Infrared Emission Spectra and Equilibrium Structures of Gaseous HgH 2 and HgD 2

Transcription

1 10280 J. Phys. Chem. A 5, 109, Infrred Emission Spectr nd Equilibrium Structures of Gseous HgH 2 nd HgD 2 Alirez Shyesteh, Shnshn Yu, nd Peter F. Bernth* Deprtment of Chemistry, UniVersity of Wterloo, Wterloo, ON, N2L 3G1, Cnd ReceiVed: July 20, 5; In Finl Form: September 15, 5 A detiled nlysis of the high-resolution infrred emission spectr of gseous HgH 2 nd HgD 2 in the 1-2 cm -1 spectrl rnge is presented. The ν 3 ntisymmetric stretching fundmentl bnds of 204 HgH 2, HgH 2, 201 HgH 2, HgH 2, 199 HgH 2, 198 HgH 2, 204 HgD 2, HgD 2, 201 HgD 2, HgD 2, 199 HgD 2, nd 198 HgD 2, s well s few hot bnds involving ν 1, ν 2, nd ν 3 were nlyzed rottionlly, nd spectroscopic constnts were obtined. Using the rottionl constnts of the 000, 100, , nd 001 vibrtionl levels, we determined the equilibrium rottionl constnts (B e ) of the most bundnt isotopologues, HgH 2 nd HgD 2, to be (24) cm -1 nd (16) cm -1, respectively, nd the ssocited equilibrium Hg-H nd Hg-D internucler distnces (r e ) re (1) Å nd (1) Å, respectively. The r e distnces of HgH 2 nd HgD 2 differ by bout 0.005%, which cn be ttributed to the brekdown of the Born-Oppenheimer pproximtion. 1. Introduction Mercury nd its compounds hve been studied extensively s toxic chemicls in the environment. 1-5 Two mjor nthropogenic sources of mercury in the environment re col combustion nd wste incinertion. 1 Mercury in the tmosphere exists minly s neutrl Hg vpor, wheres mercuric slts nd methyl-mercury compounds cn be found in nturl wters nd sediments. 4 Anerobic bcteri in nturl wters cn reduce Hg(II) to Hg 0, which is re-emitted to the tmosphere s vpor phse elementl mercury. 5,6 The reduction of Hg(II) to Hg 0, followed by the gs-phse detection of tomic mercury, is in fct well-known method for detecting trce mounts of mercury in liquid nd solid smples. The method is clled cold vpor genertion, which ws developed in the lte 1960s, nd is bsed on the reduction of queous Hg(II) by SnCl 2 or NBH 4 nd detection of gs-phse Hg 0 by tomic bsorption spectroscopy. 7,8 A similr technique clled hydride genertion is bsed on the reduction of cidified solutions of group 13, 14, 15, nd 16 elements by NBH 4 to form voltile hydrides, which cn be detected in the gs phse fter tomiztion. 8 The hydride genertion technique ws exmined recently for mercury, nd it ws found tht both tomic nd moleculr Hg species re formed in the reduction process. 9 Although this voltile mercurycontining molecule hs not been identified, it might be HgH 2. In nother experiment, methyl-mercury chloride (CH 3 HgCl) ws reduced by NBH 4, nd the voltile CH 3 HgH molecule ws detected in the gs phse by FT-IR nd mss spectrometry. 10 Considering the fct tht nerobic bcteri cn reduce queous Hg(II) nd queous ions of group 14, 15, nd 16 elements to form voltile Hg 0, SnH 4,PH 3, AsH 3, nd H 2 S in the environment, 5,6,11,12 further reduction of Hg 0 by these bcteri my result in formtion of voltile HgH 2. There hve been severl b initio theoreticl studies of the electronic structure nd geometry of gseous HgH 2, predicting liner H-Hg-H structure nd closed-shell X 1Σ + g ground * Corresponding uthor. Deprtment of Chemistry, University of Wterloo, University Avenue West, Wterloo, ON, N2L 3G1, Cnd. Tel: Fx: E-mil: bernth@uwterloo.c. electronic stte The equilibrium Hg-H internucler distnces estimted by vrious theoreticl models were in the rnge of Å For hevy tom like Hg, reltivistic effects re significnt nd should be included in the clcultions. Nonreltivistic clcultions overestimte the Hg-H internucler distnce by more thn 0.1 Å Hrmonic vibrtionl frequencies of HgH 2, HgHD, nd HgD 2 hve been clculted t the DFT(B3LYP), MP2, nd CCSD(T) levels of theory with reltively lrge bsis sets Recently, Li et l. 22 performed very high level b initio clcultion on this molecule nd predicted the energies for