Electronic States of SnS and SnS + : A Configuration Interaction Study

Transcription

1 J. Phys. Chem. A 2005, 09, Electronic Sttes of SnS nd SnS + : A Configurtion Interction Study Dipnkr Giri nd Klyn Kumr Ds* Physicl Chemistry Section, Deprtment of Chemistry, JdVpur UniVersity, Kolkt 70002, Indi ReceiVed: Mrch 2, 2005; In Finl Form: My 27, 2005 Ab initio bsed multireference configurtion interction clcultions re crried out for SnS nd its monopositive ion using effective core potentils. Potentil energy curves nd spectroscopic constnts of the low-lying sttes of SnS nd SnS + re computed. The ground-stte dissocition energies of the neutrl nd ionic species re bout.7 nd 2.86 ev, respectively which compre well with the vilble thermochemicl dt. The effect of d-electron correltion on the spectroscopic constnts of few low-lying sttes hs been studied. The spinorbit interction hs lso been included to investigte its effect on the spectroscopic properties of both SnS nd SnS +. Dipole moment nd trnsition moment curves re lso constructed s function of the bond length. Trnsition probbilities of some dipole-llowed nd spin-forbidden trnsitions re studied. Rditive lifetimes of few low-lying sttes re estimted. The E Σ + -X Σ + trnsition of SnS is predicted to be the strongest one. The components of the A 2 Σ + /2-X 22 Π /2 trnsition with prllel nd perpendiculr polriztion re seprtely nlyzed. The verticl ioniztion energies of the ground-stte SnS to the ground nd low-lying excited sttes of the monopositive ion re clculted. I. Introduction The oxides nd sulfides of group IV re often used in chemicl lsers. The electronic structure nd spectroscopic properties of these molecules re the subject of mny experimentl nd theoreticl reserch for severl yers in the pst. -26 The spectr of these molecules re comprble with those of CO which is well-known in the literture. In the mid-90s of the 20th Century, severl investigtions - of the bsorption nd emission spectr of the ditomic tin sulfide molecule hd been crried out. Dougls et l. 5 studied high-resolution bsorption nd emission spectr of SnS using the 20 Sn isotope. A simple Π- Σ + bnd system ws found between 000 nd 00 Å. The rottionl nd vibrtionl constnts of the ground stte of SnS re determined from these bnds. Moreover, bnd system, which lies between 00 nd 2500 Å, hs been shown to be Σ + - Σ + system. Brrow et l. 6 hve studied the bsorption spectrum of SnS vpor in the ultrviolet nd Schumnn region. The spectroscopiclly determined dissocition energy (D 0 0) of SnS is ( 6 kcl mol -. A much lower vlue D 0 0(SnS) e 68.5 kcl mol - hs been predicted on the bsis of supposed predissocition, in the A Π-X Σ + system. A mss-spectrometric investigtion of the vpor in equilibrium with solid SnS nd PbS, nd mixture of SnS nd PbS hs been mde by Collin nd Drowrt. 7 A vlue of D 0 0(SnS) ) 0 (.0 kcl mol - hs been reported nd compred with the spectroscopiclly determined vlue. 6 Ymdgni nd Joshi 8 hve reinvestigted the visible bsorption spectrum of SnS. Two systems such s B-X nd C-X hve been recognized. The bsorption nd fluorescence spectr of SnS nd SnO hve been studied in the cm - region in inert gs mtrixes 9 t 20 K. It showed one cler nd shrp bsorption due to the D Π-X Σ + system consisting of progression of vibrtionl bnds. The trnsition energy of the D Π stte of SnS hs been reported to be 2860 cm -. The excittion of the D stte for SnO nd SnS hs resulted strong * Corresponding uthor. E-mil: ds_klynk@yhoo.com or kkds@ chemistry.jdvu.c.in. fluorescence which is ttributed to the spin-forbidden Π- X Σ + trnsition. The reported trnsition energy of the Π stte of SnS is 800 cm -. The infrred spectr of some mtrixisolted germnium, tin, nd led chlconides re reported 0 in rgon nd nitrogen mtrices t 2 K. The electronic spectrum of SnS, which is excited in chemiluminescence, hs led to the chrcteriztion of two low-lying excited sttes such s Ω- ( Σ + ) with T e ) 8.9 cm - nd A0 + ( Π) with T e ) cm -. The extended rottionl nlyses of the perturbed bnds observed in the bsorption spectrum enble the ssignments of the Ω0 + nd Ω components of Σ -, nd Ω of Π for SnS. The observed T e vlues of C0 + ( Σ - ) nd C ( Σ - ) re 2280 nd 2280 cm -, respectively, while tht of BΩ( Π) is bout 220 cm -. The observed spectrum hs been found to be quite complex in chrcter. As result, the ssignments of mny observed progressions into the electronic bnd systems hve been mde with difficulties nd uncertinties. In generl, theoreticl studies of tin chlconides re limited in number. Ab initio bsed reltivistic configurtion interction (CI) clcultions of the low-lying electronic sttes of SnO nd SnS re performed by Blsubrmnin nd co-workers. 