Enthalpy of Formation of 2 Π 3/2 SH

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1 Enthlpy of Formtion of 2 Π 3/2 SH Attil G. Császár* Deprtment of Theoreticl Chemistry, EötVös UniVersity, H-1518 Budpest 112, P.O. Box 32, Hungry Mtthew L. Leininger Sndi Ntionl Lbortory, MS 9217, LiVermore, Cliforni Alexnder Burct Fculty of Aerospce Engineering, Technion-Isrel Institute of Technology, Hif 32000, Isrel ReceiVed: July 25, 2002; In Finl Form: Jnury 2, 2003 The stndrd enthlpy of formtion, f H, of 2 Π 3/2 SH hs been determined t converged levels of b initio electronic structure theory, including high-order coupled cluster nd full configurtion interction benchmrks. The tomic Gussin bsis sets employed include the (ug)-cc-p(wc)vnz fmily with n ) 3, 4, 5, nd 6. Extrpoltions to the complete one-prticle bsis set nd the full configurtion interction limits, where pproprite, hve been performed to reduce remining computtionl errors. Additionl improvements in the enthlpy of formtion of 2 Π SH were chieved by ppending the vlence-only tretment with core-vlence correltion, sclr reltivistic nd spin-orbit effects, nd the digonl Born-Oppenheimer correction. The recommended vlues for f H 0 nd f H 298 of 2 Π SH re nd kj mol -1, respectively, corresponding to recommended D e ) kj mol -1. The corresponding enthlpy of formtion of 2 Π SD is f H 0 ) kj mol -1. * Corresponding uthor. E-mil: csszr@chem.elte.hu. 1. Introduction H 2 S is the mjor source of sulfur compounds in the erth s tmosphere. This compound is generted nturlly by volcnic ctivity, by bcteri, nd minly by mn-mde pollution due to the burning of fossil fuels contining lrge mounts of S. The mjor source of the mercpto rdicl, SH, in the erth s tmosphere is S-H bond fission following ner-ultrviolet photoexcittion of H 2 S. Thermochemicl dt for SH re of specil importnce becuse of the role SH plys s n intermedite in rections generting sulfur-contining pollutnts (e.g., cid rin) s well s in complex rection mechnisms explining fossil combustion processes. 1 New, ever more efficient techniques for the solution of the electronic structure problem coupled with dvnces in computer rchitecture mke possible, with unprecedented ccurcy, 2-11 the theoreticl reevlution of thermochemicl properties. Becuse of their crucil importnce in rection kinetics studies, temperture-dependent stndrd enthlpies of formtion, f H T, re of the gretest interest. For the smllest rdicls, the ccurcy of the best b initio computtions (see, for exmple, refs 10 nd 11) of f H T cn exceed tht of trditionl experimentl determintions The most strightforwrd wy to determine the converged b initio f H 0 of 2 Π 3/2 SH goes through the determintion of its tomiztion energy, though there re more efficient computtionl routes for systems with more toms. The best theoreticl scheme for this study is offered by the focl-point pproch. 19,20 The converged b initio determintion of the enthlpy of formtion of 2 Π 3/2 SH is mde simpler by the reltively smll size of the system, llowing for the utiliztion of full configurtion interction (FCI) techniques. 21 The clcultions reported herein for the SH rdicl re the most extensive reported to dte, though clcultions with similr purpose hve been performed before Mjor thermochemicl tbles nd dtbnks recommend vlues for the tomiztion energy, D 0/e, nd for f H T of 2 Π 3/2 SH. The best vilble vlue of the zero-point-corrected tomiztion energy of 2 Π 3/2 SH is D e ) ( 1.20 kj mol -1, 26 obtined from creful experimentl nd theoreticl nlysis of the secondry photolysis of ground-stte SH rising from the nm photodissocition of H 2 S. Note tht this vlue corresponds to the V ) 0, J ) 3 / 2 level of the X 2 Π 3/2 spinorbit component nd the lowest-energy products, S( 3 P 2 ) nd H( 2 S). The vilble enthlpies of formtion 12,13,16,27-38 re summrized in Tble 1. The vilble vlues for f H 298 (SH) sctter round 140 kj mol -1, with recent reviews (e.g., ref 37) settling t ( 3.0 kj mol -1. A slightly higher men vlue, ( 3.0 kj mol -1, hs lso been suggested nd ccepted 13 on the bsis of the high-qulity work of Nicovich et l. 31 Both vlues re in ccord with the vlue obtined by Nourbkhsh nd co-workers. 