Assessment of Several DFT Functionals in Calculation of the

Jan 13, 2015 - Reduction Potentials for Ni−, Pd−, and Pt−Bis-ethylene-1,2- dithiolene and -Diselenolene Complexes. Eric A. C. Bushnell and Russe...
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Assessment of Several DFT Functionals in Calculation of the Reduction Potentials for Ni−, Pd−, and Pt−Bis-ethylene-1,2dithiolene and -Diselenolene Complexes Eric A. C. Bushnell and Russell J. Boyd* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4R2, Canada S Supporting Information *

ABSTRACT: We performed an assessment of 10 common DFT functionals to determine their suitability for calculating the reduction potentials of the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−), ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−), ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−), and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples (M = Ni, Pd, and Pt). Overall it was found that the M06 functional leads to the best agreement with the gold standard CCSD(T) method with an average difference of only +0.07 V and a RMS of 0.07 V in calculated reduction potentials. The variability in calculated reduction potentials between the various DFT functionals arise, in part, from the multireference character of these systems, which was determined by the T1 diagnostic values. Thus, the bisdiselenolene complexes show similar multireference character as the bisdithiolene complexes, which were previously shown to have such character. In particular, for the Ni−, Pd−, and Pt−bisdiselenolene complexes the average T1 values are 0.05, 0.03, and 0.02, respectively. For the CCSD(T) calculations the similarities in the reduction potentials between analogous bisdithiolene and bisdiselenolene redox couples, which appear to be independent of the metal, is a result of the noninnocence of the dithiolene and diselenolene ligands. Thus, the reduction potential is more dependent on the ligand than the metal.

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dihydro-1,4-dithiin-2,3-diselenolene) redox couples ΔE° is only 0.01 V.11 These insignificant differences led Nomura et al.11 to state that the redox potentials of analogous dithiolene and diselenolene complexes do not strongly depend on the nature of the chalcogen atoms. However, in their work they only studied CpNi−dithiolene and −diselenolene complexes. It has been stated23 that the identification of new ligands that undergo redox chemistry (i.e., noninnocent ligands) will allow the design of new catalysts to solve many contemporary problems. Given the unique chemistry that dithiolene complexes undergo and the limited information on diselenolene complexes further study is warranted. Recently, Dang et al.24 assessed several DFT functionals for the reaction between Ni(S2C2H2)2 and C2H4. They looked at the geometries of key transition states and intermediates as well as the reaction energies. Overall it was found that the geometric parameters are rather insensitive to functional choice; however, the reaction energies are quite sensitive. M06 and HSE06 yield results close to those from CCSD(T), whereas ω-B97XD gives relative energies closest to those from CCSD. Furthermore, they found that the variations of the relative energies from the different density functionals arise, in part, from the presence of multireference character. Such multireference character was previously shown for the neutral Ni−, Pd−, and Pt− bis(3,5-tBu-benzene-1,2-dithiolene) complexes which were

INTRODUCTION The noninnocence of dithiolene ligands and the reversible oneelectron-transfer processes of the complexes they form result in unique optical, magnetic, and conductive properties.1−13 These properties have been crucial to the development of dyesensitized solar cells14−17 and photocatalysts18 for the splitting of water to produce H2 as a means for renewable energy. However, while homo- and heteroleptic dithiolene complexes have been intensively studied both experimentally and computationally (see, for instance, refs 19 and 20 and references therein), the analogous diselenolene complexes are not as well studied. Previously, Pierpont and Eisenberg21 have shown that crystal structures of Mo(Se2C2(CF3)2)3 are perfectly trigonal prismatic like the analogous sulfur complex. This similarity in geometry implies similar redox behavior of the diselenolene and dithiolene ligands.21 Nomura et al.11 showed, via X-ray crystallography, CpNi(diselenolene) complexes are isostructural to the analogous CpNi(dithiolene) complexes.11,22 Furthermore, the diselenolene complexes investigated have reversible one-electron transfer processes for the Ni+/Ni redox couple like the analogous dithiolene complexes.11 Notably, the measured reduction potentials of analogous dithiolene and diselenolene complexes are essentially the same. In particular, ΔE0 for the (CpNi(bdt)+/CpNi(bdt)) (bdt = benzene-1,2ditholene) and (CpNi(bds)+/CpNi(bds)) (bds = bdt = benzene-1,2-diselenolene) redox couples is 0.04 V. For the (CpNi(dddt)+/CpNi(dddt)) (dddt = 5,6-dihydro-1,4-dithiin2,3-dithiolene) and (CpNi(ddds)+/CpNi(ddds)) (ddds = 5,6© XXXX American Chemical Society