2, Nir et l. hve clculted the potentil energy curves nd dissocition energies of the oxides nd sulfides of group IVA elements for which sufficient spectroscopic dt re vilble. Recently, 5 MRDCI study hs been mde on the electronic spectrum of tin oxide. Dipole moments of the sulfides of Pb, Sb, nd Sn hve been clculted from the Strk effect mesurements. Hoeft et l. 6,7 hve reported the electric dipole moment of the ground-stte 20 Sn 2 S s.8 ( 0.0 D, while the vlue obtined by Nrsimh nd Curl 8 is bout.8 ( 0.07 D. Nonreltivistic nd reltivistic high level correlted clcultions hve been crried out recently 9 for the determintion of the dipole moments of the oxides nd sulfides of led nd tin. Lfebvre et l. 20 hve clculted the electronic structures of tin monochlconides (SnX; X ) O, S, Se, nd Te) using density functionl pseudo-potentil nd tight binding theories. Although the spectroscopy of the neutrl oxides nd sulfides of group IVA elements is well studied, the corresponding 0.02/jp05290e CCC: $ Americn Chemicl Society Published on Web 07/2/2005

2 7208 J. Phys. Chem. A, Vol. 09, No. 2, 2005 Giri nd Ds monopositive ions re less known. The photoelectron spectr of the isovlent CO molecule re, however, well-known in the literture. A few decdes go, the vcuum UV photoelectron spectr of silicon nd germnium monoxides hve been recorded in the gs phse. 2-2 The He I photoelectron spectr of the ground stte of the SnO molecule hve been studied by Dyke et l. 2 These spectr re found to be very similr to those of CO. Two low-lying sttes such s 2 Σ + nd 2 Π of SnO + re chrcterized, nd two bnds re observed in the ioniztion energy rnge ev becuse of heting SnO 2. The vibrtionl structure of the first bnd provides spectroscopic constnts of the X 2 Π stte of SnO +. Recently, 25 four ioniztion energies of tin monoxide hve been determined from the bsorption spectrum in the rnge Å. However, the photoelectron spectrum of the ground-stte SnS molecule is not yet known. Theoreticl clcultions of SnS + re lso lcking. Ab initio bsed MRDCI clcultions of the low-lying sttes of the isovlent SnO + hve been crried out recently 26 using reltivistic effective core potentils. The potentil energy curves nd spectroscopic prmeters of the lowest few sttes re reported. Trnsition probbilities of different components of the A-X trnsition in the presence of the spin-orbit coupling re nlyzed. In this work we hve performed b initio bsed MRDCI clcultions to study the structurl nd spectroscopic spects of low-lying electronic sttes of SnS nd SnS + including reltivistic effects nd the spin-orbit coupling. Some of the importnt trnsitions re investigted. The nture of the dipole moment nd trnsition dipole moment functions for both neutrl nd ionic species is lso the subject of the present study. The verticl ioniztion energies of the ground-stte SnS re computed. The rditive lifetimes of some of the excited sttes re estimted. II. Method of Computtion The reltivistic effective core potentils (RECP) of both Sn nd S toms re used in the present clcultions. For the hevier Sn tom, the RECP of LJohn et l. 27 hve been substituted for the core electrons, while d 0 5s 2 5p 2 electrons remin in the vlence spce. The RECP of Pcios nd Christinsen 28 re used for the sulfur tom with the s 2 p electrons in the vlence spce. The totl numbers of ctive electrons to be treted in the CI clcultions re 20 for SnS, nd 9 for SnS +. The strting primitive Gussin bsis functions 27 of Sn re (spd) without ny contrction. These re comptible with the semicore RECP mentioned bove. These bsis functions of Sn re ugmented with d nd f polriztion functions 29 (ζ d ) 0.08 o -2 nd ζ f ) 0.20 o -2 ). A set of diffuse s function (ζ s ) 0.05 o -2 ) nd p functions (ζ p ) 0.02 o -2 ) is dded to mke the finl bsis set of the type (sp5df) for the Sn tom. The (sp) Gussin bsis sets of the sulfur tom, tken from Pcios nd Christinsen, 28 hve been extended by dding two-member d- polriztion functions of exponents 0.66 nd 0.8 o -2 which re optimized by Lingott et l. 0 for the P stte of the sulfur tom t the CI level. A set of f functions with exponent 0.9 o -2, optimized by these uthors from the CI clcultions of the D excited stte of S, hs lso been included in the bsis. Therefore, the finl bsis set of S is of the type (sp2df). The molecule nd its ion re kept long the +z xis with Sn t the origin. The computtions re crried out in the C 2V symmetry. Using the bove-mentioned ECP nd bsis sets, the self-consistent field (SCF) clcultions re crried out for prticulr low-lying stte to generte optimized symmetry dpted moleculr orbitls (MO). The SCF-MOs of the (π π* 2 ) Σ - stte of SnS nd those of the (σπ ) 2 Σ + stte of SnS + re used s one-electron bsis orbitls for the genertion of configurtions