Thermochemistry of Iron Chlorides and Their Positive and Negative Ions

Transcription

1 8770 J. Phys. Chem. 1996, 100, Thermochemistry of Iron Chlorides nd Their Positive nd Negtive Ions Robert D. Bch,* Dvid S. Shobe, nd H. Bernhrd Schlegel Deprtment of Chemistry, Wyne Stte UniVersity, Detroit, Michign Christopher J. Ngel Molten Metl Technology, 51 Swyer Rod, Wlthm, Msschusetts ReceiVed: December 13, 1995 X The iron chlorides, 2, nd 3 nd their ions +, 2+, -, 2-, nd 3- were investigted using MP2 nd QCISD(T) clcultions with double- nd triple-ζ bsis sets ugmented with multiple sets of diffuse nd polriztion functions. The dissocition enthlpies for f Fe + Cl, 2 f + Cl, nd 3 f 2 + Cl re predicted to be 82.5, 109.6, nd 59.6 kcl/mol t K, respectively. The clculted hets of formtion of these species in the gs phse t K re kcl/mol for, kcl/mol for 2, nd kcl/mol for 3. The clculted het of formtion of is 15 kcl/mol lower thn the estimted vlue of ((20.0) kcl/mol reported in the JANAF tbles, but is in resonbly good greement with recent experimentl determintion (+49.5 ( 1.6 kcl/mol). The clculted ioniztion potentil of is 7.89 ev nd tht of 2 is ev. The electron ffinities re 1.54 ev for, 0.99 ev for 2, nd 3.90 ev for 3. Comprison of the bond dissocition enthlpies in n, n+, nd n- revels preference for iron to exist in the +2 oxidtion stte (s 2, +, or 3- ); this preference is lso seen when compring IPs nd the EAs of the iron chlorides. We lso evluted the dissocition energies, IPs nd EAs of the iron chloride species using the B3LYP version of density functionl theory. Comprison to the high-level b initio results shows tht density functionl theory with the lrge bsis set is ccurte to 5-10 kcl/mol for these species. I. Introduction The enthlpies, entropies, nd free energies of formtion of simple binry nd ternry compounds re fundmentl thermochemicl dt. The bond dissocition enthlpies (BDEs) nd bond dissocition free energies (BDFEs) of these compounds re essentil in understnding free rdicl rections nd other processes. We re prticulrly interested in the thermochemistry of the trnsition metls used in metllurgy nd chemicl processes. Iron is rgubly one of the more importnt of these metls, so we begin with study of the monomeric chlorides of tht metl. The iron chlorides 3, 2, nd exhibit quite different therml behviors. 3 begins to decompose into 2 + Cl 2 t its melting point of 577 K. 2, on the other hnd, hs high therml stbility nd cn be distilled unchnged t its norml boiling point of 1297 K., though known spectroscopiclly 1 nd listed in stndrd thermochemicl reference works, 2,3 is unstble towrd disproportiontion nd exists only in dilute gs phse. These fcts suggest tht s one successively dds chlorine toms to iron, the first bond formed is reltively wek, the second bond (forming 2 ) is significntly stronger, nd the third bond (forming 3 ) is gin wek. The BDEs nd BDFEs derived from published stndrd thermochemicl dt 3 re listed in Tble 1. Some theoreticl work hs been done previously on iron chlorides. Delvl nd Schmps 4 hve studied the electronic energy levels of t the SCF level. Bominr et l. 5 hve clculted the electronic energy levels nd Mossbuer spectroscopic prmeters of 2 t vrious levels of theory. Mishr et l. 6 hve lso clculted Mossbuer spectroscopic prmeters of 2 t the SCF level, nd Chou et l. 7 nd Vel et l. 8 hve clculted X-ry properties of 2 using density X Abstrct published in AdVnce ACS Abstrcts, April 15, S (95) CCC: $12.00 TABLE 1: n (g) functionl theory. Mndich et l. 9 hve clculted the bond length nd orbitl structure of + t the SCF level. The species 4- hs been the subject of severl studies. Deeth et l. 10 hve clculted its spin density nd X-ry properties, Butcher et l. 11 hve clculted its orbitl structure nd photoelectron spectrum, nd Oliphnt nd Brtlett 12 hve clculted its electronic energy levels. All three of these studies employed density functionl theory to describe the 4- ion. We hve performed high-level b initio clcultions on the neutrl iron chlorides n (n ) 1-3) nd the corresponding nions with n ) 1-3 nd ctions with n ) 1-2. Our primry focus is on the bond dissocition enthlpies nd free energies nd the ioniztion potentils nd electron ffinities of these species. We compre the results of the high-level clcultions with less-demnding levels of theory, nd prticulrly with density functionl theory. A brief description of the electronic structures of ech species is given. II. Methods Experimentl Thermochemicl Dt on species T H f G f BDE b BDFE c From ref 3. Tempertures re in K; energy units re kcl/mol. b BDE is H for the rection n(g) f n-1(g) + Cl(g). c BDFE is G for the rection n(g) f n-1(g) + Cl(g). For most clcultions we used double-ζ-plus-polriztion bsis set, which we will refer to s the WHsf bsis set. For 1996 Americn Chemicl Society

