Electron Affinities, Fluoride Affinities, and Heats of Formation of the

J. Phys. Chem. A 2010, 114, 7571–7582

7571

Electron Affinities, Fluoride Affinities, and Heats of Formation of the Second Row Transition Metal Hexafluorides: MF6 (M ) Mo, Tc, Ru, Rh, Pd, Ag) Raluca Craciun, Rebecca T. Long, and David A. Dixon* Department of Chemistry, The UniVersity of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336

Karl O. Christe Loker Hydrocarbon Research Institute and Department of Chemistry, UniVersity of Southern California, UniVersity Park, Los Angeles, California 90089 ReceiVed: March 13, 2010; ReVised Manuscript ReceiVed: June 1, 2010

High-level electronic structure calculations were used to evaluate reliable, self-consistent thermochemical data sets for the second row transition metal hexafluorides. The electron affinities, heats of formation, first (MF6 f MF5 + F) and average M-F bond dissociation energies, and fluoride affinities of MF6 (MF6 + Ff MF7-) and MF5 (MF5 + F- f MF6-) were calculated. The electron affinities are higher than those of the corresponding third row hexafluorides, making them stronger one-electron oxidizers. The calculated electron affinities, in good agreement with the available experimental values, are 4.23 eV for MoF6, 5.89 eV for TcF6, 7.01 eV for RuF6, 6.80 eV for RhF6, 7.95 eV for PdF6, and 8.89 eV for AgF6. The corresponding pentafluorides are also very strong Lewis acids, although their acidities on the pF- scale are about one unit lower than those of the third row pentafluorides. The performance of a wide range of DFT exchange-correlation functionals was benchmarked by comparing them to our more accurate CCSD(T) results. Introduction There is substantial interest in the development of strong electron acceptors which can serve as strong oxidizers. We have just reported the reliable prediction of the electron affinities of the MF6 compounds for the third row transition metals.1 We showed that the electron affinities increase monotonically from WF6 to AuF6 and that the inclusion of spin-orbit corrections is essential to obtain the correct qualitative order for the electron affinities. In addition, we predicted the fluoride affinities of the MF6 compounds and the corresponding pentafluorides. Our calculations show that these fluorides are strong Lewis acids. A new type of structure was predicted for PtF7- and AuF7with a very weak external MF6--F bond between an MF6fragment and a fluorine atom. We now extend our efforts to the second row transition metal MF6 compounds. MF6 molecules with the metal ion M in the +VI oxidation state surrounded by six F-’s in an octahedral field can exhibit Jahn-Teller distortions.2 For the second row transition metals, studies3-6 of the experimental vibrational spectra of TcF6 and RuF6 showed Jahn-Teller effects. Seppelt has reviewed the structures and properties of a series of main group, actinide, and transition metal hexafluorides, including MoF6, TcF6, RuF6, and RhF6.7 Experimentally, the M-F bond lengths have been found to be essentially the same for M ) Mo, Tc, and Ru and slightly longer for M ) Rh from single-crystal X-ray diffraction measurements.8 This is consistent with the result that, in the third row transition metal series, the M-F bond lengths for M ) W, Re, and Os are approximately the same, with the Ir-F and Pt-F bond lengths being longer.9 Holloway and coworkers10 found in their EXAFS study that the M-F bond * To whom correspondence should be addressed. E-mail: dadixon@ bama.ua.edu.

distance increased from Mo to Ru to Rh. Bartlett and coworkers11 used synchrotron X-ray powder diffraction to study the LiMF6 salts and obtained single-crystal data for KRhF6. A number of theoretical studies have predicted the M-F bond distances in MoF6,12-14 MoF6-,15 TcF6,12 RuF6,12 RhF6,12 PdF6,16 and AgF6-.17 Riedel and Kaupp have studied and extensively reviewed18 the highest oxidation state possible in transition metal compounds with an emphasis on the fluorides and oxyfluorides, for example, TcF7.19 For the second row transition metal hexafluorides, MoF6 has been the most studied in terms of its electron affinity (EA) both experimentally and theoretically. Mathur et al.20 set a lower limit for EA(MoF6) ) 4.5 eV from their study of ionization reactions between MoF6 and alkali metal atoms. Compton and coworkers21 also studied the collisions of alkali metal atoms with a series of hexafluorides including MoF6 and found that EA(MoF6) should be at least 5.1 eV. Sidorov and co-workers22 investigated the electron affinities of higher molybdenum fluorides by measuring the equilibrium constants of ion-molecule reactions using high temperature Knudsen cell mass spectroscopy and determined EA(MoF6) ) 3.6 eV; later, this group23 revised the value to EA(MoF6) ) 3.8 eV. This group24 also reported EA(RuF6) ) 6.47 eV and later23 revised it to EA(RuF6) ) 7.5 eV. These results showed that EA(RuF6) is higher than that of the corresponding third row OsF6 (EA ) 5.94 eV), in agreement with the observation that O2 can be oxidized to O2+ by RuF6, which in the third row hexafluorides does not occur until PtF6.25 Selig and co-workers26 estimated EA(TcF6) ) 6.94 eV based on the correlation of layer spacing and charge transfer with the electron affinities of transition metal hexafluorides intercalated into graphite. Bartlett27 found that the O2RhF6 salt is less stable toward dissociation to its constituent molecules than O2RuF6 and also has a larger unit cell volume, unlike the

10.1021/jp1022949  2010 American Chemical Society Published on Web 06/29/2010

7572

J. Phys. Chem. A, Vol. 114, No. 28, 2010

Craciun et al.

TABLE 1: MF6 Electron Affinities (eV) metal

calcda

experiment

Mo Tc Ru Rh Pd Ag

4.23 5.89 7.01 6.80 7.95 8.89

4.50,b >5.1,c 3.6,d 3.8e 7.5,e 6.47i

reactivity estimate 6.94h EA(WF6) by ∼2 eV. Adding an f function to the metal basis set and a d function to the fluorine basis set led to a value of 5.37 eV for EA(MoF6). Seppelt and co-workers12 predicted the electron affinities of MoF6, TcF6, RuF6, and RhF6 to be 4.11, 5.64, 6.98, and 6.60 eV, respectively, at the B3LYP level with the Hay-Wadt (n + 1) VDZ ECP basis set for the metals and the aug-cc-pVTZ basis set for F. The available experimental and calculated values of the electron affinities are summarized in Table 1. There are only a few experimental studies of the heats of formation of the second row transition metal hexafluorides and no theoretical predictions. For MoF6, the first reported value of -388 kcal/mol for ∆Hf,298 K(MoF6) is from solution calorimetry.29 A second value of -372.3 ( 0.2 kcal/mol is from direct combination of the elements in a bomb calorimeter.30 Molecular fluoride affinities provide an estimate of the Lewis acid strength of a given species.31 From the infrared spectra of UF6, WF6, and MoF6 complexes codeposited with hydrogen fluoride, the fluoride affinity of MoF6 was estimated to be greater than 70 kcal/mol.32 The prediction was based on the assumption of a linear relationship between the fluoride affinities and the frequency shift of the HF stretching mode in the complex. We describe here the results of high-level electronic structure calculations at the CCSD(T) level of the structures, electron affinities, heats of formation, first (MF6 f MF5 + F) and average M-F bond dissociation energies, and fluoride affinities (MF6 + F- f MF7-) of MF6 for M ) Mo, Tc, Ru, Rh, Pd, and Ag. We also report the fluoride affinities of MF5 as these can be directly calculated from our data. The electron affinities can be used in the development of a quantitative scale of the strength of very strong oxidizers. The electron affinity and the fluoride affinity often compete with each other, so good values for both are required for the design of the best oxidizing agent. In addition, we report on the ability of the DFT method to predict these energetic properties. Computational Methods We have followed the approach described in our previous paper on the third row transition metal hexafluorides.1 Equilibrium geometries and vibrational frequencies were calculated first at the density functional theory (DFT) level with a range of local, gradient-corrected, and hybrid exchange-correlation

functionals (see Supporting Information for a list of functionals) and then at the R/UCCSD(T) level.33-36 In this approach, a restricted open shell Hartree-Fock (ROHF) calculation was initially performed and the spin constraint was relaxed in the coupled cluster calculation.37-39 The DFT and CCSD(T) geometry optimizations were performed with the augmented correlation consistent aug-cc-pVnZ basis sets for F40 and the aug-cc-pVnZ-PP basis sets with the accompanying small-core relativistic pseudopotentials for the transition metal atoms with n ) D and/or T.41 We label this combination of basis sets as AnZ-PP. An additional single point CCSD(T) calculation with n ) Q at the CCSD(T)/aug-cc-pVTZ (or the best available) geometry was done for the energy extrapolation. The CCSD(T) energies were extrapolated to the complete basis set (CBS) limit by using a mixed Gaussian/exponential formula of eq 1:

E(n) ) ECBS + A exp[-(n - 1)] + B exp[-(n - 1)2] (1) with n ) 2 (aVDZ-PP), 3 (aVTZ-PP), and 4 (aVQZ-PP), as first proposed by Peterson et al.42 Our recent studies on the group VIB transition metal trioxide clusters have shown that the effect of the choice of the cardinal numbers in this extrapolation scheme is fairly small.43 Several corrections have been used to adjust the CBS valence electronic energies: (1) a core-valence correlation correction (∆ECV); (2) scalar relativistic corrections on the F atoms and corrections for any errors in the metal pseudopotentials for the electron affinities (EAs), with the latter calculated by taking the difference between the EA calculated at the Douglas-Kroll-Hess44 level with the CCSD(T)-DK method and the aT-DK basis set45-47 and the EA calculated at the CCSD(T)/aTZ-PP level (a separate estimate of just the pseudopotential error is described in the Supporting Information); (3) molecular spin-orbit corrections calculated using the spin-orbit approach and scalar two-component zero-order regular approximation (ZORA)48 as implemented in the ADF 2008.01 program;49 (4) the zero point energy calculated at the DFT level. The electron affinity was calculated as the sum of the different contributions (eq 2).