mny vibrtionl levels of HgH 2, HgHD, nd HgD 2 for J ) 0 (no rottion) using vritionl clcultion. They lso clculted tht the gs-phse rection: Hg(g) + H 2 (g) f HgH 2 (g) is endoergic by 20.8 kcl mol -1 for ground-stte ( 1 S) mercury toms. 22 The first excited stte of Hg, the metstble 3 P stte, lies bout 120 kcl mol -1 bove the ground stte, 24 so the formtion of gseous HgH 2 from the gsphse rection of Hg( 3 P) with H 2 is highly exoergic. The gs-phse rection of excited mercury toms Hg( 3 P) with moleculr hydrogen hs been studied by both theoreticl clcultions nd lser pump-probe techniques The groundstte Hg( 1 S) does not rect with H 2 becuse of high energy brrier, but excited mercury toms in the 3 P stte cn insert into the H-H bond nd form the excited bent [H-Hg-H]* complex This intermedite cn dissocite into the HgH nd H free rdicls. The theoreticl nd experimentl studies of this rection were focused minly on the production of HgH nd H, nd little ttention ws given to the formtion of the ground-stte liner H-Hg-H molecule in the gs phse. 28 The rections of H 2 with excited Mg, Zn, Cd, nd Hg toms hve been reviewed by Breckenridge. 32 Solid HgH 2 ws first synthesized in the 1950s, from the rection of HgI 2 with LiAlH 4 in ether-thf-petroleum ether solution t -135 C This solid ws reported to be extremely unstble, decomposing t tempertures bove -125 C, nd it is probbly not possible to produce gseous HgH /jp CCC: $ Americn Chemicl Society Published on Web 10/21/5

2 Gseous HgH 2 nd HgD 2 J. Phys. Chem. A, Vol. 109, No. 45, by heting the solid. Recently, Wng nd Andrews 21,36 recorded the infrred spectr of solid HgH 2, HgHD, nd HgD 2 nd proposed tht HgH 2 forms covlent moleculr solid, unlike zinc nd cdmium dihydrides. Aldridge nd Downs 37 hve reviewed the chemicl properties of group 12 nd other min-group hydrides. Mny trnsitionmetl hydrides hve been trpped in solid mtrices t tempertures below 12 K nd studied by infrred bsorption spectroscopy. 38 Mercury dihydride hs been formed in solid hydrogen, nitrogen, neon, nd rgon mtrices from the rection of excited mercury toms with hydrogen. 21,36,39,40 The infrred bsorption spectr of HgH 2, HgHD, nd HgD 2 (trpped in solid mtrices) were recorded, nd vibrtionl frequencies of the infrred-ctive modes were obtined. 21,36,39,40 HgH 2 hs lso ppered s byproduct in the mtrix isoltion experiments designed to study the HHgOH nd Hg(OH) 2 molecules. 41,42 We hve reported the first observtion of HgH 2 nd HgD 2 molecules in the gs phse recently. 43 The molecules were generted by the rection of mercury vpor with moleculr hydrogen or deuterium in the presence of n electricl dischrge nd were identified unmbiguously by their high-resolution infrred emission spectr. Rottionl nlysis of the ntisymmetric stretching fundmentl bnds (ν 3 )ofhgh 2 nd HgD 2 yielded the r 0 Hg-H nd Hg-D internucler distnces. 43 Gseous ZnH 2, ZnD 2, CdH 2, nd CdD 2 hve lso been studied in our lbortory, nd detiled nlyses of their high-resolution infrred emission spectr hve been published A detiled nlysis of ll of the vibrtion-rottion bnds observed in the infrred emission spectr of gseous HgH 2 nd HgD 2 is presented in this pper. 2. Experimentl Section The emission source used to generte gseous HgH 2 nd HgD 2 molecules hs been described in our erlier pper. 43 A smll zirconi bot contining bout 100 g of mercury ws plced inside the centrl prt of n lumin tube. The tube contined stinless steel electrodes in both ends nd ws seled with brium fluoride windows. Pure hydrogen or deuterium flowed slowly through the tube t room temperture, nd the totl pressure ws held t 0.7 Torr using rotry pump. A dc dischrge (3 kv/333 ma) ws creted between the electrodes, nd the resulting emission ws focused onto the entrnce perture of Bruker IFS 120 HR Fourier trnsform spectrometer using brium fluoride lens. The infrred emission spectrum of HgH 2 ws recorded using KBr bem splitter nd n InSb detector