion constants,rovibrational (αi) and anharmonic terms (xij), and fundamen-tal frequencies (ν i). These data, listed in Table VI, are pre-

dictive and can be used, in the future, for the assignmentof the microwave, IR and rotationally resolved Photo Elec-tron Spectra, and the photodetachment spectra of HPS andof HSP.

E. Variationally determined vibrational spectra

The variational calculations of the vibrational levelsand wavefunctions have been done up to 4000 cm−1 abovethe equilibrium minimal energy structures of each surface.Results are shown in Table VII, together with the tentativeassignment of the levels in terms of vibrational quantum num-bers v1, v2, v3 for the HP (or HS) stretching, for the bending,and PS stretching, in the same order. For HPS, we computeν1 = 2263.9, ν2 = 894.1, and ν3 = 655.9, in cm−1. For HSP,the fundamentals are calculated ν1 = 2595.4, ν2 = 720.1, andν3 = 510.4, in cm−1. The largest differences between the ω’sand the corresponding ν’s are seen for the HS stretch in HSP(80 cm−1) and for the PS stretch in HPS (30 cm−1) (cf. TableVI). In HPS− and HSP−, the largest differences are seen in theHP (41 cm−1) and HS (53 cm−1) stretching modes. In HPS+,differences are not greater than 20 cm−1, while in HSP+ slightinverted anharmonicity is predicted for the bending mode(26 cm−1).

For neutral HPS, HPS−, and HSP molecules, the analy-sis of the spectrum reveals that the fundamental frequencies

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174313-10 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

(0,0,1) @ E = 628.3 (0,1,0) @ E = 762.6 (0,0,2) @ E = 1253.6

(0,2,0) @ E = 1544.6 (0,1,1) @ E = 1394.7

FIG. 3. Contour plots of the HSP+(X̃2A′) vibrational wave functions of the (0,1,0), (0,0,1), (0,2,0), (0,1,1), and (0,0,2) levels along the SN stretching and thebending coordinates. The HS distance is fixed at its equilibrium value for HSP+(X̃2A′).

are reasonably well represented by the harmonic approxima-tion. Whereas strong anharmonic resonances are observed forthe HPS+ and HSP+ cations and for the HSP− anion. In-spection of these wavefunctions reveals that such anharmonicresonances occur for all the levels marked by an asterisk inTable VII. Their wavefunctions correspond to a linear com-bination of the unperturbed levels. Here they are tentativelyassigned to the harmonic wavefunction having the dominantcontribution. For illustration, we depict in Figures 2–4 the

two-dimensional cuts of the vibrational wavefunction of theirlow vibrational levels expressed as a function of internal co-ordinates. The change of the sign of the wavefunction is in-dicated by the change from blue to red lines. In each cut,the third coordinate is fixed at the equilibrium value of thecorresponding electronic state. For example, the two levelsof HPS+(X̃2A′) located at 551.3 and 674.0 cm−1 are a mix-ture of (0,1,0) and (0,0,1) vibrational wavefunctions. For theselevels, Figure 2 depicts the two-dimensional contours of the

@)2,1,0(4.1751=E@)0,2,0(9.7431=E@)3,0,0( E = 1678.2

FIG. 4. Contour plots of the HSP−(X̃2A′) vibrational wave functions of the (0,1,0), (0,0,1), (0,2,0), (0,1,1), and (0,0,2) levels along the SN stretching and thebending coordinates. The HS distances is fixed at its equilibrium value for HSP−(X̃2A′).

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174313-11 Ben Yaghlane et al. J. Chem. Phys. 139, 174313 (2013)

vibrational parts of their corresponding wavefunctions alongthe PS stretching and the bending coordinates. From Figure2, it is clear that the nodes of the wavefunctions are not lo-cated along the vibrational coordinates. Figure 3 presents anillustration of occurrence of anharmonic resonances in thecase of the ground state of HSP+ for the levels located at628.3, 762.6, 1253.6, 1394.7, and 1544.6 cm−1 dominantlyassignable to the (0,0,1), (0,1,0), (0,0,2), (0,1,1), and (0,2,0)levels. Finally, Figure 4 gives an example of anharmonic reso-nances in the case of the HSP− anion, where the levels locatedat 1347.9, 1571.4, and 1678.2 are a mixture of the (0,0,3),(0,2,0), and (0,1,2) unperturbed states. For all species and wellabove the corresponding ground states, a high density of vi-brational levels is noticeable. This favors the mixing of theirwavefunctions and the occurrence of various types of anhar-monic resonances.

IV. CONCLUSION

Accurate ab initio calculations have been carried outto determine molecular equilibrium structures, rotationalconstants, and energetics of neutral HPS/HSP and relativecations-anions. Adiabatic ionization potentials and electronaffinities, as well as singlet-triplet energy separation forthe neutral species, have been evaluated. For the ionizationenergy and electron affinity of HPS, at the best level of theoryadopted here, we obtain 215.1 (9.33) and 37.0 (1.60) kcalmol−1 (eV), respectively. Corresponding values for HSPare 192.4 (8.34) and 31.8 (1.38) kcal mol−1 (eV). For HPSsinglet, structural parameters agree well with the availableexperimental values, which are missing for the other species.Spectroscopic parameters have been deduced from second-order perturbation theory and the calculated 3D ground statepotential energy surfaces. The latter were also used in avariational treatment to compute the set of vibrational levelsup to 4000 cm−1 above the equilibrium structure of minimumenergy. Inspection of the vibrational wavefunctions shows theoccurrence of strong anharmonic resonances in the lowest-lying levels of HPS+, HSP+, and HSP−. This work shouldhelp in the spectroscopic identification and characterizationof these sulfur-phosphorous-based molecular entities inlaboratory and in the interstellar medium.

ACKNOWLEDGMENTS

M.H. thanks a financial support from the PCMI pro-gram (INSU, CNRS, France). This research was supportedby the 7th European Community Framework Program underthe COST Action CM1002 CODECS.

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