2 Thermochemistry of Iron Chlorides J. Phys. Chem., Vol. 100, No. 21, TABLE 2: Clculted Electronic Energies in Hrtrees MP2/WHsf QCISD/WHsf DFT/WHext est-qcisd(t)/whext// QCISD/WHsf Fe( 5 D) Fe + ( 6 D) Cl Cl Cl b ( ) c d At BD(T)/WHsf. b See Methods. c At MP3(fc)/WH. d At est-qcisd(t)/whext//mp3(fc)/wh. iron, this is bsed on the Wchters primitive bsis set 13 (14s11p5d), which ws contrcted to [8s6p2d]. To this were dded the diffuse d function optimized by Hy 14 nd the diffuse s nd three f functions dded by Rghvchri nd Trucks, 15 mking bsis set of (15s11p6d3f) primitives contrcted to [9s6p3d3f]. A bsis set using the sme primitives (but contrcted differently) hs been used to reproduce the excittion energy nd ioniztion potentil of iron. 15,16 For chlorine, the Dunning-Huzing double-ζ bsis set 17 ws ugmented with set of diffuse s nd p functions 18 nd set of polriztion d functions. 19 This bsis set consists of (13s9p1d) primitives contrcted to [7s5p1d]. The WHsf bsis set hs 63 functions per iron tom nd 27 functions per chlorine tom. We occsionlly mde use somewht smller bsis set (WH), which for iron consists of the Wchters primitive bsis set, contrcted s in WHsf, nd the Hy d function; for chlorine the sme functions re used s in the WHsf bsis set. Some singlepoint clcultions were performed using lrger bsis set, which will be referred to s the WHext bsis set. This consists of the WHsf bsis set for iron ugmented by two dditionl diffuse d functions (exponents nd ) nd the G(3df) bsis set of chlorine. For iron the WHext bsis set is (15s11p8d3f) contrcted to [9s6p5d3f], nd for chlorine it is (14s11p3d1f) contrcted to [7s6p3d1f]. This is 73 bsis functions per iron tom nd 47 per chlorine tom. One of the difficulties in studying trnsition metl species is to determine the proper spin stte. According to lignd-field theory, complexes with only few lignds (nd thus hving only wek lignd field ) should hve high-spin ground sttes: quintet for Fe(II) nd Fe(0), sextet for Fe(III) nd Fe(I). Thus, we hve studied 2, (, nd 3- in their quintet sttes nd, 3, nd 2( in their sextet sttes. 2 hs been shown to exist in the 5 stte 5 nd in the 6 stte. 4 To test the qulity of the wve functions, we performed stbility test of ech wve function nd exmined S 2 for signs of spin contmintion. Ech species proved to hve stble wve function, nd with one exception ( -, S 2 ) 6.11) the S 2 were within (0.02 of their proper vlue of S(S + 1), where 2S + 1 is the spin multiplicity of the species. Clcultions were performed using development versions of GAUSSIAN The procedure used for ech species ws to optimize the geometry nd clculte the frequencies t MP2- (full)/whsf nd then to optimize t the QCISD/WHsf level of theory. At the QCISD/WHsf geometry, single-point clcultions were performed t QCISD(T)/WHsf nd t MP2(full)/WHext. The rection energy t 0 K is tken to be the QCISD(T)/WHsf rection energy plus the difference between the MP2/WHext nd MP2/WHsf energies, clculted t the QCISD/WHsf geometries. This should be very good estimte of the QCISD- (T)/WHext//QCISD/WHsf energy since the effect of the lrger bsis set (WHext vs WHsf) nd the effect of the higher correltion method (QCISD(T) vs MP2) re very nerly dditive. 21 The ioniztion potentil (IP) of Fe ws used s test of ccurcy. At this level of theory (herefter referred to s est- QCISD(T)/WHext//QCISD/WHsf) the IP is 7.80 ev; pplying the reltivistic correction of 0.06 ev determined by Mrtin nd Hy 22 gives 7.86 ev, so tht the difference between our highest level of theory nd the experimentl vlue of 7.90 ev is only 0.04 ev (1 kcl/mol). Electronic energy levels of the molecules nd ions of interest re provided in Tble received different tretment since the high NORM- (A) vlues 23 (in excess of 2.0) in the QCISD clcultion indicted tht the molecule ws not dequtely described t this level of theory. Exmintion of the principl contributions to the QCISD wve function showed tht configurtions other thn the Hrtree-Fock ground stte re importnt in + 2. Since most of the principl non-ground-stte configurtions were single excittions, it ws nticipted tht Brueckner doubles (BD) 24 would provide more dequte description of the ion. The BD wve function is closely relted to the QCISD wve function, but differs in tht the contribution of single excittions is eliminted by explicit trnsformtion of the orbitls. Hence, in the BD model the orbitls relx in the presence of dynmic correltion through double excittions. We used the BD(T) model, which includes perturbtionl correction for triple excittions. The NORM(A) vlues for the BD(T) clcultion of 2+ were quite resonble (round 1.1). Therefore, we optimized the geometry of 2+ numericlly t the BD(T)/ WHsf level of theory. To evlute the energies of rections involving 2+, we lso evluted the BD(T)/WHsf energy of 2 t the QCISD/WHsf geometry. The est-qcisd(t)/ WHext//QCISD/WHsf energy of 2+, used to clculte energies of ll rections involving this ion, ws defined to be (E[ 2, QCISD(T)//QCISD/WHsf] + IP[ 2, BD(T)/ WHsf]) + (E[ 2+, MP2/WHext//BD(T)/WHsf] - E[ 2+, MP2/WHsf//BD(T)/WHsf]). The first term provides n energy of 2+ which cn be compred to the QCISD(T)/WHsf energies of the other species; the second term is the bsis set correction. Equivlently, the est-qcisd(t)/whext//qcisd/ WHsf energy of 2+ cn be expressed s E[ 2, est- QCISD(T)/WHext//QCISD/WHsf] + IP[ 2, BD(T)/WHsf] + (IP[ 2, MP2//WHext] - IP[ 2, MP2/WHsf]). We lso performed BD(T)/WHsf//QCISD/WHsf clcultions on Fe nd. The clculted D e vlues (kcl/mol) for Fe-Cl (78.2) nd -Cl (105.2) t BD(T)/WHsf//QCISD/WHsf re essentilly the sme s the D e vlues clculted t QCISD(T)/ WHsf//QCISD/WHsf (78.5 nd 105.6, respectively).

