# Samarium Diiodide Acting on Acetone—Modeling Single Electron Transfer Energetics in Solution

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Optimized Structures

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ system shown in Figure 1 by the use of two different large-core pseudopotentials for Sm. Kefalidis et al. describe the strategy in great detail [17,35]. With the 4f electrons in the core, the ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ system is a closed-shell system, and the ACE is bound in its electronic ground state configuration to Sm. The Sm-ACE distance is quite long, at $2.68$ Å, which indicates a weak bond. This is different in the case of ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$, where the ECP51MWB models Sm

^{III}. The one explicitly treated f-electron of the Sm is readily transferred to acetone, forming a ketyl radical. The Sm-ACE bond length significantly shrinks to $2.12$ Å. The bond angle ${\measuredangle}_{SmOC}$ increases significantly by $22.1$ ${}^{\circ}$, which can be related to both a cause and a result of the bond length shortening of Sm-ACE. This can possibly be traced to the change of the proportion between the covalent bonding and the electrostatic attraction. The antibonding ${\pi}^{*}$ orbital of ACE is filled with an electron in ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$, which will be further discussed. Bond shortening upon electron transfer is expected due to the oxidation-induced contraction of the electron cloud around Sm

^{III}, which is further discussed in the literature [36]. The SET-induced Sm-ACE bond length shortening causes a polarizing effect, which leads to anisotropic bond length changes in the surrounding THF ligand. Changes in the bond lengths of Sm-I are greater than changes in THF because iodine is already charged and attractive forces rise from the SET. Hence, the SET leads to a tighter binding situation through increased electrostatic attraction and bond formation.

#### 2.2. Electron Transfer Reaction Energy

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ are calculated by CASPT2 and density functional theory in this section (cf. Table 1). The CAS result states that the equilibrium is on the side of acetone. The energy of the SET is $48.94$ kJ/mol according to the CASPT2(6,13) septet calculation. The energy difference takes into account the first solvation shell (by THF), static and dynamic correlation and scalar relativistic effects. Thermal corrections, spin orbit coupling and the second solvation shell are not taken into account. Correction from perturbation theory is only $3.00$ kJ/mol, which indicates that the CASSCF(6,13) accounts quite well for the dynamic correlation. An initial active space consisting of the seven 4f orbitals and the ligand orbital of interest was selected, along with the appropriate number of electrons resulting in a CAS(6,8). The smaller active space is further discussed in the Supplementary Materials SI.2. However, calculations with an additional five correlating orbitals were performed. If one thinks in terms of the Sm atomic orbitals, these five orbitals were expected to represent the 5d shell. During orbital optimization, higher angular momentum functions are mixed in the molecular orbitals, as is often the case. This larger (6,13) active space resulted in reasonably large changes in the triplet-quintet spin splitting energies compared to the smaller space, and for this reason, only the larger active space is reported.

#### 2.3. Comparison of Quintet and Septet Spin State

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$) and the ketyl system (ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$). The CASPT2 calculation predicts large differences between the septet and quintet for the acetone system. The actual energy difference of 240 kJ/mol has to be taken with care as the ${\pi}^{*}$ orbital is not in the active space. However, the spin crossover energy is high for the f-electrons localized at the Sm core. That is totally different for the ketyl moiety, where the septet and quintet are quasi-degenerate, as expected with one electron being delocalized at the organic substrate. The degenerate states’ SET-electron shows only minor interactions with the spins at the samarium core.

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ case, there is also a large energy difference between the septet and the quintet, while in the ketyl case, the septet and the quintet are significantly closer in energy. However, the energy difference of $35.5$ kJ/mol is still ten times larger then in the CASPT2 result. As the electron is not fully transferred in the DFT calculation (for further details, see Supplementary Materials SI.3), the spin flip needs more energy. Exact exchange is one possible reason for the inaccurate difference in energy between the quintet and the septet, while the spin contamination of approximately 10% may also impact the energy as well as a self-interaction error. Although the CASPT2 picture of the SET is not perfectly reproduced, PBE0-D3 describes the situation surprisingly well.