30 Nevertheless, in the sme study, Nourbkhsh et l. suggested tht f H 0 ) ( 8.4 kj mol -1 for the enthlpy of formtion of CH 3 S, which is substntilly different from the generlly ccepted low vlue of Nicovich, ( 2.3 kj mol -1. To resolve this discrepncy, it is lso mndtory to hve highly dependble estimte of the enthlpy of formtion of SH. 2. Computtionl Approch The X 2 Π ground electronic stte of the mercpto rdicl hs(1σ) 2 (2σ) 2 (3σ) 2 (1π) 4 (4σ) 2 (5σ) 2 (2π) 3 electronic configurtion. Single-reference methods re pproprite for the descrip /jp026605u CCC: $25.00 xxxx Americn Chemicl Society Published on Web 00/00/0000 PAGE EST: 4.5

2 B J. Phys. Chem. A Császár et l. TABLE 1: Literture Dt for the Enthlpy of Formtion of 2 Π SH fh 298 reference yer method b comments Mesurements ( 16.7 Mckle KE c ( 4.6 Hwng nd Benson KE d ( 0.4 Treger PIMS-IE e ( 6.3 Nourbkhsh et l PIMS-IE f ( 2.8 Nicovich et l KE g Computtions Curtiss et l G3 h Curtiss et l AI i Prthibn nd Mrtin W2 j Jnoschek nd Rossi G3MP2B3 k Peebles nd Mrshll AI Reviews nd Evlutions 149 ( 12 Kerr CDE l ( 4.6 McMillen nd Golden CDE m ( 3.5 Gurvich et l CDE ( 3.0 Berkowitz et l CDE n ( 3.0 Chse et l CDE o ( 5.0 Burct CDE p All vlues re in kj mol -1. b KE ) kinetic equilibrium study. PIMS-IE ) photoioniztion mss spectrometry- ioniztion energy determintion. AI ) b initio computtion using model chemistry. CDE ) criticl dt evlution. c Averge of three independent mesurements: the dissocitions of H 2S f HS + H, the ioniztion potentil of HS, nd the ppernce potentil of HS + from H 2S. d Clculted from H 2S + I 2 rection kinetics in the K rnge. e PIMS hs been used to mesure the ppernce energies of [C 2H 5] + from ethnethiol, [C 3H 7] + from 2-propnethiol, nd [C 3H 5] + from 2-methylthiirne. f fh 0 ) ( 6.3 kj mol -1 ws deduced from time-of-flight mesurements of CH 3 nd SH photofrgments from the photodissocition of CH 3SH in supersonic moleculr bem. g Kinetics of the rection Br( 2 P 3/2) + H 2S f SH + HBr using resonnce fluorescence temperture-dependent experiments result in fh 0 ) ( 3.01 kj mol -1 nd fh 298 ) ( 2.85 kj mol -1. h G2 nd G3 model chemistry vlues re both reported. i G3(MP2/6-31G(d)) computtion. j Weizmnn model W2. The W1 vlue is kj mol -1. k The estimted verge error in the G3MP2B3 clcultions is 8 kj mol -1. l The old vlue of Kerr is n uncertin estimte bsed on the dissocition energy of the H-S bond s 90 ( 2 kcl/mol from the pyrolysis of benzyl sulfide. m Refers to the vlue of Hwng nd Benson. 28 n Extensive clcultion of dt (minly kinetic determintions) published until The recommended vlue is tht of Nicovich et l. 31 o Bsed on photoioniztion ppernce energy (AE) of SH + produced from H 2S (Dibeler, V. H.; Liston, S. K. J. Chem. Phys. 1968, 49, 482) nd the spectroscopic ioniztion energy for the SH rdicl (Morrow, B. A. Cn. J. Phys. 1966, 44, 2447). These dt were not reviewed fter As pointed out by Treger, 29 using better estimte for the AE of SH + ( ( ev; Prest, H. F.; Tzeng, W.