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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Quantum Chemical Study of the Redox Potential of the Co(OH2)62+/3+ Couple and the Singlet−Quintet Gibbs Energy Difference of the Co(OH2)63+ Ion François P. Rotzinger*,† and Hui Li*,‡ †

Scientifique Indépendant, Chemin des Vignes 20, CH-1373 Chavornay, Switzerland Department of Chemistry, Nebraska Center for Materials and Nanoscience, and Center for Integrated Biomolecular Communication, University of Nebraska−Lincoln, Lincoln, Nebraska 68588, United States

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‡

S Supporting Information *

ABSTRACT: The geometry and vibrational frequencies of Co(OH2)62+ in the quartet state and Co(OH2)63+ in the singlet and quintet states were computed with quantum mechanics/molecular mechanics (QM/MM), whereby the LC-BOP-LRD functional was used for the QM part involving the Co(OH2)6n+ (n = 2, 3) ions. The surrounding 124 MM water molecules were treated with the MMFF94 force field. The hydration energy differences between low-spin Co(OH2)63+ and Co(OH2)62+ or Co(OH2)63+ in the quintet state were also calculated using this method. The electronic energy of the Co(OH2)6n+ (n = 2, 3) ions was calculated with wave function theory, multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory and spin−orbit configuration interaction. The redox potential of the Co(OH2)62+/3+ couple, and the singlet−quintet (adiabatic) Gibbs energy difference of Co(OH2)63+, computed based on these data, agree with the experiment.

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INTRODUCTION The standard redox potential (E°) of the Co(OH2)62+/3+ couple in aqueous solution, shown in reaction 1, Co(OH 2)6 3 + + e V Co(OH 2)6 2 +

computation of the electronic energy change involving a singlet to quartet spin multiplicity change. The currently available approximate exchange-correlation functionals are not able to reproduce spin-multiplicity changes, near-degeneracy, and static correlation of any system. Multiconfiguration pairdensity functional theory (MC-PDFT)6 and multiconfiguration wave function theory (WFT) are reliable methods. Hence, in this study, the electronic energies were computed with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory (nst-XGMCQDPT2)7−11 and spin−orbit configuration interaction (SO− CI). Using these quantum chemical techniques, the experimental E° value was reproduced. Oxidations by Co(OH2)63+ involve a large spin change and might proceed via the quintet state of Co(OH2)63+, described by reaction 2,

(1)

was investigated with quantum mechanical/molecular mechanical (QM/MM) methods. The strong oxidant Co(OH2)63+ exhibits a low-spin electron configuration and a singlet ground state. In contrast, Co(OH2)62+ has a high-spin electron configuration and a quartet ground state. The experimental E° value is 1.93 ± 0.03 V.1 Ions with 2+ and 3+ charges exhibit large hydration energies, which is difficult to compute with sufficient accuracy with continuum solvation models.2,3 This is illustrated in a computational study of redox potentials of ruthenium-based water-oxidation catalysts.4 Most of these redox reactions involve the transfer of an electron and a proton and, therefore, no change in the net charge. In these cases, dielectric continuum models perform well. However, the computed E° value of the RuV(O)3+ + e → RuIV(O)2+ reaction, a 2+/3+ couple, exhibits a sizable error of 0.23−0.29 V.4 The E° value for the Ru(OH2)62+/3+ system, including an explicit second coordination sphere as presented in the study of Uudsemaa and Tamm,5 agrees with the experiment. This illustrates that an accurate hydration energy difference (ΔEhyd) is required for the computation of E°. It will be shown that QM/MM calculations provide ΔEhyd with an appropriate accuracy. The other challenge in the computation of E° is the © XXXX American Chemical Society

Co(OH 2)6 3 + (singlet) V Co(OH 2)6 3 + (quintet)

(2)

whose Gibbs energy (ΔG) lies 38 ± 16 kJ mol−1 above the singlet ground state.12 This singlet−quintet conversion is accompanied by large changes in the Co−O bond length, giving rise to a sizable hydration energy difference, which cannot be computed accurately with continuum solvation models. The present quantum chemical technique allowed Received: May 14, 2018

A

DOI: 10.1021/acs.inorgchem.8b01308 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry reproduction of the experimental12 ΔG and ΔS (= 40 ± 39 J K−1 mol−1) values of reaction 2.