cooled by liquid nitrogen. The spectrl rnge ws limited to cm -1 by the detector response nd 2 cm -1 long-wve pss filter. The instrumentl resolution ws set to 0.01 cm -1 nd, to improve the signl-to-noise rtio, 100 spectr were co-dded during 90 min of recording. The spectrum of HgD 2 ws recorded using the sme bem splitter nd liquidnitrogen-cooled HgCdTe (MCT) detector. The spectrl rnge for HgD 2 ws 1-2 cm -1, set by the trnsmission of the 2 cm -1 long-wve pss filter. The instrumentl resolution ws 0.01 cm -1, nd 400 spectr were co-dded during 6hof recording. The signl-to-noise rtios for the strongest emission lines of HgH 2 nd HgD 2 were bout 100 nd 40, respectively. 3. Results nd Anlysis 3.1. Vibrtion-Rottion Bnds. The WSPECTRA progrm, written by M. Crleer (Université Libre de Bruxelles), ws used to mesure the line positions in HgH 2 nd HgD 2 spectr. Emission lines of crbon monoxide (impurity) ppered in both Figure 1. Overview of the infrred emission spectrum of gseous HgD 2 in the ν 3 region, recorded t resolution of 0.01 cm -1. Figure 2. Very smll portion of the HgH 2 spectrum showing the isotope splitting in two R-brnch lines of the 001f 000 nd 002 f 001 vibrtion-rottion bnds. The lines mrked with circles re from HgH 2 nd those mrked with strs re from minor isotopes of mercury. The strong lines with no isotope splitting re from impurity CO. spectr nd were used for bsolute wvenumber clibrtion. 47 The bsolute ccurcy of our clibrted line positions is better thn cm -1. Rottionl ssignments of the vibrtionrottion bnds of HgH 2 nd HgD 2 were fcilitted using color Loomis-Wood progrm. An overview of the HgD 2 spectrum is shown in Figure 1. Mercury hs seven stble isotopes, nd their terrestril bundnces re the following: 204 Hg (6.9%), Hg (29.8%), 201 Hg (13.2%), Hg (23.1%), 199 Hg (16.9%), 198 Hg (10.0%), nd 196 Hg (0.1%). Lines from six isotopes (ll except 196 Hg) were observed in both spectr, nd their intensity rtios mtch their nturl bundnces. Figure 2 is very smll portion of the HgH 2 spectrum, showing the isotope splitting in two rottionl lines. The djcent rottionl lines in HgH 2 nd HgD 2 spectr hd 3:1 nd 1:2 intensity rtios, respectively, becuse of the orthopr nucler spin sttisticl weights ssocited with hydrogen (I ) 1 / 2 ) nd deuterium (I ) 1) nuclei. 48 An expnded view of the HgD 2 spectrum in Figure 3 shows the 1:2 intensity lterntion. In ddition to the ν 3 fundmentl bnd, tht is, 001 (Σ + u ) f 000 (Σ + g ), the following hot bnds were observed for HgH 2, HgH 2, HgD 2, nd HgD 2 : 002 (Σ + g ) f 001 (Σ + u ), 003 (Σ + u ) f 002 (Σ + g ), 101 (Σ + u ) f 100 (Σ + g ), nd (Π g ) f (Π u ). Fewer hot bnds were detectble for the other isotopes of mercury becuse of their lower bundnces.

3 10282 J. Phys. Chem. A, Vol. 109, No. 45, 5 Shyesteh et l. Figure 3. Expnded view of the HgD 2 spectrum showing the 1:2 intensity lterntion nd the mercury isotope splitting in P-brnch lines of the ν 3 fundmentl bnd. The weker lines re from the hot bnds of HgD 2. The vibrtionl energy of liner tritomic molecule in the 1 Σ + g ground electronic stte cn be expressed by the following eqution 48 G(V 1, V l 2, V 3 ) ) ω 1 (V 1 + (1/2)) + ω 2 (V 2 + 1) + ω 3 (V 3 + (1/2)) + x 11 (V 1 + (1/2)) 2 + x 22 (V 2 + 1) 2 + x 33 (V 3 + (1/2)) 2 + g 22 l 2 + x 12 (V 1 + (1/2))(V 2 + 1) + x 13 (V 1 + (1/2))(V 3 + (1/2)) + x 23 (V 2 + 1)(V 3 + (1/2)) (1) in which ω i vlues re the hrmonic vibrtionl frequencies nd x ij vlues re second-order nhrmonicity constnts. The vibrtionl quntum numbers for the symmetric stretching (σ g ), bending (π u ), nd ntisymmetric stretching (σ u ) modes re represented by V 1, V 2, nd V 3, respectively, nd l is the vibrtionl ngulr momentum quntum number. The rottionl energy for the Σ (l ) 0) nd Π (l ) 1) sttes cn be expressed by the following eqution 49 F [V] (J) ) B[J(J + 1) - l 2 ] - D[J(J + 1) - l 2 ] 2 ( 1 2 [qj(j + 1) + q D J2 (J + 1) 2 ] (2) in which J is the totl ngulr momentum quntum number (including rottion), B is the inertil rottionl constnt, nd D is the centrifugl distortion constnt. The rottionl l-type doubling prmeters, q nd q D, re nonzero only for the Π sttes, nd the + (-) sign refers to the e (f) prity component. 