in the CI clcultions. It hs been noted erlier tht the Σ - nd 2 Σ + sttes of the isovlent SnO nd SnO +, respectively re suitble choices for the SCF-MO clcultions s these will tret the π x nd π y components in equl footing. The eigenvlues nd eigenfunctions in the B nd B 2 representtions re retined in their perfect symmetries so tht there re no symmetry breking solutions throughout the clcultions. In the CI steps, the d 0 electrons of Sn re found to be loclized nd they do not prticipte in the formtion of low-lying electronic sttes of both SnS nd SnS +. Therefore, only 0 vlence electrons for SnS nd 9 for SnS + re llowed to excite for the construction of the configurtion stte functions. The MRDCI method of Buenker nd co-workers -7 hs been used throughout the clcultions. The perturbtive corrections nd energy extrpoltion techniques re employed here. For ech sptil nd spin symmetry, set of reference configurtions is chosen representing prticulr low-lying stte. The number of reference configurtions vries depending upon the sptil nd spin symmetry. Singlet, triplet, nd quintet sttes of SnS nd doublet nd qurtet sttes of SnS + re studied here. A mximum of eight roots in ech symmetry is optimized. Within chosen set of reference configurtions, the number of generted configurtions rising out of ll single nd double excittions becomes s lrge s 0 million. However, with the choice of configurtion-selection threshold T ).0 µe h, the number of selected configurtions reduces below for both the neutrl nd ionic species. The sums of the squres of the coefficients of reference configurtions for the lowest few roots do not go below Using the energy extrpoltion method, one gets n estimte of energy t T ) 0. The higher order excittions re tken into ccount by the multireference nlogue of the Dvidson correction. 8 The full-ci energies of the Λ-S sttes re thus estimted. The effect of the spin-orbit coupling hs been determined from seprte two-step vritionl clcultions. In the spinincluded Hmiltonin mtrix, the digonls re the full-ci energies of the Λ-S CI clcultions, while the off-digonls re computed from the RECP bsed spin-orbit opertors nd CI wve functions. The Wigner-Eckrt theorem is employed to compute the spin-orbit mtrix elements. The low-lying Ω-sttes belong to A,A 2, nd B representtions for SnS, nd to the degenerte E nd E 2 representtions for SnS + in the C 2V double group. The spectroscopic constnts re estimted from the potentil curves. The rditive lifetime of given vibrtionl level cn then be computed from the Einstein spontneous emission coefficients. III. Spectroscopic Properties of Low-Lying Λ-S Sttes A. SnS. The ground sttes of both Sn nd S toms belong to the P g stte. The interction between these two sttes genertes s mny s 8 sttes of singlet, triplet, nd quintet spin multiplicities. On the other hnd, the first excited stte ( D g )of Sn combines with the ground stte of S to correlte with nine triplets. Tble shows the difference between the reltive energies of the lowest two dissocition limits of SnS. The greement between the computed dt nd the observed one from the tomic spectrl study 9 is found to be good. The discrepncy is only within 00 cm -. Potentil energy curves of ll 8 Λ-S sttes dissociting into the lowest symptote Sn- ( P g ) + S( P g ) re shown in Figure. Spectroscopic constnts of sttes of Λ-S symmetries within 7 ev of energy re tbulted in Tble 2. The ground

3 Electronic Sttes of SnS nd SnS + J. Phys. Chem. A, Vol. 09, No. 2, TABLE : Moleculr Sttes of SnS nd Their Correltion with Atomic Limits reltive energy/cm - moleculr stte tomic stte Sn + S exptl clcd Σ + (2), Σ -, Π(2),, P g + P g 0 0 Σ + (2), Σ -, Π(2),, 5 Σ + (2), 5 Σ -, 5 Π(2), 5 Σ +, Σ - (2), Π(), (2), Φ D g + P g Reference 9. Figure. Potentil energy curves of low-lying Λ-S sttes of SnS. stte of SnS is X Σ + comprising dominnt closed shell configurtion, σ 2 π. The MRDCI estimted bond length of the ground stte is 2.25 Å, which is longer thn the experimentl one by bout 0.0 Å. However, the present vlue is n improved one over the erlier clculted dt. The inclusion of ll d 0 electrons in the CI clcultions reduces the bond length by 0.0 Å. The computed ground-stte vibrtionl frequency of 82 cm - grees very well with the experimentlly determined vlue of cm -. The d-correltion does not chnge the frequency much. Thermochemicl 6 dissocition energy of the ground-stte SnS is reported to be bout.77 ev, which lso compres well with the clculted vlue of.7 ev without considering the spin-orbit coupling. However, the previous reltivistic clcultions show somewht smller D e vlue of.2 ev. The first excited stte of SnS is of the Σ + symmetry. In the chemiluminescence of SnS, n excited stte, Ω( Σ + ) with T e ) 8.9 cm - hs been reported by Greenwood et l. As seen in Tble 2, the computed trnsition energy of the Σ + stte without spin-orbit coupling is bout 8080 cm -, which compres well with the observed vlue. The Σ + stte hs been detected only in the mtrix spectr of the Σ + -X Σ system in fluorescence. 