-B.; Brom, J. M., Jr.; Ng, C. Y. Int. J. Mss Spectrom. Ion Phys. 1983, 50, 315) increses fh 298 to 142 ( 3kJmol -1, in perfect greement with our recommended (computtionl) vlue of kj mol -1. p Thermochemicl dtbse for combustion. The old clcultion ws bsed on 1977 JANAF 16 tbles. tion of the electronic structures of H, S, nd SH. Becuse electronic energy clcultions bsed on the correltion-consistent (cc) fmily of Gussin bsis sets (ug)-cc-p(c)vxz (with crdinl number X ) 2(D), 3(T), 4(Q), 5, nd 6) of Dunning nd co-workers usully pproch the complete bsis set limit in systemtic fshion, these bsis sets were employed in the focl-point bsis set extrpoltions of the present study. Nevertheless, severl problems with the originl correltionconsistent bsis sets for S hve been observed (see, for exmple, refs 43 nd 44). Convergence problems t the Hrtree-Fock level led to the development of new stndrd set of cc bsis sets, denoted (ug)-cc-pv(x+d)z, 41,42 which hve been employed in this study insted of the originl cc bsis sets. Since no core-correlted bsis sets re vilble in ref 41, CVXZ bsis sets, with X ) 4, 5, nd 6, were constructed 45 s n eventempered extension, with fctor of 3, of the corresponding completely uncontrcted cc-pvx Z sets by dding two tight functions to ech shell beyond p. A lck of optimiztion of the exponents in the CVXZ bsis sets leds to convergence problems. Therefore, n unpublished set 46 of polriztionweighted bsis sets for S hs lso been employed, denoted ccpwcvxz, with X ) 3, 4, nd 5. Complete bsis set limit energies hve been estimted through the equtions E X ) E limit + exp(-bx) 47 nd E X ) E limit + cx -348 for the HF nd correltion energy limits, respectively, employing the best three nd two energies vilble, in order. Reference electronic wve functions hve been determined by the single-configurtion restricted (open-shell) Hrtree-Fock [R(O)HF] method. Dynmicl electron correltion ws ccounted for by the coupled cluster (CC) method including ll single nd double (CCSD) 49 nd triple excittions (CCSDT). 50 The CCSD(T) method, 51,52 which estimtes the effect of connected triple excittions through perturbtive term [(T)], ws lso employed extensively. The full configurtion interction (FCI) computtions 21 utilized n ROHF reference wve function. During vlence correltion energy computtions, the 1s, 2s, nd 2p core orbitls of sulfur were excluded from the ctive spce. No virtul orbitls were frozen in ny of the clcultions. The experimentl equilibrium bond distnce r e /Å ) ws dopted for ll electronic structure computtions in the vlence focl-point nlysis nd during the uxiliry energy clcultions. Core-correltion effects were determined by mens of ll-electron nd frozen-core tretments up to CCSDT with (pw)cvxz (X ) 3, 4, nd 5) nd CVXZ (X ) 4, 5, nd 6) bsis sets. Sclr reltivistic effects 54,55 were guged by first-order perturbtion theory pplied to the one-electron mss-velocity nd Drwin terms (MVD1). The computtion of the digonl Born-Oppenheimer (DBOC) correction 56,57 ws performed t the Hrtree-Fock level within the formlism of Hndy, Ymguchi, nd Schefer. 56 Different versions of the progrm pckges ACES II 58 nd PSI 59 were used for the electronic structure computtions. The totl energies computed s prt of this study for H( 2 S), S( 3 P), nd SH ( 2 Π) re given in Tbles 4S-6S of the Supporting Informtion. 3. Discussion Tbles 2 nd 3 summrize the tomiztion energy results obtined using the focl-point scheme 19,20 for the vlence-only nd core-vlence tretments, respectively. The symbol δ in