function theory (WFT) calculations on Co(OH2)63+ in the singlet and quintet states, and those of Co(OH2)62+ in the quartet state were based on the corresponding QM/MM geometries. In octahedral symmetry, the quintet and the quartet states are triply degenerate. Since the QM/MM geometries are not exactly octahedral, because of the MM water environment, which does not exhibit octahedral symmetry, and the broken-symmetry approach, which had to be used with density functional theory (DFT), these states are near-degenerate, but will often be referred to as degenerate. Co(OH2)63+ in the triply degenerate quintet state and Co(OH2)62+ with a triply degenerate quartet ground state require state-of-the-art quantum chemical methods treating static and dynamic electron correlation, (near-)degeneracy, and spin−orbit coupling. These calculations were performed with extended general multiconfiguration quasi-degenerate second-order perturbation theory at the n-state level (nstXGMC-QDPT2).7−11 For Co(OH2)63+ with a singlet ground state, the computations were performed for two active spaces. The latter were determined as described in earlier work,28 using the iterative natural orbital method (INO).29 Pertinent details are given in the Supporting Information. The (10/10) active space involved the two σ(Co−O) molecular orbitals (MOs) of eg type, the five 3d MOs and the three 4dπ MOs of t2g type, which were used for a CASSCF(10/10) wave function. Alternatively, a multiconfiguration self-consistent field (MCSCF) calculation was performed with a larger active space, the (10/10) space extended by the two 4dσ* MOs of eg* type and the 4s MO. The MCSCF computations were based on the occupationally restricted multiple active space (ORMAS)30 technique using three active spaces: the first subspace contained the two σ(Co−O) MOs of eg type, the second subspace contained the five 3d MOs, and third subspace contained the five 4d and 4s MOs. Displacements of one or two electrons between all subspaces were allowed. Since, at the single-state level, the XGMC-QDPT2 energy was not converged, 4-state CASSCF and MCSCF calculations were performed, whereby equal weights were attributed to the ground and the first triply degenerate excited state. Thus, for Co(OH2)63+ in its singlet ground state, 4st-CASSCF(10/10) and 4st-MCSCF(2−4/2,4−8/5,0−2/6,10)16 wave functions were used. The numbers before the slash represent the minimum and maximum number of electrons, the numbers after the slash represent the number of orbitals in a subspace. The data for each subspace are separated by commas, and the last number is the total number of electrons in the active space. The corresponding XGMC-QDPT2 computations (kxgmc = .t., krot = .t., kszdoe = .t.) were based on these two wave functions, denominated as 4st-XGMC-QDPT2(10/10) and 4st-XGMC-QDPT2(2−4/2,4−8/5,0−2/6,10). The 3s and 3p MOs of Co were included in the PT2 treatment, and the electronic energy was based on the first state (the ground state). Spin−orbit (SO) coupling was treated at the stateinteractive configuration interaction (SO−CI) level using the full Breit−Pauli Hamiltonian including a partial two-electron operator.31−33 SO−CI was based on the CASSCF or MCSCF wave function. A (6/5) active space involving the five 3d MOs was taken, whereby one singlet, one triply degenerate triplet, and one triply degenerate quintet states were allowed to interact. The WFT energy, E(WFT), is equal to the sum of E(XGMC-QDPT2) and E(SO). For Co(OH2)63+ in the (triply degenerate) quintet state, a 5st-MCSCF(2−4/2,4−8/5,0−2/5,10) wave function was