3 8772 J. Phys. Chem., Vol. 100, No. 21, 1996 Bch et l. For 3- the geometry nd frequencies were obtined t MP2(fc)/WH becuse of the lrge size of this nion. Singlepoint QCISD(T)/WHsf nd MP2(full)/WHext clcultions were then performed t this geometry. For - the difference in the bond lengths clculted t MP2(fc)/WH nd QCISD/WHsf is 0.09 Å. Since the clculted force constnt for the symmetric Fe-Cl stretch in 3- is hrtree/bohr, 2 similr error in the Fe-Cl bond length in 3 would led to n error in energy of pproximtely hrtree or 3 kcl/mol. Using the therml energies nd entropies obtined from the unscled MP2/WHsf frequency clcultions, the 0 K energies were converted to enthlpies nd free energies t nd 2000 K. The therml energies were computed s the sum of trnsltionl, rottionl, nd vibrtionl (including zero-point energy) contributions; the entropies were computed s the sum of trnsitionl, rottionl, vibrtionl, nd electronic contributions. Stndrd formuls for n idel gs in the cnonicl ensemble, 25 using the rigid-rotor nd hrmonic-oscilltor pproximtions, were employed in the clcultions. For montomic species, the only contribution to the therml energy is trnsltionl; for the entropy, there is trnsltionl contribution nd n electronic contribution. Spectroscopiclly derived electronic energy levels 26 were used in the clcultions of the electronic entropy of the open-shell montomic species. The levels in the 5 D (ground, , , , nd cm -1 ) nd 5 F ( , , , , nd cm -1 ) terms of Fe, the 6 D (ground, , , , nd cm -1 ), 4 F ( , , , nd cm -1 ), nd 4 D ( , , , nd cm -1 ) terms of Fe +, nd the 3 P (ground, 881 cm -1 ) term of Cl were included in the entropy clcultion. Literture electronic energy levels re lso vilble for 4 nd 2, 27 nd these were used in the clcultion of the entropy of these species. For the 6 (ground), 6 Σ (1211 cm -1 ), nd 6 Π (2515 cm -1 ) sttes were included in the entropy clcultion; for 2 the 5 (ground), 5 Π (4800 cm -1 ), nd 5 Σ (7140 cm -1 ) sttes were included. 3 is not expected to hve excited sttes low enough to contribute significntly to the entropy since the corresponding ion, 6 Fe 3+, hs hlf-filled (d 5 ) rrngement. Thus, neglect of the entropy due to electronic excittions should be vlid for this molecule. The entropy due to electronic excittions ws neglected for the ionic iron hlide species s well. The entropies for these species t K should be ccurte since electronic excittions ccounted for 0.02 nd <0.01 cl mol -1 K -1 for nd 2, respectively, t this temperture. 28 At 2000 K electronic excittions still contribute only 1.3 nd 0.3 cl mol -1 K -1 to the entropies of nd 2, respectively, so the entropies of the ionized iron hlides should be t worst underestimted by 1-2 cl mol -1 K -1. To determine the performnce of density functionl theory on these species, we performed clcultions using the B3LYP hybrid density functionl 29 with the WHext bsis set. Density functionl methods provide results t frction of the cost of explicit electron-correltion methods (for + QCISD/WHsf required 166 min per optimiztion cycle nd 745 Mbyte of disk spce; B3LYP/WHext required only 19 min per cycle nd 128 Mbyte of disk spce), but to dte only few key exmples of nonlocl density functionl theory clcultions hve been reported for iron compounds. 30 Comprison of density functionl theory results to those from higher level clcultions will be discussed in the followng section. III. Results nd Discussion A. Geometries. The bond length in 2 hs been mesured in the gs phse by Hrgitti et l.; 31 our theoreticl TABLE 3: Ground Electronic Sttes nd Equilibrium Geometries stte symm R Fe-Cl Cl-Fe-Cl 6 C V b (2.168 c d ) 2 5 D h b (2.129 c d ) A 1 D 3h b (2.105 c d ) C V b (2.056 c d ) A 1 C 2V e (2.028 c d ) e (149.8 c d ) - 5 C V b (2.250 c d ) A 1 C 2V b (2.260 c d ) b (110.1 c d ) A 1 D 3h f Distnces re in ngstroms, nd ngles re in degrees. b QCISD/ WHsf. c MP2/WHsf. d B3LYP/WHsf. e BD(T)/WHsf. f MP2(fc)/WH, where WH is the Wchters-Hy bsis set without the dded s nd f functions. TABLE 4: Clculted (MP2/WHsf) Vibrtionl Frequencies (Unscled), Zero-Point Energies (ZPEs), Therml Energies, nd Entropies t K nd t 2000 K th frequencies ZPE E th E 2000 S S 2000 Fe Fe Cl Cl Cl , b 362, , 113, b 399, 513 b , 471, , 321, , b 123, 283, 370 b