A Theoretical Study on the Stability of PtL₂ Complexes of Endohedral Fullerenes: The Influence of Encapsulated Ions, Cage Sizes, and Ligands

Abstract

The {η²-(X@C_n)}PtL₂ complexes possessing three kinds of encapsulated ions (X = F^–, Ø, Li⁺), three various ligands (L = CO, PPh₃, NHC^Me), and twelve cage sizes (C₆₀, C₇₀, C₇₂, C₇₄, C₇₆, C₇₈, C₈₀, C₈₄, C₈₆, C₉₀, C₉₆, C₁₀₀) are theoretically examined by using the density functional theory (M06/LANL2DZ). The present computational results demonstrate that the backward-bonding orbital interactions, rather than the forward-bonding orbital interactions, play a dominant role in the stability of {η²-(X@C_n)}PtL₂ complexes. Additionally, our theoretical study shows that the presence of the encapsulated Li⁺ ion can greatly improve the stability of {η²-(X@C_n)}PtL₂ complexes, whereas the existence of the encapsulated F^– ion can heavily reduce the stability of {η²-(X@C_n)}PtL₂ complexes. Moreover, the theoretical evidence strongly suggests that the backward-bonding orbital interactions as well as the stability increase in the order {η²-(X@C_n)}Pt(CO)₂ < {η²-(X@C_n)}Pt(PPh₃)₂ < {η²-(X@C_n)}Pt(NHC^Me)₂. As a result, these theoretical observations can provide experimental chemists a promising synthetic direction.

1. Introduction

About three decades ago, Fagan and co-workers reported the synthesis of the first fullerene-transition metal complex (FTMC), (η²-C₆₀)Pt(PPh₃)₂.¹ From then on, various kinds of FTMC have been prepared and structurally characterized.^2,3 An interesting characteristic for such an FTMC is that it can encage atoms, ions, and small molecules to form endohedral complexes,⁴ which is named endohedral metallofullerenes,⁵ because the metal atoms are encapsulated within a hollow carbon cage. Since then, many other experimental and computational works in such fields concerning cation-/anion-encapsulated fullerene chemistry have been greatly achieved.⁶⁻¹³ Recently, Tobita and co-workers reported the preparations and structural characterizations of the intriguing FTMC, that is, iridium and platinum complexes of the lithium-cation-encapsulated fullerene Li⁺@C₆₀.¹⁴

In principle, from the theoretical viewpoint, two kinds of intramolecular orbital interactions, which can affect the kinetic as well as the thermodynamic stability of such an FTMC, are noted.^15,16 One is the forward-bonding interaction, which is named σ forward-donation. The other is the backward-bonding interaction, which is called π backward-donation.¹⁷ Basically, both bonding orbital interactions can be influenced by several factors, including the central transition metal element, the encapsulated ion, the attached ligand, and the cage size. The effects of the transition metal elements and the encapsulated ions on the stability of the FTMC have been discussed by the same authors.¹⁸ Nevertheless, in the present work, we extend our previous study by considering the other factors, such as various ligands and carbon cages, by way of either forward-bonding or backward-bonding interactions, to study how they qualify the stability of FTMC. In this regard, the following chemical reaction is selected as the model system

1

where the encapsulated site X could be F^–, Ø, or Li⁺; the ligand L could be CO, PPh₃, or NHC^Me (methyl-substituted N-heterocyclic carbenes); and the cage size n could be 60, 70, 72, 74, 76, 78, 80, 84, 86, 90, 96, or 100. That is to say, a theoretically sophisticated method, that is, energy decomposition analysis (EDA),¹⁹ has been utilized in this study to investigate the intramolecular orbital interactions between the various fullerenes and the platinum fragment (PtL₂). It should be noted that the PtL₂ fragment is generated by the decoordination of C₂H₄ from the (η²-C₂H₄)PtL₂ complex. The decoordination of C₂H₄ involves a small change in energy [(η²-C₂H₄)PtL₂ → C₂H₄ + PtL₂, ΔE = 15.5, 21.5, and 6.7 kcal/mol for L = CO, PPh₃, and NHC^Me, respectively]. Hopefully, the present theoretical conclusions can provide experimental chemists to design and to synthesize the novel FTMC.