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COMPUTATIONAL DETAILS Software and Basis Sets. The calculations were performed with the GAMESS programs.13,14 For Co, O, and H, Jensen’s polarization-consistent segmented basis sets pc-1 and pc-2 with fewer polarization functions were used.15 The Co basis sets contained no (pcsc-1-) or one (pcsc-1, pcsc-2-) f polarization function, which were reoptimized as described previously:16 the energy of the 4F ground state was minimized at the configuration interaction singles-doubles (CISD) level, whereby the 1s−3s and the 2p and 3p MOs were treated as frozen cores. Similarly, the d and p polarization functions for O and H were optimized as described.16 The pcsc-1- (without f and p polarization functions), pcsc-1, and pcsc-2- basis sets are given in the Supporting Information. pcsc-1- and pcsc-1 are of double-ζ valence quality, and pcsc-2- is of triple-ζ valence quality. Figure 1 was generated with Avogadro.17 Quantum Mechanical/Molecular Mechanical (QM/ MM) Calculations. The QM/MM calculations were performed with QuanPol.18 For the QM part, Co(OH2)6n+ (n = 2, 3), the LC-BOP-LRD functional19,20 with a finer grid (nrad = 160, nleb = 770) than the default and the pcsc-2- basis set were used. The MM part involving 124 water molecules was treated with the MMFF94 force field,21−25 whereby for Co the Lennard-Jones (LJ) parameters of Fe were taken. The system was prepared as follows: the geometry of Co(OH2)63+ in the singlet ground state was optimized with LC-BOP-LRD, SMD hydration,26 and the pcsc-2- basis set. A sphere containing 128 water molecules was equilibrated at the MM level with spherical boundary conditions (SBC, sphrad = 9.7) and 100 °C for 1 ns with a time step of 1 fs. Subsequently, an additional simulation was performed at 25 °C also for 1 ns with SBC. This water sphere and Co(OH2)63+ were combined (icombin = 2), with Co being at the center of the sphere. The MM H2Os overlapping with Co(OH2)63+ were deleted (idelete = 19), and some additional MM atoms, which were too close to Co(OH2)63+, were removed manually. The thus-obtained system was equilibrated with QM/MM for 10 ps at 25 °C with a time step of 1 fs and fixed atomic positions of the CoO6 chromophore, SBC (sphrad = 9.7), and QM = HF/pcsc-1-. Subsequently, a QM/MM simulation of 1 ps at 25 °C, SBC, QM = LC-BOP-LRD/pcsc-1- without fixed positions of the CoO6 atoms was performed by keeping the Co atom close to the center of the sphere. The geometry was optimized at the QM/MM level with QM = LC-BOP-LRD and the pcsc-2- basis set starting from the coordinates of the last QM/MM simulation at 1 ps. Bulk solvation was treated with the modified conductor-like screening model FixSol (ntsatm = 240).27 All of the vibrational frequencies of the converged geometry were real. The thermal corrections for the Gibbs energy (g), and the entropy (S) were calculated for 25 °C. The geometry and frequencies of Co(OH2)63+ in the quintet state were computed starting from the optimized structure of the singlet. This ensures minimal changes of the system, in particular, the MM waters. The geometry of Co(OH2)62+ in the quartet state was calculated starting from the quintet Co(OH2)63+ geometry. The atomic coordinates are listed in the Supporting Information. Quantum Chemical Computation of Co(OH2)6n+ (n = 2, 3) with Wave Function Theory (WFT). The wave B


Article

Inorganic Chemistry

frequencies of Co(OH2)6n+ (n = 2, 3), used for the calculation of g and S, were evaluated in the field of the point charges and the LJ potentials of the MM atoms. Computation of ΔG and E°. The Gibbs energy difference (ΔG) of reactions 1 and 2 was computed with QM/MM, as described below. The electronic energy E(QM/MM) (see eq 3) consists of the following components: E(QM), the energy of the QM system, Co(OH2)6n+ (n = 2, 3); E(MM), the energy of the MM waters; E(QM-MM), the interaction energy of the QM and the MM systems, which involves the interaction of the point charges of the MM atoms with the wave function and the LJ energy; and E(FixSol), the solvation energy of the QM/ MM system by bulk water.

used. The 4s MO was not included into the active space, because of its low natural orbital occupation. Equal weights were used for the triply and doubly degenerate states. The electronic energy was based on the average of the three lowest near-degenerate 5st-XGMC-QDPT2(2−4/2,4−8/5,0−2/ 5,10) energies (the 5T2g state). The SO−CI step was performed similar to that done for the singlet state and also involved the average of the three energies of the neardegenerate quintet state. Co(OH2)62+ was investigated with two wave functions: 6stCASSCF(7/10) and 6st-MCSCF(2−4/2,5−9/5,0−2/5,11). The (7/10) active space involved the five 3d and the five 4d MOs (without σ(Co−O) MOs of the eg type), whereas the active space of the MCSCF wave function was the same as for the quintet state (including the two σ(Co−O) MOs of the eg type). The electronic energy was based on the average of the three lowest near-degenerate 6st-XGMC-QDPT2(2−4/2,5− 9/5,0−2/5,11) energies (the 4T1g ground state). Equal weights were used for the two triply degenerate states. The SO−CI(7/ 5) calculation involved the interaction of the triply degenerate quartet and the doubly degenerate doublet states. The thus-computed electronic energies (E(WFT)) included the nst-XGMC-QDPT2 and the SO−CI energies in the gas phase.