9 The CI clcultions involving ll 0 TABLE 2: Spectroscopic Constnts of Low-Lying Λ-S Sttes of SnS stte T e/cm - r e/å ω e/cm - X Σ (2.2) 82 (8) b b 2.2 c 9 c Σ (660) 2.5 (2.8) 05 (2) 286 c 2.55 c 56 c 8.9 d 2000 (920) 2.5 (2.59) 27 (7) 2000 c Σ c 2.62 c 07 c 20 (2090) 2.5 (2.5) 8 (06) c Σ b Π 220 (2260) 2.5 (2.7) 6 (5) c 2.2 c 77 c D Π (26780) 2. (2.6) 6 () b b.5 b 2707 c 2.8 c 7 c E Σ (90) 2.59 (2.50) 287 (2) 07.0 b b 28 c 2.6 c 6 c 2 Π Π Π Σ Numbers in prentheses refer to the 20-electron CI clcultions. b Reference 9. c Reference. d Energy refers to the observed stte, Ω( Σ + ). electrons of Sn in the d orbitl produce lower trnsition energy of 660 cm -. The computed equilibrium bond length nd vibrtionl frequency of the Σ + stte re 2.5 Å nd 05 cm -, respectively. The d-correltion is shown to reduce the bond length of this stte to 2.8 Å, while the ω e vlue does not chnge much. The present spectroscopic prmeters of this stte re found to be improved over those of erlier clcultions. Like the oxide, the Σ + stte of SnS is chrcterized minly by singly excited π f π* configurtion. The stte is strongly bound with binding energy of bout 2.7 ev s clculted from the MRDCI energies. Five other sttes, nmely,, Σ -,,c Σ -, nd E Σ +, which re dominted by the sme π π* configurtion s tht in Σ +, re lso bound. The clcultions suggest tht the Σ -, Σ -, nd sttes re nerly degenerte. The computed trnsition energies (T e ) of these sttes lie in the rnge cm -. The stte is lying somewht lower thn these three sttes with trnsition energy of 2000 cm -. The d-electron correltion reduces the trnsition energies of these sttes by bout cm -. The computed bond lengths of these sttes except E Σ + fll in the rnge Å. Although, Σ -,, nd c Σ - sttes re not so importnt for trnsitions to the ground stte, some of the spin components such s,c Σ - 0 +, nd C Σ - my undergo wek spin-forbidden trnsitions to the ground-stte component (X Σ ). Specificlly, the Σ - 0 +,- X Σ trnsitions re expected to tke plce in the region cm -. The E Σ + stte is, however, less strongly bound with MRDCI estimted binding energy of bout.0 ev. This stte is the second root of the Σ + symmetry. The computed T e of the stte is close to 250 cm - s compred with the observed T 00 of 07 cm -. The vibrtionl frequency computed here grees well with the experimentlly determined ω e vlue. The potentil minimum of the stte is expected to be round 2.59 Å, which is 0. Å longer thn tht of the ground stte. However, the 20-electron CI clcultions reduce r e of the E Σ + stte by 0.09 Å. The potentil energy curve shows tht there is smll brrier ner the bond length

4 720 J. Phys. Chem. A, Vol. 09, No. 2, 2005 Giri nd Ds TABLE : Moleculr Sttes of SnS + nd Their Correltion with Atomic Limits moleculr stte reltive energy/cm - tomic stte Sn + + S exptl clcd 2 Σ +, 2 Σ - (2), 2 Π(2), 2, 2 P u + P g 0 0 Σ +, Σ - (2), Π(2), 2 Σ + (2), 2 Σ -, 2 Π(), 2 (2), 2 Φ 2 P u + D g Reference 9. of.5 Å ( 6.5 o ). As result of the voided crossing with the higher repulsive Σ + stte, the E Σ + stte dissocites into the lowest limit Sn( P g ) + S( P g ). In the Frnck-Condon region, the π π* configurtion intercts predominntly with closed shell π nd couple of excited configurtions such s π 2 π* 2 nd σσ*π. The E Σ + -X Σ + trnsition is expected to hve stronger intensity. The b Π stte of SnS is locted just bove the set of nerly degenerte Σ - nd sttes. The computed trnsition energy of the b Π stte t equilibrium is round 220 cm - with r e ) 2.5 Å nd ω e ) 6 cm -. The b Π-X Σ + spin-forbidden bnd is very similr to the Cmeron bnd of CO. In fct, Greenwood et l. hve investigted severl bnds from the rottionl nlysis of the SnS molecule. The ssignments of the B( Π)-X Σ + nd A Π 0 + -X Σ + systems hve been mde round 220 nd 2202 cm -, respectively. The CI wve functions of the b Π stte re chrcterized minly by σπ π*, nd in the Frnck-Condon region, it contributes more thn 80%. As result of the σ f π* excittion, the Sn-S bond in the b Π stte is weker thn tht in the ground stte. In erlier clcultions, the spectroscopic prmeters of this stte re overestimted s compred in Tble 2. The sme singly excited configurtion domintes in the singlet counterprt of the b Π stte, nd it is designted here s D Π. The compositions of these two sttes re quite similr. The D Π-X Σ + bsorption system of SnS hs been reported in the inert mtrices with T 00 ) 2892 cm -. The sme types of bnds re known for other isovlent molecules such s GeO, SiO, SiS, SnO, etc. The computed trnsition energy (T e ) of the D Π stte of SnS is smller thn the observed vlue by bout 600 cm -. The equilibrium bond length of this stte is clculted to be longer thn the experimentlly determined vlue by 0.07 Å, while ω e is smller only by 5 cm -. Spectroscopiclly, the D Π-X Σ + trnsition is expected to be strong. The estimtion of the rditive lifetime for such trnsition shows the quntittive feture which is discussed in the lter section. A few more excited sttes of SnS re lso reported in Tble 2. The potentil curves of higher Π sttes such s 2 Π nd 2 Π re shllow. The third root of the Σ + symmetry undergoes n voided crossing with repulsive higher root ner r ) 2.5 Å. A very shrp minimum in the Σ + curve is locted in the energy region of cm - with shorter bond length of 2.26 Å. B. SnS +. The monopositive tin nd neutrl sulfur both in their ground sttes correlte with the lowest dissocition limit of the SnS + ion. As shown in Tble, there re six doublets nd six qurtets of Σ +, Σ - (2), Π(2), nd symmetries correlting with the Sn + ( 2 P u ) + S( P g ) limit. Another set of nine excited doublet sttes of SnS + correltes with the second dissocition limit Sn + ( 2 P u ) + S( D g ). The computed energy seprtion between the lowest two dissocition limits is lrger thn the vlue obtined from the tomic spectrl energy levels 9 by bout 000 cm -. Figure 2 shows the potentil energy curves of ll 2 electronic sttes, which correlte with the lowest Figure 2. Potentil energy curves of low-lying Λ-S sttes of SnS +. TABLE : Spectroscopic Constnts of Low-Lying Λ-S Sttes of SnS + stte T e/cm - r e/å ω e/cm - X 2 Π 0 2. (2.) 75 (86) A 2 Σ (5) 2.25 (2.26) 2 (2) Π Π Σ (959) 2.6 (2.69) 75 (69) Π B 2 Σ Numbers in prentheses refer to 9-electron CI clcultions. dissocition limit. Spectroscopic constnts of seven Λ-S sttes of SnS + re reported in Tble. The ground-stte symmetry of SnS + is X 2 Π. The computed r e nd ω e vlues of X 2 Π re 2. Å nd 75 cm -, respectively. These constnts do not chnge much when clculted with 9 electrons in the CI step. The ground-stte bond of SnS + is bout 0.5 Å longer thn tht of SnO +. The first excited stte, A 2 Σ + is locted only 880 cm - bove the ground stte. However, 9-electron CI clcultions reduce the gp by 55 cm -. The equilibrium bond length of SnS + in the A 2 Σ + stte is shorter by 0.5 Å, while the vibrtionl frequency t equilibrium is lrger by bout 60 cm - s compred to the ground-stte prmeters. The experimentl photoelectron spectrum of SnS is not clerly known. The A 2 Σ + -X 2 Π trnsition is expected to crry sufficient intensity. The quntittive spect of this trnsition is discussed lter on. The ground stte of SnS + is dominted by the σ 2 π configurtion, while the σ f π trnsition genertes the A 2 Σ + stte. Three wekly bound qurtets such s Π, Σ +, nd re low-lying (see Figure 2). The computed trnsition energy of Π is bout 6060 cm - t r e ) 2.96 Å. The potentil energy curve of is very shllow with ω e ) 75 cm - only. However, none of these qurtets is spectroscopiclly significnt. The second root of the 2 Π symmetry hs very brod potentil minimum round 880 cm -.

5 Electronic Sttes of SnS nd SnS + J. Phys. Chem. A, Vol. 09, No. 2, TABLE 5: Spectroscopic Constnts of Ω Sttes of SnS stte T e/cm - r e/å ω e/cm - (% contribution) composition t r e X Σ X Σ + (99) Σ Σ + (90), c Σ - (9) (8.9) (7.7) Σ Σ + (95), Σ - (5) (7), (27) (99) (99) Σ Σ - (9), Σ + (5) C Σ Σ - (98), b Π () (2280) C Σ Σ - (89), Σ + (0) (2280) A Π b Π - (57), c Σ - () (2202.) (7), (27) 0 - (III) b Π (57), Σ - () B b Π (8), c Σ - (2) (220) Π b Π (9) D Π D Π (96), b Π () (2860) b E Σ E Σ + (98) Reference. b Reference 9. The computed equilibrium bond length of 2 2 Π is.0 Å with ω e ) 78 cm -. The potentil energy curve of the B 2 Σ + stte undergoes n voided crossing. The fitted r e nd ω e of this stte re 2. Å nd 95 cm -, respectively. The estimted trnsition energy t equilibrium is bout cm -. The dissocition energies (D e )ofx 2 Π nd A 2 Σ + sttes of SnS + re 2.86 nd 2.9 ev, respectively from nine-electron CI clcultions. The d-electron correltion increses the dissocition energies by bout 0.5 ev. IV. Spectroscopic Properties of Low-Lying Ω Sttes A. SnS. All 8 Λ-S sttes of SnS re included in the spinorbit coupling. In Figure, prts nd b, we hve shown the computed potentil energy curves of 0 + nd sttes, respectively. Spectroscopic constnts of 6 spin-orbit components re reported in Tble 5. The ground-stte component (X Σ ) remins unchnged due to the spin-orbit coupling. The energy seprtion between the 0 - nd components of Σ + is only 20 cm -. The computed trnsition energy of the Σ + -X Σ trnsition is round 770 cm -, which is somewht smller thn T e ) 8.9 cm - observed for ( Σ + ) in the chemiluminescent flme spectrum of SnS. Three components of split in the energy order 2 <. The lrgest splitting is bout 650 cm -. The components of Σ -, denoted s C Σ nd C Σ -, re seprted by 00 cm -. The extended rottionl nlyses of the perturbed bnds observed in the bsorption spectrum hve mde the ssignments of the 0 + nd components of Σ -. The MRDCI-estimted trnsition energies of both the spin-forbidden trnsitions, C Σ X Σ nd C Σ - - X Σ re smller thn the observed vlues by cm -. There is considerble mount of mixing between Π 0 + nd Σ ner the potentil minimum of Π. The dibtic curve of the third root of 0 + is fitted nd designted s A Π 0 +. The estimted r e nd ω e of the A Π 0 + component re 2.5 Å nd 60 cm -, respectively. The computed trnsition energy of the A Π 0 + component grees well with the observed Te of cm -. The Π curve undergoes severl voided crossings (Figure b) in the Frnck-Condon region. We hve fitted this dibtic curve nd denoted the component s B. The trnsition energy of the dibticlly fitted curve of B( Π) is found to Figure. Potentil energy curves of some Ω sttes of SnS for () Ω ) 0 + nd (b) Ω ) nd. be 270 cm -. Both A Π 0 + -X Σ nd B-X Σ trnsitions of SnS re nlogous to the strongest spin-forbidden systems in CO, nmely the Cmeron bnd ( Π-X Σ + ). The Ω ) 2 component of Π lso experiences voided curve crossings with the 2 nd 2 components. The trnsition energy of Π 0 -, estimted by fitting its dibtic curve, is bout 220 cm -. However, this component is spectroscopiclly less

6 722 J. Phys. Chem. A, Vol. 09, No. 2, 2005 Giri nd Ds TABLE 6: Spectroscopic Constnts of Ω Sttes of SnS + stte T e/cm - r e/å ω e/cm - (% contribution) composition t r e X 2 Π / X 2 Π (98) X 22 Π / X 2 Π (98) A 2 Σ + / A 2 Σ + (96), X 2 Π () Π / Π (7), 2 2 Π (20) Π 5/ Π (99) importnt. The D Π -X Σ bnd system of SnS is observed in the bsorption spectrum. The computed trnsition energy of D Π is 2802 cm - which is in good greement with the experimentl vlue of 2860 cm -. The only spin component of the excited Σ + stte hs potentil minimum round 2.59 Å, nd it remins lmost s pure E Σ + in the Frnck-Condon region. B. SnS +. Prts nd b of Figure show potentil energy curves of the low-lying Ω sttes rising from the spin-orbit interction mong 2 doublet nd qurtet sttes which correlte with Sn + ( 2 P u ) + S( P g ). The computed spin-orbit splitting of the ground stte of SnS + is bout 670 cm -. Spectroscopic constnts of few low-lying Ω sttes re given in Tble 6. The ground-stte component of SnS + is X 2 Π /2 with lmost the sme spectroscopic prmeters s those of the spin-pure X 2 Π stte. There is n voided crossing (Figure ) between the curves of X 22 Π /2 nd A 2 Σ + /2 components round.2 o.it hs decresed ω e of X 2 2 Π /2 only mrginlly, while the vibrtionl frequency of A 2 Σ + /2 is incresed by bout 70 cm -. The trnsition energy of the A 2 Σ + /2 component is computed to be 260 cm -. The /2 nd 5/2 components of Π re lso fitted for the estimtion of the spectroscopic constnts. The energy gp between these two components is s lrge s 790 cm -. Figure. Potentil energy curves of some Ω sttes of SnS + for () Ω ) / 2 nd (b) Ω ) / 2. V. Dipole Moments, Trnsition Moments, nd Rditive Lifetimes A. SnS. Dipole moments (µ e ) of nine low-lying sttes of SnS t r e clculted from the MRDCI wve functions without spinorbit coupling re given in Tble 7. Figure 5 shows the dipole moment functions of these sttes. All the dipole moment curves hve minim between 5 nd 7 o. These curves tend to zero when the bond is elongted to very lrge distnce. The groundstte dipole moment of SnS is estimted s -. D with the Sn + S - polrity. This is very much comprble with the experimentl vlue of -.8 ( 0.0 D obtined from the Strkeffect mesurements on the rottionl trnsitions of SnS. The CCSD(T) clcultions of Kellö et l. 9 hve estimted vlue of -.05 D. The bsolute vlues of the dipole moments of other excited sttes re smller thn the ground-stte one, but with the sme direction of polrity. As expected, the SnS molecule is less polr thn the corresponding oxide [µ e (SnO) )-.58 D]. Trnsition dipole moments of five trnsitions re lso plotted in Figure 5 s function of the bond length. The trnsitionmoment curve for the E Σ + -X Σ + trnsition shows mximum in the Frnck-Condon region, while the trnsition moment of the D Π-X Σ + trnsition decreses monotoniclly with the increse in the bond length. The trnsition-moment curves of D Π-,b Π-, nd b Π- Σ + re slowly vrying nd the trnsition moment vlues re comprtively smll. The nture of these trnsition moment curves of SnS is strikingly similr to those of SnO. In generl, trnsition moment vlues of the E Σ + -X Σ + trnsition in the equilibrium region re quite lrge, which mkes the trnsition more probble thn others. The computed prtil rditive lifetimes for some importnt trnsitions t V ) 0 re tbulted in Tble 8. We hve lso displyed the effect of the spin-orbit coupling on those trnsitions in the sme tble. The lifetime of the E Σ + stte of SnS is expectedly smller ( 8 ns) thn the other excited sttes. The D Π stte undergoes three possible trnsitions such s D Π-X Σ +,D Π- Σ -, nd D Π-. The trnsition to the ground stte is stronger