2. Methodology

The following fullerenes that comply with the isolated pentagon rule are used to develop a correlation: Ih-C₆₀, D_5h-C₇₀, D_6d-C₇₂, D_3h-C₇₄, D₂-C₇₆, C_2v(3)-C₇₈, D_5d(1)-C₈₀, D_2d(23)-C₈₄, C_s(16)-C₈₆, D_5h(1)-C₉₀, D_3d(3)-C₉₆, and D_5d(1)-C₁₀₀. Most of these fullerenes have been experimentally isolated and identified.²⁰⁻²⁵ The symmetry and numbering scheme for fullerene isomers are in accordance with an approved classification.²⁶ The geometry optimizations have no symmetry restrictions for the M06²⁷/LANL2DZ^28,29 level of theory. The harmonic vibrational frequency calculations are used to verify the nature of the stationary points. The local minima are confirmed by the absence of imaginary frequencies. The natural charges are obtained using NBO 5.9, as implemented in the Gaussian 09 program.³⁰ Advanced EDA unites the natural orbitals for chemical valence (NOCV), so the total orbital interactions are separated into pairwise contributions.^31,32 Advanced EDA (i.e., EDA-NOCV) further divides the interaction energy [ΔE(INT)] into three main components: ΔE(INT) = ΔE_elstat + ΔE_Pauli + ΔE_orb. This enables a quantitative study of π back-bonding to fullerene ligands that uses the M06/TZP level of theory with the ADF 2016 program package.³³ The relativistic effect is accounted for by applying a scalar zero-order regular approximation.³⁴ The interaction energy and its decomposition terms are obtained from a single-point calculation, using the M06/TZP basis set from the Gaussian 09 optimized geometry.

3. Results and Discussion

On the basis of the isolated pentagon rule,²⁶ one may obtain the following fullerenes: Ih-C₆₀, D_5h-C₇₀, D_6d-C₇₂, D_3h-C₇₄, D₂-C₇₆, C_2v(3)-C₇₈, D_5d(1)-C₈₀, D_2d(23)-C₈₄, C_s(16)-C₈₆, D_5h(1)-C₉₀, D_3d(3)-C₉₆, and D_5d(1)-C₁₀₀, whose Cartesian coordinates are given in the Supporting Information (Scheme 1). The choice of these fullerene cages is arbitrary and just for consistency, in spite of the fact that some of them have been successfully identified by experimental methods³⁸⁻⁴⁰ and some of them are still not observed experimentally. For fullerene isomers shown in Scheme 1, their symmetries and numbering schemes are in accordance with an approved classification.⁴¹ It has to be noted that Hückel molecular orbital calculations indicate the 6:6 ring junctions at the poles of the molecules, which usually have the highest π bond orders (B) and then presumably should be the highest reactive sites. In other words, these sites having the highest π bond orders should be easily attacked (Scheme 1).³⁵ After considering the cost and available computational facilities, however, we have no choice but to select one isomer, which has an oval-shaped structure, for different kinds of fullerenes. Nevertheless, it may or may not influence the final conclusions presented in this work.

Scheme 1. Sites of Attack for Addition to the Fullerenes Ih-C₆₀, D_5h-C₇₀, D_6d-C₇₂, D_3h-C₇₄, D₂-C₇₆, C_2v(3)-C₇₈, D_5d(1)-C₈₀, D_2d(23)-C₈₄, C_s(16)-C₈₆, D_5h(1)-C₉₀, D_3d(3)-C₉₆, and D_5d(1)-C₁₀₀.

3.1. Optimized Geometries

The structures of {η²-(X@C_n)}PtL₂ complexes possessing the encapsulated site X (=F^–, Ø, Li⁺), the ligand L (=CO, PPh₃, and NHC^Me), and cage size n (=60, 70, 72, 74, 76, 78, 80, 84, 86, 90, 96, 100) were optimized at the M06/LANL2DZ level of theory. The geometries obtained and their key structural parameters for n = 60 are given in Figure 1 and Table 1, respectively. The key structural parameters for other cage sizes are presented in the Supporting Information.

Figure 1.

Optimized geometries for {η²-(X@C₆₀)}PtL₂ complexes.

Table 1. Selected Geometrical Parameters (Bond Distances in Å) and the Natural Population Analysis (NPA) Atomic Charge for Optimized Complexes [{η²-(X@C₆₀)}PtL₂] at the M06/LANL2DZ Level of Theory.