Received: November 12, 2014 Revised: January 13, 2015

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The calculated electronic energies were then corrected by adding the appropriate Gibbs energy corrections obtained via harmonic frequency calculations from the geometry optimizations. The IEFPCM approach was used to implicitly model the solvent where acetonitrile was chosen. Absolute reduction potentials were obtained as per the equations

found to have 32%, 50%, and 30% singlet diradical character, respectively.25 The unpaired electrons on each ligand are strongly antiferromagnetically coupled through the closed shell central metal atom via a superexchange mechanism. However, such multireference character for bisdiselenolene complexes still remains unknown. Given the lack of computational studies on diselenolene complexes we present an assessment of 10 DFT functionals in the prediction of reduction potentials for the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples. The values obtained with the DFT functionals will be compared to values obtained with the gold standard CCSD(T) method. In addition, we studied ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples to study the effect of substituting Se with S. Recently, we26,27 assessed several DFT functionals in the calculation of reduction potentials for the individual ligands. While it was found that the M06-L/6-311+G(d,p) level of theory was sufficient to calculate reduction potentials in reasonable agreement with the QCISD/cc-pVTZ level of theory, it is unknown if the M06-L functional is still sufficient for calculating reduction potentials of both bisdithiolene and bisdiselenolene complexes when metals are present.

[M(S2 C2H 2)2 ]0 + e− → [M(S2 C2H 2)2 ]1 − [M(S2 C2H 2)2 ]1 − + e− → [M(S2 C2H 2)2 ]2 − with Δr Gs o = μg o(RED) + ΔGs o(RED) − μg 0 (OX) − ΔGs o(OX) − μg o(e−)

where μg°(X) is the chemical potential and ΔGs°(X) is the bulk energy of solvation for the respective species. For the calculation of ΔrGs° the chemical potential of the electron (μgo(e−)) was set to zero. The reduction potential was calculated via E° = −ΔrG°/F. The details of such an approach can be found in refs 67 and 68. The equations for the diselenolene complexes are identical with S2C2H2 changed to Se2C2H2. In addition, a T1 diagnostic was performed with the CCSD/ 6-311G(d,p) level of theory. This method was developed by Lee and Taylor as a diagnostic tool for determining the quality of single-reference electron correlation methods.69 Notably, the T1 values have been shown to be an excellent measure of the importance of nondynamical electron correlation.69 In the work of Dang et al.24 it was found that for the reaction of Ni(S2C2H2)2 with C2H4 the T1 diagnostic value was >0.02, which indicated the need for a multireference method.

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COMPUTATIONAL METHODS For all calculations discussed herein the Gaussian 09 software suite was used.28 The geometries of [M(Se2C2H2)2]0,1−,2− and [M(S2C2H2)2]0,1−,2− (M = Ni, Pd, and Pt) were optimized with the density functional theory (DFT) M06-L functional.29,30 For the valence and core electrons of metal atoms the LANL2DZ(f) basis set was used. For all other atoms the 6-311+G(2df,p) basis set was used. However, it is noted that the core electrons of the S and Se atoms were described using the LANL2 ECPs due to the high computational cost of using the CCSD(T) method.31−36 This combination of basis sets will hereafter be referred to as BS1 for convenience. It is noted that all optimized structures have D2h symmetry in agreement with previous work.25,37−42 Single-point electronic energies were obtained at the IEFPCM-DFTi/BS1//M06-L/BS1 levels of theory (DFTi = M06-L, M06, B3LYP, BP86, PBE, PBE0, HSE06, ω-B97XD, TPSS, and TPSSh).29,30,43−66 However, for brevity and clarity we will hereafter only refer to the DFT functional or CCSD(T) method rather than the level of theory when discussing the differences in reduction potentials or other properties. It is noted that while all reduction potentials have been calculated using the geometries optimized with M06-L, Dang et al.24 have shown that the choice of functional has a marginal effect on the geometry of dithiolene complexes (see Introduction). Moreover, from the investigation24 into the oxidation of S2C2H22− it was found that M06-L leads to the best agreement with the QCISD/cc-pVTZ level geometries. Thus, we think the approach taken for the optimization of geometries in the present work is appropriate. We note that while several dithiolene complexes have been characterized via X-ray crystallography the present work compares the differences and changes between dithiolene and diselenolene complexes in order to better understand the similarities between the analogous complexes. We have chosen not to compare to experiment, the reason being that the present complexes were optimized in the gas phase whereas the experimental structures have been obtained in the condensed phase where crystalpacking effects are present.