#### 2.4. Effects of HMPA as Cosolvent

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$, ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{2}$${\left(\mathrm{HMPA}\right)}_{1}$, ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{3}$, ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$ and the corresponding structures of ACE-Sm

^{III}${}^{\u2022}$${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{\mathrm{m}}$(HMPA)

_{n}, for which examples are shown in Figure 3. The bond length shortening of the SET step causes a structural distortion for ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$ compared to ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$ in the upper part of Figure 3. There, the fourth HMPA ligand is pushed out of plane, which bends the ISmI angle. Therefore, we introduced sixfold coordinated structures, which are seen as distortion-free. The ACE-Sm${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{3}$ structure reflects the substitution of one HMPA molecule by acetone. HMPA is in the trans-position to the acetone molecule in $\mathrm{ACE}-\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{2}\left(\mathrm{HMPA}\right)$ since we expect the highest influence on the binding in this position by the polarization of the Sm-ACE bond. The structures with a coordination number of 6 do not show distortion through SET, which is highlighted by ${\measuredangle}_{ISmI}$.

^{II}${\mathrm{I}}_{2}$ structures with ECP28MWB causes low structural changes, which are also reported [35]. The substitution of all THF by four HMPA leads to an increased Sm-I bond length of $0.2$ Å, which is in agreement with the crystal structures [32]. The same substitution leads to changes in the Sm-ACE bond length of $0.05$ Å.

^{II}${\mathrm{I}}_{2}$ by 10 kJ/mol. One exception is the molecule with four HMPA ligands, which is less stabilized. The replacement of two THF by one HMPA molecule has an effect on the reduction potential only when COSMO is applied. Implicit solvation shifts the equilibrium towards ACE-Sm

^{II}${\mathrm{I}}_{2}$ and increases the effect of HMPA on the SET, which is further discussed in the Supplementary Materials SI.4. It can be seen from the differences between $\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{4}$ and $\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{2}{\left(\mathrm{HMPA}\right)}_{1}$ that COSMO has a special effect on the 6-fold coordinated structure. Two small THF molecules and two other ligands form the solvent accessible surface (SAS) of the implicit solvation model. The samarium atom is shielded by the explicit solvent environment, as is indicated by electron surface potential maps in the Supplementary Materials SI.4. The application of COSMO for optimization and SET energy calculation significantly increases the total influence of HMPA.

^{II}${\mathrm{I}}_{2}$ structures are given in Table 2. Optimization with a small-core ECP is necessary to interpret the SOMO energies. Therefore, the values of ${\u03f5}_{P52,g}$ are not interpreted. The application of COSMO shifts SOMO energies constantly by about $-25$ kJ/mol. The SOMO energy change of ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$ to ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ is 89 kJ/mol, which reasonably reproduces the magnitude of linear sweep experiments. The change from ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{3}$ to ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ is 67 kJ/mol, which is also reasonable compared to the experimental value of $59.8$ kJ/mol (3 eq. HMPA). The difference towards the experiment is surprisingly small when we think about the approximations and about the fact that the discussed energies come from Kohn–Sham orbitals. Hence, this shows that our DFT results reproduce the HMPA effect in agreement with measurements coming from linear sweeps as well as the one from the rate experiments [28,34].

## 3. Methodology

^{II}) and ECP51MWB-SV [22,23] (Sm

^{III}) in conjunction with the corresponding large-core Stuttgart–Dresden ECPs. Single-point energies were calculated with the def2-TZVP basis set with ECP28MWB for samarium and iodine. The density functional benchmark includes single-point energy calculations with the following functionals: PBE0 [42,43,44,45,46], B3LYP [42,43,47,48,49,50], BHLYP [42,43,48,49,51], PBE [42,43,44,45], TPSS [42,43,44,52], TPSSH [42,43,44,52,53], and B3PW91 [42,43,45,48]. The exchange correlation functionals were integrated with multigrid m4. The thermal smearing of electrons improved the initial wavefunction guess of single-point energy calculations. The SCF energy convergence threshold was ${10}^{-6}$$\mathrm{au}$, and gradients were converged to ${10}^{-3}$$\mathrm{au}$.