Frequencies re in cm -1, ZPEs nd therml energies re in kcl/ mol, nd entropies re in cl/(mol K). b Doubly degenerte. bond length of Å is in good greement with the experimentl vlue of Å. The clculted vibrtionl frequencies (unscled) in this molecule (86, 362, nd 528 cm -1 ) re in greement with the experimentlly determined frequencies (88, 350, nd 492 cm -1 ) listed in tht work. The clculted geometries for the neutrl nd ionized iron chlorides re presented in Tble The vibrtionl frequencies, zero-point nd therml energies, nd stndrd entropies t nd 2000 K for these species re given in Tble 4. The number of chlorines ttched to the iron hs very little effect on the Fe- Cl bond length. This is contrry to wht one would expect from n ionic model of the bonding in these compounds, which would predict shorter bond lengths due to incresed electrosttic ttrction s the chrge on the centrl tom increses. Neutrl is n exception in tht it does not hve somewht longer bond length thn 2 nd 3. There is, in contrst, mrked dependence of the bond length on the chrge of the system: s one goes from - to to +, the Fe-Cl distnces become shorter by pproximtely 0.1 Å per electron. Although 2 is liner, both 2+ nd 2- re significntly distorted from linerity, with bond ngle of 144 for the ction nd 110 for the nion. 3 nd 3- re trigonl plnr. The geometries chnge little on going from MP2/WHsf or B3LYP/WHext to QCISD/WHsf. B. Bond Energies. The energies required to brek the Fe- Cl bonds in the iron chlorides nd their ions re displyed in Tble 5. Dissocition energies my be mesured from the minimum of the potentil surfce (D e ) or from the ground vibrtionl stte (D 0 ). D 0 is equl to the bond dissocition enthlpy t 0 K. The BDEs chnge by less thn 1 kcl/mol on going from 0 to K nd chnge only by 1-3 kcl/mol on going to 2000 K. The BDE of the Cl-Cl bond (experi-

4 Thermochemistry of Iron Chlorides J. Phys. Chem., Vol. 100, No. 21, TABLE 5: Clculted Dissocition Energies (D e nd D 0 ), Bond Dissocition Enthlpies (BDE), nd Bond Dissocition Free Energies (BDFE) for Fe-Cl nd Cl-Cl Bonds b bond D e D 0 BDE BDE 2000 BDFE BDFE 2000 Cl-Cl Fe-Cl ClFe-Cl Cl 2Fe-Cl Fe + -Cl ClFe + -Cl Fe-Cl ClFe-Cl Cl 2Fe-Cl At est-qcisd(t)/whext//qcisd/whsf, except s noted in Methods. b Energy units re kcl/mol. TABLE 6: Effect of Level of Theory on Dissocition Energies (D e ) of Iron Chlorides nd Cl 2 MP2/ WHsf QCISD/ WHsf D e (kcl/mol) DFT/ WHext est-qcisd(t)/whext //QCISD/WHsf Cl-Cl Fe-Cl b ClFe-Cl b Cl 2Fe-Cl Fe + -Cl ClFe + -Cl c Fe-Cl ClFe-Cl E[est-QCISD(T)/WHext] ) E[QCISD(T)/WHext] - (E[MP2/ Whext] - E[MP2/WHsf]). b At BD(T)/WHst//QCISD/WHsf the D e of Fe-Cl is nd the D e of -Cl is c See methods. mentlly 58.0 kcl/mol t K nd 60.7 kcl/mol t 2000 K) 3 is well produced (clculted 57.1 kcl/mol t K nd 59.0 kcl/mol t 2000 K). The lrger G(3df) bsis set used in the WHext is required to reproduce this BDE; use of the D95+(d) bsis set (WHsf) leds to gross underestimtion of the Cl-Cl dissocition energy (see Tble 6). The BDEs of the Fe-Cl bond vry widely, from 37.0 kcl/mol for the bond in - to kcl/mol for the bond in 2. As implied by the therml behvior of the iron chlorides, the ClFe-Cl bond is stronger thn the Fe-Cl bond, nd the Cl 2 Fe-Cl bond is much weker thn the ClFe-Cl bond. The clculted D e s depend strongly on the level of theory used (Tble 6). The B3LYP/WHext method ctully performs better thn QCISD/ WHsf for mny of these dissocition energies, showing not only the utility of density functionl theory for these species but lso the importnce of using the lrger bsis set with multiple polriztion functions on these molecules. Even in the worst cses, B3LYP/WHext ppers to be ccurte to 5-10 kcl/mol. The nions tend to hve wek Fe-Cl bonds, reflecting the popultion of n ntibonding orbitl by the dditionl electron; the bonds in the ctions re not significntly wekened. Entropy is importnt t elevted tempertures: t 2000 K mny of the species become unbound or nerly so, hving BDFEs ner or below zero. C. Ioniztion Potentils. Adibtic ioniztion potentils (IP) nd electron ffinities (EA) re tbulted in Tble 7. The clculted IP of Fe (7.80 ev) devites from the experimentl IP (7.90 ev) by 0.10 ev (2.3 kcl/mol); 0.06 ev of this difference is scribed to reltivistic effects, s described