EA0 K ) EACBS + ∆(EAZPE) + ∆(EACV) + ∆(EARel) + ∆(EASO) (2) Total atomization energies (TAEs) for the prediction of the heats of formation were calculated using an equation similar to eq 2. In calculating the TAEs, we chose the lowest lying metal atomic state with no spin-orbit (SO) splitting, and used the experimental SO splittings if needed.50 The experimental atomic heats of formation at 0 K were taken from the JANAF Tables51 for F and from the compilation of Wagman et al.52 for the metals. The atomic heats of formation have also been given by Greenwood and Earnshaw,53 and these can be used to help provide an estimate of the range of errors for the molecular heats of formation due to the atomic heats of formation. The appropriate enthalpy change from 0 to 298 K (∆H0 Kf298 K) is 1.05 for F. For all the metal atoms we have used a value of 1.2 kcal/mol for ∆H0 Kf298 K as a best estimate from the available data.1 The initial DFT calculations were done with the Gaussian program system54 and the CCSD(T) calculations with the Molpro program system.55 The calculations were performed on computers at The University of Alabama, the Alabama Supercomputing Center, and the Molecular Sciences Computing

Thermochemical Calculations for MF6

J. Phys. Chem. A, Vol. 114, No. 28, 2010 7573

TABLE 2: Optimized Metal-Fluorine Bond Lengths (Å) and Bond Angles (deg) at the CCSD(T) Level with the ATZ-PP Basis Set and at the ADF/ZORA/BLYP Level with the TZ2P Basis Set for MF6 and MF6molecule

state/sym

MoF6

1

A1g/Oh

MoF6-

2

B2g/D4h

2

A1g/D3d

2

B2g/D4h

2

A1g/D3d

3

A1g/D4h

3

A1g/D3d

3

A1g/D4h

TcF6

TcF6-

RuF6

3

A1g/D3d

RuF6RhF6

4 4

A1g/Oh A1g/Oh

RhF6-

3

A1g/D4h

3

A1g/D3d

PdF6

3

A1g/D4h

CCSD(T)/ATZ-PP

state/sym, ZORA

ZORA/TZ2P

sym ZORA-SO

1.825 (×6)

1

A1g/Oh

1.870

Oh

1.855 (×2) 1.906 (×4) 1.888 91.9° 1.794 (×2) 1.827 (×4) 1.816 91.2° 1.903 (×2) 1.855 (×4) 1.871 90.4° 1.833 (×2) 1.804 (×4) 1.813 90.4° 1.860 (×6) 1.815 (×6)

2

A1g/D3d

1.932 91.9°

D4h

4

A1g/Oh A1g/Oh

1.921 1.883

Oh Oh

1.828 (×2) 1.870 (×4) 1.855 90.8° 1.850 (×2) 1.849 (×4)

3

A1g/D3d

1.924 90.6°

D4h

D3d 2

A1g/D3d

1.868 91.2°

D4h D3d

3

A1g/D3d

1.921 88.9°

D4h D3d

3

A1g/D3d

1.874 90.7

D4h D3d

4

D3d 3

A1g/Oh

1.911

D4h D3d

PdF6-

2

A1g/D4h

1.891 (×2) 1.847 (×4)

2

A1g/Oh

1.943

AgF6

2

B2g/D4h

1.904 (×2) 1.874 (×4)

2

A1g/Oh

1.948 (×2) 1.950 (×4)

AgF6-

1

A1g/Oh

1.884 (×6)

1

A1g/Oh

1.959

a

b

D4h Oh Oh Oh

ZORA-SO/TZ2P 1.870 1.936 (×2) 1.931 (×4) 1.933 91.7° 1.871 (×2) 1.866 (×4) 1.867 91.3° 1.909 (×2) 1.928 (×4) 1.923 88.8° 1.889 (×2) 1.868 (×4) 1.876 90.3° 1.921 1.883 1.937 (×2) 1.919 (×4) 1.924 89.6° 1.916 (×2) 1.908 (×4) 1.910 90.1° 1.939 (×2) 1.944 (×4) 1.942 1.947 (×2) 1.949 (×2) 1.951 (×2) 1.960

expt 1.817a 1.809b

1.812a

1.818a 1.824b 1.851c 1.824a 1.838b 1.855c 1.853c

c

Reference 12. Reference 10. Reference 11.

Facility in the William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory. Results and Discussion Geometries of the Hexafluorides. Table 2 lists the metalfluorine bond distances of the neutral hexafluorides and their anions optimized at the CCSD(T) levels with aTZ-PP basis set and the ZORA and ZORA-SO BLYP/TZ2P levels. The Cartesian coordinates as well as the geometries optimized with the various DFT exchange correlation functionals and the CCSD(T)/ aDZ-PP method are given as Supporting Information. We explored a variety of structures (symmetries) and orbital combinations in our studies of the open shell molecules in order to obtain the ground state structures. We have previously discussed1 the geometry behavior on the orbital occupancies of the t2g orbitals that are being filled for the third row transition metal atoms, and the same models apply here. The T1 diagnostics56 are given as Supporting Information for all molecules at the CCSD(T)/aTZ-PP level. The values, in general, fall between 0.02 and 0.04, typical of what we have found for many transition metal compounds,1,43,57,58 so most are dominated by a single reference configuration. MoF6. The calculated Mo-F bond distance for MoF6 (Oh) of 1.825 Å is in good agreement with the value of 1.817 Å reported by Seppelt12 in a single crystal structure determination and that of 1.809 Å reported by Holloway10 in the EXAFS study

of MF6 (M ) Mo, Ru, and Rh). The ZORA-SO/BLYP/TZ2P bond distance for MoF6 is 1.870 Å, too long as compared to the CCSD(T) and the measured values. MoF6- and TcF6. The D4h structures of MoF6- and TcF6 have two short and four long bond distances with averages of 1.889 Å for r(Mo-F) and 1.816 Å for r(Tc-F). The Oh structures, with the M-F bond distance calculated as the average of the bonds in the D4h structures, were found to be less than 1 kcal/mol higher in energy than the D4h structures for both MoF6and TcF6. The Mo-F and Tc-F bond lengths in the D3d structures, which have essentially the same energy as the D4h structure at the CCSD(T)/CBS level, are 1.888 Å for r(Mo-F) and 1.816 Å for r(Tc-F). Our calculated value for r(Tc-F) is in excellent agreement with the experimentally determined value12 of 1.812 Å. ZORA-SO predicted that the D4h structures for both MoF6- and TcF6 are less than 1 kcal/mol lower in energy than the D3d structures. For both MoF6- and TcF6 at the ZORA-SO level, the D4h structures have two long and four short bond distances (an opposite bonding pattern from the predicted CCSD(T) structure) that differ by only 0.005 Å. Energetically, the D4h structures are lower at the CCSD(T)/CBS and ZORASO levels, but after all corrections are included, the MoF6- D3d structure is 1.1 kcal/mol lower in energy and the TcF6 D3d structure has basically the same energy, being lower by only 0.04 kcal/mol. (See Figure 1 for energy splittings.) The D3d

7574

J. Phys. Chem. A, Vol. 114, No. 28, 2010

Craciun et al.

Figure 1. Schematic energy level diagram for use in predicting the molecular electron affinities for the MF6 molecules in kcal/mol.

structure becomes lower in energy due to the difference in zero point energies. TcF6- and RuF6. The 3A1g/D4h structure is predicted to be the ground state for TcF6- with the 1A1g/D4h structure 29.1 kcal/ mol higher in energy at the CCSD(T)/ADZ-PP level. The 3A1g/ D3d structure, after all corrections have been included, is above the 3A1g/D4h structure by 0.6 kcal/mol. For RuF6, the 1A1g/D4h structure is 23.4 kcal/mol above the 3A1g/D4h structure. The 3A1g/ D3d structure is predicted to be higher than the 1A1g/D4h structure by 0.54 kcal/mol at the CBS level, but lower by 0.24 kcal/mol at the ZORA-SO level, and after all corrections are included, the 3A1g/D3d structure is more stable by almost 2 kcal/mol. This is mostly due to the difference in the zero point energies. As for MoF6- and TcF6, the Oh geometries are less than 1 kcal/ mol above the D4h structures. The two long and four short bond distances in the D4h structures of both TcF6- and RuF6 average to 1.871 and 1.814 Å, respectively, and the D3d structures have the same values. Our calculated average value for r(Ru-F) is in excellent agreement with the values of 1.818 Å reported by Seppelt12 and of 1.824 Å reported by Holloway.10 ZORA-SO/ BLYP/TZ2P predicts an average bond distance of 1.921 Å for the TcF6- D4h structure with two short and four long bond distances. The more stable D3d structure at ZORA-SO in the case of RuF6 shows a r(Ru-F) bond length of 1.876 Å, longer than the experimental and CCSD(T) values by ∼0.05 Å. RuF6- and RhF6. Both RuF6- and RhF6 have Oh symmetry. The calculated Ru-F bond distance of 1.860 Å is very close to the value of 1.851 Å reported by Bartlett and co-workers11 in the X-ray powder diffraction study of the LiRuF6 salt. The calculated Rh-F bond distance of 1.815 Å is also close to the measured values of 1.82412 and 1.838 Å.10 ZORA-SO predicts Oh structures with bond distances of 1.921 Å for r(Ru-F) and 1.883 Å for r(Rh-F), again too long as compared to experiment. RhF6- and PdF6. At the CCSD(T)/CBS level, the 3A1g/D4h structure is predicted to be the ground state for both RhF6- and PdF6. The 1A1g/D4h structure is higher by 24.1 and 11.5 (12.1 CCSD(T)/CBS) kcal/mol for RhF6- and PdF6, respectively, at the CCSD(T)/ADZ-PP level, and the Oh structure is within 0.5 kcal/mol of the ground state structure for both. ZORA-SO predicts the D3d structure to be more stable by 0.16 and 0.13 kcal/mol for both RhF6- and PdF6, and after all corrections are