^{II}. The application of COSMO [54] ($\u03f5=7.4$, THF) in single-point calculations and structure optimization was also evaluated. Other parameters were used as described above.

^{II}species was calculated. The Sm

^{III}species’ active space included seven 4f orbitals, five 5f orbitals and the $\pi *$ orbital of the organic environment. The all-electron ANO-RCC basis sets were used with the following contractions: 8s7p4d3f2g1h for Sm, 4s3p2d1f for O, 4s3p2d1f for C, 7s6p4d2f1g for I, and 1s for H [56,57]. Scalar relativistic effects were included with the second-order Douglas–Kroll–Hess Hamiltonian (DKH2). The cost of integral evaluation was reduced using Cholesky decomposition in combination with local exchange screening. For both complexes, the septet and quintet states were calculated. Spin-splitting energies were reported for second-order multireference perturbation theory (CASPT2). In the CASPT2 zeroth-order Hamiltonian, both an imaginary shift of $0.2$ au and an IPEA shift of 0.25 were employed.

## 4. Conclusions

^{II}${\mathrm{I}}_{2}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$ in explicit THF solvent under CASPT2 and various DFT methods. Furthermore, the effect of the cosolvent HMPA on the single electron transfer (SET) was modelled by replacing THF with explicit HMPA molecules.

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ quintet and septet tells us that the quintet is not involved in the SET on the ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ side of the reaction. An almost degenerate quintet/septet state of the ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ structure is foretold by the CASPT2 calculation. The degenerate state is not as well reproduced by PBE0-D3 because of spin contamination, self-interaction and/or overestimated exchange energy. Hence, SET reactions need further investigations for unambiguous statements as to the DFT picture of samarium diiodide reactions.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DFT | Density functional theory |