L = CO; X = Li+
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.119	2.119	2.336	2.335	1.534	+0.50	–0.28	–0.28	+0.86

L = CO; X = Ø
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.162	2.162			1.489	+0.47	–0.22	–0.22

L = CO; X = F–
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.258	2.258	3.119	3.120	1.453	+0.41	–0.16	–0.16	–0.93

L = PPh3; X = Li+
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.106	2.103	2.278	2.279	1.552	+0.24	–0.28	–0.28	+0.85

L = PPh3; X = Ø
	geometrical parameters					NPA atomic charge
system	P–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.114	2.116			1.513	+0.22	–0.23	–0.23

L = PPh3; X = F–
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.129	2.127	3.165	3.165	1.492	+0.18	–0.20	–0.20	–0.93

L = NHCMe; X = Li+
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.121	2.121	2.291	2.290	1.570	+0.48	–0.32	–0.32	+0.86

L = NHCMe; X = Ø
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.124	2.123			1.535	+0.46	–0.27	–0.27

L = NHCMe; X = F–
	geometrical parameters					NPA atomic charge
system	Pt–C1	Pt–C2	X–C1	X–C2	C1–C2	Pt	C1	C2	X
PtL2X@C60	2.127	2.126	3.184	3.183	1.508	+0.43	–0.23	–0.23	–0.93

First, the geometric changes that are caused by encapsulated ions are considered. For the Pt(PPh₃)₂-C₆₀ complex in the absence of encapsulated ions, Table 1 shows the optimized Pt–C₁(C₂) and C₁–C₂ bond distances [2.114 (2.116) and 1.513 Å, respectively], which agree well with the corresponding experimental values [2.145 (2.115) and 1.502 Å, respectively].¹ After the Li⁺ ion is introduced into the cage, the optimized Pt–C₁(C₂), C₁–C₂, and Li–C₁(C₂) bond distances [2.106 (2.103), 1.552, 2.278 (2.279) Å, respectively] are also consistent with the experimentally observed values [2.083 (2.084), 1.534, and 2.251 (2.249) Å, respectively].¹⁴ It is known that in a strained olefin complex, strain reduces the energy of π* orbitals and increases π backward-donation, which stretches the interacting C–C bond. Also, it is noted that, in the presence of a Li⁺ ion, its C–C bond distance is 0.039 Å longer than the corresponding distance for an empty complex. On the other hand, if a F^– ion is encapsulated, its C–C distance is 0.021 Å shorter than the corresponding distance for an empty complex. These results clearly show that a F^– ion causes geometric changes that are opposite to those that are caused by a Li⁺ ion, so the effect on π backward-bonding orbital interactions is diverse. The F–C bond (3.165 Å) is also substantially longer than the Li–C bond (2.278 Å). The F^– ion is located at a site farther from the Pt atom. In other words, this phenomenon can be explained by the electrostatic interaction.

Besides these, the Pt-coordinated carbon atoms of C₆₀ are negatively charged because there is π backward-donation from the Pt center. From Table 1, the NPA shows that, for a Pt(PPh₃)₂-C₆₀ complex without encapsulated ions, the atomic charges on the C₁ (C₂) atoms are −0.23 (−0.23). On the other hand, if the cage is encapsulated by a Li⁺ ion, the computational data given in Table 1 indicate that the atomic charges on the C₁ (C₂) atoms are increased to −0.28 (−0.28) and the atomic charge on the Li atom is +0.86. That is to say, the theoretical evidence demonstrates that the encaged Li⁺ ion is attracted toward these negatively charged carbon atoms. However, if a F^– ion is encapsulated, the NPA results collected in Table 1 reveal that the atomic charges on the C₁ (C₂) atoms are decreased to −0.20 (−0.20) and the atomic charge on the F atom is negative (−0.93). These theoretical data strongly suggest that the negatively charged carbon atoms repel the encaged F^– ion.

The effect of ligands on the geometric changes is also examined in this work. As seen in Table 1, for the case of the Pt(NHC^Me)₂-C₆₀ complex, which has a deficiency of encapsulated ion, its C–C bond distance (1.535 Å) is longer than the corresponding distance for an empty Pt(PPh₃)₂-C₆₀ complex (1.513 Å). By contrast, if the ligand is replaced by CO, its C–C bond distance for the Pt(CO)₂-C₆₀ complex (1.489 Å) is shorter than the corresponding distance for an empty Pt(PPh₃)₂-C₆₀ complex. Therefore, similar to encapsulated ions (Li⁺ and F^– ions), ligands (NHC^Me and CO) also produce geometric changes that are opposite. As a result, their effect on π back-bonding is specific. A detailed discussion of the effect on π backward-donation is given in Section 3.3. Similar geometric changes and charge populations are also seen for other cage sizes and are presented in Tables S1–S11.