48 An experimentl uncertinty of cm -1 ws used for the rottionl lines of the 001 f 000 fundmentl bnd of HgH 2 nd HgD 2. Lines from the hot bnds were less intense nd were given n uncertinty of cm -1. The bsolute rottionl ssignments of the 001 (Σ u + ) f 000 (Σ g + ) fundmentl bnds of HgH 2 nd HgD 2 were obtined esily becuse we observed ll of the rottionl lines ner the bnd origins. The intensity rtios of djcent rottionl lines further confirmed our bsolute J ssignments. The rottionl ssignment of the 002 (Σ g + ) f 001 (Σ u + ) nd 003 (Σ u + ) f 002 (Σ g + ) hot bnds were obtined consecutively using lower stte combintion differences. All of the rottionl lines of the 001 (Σ u + ) f 000 (Σ g + ), 002 (Σ g + ) f 001 (Σ u + ), nd 003 (Σ u + ) f 002 (Σ g + ) bnds were fitted together using the energy expression in eq 2, nd the spectroscopic constnts were determined. A complete list of the observed line positions for ll isotopologues nd the outputs of our lest-squres fitting progrm hve been plced in Tbles 1S-12S, provided s Supporting Informtion. The spectroscopic constnts for HgH 2, HgH 2, HgD 2, nd HgD 2 re presented in Tbles 1 nd 2, nd those for the minor isotopes of mercury re in Tbles 5S-12S. The ground-stte vibrtionl energy (G 000 ) ws set to zero in the lest-squres fitting, nd the reported constnts cn reproduce the dt within the experimentl uncertinty ( cm -1 ). One of the hot bnds in both HgH 2 nd HgD 2 spectr hd lrge l-type doubling, nd ws ssigned to the (Π g ) f (Π u ) trnsition. The bsolute J ssignment for this bnd ws obtined bsed on the intensity lterntion nd the fct tht e nd f prity components of Π stte hve the sme vibrtionl bnd origins. Rottionl lines of the (Π g ) f (Π u ) bnds of HgH 2 nd HgD 2 were fitted using the energy expression in eq 2 with l ) 1. The vibrtionl energy of the stte ws set to zero becuse we cn only determine the difference between the nd vibrtionl energies using our dt. Rottionl constnts nd the l-type doubling constnts of the nd sttes re reported in Tbles 1 nd 2 for HgH 2, HgH 2, HgD 2, nd HgD 2. The bsolute J ssignments of the 101 (Σ u + ) f 100 (Σ g + ) hot bnds of HgH 2 nd HgD 2 were difficult to obtin becuse few rottionl lines ner the bnd origins were missing. Therefore, we hd to estimte the rottionl constnts (B) of the 100 (Σ g + ) sttes of HgH 2 nd HgD 2 to obtin definite J ssignments for these bnds. Rottionl constnts (B) of the 000, , nd 001 sttes were used to clculte the vibrtionrottion interction constnts, R 2 nd R 3, for HgH 2 nd HgD 2 using the following liner eqution: 48 B [V] ) B e -R 1 (V 1 + (1/2)) -R 2 (V 2 + 1) -R 3 (V 3 + (1/2)) (3) Within the Born-Oppenheimer pproximtion, the rtio of the B e vlues of HgH 2 nd HgD 2 is simply given by B e ( HgH 2 ) B e ( HgD 2 ) ) m D m H (4) in which m D nd m H re tomic msses of deuterium nd hydrogen, respectively. In ddition, simple mss-scling rtio exists for the R 1 constnts of HgH 2 nd HgD 2 : 46,49 R 1 ( HgH 2 ) R 1 ( HgD 2 ) ) ( m D 3/2 m H) Using the B 000, R 2, nd R 3 constnts of both HgH 2 nd HgD 2, we were ble to estimte R 1 nd B e for these isotopologues by tking dvntge of their isotopic rtios, eqs 3-5. The bsolute J ssignments of the 101 (Σ + u ) f 100 (Σ + g ) hot bnds of HgH 2 nd HgD 2 were then obtined immeditely becuse we hd resonble estimtes for the R 1 constnts. Rottionl lines of the 101 (Σ + u ) f 100 (Σ + g ) hot bnds were fitted using the energy expression in eq 2 with l ) 0, nd the unknown vibrtionl energy of the lower stte (100, Σ + g ) ws set to zero in the lest-squres fitting (see Tbles 1 nd 2). In our previous studies on CdH 2 nd ZnH 2, we observed locl perturbtions nd Fermi resonnce in some vibrtionl levels. 45,46 The 001 vibrtionl levels of CdH 2 nd ZnH 2 were perturbed loclly by the nerby 030 levels becuse ν 3 3ν 2 for these molecules. Strong Fermi resonnces were lso observed between the 002 (Σ + g ) nd (Σ + g ) levels becuse ν 3 ν 1 for both (5)

