Density Functional and Ab Initio Study of Cr(CO) n (n ) 1-6) Complexes

Transcription

1 J. Phys. Chem. A 2007,, Density Functionl nd Ab Initio Study of Cr(CO) n (n ) -6) Complexes Joonghn Kim, Te Kyu Kim, Jngbe Kim, Yoon Sup Lee, nd Hyotcherl Ihee* Deprtment of Chemistry nd School of Moleculr Science (BK2), Kore AdVnced Institute of Science nd Technology (KAIST), Dejeon, 0-70, Republic of Kore ReceiVed: September 8, 2006; In Finl Form: Mrch 6, 2007 Cr(CO) n (n ) -6) systems were studied for ll possible spin sttes using density functionl nd high-level b initio methods to provide more complete theoreticl understnding of the structure of species tht my form during lignd dissocition of Cr(CO) 6. We crried out geometry optimiztions for ech system nd obtined vibrtionl frequencies, sequentil bond dissocition energies (BDE), nd totl CO binding energies. We lso compred the performnce of vrious DFT functionls. Generlly, the ground sttes of Cr(CO) 6, Cr(CO), nd Cr(CO) 4, whose spin multiplicity is singlet, re in good greement with both previous theoreticl results nd currently vilble experimentl dt. Clcultions on Cr(CO), Cr(CO) 2, nd CrCO provide new findings tht the ground stte of Cr(CO) might be quintet with C 2V symmetry insted of singlet with C V symmetry, nd the ground stte of Cr(CO) 2 is not liner quintet, s suggested by previous DFT clcultions, but rther liner septet. We lso found tht nonet sttes of Cr(CO) 2 nd CrCO disply prtil C-O bond brekge. Introduction Trnsition metl crbonyl compounds, M(CO) n, serve s building blocks in orgnometllic chemistry nd ply importnt roles in heterogeneous ctlysis.,2 To understnd the mechnism of such ctlytic ctivity nd to id in the design of better ctlysts, the nture of relevnt rection intermedites need to be understood. Towrd this gol, there hve been numerous experimentl -6 nd theoreticl investigtions. 7-9 Among these studies, ultrfst diffrction is unique becuse it cn give direct structurl informtion bout rection intermedites nd rection pthwys.,,6,0-6 Severl orgnic molecules hve been studied using ultrfst electron diffrction,,2,,6 but orgnometllic molecules hve received less ttention. 0, Due to the rich chemistry of Cr(CO) n, this system is n interesting subject for ultrfst diffrction. The dt obtined from such tools cn be used for comprisons with theoreticl vlues predicted by vrious b initio nd density functionl theory (DFT) clcultions, thus providing useful dtbse with which to judge the ccurcy of ech theoreticl method. Depending on the excittion wvelength, ll sorts of frgmented Cr(CO) n cn be populted during the photodissocition of Cr- (CO) 6. Therefore, it is prerequisite to hve dtbse of ll possible cndidte intermedite structures tht cn occur during lignd dissocition of Cr(CO) 6. Cr(CO) 6 exemplifies metl-crbonyl bonding nd hs been studied extensively both theoreticlly 7-9 nd experimentlly DFT studies t vrious levels hve been conducted on Cr(CO) 6 nd CrCO, nd the greement with experimentl results hs been demonstrted. 9,20,22,27,29,0,2-6,8,9,-62 In ddition, less ttention hs been pid to other unsturted Cr(CO) n (n ) 2-) complexes, likely to be mjor photolysis intermedites of Cr- (CO) 6, nd only few detiled theoreticl results hve been reported. Li et l. clculted singlet sttes of Cr(CO) nd Cr- (CO) 4 t DFT level with double-ζ bsis set, but their optimized * To whom correspondence should be ddressed. E-mil: hyotcherl. ihee@kist.c.kr. geometricl prmeters re not shown. 6,64 Hyl-Kryspin et l. lso investigted Cr(CO) nd Cr(CO) 4 using DFT methods nd provided geometricl prmeters. However, only A stte (C 2V for Cr(CO) 4 nd C V for Cr(CO) ) hs been investigted lthough both Cr(CO) 4 nd Cr(CO) cn dopt other symmetries. 6 Sequentil bond dissocition energies (BDE) of Cr(CO) n complexes hve been investigted using DFT nd b initio methods. 6 However, the previous study clculted BDEs up to Cr(CO) nd between only singlet species. 6 Obviously, there is demnd for systemtic pproches to theoreticl tretment. For this reson, we crried out systemtic clcultions on the Cr(CO) n system using both DFT nd high-level b initio clcultions. We chose DFT s our mjor tool, which is now widely used to determine structures nd rection energy digrms for vriety of molecules. Compred to high-level b initio moleculr orbitl theories, DFT requires less computtionl time nd storge memory. 66,67 Moreover, the functionls give results quite close to those for high-level b initio clcultions.,68,69 For this reson, in this work, moleculr structures, s well s vibrtionl frequencies nd sequentil bond dissocition energies of Cr(CO) n (n ) -6) hve been investigted through vrious DFT methods. The clculted results for vibrtionl frequency nd bond dissocition energy should be useful for experimentl studies. High-level b initio methods such s coupled cluster singles nd doubles (CCSD) nd CCSD with perturbed triples (CCSD- (T)) were lso used for some cses where their use ws criticl for clrifying importnt issues. The clculted results were compred with the vilble experimentl vlues nd excellent greement between theory nd experiment in geometries nd bond dissocition energies of Cr(CO) n (n ) 4-6) ws found. The high spin sttes of Cr(CO) n (n ) -4) re lso discussed. For Cr(CO), the singlet C V structure ws observed experimentlly. 46,70,7 However, the lowest-energy stte my hve C 2V symmetry with higher spin stte. In both Cr(CO) 2 nd CrCO cses, it is of importnce whether their structures re bent 0.02/jp06608o CCC: $ Americn Chemicl Society Published on Web 0/09/2007