bove in the Methods section. The clculted EA of Cl(3.51 ev) differs from the experimentl EA (3.61 ev) lso by 0.10 ev. We clculte n IP of 7.89 ev for nd n IP of ev for 2. Schoonmker nd Porter 33 in their mss spectroscopic study of 2 report n ppernce potentil of 11.5 ( 0.5 for 2+ nd n ppernce potentil of 12.8 ( 0.5 for +. TABLE 7: Adibtic Ioniztion Potentils (IP) nd Electron ffinities (EA) in ev MP2/ WHsf QCISD/ DFT/ WHsf WHext est-qcisd(t)/whext //QCISD/WHsf expt Fe (IP) (IP) e8.08 ( 0.10 b 2 (IP) c e10.34 d (EA) (EA) (EA) e Cl (EA) E[est-QCISD(T)/WHext] ) E[QCISD(T)/WHsf] + (E[MP2/ WHest] - E[MP2/WHsf]). b Reference 32. c See Methods. d Reference 34. e Anion t MP2(fc)/WH geometry. The + 2 ppernce potentil is n experimentl upper bound for the IP of 2. Since the + is formed by the process [e f + + Cl + 2e - ], the ppernce potentil is n upper bound for the E of this rection, which is equl to D 0 (ClFe-Cl) + IP(). Assuming our clculted D 0 (ClFe- Cl) is correct, the upper bound for IP() is thus 8.1 ( 0.5 ev. In more recent mss spectrometric study by Hildenbrnd 34 the ppernce potentil for + 2 is ( 0.10 ev nd the ppernce potentils for + were 12.6 ( 0.03 ev from 2 nd 8.08 ( 0.10 ev from. Using the dtum with the smller uncertinty, we thus hve 8.08 ( 0.10 ev s n upper bound for the IP of. Berkowitz et l. 35 nd Lee et l. 36 hve independently mesured the verticl ioniztion potentil of 2 by photoelectron spectroscopy to be nd ev, respectively; the verticl IP is lso n upper bound for the dibtic IP which we clculte. The positive EAs for, 2, nd 3 indicte tht ll three of the corresponding nions re bound in the gs phse. The IPs of EAs clculted t MP2/WHsf nd QCISD/WHsf re pproximtely s ccurte s the D e s; tht is, they differ from the est-qcisd- (T)/WHext//QCISD/WHsf vlues by 5-10 kcl/mol or ev. However, MP2/WHsf severely underestimtes the EA of 1.12 vs 1.54 ev t est-qcisd(t)/whext//qcisd/ WHsf). 37 B3LYP/WHext overestimtes the EA of (1.84 ev), despite its good greement with est-qcisd(t)/whext// QCISD/WHsf on the EA of 2 nd the IP of. D. Thermochemistry. From the clculted BDEs nd BDFEs of the iron chlorides nd of Cl 2 nd the experimentl H vp nd S vp of iron, which re kcl mol -1 nd cl mol -1 K -1 t K nd kcl mol -1 nd cl mol -1 K -1 t 2000 K, 3 it is possible to obtin enthlpies nd free energies of formtion for the iron chlorides using thermodynmic cycle. The sme cn be done for the ions provided stndrd stte for chrge cn be greed upon. The therml electron convention, in which the free electron is tken s stndrd stte ( H f (e - ) ) 0 nd G f (e - ) ) 0), is used here. 38 Tble 8 shows the het cpcities t constnt pressure (C p ), stndrd entropies (S), hets of formtion ( H f ), nd free energies of formtion ( G f ) of the iron chlorides t selected tempertures. For the H vp nd S vp of iron, the experimentl vlues t ech temperture were used. It should be noted tht the stndrd stte of iron chnges with the temperture: t K the solid R phse is the stndrd stte for iron, nd t 2000 K the liquid phse is the stndrd stte. The clculted thermochemicl prmeters for 2 re in excellent greement with experiment; the clculted het of formtion of 3 is 5-6 kcl mol -1 too low, but the entropy nd het cpcity re in good greement. The discrepncy for deserves some explntion. Since no ccurte thermochemicl dt were vilble for due to its instbility, n educted guess of ( 20.0 kcl mol -1 for the het of formtion of t K ws used in the JANAF tbles. 2

5 8774 J. Phys. Chem., Vol. 100, No. 21, 1996 Bch et l. TABLE 8: Het Cpcities (C p ), Stndrd Entropies (S), Hets of Formtion ( H f ), nd Free Energies of Formtion ( G f ) of Iron Chlorides in the Gs Phse (Experimentl Vlues (Ref 3) Are Given in Prentheses for Comprison) T (K) C p S H f G f (9.16) (61.6) (+60.0) (+51.5) (9.60) (79.6) (+49.2) (+9.9) (13.76) (71.5) (-33.7) (-37.2) (15.75) (99.6) (-42.7) (-52.0) (18.56) (82.3) (-60.5) (-59.2) (19.84) (119.4) (-69.2) (-48.0) Units re kcl mol -1 K -1 s pproprite. For ions the therml electron convention is used. Subsequent compiltions of thermochemicl dt (e.g. ref 3) hve quoted the JANAF vlues. Our clcultions show tht this estimte ws pproximtely 15 kcl mol -1 too high, nd the enthlpies nd free energies should be djusted ccordingly. In contrst, the JANAF enthlpic dt for 2 nd 3 re bsed on ctul experimentl mesurements, nd the experiments re in greement with ech other to (1 kcl mol -1. Spinorbit coupling ccounts for 1.15 kcl/mol of the difference between experimentl nd clculted hets of formtion of 3 (g). The clculted het of formtion is bsed on the rection Fe(g) + 3 / 2 Cl 2 (g) f 3 (g), nd spin-orbit coupling lowers the energy of the Fe tom by 1.15 kcl/mol, 39 wheres the spin-orbit coupling energies of Cl 2 nd 3 re zero since molecule in nondegenerte electronic stte hs zero orbitl ngulr momentum. 