SET | Single electron transfer |

ACE | Acetone |

ACE${}^{-\u2022}$ | Ketyl radical anion |

ECP | Electron core potential |

## References

- Namy, J.L.; Girard, P.; Kagan, H. A new preparation of some divalent lanthanide iodides and their usefulness in organic synthesis. 1977. Available online: https://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL7760218279 (accessed on 6 December 2022).
- Girard, P.; Namy, J.; Kagan, H. Divalent lanthanide derivatives in organic synthesis. 1. Mild preparation of samarium iodide and ytterbium iodide and their use as reducing or coupling agents. J. Am. Chem. Soc.
**1980**, 102, 2693–2698. [Google Scholar] [CrossRef] - Molander, G.A.; McKie, J.A. Samarium (II) iodide-induced reductive cyclization of unactivated olefinic ketones. Sequential radical cyclization/intermolecular nucleophilic addition and substitution reactions. J. Org. Chem.
**1992**, 57, 3132–3139. [Google Scholar] [CrossRef] - Molander, G.A.; Harris, C.R. Sequencing reactions with samarium II iodide. Chem. Rev.
**1996**, 96, 307–338. [Google Scholar] [CrossRef] [PubMed] - Szostak, M.; Fazakerley, N.J.; Parmar, D.; Procter, D.J. Cross-coupling reactions using samarium II iodide. Chem. Rev.
**2014**, 114, 5959–6039. [Google Scholar] [CrossRef] [PubMed] - Edmonds, D.J.; Johnston, D.; Procter, D.J. Samarium(II)-iodide-mediated cyclizations in natural product synthesis. Chem. Rev.
**2004**, 35, 3371–3404. [Google Scholar] [CrossRef] [PubMed] - Gopalaiah, K.; Kagan, H.B. Recent developments in samarium diiodide promoted organic reactions. Chem. Rec.
**2013**, 13, 187–208. [Google Scholar] [CrossRef] [PubMed] - Berndt, M.; Gross, S.; Hölemann, A.; Reissig, H.U. New samarium diiodide-induced ketyl couplings - From analogous reactions to serendipitously discovered processes. Synlett
**2004**, 422–438. [Google Scholar] [CrossRef] - Procter, D.J.; Flowers, R.A.; Skrydstrup, T. Organic synthesis using samarium diiodide; Royal Society of Chemistry: London, UK, 2010. [Google Scholar] [CrossRef]
- Beemelmanns, C.; Reissig, H.U. Samarium diiodide induced ketyl-het arene cyclisations towards novel N-heterocycles. Chem. Soc. Rev.
**2011**, 40, 2199–2210. [Google Scholar] [CrossRef] - Szostak, M.; Spain, M.; Procter, D.J. Recent advances in the chemoselective reduction of functional groups mediated by samarium II iodide: A single electron transfer approach. Chem. Soc. Rev.
**2013**, 42, 9155–9183. [Google Scholar] [CrossRef] - Ashida, Y.; Arashiba, K.; Nakajima, K.; Nishibayashi, Y. Molybdenum-catalysed ammonia production with samarium diiodide and alcohols or water. Nature
**2019**, 568, 536–540. [Google Scholar] [CrossRef] - Gong, J.; Chen, H.; Liu, X.Y.; Wang, Z.X.; Nie, W.; Qin, Y. Total synthesis of atropurpuran. Nat. Commun.
**2016**, 7. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Leung, J.C.; Bedermann, A.A.; Njardarson, J.T.; Spiegel, D.A.; Murphy, G.K.; Hama, N.; Twenter, B.M.; Dong, P.; Shirahata, T.; McDonald, I.M.; et al. Total synthesis of (A)-phomoidride D. Angew. Chem. Int. Ed.
**2018**, 57, 1991–1994. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Boekell, N.G.; Flowers, R.A. Coordination-induced bond weakening. Chem. Rev.
**2022**, 122, 13447–13477. [Google Scholar] [CrossRef] - Achazi, A.J.; Dirk, A.; Reissig, H.U.; Paulus, B. A computational study of samarium diiodide-induced cyclizations of N-oxoalkyl-substituted methyl indole-3-carboxylates—A rationale of the diastereoselectivity. J. Comput. Chem.
**2017**, 38, 2693–2700. [Google Scholar] [CrossRef] [PubMed] - Kefalidis, C.E.; Essafi, S.; Perrin, L.; Maron, L. Qualitative estimation of the single-electron transfer step energetics mediated by samarium (II) complexes: A “SOMO–LUMO Gap” Approach. Inorg. Chem.
**2014**, 53, 3427–3433. [Google Scholar] [CrossRef] [PubMed] - Kefalidis, C.E.; Castro, L.; Perrin, L.; Del Rosal, I.; Maron, L. New perspectives in organolanthanide chemistry from redox to bond metathesis: Insights from theory. Chem. Soc. Rev.