2 4698 J. Phys. Chem. A, Vol., No. 2, 2007 Kim et l. Figure. Moleculr structure of Cr(CO) 6 (moleculr stte/moleculr symmetry). or liner. In the cse of Cr(CO) 2, no higher-level clcultion hs been performed to dte. For the ground stte of CrCO, b initio 8,9 nd DFT,60,6 methods hve provided results contrry to ech other. The former gve liner structure with septet wheres the ltter gve bent structure s septet. Recently, we demonstrted tht the ground stte of CrCO is septet bent structure using the CCSD(T) method. 72 In ddition, we ccurtely reproduced the BDE of CrCO. In this work, we extend the clcultion to other spin sttes of CrCO. We hope this work ids further experimentl studies in determining geometry nd dissocition energies of Cr(CO) n (n ) 2-), which hve not yet been vilble. Computtionl Detils All clcultions hve been crried out using the Gussin 0W nd Gussin 0 progrm pckges. 7 We performed DFT clcultions using functionls (BLYP, 74,7 BPW9, 74 BP86, 74,76 mpwpw9 77,78 ) nd generlized grdient pproximtion () functionls (BLYP, 7,79 BPW9, 78,79 BP86, 76,79 PBE 80 ). The 6-+G(df) bsis sets hve been used Figure 2. Moleculr structures of Cr(CO) (moleculr stte/moleculr symmetry). for both crbon nd oxygen tom ((2s6pdf)/[s4pdf]), wheres Wchters-Hy 8,82 ll electron bsis set using the scling fctors of Rghvchri nd Trucks, 8 three sets of polriztion functions, nd set of diffuse functions ((sp6dfg)/ [0s7p4dfg]) hve been employed for chromium. A combintion of these bsis sets re referred to s 6-+G(df). For the BLYP functionl, we performed dditionl clcultions using the 6-+G(d) bsis set (Cr, (sp6df)/[0s7p4df]; C nd O, (2s6pd)/[s4pd]) to check for bsis set dependency. The structures of possible spin sttes were fully optimized nd subsequent hrmonic vibrtionl frequencies hve been clculted t the optimized structures. We used the restricted DFT method for singlet cses. The clculted BDE includes the corrections for zero point energies (ZPE), therml enthlpy (298 K), nd the bsis set superposition error (BSSE) corrected by the counterpoise method. 84 The clculted reltive energies, BDE, full-optimized geometricl prmeters nd C-O stretching vibrtionl frequencies in Cr(CO) n re shown in Figures -6 nd Tbles -. In ddition, we performed the clcultion of ditomic CO using vrious DFT functionls nd b initio methods to select n TABLE : Geometricl Prmeters (Lengths in Å, Angles in Deg) nd Scled C-O Stretching Vibrtionl Frequencies (cm - ) of the A g Stte of Cr(CO) 6 from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) A g BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp geom r(cr-c).926 (.928) b r(c-o).8 (.4) b freq A g (209.8) c E g (2002.2) c T u 988. (982.9) d The moleculr structure is depicted in Figure. b Reference 4 nd 4. c Reference 0. d Reference 70. TABLE 2: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), nd Dipole Moment (Debye) of the C 4W ( A ) Structure of Cr(CO) from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) A BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp geom r(cr-c x).8 (.8) r(c x-o x).46 (.49) r(cr-c eq).926 (.927) r(c eq-o eq).40 (.4) C xcrc eq (90.87) C eqcrc eq (89.99) CrC eqo eq 78. (78.20) freq A (207.8) B (989.4) E (966.4) , b 976 c A 90.6 (94.8) , b 90 c µ (2.24) The moleculr structure is depicted in Figure 2. b Reference 46. c Reference 70.

3 Density Functionl nd Ab Initio Study of Cr(CO) n J. Phys. Chem. A, Vol., No. 2, TABLE : Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), S 2, nd Reltive Energies (kcl/mol) of the D h ( A ) Structure of Cr(CO) from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) A BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE geom r(cr-c x).92 (.92) r(c x-o x).4 (.44) r(cr-c eq).94 (.96) r(c eq-o eq).8 (.4) freq A (206.) E (984.) A (974.8) A (97.0) S (2.09) b rel.2 (.6) c rel 0.6 (0.9) The moleculr structure is depicted in Figure 2. b rel ) E( A ) - E( A ). c rel ) H( A ) - H( A ). TABLE 4: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of the C 2W ( A nd B 2 ) nd D 2d ( B 2 ) Structures of Cr(CO) 4 from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp A geom r(cr-c A).92 (.924) r(c A-O A).42 (.4) r(cr-c B).842 (.84) r(c B-O B).49 (.2) C ACrC A (80.00) C BCrC B 9.2 (9.6) C ACrC B (90.00) CrC AO A 76.2 (76.22) CrC BO B (79.89) freq A (204.8) B (949.6) , b 94 c A (99.4) B (9.8) , b 96 c µ.78 (.790) B 2 geom r(cr-c A).92 (.926) r(c A-O A).44 (.47) r(cr-c B).94 (.94) r(c B-O B).40 (.4) C ACrC A 7.2 (7.29) C BCrC B. (0.0) C ACrC B 9.8 (9.8) CrC AO A (78.82) CrC BO B 7.6 (7.) freq A (2047.7) B (97.9) A (94.2) B 90.6 (924.) µ.86 (.24) S (2.070) d rel 7. (7.) e rel 6. (6.7) B 2 geom r(cr-c).989 (.992) r(c-o).40 (.4) CCrC 4.2 (4.8) C ACrC B 9. (9.02) CrCO (74.02) freq A (2048.6) B (962.9) E (96.) S (6.07) f rel 8.7 (8.9) g rel 7.7 (7.8) The moleculr structures re depicted in Figure. b Reference 46. c Reference 70. d rel ) E( B 2) - E( A ). e rel ) H( B 2) - H( A ). f rel ) E( B 2) - E( A ). g rel ) H( B 2) - H( A ). pproprite method. The results re summrized in Tble S in the Supporting Informtion. For Cr(CO) 2 nd Cr(CO), where the discrepncy between our DFT clcultions nd previously reported results ws found, we performed dditionl b initio clcultions such s MP2, 8,86 CCSD, 87,88 nd CCSD(T) 89 (for Cr(CO) 2 only) with the 6-+G- (d) bsis set for selected molecules. Due to the computtionl cost, we used the 6-+G(d) bsis set for b initio clcultions.