7 Electronic Sttes of SnS nd SnS + J. Phys. Chem. A, Vol. 09, No. 2, TABLE 7: Dipole Moment (µ e ) of Some Low-Lying Sttes of SnS t r e stte µ e/d X Σ + -. (-.8 ( 0.) (-.05) b Σ Σ c Σ b Π -2.0 D Π E Σ Reference 6. b Reference 9. TABLE 8: Rditive Lifetimes (s) for Some Trnsitions of SnS t W ) 0 prtil lifetime of trnsition the upper stte E Σ + -X Σ +.8(-8) D Π-X Σ +.2(-7) D Π- Σ -.26(-) D Π-.55(-) b Π- Σ +.98(-) b Π-.86(-) E Σ X Σ (-8) D Π -X Σ (-7) B-X Σ (-6) A Π 0+ -X Σ (-6) C Σ X Σ (-6) C Σ - -X Σ (-) Σ + -X Σ (-) Numbers in prentheses refer to the power to the bse 0. Figure 5. Dipole-moment curves of eight low-lying Λ-S sttes of SnS nd trnsition-moment curves of five trnsitions involving Λ sttes of SnS. nd its prtil rditive lifetime is much shorter thn the other two. The predicted rditive lifetime of the D Π stte is bout 2 ns. Both b Π- Σ + nd b Π- trnsitions re found to be wek. The energy differences nd trnsition moment vlues of these two trnsitions re smll. The Frnck-Condon fctors re lso smll becuse of the lrger differences in their equilibrium bond lengths. The totl rditive lifetime of the b Π stte is bout 0. ms. After the inclusion of the spin-orbit coupling, the trnsition probbilities of E Σ X Σ nd D Π -X Σ trnsitions do not chnge much, hence the chnges in the rditive lifetimes for these trnsitions re insignificnt. The lifetimes for some spin-forbidden trnsitions re lso listed in Tble 8. Both B- X Σ nd A Π 0 + -X Σ trnsitions re found to be significnt. The prtil rditive lifetimes of B nd A Π 0 + re computed to be round 7 µs t the lowest vibrtionl level. The present clcultions predict tht the C Σ - -X Σ trnsition is weker (τ 0.8 ms) thn C Σ X Σ (τ 8 µs). Trnsition probbilities for nother spin-forbidden trnsition, Figure 6. Dipole-moment curves of X 2 Π,A 2 Σ +, Σ +, nd sttes, nd trnsition-moment curves of A 2 Σ + -X 2 Π nd 2 2 Π-X 2 Π trnsitions of SnS + (Sn tom is t the origin of the coordinte system). Σ + -X Σ hve been computed here. The prtil rditive lifetime for this trnsition is only.5 ms. B. SnS +. The dipole moment functions of the X 2 Π,A 2 Σ +, Σ +, nd sttes of the ion re shown in Figure 6. The dipole moment vlues shown in the curves re clculted by keeping Sn t the origin of the Crtesin coordinte system. All the curves re found to be smooth. The doublets of SnS + hve minim, while the qurtets show mxim in their dipole moment curves. The µ e vlues, which re clculted by keeping the origin t the center of mss of SnS +, re listed in Tble 9. The groundstte µ e of SnS + is bout -.0 D, while for the first excited stte (A 2 Σ + ), it is D. The experimentl vlues re not yet known. The knowledge of the dipole moments of the moleculr ions my be useful for microwve spectroscopy. Four low-lying trnsitions such s A 2 Σ + -X 2 Π,2 2 Π-X 2 Π, B 2 Σ + -X 2 Π, nd B 2 Σ + -A 2 Σ + for SnS + re reported here. In Figure 6, trnsition dipole moments of A 2 Σ + -X 2 Π nd 2 2 Π-

8 72 J. Phys. Chem. A, Vol. 09, No. 2, 2005 Giri nd Ds TABLE 9: Dipole Moment (µ e ) of Few Low-Lying Sttes of SnS + t r e stte µ e/d X 2 Π re plotted s function of r. The trnsition moment curve for the A-X trnsition is monotoniclly decresing, while the other one for the 2 2 Π-X 2 Π trnsition shows mximum. Both the curves converge smoothly to zero t lrge r. The computed trnsition moments of B 2 Σ + -X 2 Π re lrger thn those of B 2 Σ + -A 2 Σ + in the Frnck-Condon region. As result, the prtil lifetime of the former trnsition is shorter thn the lter one. After the introduction of the spin-orbit coupling, the potentil curve of the B 2 Σ + /2 component becomes complex in nture due to severl voided curve-crossings. However, both A 2 Σ + /2-X 2 Π /2 nd A 2 Σ + /2-X 2 2 Π /2 trnsitions re llowed in the rnge cm -. There re three trnsition components rising out of the A-X trnsition. Two components such s A-X nd A-X 2 hve perpendiculr ( ) polriztions, while the A-X 2 trnsition component hs prllel ( ) polriztion. It is predicted here tht the (A-X 2 ) trnsition is stronger thn (A-X 2 ), while the (A-X ) trnsition is the strongest mong them. At the lowest vibrtionl level, the prtil rditive lifetime for the (A-X ) trnsition