included, the D3d structure remains lower in energy than the D4h structure for RhF6-. The calculated values of 1.856 Å for r(Rh-F) in the D4h structure and of 1.855 Å in the D3d structure are in excellent agreement with the experimentally determined values of 1.855(5) Å11 and 1.853(1) Å.59 Our calculated average value of 1.849 Å for r(Pd-F) is consistent with the value of 1.852 Å for r(Pt-F) determined from electron diffraction measurements.9 A calculated value of 1.89360 at the B3LYP level with a smaller basis set than ours is clearly too long. The T1 diagnostic is reasonable for the singlet state of PdF6 but is somewhat higher for the triplet state, suggesting that this state may have some multireference character. The T1 diagnostic for RhF6- is a normal value for this type of compound. PdF6- and AgF6. The D4h structure has two long bonds and four short bonds with average values of 1.862 Å for PdF6- and 1.884 Å for AuF6. At the CCSD(T)/CBS level, the D4h structure is predicted to be more stable than the D3d structure by 0.87 kcal/mol for PdF6- and less stable by 0.56 kcal/mol for AgF6. The Oh structure is 0.6 kcal/mol higher in energy than the D4h structure for PdF6- and 0.8 kcal/mol higher than the D3d structure for AgF6, both at the B3LYP/ADZ-PP level. After all corrections are included, the ground state for PdF6- is predicted to be the D4h structure and for AgF6 is predicted to be the D3d structure. At the ZORA-SO level, the D4h and D3d structures for PdF6have essentially the same energy within 0.1 kcal/mol with an average bond distance of 1.942 Å, and AgF6 is predicted to be octahedral with a bond length of 1.949 Å. AgF6-. The AgF6- anion has Oh symmetry with a calculated Ag-F distance of 1.884 Å at the CCSD(T)/aDZ-PP level and 1.960 Å at the ZORA-SO level. A calculated value of 1.920 Å was reported from an MP2 optimization.61 The average calculated M-F bond distances show a slight decrease from MoF6 to TcF6 with r(Tc-F), r(Ru-F), and r(Rh-F) being essentially the same and an increase to PdF6 and AgF6. The experimental gas phase values for rg(M-F), M ) Mo to Rh, are essentially the same within 0.008 Å. The average calculated M-F bond distances in the MF6- anions decrease from 1.889 Å for Mo-F to 1.856 Å for Rh-F and increase to 1.862 Å for Pd-F and 1.884 Å for Ag-F. Our calculated value for r(Ru-F) in RuF6- is within 0.009 Å of the powder diffraction value.11

Thermochemical Calculations for MF6

J. Phys. Chem. A, Vol. 114, No. 28, 2010 7575

TABLE 3: Experimental and Calculated MF6 Vibrational Frequencies (cm-1) and IR Intensities (km/mol) in Parentheses at the B3LYP/ATZ-PP or BP86/ADZ-PP Level a1g M

state/sym a

Mo Tcd

Rua

Rha Pda Agd

d

1

calc

eg expt

A1g/Oh A1g/D3d

734 671

741

2

2

B2g/D4h

672

3

A1g/D3d

696

3

A1g/D4h

4 3

2

b

calc

t1u expt b

641 499

652

713b

a1g 612 b1g 606 463

[639]e

695

[675]f

[624]e

A1g/Oh A1g/D4h

665 608

[634]f

B2g/D4h

515

b1g 630 a1g 624 603 a1g 569 b1g 580 a1g 502 b1g 505

[595]f

calc 731(652) eu 707 (426) a2u 696 (211) a2u 716 (219) eu 696 (208) a2u 735 (223) eu 729 (444) eu 735 (436) a2u 721 (224) 724 (525) a2u 692 (124) eu 671 (80) a2u 624 (59) eu 587 (11)

t1u expt 741

b

748c

735f 724f

calc 250(93) eu 271 (30) a2u 267 (16) eu 277 (24) a2u 232 (27) eu 297 (28) a2u 275 (18) a2u 313 (9) eu 269 (42) 288 (52) eu 296 (18) a2u 240 (24) a2u 271 (0) eu 258 (20)

t2g expt 264

c

265c

275f 283f

calc 300 a1g 275 eg 262 eg 357 b2g 237 a1g 284 eg 239 eg 372 b2g 320 275 eg 271 b2g 218 b2g 250 eg 193

t2u expt 318

b

[297]e

[283]e [269]f

calc

expt

112(0) eu 152 (6) a2u 128 (0) eu 161 (2) b2u 109 (0) a2u 206 (0) eu 141 (6) b2u 204 (0) eu 148 (5) 182 (0) eu 206 (16) b2u 130 (0) b2u 195 (0) eu 194 (2)

[116]b

a B3LYP/AVZ-PP. b Reference 3. Experimental values in brackets calculated from combination bands or overtones. BP86/ADZ-PP. e Reference 4. f Reference 6.

Vibrational Frequencies. The six normal modes for MF6 with Oh symmetry are ν1(a1g), ν2(eg), ν3(t1u), ν4(t1u), ν5(t2g), and ν6(t2u). Under the Jahn-Teller distortion from Oh to D4h, the vibrational modes split as follows: a1g f a1g, eg f a1g + b1g, each of the two t1u f a2u + eu, t2g f b2g + eg, and t2u f b2u + eu. Under the Jahn-Teller distortion from Oh to D3d, the modes split as follows: a1g f a1g, eg f eg, each of the two t1u f a2u + eu, t2g f a1g + eg, and t2u f a2u + eu. In Table 3, the experimental frequencies3-6 are compared to those calculated at the B3LYP/ATZ-PP and/or BP86/ADZ-PP levels. MoF6 and RhF6, which have Oh symmetry, do not exhibit splittings of the vibrational modes. Our calculated B3LYP/ATZPP values for MoF6 are smaller than the experimental values by 7-18 cm-1, showing excellent agreement between theory and experiment.3,5 For RhF6, the B3LYP/ATZ-PP values for all modes except for the a1g one are larger by up to 10 cm-1, in good agreement with the experimental values.6 The calculated value for the a1g mode is larger than the experimental value by ∼30 cm-1. Weinstock6 described the Jahn-Teller effect on the eg vibrational mode of the 4d and 5d hexafluoride molecules. He noted that the low intensity and the broad shape of the ReF6 and OsF6 ν2(eg) vibrational modes are evidence for the Jahn-Teller effect. For the 4d MF6 molecules, the broadening was even more pronounced for TcF6, and for RuF6, the unusually large splitting did not allow for the assignment of the bandwidth. Our calculated BP86/ADZ-PP frequencies for D4h TcF6 can be compared to the experimental values.3-5 The a1g stretch is smaller than the experimental value3 by 41 cm-1 and there is a small splitting of 6 cm-1 of the eg mode. There are larger splittings of the t1u modes, of 20 and 45 cm-1, with their averages being in reasonable agreement with the experiment.5 The t2g scissoring mode shows a large splitting of 120 cm-1, but the average is qualitatively in agreement with experiment.4 The value of the t2g splitting is smaller than that of 253 cm-1 predicted1 for the corresponding third row hexafluoride ReF6. The D3d structure of TcF6 shows frequencies similar to those of the D4h structure. The t2g splitting is 13 cm-1 in the D3d structure, much lower than that in the D4h structure. The eg mode does not split under D3d symmetry and is 110 cm-1 lower than the average of the a1g and b1g modes in D4h symmetry, and 140 cm-1 lower than the experimental value. This suggests that TcF6 has D4h symmetry.

c

[145]b

[186]e [192]f

Reference 5.

In the other MF6 compounds, the t2g scissoring mode shows splitting ranging from 52 to 57 cm-1. For the D4h structures of TcF6 (BP86/ADZ-PP) and PdF6 (B3LYP/ATZ-PP), the eg mode has the higher frequency, whereas for the AgF6 D4h structure the b2g mode has the higher frequency. This behavior can be explained1 by the two different types of bonding that appear on lowering the symmetry from Oh to D4h when the Oh t2g mode splits into a b2g equatorial scissoring mode and an eg axial scissoring mode. For TcF6 and PdF6 there are two shorter M-F axial bonds which lead to the eg axial mode having the higher frequency. For AgF6 (BP86/ADZ-PP) there are four shorter equatorial bonds which lead to the b2g equatorial scissoring mode having the higher frequency. The B3LYP/ATZ-PP calculated values for the frequencies of the RuF6 D4h and D3d structures are similar to those of TcF6 (BP86/ADZ-PP). For both geometries, the a1g stretch is larger than experiment6 by 20 cm-1. The eg mode splits by 14 cm-1 in the D4h structure and is larger by 3 cm-1 than the experimental value,4 whereas in the D3d structure, it is lower than experiment by 161 cm-1 and does not split. The t1u modes split by 14 and 44 cm-1 in the D4h structure, and their averages are within 10 cm-1 of the experimental values.6 In the D3d structure, the t1u modes split by 6 and 22 cm-1, with the averages being within 14 cm-1 of experiment.6 Our calculated values show larger splittings for the t2g and t2u modes. In the D4h structure, the t2g mode splits by 52 cm-1 and the t2u mode splits by 56 cm-1. In the D3d structure, the splittings are 45 and 65 cm-1 for the t2g and t2u modes, respectively. The presence of the Jahn-Teller effect and the resulting energetically close lying structures can account for the differences between the calculated harmonic frequencies and the observed anharmonic frequencies. The calculated frequencies are obtained from the second derivatives at a minimum energy structure. The energetically low lying structures around the conical intersection could make the actual potential energy surface quite anisotropic, leading to large anharmonicities. This is expected to be most pronounced for the bends which are the Jahn-Teller distortion modes. This type of issue has been dealt with in the case of closed shell XeF6, which has a number of low lying structures62 by using a crystal-field model;63 however, the detailed coupling is more complex in the current molecules and a more detailed treatment of the vibrational spectra is beyond the scope of the current work. Our results are consistent

7576

J. Phys. Chem. A, Vol. 114, No. 28, 2010

Craciun et al.