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RESULTS AND DISCUSSION For the 10 DFT functionals used the differences between the absolute reduction potentials calculated at the IEFPCM-DFTi/ BS1//M06-L/BS1 levels of theory to those calculated at the IEFPCM-CCSD(T)/BS1//M06-L/BS1 level of theory (Table 1) are shown in Figure 1. In particular, for each of the 10 DFT Table 1. Reduction Potentials Calculated at the IEFPCMCCSD(T)/BS1//M06-L/BS1 Level of Theory for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/ [M(S2C2H2)2]2−) Redox Couples redox couple

Ni

Pd

Pt

([M(S2C2H2)2]0/[M(S2C2H2)2]1−) ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−)

4.42 V 3.50 V

4.47 V 3.78 V

4.31 V 3.49 V

functionals in Figure 1 the 6 differences given represent the difference relative to the corresponding potential given in Table 1 for the ([M(S2C2H2) 2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples. Absolute reduction potentials calculated at the IEFPCM-DFTi/BS1// M06-L/BS1 levels of theory are provided in Table S1, Supporting Information. As seen in Figure 1, the use of GGA functionals generally results in a more reducing ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) redox couple than with the use of the CCSD(T) method. On average, the GGA functionals calculate a reduction potential 0.09 V more negative. However, it is noted that the BP86 functional calculates reduction potentials that are on average 0.01 V more positive with a root-mean-square (RMS) of only 0.01 V. The TPSS and PBE functionals calculate average B

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Figure 1. Differences in reduction potentials calculated at the IEFPCM-DFTi/BS1 levels of theory relative to those calculated at the IEFPCMCCSD(T)/BS1//M06-L/BS1 level of theory for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples (M = Ni, Pd, and Pt).

M06 functional is in best agreement with the CCSD(T) method with an average difference of only +0.07 V than CCSD(T) with a RMS of 0.05 V. The BP86 is next best with an average difference of only −0.08 V with a RMS of 0.09 V. In a recent computational study24 of the reaction of C2H4 with Ni(S2C2H2)2 to form an S,S-adduct the energies obtained with the HSE06 and M06 functional were in best agreement with values obtained with the CCSD(T) method. However, for the 6 calculated reduction potentials of the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples HSE06 has an average difference of +0.10 V with a RMS of 0.12 V with respect to values obtained with the CCSD(T) method. For the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) (M = Ni, Pd, or Pt) redox couples the absolute reduction potentials calculated at the IEFPCM-CCSD(T)/BS1//M06-L/BS1 level of theory are provided in Table 2. Absolute reduction potentials calculated at the IEFPCM-DFTi/BS1//M06-L/BS1 levels of theory are provided in Table S1, Supporting Information.

potentials 0.08 and 0.10 V more negative than the reference with RMSs of 0.01 and 0.01 V, respectively, and thus have considerably larger errors in the calculated reduction potentials. It is noted that the M06-L functional which performed best in the calculation of the reduction potentials for the (S2C2H21−/S2C2H22−) redox couple24 has an average reduction potential 0.18 V more negative for the ([M(S2C2H2)2]0/ [M(S2C2H2)2]1−) redox couples with a RMS of 0.01 V. The hybrid functionals on the other hand predict, on average, a potential 0.21 V more positive than the CCSD(T) method. Of the hybrid functionals, the TPSSh functional calculates reduction potentials that are on average only 0.05 V more positive than the CCSD(T) values with an RMS of 0.01 V. The ω-B97XD, which performs poorest of all, calculates on average reduction potentials 0.46 V more positive and thus is in very poor agreement with the CCSD(T) values. For the ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples the GGA functionals predict a far more reducing couple than the reference CCSD(T) level of theory (Figure 1). Indeed, on average the GGA functionals calculate a reduction potential that is 0.28 V more negative. The BP86 functional, which was in best agreement with the CCSD(T) method for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) redox couples, calculates potentials that are on average 0.16 V too negative with a RMS of 0.06 V. For the M06-L functional the calculated potentials are on average 0.35 V too negative with a RMS of 0.04 V and, thus, is in very poor agreement with the values obtained with the CCSD(T) method. The hybrid functionals calculate reduction potentials that are in far better agreement with the reference values (with the exception of ω-B97XD). However, unlike the GGA functionals, which calculate reduction potentials that are more negative than the CCSD(T) values for all three redox couples, the hybrid functionals generally predict more positive potentials for the Ni- and Pt-containing redox couples and a more negative potential for the Pdcontaining couple. Of the hybrid functionals, the HSE06, M06, B3LYP, and PBE0 hybrid functionals all predict reduction potentials that are on average only 0.05 V in error relative to the CCSD(T) reference values with RMSs of 0.06, 0.04, 0.05, and 0.06 V, respectively. However, overall for the 6 calculated reduction potentials of the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) and ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples the