is bout 0.7 ms. The trnsition probbilities of spin-forbidden trnsition such s Π /2 -X 2 Π /2 hve lso been computed, nd the rditive lifetime of Π /2 t V ) 0 is bout 8 µs. The verticl ioniztion energies (VIE) of the ground-stte SnS to the ground nd some low-lying excited sttes of SnS + re clculted from the differences in the estimted full CI energies. The clcultions of both neutrl nd ionic species hve been crried out with the sme set of bsis functions nd configurtion-selection threshold. The ground-stte equilibrium bond length hs been chosen t.25 o for the clcultions of verticl ioniztion energies. For some of the sttes such s X 2 Π,A 2 Σ +, Σ +, Π, nd, the effect of d-correltion on the ioniztion energies hs been estimted. From the 9-electron CI clcultions, the VIEs of the ground stte of SnS to X 2 Π nd A 2 Σ + sttes of SnS + re 9.5 nd 9.28 ev, respectively, which re comprtively smller thn the vlues reported for SnO The ioniztion to the excited B 2 Σ + stte of SnS + requires 2.52 ev energy. Like the oxide ion, the X 2 2 Π /2 -X 2 Π /2 trnsition is extremely difficult to observe becuse the trnsition moment vlues in the Frnck-Condon region re only of the order of 0.0 e o nd the energy difference is less thn 000 cm -. The clculted rditive lifetime for the X 2 -X trnsition is in the rnge of 20-0 s only. VI. Summry X 2 Π -.0 A 2 Σ Π.05 Π.6 Σ Origin is t the center of mss. Severl low-lying electronic sttes of SnS nd SnS + hve been computed by the b initio bsed MRDCI clcultions which include RECP of both Sn nd S toms. The ground stte (X Σ + ) of SnS hs closed shell configurtion, while the ground stte (X 2 Π)ofSnS + is dominted by n open shell configurtion, σ 2 π. The computed r e of the ground stte of SnS is overestimted by bout 0.0 Å, while the clculted ω e grees well with the observed vlue. The inclusion of d electrons in the CI steps does not lter r e nd ω e of the ground stte of SnS TABLE 0: Rditive Lifetimes (s) for Some Trnsitions of SnS + t W ) 0 prtil lifetime of trnsition the upper stte A 2 Σ + -X 2 Π 6.0(-) 2 2 Π-X 2 Π.9(-6) B 2 Σ + -X 2 Π 6.0(-7) B 2 Σ + -A 2 Σ +.62(-6) A 2 Σ + /2-X 2 Π /2( ) 6.87(-) A 2 Σ + /2-X 22 Π /2( ).(-) A 2 Σ + /2-X 22 Π /2( ) 6.29(-) Π /2-X 2 Π /2 8.58(-6) Numbers in prentheses refer to the power to the bse 0. TABLE : Verticl Ioniztion Energies (ev) of SnS clculted IE ionic stte without d-electron with d-electron X 2 Π A 2 Σ Π Π. Σ Π.5 B 2 Σ significntly. Trnsition energies (T e ) of the excited bound sttes re, however, reduced to some extent becuse of the d- correltion. At the Λ-S level, the E Σ + -X Σ + nd D Π-X Σ + trnsitions of SnS re stronger. The estimted prtil lifetimes of these two trnsitions re 8 nd 2 ns, respectively. The spin-orbit coupling introduces severl voided curve crossings in the potentil curves of Ω sttes of SnS. The spin-forbidden trnsitions such s Σ + -X Σ + 0 +,C Σ X Σ + 0 +,C Σ - - X Σ + 0 +,A Π 0 + -X Σ + 0 +, nd B-X Σ hve been computed nd compred with the experimentl results. The E Σ X Σ trnsition remins the strongest of ll. The ground-stte dipole moment (µ e ) of SnS is estimted to be -. D which compres well with the experimentlly determined vlue of -.8 ( 0.0 D. The ground nd first excited sttes of SnS + re X 2 Π nd A 2 Σ +, respectively. Their spectroscopic constnts do not chnge much due to the d-correltion. On ioniztion, the ground-stte Sn-S bond is enhnced by bout 0.6 Å, while the vibrtionl frequency is reduced by bout 00 cm -. The ground-stte dissocition energy of SnS + is bout 2.86 ev, while tht of the neutrl species is estimted to be.7 ev. The A 2 Σ + stte of SnS + hs shorter bond length nd lrger vibrtionl frequency thn the ground-stte vlues. Other excited qurtets nd doublets computed here re wekly bound. The spin-orbit splitting between the two components of X 2 Π of SnS + is found to be round 700 cm -. Mny of the excited /2 nd /2 components of SnS + predissocite through vrious chnnels. The computed prtil lifetimes of the A-X nd A-X 2 trnsitions with perpendiculr polriztion re somewht shorter thn tht of the A-X 2 trnsition with prllel polriztion. The totl predicted lifetime of the A stte is bout 0. ms. The X 2 - X trnsition is very wek, nd hence difficult to detect experimentlly. By keeping the origin t the center of mss, one cn predict the dipole moment of the ground stte of SnS + to be -.0 D. Finlly, the verticl ioniztion energy of the ground-stte SnS to the ground stte of its ion is bout 9. ev. Acknowledgment. We thnk Prof. Dr. Robert J. Buenker, Wuppertl, Germny, for mking vilble the CI codes. The finncil support from CSIR, Govt. of Indi under the scheme 0(759)/02/EMR-II is grtefully cknowledged.

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