TABLE 4: Energy Components for Calculated Electron Affinities (kcal/mol) M Mo Tc Ru Rh Pd Ag

MF6 state/sym

MF6- state/sym

1

2

1

2

A1g/Oh A1g/Oh 2 A1g/D3d 2 B2g/D4h 2 A1g/D3d 3 A1g/D4h 3 A1g/D3d 4 A1g/Oh 4 A1g/Oh 3 A1g/D4h 3 A1g/D3d 2 B2g/D4h 2 A1g/D3d

B2g/D4h A1g/D3d 3 A1g/D4h 3 A1g/D4h 3 A1g/D3d 4 A1g/Oh 4 A1g/Oh 3 A1g/D4h 3 A1g/D3d 2 B2g/D4h 2 A1g/D3d 1 A1g/Oh 1 A1g/Oh

∆ECBSa

∆EZPE

∆ECVb

∆Erelc

EA

SOd

EA + SO

96.41 96.21 132.03 131.73 131.18 165.28 165.82 155.79 155.20 183.54 185.61 205.25 204.68

e

0.30 0.19 -0.54 -0.56 -0.47 -1.17 -1.28 -1.17 -1.10 -0.74 0.87 -0.19 0.62

-0.93 -0.61 3.95 3.95 3.94 -1.43 -2.41 -0.30 0.32 -0.14 -1.49 -0.22 -4.92

96.09 97.26 135.77 135.95 135.41 163.68 162.25 154.83 155.54 182.87 185.31 204.94 200.37

0.27 0.20 0.17 0.03 -0.06 -0.41 -0.64 1.08 1.24 0.45 0.23 -0.03 -0.87

96.4 97.5 135.9 136.0 135.3 163.3 161.6 155.9 156.8 183.3 185.5 204.9 199.5

0.31 1.47e 0.33e 0.83e 0.76e 1.00f 0.12f 0.51e 1.12e 0.21f 0.32f 0.10e -0.01e

a Valence CCSD(T) electronic energy contribution extrapolated using the mixed Gaussian/exponential formula. b Core-valence correction obtained at the CCSD(T)/awCVTZ level. c ∆(EARel) ) EA(CCSD(T)-DK/aT-DK) - EA(CCSD(T)/ATZ-PP). d Spin-orbit correction from BLYP/ZORA + SO/TZ2P calculation. e BP86/ADZ-PP. f B3LYP/ATZ-PP.

with this analysis in that the molecules MoF6 and RhF6 which are not required to exhibit a Jahn-Teller distortion would be expected to have normal, small anharmonic effects and the calculated harmonic frequencies for these two molecules do show very good agreement with the anharmonic experimental values. The differences between the calculated and the experimental3-6 zero point energies (ZPEs) are given in Table 6. All ZPEs calculated at the B3LYP/ATZ-PP level, except for RuF6, are within 0.3 kcal/mol of the experimental values, as is the ZPE calculated at the BP86/ADZ-PP level for TcF6. The calculated ZPE for RuF6 is 0.6 kcal/mol smaller than experiment. Electron Affinities and Oxidizer Strengths. Table 4 lists the valence CBS energies, the various additive energy corrections, and the calculated composite electron affinities. In Table 1, the electron affinities are compared with the experimental values. The ZPE corrections, calculated at the BP86/ADZ-PP or B3LYP/ATZ-PP levels, slightly increase the electron affinities (except for the EAs of the D3d structure of AgF6), whereas the core-valence corrections, calculated at the CCSD(T)/awCVTZ level, slightly decrease the electron affinities except for MoF6 and the D3d structures of PdF6 and AgF6. An energy diagram showing the different states for the anions and neutrals used in predicting the electron affinities is shown in Figure 1. The SO correction (Table 4) to the EA was calculated as the difference between EA(ZORA + SO) and EA(ZORA). The electron affinities calculated with ZORA and ZORA + SO are given in the Supporting Information. The SO corrections increase the electron affinities for MoF6, TcF6, RhF6, and PdF6 and decrease those for RuF6 and AgF6; all of the SO corrections are small and are within 1.3 kcal/mol. We were specifically interested in the SO effect on the electron affinities of RuF6 and RhF6. The SO effect slightly decreases EA(RuF6) by 0.41 kcal/mol and slightly increases EA(RhF6) by 1.24 kcal/mol. The addition of the SO corrections to the CCSD(T)/CBS values does not reverse the order of the electron affinities for RuF6 and RhF6. This is in contrast to the difference in the electron affinities of OsF6 and IrF6, where the inclusion of molecular spin-orbit corrections inverted the order of the EAs from that at the CCSD(T)/CBS level and proved to be essential for predicting the correct monotonic increase of the EAs in the third row MF6 compounds. This is consistent with the fact that the relativistic effects should be much smaller in the second row than in the third row transition metal compounds. Each second row transition metal hexafluoride has an electron affinity that is larger than the corresponding third row species in the same column, making them more powerful oxidizers.

TABLE 5: Electronic Component of the Adiabatic Electron Affinities of MF6, Vertical Electron Detachment Energies (VDEs) of MF6-, and Vertical Electron Attachment Energies (VAEs) of MF6 (kcal/mol) Calculated at the CCSD(T)/ ATZ-PP Level metal Mo Tc Ru Rh Pd Ag

MF6 state/sym

MF6- state/sym

1

2

2

3

A1g/Oh A1g/D3d 3 A1g/D3d 4 A1g/Oh 3 A1g/D4h 2 A1g/D3d

A1g/D3d A1g/D4h 4 A1g/Oh 3 A1g/D3d 2 B2g/D4h 1 A1g/Oh

a VDE ) Eneutral at anion geom - Eanion. Eanion at neutral geom.

ADE

VDEa

VAEb

95.4 131.1 164.6 152.8 180.7 201.4

105.7 144.4 173.4 160.8 188.1 202.9

88.6 122.8 162.1 149.7 179.7 201.4

b

VAE ) Eneutral -

In Table 1, our calculated electron affinities are compared to those either determined experimentally or predicted from lower level calculations. There has not been a consensus for EA(MoF6). The reported values range from 3.6 eV to at least 5.1 eV. Our calculated value of 4.23 eV is closest to the value of 4.5 eV reported by Mathur.20 Our calculated value for EA(RuF6) falls halfway between the experimental values of 7.523 and 6.47 eV.24 Our results support the conclusion of Bartlett27 that the EA(RuF6) is greater than that of RhF6. Lower level DFT calculations for the EAs of MoF6, TcF6, RuF6, and RhF6 are only in qualitative agreement with our CCSD(T)/CBS values. Vertical electron detachment (VDE) and attachment (VAE) energies have been calculated for the second row transition metal hexafluorides at the different levels of theory with the ATZ-PP basis set (Table 5). The VDEs of MF6- are larger than the adiabatic EAs by up to ∼14 kcal/mol, and the VAEs are smaller than the adiabatic EAs by up to 11 kcal/mol, with the largest differences between the VDEs and VAEs and the adiabatic EAs occurring for the earlier transition metal atoms. For example, for Ag, the adiabatic EA, VDE, and VAE are all within 1.5 kcal/mol of each other. Based on their extraordinarily high electron affinities, all the second row transition metal hexafluorides fall in the category “superhalogens”, a term created in 1981 for compounds having electron affinities exceeding those of the halogens (3.0-3.6 eV).64 The high EA of 8.89 eV for AgF6 would make it a better superhalogen than AuF6 with EA ) 8.20 eV. Heats of Formation. Total atomization energies (Table 6) for the prediction of ∆Hf,0 K and ∆Hf,298 K (Table 7) were calculated at the CCSD(T)/CBS level. The ground states of Mo (7S3), Tc (6S1/2), Pd (1S0), and Ag (2S1/2) do not have any

Thermochemical Calculations for MF6

J. Phys. Chem. A, Vol. 114, No. 28, 2010 7577

TABLE 6: Energy Components for Atomization Energies of MF6 (kcal/mol) at 0 K (∑D0) M

state/sym

Mo Tc Ru Rh Pd Ag

1

A1g/Oh B2g/D4h 2 A1g/D3d 3 B2g/D4h 3 A1g/D3d 4 A1g/Oh 3 A1g/D4h 2 B2g/D4h 2

∆ECBSa

∆EZPE

649.54 562.25 561.94 476.79 476.25 396.19 264.24 175.90

-8.86 (-9.09) -8.81h (-9.09)g -8.32h -9.37f (-9.98)g -8.49f -8.98f (-8.90)g -8.47f -7.71h f

g

∆ECVb

∆Erelc

atomic ∆ESOd

∑D0,0 Ke

0.06 2.40 2.37 3.95 4.09 6.62 10.59 6.90

2.65 1.69 1.68 0.66 1.64 -0.77 -0.37 -1.03

-2.33 -2.33 -2.33 -6.27 -6.27 -6.59 -2.33 -2.33

641.06 555.19 555.34 465.76 467.22 386.46 263.65 171.73

a ∆E ) ∆E(M) + 6[∆E(F)] - ∆E(MF6). b CCSD(T)/awCVTZ-DK. c ∆(EARel) ) EA(CCSD(T)-DK/aT-DK) - EA(CCSD(T)/ATZ-PP). d The spin-orbit splitting is -0.39 kcal/mol for the (2P3/2) state of F; 0.00 kcal/mol for the ground states (7S3) of Mo, (6S1/2) of Tc, (1S0) of Pd, and (2S1/2) of Ag; and 3.94 kcal/mol for Ru (5F5) and 4.26 kcal/mol for Rh (4F9/2). e ∑D0,0 K ) ∆ECBS + ∆EZPE + ∆ECV + ∆Erel + ∆ESO. f B3LYP/ATZ-PP. g Experimental ZPEs. h BP86/ADZ-PP.