Table 2. Reduction Potentials Calculated at the IEFPCMCCSD(T)/BS1//M06-L/BS1 Level of Theory for the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) Redox Couples redox couple

Ni

Pd

Pt

([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−)

4.40 V 3.79 V

4.57 V 3.96 V

4.43 V 3.70 V

Comparing the calculated reduction potentials for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) in Table 1 and ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) in Table 2 the average difference between the reduction potentials is only 0.07 V, with the latter being, in general, more oxidizing. Moreover, for ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) and ([M(Se2C2H2)2]1−/ [M(Se2C2H2)2]2−) redox couples the average difference between the reduction potentials is 0.22 V. This similarity in reduction potentials between analogous dithiolene and diselenolene complexes was also observed in the work of Nomura et al.11 and Fourmigue and Avarvari22 as discussed in the Introduction. From previous investigations26,27 it was found C

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change in the ordering of the MOs for the diselenolene ligand such that both the bisdithiolene and the bisdiselenolene neutral complexes have π-type LUMOs. This results in the observation that the reduction potentials do not appear to be dependent on the chalcogen present. In the case of the bisdiselenolene complexes the differences between the absolute reduction potentials calculated at the IEFPCM-DFTi/BS1//M06-L/BS1 levels of theory to those calculated at the IEFPCM-CCSD(T)/BS1//M06-L/BS1 level of theory (Table 1) are shown in Figure 3. In particular, for each of the 10 DFT functionals in Figure 3 the 6 differences given represent the difference in the corresponding potential given in Table 2 for the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples. For the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) redox couples the GGA functionals, in general, calculate reduction potentials more reducing, whereas the hybrid functionals calculate more oxidizing potentials than the CCSD(T) method. Of the GGA functionals BP86 again leads to the best agreement with the CCSD(T) values where the average difference is only 0.02 V and a RMS of 0.06 V. For the M06-L, TPSS, and PBE functionals the calculated potentials are on average 0.08, 0.07, and 0.10 V more negative than the CCSD(T) values, respectively. The RMSs for these methods are 0.07, 0.06, and 0.06 V, respectively. For the hybrid functionals the TPSSh functional calculates an average difference of only 0.06 V with a RMS of 0.08 V. The remaining hybrid functionals calculate on average reduction potentials that are at least 0.16 V more positive than CCSD(T). The ω-B97XD method again performs poorest with an average reduction potential 0.49 V more positive than CCSD(T). For the ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples most DFT functionals predict a more reducing couple than the reference CCSD(T) level of theory (Figure 3). The BP86 functional, which is in best agreement with the CCSD(T) method for the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) redox couple, calculates a potential that is on average 0.21 V more negative with a RMS of 0.06 V. The hybrid functionals, however, calculate reduction potentials that are in far better agreement with the reference values (except ω-B97XD). Specifically, the HSE06, M06, B3LYP, and PBE0 functionals predict reduction potentials that are on average only 0.06, 0.03, 0.05, and 0.04 V in disagreement with the CCSD(T) values, respectively. The calculated RMSs for these methods are 0.03, 0.03, 0.03, and 0.03 V, respectively. The reduction potentials calculated with TPSSh, however, are on average 0.21 more negative than CCSD(T) with an RMS of 0.05 V. Overall for the 6 calculated reduction potentials of the Ni−, Pd−, and Pt− bisdiselenolene redox couples the M06 functional is in best agreement with the CCSD(T) method with an average difference of only +0.08 V and a RMS of 0.09 V. BP86 and B3LYP are next best with average differences of −0.09 and +0.09 V and RMSs of 0.11 and 0.12 V, respectively. However, overall for the 12 calculated reduction potentials, the M06 functional is in best agreement with the CCSD(T)