E(QM/MM) = E(QM) + E(MM) + E(QM‐MM) + E(FixSol) (3)

Geometries and vibrational frequencies were calculated with QM = DFT (LC-BOP-LRD). As already mentioned, the currently available functionals are not suitable for the computation of ΔG and E° (reaction 1), and ΔG for the (adiabatic) singlet-quintet Gibbs energy difference of Co(OH2)63+ (reaction 2). E(QM = DFT), and, therefore also E(QM = DFT/MM), are likely to be inaccurate, because static electron correlation and (near-)degeneracy are treated approximately with common single-state single-configuration DFT. Furthermore, DFT involving an approximate exchange energy is unlikely to yield accurate singlet−quartet and singlet−quintet energy differences. These errors arising from approximate exchange-correlation functionals are expected to cancel (largely) in the difference of E(DFT/MM) − E(DFT), since the same species with the same geometry and electronic state are involved. Hence, E(QM = WFT/MM) was evaluated according to eq 4:

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RESULTS AND DISCUSSION QM/MM Calculations. The geometry of the Co(OH2)6n+ (n = 2, 3) species surrounded by 124 water molecules (see Figure 1), the hydration energy difference (ΔEhyd) for

E(WFT/MM) = E(DFT/MM) − E(DFT) + E(WFT) (4)

E(QM-MM) and E(FixSol) (from eq 3) are based on DFT. The corresponding Gibbs energy (G) is given by eq 5, G = E(WFT/MM) + g

(5)

whereby g represents the thermal corrections for 25 °C. The Gibbs reaction energy (ΔG) was calculated via eq 6: ΔG = ΔE(WFT/MM) + Δg

(6)

The hydration energy difference (ΔEhyd) is available from eq 7: ΔE hyd = ΔE(DFT/MM) − ΔE(DFT)

(7)

Equation 6 can be rewritten as eq 8, by combining eqs 4, 6, and 7: ΔG = ΔE hyd + ΔE(WFT) + Δg

(8)

The redox potential E° is given by eq 9, ΔG − E(SHE) (9) F where F is the Faraday constant and E(SHE) is the standard hydrogen electrode potential (4.28 V).36−40 The parameters obtained with DFT have already been summarized in Table 1; those calculated with WFT are shown in Table 2, and those for reactions 1 and 2 are given in Table 3. Redox Potential of the Co(OH2)62+/3+ Couple. The redox potential of transition-metal 2+/3+ couples was investigated by Uudsemaa and Tamm,5 using the BP86 E° = −

Figure 1. Co(OH2)63+ in its singlet ground state surrounded by 124 MM water molecules.

reactions 1 and 2, and the thermal corrections for the Gibbs energy (g) and the entropy (S), both at 25 °C, were obtained with QM/MM at the QM = LC-BOP-LRD level (see Table 1), as described in the Computational Details Section. Experimental34,35 and computed Co−O bond lengths of Co(OH2)63+ and Co(OH2)62+ agree (Table 1). The vibrational C


Article

Inorganic Chemistry Table 1. Co−O Bond Lengths, Energies, and Entropy Computed with DFT/MM d(Co−O)av (Å) exp 1.873 ± 0.003

a

3+

Co(OH2)6 (singlet) Co(OH2)63+ (quintet) Co(OH2)62+ (quartet) a

2.081 ± 0.001b

calc

E(DFT/MM) (hartree)

E(DFT) (hartree)

g (kJ mol−1)

S (J K−1 mol−1)

1.871 1.961 2.081

−1842.590841 −1842.556187 −1842.803204

−1839.213819 −1839.200723 −1839.885265

372.080 353.301 345.947

356.612 391.815 412.496

b

Data taken from ref 34. Data taken from ref 35.