TABLE 7: Heats of Formation of MF6 (kcal/mol) at 0 and 298 K (∆Hf,0 K and ∆Hf,298 K) Calculated at the CCSD(T) Levela state/ sym

∆Hf,0 Kb

∆Hf,298 Kb

∆Hf,0 Kc

∆Hf,298 Kc

expt

A1g/Oh

-373.3

-374.9

-371.5

-373.1

B2g/D4h A1g/D3d 3 B2g/D4h 3 A1g/D3d 4 A1g/Oh 3 A1g/D4h 2 B2g/D4h

-282.5 -282.7 -201.7 -203.2 -142.9 -62.6 7.0

-284.3 -284.3 -203.8 -204.9 -144.6 -64.3 5.5

-388,29 -372.3 ( 0.230

-201.9 -203.4 -142.7 -62.7 7.0

-204.0 -205.1 -144.5 -64.4 5.5

M Mo

1

Tc

2 2

Ru Rh Pd Ag

a Heat of formation of F from the JANAF Tables. ∆Hf,298 K(MF6) ) ∆Hf,0 K(MF6) + ∆H0 Kf298 K(MF6) - ∆H0 Kf298 K(M) 6[∆H0 Kf298 K(F)]. The experimental enthalpy change from 0 to 298 K (∆H0 Kf298 K) is 1.05 for F. For the metal atoms we have used a value of 1.20 kcal/mol. b Wagman et al.52 values for all metals. c Greenwood and Earnshaw53 values for all metals.

spin-orbit splitting, so they are used directly to calculate the TAEs. For Ru and Rh, there are no convenient low lying excited states, so we used the experimental ground states of Ru (5F5) and Rh (4F9/2) with J-averaged spin-orbit corrections of -3.94 and -4.26 kcal/mol, respectively. The TAEs decrease in the series from MoF6 to AgF6, just as in the third row series, and are ∼100 kcal/mol lower than the TAEs of the corresponding third row transition metal hexafluorides in the same column. In Table 7, our calculated heats of formation are compared with the available experimental values. Our calculated value of -374.9 kcal/mol for ∆Hf(MoF6) is in excellent agreement with the value of -372.3 ( 0.2 kcal/mol from the direct combination of the elements in a bomb calorimeter,30 and slightly less negative than the value of -388 kcal/mol from a solution calorimetry experiment.29 Besides errors in the electronic structure calculations, the major errors in the calculated heats of formation arise from the experimental heats of formation of the metal atoms, as the heats of formation of these transition metal atoms in the gas phase are not as well established and have larger error bars than those of most main group elements (see Supporting Information). Another source of error is the molecular spin-orbit effect, which was not included in the calculated heats of formation because of the difficulty in calculating the appropriate quantities for the atoms. However, based on the electron affinity calculations, we do not expect this contribution to be large. Bond Dissociation Energies. Total atomization energies have been used to calculate the average adiabatic bond dissociation energies (BDEs) (Table 8). The average BDEs decrease in the series from Mo to Ag. The average BDEs range from 106.8 kcal/mol for MoF6 to 28.6 kcal/mol for AgF6. This decrease in

the average bond energies with filling of the t2g orbitals was also predicted for the third row hexafluorides. The second row hexafluorides have smaller BDEs than the corresponding third row compounds. For example, the average bond dissociation energy in PdF6 is ∼18 kcal/mol lower than that in PtF6. The first adiabatic M-F BDEs have also been calculated at different levels of theory from the reaction MF6 f MF5 + F with all species in their ground states. DFT optimized geometries at the B3LYP/ADZ-PP level as well as scalar relativistic ZORA and ZORA-SO optimized geometries at the BLYP/TZ2P level are given in the Supporting Information. The geometries of the MF5 molecules depend on the way the 4d orbitals split in the trigonal bipyramidal (D3h) and square pyramidal (C4V) ligand fields. MoF5 with one 4d electron distorts to a C2V (2A2) structure with an average bond length of 1.849 Å. TcF5 with two 4d electrons has, at the B3LYP/ADZ-PP level, a 3A1′/D3h ground state with an average bond length of 1.839 Å, 8.7 kcal/mol more stable than the C4V structure. RuF5 with three 4d electrons has a 4B1/C4V ground state with an average bond distance of 1.842 Å. The most stable state for RhF5 is the 3B2/C2V state with an average bond distance of 1.842 Å. The singlet, triplet, and quintet C4V states are 16.2, 4.0, and 5.8 kcal/mol, respectively, higher in energy. The PdF5 2B1/C4V ground state has an average bond distance of 1.856 Å. AgF5 has a 1A1/C4V ground state with an average bond distance of 1.880 Å. The triplet C4V and D3h states are higher in energy by 1.7 and 3.1 kcal/mol, respectively, at the B3LYP/ADZ-PP level. The average M-F bond distances in the MF5 series are approximately constant for the first four metals and increase for Pd and Ag, following the same trend as for the hexafluorides. The calculated first adiabatic BDEs follow the same trend as the average BDEs, decreasing from Mo to Ag, and, in all cases, are significantly lower than the average BDEs by up to 39 kcal/ mol. For the first BDEs, there is a large change of more than 30 kcal/mol from MoF6 to TcF6 and a much smaller decrease of less than 10 kcal/mol from TcF6 to RuF6. The first BDE in RhF6 is only 3 kcal/mol less than that in RuF6. There is a much larger change again in the first BDE between RhF6 and PdF6 than between PdF6 and AgF6. We predict that AgF6 is thermodynamically unstable with respect to loss of an F atom to form AgF5. For all species, the spin-orbit corrections to the first BDEs were calculated to be less than 2 kcal/mol. In general, the spin-orbit effect reduces the first BDE except for M ) Ru and Pd, where the first BDE is slightly increased by up to 0.5 kcal/mol. Fluoride Affinities and Lewis Acidities. Table 9 lists the valence CBS energies and the various additive corrections included in the calculation of the MF6 fluoride affinities. The

7578

J. Phys. Chem. A, Vol. 114, No. 28, 2010

Craciun et al.

TABLE 8: Calculated Energy Components for the First Adiabatic and Average M-F Bond Dissociation Energies for MF6 (kcal/mol) Calculated at CCSD(T) Level M

MF5 state/sym

Mo Tc

MF6 state/sym

2

1

3

2

A2/C2V A1′/D3h 3 A1′/D3h 4 B1/C4V 4 B1/C4V 3 B2/C2V 2 B1/C4V 1 A1/C4V

Ru Rh Pd Ag

A1g/Oh B2g/D4h 2 A1g/D3d 3 A1g/D4h 3 A1g/D3d 4 A1g/Oh 3 A1g/D4h 2 B2g/D4h

∆ECBSa

∆EZPE

∆ECVb

∆Erelc

∆ESOd

first BDEe

avg BDEf

87.6 52.1 51.8 37.7 37.1 43.9 41.5 -0.40

-2.09g -2.01h -1.51h -2.14g -1.55g -2.00g -1.69g -1.82h

0.62 1.86 1.83 2.41 2.52 2.59 4.91 2.02

0.43 1.14 1.13 5.78 6.76 -0.60 -0.12 0.12

-0.54 -0.10 -0.24 -0.03 0.21 -1.65 0.51 -0.62

86.0 53.0 53.0 43.7 45.0 42.2 25.9 -0.2

106.8 92.5 92.6 77.6 77.9 64.4 43.9 28.6

a Extrapolated using the mixed Gaussian/exponential formula. b CCSD(T)/awCVTZ. c ∆(EARel) ) EA(CCSD(T)-DK/aT-DK) EA(CCSD(T)/ATZ-PP). d SO correction at the ADF ZORA BLYP/TZ2P level plus the experimental spin-orbit correction of -0.39 kcal/mol for F. e First BDE calculated as the sum of ∆ECBS and all corrections. f BDE ) ∑D0,0 K(MF6)/6. g B3LYP/ADZ-PP. h BP86/ADZ-PP.

TABLE 9: MF6 Fluoride Affinities (kcal/mol) Calculated at CCSD(T) Level for the Lowest Energy Classical and Nonclassical Structures M Mo Tc Ru Rh Pd Ag

d

MF6 state/sym 1

A1g/Oh 1 A1g/Oh 2 A1g/D3d 2 A1g/D3d 3 A1g/D3d 3 A1g/D3d 4 A1g/Oh 4 A1g/Oh 3 A1g/D4h 3 A1g/D4h 2 B2g/D4h 2 B2g/D4h

MF7- state/sym 1

A1/C2V 3 A′/Cs 2 A2/C2V 4 A′′/Cs 3 A1′/D5h 5 A′′/Cs 2 B1/C2V 4 A′′/Cs 1 A1′/D5h 3 A′/Cs 2 B2/C2V 2 A′/Cs

CCSD(T)/ADZ-PP

CCSD(T)/ATZ-PP

∆ECBSa

∆EZPE

∆ECVb

∆Esrc

∆ESOd

74.11 25.05 77.82 61.75 85.22 94.18 63.17 78.79 88.66 107.91 100.20 126.77

76.23 19.47 78.05 55.78 85.08 88.34 63.10 75.27 88.86 105.63 99.22 127.14

75.49

-1.30e 0.08e -0.88e -0.32e -1.49e -0.25e -0.28f 0.04f -0.95g -0.32e -0.36e 0.70f

0.06

-0.24 -0.07 -0.21 -0.08 -0.19 -0.10 -0.13 -0.12 -0.17 -0.20 -0.11 -0.18

0.01

77.21 84.89 63.09 89.87 99.20

0.54 0.51 0.03 -0.81 -1.05

-0.06 -0.75 -0.63 0.43 0.35 -1.08 0.66 0.05 0.01

FA 74.0 19.5 76.6 55.4 83.0 87.4 63.1 75.5 86.9 105.8 97.7 127.7

a Extrapolated using the mixed Gaussian/exponential formula. b CCSD(T)/awCVTZ. c ∆ESR ) 6[∆ESR(F)] + ∆ESR(MF6) - ∆ESR(MF6-). SO correction at the ADF ZORA BLYP/TZ2P level. e B3LYP/ADZ-PP. f BP86/ADZ-PP. g B3LYP/ATZ-PP.

fluoride affinities from DFT calculations using different functionals and basis sets are given in the Supporting Information. The heptafluoride anions, formed by the addition of a closed shell F- to MF6, nominally have the same number of d electrons as the neutral hexafluorides if electrons are not transferred from the F- to the metal. On the basis of the known main group structures, the addition of an F- ion to an octahedral MF6 molecule would be expected to lead to three possible geometries: pentagonal bipyramid (PBP, D5h), monocapped octahedron (MCO, C3V), or monocapped trigonal prism (MCTP, C2V). The average M-F bond distances in these classical MF7- structures follow the same trend as in the MF6 and MF5 series, with M-F bonds of approximately the same length for M ) Mo, Tc, and Ru and increasing for M ) Rh, Pd, and Ag. From MoF7- to AgF7-, the average M-F bond distances for the classical structures are 1.901, 1.897, 1.898, 1.906, 1.922, and 2.015 Å, respectively. It is also possible to form a nonclassical structure that can be best described as a Cs structure with one F atom bonded to an F ligand of the MF6- cluster.1 The Fligand-Fexternal average bond length in the nonclassical MF7- structures is 2.060 Å, which is considerably longer than r(F-F) ) 1.412 Å65 in F2 or even r(F-F) ) 1.920 Å (CCSD(T)/aQ) in F2-. The M-Fexternal bond distance is ∼3.5 Å and is much longer than any of the average M-F bonds in the MF6 structures. For MoF7-, the three classical structures are very close in energy with MCTP lowest at the B3LYP/ADZ-PP level. The 3 A′/Cs nonclassical structure, a local minimum on the potential energy surface, is substantially higher in higher in energy, 54.5 kcal/mol, than the MCTP structure at the CCSD(T) level (Table 9). The high spin, nonclassical structure 4A′′/Cs is 21.2 kcal/ mol above the lowest energy classical MCTP structure at the CCSD(T) level (Table 9) for TcF7-. All three triplet classical