that the absolute reduction potentials in the gas phase for the (S2C2H21−/S2C2H22−) couple is −3.28 V (at the QCISD/ccpVTZ level of theory), whereas the absolute reduction potential in the gas phase for the (Se2C2H21−/Se2C2H22−) redox couple is −2.45 V (at the QCISD/cc-pVTZ level of theory). Thus, the (Se2C2H21−/Se2C2H22−) redox couple is 0.82 V more oxidizing. Yet, the difference in potentials for the bisdithiolene and bisdiselenolene metal complexes is considerably less as discussed above. However, as discussed by Bushnell et al.26,27 the oxidation of S2C2H22− results in the lone electron being partly delocalized into the C−C bond and S atoms, whereas for Se2C2H22− the radical electron remains localized only on the Se atoms, that is, upon oxidation of S2C2H22− the electron is removed from the π-type HOMO. As seen in Figure 2a this

Figure 2. HOMO of (a) S2C2H22−, (b) Se2C2H22−, (c) [Ni(S2C2H2)2]2−, and (d) [Ni(Se2C2H2)2]2−.

MO has a bonding interaction between the two carbons of the C−C bond. Thus, oxidation of this MO results in a lengthening of the bond. However, for Se2C2H22− the electron is removed from the HOMO that contains lone pairs on the selenium atoms (Figure 2b). This difference results in the lengthening of the C−C bond of S2C2H21−, whereas for Se2C2H21− no lengthening occurs. However, if we compare key bond lengths (Table 3) of [Ni(S2C2H2)2]0 and [Ni(Se2C2H2)2]0 both complexes have elongated C−C bonds. The results for the Pd and Pt complexes are essentially identical to the Ni complexes and therefore are not discussed. As seen in Figure 2c and 2d the HOMOs of [Ni(S2C2H2)2]2− and [Ni(Se2C2H2)2]2− have a bonding interaction between carbons, and thus, oxidation of this π-type orbital would result in a lengthening of the C−C bond. Indeed, as seen in Table 3, successive reductions result in the shortening of the C−C bond. Notably, it has been previously stated25,70,71 that the degree of lengthening in the C−C bond is an indicator of the redox level of the dithiolene ligand. Thus, while the reduction potentials for the sole ligands (i.e., S2C2H21− and Se2C2H21−) have considerable differences, it appears that the bonding of the ligands to the metal results in a

Table 3. Selected Average Bond Lengths for the [Ni(S2C2H2)2]0,1−,2− and [Ni(Se2C2H2)2]0,1−,2− Complexes complex

r(Ni−S)

r(C−S)

r(C−C)

complex

r(Ni−Se)

r(C−Se)

r(C−C)

Ni(S2C2H2)20 Ni(S2C2H2)21− Ni(S2C2H2)22−

2.152 2.187 2.245

1.694 1.725 1.749

1.368 1.351 1.346

[Ni(Se2C2H2)2]0 [Ni(Se2C2H2)2]1− [Ni(Se2C2H2)2]2−

2.278 2.312 2.368

1.844 1.875 1.899

1.359 1.344 1.340

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Figure 3. Differences in reduction potentials calculated at the IEFPCM-DFTi/BS1 levels of theory relative to those calculated at the IEFPCMCCSD(T)/BS1//M06-L/BS1 level of theory for the ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−) and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples (M = Ni, Pd, and Pt).

Table 4. T1 Diagnostic Values Obtained with the CCSD Method complex

T1 0

[Ni(S2C2H2)2] [Ni(Se2C2H2)2]0 [Ni(S2C2H2)2]1− [Ni(Se2C2H2)2]1− [Ni(S2C2H2)2]2− [Ni(Se2C2H2)2]2−

0.05 0.06 0.05 0.06 0.04 0.05

complex

T1 0

[Pd(S2C2H2)2] [Pd(Se2C2H2)2]0 [Pd(S2C2H2)2]1− [Pd(Se2C2H2)2]1− [Pd(S2C2H2)2]2− [Pd(Se2C2H2)2]2−