3 Enthlpy of Formtion of 2 Π 3/2 SH J. Phys. Chem. A C TABLE 2: Vlence Focl-Point Anlysis of the Dissocition Energy of 2 Π SH in kj mol -1 bsis ROHF δ[ccsd] δ[ccsd(t)] δ[ccsdt] δ[fci] FCI ug-cc-pv(d+d)z(9/32) cc-pwcvtz(14/59) ug-cc-pv(t+d)z(23/55) b cc-pwcvqz(30/109) ug-cc-pv(q+d)z(46/89) b CVQZ(30/134) cc-pwcv5z(55/181) ug-cc-pv(5+d)z(80/136) CV5Z(55/185) ug-cc-pv(6+d)z(127/185) CV6Z(91/273) extrpolted[4-6] See text for n explntion of column hedings nd bsis sets nd for detils bout the extrpoltion to the bsis set limit for ROHF, δ[ccsd], nd δ[ccsd(t)]. After ech bsis set, the number of contrcted Gussin bsis functions for H/S is given in prentheses. Reference geometry: r(s-h) ) Å. b Obtined using SHOC fctors (see text for detils). TABLE 3: Core-Vlence Correltion Corrections (kj mol -1 ) to the Totl Atomiztion Energy of 2 Π SH bsis δ[ccsd] δ[ccsd(t)] δ[ccsdt] E e(cc) cc-pwcvtz cc-pwcvqz cc-pwcv5z extrpolted[4,5] [+0.021] CVQZ CV5Z See text for n explntion of column hedings nd bsis sets nd for detils bout the extrpoltion to the bsis set limit for ROHF, δ[ccsd], nd δ[ccsd(t)]. Reference geometry: r(s-h) ) Å. these Tbles denotes the increment in the reltive energy ( E e ) with respect to the preceding level of theory, s given by the hierrchy ROHF f CCSD f CCSD(T) f CCSDT f FCI. In recent study, 60 simple multiplictive procedure, termed scled higher-order correltion or SHOC, ws suggested to estimte higher-order correltion (HOC) energies not covered, for exmple, in CCSD(T) or CCSDT tretments. This procedure utilizes the observtion tht HOC energy increments show limited bsis set dependence nd thus even t the complete bsis set limit they cn be estimted from explicit smll bsis set FCI nd CCSD(T) or CCSDT clcultions. From our extensive previous computtions, it becme cler tht the ugmented bsis sets re more menble for this correction. The ug-cc-pvxz CCSDT SHOC scle fctors for S( 3 P) re nd for X ) 2 nd 3, respectively. The ug-cc-pvdz CCSDT SHOC scle fctor for SH( 2 Π) is As expected, it is very similr to the corresponding S( 3 P) SHOC fctor. The SHOC fctors t the CCSD(T) level re substntilly lrger; using the ug-cc-pv(d+d)z bsis set, they re nd for S( 3 P) nd SH( 2 Π), respectively. To mke blnced tretment, the CCSDT SHOC fctors of nd were employed for the vlence-only tretments of S( 3 P) nd SH( 2 Π), respectively, where the ltter fctor ws obtined by scling the former one by / Using the best CCSD(T) nd CCSDT sets of SHOC fctors shows greement within 0.1 kj mol -1 for the tomiztion energy of 2 Π SH. The directly computed vlence-only tomiztion energies provide lower limits to the correct result, s n extension of the bsis set s well s the electron correltion tretment increses, s expected, the clculted tomiztion energies. The vlence-only complete bsis set ROHF tomiztion energy is ( 0.04 kj mol -1, obtined fter verging the extrpolted ug-cc-pvxz nd CVXZ, X ) 4, 5, nd 6 estimtes nd multiplying their devition from the verge by 2 to ttch n error estimte to the recommended vlue. Estimting δ[ccsd] t the complete bsis set limit presents, s usul, some difficulty. Nevertheless, the complete bsis set CCSD vlue obtined from the ug-cc-pvxz, X ) 5 nd 6, bsis set results differs from the ug-cc-pv(6+d)z nd CV6Z vlues by only 0.28 nd 0.44 kj mol -1, respectively, which re comfortbly smll. Our best estimte for δ[ccsd] is kj mol -1. The extrpolted CCSD(T) increment, obtined the sme wy, is kj mol -1. It is impossible to estimte the δ[ccsdt] nd δ[fci] increments ccurtely from the limited dt vilble. Our best estimte for their combined effect is ( 0.10 kj mol -1. Therefore, the vlence-only complete bsis set FCI tomiztion energy of 2 Π 3/2 SH (see Tble 2) is kj mol -1. As seen in Tble 3, the core contribution to the tomiztion energy of SH( 2 Π) is rther smll. The best estimte is ( 0.15 kj mol -1 t the estimted complete bsis set FCI limit, obtined from the extrpolted cc-pwcvxz, X ) 4 nd 5 results. It is notble how different