4 Gseous HgH 2 nd HgD 2 J. Phys. Chem. A, Vol. 109, No. 45, TABLE 1: Spectroscopic Constnts (in cm -1 )of HgH 2 nd HgH 2 molecule stte G [V] - G 000 B D/10-5 q/10-2 q D/ (Σ + g ) (37) (76) 001 (Σ + u ) (6) (34) (63) 002 (Σ + g ) (17) (40) (94) HgH (Σ + u ) (27) (58) (19) 100 (Σ + g ) b ν (32) 2.877(24) 101 (Σ + u ) (30) + ν (32) 2.902(21) (Π u) b ν (13) (53) (18) 1.56(8) (Π g) (16) + ν (12) (44) (17) 1.44(7) 000 (Σ + g ) (39) (92) 001 (Σ + u ) (6) (36) (78) 002 (Σ + g ) (16) (41) (98) HgH (Σ + u ) (24) (55) (19) 100 (Σ + g ) b ν (67) 2.877(65) 101 (Σ + u ) (53) + ν (68) 2.896(55) (Π u) b ν (18) (88) (25) 1.46(14) (Π g) (22) + ν (16) (69) (23) 1.36(11) The numbers in prentheses re one stndrd devition sttisticl uncertinties in the lst quoted digits. b The wvenumbers of ν 1 nd ν 2 could not be determined from our dt. The best b initio vlue (ref 22) for ν 1 is 1982 cm -1, nd the neon mtrix vlue (ref 21) for ν 2 is 782 cm -1. TABLE 2: Spectroscopic Constnts (in cm -1 )of HgD 2 nd HgD 2 molecule stte G [V] - G 000 B D/10-5 q/ (Σ + g ) (26) (24) 001 (Σ + u ) (8) (26) (25) 002 (Σ + g ) (20) (30) (36) HgD (Σ + u ) (52) (77) (21) 100 (Σ + g ) b ν (21) (51) 101 (Σ + u ) (35) + ν (22) (54) (Π u) b ν (10) (20) (74) (Π g) (21) + ν (10) (23) (78) 000 (Σ + g ) (31) (31) 001 (Σ + u ) (9) (31) (31) 002 (Σ + g ) (23) (36) (45) HgD (Σ + u ) (59) (90) (24) 100 (Σ + g ) b ν (21) (44) 101 (Σ + u ) (38) + ν (21) (42) (Π u) b ν (13) (28) (86) (Π g) (25) + ν (14) (34) (89) The numbers in prentheses re one stndrd devition sttisticl uncertinties in the lst quoted digits. b The wvenumbers of ν 1 nd ν 2 could not be determined from our dt. The best b initio vlue (ref 22) for ν 1 is 1421 cm -1, nd the neon mtrix vlue (ref 21) for ν 2 is 562 cm -1. CdH 2 nd ZnH 2. 45,46 In contrst, we did not observe similr perturbtions in the vibrtion-rottion bnds of HgH 2 nd HgD 2. Bsed on the hrmonic vibrtionl frequencies predicted by Greene et l., 20 ν 1 nd 3ν 2 re considerbly lrger thn ν 3 for HgH 2 nd HgD 2, nd the bove perturbtions re not expected Determintion of Internucler Distnces. The B 000 constnts of HgH 2, HgH 2, HgD 2, nd HgD 2, tken from Tbles 1 nd 2, were used to determine the r 0 internucler distnces directly from the moment of inerti eqution. The r 0 vlues obtined for HgH 2 nd HgD 2 re (1) Å nd (2) Å, respectively. This discrepncy ( Å) is due to the fct tht the 000 ground stte of HgD 2 lies lower thn tht of HgH 2 on the potentil energy surfce. However, the r 0 distnces for different isotopes of mercury re equl within the sttisticl uncertinties. By tking the differences between the ground-stte rottionl constnt (B 000 ) nd the B [V] vlues of the 100, , nd 001 sttes, we determined the vibrtion-rottion interction constnts (R 1, R 2, nd R 3 in eq 3). The equilibrium rottionl constnts (B e )of HgH 2, HgH 2, HgD 2, nd HgD 2 were then clculted using their B 000 vlues nd the three R s. The equilibrium centrifugl distortion constnt (D e ) ws clculted for these isotopologues using liner eqution nlogous to eq 3 for the D [V] vlues. Tble 3 hs list of moleculr constnts determined for HgH 2, HgH 2, HgD 2, nd HgD 2 in this study. Using the B e vlues of (24) cm -1 nd (16) cm -1 for HgH 2 nd HgD 2, respectively, we determined the equilibrium internucler distnces (r e )tobe (1) Å nd (1) Å, respectively. The difference in the r e vlues of HgH 2 nd HgD 2 is only 0.005% but still n order of mgnitude lrger thn the sttisticl uncertinties. This discrepncy ppers to be due to the brekdown of the Born-Oppenheimer pproximtion. 46 In contrst, the r e distnces for different isotopes of mercury re equl within the sttisticl uncertinties (see Tble 3).