4 4700 J. Phys. Chem. A, Vol., No. 2, 2007 Kim et l. TABLE : Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of the D 4h ( A g ) nd D 2h ( B g ) Structures of Cr(CO) 4 from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE A g geom r(cr-c).92 (.922) r(c-o).4 (.46) freq A g (20.2) B g 972. (966.) E u 94. (99.4) b rel 0.7 (0.6) c rel 0. (0.4) B g geom r(cr-c).94 (.9) r(c-o).4 (.44) CCrC (96.98) CrCO 77.9 (77.99) freq A g (207.6) B 2u (94.0) B u (94.9) B g (87.) S (2.078) d rel 7.9 (8.0) d rel 7. (7.) The moleculr structures re depicted in Figure. b rel ) E( A g) - E( A ). c rel ) H( A g) - H( A ). d rel ) E( B g) - E( A ). e rel ) H( B g) - H( A ). In ddition, we clculted these molecules gin using vrious DFT functionls with the 6-+G(d) bsis set to compre the results with those of b initio clcultion. All b initio clcultions were performed with the frozen core pproximtion. We performed the geometry optimiztion nd clculted vibrtionl frequencies with ll methods employed in this work. For presenting the vibrtionl frequencies, we used scle fctors listed on the web pge of the Ntionl Institute of Stndrds nd Technology: , 0.97, 0.94, 0.99, nd for BLYP, BPW9, mpwpw9, BLYP, nd PBE, respectively. There re no scle fctors vilble for BP86, BPW9, nd BP86. Becuse BP86 is functionl, we used the scle fctor (0.96) of BLYP, which is lso functionl s BP86. For the sme reson, for BPW9 nd BP86, which re functionls, we used 0.99, which is originlly the scle fctor of BLYP. In the b initio clcultions, we used 0.90, 0.94, nd 0.96 for Möller-Plesset second order (MP2), CCSD, nd CCSD(T), respectively. To clrify the bonding nture between chromium nd the crbonyl groups, we performed NBO nlysis, 9 which cn id the interprettion of the metl-lignd interction in terms of the second-order perturbtive energies. In ddition, the NBO results contin the nturl electron configurtion of Cr tom. The NBO nlysis is performed only t the optimized structure using BLYP/6-+G(d). The results of NBO nlysis nd the chrges of ll species re summrized in the Supporting Informtion. Results nd Discussion A. Moleculr Structures.. Cr(CO) 6. The fully optimized structure of Cr(CO) 6 with O h symmetry is summrized in Figure nd Tble. In previous studies, the geometry of Cr- (CO) 6 ws investigted by neutron 4,4 nd X-ry diffrction. 40,4 Becuse X-ry diffrction dt hve greter uncertinty, we used neutron diffrction dt:.98 Å for r e (Cr-C) nd.4 Å for r e (C-O) including therml correction for mesurements tken t 78 K. As shown in Tble, the results from ll functionls except BLYP nd BLYP underestimte the Cr-C distnce compred to the experimentl vlue. The clcultion using BLYP gives slightly lrger Cr-C distnce (.926 Å) Figure. Moleculr structures of Cr(CO) 4 (moleculr stte/moleculr symmetry). compred with the experimentl vlue (.98 Å). Clcultions using BLYP nd the BLYP functionls give longer Cr-C distnce compred with other functionls. In the C-O bond length, ll clcultions using functionls provide resonble bond lengths. However, ll functionls overestimte the C-O bond length compred with the experimentl vlue. In the cse of the geometry of Cr(CO) 6, the BLYP gives good results. Compred with the result using 6-+G(df) bsis set, the clculted bond lengths using the 6-+G(d) bsis set is slightly longer. In the cse of the C-O stretching frequency, ll functionls show better performnce thn ll functionls which underestimte the C-O stretching frequency. The clculted frequencies using BP86 nd mpwpw9 re in excellent greement with experimentl vlues. The BLYP functionl gives resonble geometries but slightly underestimtes the stretching frequencies. In the nturl popultion nlysis (NPA), functionls generlly give lrger chrges thn those of functionls (See Tble 2S in Supporting Informtion). The BLYP nd the BLYP functionls give smll chrges compred with other functionls. 2. Cr(CO). Cr(CO) cn dopt two different symmetries nd its optimized structures re depicted in Figure 2. Experimentlly, the mtrix-isolted Cr(CO) ws shown to hve C 4V symmetry where the C x -Cr-C eq ngle is pproximtely between 90 nd 9 92 lthough the D h structure hd lso been proposed under certin conditions. 9 Although there is no vilble gsphse experimentl structurl informtion, severl theoreticl studies of Cr(CO) were performed by b initio 2,28,7,94 nd DFT

5 Density Functionl nd Ab Initio Study of Cr(CO) n J. Phys. Chem. A, Vol., No. 2, TABLE 6: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, Number of Imginry Frequencies, nd Reltive Energies (kcl/mol) of the C 2W ( A, B, nd B 2 ) Structures of Cr(CO) from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE A geom r(cr-c A).82 (.824) r(c A-O A). (.8) r(cr-c B).96 (.97) r(c B-O B).46 (.49) C BCrC B 8.6 (8.49) C ACrC B 89.9 (89.2) CrC BO B 76.2 (76.7) freq A (204.7) B (96.8) A (89.2) µ.68 (.6) b rel. (.) c rel 6.2 (6.2) B geom r(cr-c A).99 (.92) r(c A-O A).42 (.4) r(cr-c B).92 (.92) r(c B-O B).49 (.2) C BCrC B (76.2) C ACrC B 9.86 (9.87) CrC BO B (78.98) freq A (209.) A (940.7) B (88.) µ.989 (2.07) S (2.09) img freq d rel 6.4 (6.6) e rel 6.9 (7.0) B 2 geom r(cr-c A) r(c A-O A) r(cr-c B) r(c B-O B) C BCrC B C ACrC B CrC BO B freq A B A µ S img freq The moleculr structures re depicted in Figure 4. b rel ) E( A ) - E( B 2). c rel ) H( A ) - H( B 2). d rel ) E( B ) - E( B 2). e rel ) H( B ) - H( B 2). methods. Previous studies showed tht the C 4V structure is more stble thn the D h structure nd the energy difference between two symmetries re 9-0 kcl/mol 7,94 t the Hrtree-Fock (HF) level with smll bsis sets. Our clcultions confirm tht the C 4V structure ( A ) is more stble thn the D h ( A ) one for ll DFT functionls (see Tble ). The energy differences between these two sttes using functionls re lrger thn those from using functionls. Other Cr(CO) n species (n ) -4) lso show such trend (see other sections). We now consider the bond lengths shown in Tbles 2 nd. Both the nd functionls except the BLYP nd the BLYP provide similr Cr-C distnces. The results with the BLYP nd BLYP functionls show significntly longer Cr-C distnces compred with those with other functionls. This trend ws lso observed for Cr(CO) 6. All clcultions using functionls give longer C-O bond lengths compred with functionls, s in the Cr(CO) 6 cse. The equtoril metl-lignd (Cr-C) bond lengths of both the C 4V nd D h structure re longer thn the xil Cr-C bond lengths. In contrst, the equtoril C-O bond lengths of both structures re shorter thn the xil ones. These indicte tht the bonding interction between the xil C-O lignd nd the Cr tom is stronger thn tht between the equtoril lignd nd Cr nd cn be explined by considering the incresed occuption of π* orbitl in C-O becuse the bonding interction between Cr nd C-O is proportionl to the occuption of π* orbitl in C-O through π bck-bonding. The results of the NBO nlysis t the BLYP/6-+G(d) level show tht the occuption number of π* orbitl t xil C-O ( A, 0.76; A, 0.286) is lrger thn tht ( A, ; A, ) t equtoril C-O. The incresed occuption of π* orbitl lso reduces the stretching frequency of C-O. 9 As shown in Tbles 2 nd, the stretching frequencies of xil C-O of both structures ( A, A ) re smller thn those of equtoril C-O ( A :A < B 2, E nd A :A 2 < E ). Clcultions using only the BLYP nd BLYP functionls provide C x -Cr-C eq ngles tht fll within the rnge of experimentl dt. Previous theoreticl clcultions gve similr results. 2, However, the MP2 method gives rther different result tht C x CrC eq is smller thn All functionls except BLYP nd BLYP provide results similr to the MP2 result. The geometry optimiztion with BLYP/6-+G(df) produces results similr to BLYP/6-+G(d) clcultions for

6 4702 J. Phys. Chem. A, Vol., No. 2, 2007 Kim et l. TABLE 7: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of the C W ( A ) nd D h ( 7 A 2 ) Structures of Cr(CO) from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp A geom r(cr-c) r(c-o) CCrC CrCO freq A E , b 887 c µ d rel e rel A 2 geom r(cr-c) 2.0 (2.08) r(c-o).4 (.44) freq A (2020.2) E 9.6 (94.) S (2.00) f rel 6.6 (7.0) g rel 6.4 (6.7) The moleculr structures re depicted in Figure 4. b Reference 46. c Reference 70. d rel ) E( A ) - E( B 2). e rel ) H( A ) - H( B 2). f rel ) E( 7 A 2 ) - E( B 2). g rel ) H( 7 A 2 ) - H( B 2). TABLE 8: Geometricl Prmeters (Lengths in Å, Angles in Deg), Stretching Vibrtionl Frequencies b of C-O (cm - ), Dipole Moment (Debye), S 2, Number of Imginry Frequencies, nd Reltive Energies (kcl/mol) between the C 2W ( B 2 ) nd C W ( A ) Structures of Cr(CO) from Clcultions Using the 6-+G(d) Bsis Set (in Prentheses, Results of Single Point Clcultion Using the 6-+G(df) Bsis Set t Optimized Geometry Using the 6-+G(d) Bsis Set) 6-+G(d) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE MP2 CCSD C 2v ( B 2) r(cr-c A) r(c A-O A) r(cr-c B) r(c B-O B) C BCrC B C ACrC B CrC BO B A B A µ S (6.760) img freq C V ( A ) r(cr-c) r(c-o) CCrC CrCO A E µ c rel (.0) d rel The moleculr structures re depicted in Figure 4. b Unscled vlue. c rel ) E( A ) - E( B 2). d rel ) H( A ) - H( B 2). both C 4V nd D h structures. Compred with the 6-+G(d) bsis set, both bond lengths nd ngles of the 6-+G(df) bsis set re slightly reduced, but the bsis set dependency is smll in DFT clcultions, showing essentilly the sme trend s in the cse of Cr(CO) 6. All results with functionls underestimte the C-O stretching frequency, nd the functionls show better performnce. Especilly, the results of BLYP nd BPW9 re in good greement with experimentl vlues. In summry, ccording to the results of Cr(CO) 6 nd Cr(CO), both nd functionls give similr results for Cr-C bond lengths except those bsed on the LYP functionl. However, for C-O bond lengths, the functionls give better results. In generl, the functionls overestimte the bond length of C-O. For C-O stretching frequencies, the functionls give good results wheres the clcultions using functionls underestimte the C-O stretching frequency. Becuse this trend in geometries nd frequencies between the nd the functionls re the sme in ll other Cr(CO) n, we will omit comments bout these trends in other cses following. We summrize the results of NBO nlysis on the interction between the d orbitl of the Cr tom nd the ntibonding orbitl of CO in Tble 4S (Supporting Informtion). The NBO results clerly show the bck-dontion of metl. The bck-dontions to xil COs re lrger thn those of equtoril ones in ech species. Actully, it is expected tht the removl of the opposing xil CO group in Cr(CO) 6 results in reinforcing electron density into the remining xil bonding orbitl. The NPA chrges confirm these explntions (see Tbles 2S nd S in Supporting Informtion). In the C 4V structure, the toms of xil