40 The experimentl determintion of the het of formtion of gs phse 3 is complicted becuse dimeriztion nd decomposition to 2 must be tken into ccount. The difference between the clculted nd experimentl het of formtion of 3 my reflect these difficulties. It is of interest to compre the Verge bond strengths of the iron chlorides. This is the H for the rection [ n (g) f Fe(g) + ncl(g)], divided by n. The verge bond strengths (t K) re 82.5 kcl mol -1 for, 96.1 kcl mol -1 for 2, nd 83.8 kcl mol -1 for 3. The bonds in 3 nd hve essentilly the sme strength; the bonds in 2 re significntly stronger. Thus, the low BDE for Cl 2 Fe-Cl is due not to the third Fe-Cl bond being prticulrly wek but to the gin in strength in the two remining Fe-Cl bonds. Wekening of bonds on going from 2- to 3-coordintion hs been observed in nionic nd ctionic iron crbonyls; 41 there it is ttributed to the loss of sd hybridiztion, which lessens the repulsion between the σ-bonding nd unpired Fe electrons, on going from the 2-coordinte to the 3-coodinte species. With the crbonyl complexes, however, the bond strengths in the 1-coordinte nd 2-coordinte species re nerly equl. Moreover, the BDE in 3- (68.9 kcl/mol) is greter thn in 2- (51.9 kcl/ mol), indicting strengthening of the bonds on going from 2- to 3-coordintion. It is cler tht the oxidtion stte of the iron (which is kept constnt in the iron crbonyl series) is more importnt fctor in determining bond strenghts to iron. The strongest Fe-Cl bonds in the ction series re in + (80.3 vs 69.5 for + 2 ), nd the strongest Fe-Cl bonds in the nion series re in 3-, both of which like 2 contin n Fe(II). E. Electronic Structure. The electronic structures of the iron chlorides lso show the influence of the oxidtion stte. The ground electron configurtions of Fe, Fe +, Fe 2+, nd Fe 3+ re s 2 d 6, s 1 d 6, s 0 d 6, nd s 0 d 5, respectively. 26 The polr covlent bond in is primrily formed from the 4s orbitl of Festhe orbitl tht loses n electron on ioniztion to Fe + snd the 3p z orbitl of Cl. Since the Fe 4s orbitl hs double occupncy nd the Cl 3p hs single occupncy, two-center three-electron bond is formed (Figure 1). The Fe 3d orbitls prticipte little in the bonding since they re much lower in energy thn the Fe 4s nd Cl 3p orbitls nd much higher in energy thn the Cl 3s orbitl. In forming the ions + nd -, it is the 4s-3p ntibonding orbitl tht gins or loses n electron, just s the 4s orbitl is the one chnging in occupncy on going from Fe + to Fe or Fe 2+. Thus, + hs norml two-electron bond, nd there is little covlent bonding in -. This is in ccord with the vibrtionl frequencies (516, 409, nd 292 cm -1 ) in +,, nd -, nd with the low BDE of -. However, despite the higher bond order in + nd the ion/ induced dipole ttrction tht should contribute to the binding energy of +, the D 0 of + is pproximtely the sme s tht of. This gin shows the preference of iron for the +2 oxidtion stte. In ll three of these species the single Fe spin-β 3d electron is in δ orbitl. The dichloride, 2, hs n electronic structure similr to. The Fe 4s nd the symmetric combintion of the Cl 3p z orbitls form one bond, which is now two-electron bond since the two 3p z electrons of the Cl toms go into the ntisymmetric combintion of the orbitls (Figure 1). 2 hs stronger bonds thn becuse unlike in the ntibonding orbitl in 2 is unoccupied. The Fe spin-β 3d electron is in δ orbitl. 