5 10284 J. Phys. Chem. A, Vol. 109, No. 45, 5 Shyesteh et l. TABLE 3: Moleculr Constnts (in cm -1 )of HgH 2, HgH 2, HgD 2, nd HgD 2 constnt HgH 2 HgH 2 HgD 2 HgD 2 B (4) (4) (3) (3) r 0/Å (1) (1) (2) (2) R (3) (7) (2) (2) R (1) (2) (1) (1) R (5) (5) (4) (4) B e (24) (40) (16) (19) r e/å (1) (1) (1) (1) D e/ (1) 2.76(3) 0.694(3) 0.694(4) q 010/ (2) (3) (7) (9) ν (6) (6) (8) (9) x (3) (5) (4) (4) x (2) (2) -8.4(2) (3) x (1) (1) (2) (2) ω 1 (σ g) 2112 b 2112 b 1492 b 1492 b ω 2 (π u) 770 c 774 c ω 3 (σ u) (4) (5) (5) (6) The numbers in prentheses re one stndrd devition sttisticl uncertinties, clculted by propgtion of errors. b Estimted from B e nd D e using eq 8. c Estimted from q 010, B e nd ω 3 using eq 9; the neon mtrix vlues (ref 21) for ν 2 of HgH 2 nd HgD 2 re 782 cm -1 nd 562 cm -1, respectively. In polytomic molecules for which equilibrium internucler distnces (r e ) re not vilble, it is common to clculte the verge r s structure by using the moments of inerti of isotopiclly substituted molecules. In our previous work on ZnH 2 nd ZnD 2, we clculted the verge r s structure in order to compre it with the r 0 nd r e internucler distnces. 46 The ground-stte moments of inerti (I D 0 nd I H 0 ) were clculted from the B 000 vlues of HgD 2 nd HgH 2, respectively, nd were used to obtin the verge r s distnce by the following eqution 50 in which m D nd m H re the tomic msses for deuterium nd hydrogen: I 0 D - I 0 H ) 2r s 2 (m D - m H ) (6) The r s distnce estimted from eq 6 is Å, nd lies between the r 0 nd r e vlues Vibrtionl Anlysis. A few nhrmonicity constnts in eq 1 cn be clculted directly from the observed bnd origins (Tbles 1 nd 2). For HgH 2, HgH 2, HgD 2, nd HgD 2 isotopologues, we obtined x 13 by tking the difference between the 101 f 100 nd 001 f 000 bnd origins. Similrly, the difference between the f nd 001 f 000 bnd origins is equl to x 23, nd the difference between the 002 f 001 nd 001 f 000 bnd origins is equl to 2x 33 (see eq 1). All of the hot bnds of HgH 2 nd HgD 2 ppered to lower wvenumbers compred to the ν 3 fundmentl bnds, nd thus the x 13, x 23, nd x 33 constnts hve negtive vlues (see Tble 3). The equilibrium vibrtionl wvenumber of the ntisymmetric stretching mode (ω 3 ) ws then determined using the following eqution ν 3 (obs) ) G G 000 ) ω 3 + (1/2)x 13 + x x 33 (7) which is derived from eq 1. The equilibrium vibrtionl wvenumber of the symmetric stretching mode (ω 1 ) ws estimted for HgH 2, HgH 2, HgD 2, nd HgD 2 isotopologues from B e nd D e constnts, using Krtzer s eqution for symmetric liner tritomic molecules: 49 D e 4B 3 e 2 ω 1 The mgnitude of the l-type doubling constnt (q) depends on B e, ω 2, nd ω 3, nd the following third-order eqution cn be (8) used to estimte the ω 2 constnt: 51 q 010-2B 2 e ω 2 ( 1 + 4ω 2 2 (9) ω ω 2 2) For HgH 2 nd HgH 2, we solved eq 9 for ω 2 using our q 010, B e nd ω 3 vlues from Tble 3. We were unble to determine the ω 2 constnts of HgD 2 nd HgD 2 from eq 9 becuse the third-order eqution for ω 2 did not hve solution. However, when we used the neon mtrix vlue of 562 cm -1 for ν 2 of HgD 2 in eq 9, long with our B e nd ω 3 vlues, the predicted q 010 constnt turned out to be cm -1, which differs by less thn 1% from the observed vlue of (7) cm -1. It should be noted tht eqs 8 nd 9 re only pproximtely correct, nd the vlues of ω 1 nd ω 2 obtined from these equtions (Tble 3) hve more thn 1% uncertinties. The bsolute vibrtionl energies of the 100 (Σ g + ) nd (Π u ) sttes, tht is, ν 1 nd ν 2, could not be determined from our dt. The best b initio vlues for ν 1 of HgH 2 nd HgD 2 re 1982 cm -1 nd 1421 cm -1, respectively. 22 The neon mtrix vlues for ν 2 of HgH 2 nd HgD 2 re 782 cm -1 nd 562 cm -1, respectively Discussion 4.1. Isotope Effects. The vibrtionl frequencies for different isotopologues of HgH 2 re relted by the following equtions: 49 ( ω i 2 1 ω 1) ) ( m H i m H ) (10) ( ω i 2 2 ω 2) ) ( ω i 2 3 ω 3) ) ( m H i m H )( m Hg i )( M) Mi (11) m Hg In the bove equtions, m H nd m Hg re the tomic msses of hydrogen (or deuterium) nd mercury, respectively, nd M is the totl mss of the molecule. The observed Hg: Hg isotope shift for the ν 3 fundmentl bnd of HgH 2 is cm -1 nd corresponds to rtio of between the ν 3 fundmentls of HgH 2 nd HgH 2. The rtio predicted by eq 11 is Similrly, the observed Hg: Hg isotope shift for the ν 3 fundmentl bnd of HgD 2 is cm -1, corresponding