7 Density Functionl nd Ab Initio Study of Cr(CO) n J. Phys. Chem. A, Vol., No. 2, TABLE 9: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of Liner Structures ( Σ g, Σ g, Π g, 7 Π u, nd 9 Σ u ) of Cr(CO) 2 from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE Σ g geom r(cr-c).9 (.9) r(c-o). (.7) freq Σ g (97.0) Σ u 87.9 (868.4) b rel 42. (42.0) c rel 42.7 (42.6) Σ g geom r(cr-c).99 (.99) r(c-o).6 (.9) freq Σ g (960.9) Σ u 84.4 (88.) S 2 2. (2.20) d rel 6.9 (6.8) e rel 7.4 (7.4) Π g geom r(cr-c) r(c-o) freq Σ g Σ u S f rel g rel h rel i rel Π u geom r(cr-c) r(c-o) freq Σ g Σ u S Σ u geom r(cr-c).98 (.96) r(c-o).8 (.89) freq Σ u 24. (22.) Σ g 70.8 (79.9) S (20.00) j rel.9 (4.) k rel 4.4 (4.8) The moleculr structures re depicted in Figure. b rel ) E( Σ g) - E( 7 Π u). c rel ) H( Σ g) - H( 7 Π u). d rel ) E( Σ g) - E( 7 Π u). e rel ) H( Σ g) - H( 7 Π u). f rel ) E( Π g) - E( A ). g rel ) H( Π g) - H( A ). h rel ) E( Π g) - E( 7 Π u). i rel ) H( Π g) - H( 7 Π u). j rel ) E( 9 Σ u) - E( 7 Π u). k rel ) H( 9 Σ u) - H( 7 Π u). positions contin more negtive chrge thn those of equtoril positions (see Figure 2). In ddition, these chrges t xil positions contin more negtive chrge thn those of Cr(CO) 6. Therefore, the Cr(CO) ( A ) xil (Cr-C) bond length is shorter thn tht of the Cr(CO) 6 wheres equtoril (Cr-C) bond lengths re similr. In the A stte, s shown in Tble, the spin contmintion is rther smll for ll cses, nd substntilly smller for thn the s.. Cr(CO) 4. Experimentlly, Cr(CO) 4 is known to hve C 2V symmetry in n Ar mtrix 96 nd singlet ground stte. 97 There re no experimentl vlues or theoreticl clcultion results for geometricl prmeters of Cr(CO) 4. The fully optimized structures, reltive energies, C-O stretching frequencies nd dipole moments of Cr(CO) 4 re summrized in Tbles 4 nd nd Figure. The results show tht the ground stte of Cr(CO) 4 hs C 2V seesw structure nd is singlet ( A ). We note tht Cr(CO) 4 hs higher spin stte ( B 2 ) tht is low-lying excited stte. The geometricl prmeters of the seesw C 2V ( A ) structure re similr to those of the C 4V structure of Cr(CO) ( A ) (see Tbles 2 nd 4). All functionls give similr results. The Cr- C A nd C A -O A bond length (see Tble 4 nd Figure ) of C 2V ( A ) re lmost identicl to those (Cr-C eq nd C eq -O eq in Tble 2) of Cr(CO). The C B -Cr-C B ngle (see Tble 4 nd Figure ) of C 2V ( A ) is lso equl to tht (C x -Cr-C eq in Tble 2) of Cr(CO). However, ll functionls show tht the Cr-C B bond length of C 2V ( A ) is smller thn the Cr-C x bond length of Cr(CO) nd the C B -O B bond length is lrger thn C x -O x of Cr(CO). This indictes tht the removl of n equtoril CO group from the C 4V ( A ) structure of Cr(CO) results in reinforcing the electron density into remining CO groups. We clculted the BDEs using BLYP/6-+G(d) nd confirmed these. The BDEs of Cr(CO) 4 -C x O x nd Cr(CO) - C B O B re bout 4. nd 46. kcl/mol, respectively. These indicte tht the bond strength of Cr-C B in the C 2V ( A ) structure gets stronger upon the removl of C eq O eq from C 4V ( A ) structure. As shown in Tble 4, the C-O stretching frequencies clculted using the BLYP functionl re in excellent greement with those from the experiment. The BPW9 nd the BPW9 functionls lso give good results. The BP86 nd the mpwpw9 functionls overestimte the frequencies. Spin contmintions re somewht incresed to be compred with those of Cr(CO), but still not excessively lrge. As in the cse of Cr(CO), spin contmintions re lrger for functionls thn for (Tbles 4 nd ). The reltive stbilities mong severl sttes of Cr(CO) 4 cn be ssigned on the bsis of clculted energies nd enthlpies s shown in Tbles 4 nd. We note tht the results with nd functionls give different orders of energy for the structures. All results with functionls except the mpwpw9 functionl show the sme order of the energy. ( A < B 2 < B g < B 2 < A g nd A < B 2 < B 2 < B g <

8 4704 J. Phys. Chem. A, Vol., No. 2, 2007 Kim et l. TABLE 0: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of Bent Structures ( A, A 2, nd A ) of Cr(CO) 2 from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp A geom r(cr-c).804 (.80) r(c-o).6 (.64) CCrC (88.4) CrCO (78.42) freq A (99.0) B (88.6) µ 6.26 (6.2) b rel 27.8 (27.6) c rel 28. (27.9) A 2 geom r(cr-c).84 (.84) r(c-o).9 (.62) CCrC (77.70) CrCO (76.69) freq A 90.0 (92.8) B (777.7) µ 6.48 (6.22) S (2.44) d rel 4.2 (4.) e rel 4. (4.4) A geom r(cr-c) r(c-o) CCrC CrCO freq A , h 982. i B , h 82.9 i µ S f rel g rel The moleculr structures re depicted in Figure. b rel ) E( A ) - E( 7 Π u). c rel ) H( A ) - H( 7 Π u). d rel ) E( A 2) - E( 7 Π u). e rel ) H( A 2) - H( 7 Π u). f rel ) E( A ) - E( 7 Π u). g rel ) H( A ) - H( 7 Π u). h Reference 62, in solid rgon. i Reference 62, in solid neon. Figure. Moleculr structures of Cr(CO) 2 (moleculr stte/moleculr symmetry). Figure 6. Moleculr structures of CrCO (moleculr stte/moleculr symmetry). Figure 4. Moleculr structures of Cr(CO) (moleculr stte/moleculr symmetry). A g for the mpwpw9) However, in functionls except BLYP, the order of the energy is A < B 2 < B g < A g < B 2 ( A < B 2 < A g < B g < B 2 for BLYP). The min difference is the order of the A g stte nd B 2 stte. The functionls contin exct prt of exchnge energies clculted explicitly, which usully fvor high spin stte such s quintet. This is consistent with the results tht with functionls, the B 2 stte is more stble thn the A g stte. All functionls give the sme trend tht squre plnr structures ( A g nd B g ) re somewht unstble in comprison to the seesw structure ( A nd B 2 ). 