0.03 0.03 0.03 0.03 0.02 0.02

method with an average difference of only +0.07 V and a RMS of 0.07 V. The next best functionals BP86, B3LYP, and TPSSh predict reduction potentials that are on average −0.09, +0.09, and −0.07 in error relative to the CCSD(T) values with RMSs of 0.11, 0.12, and 0.14 V, respectively. It is noted that in a recent computational study24 of the reaction of C2H4 with Ni(S2C2H2)2 to form an S,S-adduct the energies obtained with the HSE06 and M06 functional were in best agreement with values obtained with the CCSD(T) method. However, in the present study for the 12 reduction potentials HSE06 has an average difference of 0.09 V with a RMS of 0.14 V for the potentials obtained with the CCSD(T) method. If we re-examine Figures 1 and 3 considerable variability in the calculated reduction potentials exists between the different DFT methods. Recently, in the reaction between C2H4 and Ni(S2C2H2)2 Dang et al.24 found that the variations in the calculated reaction energies by the different DFT functionals is caused, in part, from the multireference character of this system. Thus, given the variability in calculated reduction potentials between the various DFT functionals tested a T1 diagnostic was performed. For this calculation the CCSD method was used. The LANL2DZ(f) basis set was used for the Ni, Pd, and Pt atoms. For all other atoms the 6-311G(d,p) basis set with ECPs in the LANL2DZ basis set to describe the core electrons of the S and Se atoms was used. As seen in Table 4 all species suggest that some multireference character is present. In particular, for the Ni complexes the T1 values range from 0.04 to 0.06. For the Pd complexes the T1 values range from 0.02 to 0.03, whereas for the Pt complexes the T1 values are all 0.02. Thus, the variations in reduction potentials for the Ni, Pd, and Pt complexes seen with the use of the different density functionals arises, in part, from the multireference character of

complex

T1 0

[Pt(S2C2H2)2] [Pt(Se2C2H2)2]0 [Pt(S2C2H2)2]1− [Pt(Se2C2H2)2]1− [Pt(S2C2H2)2]2− [Pt(Se2C2H2)2]2−

0.02 0.02 0.02 0.02 0.02 0.02

these systems. As noted in the Introduction such multireference character was previously shown for the neutral Ni−, Pd−, and Pt−bis(3,5-tBu-benzene-1,2-dithiolene) complexes which were found to have 32%, 50%, and 30% singlet diradical character, respectively.25 Thus, from the values in Table 4 the neutral bisdiselenolene complexes likely have considerable singlet diradical character. However, given the likely presence of multireference character of these complexes it is interesting that the pure GGA functionals predict reduction potentials that are generally 0.30 V more reducing than those calculated with the hybrid functionals which contain a percentage of the HF exchange operator. If we re-examine the values in Table 1 the difference in reduction potentials between ([Ni(S 2 C 2 H 2 ) 2 ] 0 /[Ni(S2C2H2)2]1−), ([Pd(S2C2H2)2]0/[Pd(S2C2H2)2]1−), and ([Pt(S2C2H2)2]0/[Pt(S2C2H2)2]1−) is marginal. Similarly, the difference in reduction potentials is marginal for ([Ni(S 2 C 2 H 2 ) 2 ] 1− /[Ni(S 2 C 2 H 2 ) 2 ] 2− ), ([Pd(S 2 C 2 H 2 ) 2 ] 1− /[Pd(S2C2H2)2]2−), and ([Pt(S2C2H2)2]1−/[Pt(S2C2H2)2]2−). In particular, from the values in Table 1 the average reduction potential for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−) redox couples is 4.47 with a RMS of 0.07 V, whereas for the ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−) redox couples the average reduction potential is 3.59 V with a RMS of 0.13 V. This agrees with previous experimental25 CV spectra for the threemembered electron transfer series [M(bdt)2]0,1−,2− (M = Ni, Pd, and Pt) where the reduction and oxidation peaks were nearly independent of the metal, suggesting the redox active MO must be predominantly ligand based in nature. Like the bisdithiolene couples the same can be seen for the bisdiselenolene redox couples. From Table 2 for the ([ME