**2016**, 45, 2516–2543. [Google Scholar] [CrossRef] [PubMed] - Ramírez-Solís, A.; Boekell, N.G.; León-Pimentel, C.I.; Saint-Martin, H.; Bartulovich, C.O.; Flowers, R.A. Ammonia solvation vs aqueous solvation of samarium diiodide. A theoretical and experimental approach to understanding bond activation upon coordination to Sm (II). J. Org. Chem.
**2021**, 87, 1689–1697. [Google Scholar] [CrossRef] - Dyer, H.E.; Huijser, S.; Susperregui, N.; Bonnet, F.; Schwarz, A.D.; Duchateau, R.; Maron, L.; Mountford, P. Ring-opening polymerization of rac-lactide by bis (phenolate) amine-supported samarium borohydride complexes: An experimental and DFT study. Organometallics
**2010**, 29, 3602–3621. [Google Scholar] [CrossRef] - Perrin, L.; Kirillov, E.; Carpentier, J.F.; Maron, L. DFT Investigation of the tacticity control during styrene polymerization catalyzed by single-component allyl ansa-lanthanidocenes {(C5H4CMe2 (9-C13H8)} Ln (C3H5). Macromolecules
**2010**, 43, 6330–6336. [Google Scholar] [CrossRef] - Dolg, M.; Stoll, H.; Savin, A.; Preuss, H. Energy-adjusted pseudopotentials for the rare earth elements. Theor. Chim. Acta
**1989**, 75, 173–194. [Google Scholar] [CrossRef] - Dolg, M.; Stoll, H.; Preuss, H. A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds. Theor. Chim. Acta
**1993**, 85, 441–450. [Google Scholar] [CrossRef] - Kelly, R.P.; Toniolo, D.; Tirani, F.F.; Maron, L.; Mazzanti, M. A tetranuclear samarium (ii) inverse sandwich from direct reduction of toluene by a samarium (ii) siloxide. Chem. Commun.
**2018**, 54, 10268–10271. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Agasti, S.; Beattie, N.A.; McDouall, J.J.W.; Procter, D.J. SmI2-catalyzed intermolecular coupling of cyclopropyl ketones and alkynes: A link between ketone conformation and reactivity. J. Am. Chem. Soc.
**2021**, 143, 3655–3661. [Google Scholar] [CrossRef] [PubMed] - Dolg, M.; Stoll, H.; Preuss, H. Energy-adjusted abinitio pseudopotentials for the rare earth elements. J. Chem. Phys.
**1989**, 90, 1730–1734. [Google Scholar] [CrossRef] - Beemelmanns, C.; Blot, V.; Gross, S.; Lentz, D.; Reissig, H.U. Highly diastereoselective samarium diiodide induced ketyl cyclisations of indole and pyrrole derivatives – scope and limitations. Eur. J. Org. Chem.
**2010**, 2010, 2716–2732. [Google Scholar] [CrossRef] - Curran, D.P.; Fevig, T.L.; Jasperse, C.P.; Totleben, M.J. New mechanistic insights into reductions of halides and radicals with samarium (II) iodide. Synlett
**1992**, 1992, 943–961. [Google Scholar] [CrossRef] - Wefelscheid, U.K.; Berndt, M.; Reißig, H.U. Samarium diiodide mediated ketyl–aryl coupling reactions – influence of substituents and trapping experiments. Eur. J. Org. Chem.
**2008**, 2008, 3635–3646. [Google Scholar] [CrossRef] - Shabangi, M.; Sealy, J.M.; Fuchs, J.R.; Flowers, R.A., II. The effect of cosolvent on the reducing power of SmI2 in tetrahydrofuran. Tetrahedron Lett.
**1998**, 39, 4429–4432. [Google Scholar] [CrossRef] - Hou, Z.; Zhang, Y.; Wakatsuki, Y. Molecular structures of HMPA-coordinated samarium (II) and ytterbium (II) iodide complexes. A structural basis for the HMPA effects in SmI2-promoted reactions. Bull. Chem. Soc. Jpn.
**1997**, 70, 149–153. [Google Scholar] [CrossRef] - Shotwell, J.B.; Sealy, J.M.; Flowers, R.A. Structure and Energetics of the Samarium Diiodide HMPA Complex in Tetrahydrofuran. J. Org. Chem.
**1999**, 64, 5251–5255. [Google Scholar] [CrossRef] - Enemærke, R.J.; Hertz, T.; Skrydstrup, T.; Daasbjerg, K. Evidence for ionic samarium (II) species in THF/HMPA solution and investigation of their electron-donating properties. Chem.- Eur. J.
**2000**, 6, 3747–3754. [Google Scholar] [CrossRef] [PubMed] - Shabangi, M.; Flowers, R.A., II. Electrochemical investigation of the reducing power of SmI2 in THF and the effect of HMPA cosolvent. Tetrahedron Lett.
**1997**, 38, 1137–1140. [Google Scholar] [CrossRef] - Kefalidis, C.E.; Perrin, L.; Maron, L. Preliminary theoretical insights into SmI2-mediated reactions: Activation of ketones in THF. Eur. J. Inorg. Chem.
**2013**, 2013, 4042–4049. [Google Scholar] [CrossRef] - Hoz, S. Samarium iodide showcase: Unraveling the mechanistic puzzle. Acc. Chem. Res.