the convergence chrcteristics of the CVXZ nd cc-pwcvxz δ[ccsd] results re. This is most likely due to weknesses in our design of the CVXZ bsis sets. The sclr reltivistic correction to the tomiztion energy of 2 Π SH hs been computed t the HF nd CCSD(T) levels using the pwcvqz bsis set nd the MVD1 formlism. The correction is kj mol -1. The correltion contribution included in this vlue is kj mol -1. The fct tht twoelectron reltivistic energy corrections re usully comprble to the electron correltion contribution to the MVD1 energy correction 55 indictes tht reltivistic corrections beyond MVD1 should hve smll effect even t the level of precision sought in this study. Therefore, we set the sclr reltivistic correction to ( 0.30 kj mol -1. SH nd S hve inverted ground electronic sttes, 2 Π 3/2 nd 3 P 2, respectively. For open-shell sttes, trditionl nonreltivistic electronic structure clcultions yield the weighted verge of the vilble multiplets. To obtin the energy of the lowest sttes of S nd SH, the next reltivistic energy correction, the spin-orbit effect must be considered. We re employing literture vlues for these quntities; the experimentl weighted-verge spin-orbit splitting constnts re kj mol -1 for the 3 P stte of sulfur 61,62 nd kj mol -1 for SH. 63 The spin-orbit correction to the dissocition energy is thus ( kj mol -1. Therefore, the totl reltivistic correction is ( 0.30 kj mol -1, to be dded to the computed nonreltivistic tomiztion energy. The DBOC corrections, in cm -1, computed t the Hrtree- Fock level using medium-sized TZ2Pf+dif bsis set re , , nd for H( 2 S), S( 3 P), nd SH( 2 Π), respectively, resulting in n overll DBOC correction to the

4 D J. Phys. Chem. A Császár et l. tomiztion energy of 0.2 cm -1. Therefore, this correction is negligible for this study. Collecting ll of the terms nd ssuming independent error brs for the different terms, we obtin our best estimte for the equilibrium tomiztion energy of Π 3/2 SH s ) kj mol -1. The moleculr zero-point energy (ZPE) of 32 S 1 H is kj mol -1, 53 obtined s (1/2)ω e - (1/4)ω e x e with ω e ) cm -153 nd ω e x e ) 60 cm The error br tht cn be ttched to this quntity is perhps (0.20 kj mol -1. This brings the computed zero-point-corrected tomiztion energy, corresponding to the lowest-energy spin multiplet, to kj mol -1. This vlue is in greement with () the best experimentl vlues of ( 1.20 kj mol -126 nd ( 2.9 kj mol -1, 65 though it hs considerbly lower error br nd (b) the best previous direct theoreticl estimte of D 0 (S- H) ) ( 2.0 kj mol -125 bsed principlly on coupledcluster computtions. (Hlf of the difference between the computed men D 0 vlues is due to the use of slightly different ZPE corrections.) The clcultion of the enthlpy of formtion from the tomiztion energy requires knowledge of the enthlpy of formtion of toms H nd S in their respective ground sttes. The relevnt dt, when vilble, were tken from ref 14 nd re given, in kj mol -1,s f H 298 [S( 3 P)] ) ( 0.15, f H 298 [H( 2 S)] ) ( 0.006, H H 0 [H] ) ( 0.001, H H 0 [H 2 ] ) ( 0.001, H H 0 [S cr,rhombic ] ) ( 0.006, nd H H 0 [S gs ] ) ( The resulting 0 K tomic enthlpies of formtion re f H 0 [H( 2 S)] ) ( kj mol -1 nd f H 0 [S( 3 P)] ) ( kj mol -1. The H H 0 vlue for SH ws tken from ref 16 s kj mol -1. On the bsis of these experimentl vlues, the finl computtionl vlue for f H 0 of 2 Π 3/2 SH is kj mol -1. The best recommended computtionl vlue for f H 298 is kj mol -1. Our men vlue is significntly higher thn ( 3.0 kj mol -1 recommended by JANAF 16 nd somewht lower thn ( 3.0 kj mol -1 recommended in other dtbses 13 on the bsis of the work of Nicovich et l. 31 Our finl recommended vlues re lso significntly different from the f H 0 (SH) nd f H 298 (SH) vlues recommended in ref 25, ( 0.8 kj mol -1 nd ( 0.8 kj mol -1, respectively, on the bsis of certin combintion of computed nd mesured energy vlues. 