3.2. EDA

Before analyzing the influence of endohedral species and ligands on the stability of {η²-(X@C_n)}PtL₂ complexes, we summarized the calculated energies of the formation of encaged complexes X@C_n in Table 2. For the Li⁺@C₆₀ and F^–@C₆₀ cases, the encapsulation energies are both negative values (−13.3 and −87.3 kcal/mol, respectively), indicating Li⁺ and F^– ions are stabilized in the C₆₀ cage and the latter is much more stable. These theoretical findings agree well with the previous work by Geerlings and co-workers.⁶ Also, it is found that the encapsulation energies for other cages are similar and do not change obviously (in average, Li⁺@C_n: −17.1, F^–@C_n: −81.3 kcal/mol), implying the interaction between the encapsulated ions and fullerene is rather local and therefore not much dependent on the fullerene cage.

Table 2. Energy of Formation (in kcal/mol) of Encapsulated Complex X@C_n^a,b.

X	Cn	ΔE
Li+	C60	–13.3(−5.4)
F–	C60	–87.3(−79.5)
Li+	C70	–14.9(−9.0)
F–	C70	–83.1(−77.6)
Li+	C72	–18.8(−13.7)
F–	C72	–80.8(−74.8)
Li+	C74	–15.2(−8.5)
F–	C74	–79.5(−73.0)
Li+	C76	–16.7(−10.3)
F–	C76	–80.4(−73.7)
Li+	C78	–16.5(−9.2)
F–	C78	–79.0(−71.7)
Li+	C80	–17.7(−12.4)
F–	C80	–83.6(−77.2)
Li+	C84	–16.5(−11.1)
F–	C84	–74.5(−68.1)
Li+	C86	–17.8(−10.5)
F–	C86	–75.8(−68.5)
Li+	C90	–18.8(−13.3)
F–	C90	–83.8(−77.8)
Li+	C96	–18.5(−12.6)
F–	C96	–82.1(−75.7)
Li+	C100	–20.2(−14.4)
F–	C100	–86.0(−80.2)

^aΔE is defined as E(X@C_n) – E(X) – E(C_n). Energy differences have been zero-point-corrected and used the Gibbs free energy (ΔG, in parentheses).

^bAll at the M06/LANL2DZ level of theory.

We then perform EDA³⁵⁻³⁷ on the {η²-(X@C₆₀)}PtL₂ complexes, and their calculated results are collected in Table 3. In addition, the EDA results for other cage sizes are presented in the Supporting Information. The bonding energy (ΔE) is defined as ΔE = E({η²-(X@C_n)}PtL₂) – E(X@C_n) – E(PtL₂), using eq 1. During the formation of the Pt–C bond, the EDA results indicate that both PtL₂ and the empty C₆₀ are distorted (Table 3). The PtL₂ unit encounters greater distortion [ΔE_def(A) = 29.4 kcal/mol] than C₆₀ [ΔE_def(B) = 9.9 kcal/mol]. Likewise, similar consequences are found for X = Li⁺ or F^–. Moreover, the encapsulation of the Li⁺ ion can cause more distortion in fragments A and B of {η²-(Li⁺@C₆₀)}Pt(PPh₃)₂ than those of {η²-(F^–@C₆₀)}Pt(PPh₃)₂. That is, ΔΔE_def(X = Li⁺) = 8.0, ΔΔE_def(X = F^–) = −3.5 kcal/mol). Nevertheless, when the Li⁺ ion is encapsulated, the interaction energy increases [i.e., ΔΔE_intA(BC)(X = Li⁺) = −33.3, ΔΔE_intA(BC)(X = F^–) = +15.9 kcal/mol]. In other words, the encapsulated Li⁺ ion evokes a stronger interaction between the X@C₆₀ and Pt(PPh₃)₂ moiety. This, in turn, as demonstrated in Table 3, can make {η²-(Li⁺@C₆₀)}Pt(PPh₃)₂ to be more stable. In consequence, the relative stability decreases in the trend X = Li⁺ > X = Ø > X = F^–. When the ligand is replaced by NHC^Me, similar results are obtained for Pt(NHC^Me)₂-C₆₀ complexes, but NHC^Me causes more distortion in fragment A or B than in the corresponding Pt(PPh₃)₂-C₆₀ complex. This phenomenon can make this PtL₂ complex to be less stable. For example, ΔE(L = NHC^Me, X = Li⁺) = −64.2 > ΔE(L = PPh₃, X = Li⁺) = −69.8 kcal/mol. If the ligand is the CO group, the relative stability still follows the same order: X = Li⁺ > X = Ø > X = F^–. Nevertheless, the presence of CO causes less interaction energy between the PtL₂ unit and X@C₆₀ than for the corresponding Pt(PPh₃)₂-C₆₀, which yields a less stable complex. For instance, ΔE(L = CO, X = Li⁺) = −21.2 > ΔE(L = PPh₃, X = Li⁺) = −69.8 kcal/mol. When the cage size is increased, the encapsulated Li⁺ ion still increases the interaction energy [ΔE_intA(BC)] between the Pt fragment and X@C₆₀. Also, both NHC^Me and CO can produce more distortion energy (ΔE_def) and less interaction energy [ΔE_intA(BC)] than the corresponding Pt(PPh₃)₂-C₆₀ complex. This theoretical evidence demonstrates that an increase in the cage size has no effect on the EDA results (see Tables S12–S22).