4. Cr(CO). Experiments suggested tht Cr(CO) in CH 4 mtrix hs C V symmetry. 98 Trnsient time-resolved infrred bsorption in the gs phse showed tht Cr(CO) is C V symmetric in its singlet spin stte ccording to its rte constnt. 46,70,7 The previous DFT study (BP86/6-+G(d)) proposed tht the ground stte is A with C V symmetry, in greement with previous two experiments. 62 Our clcultion lso supports tht the C V structure is singlet spin stte ( A ). However, the results with ll functionls except the BP86 indictes tht the globl minimum of Cr(CO) is the C 2V symmetry with quintet ( B 2 ) rther thn C V ( A ). In contrst, the results with ll functionls give tht the B 2 (C 2V ) stte hs imginry frequency (ll C V structures hve no imginry frequency) nd it is less stble thn A (C V ) stte (see

9 Density Functionl nd Ab Initio Study of Cr(CO) n J. Phys. Chem. A, Vol., No. 2, TABLE : Geometricl Prmeters (Lengths in Å, Angles in Deg), Stretching Vibrtionl Frequencies b of C-O (cm - ), Dipole Moment (Debye), S 2, Number of Imginry Frequencies, nd Reltive Energies (kcl/mol) mong D h ( Π g ), C 2W ( A ), nd D h ( 7 Π u ) Structures of Cr(CO) 2 from Clcultions Using the 6-+G(d) Bsis Set (in Prentheses, Results of Single Point Clcultion Using the 6-+G(df) Bsis Set t Optimized Geometries Using the 6-+G(d)) 6-+G(d) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE MP2 CCSD CCSD(T) D h ( Π g) r(cr-c) r(c-o) Σ g Σ u S (6.704) (6.69) img freq c rel (.) 7. (4.8) d rel C 2V ( A ) r(cr-c) r(c-o) CCrC CrCO A B µ S (6.87) (6.797) e rel (2.4) 9.6 (7.6) f rel D h ( 7 Π u) r(cr-c) r(c-o) Σ g Σ u S (2.00) 2.00 (2.0) The moleculr structures re depicted in Figure. b Unscled vlue. c rel ) E( Π g) - E( 7 Π u). d rel ) H( Π g) - H( 7 Π u). e rel ) E( A ) - E( 7 Π u). f rel ) H( A ) - H( 7 Π u). Tbles 6 nd 7). As noted bove for Cr(CO) 4, the exct exchnge prt clculted like HF exchnge terms might mke high spin stte more stble. Under the frozen orbitl pproximtion, the exchnge interction of the quintet is lrger thn tht of the singlet, nd the sme my hold for relxed set of orbitls. All clcultions using functionls give tht ll C 2V ( B 2 ) structures re more stble thn C V ( A ) structures. According to these results, introducing the exct exchnge energy ffects the potentil energy surfce of high spin sttes more thn tht of low spin sttes. To clrify our DFT results, we performed clcultions of the B 2 (C 2V ) nd A (C V ) sttes using b initio methods. The results re summrized in Tble 8. The C 2V ( B 2 ) structure clculted using the MP2 method hs imginry frequency nd the C V ( A ) structure is more stble thn the C 2V ( B 2 ) structure (see Tble 8). However, in the CCSD clcultion, the reltive stbility is reversed nd the C 2V ( B 2 ) structure hs no imginry frequency. These results fvor the C 2V ( B 2 ) structure s the ground stte. However, we should consider spin contmintion. As shown in Tbles 6-8, spin contmintion is not negligible in the triplet nd quintet sttes. In generl, the spin contmintion of functionls is lrger thn tht of functionls becuse of the exct exchnge energy in the former. Ab initio methods suffer more spin contmintion thn DFT ones in the B 2 (C 2V ) stte (see Tble 8). Although the CCSD clcultion show tht the B 2 (C 2V ) stte is more stble thn the A (C V ) stte, the former might not be the ground stte of Cr(CO) becuse its wvefunction is contminted by other spin sttes. Therefore, further work should be crried out to clrify the ground stte of Cr(CO) using multireference bsed method. For the A (C V ) stte, the BLYP functionl reproduces experimentl results well, nd s except BLYP lso give good results (see Tble 7). The CCSD method provides n excellent result ( ) 88.7), which grees well with the experiment vlue (see Tbles 7 nd 8). The MP2 method underestimtes the frequency ( ) 8.8).. Cr(CO) 2. Cr(CO) 2 ws fully optimized with DFT methods using the 6-+G(df) bsis set nd the results re summrized in Tbles 9 nd 0 nd Figure. The previous DFT clcultion using BP86/6-+G(d) showed tht the ground stte of Cr- (CO) 2 is quintet with liner structure ( Π g ). 