2+ is not well described by single-reference wve function. The principl configurtions re obtined by removing n electron from either the 3dδ orbitl on Fe or one of the lonepir orbitls on Cl. In 2-, the dded electron goes into diffuse orbitl with ntibonding chrcter. The Fe spin-β 3d electron occupies n orbitl of 1 symmetry. In 3 three two-center two-electron bonds re formed using the Fe 4s nd Cl 3p orbitls. Two of the six electrons come from the 4s orbitl of the iron tom, three come from the chlorine toms, nd the remining electron hs been promoted from the iron 3d block. The Cl 2 Fe-Cl bond is presumbly wekened due to the energetic cost of this promotion. On reduction of 3-, the dditionl electron goes bck into the iron d block, more specificlly into the spin-β 3d 0 orbitl. The energy of promoting the electron from the Fe 3d orbitl is thus prtilly regined, nd s result, the EA of 3 (3.90 ev) is greter thn those of 2 (0.99 ev) nd (1.54 ev). IV. Conclusion The geometries, electronic structures, nd thermochemistry of iron chlorides nd the corresponding ctions nd nions were clculted using high-level b initio procedure. The clculted bond dissocition energies (82.5 kcl/mol for f Fe + Cl, kcl/mol for 2 f + Cl, nd 59.6 kcl/mol for 3 f 2 + Cl t K) re in ccord with the therml behvior of these compounds. Although the het of formtion of 2 is in good greement with experiment, the H f of is 15 kcl/mol lower thn the vlue found in stndrd reference works. Since the reference vlue ws bsed on n estimte rther thn on precise experimentl mesurements, we believe

6 Thermochemistry of Iron Chlorides J. Phys. Chem., Vol. 100, No. 21, Figure 1. Orbitl digrms for, 2, nd 3. UHF/WHsf orbitl energies (hrtrees) re given for the R nd β orbitls. tht our computtionlly derived H f (+45.3 kcl/mol t K) is close to the correct vlue. Oxidtion number ppers to be n importnt fctor in the thermochemistry of iron hlides. Rections (such s bond dissocition or n ioniztion) in which iron enters +2 oxidtion stte re more fvorble thn corresponding rections in which iron enters +3, +1, or 0 oxidtion stte. For exmple, the EA of 3 is 3.90 ev, wheres the EAs of 2 nd re 0.99 nd 1.54 ev, respectively. In comprison of bond dissocition energies of neutrl lignds such s CO, the coordintion number (hybridiztion) hs been found to be importnt, especilly on going from two to three lignds. 37 We were unble to observe significnt coordintion-number effect in the iron chloride system becuse the oxidtion-stte effect is much stronger. Exmintion of the Hrtree-Fock wve function revels tht in the Fe(I) nd Fe(0) species t lest one electron is plced in n ntibonding orbitl, wheres in the Fe- (II) species ll electrons re plced in bonding or nonbonding orbitls. In the Fe(III) species n electron hs been promoted from the reltively low-lying iron 3d block, which results in n increse in energy. We hve exmined the performnce of lower levels of theory in comprison to the QCISD(T) method used for the thermochemicl clcultions. It ws found tht the MP2 geometries were quite similr to the QCISD geometries, so tht little error would be introduced in evluting the energies t the MP2 geometries. Density functionl theory performed well with the iron chloride species: the B3LYP geometries were lso similr to the QCISD geometries, nd the energies (using the lrgest bsis set) were ccurte t lest to 5-10 kcl/mol ( ev). Use of the lrger chlorine bsis set ( G(3df) insted of D95+(d)) ws found to be importnt in evluting Fe-Cl s well s Cl-Cl bond energies. Although 2+ is poorly described by MPn nd QCI clcultions, the Brueckner doubles method gives good description of this ion. The B3LYP method ws found to be ccurte to 5-10 kcl/mol even for rections involving this ction. It thus ppers tht modern density functionl techniques hold promise for the modeling of more complex iron systems. Acknowledgment. We thnk Pittsburgh Supercomputing Center, CRAY Reserch, nd the Ford Motor Compny for generous mounts of computer time. References nd Notes (1) Delvl, J. M.; Dufour, C.; Schmps, J. J. Phys. B: At. Mol. Phys. 1980, 13, (2) JANAF Tbles, 3rd. ed.; Chse, Jr., M. W.; Dvies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonld, R. A.; Syverud, A. N. J. Phys. Chem. Ref. Dt Suppl , 14, 1. (3) Brin, I. Thermochemicl Dt of Pure Substnces; VCH: Weinheim, (4) Delvl, J. M.; Schmps, J. J. Phys. B: At. Mol. Phys. 1982, 15, (5) Bominr, E. L.; Guillin, J.; Swryn, A.; Trutwein, A. X. Phys. ReV. B 1989, 39, 72. (6) Mishr, K. C.; Duff, K. J.; Kelires, P.; Mishr, S. K.; Ds, T. P. Phys. ReV. B 1985, 32, 58.