Table 3. EDA for {η²-(X@C₆₀)}PtL₂ (L = CO, PPh₃, and NHC^Me) at M06/LANL2DZ^a,b.

L = CO
X	ΔEdef (ΔEdef(A), ΔEdef(B))	ΔΔEdefc	ΔEintA(BC)	ΔΔEintA(BC)c	ΔEd	ΔΔEc,d
F–	21.6 (18.2, 3.4)	–12.0	–36.3	+13.6	–14.6	+1.7
Ø	33.6 (27.0, 6.6)		–49.9		–16.3
Li+	47.4 (34.4, 13.0)	13.8	–67.4	–17.5	–21.2	–4.9

L = PPh3
X	ΔEdef (ΔEdef(A), ΔEdef(B))	ΔΔEdefc	ΔEintA(BC)	ΔΔEintA(BC)c	ΔEd	ΔΔEc,d
F–	35.8 (28.0, 7.8)	–3.5	–66.6	15.9	–29.6	+13.6
Ø	39.3 (29.4, 9.9)		–82.5		–43.2
Li+	47.3 (32.2, 15.1)	8.0	–115.9	–33.3	–69.8	–26.6

L = NHCMe
X	ΔEdef (ΔEdef(A), ΔEdef(B))	ΔΔEdefc	ΔEintA(BC)	ΔΔEintA(BC)c	ΔEd	ΔΔEc,d
F–	51.2 (41.0, 10.2)	–14.8	–67.0	+33.8	–14.7	+20.1
Ø	66.0 (52.1, 13.9)		–100.8		–34.8
Li+	74.0 (55.0, 19.0)	8.0	–136.6	–35.9	–64.2	–29.4

^aEnergies are given in kcal/mol.

^bA and B represent the PtL₂ fragment and the C₆₀ cage, respectively.

^cThe difference is relative to the corresponding quantity at X = Ø.

^dThe reaction energy without zero-point energy correction for the product, relative to the corresponding reactants.

3.3. EDA Using the Extended Transition State (ETS)-NOCV Method

In our earlier study,¹⁶ structural parameters and some characteristics were used to estimate the strength of π backward-donation for {η²-(X@C₆₀)}ML₂ (M = Pt, Pd; X = Ø, Li⁺; L = PPh₃) complexes. In other words, the changes in the chemical shift (Δδ), bond length (Δr/r₀), and bond angle (Δθ_av) can all be utilized to represent the bonding characters of the {η²-(X@C₆₀)}ML₂ complexes. In this study, from an energetic viewpoint, the strength of the π back-bonding can be estimated using an ETS-NOCV method, which is a variational way that was derived from the early EDA.^44,45 These theoretical analyses exhibit the effect of substituents, cage sizes, and encapsulated ions on the π backward-bonding interactions.