62 In our clcultion, ll DFT functionls except BPW9 nd mpwpw9 lso provide tht Π g is the ground stte. However, we note tht the triplet nd quintet sttes of Cr(CO) 2 suffer considerble spin contmintion, s shown in Tbles 9 nd 0. To clrify the true ground stte, we crried out further b initio clcultions with 6-+G(d) nd dditionl DFT clcultions with the sme bsis set for comprison. The results re summrized in Tble. All b initio methods yielded the contrry result tht Π g is less stble thn septet ( 7 Π u ) in the liner structure. Especilly, the energy difference is 7. kcl/mol t the CCSD- (T)/6-+G(d) level. Therefore, we conclude tht the ground stte of Cr(CO) 2 is 7 Π u, but further work using multireference bsed method should be performed to resolve reltive stbility of ll species. In previous experiment, Andrews et l. showed tht vibrtionl frequencies of Cr(CO) 2 pproximtely mtch the clculted vlues for A. 62 As shown in Tble 0, the BLYP functionl gives good results for the A mode. Other functionls overestimte, wheres ll functionls underestimte, the frequency. However, for the B 2 mode, ll functionls overestimte the frequency nd both nd functionls give similr results. Actully, the possibility of incorrect ssignment cnnot be ruled out. Becuse previous experiments were conducted in mtrix environment, interction with mtrix might come into ply. The influence of the noble gs on the geometry is negligible, but the interction energy between the metl nd the noble gs is bout 8-9 kcl/mol. 99

10 4706 J. Phys. Chem. A, Vol., No. 2, 2007 Kim et l. TABLE 2: Geometricl Prmeters (Lengths in Å, Angles in Deg), Stretching Vibrtionl Frequencies b of C-O (cm - ), Dipole Moment (Debye), nd Reltive Energies (kcl/mol) of Asymmetric Structures ( A) of Cr(CO) 2 A r(cr-c A) r(c A-O A) r(cr-c B) r(c B-O B) C BCrC A CrC AO A CrC BO B A (cm - ) µ S 2 c rel d rel CCSD , CCSD(T) , The moleculr structures re depicted in Figure. b Unscled vlue. c rel ) E( A) - E( Π g). d rel ) H( A) - H( Π g). TABLE : Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, Number of Imginry Frequencies, nd Reltive Energies (kcl/mol) of Liner Structures ( Σ, Σ, Π, nd 7 Σ) of CrCO from DFT Clcultions Using the 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE Σ geom r(cr-c).78 (.784) r(c-o).72 (.79) freq Σ (80.0) µ.269 (6.29) img freq 0 (0) b rel 72.4 (72.9) c rel 7.0 (7.6) Σ geom r(cr-c).799 (.769) r(c-o).8 (.7) freq Σ (89.0) µ 6.94 (4.64) S (2.0) d rel 47.4 (4.9) e rel 47.8 (44.6) Π geom r(cr-c).899 (.899) r(c-o).68 (.7) freq Σ (87.8) µ 4.97 (.0) S (6.47) img freq () f rel 2. (2.9) g rel 2. (2.6) Σ geom r(cr-c) 2.92 (2.20) r(c-o).2 (.) freq Σ (206.6) µ.676 (.64) S (2.00) img freq 2 (2) h rel 2. (2.9) i rel.7 (2.) The moleculr structures re depicted in Figure 6. b rel ) E( Σ) - E( 7 A ). c rel ) H( Σ) - H( 7 A ). d rel ) E( Σ) - E( 7 A ). e rel ) H( Σ) - H( 7 A ). f rel ) E( Π) - E( 7 A ). g rel ) H( Π) - H( 7 A ). h rel ) E( 7 Σ) - E( 7 A ). i rel ) H( 7 Σ) - H( 7 A ). There is possibility tht these interctions my perturb the reltive stbility. 62 Cr(CO) 2 cn dopt nonet stte ( 9 Σ u ) in the liner structure. As shown in Tble 9, the C-O bond length is somewht longer, nd the Cr-C bond length is shorter thn those of other sttes, which implies prtil brekge of C-O bonds. This prtil breking cn be rtionlized by considering tht the nonet stte is formed from the septet stte by moving one electron in the HOMO of the β spin orbitl into the LUMO of R spin orbitl of the septet stte. Becuse the LUMO of R spin orbitl hs strong bonding chrcter between Cr nd C nd ntibonding chrcter between C nd O, nd the HOMO of β spin orbitl hs bonding chrcter for both pirs (see Figure S in Supporting Informtion), the 9 Σ u stte gins ntibonding chrcter between C nd O nd bonding chrcter between Cr nd C compred to the septet stte. As consequence, the C-O bond length is elongted nd the Cr-C bond length is shortened. A similr trend occurs lso in the nonet stte of CrCO. 6. CrCO. Experimentlly, CrCO ws detected in n Ar mtrix t 4 K nd the observed stretching frequency ws 977 cm Like other species, there is no other experimentl structurl informtion. There is experimentl evidence tht the ground stte of CrCO is septet nd its dissocition energy is less thn. kcl/mol. 0 Previous DFT studies suggested tht the bent structure with septet is the globl minimum of CrCO species.,60,6 However, previous b initio clcultions showed tht the globl minimum is liner structure nd septet. 8,9 Recently, CrCO ws clculted using CCSD(T) with lrge bsis set. This result indicted tht CrCO is bent nd septet. 0 However, this investigtion did not contin ny informtion bout frequency. In the cse of the ground stte of CrCO, we clerly resolved these discrepncies in our recent work nd showed tht the ground stte is septet in bent structure ( 7 A ). 72 In this work, we investigted ll possible spin sttes nd the corresponding structures re summrized in Tbles nd 4. The results with ll functionls show tht bent structure with septet is the globl minimum ( 7 A ). Its liner structure with septet ( 7 Σ) hs two imginry frequencies nd is less stble thn the bent structure ( 7 A ). These results re similr to those of previous DFT clcultions.,60,6 As shown in Tbles nd 4, open shell species except the septet nd nonet hve considerble spin contmintion, nd further study using multireference bsed method is required for triplet nd quintet sttes. The nonet stte ( 9 A ) structure hs substntilly longer Cr-C nd C-O bond lengths thn other sttes s shown in Tble 4.