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The Journal of Physical Chemistry A (Se2C2H2)2]0/[M(Se2C2H2)2]1−) redox couples the average reduction potential is 4.40 with a RMS of only 0.07 V, whereas for the ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples the average reduction potential is 3.82 V with a RMS of 0.11 V. It has been previously stated41 that for bisdithiolene complexes the degree of oxidation of the ligand is related to the degree of covalency between the b2g ligand MO and the metal dxz orbital. Notably, for Ni(S2C2H2)2 and Ni(Se2C2H2)2 (Figure 2) each ligand contributes 43% and 42%, respectively (the values are marginally different for the Pd and Pt complexes) with the Ni (dxz orbital) only contributing 17% and 16%, respectively. Thus, similar covalency between the b2g ligand MO and the metal dxz orbital is observed for the bisdithiolene and bisdiselenolene complexes. For Ni(S2C2H2)21− and [Ni(Se2C 2H 2) 2]1− little difference in seen in the various contributions with the respective ligands each contributing 41% and 42%, respectively. As discussed in the work of Davison and Shawl72 unpublished EPR data for Ni(Se2C2(CF3)2)21− shows a pronounced g value anisotropy as seen in the EPR data73 for Ni(S2C2(CN)2)21−, suggesting that the ligand character for the half-filled SOMO is 70−90%. Thus, for both the dithiolene and the diselenolene complexes the reduction potential for the process would likely be independent of the metal present. Due to the noninnocence of these ligands the reduction potential is more dependent on the ligand than the metal.

contribution to the redox active MO, whereas the metal dxz orbital contributes little. Hence, due to the noninnocence of the dithiolene and diselenolene ligands the reduction potential is more dependent on the ligand than the metal.

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ASSOCIATED CONTENT

S Supporting Information *

Absolute reduction potentials for the various redox couples calculated at the IEFPCM-CCSD(T)/BS1//M06-L/BS1 and IEFPCM-DFTi/BS1//M06-L/BS1 levels of theory; all optimized xyz coordinates for the molecules investigated. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for funding. Computational facilities are provided by ACEnet, the regional high-performance computing consortium for universities in Atlantic Canada. ACEnet is funded by the Canada Foundation for Innovation (CFI), the Atlantic Canada Opportunities Agency (ACOA), and the provinces of Newfoundland and Labrador, Nova Scotia, and New Brunswick. We also thank SHARCNET and Compute Calcul Canada for additional computational resources. E.A.C.B. thanks the Killam Trusts for a Killam Post-Doctoral Fellowship.

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CONCLUSIONS For the calculation of the reduction potentials for the ([M(S2C2H2)2]0/[M(S2C2H2)2]1−), ([M(Se2C2H2)2]0/[M(Se2C2H2)2]1−), ([M(S2C2H2)2]1−/[M(S2C2H2)2]2−), and ([M(Se2C2H2)2]1−/[M(Se2C2H2)2]2−) redox couples (M = Ni, Pd, and Pt) the M06 functional is in best agreement with the CCSD(T) method with an average difference of only 0.07 V and a RMS of 0.07 V. In the case of the GGA functionals, BP86, M06-L, PBE, and TPSS predict reduction potentials that are on average −0.09, −0.24, −0.21, and −0.19 V in error relative to the CCSD(T) values with RMSs of 0.11, 0.12, 0.12, and 0.13 V, respectively. For the hybrid functionals B3LYP, HSE06, PBE0, TPSSh, and ω-B97XD predict reduction potentials that are on average +0.09, +0.09, +0.11, −0.07, and +0.36 V in error relative to the CCSD(T) values with RMSs of 0.12, 0.14, 0.14, 0.14, and 0.12 V, respectively. Like that seen24 in the calculated reaction energies for the reaction between C2H4 and Ni(S2C2H2)2 the variability in calculated reduction potentials between the various DFT functionals arises, in part, from the multireference character of these systems. However, it is noted that the pure GGA functionals predict reduction potentials that are generally 0.30 V more reducing than those calculated with the hybrid functionals. The multireference character decreases as the central metal ion becomes heavier. In particular, for the Ni, Pd, and Pt complexes the average T1 values are 0.05, 0.03, and 0.02, respectively. As noted in the Introduction such multireference character was previously shown for the neutral Ni−, Pd−, and Pt−bis(3,5-tBu-benzene-1,2-dithiolene) complexes which were found to have 32%, 50%, and 30% singlet diradical character, respectively.25 Thus, such multireference character appears to be common for the bisdiselenolene complexes investigated herein. The similarities in the reduction potentials between analogous bisdithiolene and bisdiselenolene redox couples can be partly explained by the fact that each ligand has a large

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REFERENCES

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