structures of RuF7- are higher in energy than the nonclassical 5 A′′/Cs structure with the closest being the PBP structure, which is 4.4 kcal/mol higher at the CCSD(T) level (Table 9). The CCSD(T) energetics for the relative energies of the different structures for RhF7- are complicated by the large T1 value for the 2A1 state (MCTP) suggesting a substantial amount of multireference character in the starting HF wave function. At the B3LYP/AD level, the 2B1 state (distorted D5h) for RhF7is 1.9 kcal/mol lower in energy than the 2A1, but this reverses at the B3LYP/AT level so that the 2B1 is 4.8 kcal/mol higher in energy. The 4A1/C2V (MCTP) structure is close in energy to the 2 B1 state at the DFT B3LYP level. However, at the CCSD(T)/ CBS level, the 4A1/C2V (MCTP) state is 7.2 kcal/mol higher in energy than the 2B1 state. The fact that the 2B1 state is the lowest energy classical structure is consistent with the results for PtF7-.1 At the CCSD(T)/ATZ-PP level, the nonclassical 4A′′/Cs structure is predicted to be lower in energy than the most stable classical 2 B1 structure by 12.2 kcal/mol, so the nonclassical structure is the most stable. The spin state of the nonclassical structure is consistent with the addition of the closed shell F- to RhF6, which is 4A1g in Oh symmetry. The 4A′′ state for the nonclassical structure corresponds to the high spin coupling of the F atom with the 3A1g state of RhF6-. The nonclassical 2A′′/Cs structure (low spin coupling of the F atom with the RhF6-) is 7.5 kcal/ mol higher in energy than the most stable classical 2B1 structure. The relative energies of the classical and nonclassical geometries for RhF7- and RuF7- are consistent with the high electron affinities. The singlet classical structures of PdF7- are up to 33 kcal/ mol higher in energy than the nonclassical 3A′/Cs structure at the B3LYP/ADZ-PP level. At the CCSD(T) level (Table 9), the nonclassical structure of PdF7- is 18.9 kcal/mol more stable

Thermochemical Calculations for MF6

J. Phys. Chem. A, Vol. 114, No. 28, 2010 7579

than the classical PBP structure. The nonclassical 2A′/Cs structure of AgF7- is more stable than the lowest energy classical distorted MCO structure by 30.0 kcal/mol at the CCSD(T) level (Table 9). The FAs for the classical structures were calculated by extrapolating the CCSD(T) energies to the CBS limit and adding the various corrections as listed in Table 9. The FAs for the addition of F- to form the nonclassical structures were calculated by adding only the zero-point energy, scalar relativistic, and spin-orbit corrections to the energies at the CCSD(T)/ATZPP level. The scalar relativistic correction was calculated from the expectation values of the mass-velocity and Darwin terms in the Breit-Pauli Hamiltonian66 at the CISD/ATZ-PP level for MF6 and MF7-. On the basis of our previous work on the FAs of the third row transition metal hexafluorides,1 we estimate that the error introduced by the pseudopotential approximation is small. The SO correction was not included in the calculation of FA(MoF6) and FA(TcF6) to form the nonclassical structures due to problems in converging the self-consistent field to obtain the wave function. The FAs for the addition of F- to form one of the three classical structures are between 63.1 and 97.7 kcal/mol. The lowest FA forming a classical structure is for addition to RhF6, which has the stable (t2g)3 occupancy. The FAs for the formation of the nonclassical structures show a much greater variation with the metal, from ∼20 kcal/mol for MoF6 to values of 87.4, 75.5, 105.8, and 127.7 kcal/mol for RuF6, RhF6, PdF6, and AgF6, respectively (Table 9). For these latter four molecules, the nonclassical structures are more stable than the classical structures. Again, the FA for forming the nonclassical structure is lowest for RhF6 due to the stability of its (t2g)3 orbital occupancy and its lower electron affinity. The bond energy between the F atom and MF6-, E(F)cluster, can be calculated from the following thermodynamic cycle: Using this cycle, E(F)cluster for MF7- (eq 3)

MF7- f MF6- + F

(3)

is given by E(F)cluster ) EA(F) - EA(MF6) + FA. The calculated fluoride and electron affinities of MF6 are available from our calculations, and the experimental value51 for EA(F) is 3.4012 eV (78.43 kcal/mol). The global decomposition of MF7- to F2- and MF5 as shown in eq 4 is defined as E(F2-)cluster, which is the energy difference between the MF7- and the products.

MF7- f F2- + MF5

(4)

We calculated the properties of F2- using the CCSD(T)/CBS plus additional corrections approach described above. The calculated EA(F2) ) 3.04 eV is in excellent agreement with the experimental values of 3.005 ( 0.07167 and 3.120 ( 0.070 eV.68 The heat of formation of MF5 was obtained as described above, and the heat of formation of MF7- was obtained from the fluoride affinity of MF6. The energies of eqs 3 and 4 at 0 K are given in Table 10. The energies of eq 4, E(F2-)cluster, are

TABLE 10: Energies (kcal/mol) of Reactions 2 (E(F)cluster) and 3 (E(F2-)cluster) for the Second Row Transition Metals M Mo

MF7state/sym 1

A1/C2V A′/Cs 2 A2/C2V 4 A′′/Cs 3 A1′/D5h 5 A′′/Cs 2 B1/C2V 4 A′′/Cs 1 A1′/D5h 3 A′/Cs 2 B2/C2V 2 A′/Cs

MF6state/sym 2

A1g/D3d

3

A1g/D4h

4

A1g/Oh

3

A1g/D3d

2

B2g/D4h

1

A1g/Oh

3

Tc Ru Rh Pd Ag

E(F)cluster,a reaction 2 54.9 0.4c 19.1 -2.1c -0.2 4.8d -15.3 -2.9d -18.3 -0.1d -28.4 1.6d

MF5 state/sym 2

A2/C2V

3

A1′/D3h

4

B1/C4V

3

B2/C4V

2

B1/C4V

1

A1/C4V

E(F2-)cluster,b reaction 3 131.4 76.9 101.0 79.8 99.4 104.5 76.8 89.2 103.3 121.6 68.9 98.8

a E(F)cluster ) EA(F) - EA(MF6) + FA. For the classical structures, the FAs were calculated using the CBS energies and all corrections (ZPE, CV, SR, and SO). For the nonclassical structures the FAs were calculated using the CCSD(T)/ATZ-PP energies together with the ZPE and SR corrections. b E(F2-)cluster ) ∆Hf,0 K(F2-) + ∆Hf,0 K(MF5) - ∆Hf,0 K(MF7-); ∆Hf,0 K(MF5) ) first BDE - ∆Hf,0 K(F) + ∆Hf,0 K(MF6); ∆Hf,0 K(MF7-) ) -FA(MF6) + ∆Hf,0 K(MF6) + ∆Hf,0 K(F-). Hf,0 K(F-) ) -EA(F) + ∆Hf,0 K(F) ) -78.404 + 18.47 ) -59.93 kcal/mol; Hf,0 K(F2-) ) -EA(F2) ) 70.06 kcal/mol. c Use of EA(MF6) calculated at the CCSD(T)/ ATZ-PP + ∆EZPE + ∆ESR level gives 1.2 kcal/mol for M ) Mo and 1.8 kcal/mol for M ) Tc. d Use of EA(MF6) calculated at the CCSD(T)/ATZ-PP + ∆EZPE + ∆ESR + ∆ESO level gives 1.9 kcal/ mol for M ) Ru, -1.5.8 kcal/mol for M ) Rh, 2.9 kcal/mol for M ) Pd, and 5.8 kcal/mol for M ) Ag.

substantially more endothermic (Table 10) than E(F)cluster, so eq 3 is more likely to occur thermodynamically as compared to eq 4. For the most stable classical structures, and TcF7-, E(F)cluster decreases from 55 kcal/mol for MoF7- to 19 kcal/mol for TcF7to zero or negative for the remaining structures. The E(F)cluster values for the nonclassical structures exhibit a different type of behavior. For the MF7- ions where the classical structures are more stable than the nonclassical ones (M ) Mo, Tc, Rh), the E(F)cluster (nonclassical) values are zero or negative. When the nonclassical MF7- structure is more stable than the classical one, the E(F)cluster (nonclassical) values are small (M ) Ru, Pd, Ag) or slightly negative for M ) Rh, consistent with a weak complex of a fluorine radical atom with MF6-. In fact, the E(F)cluster values of the nonclassical structures are all near zero. Hence, if the nonclassical MF7- ion were formed, even in cases where it is not the most stable structure, it would readily eliminate an F atom. The E(F2-)cluster values increase from M ) Mo to M ) Ru, decrease for M ) Rh, and increase for M ) Pd and Ag. We have also calculated the energy to release F2- from MF7- for the transition metals of the third row and compare them with our previously predicted E(F)cluster values (Table 11). The E(F)cluster and E(F2-)cluster values for the third row transition metals follow the same trends as for the second row. Again the E(F)cluster values are always less than the E(F2-)cluster values, so reaction 2 will preferentially occur as compared to reaction 3. We have previously shown1 that, when the electron affinity of MF6 becomes large enough, MF6 will bind an F- which then undergoes an electron transfer to MF6, leaving the nonclassical weak complex of an F atom with MF6-. With our additional data, we can conclude that when EA(MF6) g 6.8 eV, MF6 can abstract an electron from the F- anion and form the nonclassical complex MF6--F. Thus nonclassical complexes are expected for M ) Ru, Rh, Pd, Ag, Pt, and Au.

7580

J. Phys. Chem. A, Vol. 114, No. 28, 2010

Craciun et al.

TABLE 11: Energies (kcal/mol) of Reactions 2 (E(F)cluster), 3 (E(F2-)cluster), and 4 (FA(MF5)) for the Third Row Transition Metalsa MF7- state/sym

M

MF6- state/sym

A1′/D5h A′′/Cs 2 A2/C2V 4 A′′/Cs 3 A1′/D5h 5 A′′/Cs 2 B1/C2V 2 A′/Cs 1 A1′/D5h 3 A′/Cs 2 B2/C2V 2 A′/Cs 1

W

2

B2g/D4h

3

A1g/D4h

4

A1g/Oh

3

A1g/D4h

2

B2g/D4h

1

A1g/Oh

E(F)cluster, reaction 2b 83.7 -2.2 53.0 0.2 24.4 4.6 10.2 -28.3 -6.2 0.4 -32.3 4.7

3

Re Os Ir Pt Au a

2

A2/C2V

3

A1′/D3h

4

B1/C4V

5

B1/C4V

2

B1/C4V

1

A1/C4V

E(F2-)cluster, reaction 3

FA(MF5), reaction 4b

167.2 81.3 141.3 88.5 128.1 108.3 115.7 77.2 96.8 103.4 75.4 112.4

112.9 116.4 132.0 134.6 130.7 136.6

See footnotes to Table 10 for details of the calculations. b Reference 1.

TABLE 12: MF5 Fluoride Affinities (kcal/mol) Calculated at the CCSD(T) Level MF5 MF6M state/sym state/sym ∆FACBSa ∆EZPEb ∆ECVc ∆ESRd total FA Mo Tc Ru Rh Pd Ag

MF5 state/sym

2

A2/C2V A1′/D3h 4 B1/C4V 3 B2/C2V 2 B1/C4V 1 A1/C4V 3

2

B2g/D4h A1g/D4h 4 A1g/Oh 3 A1g/D4h 2 B2g/D4h 1 A1g/Oh 3

105.1 104.9 124.0 120.7 145.3 125.9

-0.42 -2.09 -1.31 -0.69 -1.00 -1.65

0.82 1.20 1.14 1.32 4.18 1.74

-0.28 -0.30 -0.32 -0.34 -0.40 -0.36

105.2 103.7 123.6 121.0 127.5 125.7

a Extrapolated using the mixed Gaussian/exponential formula. B3LYP/ADZ-PP. c CCSD(T)/awCVTZ. d Scalar relativistic correction at the CISD/ATZ-PP level. b

We also calculated the MF5 fluoride affinities given by eq 5 The resulting values calculated at the CCSD(T)/CBS level with

MF5 + F- f MF6-

(5)

ZPE, core-valence, and scalar relativistic corrections are given in Table 12. The MF5 FAs increase from FA(MoF5) ) 105.2 kcal/mol to FA(PdF5) ) 127.5 kcal/mol following the trends in the electron affinities. The FA(AgF5) decreases slightly to 125.7 kcal/mol, and its lower fluoride affinity as compared to FA(PdF5) may be connected to the weak Ag-F BDE in AgF6. Christe et al.31 have used fluoride ion affinities to establish a quantitative Lewis acidity scale. The strongest Lewis acid on the list, SbF5, has a fluoride affinity of 120.3 kcal/mol, lower than those of RuF5, RhF5, PdF5, and AgF5. The FAs of MF5 are larger by 14-41 kcal/mol than the FAs of the corresponding MF6 molecules, consistent with going from C4V or D3h structures for MF5 to the energetically favored approximately octahedral structures for MF6-, while the transition from MF6- to the various classical structures of MF7- might involve some steric crowding. It is useful to compare FA(MF5) (eq 5, Table 4) with E(F2-)cluster (eq 4, Table 10). If both F- and F2- are present, then MoF5 would prefer to bind F2- over F- and for TcF5 both anions are equally likely to bind to the pentafluoride. RuF5 would preferentially bind F2-, and again, RhF5 would bind both anions equally well. PdF5 and AgF5 would both preferentially bind F- over F2-. In the third row transition metal compounds (Table 11), WF5 and ReF5 will preferentially bind F2-. A crossover occurs at OsF5 and the binding of F2- and the binding of F- are comparable. IrF5, PtF5, and AuF5 will all bind Fover F2-. Performance of Density Functional Theory. The calculated values for a selection of functionals for the EAs, M-F bond

TABLE 13: Average Deviations of the MF6 Electron Affinities, MF5 and MF6 Fluoride Affinities, and First Adiabatic M-F Bond Dissociation Energies from the CCSD(T) Calculated Values method

EA(MF6)

FA(MF5)

FA(MF6)

M-F BDE

BLYP BP86 PW91 PBE TPSS B3LYP mPW1 PBE1 O3LYP TPSSh

27.3 26.5 24.5 28.7 27.1 6.4 5.1 6.5 17.8 28.3

16.0 12.5 8.1 12.8 10.7 -1.9 6.9 6.5 17.5 3.2

20.1 19.3 13.0 17.7 14.5 9.5 4.3 0.9 18.6 8.0

-17.8 -20.7 -22.1 -21.4 -17.4 -2.5 1.2 0.0 -4.6 -22.4

dissociation energies, MF5 FAs, and MF6 FAs are given in the Supporting Information. The average deviations of these properties, calculated with a selection of functionals, from the CCSD(T)/CBS values with all corrections except for spin-orbit are given in Table 13. In general, the differences in the electron affinities between the CCSD(T) and DFT values are larger for the later transition metal fluorides than for the earlier ones. For the GGA functionals, the differences from the CCSD(T) values are quite large with average deviations up to 29 kcal/mol and are even larger than for the third row compounds. The hybrid functionals B3LYP, mPW1, and PBE1 give the best performances with average deviations of 5-6.5 kcal/mol. The O3LYP and TPSSh hybrid functionals do not perform any better than the GGA functionals. For the MF5 fluoride affinities, the GGA functionals predict values that are 8-16 kcal/mol smaller than the CCSD(T) values. The hybrid functionals, except O3LYP, predict smaller values than the CCSD(T) method within 10 kcal/ mol. For the M-F adiabatic BDEs of MF6, all GGA functionals predict BDEs that are too large by up to 21 kcal/mol as compared to the CCSD(T) results. The hybrid functionals, except TPSSh, predict BDEs within 5 kcal/mol of the CCSD(T) results. Conclusions High-level coupled cluster CCSD(T) calculations, extrapolated to the complete basis set limit, were used to evaluate reliable, self-consistent thermochemical data sets for the second row transition metal hexafluorides. For MF6 and MF6-, the Jahn-Teller distorted D4h and D3d structures are very close in energy while an undistorted Oh structure is about 1.0 kcal/mol higher in energy. Thus, the MF6 molecules are highly fluxional about the conical intersection and will exhibit an average Oh geometry under most experimental conditions. The electron

Thermochemical Calculations for MF6 affinities are direct measures for the oxidizer strengths of these hexafluorides, and their oxidizing power increases from MoF6 to RuF6, decreases to RhF6 and then increases again to AgF6. The RuF6, RhF6, PdF6, and AgF6 molecules are extremely powerful oxidizers with electron affinities g6.8 eV and are excellent representatives of the class of superhalogens. Contrary to the findings for the third row transition metal hexafluorides, the inclusion of spin-orbit effects for the correct prediction of the qualitative ordering of the electron affinities was found unimportant for the second row transition metal hexafluorides. Thus, EA(RhF6) is less than EA(RuF6), consistent with simple ideas from orbital filling and electron repulsion. On the basis of their calculated fluoride ion affinities, the corresponding pentafluorides are extremely strong Lewis acids, with RuF5, RhF5, PdF5, and AgF5 significantly exceeding the Lewis acidity of SbF5. The MoF7- and TcF7- anions have classical heptacoordinated MF7- structures with the corresponding hexafluorides having fluoride affinities of 74 and 77 kcal/mol, respectively. A lower energy nonclassical structure with a very weak external F-F bond between an MF6- fragment and a fluorine atom is predicted for MF7- for M ) Ru, Rh, Pd, and Ag, consistent with their high electron affinities; thus, RuF7-, RhF7-, PdF7-, and AgF7- should be excellent F atom sources under very mild conditions. RhF6 has the lowest nonclassical FA due to its lower electron affinity consistent with the stable (t2g)3 orbital occupancy of RhF6. Except for AgF7-, the loss of F- from MF7- is much less endothermic than the loss of F2-, so the MF7- anions will always release F- rather than F2-. A wide range of DFT exchange-correlation functionals were also evaluated and only the B3LYP, mPW1PW91, and PBE1 functionals were found to approximate the coupled cluster values. Acknowledgment. We thank Dr. Shenggang Li of The University of Alabama for help with some of the larger calculations. This work was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) under Grant DEFG02-03ER15481 (catalysis center program). D.A.D. also thanks the Robert Ramsay Chair Fund of The University of Alabama for support. Part of this work was performed at the W. R. Wiley Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, operated for the DOE by Battelle. K.O.C. is indebted to the Office of Naval Research, the National Science Foundation, and the Defense Threat Reduction Agency for financial support. Supporting Information Available: Experimental atomic heats of formation in kcal/mol, benchmarked DFT exchangecorrelation functional; relative energy differences between the D4h and D3d MF6 structures; EA(MF6), FA(MF5), FA(MF6), and first M-F BDEs calculated with various exchange-correlation functionals; adiabatic electron affinities of MF6; vertical electron detachment energies (VDEs) of MF6- and vertical electron attachment energies (VAEs) of MF6 in kcal/mol calculated at the CCSD(T)/ATZ-PP//CCSD(T)/ADZ-PP, B3LYP/ATZ-PP// B3LYP/ADZ-PP, and CCSD(T)/ATZ-DK//CCSD(T)/ATZ-PP levels; MF6, MF6-, MF5, and MF7- T1 diagnostics at the CCSD(T)/ATZ-PP level; MF6, MF6-, MF5, and MF7- total electronic energies and vibrational frequencies at the DFT level with various exchange-correlation functionals and the ADZPP basis set; zero point energies (ZPE); CCSD(T) total energies as a function of basis set, core, and valence energies at the CCSD(T)/aug-cc-pWCVTZ-PP level; scalar relativistic energies