Table 2. Energies Calculated with WFT 3+

Co(OH2)6

(singlet)

Co(OH2)63+ (quintet) Co(OH2)62+ (quartet)

wave functiona

E(XGMC-QDPT2) (hartree)

E(SO) (hartree)

E(WFT)b (hartree)

4st-CASSCF 4st-MCSCF 5st-MCSCF 6st-CASSCF 6st-MCSCF

−1838.353552 −1838.351351 −1838.350968 −1839.029007 −1839.032695

−0.000953 −0.001431 −0.000552 −0.000628 −0.000680

−1838.354505 −1838.352782 −1838.351490 −1839.029635 −1839.033375

a

See the Computational Details section. bE(WFT) = E(XGMC-QDPT2) + E(SO).

Table 3. Gibbs Reaction Energies, Entropies, and Redox Potentials reaction

wave function

1

a

2

ΔE(WFT) (kJ mol−1)

ΔEhyd (kJ mol−1)

Δg (kJ mol−1)

exp CASSCF MCSCF

−1772.6 −1786.9

1205.3

−26.1

expb MCSCF

3.4

56.6

−18.8

ΔG (kJ mol−1)

ΔS, (J K−1 mol−1)

E° (V)

−593.4 −607.7

55.9

1.93 ± 0.03 1.87 2.02

38 ± 16 41.2

40 ± 39 35.2

a

Data taken from ref 1. bData taken from ref 12.

ΔE(WFT), ΔEhyd, and Δg are of comparable magnitude, they all must be computed accurately. The agreement of ΔS with experiment suggests that the present approximations in the calculation of the vibrational frequencies, where the frequencies of the MM waters are neglected, are appropriate. The Co(OH2)62+/3+ redox couple is the most demanding one among the hexa aqua transition-metal 2+/3+ couples, because of its singlet−quartet spin multiplicity change and its large changes in bond length (0.21 Å). The singlet−quintet Gibbs energy difference of Co(OH2)63+ is similarly difficult to compute. The agreement of computed and experimental data for reactions 1 and 2 suggests that the present computational methods are suitable for the computation of other redox couples and adiabatic spin multiplicity changes.

functional. The second coordination sphere of the hexa aqua ions, represented by 12 water molecules, was also treated quantum chemically, and bulk solvation was modeled with COSMO. For the Cr(OH2)62+/3+ and the Fe(OH2)62+/3+ couples, they obtained an agreement with experiment better than 0.15 V, if their data are corrected for E(SHE) = 4.28 V instead of 4.43 V. For the Co(OH2)62+/3+ couple, however, the deviation from the experiment (approximately −0.7 V) is sizable, most likely because DFT is not suitable for this system as already mentioned (see the Introduction and Results and Discussion sections). As can be seen in Table 3, E° computed with the present methodology agrees with the experiment. Accurate Co−O bond lengths are necessary for a correct calculation of the singlet-quartet spin change energy. The Co−O bond lengths of Co(OH2)63+ (singlet ground state) and Co(OH2)62+ (quartet ground state), obtained with DFT/MM and FixSol hydration, agree with the experiment (see Table 1). ΔE(WFT) and ΔEhyd (see Table 3) are large and exhibit opposite signs, while Δg is small. The agreement of E° with the experiment is due to the accurate ΔE(WFT), ΔEhyd, and Δg values, whereby ΔE(WFT) is most demanding. Adiabatic Singlet−Quintet Gibbs Energy Difference of Co(OH2)63+. The present computational methods allowed to obtain E° of the Co(OH2)62+/3+ couple being in agreement with experiment. Hence, the corresponding ΔG value is accurate, and the adequacy of the method for its computation is validated. The appropriateness of the computational method is corroborated by the agreement of ΔG for reaction 2 with the experiment (see Table 3). It is interesting to note that ΔE(WFT) is small, close to zero (at the geometries of the hydrated Co(OH2)63+ species). ΔG is dominated by ΔEhyd, Δg having an opposite sign and being one-third of ΔEhyd. Since

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01308. Method for the determination of the active space; pcsc1-, pcsc-1, and pcsc-2- basis sets for Co, O, and H; atomic coordinates of Co(OH2)63+ (singlet and quintet states) and Co(OH2)62+, surrounded by 124 MM water molecules (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (F. Rotzinger). *E-mail: [email protected] (H. Li). ORCID