6 Gseous HgH 2 nd HgD 2 J. Phys. Chem. A, Vol. 109, No. 45, TABLE 4: Vibrtionl Wvenumbers nd Metl-Hydrogen Internucler Distnces of ZnH 2, ZnD 2, CdH 2, CdD 2, HgH 2, nd HgD 2 molecule ν 3 (σ u)/cm -1 gs phse ν 3 (σ u)/cm -1 neon mtrix ν 2 (π u)/cm -1 neon mtrix r 0/Å experiment r e/å experiment r e/å b initio 64 ZnH (2) b c c (2) b (1) b d 64 ZnD (2) b c c (3) b (1) b d 114 CdH (2) e c c (2) e d 114 CdD (3) e c c (5) e d HgH (6) f f (1) (1) g HgD (8) f f (2) (1) g The numbers in prentheses re one stndrd devition sttisticl uncertinties. b From ref 46. c From ref 56. d From ref 20. e From ref 45. f From ref 21. g From ref 22; the best b initio vlues for the ν 3 of HgH 2 nd HgD 2 (ref 22) re cm -1 nd cm -1, respectively. to rtio of between the ν 3 fundmentls of HgD 2 nd HgD 2, wheres rtio of is predicted by eq 11. The observed rtio between the ν 3 fundmentls of HgH 2 nd HgD 2 (Tbles 1 nd 2) is nd the predicted rtio from eq 11 is If we use our ω 3 wvenumbers from Tble 3 insted, the greement becomes better nd rtio of is obtined. The observed H:D isotopic rtio for ω 1 of HgH 2 nd HgD 2 (Tble 3) is , nd the predicted rtio from eq 10 is The B e, R 1, nd D e constnts of HgH 2 re not sensitive to the mss of mercury, nd they should chnge only when hydrogen is substituted with deuterium. 46 The mss dependences of B e nd R 1 re given in eqs 4 nd 5, nd the mss dependence of D e is obtined esily by combining eqs 4, 8, nd 10. The observed rtios between the B e, R 1, nd D e constnts of HgH 2 nd HgD 2 (Tble 3) re , 2.840, nd 3.984, respectively, wheres the predicted rtios re , 2.825, nd 3.994, respectively. Equtions 4, 9, nd 11 cn be combined to obtin the mss dependence of the l-type doubling constnt (q). The observed rtio between q 010 constnts of HgH 2 nd HgD 2 is nd the predicted rtio is Overll, the observed isotope effects re in good greement with the theoreticl predictions. Within the Born-Oppenheimer pproximtion, ll of the isotopologues should hve the sme equilibrium internucler distnce (r e ). We found tht r e vlues (Tble 3) re the sme for different isotopes of mercury, within their experimentl uncertinties. The 0.005% difference between the r e vlues of HgH 2 nd HgD 2 cn be ttributed to the brekdown of the Born-Oppenheimer pproximtion Comprison with Theory. A high level b initio clcultion hs been performed by Li et l. 22 to obtin the potentil energy surfce of the X 1Σ + g ground electronic stte of HgH 2. They computed the potentil energy t points using the multireference configurtion interction (MRCI) method with very lrge bsis sets. The potentil energy surfce ws constructed from the b initio points, nd the vibrtionl energy levels (t J ) 0) were obtined for HgH 2, HgHD, nd HgD 2 by solving the exct vibrtion-rottion Schrödinger eqution vritionlly on this surfce. The best vilble theoreticl vlues for the vibrtionl energy levels of HgH 2, HgHD, nd HgD 2 re thus those obtined by Li nd coworkers. 