J. Phys. Chem. A, Vol. 114, No. 28, 2010 7581 at the CISD/ATZ-PP and CCSD(T)-DK/aug-cc-pVTZ-DK levels; energy differences in kcal/mol of D4h vs Oh structures for the same spin state and singlet-triplet splitting energies for the D4h structures; optimized geometry parameters with different DFT functionals; pseudopotential errors and scalar relativistic corrections for EA(MF6); first M-F BDEs and total atomization energies; electron affinities calculated at the ZORA and ZORA + SO levels; Mulliken charges, NBO charges, and spin densities for MF6 and MF6- and figures for the spin densities; first M-F BDEs, FA(MF6), and FA(MF5) calculated at the DFT and CCSD(T) levels as a function of basis set; MF5 optimized geometries at the B3LYP/ATZ-PP, BLYP/TZ2P scalar relativistic ZORA, and ZORA plus spin-orbit levels; and a set of Cartesian xyz coordinates for all molecules. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Craciun, R.; Picone, D.; Long, R. T.; Li, S.; Dixon, D. A.; Peterson, K. A.; Christe, K. O. Inorg. Chem. 2010, 49, 1056. (2) Moffit, W.; Goodman, G. L.; Fred, M.; Weinstock, B. Mol. Phys. 1959, 2, 109. (3) Claassen, H. H.; Goodman, G. L.; Holloway, J. H.; Selig, H. J. Chem. Phys. 1970, 53, 341. (4) Weinstock, B.; Goodman, G. AdV. Chem. Phys. 1965, 9, 169. (5) Claassen, H. H.; Selig, H.; Malm, J. G. J. Chem. Phys. 1962, 36, 2888. (6) Weinstock, B.; Claassen, H. H.; Chernick, C. L. J. Chem. Phys. 1963, 38, 1470. (7) Molski, M. J.; Seppelt, K. Dalton Trans. 2009, 3379. Seppelt, K. Acc. Chem. Res. 2003, 36, 147. (8) Drews, T.; Super, J.; Hagenbach, A.; Seppelt, K. Inorg. Chem. 2006, 45, 3782. (9) Richardson, A. D.; Hedberg, K.; Lucier, G. M. Inorg. Chem. 2000, 39, 2787. (10) Brisdon, A. K.; Holloway, J. H.; Hope, E. G.; Levason, W.; Ogden, J. S.; Saad, A. K. J. Chem. Soc., Dalton Trans. 1992, 447. (11) Graudejus, O.; Wilkinson, A. P.; Chacon, L. C.; Bartlett, N. Inorg. Chem. 2000, 39, 2794. (12) Drews, T.; Supel, J.; Hagenbach, A.; Seppelt, K. Inorg. Chem. 2006, 45, 3782. (13) Miyoshi, E.; Sakai, Y.; Murakami, A.; Iwaki, H.; Terashima, H.; Shoda, T.; Kawaguchi, T. J. Chem. Phys. 1988, 89, 4193. (14) Van Wu¨llen, C. J. Comput. Chem. 1999, 20, 51. (15) Miyoshi, E.; Sakai, Y.; Murakami, A.; Iwaki, H.; Terashima, H.; Shoda, T.; Kawaguchi, T. J. Chem. Phys. 1988, 89, 4193. (16) Aullo´n, G.; Alvarez, S. Inorg. Chem. 2007, 46, 2700. (17) Seth, M.; Cooke, F.; Schwerdtfeger, P.; Heully, J. L.; Pelissier, M. J. Chem. Phys. 1998, 109, 3935. (18) Riedel, S.; Kaupp, M. Coord. Chem. ReV. 2009, 253, 606. (19) Riedel, S.; Renz, M.; Kaupp, M. Inorg. Chem. 2007, 46, 5734. (20) Mathur, B. P.; Rothe, E. W.; Reck, G. P. J. Chem. Phys. 1977, 67, 377. (21) Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J. Chem. Phys. 1978, 68, 2023. (22) Sidorov, L. N.; Borshchevsky, A. Ya.; Rudny, E. B.; Butsky, V. D. Chem. Phys. 1982, 71, 145. (23) Rudnyi, E. B.; Kaibicheva, E. A.; Sidorov, L. N. Rapid. Commun. Mass. Spectrom. 1992, 6, 356. (24) Korobov, M. V.; Kuznetsov, S. V.; Sidorov, L. N.; Shipachev, V. A.; Mit’kin, V. N. Int. J. Mass. Spectrom. Ion Processes 1989, 87, 13. (25) Edwards, A. J.; Falconer, W. E.; Griffiths, J. E.; Sunder, W. A.; Vasile, M. J. J. Chem. Soc., Dalton Trans. 1974, 1129. (26) Selig, H.; Vaknin, D.; Davidov, D.; Yeshurun, Y. Synth. Met. 1985, 12, 479. (27) Bartlett, N. J. Fluorine Chem 2006, 127, 1285. (28) Sakai, Y.; Miyoshi, E. J. Chem. Phys. 1987, 87, 2885. (29) Myers, O. E.; Brady, A. P. J. Phys. Chem. 1960, 64, 591. (30) Settle, J. L.; Feder, H. M.; Hubbard, W. N. J. Phys. Chem. 1961, 65, 1337. (31) Christe, K. O.; Dixon, D. A.; McLemore, D.; Wilson, W. W.; Sheehy, J. A.; Boatz, J. A. J. Fluorine Chem. 2000, 101, 151. Chem. Eng. News 2003, March 3, 48-49. (32) Hunt, R.; Andrews, L.; Toth, L. M. J. Phys. Chem. 1991, 95, 1183. (33) Purvis, G. D., III; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (34) Raghavachari, K.; Truck, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (35) Watts, J. D.; Gauss, J.; Bartlett, R. J. J. Chem. Phys. 1993, 98, 8718.

7582

J. Phys. Chem. A, Vol. 114, No. 28, 2010

(36) Bartlett, R. J.; Musial, M. ReV. Mod. Phys. 2007, 79, 291. (37) Rittby, M.; Bartlett, R. J. J. Phys. Chem. 1988, 92, 3033. (38) Knowles, P. J.; Hampel, C.; Werner, H.-J. J. Chem. Phys. 1994, 99, 5219. (39) Deegan, M. J. O.; Knowles, P. J. Chem. Phys. Lett. 1994, 227, 321. (40) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys. 1994, 96, 6796. (41) Figgen, D.; Peterson, K. A.; Dolg, M.; Stoll, H. J. Chem. Phys. 2009, 130, 164108. (42) Peterson, K. A.; Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1994, 100, 7410. (43) Li, S.; Dixon, D. A. J. Phys. Chem. A 2007, 111, 11908. (44) (a) Douglas, M.; Kroll, N. M. Ann. Phys. 1974, 82, 89. (b) Hess, B. A. Phys. ReV. A 1985, 32, 756. (c) Hess, B. A. Phys. ReV. A 1986, 33, 3742. (45) Figgen, D.; Peterson, K. A.; Dolg, M.; Stoll, H. J. Chem. Phys. 2009, 130, 164108. (46) de Jong, W. A.; Harrison, R. J.; Dixon, D. A. J. Chem. Phys. 2001, 114, 48. (47) EMSL basis set library. http://www.emsl.pnl.gov/forms/basisform. html. (48) (a) van Lenthe, E.; Ehlers, A. E.; Baerends, E. J. J. Chem. Phys. 1999, 110, 8943. (b) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (c) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994, 101, 9783. (d) van Lenthe, E.; Snijders, J. G.; Baerends, E. J. J. Chem. Phys. 1996, 105, 6505. (e) van Lenthe, E.; van Leeuwen, R.; Baerends, E. J.; Snijders, J. G. Int. J. Quantum Chem. 1996, 57, 281. (49) (a) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (b) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391. (c) ADF 2008.01, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com. (50) Moore, C. E. Atomic energy leVels as deriVed from the analysis of optical spectra, Vol. 1, H to V; U.S. National Bureau of Standards Circular 467; U.S. Department of Commerce, National Technical Information Service: Washington, DC, 1949; COM-72-50282. (51) Chase, M. W., Jr. NIST-JANAF Thermochemical Tables, 4th ed. J. Phys. Chem. Ref. Data, Monogr. 1998, No. 9, Suppl. 1. (52) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data, Suppl., 1982, 11, Suppl. 2. (53) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon Press: Oxford, 1984 (Mo, Chapter 23, p 1170; Ru, Chapter 25, p 1248; Rh, Chapter 26, p 1294; Pd, Chapter 27, p 1333, Ag, Chapter 28, p 1368).

Craciun et al. (54) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision E.01; Gaussian, Inc.: Wallingford, CT, 2004. (55) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schu¨tz, M.; Celani, P.; Korona, T.; Rauhut, G.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Hampel C.; Hetzer, G.; Lloyd, A. W.; McNicholas, S. J.; Meyer W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pitzer, R.; Schumann, U.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T. Molpro, Version 2008.1, a package of ab initio programs; see http://www.molpro.net. (56) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. Symp. 1989, 23, 199. (57) Li, S.; Dixon, D. A. J. Phys. Chem. A 2008, 112, 6646. (58) Li, S.; Hennigan, J. M.; Dixon, D. A. J. Phys. Chem. A 2009, 113, 7861. (59) Fitz, H.; Muller, B. G.; Graudejus, O.; Bartlett, N. Z. Anorg. Allg. Chem. 2002, 628, 133. (60) Aullon, G.; Alvarez, S. Inorg. Chem. 2007, 46, 2700. (61) Seth, M.; Cooke, F.; Schwerdtfeger, P.; Heully, J.-L.; Pelissier, M. J. Chem. Phys. 1998, 109, 3935. (62) Dixon, D. A.; de Jong, W. A.; Peterson, K. A.; Christe, K. O.; Schrobilgen, G. J. J. Am. Chem. Soc. 2005, 127, 8627. Grant, D. J.; Wang, T.-H.; Dixon, D. A.; Christe, K. O. Inorg. Chem. 2010, 49, 261. (63) Wang, S. Y.; Lohr, L. L., Jr. J. Chem. Phys. 1974, 60, 3901. (64) Gutsev, G. L.; Boldyrev, A. I. Chem. Phys. 1981, 56, 277. (65) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1979. (66) Davidson, E. R.; Ishikawa, Y.; Malli, G. L. Chem. Phys. Lett. 1981, 84, 226. (67) Wenthold, P. G.; Squires, R. R. J. Phys. Chem. 1995, 99, 2002. (68) Artau, A.; Nizzi, K. E.; Hill, B. T.; Sunderlin, L. S.; Wenthold, P. G. J. Am. Chem. Soc. 2000, 122, 1066.

JP1022949