**2020**, 53, 2680–2691. [Google Scholar] [CrossRef] [PubMed] - Inanaga, J.; Ishikawa, M.; Yamaguchi, M. A mild and convenient method for the reduction of organic halides by using a SmI2-THF solution in the presence of hexamethylphosphoric triamide (HMPA). Chem. Lett.
**1987**, 16, 1485–1486. [Google Scholar] [CrossRef] [Green Version] - Enemærke, R.J.; Daasbjerg, K.; Skrydstrup, T. Is samarium diiodide an inner-or outer-sphere electron donating agent? Chem. Commun.
**1999**, 343–344. [Google Scholar] [CrossRef] - Sadasivam, D.V.; Teprovich, J.A.J.; Procter, D.J.; Flowers, R.A.I. Dynamic ligand exchange in reactions of samarium diiodide. Org. Lett.
**2010**, 12, 4140–4143. [Google Scholar] [CrossRef] - Yang, J.; Dolg, M. Valence basis sets for lanthanide 4f-in-core pseudopotentials adapted for crystal orbital ab initio calculations. Theor. Chem. Acc.
**2005**, 113, 212–224. [Google Scholar] [CrossRef] - Weigand, A.; Cao, X.; Yang, J.; Dolg, M. Quasirelativistic f-in-core pseudopotentials and core-polarization potentials for trivalent actinides and lanthanides: Molecular test for trifluorides. Theor. Chem. Acc.
**2010**, 126, 117–127. [Google Scholar] [CrossRef] - Dirac, P.A.M.; Fowler, R.H. Quantum mechanics of many-electron systems. Proc. R. Soc. Lond. Ser. A Contain. Pap. A Math. Phys. Character
**1929**, 123, 714–733. [Google Scholar] [CrossRef] [Green Version] - Slater, J.C. A Simplification of the Hartree-Fock Method. Phys. Rev.
**1951**, 81, 385–390. [Google Scholar] [CrossRef] - Perdew, J.P.; Wang, Y. Erratum: Accurate and simple analytic representation of the electron-gas correlation energy [Phys. Rev. B 45, 13244 (1992)]. Phys. Rev. B
**2018**, 98, 079904. [Google Scholar] [CrossRef] [Green Version] - Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett.
**1996**, 77, 3865–3868. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Perdew, J.P.; Ernzerhof, M.; Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys.
**1996**, 105, 9982–9985. [Google Scholar] [CrossRef] - Vosko, S.H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys.
**1980**, 58, 1200–1211. [Google Scholar] [CrossRef] [Green Version] - Becke, A.D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A
**1988**, 38, 3098–3100. [Google Scholar] [CrossRef] - Lee, C.; Yang, W.; Parr, R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B
**1988**, 37, 785–789. [Google Scholar] [CrossRef] [Green Version] - Becke, A.D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys.
**1993**, 98, 5648–5652. [Google Scholar] [CrossRef] [Green Version] - Becke, A.D. A new mixing of Hartree–Fock and local density-functional theories. J. Chem. Phys.
**1993**, 98, 1372–1377. [Google Scholar] [CrossRef] - Tao, J.; Perdew, J.P.; Staroverov, V.N.; Scuseria, G.E. Climbing the density functional ladder: Nonempirical meta–generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett.
**2003**, 91, 146401. [Google Scholar] [CrossRef] [Green Version] - Staroverov, V.N.; Scuseria, G.E.; Tao, J.; Perdew, J.P. Comparative assessment of a new nonempirical density functional: Molecules and hydrogen-bonded complexes. J. Chem. Phys.
**2003**, 119, 12129–12137. [Google Scholar] [CrossRef] - Schäfer, A.; Klamt, A.; Sattel, D.; Lohrenz, J.C.; Eckert, F. COSMO Implementation in TURBOMOLE: Extension of an efficient quantum chemical code towards liquid systems. Phys. Chem. Chem. Phys.
**2000**, 2, 2187–2193. [Google Scholar] [CrossRef] [Green Version] - Fdez. Galván, I.; Vacher, M.; Alavi, A.; Angeli, C.; Aquilante, F.; Autschbach, J.; Bao, J.J.; Bokarev, S.I.; Bogdanov, N.A.; Carlson, R.K.; et al. OpenMolcas: From source code to insight. J. Chem. Theory Comput.
**2019**, 15, 5925–5964. [Google Scholar] [CrossRef] - Roos, B.O.; Lindh, R.; Malmqvist, P.Å.; Veryazov, V.; Widmark, P.O. Main group atoms and dimers studied with a new relativistic ANO basis set. J. Phys. Chem. A
**2003**, 108, 2851–2858. [Google Scholar] [CrossRef] - Roos, B.O.; Lindh, R.; Malmqvist, P.Å.; Veryazov, V.; Widmark, P.O.; Borin, A.C. New relativistic atomic natural orbital basis sets for lanthanide atoms with applications to the Ce diatom and LuF3. J. Phys. Chem. A
**2008**, 112, 11431–11435. [Google Scholar] [CrossRef]