11 Density Functionl nd Ab Initio Study of Cr(CO) n J. Phys. Chem. A, Vol., No. 2, TABLE 4: Geometricl Prmeters (Lengths in Å, Angles in Deg), Scled C-O Stretching Vibrtionl Frequencies (cm - ), Dipole Moment (Debye), S 2, nd Reltive Energies (kcl/mol) of Bent Structures ( A, A, A, 7 A, nd 9 A ) of CrCO from DFT Clcultions Using 6-+G(df) Bsis Set (in Prentheses, Clculted Results Using the 6-+G(d) Bsis Set) BLYP BPW9 BP86 mpwpw9 BLYP BPW9 BP86 PBE exp A geom r(cr-c).79 (.789) r(c-o).72 (.77) CrCO 77.2 (77.0) freq A 77.8 (766.7) µ.62 (.804) b rel 72.7 (72.8) c rel 72.7 (72.8) A geom r(cr-c).799 (.769) r(c-o).8 (.7) CrCO 78.4 (77.) freq A (89.6) µ 6.94 (4.6) S (2.0) d rel 47.4 (4.9) e rel 47.4 (44.2) A geom r(cr-c) 2.04 (2.042) r(c-o).9 (.4) CrCO 6.9 (64.02) freq A (88.4) µ 0.66 (0.80) S (6.7) f rel 9.8 (0.) g rel 9.7 (0.) A geom r(cr-c) 2.20 (2.2) r(c-o).42 (.46) CrCO 9.48 (7.47) freq A (9.0) , j 97. k µ (0.827) S (2.004) A geom r(cr-c) 2.28 (2.26) r(c-o).27 (.280) CrCO 9.7 (97.09) freq. A 20.9 (7.7) µ 2. (2.744) S (20.009) h rel 6.2 (.) i rel. (4.2) The moleculr structures re depicted in Figure 6. b rel ) E( A ) - E( 7 A ). c rel ) H( A ) - H( 7 A ). d rel ) E( A ) - E( 7 A ). e rel ) H( A ) - H( 7 A ). f rel ) E( A ) - E( 7 A ). g rel ) H( A ) - H( 7 A ). h rel ) E( 9 A ) - E( 7 A ). i rel ) H( 9 A ) - H( 7 A ). j Reference 00. IR spectroscopy in Ar mtrices t 4 K. k Reference 06. Lser-blted generted Cr toms recting with CO 2 nd isolted in Ar mtrices. This prtil bond breking of C-O cn be rtionlized in the sme mnner s in the nonet stte of Cr(CO) 2. The LUMO of the R spin orbitl in the septet stte hs ntibonding chrcter for Cr-C nd C-O wheres the HOMO of β spin orbitl hs bonding chrcter (see Figure 4S in Supporting Informtion). Becuse the 9 A stte cn be considered to be formed from the septet stte by moving one electron from the HOMO of β spin orbitl to the LUMO of R spin orbitl of the septet s in Cr- (CO) 2, the bonding chrcter for Cr-C nd C-O is wekened nd the corresponding bond lengths re elongted. As shown in Tbles nd 4, ll liner structures in the quintet nd septet sttes re less stble thn the bent structure in ech spin stte. The results of NBO nlysis re listed in Tble 6S in the Supporting Informtion. The stbility of the bent structure cn be correlted with its stronger s chrcter in Cr-C bonding compred with tht in the liner structure. B. Bond Dissocition Energy nd Totl CO Binding Energy. The sequentil bond dissocition energies (BDEs) of Cr(CO) n (n ) -6) re summrized in Tble. In this work, we used t 298 K becuse this quntity is commonly designted s the BDE. 02,0 All clcultions provide resonble BDEs of Cr(CO) 6 tht gree well with the experimentl vlue but overestimte the BDE of Cr(CO). An exception is found in the BLYP nd BLYP functionls, which give reltively good results. There is uncertinty in determining the BDE of Cr(CO) 4 due to the fct tht the ground stte of Cr(CO) is not known, but the BDEs clculted using functionls for both possibilities (Cr(CO) 4 ( A ) f Cr(CO) ( B 2 ) + CO nd Cr(CO) 4 - ( A ) f Cr(CO) ( A ) + CO) re close to the experimentl vlue. The performnce of is worse in this regrd. Even more possibilities rise for the BDE of Cr(CO). All clcultions using functionls overestimte the experimentl BDE for ll chnnels, nd those using functionls provide vlues slightly closer to the experimentl one. The clculted BDEs of Cr(CO) 2 re underestimted compred with the experiment. Recently, we stisfctorily reproduced the BDE of CrCO using CCSD(T) in our previous study. 72 When the products (Cr(CO) 6 nd Cr(CO) ) re ll singlets, the BDEs clculted by DFT methods re resonble. However, if the products contin open shell chrcter, the clcultions using functionls generlly underestimte the BDEs becuse of the preference for high spin sttes. In contrst, generlly the results with functionls overestimte the BDEs. The totl CO binding energies for Cr(CO) 6 re summrized in Tble. The experimentl vlue corresponding to D o 298 is kcl/mol. 04 Wheres the results with functionls seriously overestimte the experimentl vlue, the BPW9 nd