François P. Rotzinger: 0000-0001-8759-4427 D


Article

Inorganic Chemistry

(16) Rotzinger, F. P. Structure and Properties of the Precursor/ Successor Complex and Transition State of the CrCl2+/Cr2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway. Inorg. Chem. 2014, 53, 9923−9931. (17) Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: an advanced semantic chemical editor, visualization, and analysis platform. J. Cheminf. 2012, 4, 1−17. (18) Thellamurege, N. M.; Si, D.; Cui, F.; Zhu, H.; Lai, R.; Li, H. QuanPol: A Full Spectrum and Seamless QM/MM Program. J. Comput. Chem. 2013, 34, 2816−2833. (19) Sato, T.; Nakai, H. Density functional method including weak interactions: Dispersion coefficients based on the local response approximation. J. Chem. Phys. 2009, 131, 224104. (20) Sato, T.; Nakai, H. Local response dispersion method. II. Generalized multicenter interactions. J. Chem. Phys. 2010, 133, 194101. (21) Halgren, T. A. Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94. J. Comput. Chem. 1996, 17, 490−519. (22) Halgren, T. A. Merck molecular force field. II. MMFF94 van der Waals and electrostatic parameters for intermolecular interactions. J. Comput. Chem. 1996, 17, 520−552. (23) Halgren, T. A. Merck molecular force field. III. Molecular geometries and vibrational frequencies for MMFF94. J. Comput. Chem. 1996, 17, 553−586. (24) Halgren, T. A.; Nachbar, R. B. Merck molecular force field. IV. conformational energies and geometries for MMFF94. J. Comput. Chem. 1996, 17, 587−615. (25) Halgren, T. A. Merck molecular force field. V. Extension of MMFF94 using experimental data, additional computational data, and empirical rules. J. Comput. Chem. 1996, 17, 616−641. (26) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378−6396. (27) Thellamurege, N. M.; Li, H. Note: FixSol solvation model and FIXPVA2 tessellation scheme. J. Chem. Phys. 2012, 137, 246101. (28) Rotzinger, F. P. The Water-Exchange Mechanism of the [UO2(OH2)5]2+ Ion Revisited: The Importance of a Proper Treatment of Electron Correlation. Chem.Eur. J. 2007, 13, 800− 811. (29) Bender, C. F.; Davidson, E. R. A Natural Orbital Based Energy Calculation for Helium Hydride and Lithium Hydride. J. Phys. Chem. 1966, 70, 2675−2685. (30) Ivanic, J. Direct configuration interaction and multiconfigurational self-consistent-field method for multiple active spaces with variable occupations. I. method. J. Chem. Phys. 2003, 119, 9364− 9376. (31) Furlani, T. R.; King, H. F. Theory of spin-orbit coupling. Application to singlet−triplet interaction in the trimethylene biradical. J. Chem. Phys. 1985, 82, 5577−5583. (32) King, H. F.; Furlani, T. R. Computation of one and two electron spin-orbit integrals. J. Comput. Chem. 1988, 9, 771−778. (33) Fedorov, D. G.; Gordon, M. S. A study of the relative importance of one and two-electron contributions to spin−orbit coupling. J. Chem. Phys. 2000, 112, 5611−5623. (34) Beattie, J. K.; Best, S. P.; Skelton, B. W.; White, A. H. Structural Studies on the Caesium Alums, CsMIII[SO4]2 · 12 H2O. J. Chem. Soc., Dalton Trans. 1981, 2105−2111. (35) Ray, S.; Zalkin, A.; Templeton, D. H. Crystal structures of the fluosilicate hexahydrates of cobalt, nickel and zinc. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1973, 29, 2741−2747. (36) Truhlar, D. G.; Cramer, C. J.; Lewis, A.; Bumpus, J. A. Molecular Modeling of Environmentally Important Processes: Reduction Potentials. J. Chem. Educ. 2004, 81, 596−604. (37) Truhlar, D. G.; Cramer, C. J.; Lewis, A.; Bumpus, J. A. Molecular Modeling of Environmentally Important Processes: Reduction PotentialsCorrections. J. Chem. Educ. 2007, 84, 934.

Hui Li: 0000-0003-0580-7033 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Some of the computations were performed at the Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. This work was partially supported by a seed grant from the Nebraska Center for Integrated Biomolecular Communication (NIH, National Institutes of General Medical Sciences, No. P20-GM113126). The reviewers’ helpful comments are gratefully acknowledged.

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