**Figure 1.**ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ (

**left**) is optimized with PBE0-D3/def2-TZVP (I, C, O, H) and ECP52MWB-II (Sm), while ECP51MWB-SV (Sm) converges to the ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ structure. Spin difference density of the doublet (

**right**) is shown for a density value of the isosurface of $0.002$ au. Bond distances (d) are printed in (Å). Important bond angles are ACE-Sm

^{II}${\mathrm{I}}_{2}$: ${\measuredangle}_{ISmI}=$$176.6$${}^{\circ}$, ${\measuredangle}_{SmOC}=$$142.1$${}^{\circ}$; ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$: ${\measuredangle}_{ISmI}=$$170.6$${}^{\circ}$, ${\measuredangle}_{SmOC}=$$164.2$${}^{\circ}$.

**Figure 2.**Single-point energies in ($\mathrm{kJ}/\mathrm{mol}$) for the structures ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{4}$, calculated as septet (M = 7) and quintet (M = 5), with CASPT2 (6,13) (

**left**) and with PBE0-D3 together with spin difference densities (

**right**). The PBE0-D3 quintet calculations show spin contamination ($\langle {\widehat{\mathrm{S}}}^{2}\rangle =7.0$ instead of $7.75$).

**Figure 3.**The ACE-Sm

^{II}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$ structure is optimized with PBE0-D3/def2-TZVP (H, C, N, O, P, I) and ECP52MWB-II (Sm), while ECP51MWB-SV (Sm) is used for optimization of ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{THF}\right)}_{2}$${\left(\mathrm{HMPA}\right)}_{1}$, ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{3}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$. ${\measuredangle}_{ISmI}$ indicate the structural change in ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$${\left(\mathrm{HMPA}\right)}_{4}$.

**Table 1.**Gas phase SET energies are shown in ($\mathrm{kJ}/\mathrm{mol}$) ($\mathsf{\Delta}E={E}_{{\mathrm{ACE}}^{\u2022}-\mathrm{Sm}\mathrm{III}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{4}}-{E}_{\mathrm{ACE}-\mathrm{Sm}\mathrm{II}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{4}}$). CAS (6,13), and DFT energies are calculated as described in the methodology section. Structures ACE-Sm

^{II}${\mathrm{I}}_{2}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$ are optimized with ECP52MWB-II and ECP51MWB-SV, respectively, and the PBE0-D3 functional in gas phase.