4. Conclusions In this pper, we hve clculted b initio the equilibrium nd zero-point-energy-corrected dissocition energies of 2 Π 3/2 SH with recommended vlues of nd kj mol -1, respectively. These results llow us to estimte the stndrd enthlpy of formtion, f H T,of 2 Π 3/2 SH. The results obtined, nd kj mol -1 for f H 0 nd f H 298, respectively, re somewht different from the best vilble experimentl results nd hve smller error brs. Our finl results for the enthlpy of formtion of 2 Π 3/2 SH shows tht we cn relibly clculte f H T for such smll species within bout 0.5 kj mol -1. To get converged theoreticl estimte of the enthlpy of formtion of 2 Π SD, only few extr dt points re necessry over the benchmrk-qulity results obtined for SH. The difference in the zero-point energies of SH nd SD is 4.85 ( 0.20 kj mol -1 bsed on ω e ) cm -153 nd ω e x e ) 31 cm -164 for SD. The difference in the spin-orbit splitting constnts of SH nd SD 18 is only kj mol -1, which is negligible for this study. Since the DBOC correction ws found to be negligible for SH, the sme cn sfely be ssumed for SD. The enthlpy of formtion of D( 2 S) cn be obtined from stndrd tbles: f H 0 [D( 2 S)] ) kj mol -1. Therefore, we obtin the result f H 0 [SD( 2 Π)] ) kj mol -1. Acknowledgment. The work of A.G.C. hs been supported by the Scientific Reserch Fund of Hungry (OTKA T033074). M.L.L. ws supported by Sndi Ntionl Lbortories. Sndi is multiprogrm lbortory operted by Sndi Corportion, Lockheed Mrtin Compny, for the United Sttes Deprtment of Energy under contrct DE-AC04-94AL The reserch described forms prt of n effort by tsk group of the Interntionl Union of Pure nd Applied Chemistry ( ) to determine structures, vibrtionl frequencies, nd thermodynmic functions of free rdicls of importnce in tmospheric chemistry. Supporting Informtion Avilble: ROHF energies for H( 2 S), vlence-only nd ll-electron energies for S( 3 P), nd vlence-only nd ll-electron energies for 2 Π SH. This mteril is vilble free of chrge vi the Internet t References nd Notes (1) Hynes, A. J.; Wine, P. H. Kinetics nd Mechnism of the Oxidtion of Gseous Sulfur Compounds. In Gs-Phse Combustion Chemistry; Grdiner, W. C., Jr., Ed.; Springer-Verlg, New York, 2000; Chpter 3, p 343. (2) Est, A. L. L.; Allen, W. D. J. Chem. Phys. 1993, 99, (3) Ruscic, B.; Feller, D.; Dixon, D. A.; Peterson, K. A.; Hrding, L. B.; Asher, R. L.; Wgner, A. F. J. Phys. Chem. A 2001, 105, 1. (4) Dixon, D. A.; Feller, D.; Peterson, K. A. J. Chem. Phys. 2001, 115, (5) Dixon, D. A.; Feller, D.; Sndrone, G. J. Phys. Chem. A 1999, 103, (6) Mrtin, J. M. L.; de Oliveir, G. J. Chem. Phys. 1999, 111, (7) Irikur, K. K.; Frurip, D. J. Computtionl Thermochemistry: Prediction nd Estimtion of Moleculr Thermodynmics; Americn Chemicl Society: Wshington, DC, (8) Feller, D.; Dixon, D. A. J. Phys. Chem. A 2000, 104, (9) Feller, D. J. Comput. Chem. 1996, 17, 1571; the dtbse is vilble t (10) Ruscic, B.; Wgner, A. F.; Hrding, L. B.; Asher, R. L.; Feller, D.; Dixon, D. A.; Peterson, K. A.; Song, Y.; Qin, X.; Ng, C.-Y.; Liu. J.; Chen, W.; Schwenke, D. W. J. Phys. Chem. A 2002, 106, (11) Császár, A. G.; Szly, P. G.; Leininger, M. L. Mol. Phys. 2002, 100, (12) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynmic Properties of IndiVidul Substnces, 4th ed.; Hemisphere: New York, 1989; Vols. 1 nd 2. (13) Berkowitz, J.; Ellison, G. B.; Gutmn, D. J. Phys. 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