7 8776 J. Phys. Chem., Vol. 100, No. 21, 1996 Bch et l. (7) Chou, S. H.; Kutzler, F. W.; Ellis, D. E.; Shenoy, G. K.; Morrison, T. I.; Montno, P. A. Phys. ReV. B 1985, 31, (8) Vel, B. W.; Ellis, D. E.; Lm, D. J. Phys. ReV. B 1985, 32, (9) Mndich, M. L.; Steigerweld, M. L.; Reents, W. D., Jr. J. Am. Chem. Soc. 1986, 108, (10) Deeth, R. J.; Figgis, B. N.; Ogden, M. I. Chem. Phys. 1988, 121, 115. (11) Butcher, K. D.; Didziulis, S. V.; Brit, B.; Solomon, E. I. J. Am. Chem. Soc. 1990, 112, (12) Oliphnt, N.; Brtlett, R. J. J. Am. Chem. Soc. 1994, 116, (13) Wchters, A. J. H. J. Chem. Phys. 1970, 52, (14) Hy, P. J. J. Chem. Phys. 1977, 66, (15) Rghvchri, K.; Trucks, G. W. J. Chem. Phys. 1989, 91, (16) Rghvchri, K.; Trucks, G. W. J. Chem. Phys. 1989, 91, (17) Dunning, T. H.; Hy, P. J. Modern Theoreticl Chemistry; Plenum: New York, 1976; Chpter 1, pp (18) Clrk, T.; Chndrsekhr, J.; Spitzngel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 294, (19) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, (20) Gussin 94; Frisch, M. J., Trucks, G. W., Schlegel, H. B., Gill, P. M. W., Johnson, B. G., Robb, M. A., Cheesemn, J. R., Keith, T. A., Petersson, G. A., Montgomery, J. A., Rghvchri, K., Al-Lhm, M. A., Zkrzewski, V. G., Ortiz, J. V., Foresmn, J. B., Cioslowski, J., Stefnov, B. B., Nnykkr, A., Chllcombe, M., Peng, C. Y., Ayl, P. Y., Wong, M. W., Andres, J. L., Replogle, E. S., Gomperts, R., Mrtin, R. L., Fox, D. J., Binkley, J. S., Defrees, D. J., Bker, J., Stewrt, J. P., Hed-Gordon, M., Gonzlez, C., Pople, J. A., Eds.; Gussin, Inc.: Pittsburgh, PA, (21) () Pople, J. A.; Hed-Gordon, M.; Fox, D. J.; Rghvchni, K.; Curtiss, L. A. J. Chem. Phys. 1989, 90, (b) Curtiss, L. A.; Rghvchri, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, (22) Mrtin, R. L.; Hy, P. J. J. Chem. Phys. 1981, 75, (23) A correlted wve function my be expressed s D 0 + 1D 1 + 2D , where D 0 is the determinnt expressing the Hrtree-Fock wve function nd D 1, D 2,... re obtined from D 0 by substituting unoccupied cnonicl MOs for occupied ones. NORM(A) is the Eucliden norm of the vector A ) (1, 1, 2,...). (24) Hndy, H. C.; Pople, J. A.; Hed-Gordon, M.; Rghvchri, K.; Trucks, G. W. Chem. Phys. Lett. 1989, 164, 185. (25) McQurrie, D. A. Sttisticl Thermodynmics; Hrper & Row: New York, (26) Moore, C. E. Atomic Energy LeVels; U.S. GPO: Wshington, DC, 1952; Circ. 467, Vol. 2. (27) DeKock, C. W. J. Chem. Phys. 1988, 49, (28) The electronic contribution to the entropy (S elec) of is 4.96 cl mol -1 K -1 t K nd 6.26 cl mol -1 K -1 t 2000 K. If the excited levels were excluded from the clcultion, S elec would be 4.94 cl mol -1 K -1 t ll tempertures. For 2, S elec is 4.58 cl mol -1 K -1 t K nd 4.88 cl mol -1 K -1 t 2000 K. Without the excited levels S elec would be 4.58 cl mol -1 K -1 t ll tempertures. (29) The B3LYP density functionl consists of the exchnge functionl found in Becke, A. D. J. Chem. Phys. 1993, 98, 5648, plus the correltion functionl found in Lee, C.; Yng, W.; Prr, R. G. Phys. ReV. B 1988, 37, 785. (30) () Zeigler, T.; Li. J. Cn. J. Chem. 1994, 72, 783. (b) Young, C.; Lee, S. A.; Freiser, B. S.; Buschlicher, C. W., Jr. J. Am. Chem. Soc. 1995, 117, (c) Ricc, A.; Buschlicher, C. W., Jr. Theor. Chim. Act 1995, 92, 123. (31) Hrgitti, M.; Subbotin, N. Y.; Kolonits, M.; Gershikov, A. G. J. Chem. Phys. 1991, 94, (32) Iron nd chlorine toms nd montomic ions were clculted in their ground sttes ( 5 D for Fe, 6 D for Fe +, 2 P for Cl, nd 1 S for Cl - ). The bond length clculted for Cl 2 t the QCISD/WHsf level is Å. (33) Schoonmker, R. C.; Porter, R. F. J. Chem. Phys. 1958, 29, 116. (34) Hildenbrnd, D. L. J. Chem. Phys. 1995, 103, (35) Berkowitz, J.; Streets, D. G.; Grritz, A. J. Chem. Phys. 1979, 470, (36) Lee, E. P. F.; Potts, A. W.; Dorn, M.; Hillier, I. H.; Delney, J. J.; Hwksworth, R. W.; Guest, M. F. J. Chem. Soc., Frdy II 1980, 76, 506. (37) The poor performnce of MP2 reltive to QCISD my be rtionlized by n exmintion of the principl configurtions contributing to the QCISD wve function of -. The four most importnt of these configurtions (hving bsolute vlues of their coefficients in the rnge) re ll single substitutions from the β HOMO (σ-ntibonding orbitl) in the SCF determinnt. Since single substitutions do not contribute to the MP2 wve function, this pprently importnt contribution to the correltion energy of - does not pper in the MP2 energy. (38) For the ion convention, where H f(e - ) ) 2.5RT, for n ion of chrge q dd (-1.48)q kcl/mol t K nd (-9.93)q kcl/mol t 2000 K to H f nd G f. (39) Computed using energy levels from ref 26. (40) Herzberg, G. Moleculr Spectr nd Moleculr Structure, Vol. 3: Electronic Spectr nd Electronic Structure of Polytomic Molecules; Vn Nostrnd: New York, 1966; p 12. (41) () Ricc, A.; Buschlicher, C. W., Jr. J. Phys. Chem. 1994, 98, (b) Ricc, A.; Buschlicher, C. W., Jr. J. Phys. Chem. 1995, 99, JP953687W