$\mathbf{\Delta}\mathit{E}$ | |
---|---|

CASSCF (6,13) | 51.94 |

CASPT2 (6,13) | 48.94 |

TPSS-D3 | 12.76 |

PBE-D3 | 28.91 |

TPSSH-D3 | 27.28 |

PBE0-D3 | 53.19 |

B3LYP-D3 | 55.40 |

BHLYP-D3 | 38.42 |

B3PW91-D3 | 69.66 |

B3PW91 | 40.02 |

**Table 2.**SET energies $\mathsf{\Delta}E={E}_{{\mathrm{ACE}}^{\u2022}-{\mathrm{Sm}}^{\mathrm{III}}{\mathrm{I}}_{2}}-{E}_{\mathrm{ACE}-{\mathrm{Sm}}^{\mathrm{II}}{\mathrm{I}}_{2}}$ are calculated for different numbers and types of solvents with PBE0-D3/def2-TZVP. $\mathsf{\Delta}{E}_{P52,g}$ is calculated with the usual methodology. $\mathsf{\Delta}{E}_{P28,g}$, $\mathsf{\Delta}{E}_{P28,g}$ and $\mathsf{\Delta}{E}_{P28,solv}$ use ECP28MWB instead of ECP52MWB for Sm in the structure optimization of ACE-Sm

^{II}${\mathrm{I}}_{2}$, while ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$ structures are optimized with ECP51MWB in both the gas phase (g) and with the COSMO model of solvation ($solv$). For $\mathsf{\Delta}{E}_{P28,solv}$, implicit solvation is used in structure optimization as well as single-point calculation of ACE-Sm

^{II}${\mathrm{I}}_{2}$ and ACE${}^{\u2022}$-Sm

^{III}${\mathrm{I}}_{2}$. SOMO energies ($\u03f5$) are shown for ACE-Sm

^{II}${\mathrm{I}}_{2}$ and the herein-mentioned methodology.

Molecule | $\mathbf{\Delta}{\mathit{E}}_{\mathit{P}52,\mathit{g}}$ | $\mathbf{\Delta}{\mathit{E}}_{\mathit{P}28,\mathit{g}}$ | $\mathbf{\Delta}{\mathit{E}}_{\mathit{P}28,\mathit{solv}}$ | ${\mathit{\u03f5}}_{\mathit{P}52,\mathit{g}}$ | ${\mathit{\u03f5}}_{\mathit{P}28,\mathit{g}}$ | ${\mathit{\u03f5}}_{\mathit{P}28,\mathit{solv}}$ |
---|---|---|---|---|---|---|

$\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{4}$ | 53.19 | 66.92 | 84.61 | −331.54 | −335.73 | −359.60 |

$\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{THF}\right)}_{2}{\left(\mathrm{HMPA}\right)}_{1}$ | 52.74 | 65.80 | 77.70 | −333.64 | −336.55 | −357.36 |

$\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{HMPA}\right)}_{3}$ | 37.50 | 52.74 | 58.14 | −262.95 | −262.06 | −292.57 |

$\mathrm{S}\mathrm{m}{\mathrm{I}}_{2}{\left(\mathrm{HMPA}\right)}_{4}$ | 47.90 | 51.56 | 63.26 | −270.83 | −245.93 | −271.51 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Steiner, L.; Achazi, A.J.; Vlaisavljevich, B.; Miro, P.; Paulus, B.; Kelterer, A.-M.
Samarium Diiodide Acting on Acetone—Modeling Single Electron Transfer Energetics in Solution. *Molecules* **2022**, *27*, 8673.
https://doi.org/10.3390/molecules27248673

**AMA Style**

Steiner L, Achazi AJ, Vlaisavljevich B, Miro P, Paulus B, Kelterer A-M.
Samarium Diiodide Acting on Acetone—Modeling Single Electron Transfer Energetics in Solution. *Molecules*. 2022; 27(24):8673.
https://doi.org/10.3390/molecules27248673

**Chicago/Turabian Style**

Steiner, Luca, Andreas J. Achazi, Bess Vlaisavljevich, Pere Miro, Beate Paulus, and Anne-Marie Kelterer.
2022. "Samarium Diiodide Acting on Acetone—Modeling Single Electron Transfer Energetics in Solution" *Molecules* 27, no. 24: 8673.
https://doi.org/10.3390/molecules27248673