22 However, the ν 3 vlues predicted for HgH 2 nd HgD 2 in their clcultion re cm -1 nd cm -1, respectively, wheres the observed ν 3 vlues in HgH 2 nd HgD 2 in this study re (6) cm -1 nd (8) cm -1, respectively (Tble 3). It is interesting tht even t this high level of theory, the ν 3 vlues of HgH 2 nd HgD 2 re underestimted by bout 27 nd 20 cm -1, respectively. The equilibrium internucler distnce (r e ) predicted by Li et l. is Å, 22 which is lrger thn our experimentl r e vlues (Tble 3) by bout Å. Similr b initio clcultions performed by the sme group on mgnesium dihydride 52 showed somewht Figure 4. Digrm showing the reltive energies of gseous MH nd MH 2 molecules (M ) Zn, Cd, nd Hg). For ech metl, the energy of the ground-stte M(g) + H 2(g) ws tken s zero. better greement with experiment. The theoreticl ν 3 vlues of MgH 2 nd MgD 2 were smller thn the experimentl ones 53,54 by bout 13 nd 10 cm -1, respectively Compring HgH 2 to ZnH 2 nd CdH 2. The internucler distnces nd vibrtionl wvenumbers of the most bundnt isotopologues of ZnH 2, ZnD 2, CdH 2, CdD 2, HgH 2, nd HgD 2 re compred in Tble 4. The metl-hydrogen internucler distnce in HgH 2 is shorter thn tht of CdH 2 becuse of reltivistic effects, 13,18 nd the vibrtionl wvenumbers of HgH 2 re lrger thn those of ZnH 2 nd CdH 2. A combintion of experimentl nd theoreticl dt cn be used to estimte the dissocition energies of the Hg-H bonds in gseous HgH 2. High level b initio clcultions 22 predicted tht the gs-phse rection Hg(g) + H 2 (g) f HgH 2 (g) is endoergic by 20.8 kcl mol -1 for ground-stte mercury toms. The experimentl vlues for dissocition energies of H 2 nd HgH re nd 8.6 kcl mol -1, respectively, 55 nd it is strightforwrd to clculte tht the dissocition energy of the first Hg-H bond in HgH 2 is 73.9 kcl mol -1, significntly lrger thn tht of the second bond HgH 2 (g) f HgH(g) + H(g) E ) 73.9 kcl mol -1 HgH(g) f Hg(g) + H(g) E ) 8.6 kcl mol -1 Similr ptterns exist in the bond energies of gseous ZnH 2 nd CdH 2, suggesting tht verge bond strengths should not be used to discuss bonding in these molecules. The best b initio vlues for the hets of formtion of gseous ZnH 2 nd CdH 2 from ground-stte metl toms nd moleculr hydrogen re +7.6 nd kcl mol -1, respectively, 20 nd the experimentl vlues for the dissocition energies of ZnH nd CdH re 19.6 nd 15.6 kcl mol -1, respectively. 55 Therefore, the dissocition energies of the first metl-hydrogen bond in gseous ZnH 2 nd

7 10286 J. Phys. Chem. A, Vol. 109, No. 45, 5 Shyesteh et l. CdH 2 re estimted to be 76.1 nd 70.7 kcl mol -1, respectively. The reltive energies of gseous MH nd MH 2 molecules (M ) Zn, Cd, nd Hg) re compred in simple digrm in Figure Conclusions High-resolution infrred emission spectr of gseous HgH 2 nd HgD 2 in the ν 3 region were nlyzed for six nturlly bundnt isotopes of mercury. The ν 3 fundmentls of HgH 2, HgH 2, HgD 2, nd HgD 2 were observed t (6), (6), (8), nd (9) cm -1, respectively, nd the mercury isotope shifts were consistent with the theoreticl predictions of eq 11. In ddition to the ν 3 fundmentl bnds of 204 HgH 2, HgH 2, 201 HgH 2, HgH 2, 199 HgH 2, 198 HgH 2, 204 HgD 2, HgD 2, 201 HgD 2, HgD 2, 199 HgD 2, nd 198 HgD 2, few hot bnds involving ν 1, ν 2, nd ν 3 were ssigned nd nlyzed rottionlly to determine spectroscopic constnts. Using the rottionl constnts of the 000, 100, , nd 001 vibrtionl levels, the equilibrium rottionl constnts (B e ) of the most bundnt isotopologues, HgH 2 nd HgD 2, were determined to be (24) cm -1 nd (16) cm -1, respectively, nd the ssocited equilibrium Hg-H nd Hg-D internucler distnces (r e ) re (1) Å nd (1) Å, respectively. The r e distnces of HgH 2 nd HgD 2 differ by bout 0.005%, which cn be ttributed to the brekdown of the Born-Oppenheimer pproximtion. Acknowledgment. This project ws supported finncilly by the Nturl Sciences nd Engineering Reserch Council (NSERC) of Cnd. Supporting Informtion Avilble: A complete list of the observed line positions nd the outputs of lest-squres fitting progrm (Tbles 1S-12S). This mteril is vilble free of chrge vi the Internet t References nd Notes (1) Stokstd, E. Science 4, 303, 34. (2) Lu, D. Y.; Grntstein, D. L.; Rose, D. J. Ind. Eng. Chem. Res. 4, 43, (3) Schroeder, W. H.; Munthe, J. Atmos. EnViron. 1998, 32, 809. (4) Stein, E. 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