3.3.1. Effect of Encapsulated Ions on π Backward-Bonding

In Section 2.2, it has been demonstrated that stabilities increase in the order X = F^– < X = Ø < X = Li⁺, because the interaction energy [ΔE_intA(BC)] is increased. The interaction between X@C_n and PtL₂ is now studied using the ETS-NOCV method, from which one may separate ΔE_intA(BC) into three components: ΔE_elstat (electrostatic interaction energy) + ΔE_Pauli (repulsive Pauli interaction energy) + ΔE_orb (orbital interaction energy). In the present work, only the important pairwise contributions to ΔE_orb are considered, which are listed in Tables 4–6 (similar ETS-NOCV results for the other cage sizes are given in the Supporting Information). A plot of the deformation density and a qualitative drawing of the orbital interactions between PtL₂ and X@C₆₀ are schematically shown in Figure 2.

Table 4. ETS-NOCV Results for {η²-(X@C₆₀)}PtL₂^a (L = PPh₃; X = F^–, Ø, Li⁺) at the M06/TZP Level of Theory.

fragments	L2Pt and F–@C60	L2Pt and C60	L2Pt and Li+@C60
ΔEint	–78.4	–98.5	–131.6
ΔEPauli	243.2	245.5	242.8
ΔEelstatb	–202.3 (62.9%)	–205.5 (59.7%)	–201.4 (53.8%)
ΔEorbb	–119.2 (37.1%)	–138.5 (40.3%)	–173.1 (46.2%)
ΔEπc	–72.3 (60.7%)	–92.2 (66.6%)	–115.1 (66.5%)
ΔEσc	–24.5 (20.6%)	–21.2 (15.3%)	–19.5 (11.3%)

^aOptimized structures at the M06/LANL2DZ level of theory. The fragments are PtL₂ and X@C₆₀ in a singlet electronic state. Also, see Figure 2. All energy values are in kcal/mol.

^bThe values in parentheses give the percentage contribution to the total attractive interactions, ΔE_elstat + ΔE_orb.

^cThe values in parentheses give the percentage contribution to the total orbital interactions, ΔE_orb.

Table 6. ETS-NOCV Results for {η²-(X@C₆₀)}PtL₂^a (L = CO; X = F^–, Ø, Li⁺) at the M06/TZP Level of Theory.

fragments	L2Pt and F–@C60	L2Pt and C60	L2Pt and Li+@C60
ΔEint	–38.6	–55.1	–72.2
ΔEPauli	162.4	202.9	214.6
ΔEelstatb	–131.4 (65.4%)	–155.3 (60.2%)	–152.7 (53.2%)
ΔEorbb	–69.6 (34.6%)	–102.7 (39.8%)	–134.1 (46.8%)
ΔEπc	–34.5 (49.6%)	–65.6 (63.9%)	–91.9 (68.5%)
ΔEσc	–24.4 (35.1%)	–23.8 (23.2%)	–23.8 (17.7%)

^aOptimized structures at the M06/LANL2DZ level of theory. The fragments are PtL₂ and X@C₆₀ in a singlet electronic state. Also, see Figure 2. All energy values are in kcal/mol.

^bThe values in parentheses give the percentage contribution to the total attractive interactions, ΔE_elstat + ΔE_orb.

^cThe values in parentheses give the percentage contribution to the total orbital interactions, ΔE_orb.

Figure 2.

(a) Qualitative drawing of the orbital interactions between the PtL₂ fragment and Li⁺@C₆₀; (b) the shape of the most important interacting occupied and vacant orbitals of the PtL₂ fragments and Li⁺@C₆₀; (c) a plot of the deformation densities Δρ of the pairwise orbital interactions between the two fragments in their closed-shell state, the associated interaction energies ΔE_orb (kcal/mol), and the eigenvalues ν. The eigenvalues ν indicate the size of the charge flow. The direction of charge flow is from yellow to green.

Table 4 reveals that both ΔE_elstat and ΔE_orb can stabilize the Pt(PPh₃)₂-C₆₀ complexes because they are negative terms. Nevertheless, the percentage of ΔE_orb decreases in the order ΔE_orb (X = Li⁺) > ΔE_orb (X = Ø) > ΔE_orb (X = F^–). In other words, the encapsulated Li⁺ ion plays a decisive role for the stability of FTMC. Besides, Table 4 indicates that ΔE_π contributes significantly to ΔE_orb: 60.7 for X = F^–, 66.6 for X = Ø, and 66.5% for X = Li⁺. Moreover, the energy order for ΔE_π (kcal/mol) is |ΔE_π (X = F^–)| = 72.3 < |ΔE_π (X = Ø)| = 92.2 < |ΔE_π (X = Li⁺)| = 115.1. Therefore, ΔE_π is increased when there is an encapsulated Li⁺ ion but decreased when there is a F^– ion. Indeed, as seen in the deformation densities in Figure 2, the electron densities come from the π backward-donation of a filled d orbital to the π* orbitals of C₆₀ (the charge flow is yellow to green in Figure 2). In other words, these EDA findings for the large contribution of ΔE_π in ΔE_orb demonstrate that the Pt–C bonds are principally formed by π backward-donation, which agrees well with the previous work.¹⁴

On the other hand, the second contribution, which is named the σ forward-donation (ΔE_σ), results from a filled π orbital of C₆₀ to the σ orbital of Pt, as depicted in Figure 2. Comparing ΔE_σ with ΔE_π shown in Table 4, the contribution of ΔE_σ to ΔE_orb is small: 20.6 for X = F^–, 15.3 for X = Ø, and 11.3% for X = Li⁺. Similar results are found for NHC^Me and CO ligands, as analyzed in Tables 5 and 6, respectively.

Table 5. ETS-NOCV Results for {η²-(X@C₆₀)}PtL₂^a (L = NHC^Me; X = F^–, Ø, Li⁺) at the M06/TZP Level of Theory.

fragments	L2Pt and F–@C60	L2Pt and C60	L2Pt and Li+@C60
ΔEint	–67.7	–100.8	–133.0
ΔEPauli	257.2	235.8	227.6
ΔEelstatb	–189.0 (58.2%)	–178.8 (53.1%)	–173.8 (48.2%)
ΔEorbb	–135.8 (41.8%)	–157.7 (46.9%)	–186.9 (51.8%)
ΔEπc	–94.4 (69.5%)	–118.6 (75.2%)	–142.8 (76.4%)
ΔEσc	–24.4 (18.0%)	–20.6 (13.1%)	–18.6 (10.0%)

^aOptimized structures at the M06/LANL2DZ level of theory. The fragments are PtL₂ and X@C₆₀ in a singlet electronic state. Also, see Figure 2. All energy values are in kcal/mol.

^bThe values in parentheses give the percentage contribution to the total attractive interactions, ΔE_elstat + ΔE_orb.

^cThe values in parentheses give the percentage contribution to the total orbital interactions, ΔE_orb.

In brief, our computational results strongly suggest that the π backward-bonding is crucial to the stability of {η²-(X@C₆₀)}PtL₂ complexes and that an encapsulated Li⁺ ion increases the π backward-bonding, whereas an encapsulated F^– decreases the π backward-bonding. The effect of encapsulated ions on π backward-bonding interactions is the same for other cage sizes (see the Supporting Information).

3.3.2. Effect of Ligands on π Backward-Bonding

A comparison of the results in Tables 4 (L = PPh₃) and 5 (L = NHC^Me) demonstrates that the value of ΔE_π for Pt(NHC^Me)₂-C₆₀ is larger than the corresponding value for Pt(PPh₃)₂-C₆₀. Thus, our theoretical findings indicate that the π backward-bonding promoted by the NHC^Me ligand is stronger than that by the PPh₃ ligand. For instance, |ΔE_π (L = PPh₃, X = Li⁺)| = 115.1 < |ΔE_π (L = NHC^Me, X = Li⁺)| = 142.8 kcal/mol. However, a comparison of Tables 4 (L = PPh₃) and 6 (L = CO) reveals that the value of ΔE_π for Pt(CO)₂-C₆₀ is smaller than that for Pt(PPh₃)₂-C₆₀. In other words, the π backward-bonding induced by a CO group is weaker than that by a PPh₃ ligand. For example, |ΔE_π (L = CO, X = Li⁺)| = 91.9 < |ΔE_π (L = PPh₃, X = Li⁺)| = 115.1 kcal/mol. This theoretical evidence indicates that the π backward-bonding is promoted by the ligand, which increases in the order |ΔE_π (L = CO)| < |ΔE_π (L = PPh₃)| < |ΔE_π (L = NHC^Me). This order is governed by the nature of ligands. It is well known that CO is a strong π-acceptor ligand.³⁸ This, in turn, can greatly reduce electrons from the σ orbitals of Pt to the π* orbitals of C₆₀, leading to fewer electrons in the π orbitals of C₆₀. On the other hand, NHC^Me is a weaker π-acceptor ligand.^39,40 As a result, fewer electrons from the d orbital of Pt transfer to the π* orbitals of NHC^Me, resulting in more electrons in the π* orbitals of C₆₀.

In addition, the ETS-NOCV results (Tables 4–6) demonstrate that the {η²-(X@C₆₀)}PtL₂ complexes exhibit a relatively strong σ character when X = F^– or L = CO and a relatively strong π character when X = Li⁺ or L = NHC^Me. For instance, in the {η²-(F^–@C₆₀)}Pt(CO)₂ complex, its ΔE_σ and ΔE_π contributions to the orbital interaction (ΔE_orb) are calculated to be 35.1 and 49.6%, respectively. Moreover, in the {η²-(Li⁺@C₆₀)}Pt(NHC^Me)₂ complex, its ΔE_σ and ΔE_π contributions to ΔE_orb are computed to be 10.0 and 76.4%, respectively. To the authors’ best knowledge, many of the known organometallic compounds that have fullerene (C₆₀) as a ligand exhibit η² hapticity and examples of other forms of hapticity (such as η¹ or η^5,6) are few. The reason for this could be due to the high degree of curvature of a C₆₀ cage. Theoretically, complexes with η¹ or η^5,6 hapticity can be constructed using an artificial force¹⁶ or a symmetry constraint.⁴² However, this work demonstrates that another way to construct a complex with η¹ hapticity is to use X = F^– or L = CO in the complex. This study successfully locates the {η¹-(F^–@C₆₀)}Pt(CO)₂ complex without using an artificial force or a symmetry constraint (see Figure S1).

3.3.3. Effect of Cage Sizes on π Backward-Bonding

A plot of the ΔE_π values versus cage sizes n (=60, 70, 72, 74, 76, 78, 80, 84, 86, 90, 96, and 100) for {η²-(X@C_n)}Pt(PPh₃)₂ is presented in Figure 3. Also, the computational data concerning ΔE_π versus n for {η²-(X@C_n)}Pt(CO)₂ and {η²-(X@C_n)}Pt(NHC^Me)₂ are given in Figures S2 and S3, respectively. As seen in Figure 3, the ΔE_π values are calculated to be −115.0, −95.0, and −75.0 kcal/mol for X = Li⁺, Ø, and F^– for each cage size, respectively. In other words, the difference in the size of carbon clusters does not have an apparent trend on π backward-bonding orbital interactions for the platinum center. Presumably, the cage sizes we have chosen in this work are enough to represent a clear relationship between the cage size and the π backward-donation.

Figure 3.

Correlation between ΔE_π and cage sizes for {η²-(X@C_n)}Pt(PPh₃)₂ (n = 60, 70, 72, 74, 76, 78, 80, 84, 86, 90, 96, and 100) complexes. The solid circles, hollow circles, and solid triangles represent the values of ΔE_π for X = Li⁺, Ø, and F^–, respectively.

4. Conclusions

This study uses the density functional theory to determine the roles played by forward-bonding orbital interactions (σ forward-donations) and backward-bonding orbital interactions (π backward-donations) on the stability of {η²-(X@C_n)}PtL₂ complexes. Three factors, including encapsulated ions, ligands, and cage size, have been chosen to examine their influences on both orbital interactions. The computations studied in this work demonstrate that the π backward-donation interactions rather than the σ forward-donation interactions play a crucial role in rendering {η²-(X@C_n)}PtL₂ complexes synthetically accessible. Moreover, our theoretical investigations suggest that the π backward-donation for {η²-(X@C_n)}PtL₂ complexes can be improved by the presence of an encapsulated Li⁺ ion. This, in turn, can greatly increase the stability of the {η²-(X@C_n)}PtL₂ complex and promote its synthetic formation. Also, because the electron donation ability increases in the order CO < PPh₃ < NHC^Me, our theoretical observations again show that the electron donation of the attached ligand of a platinum fragment greatly enhances the stability of the {η²-(Li⁺@C_n)}PtL₂ complex.

Supporting Information Available

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b02469.

• Optimized geometries and the absolute energies (in Hartrees) for all the points on the potential energy surfaces of {η²-(X@C_n)}PtL₂ complexes with three different encapsulated ions (X = F^–, Ø, Li⁺), ligands (L = CO, PPh₃, NHC^Me), and twelve cage sizes (C₆₀, C₇₀, C₇₂, C₇₄, C₇₆, C₇₈, C₈₀, C₈₄, C₈₆, C₉₀, C₉₆, C₁₀₀) determined using the M06/LANL2DZ level of theory (PDF)

The authors declare no competing financial interest.