Open access peer-reviewed chapter

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes? Role of Cage Sizes, Encapsulated Ions and Metal Ligands

By Ming-Chung Yang and Ming-Der Su

Submitted: March 16th 2017Reviewed: June 8th 2017Published: December 20th 2017

DOI: 10.5772/intechopen.70068

Downloaded: 234

Abstract

A density functional study of {η2-(X@Cn)}ML2 complexes with various cage sizes (C60, C70, C76, C84, C90, C96), encapsulated ions (X = F−, 0, Li+) and metal fragments (M = Pt, Pd) is performed, using M06/LANL2DZ levels of theory. The importance of π back-bonding to the thermodynamic stability of fullerene-transition metal complexes ({η2-(X@Cn)}ML2) and the effect of encapsulated ions, metal fragments and cage sizes on the π back-bonding are determined in this study. The theoretical computations suggest that π back-bonding plays an essential role in the formation of fullerene-transition metal complexes. The theoretical evidence also suggests that there is no linear correlation between cage sizes and π back-bonding, but the encapsulated Li+ ion enhances π back-bonding and F− ion results in its deterioration. These computations also show that a platinum center produces stronger π back-bonding than a palladium center. It is hoped that the conclusions that are provided by this study can be used in the design, synthesis and growth of novel fullerene-transition complexes.

Keywords

  • fullerene-transition metal complex
  • π back-bonding
  • encapsulated ions
  • metal fragments and cage sizes

1. Introduction

The first fullerene-transition metal complex, (η2-C60)Pt(Ph3)2, was prepared and structurally characterized by Fagan et al. in 1991 [1]. It was the starting point for a new class of study for fullerene chemistry. Since then, various fullerene-transition metal complexes have been synthesized and these have potential applications in solar cells, spintronics, catalysis and drug delivery [2]. Balch et al. then studied the reactions of C60 with electron-rich fragments, IrCl(CO)(PPh3)2 and produced the fullerene-iridium complex (η2-C60)IrCl(CO)(PPh3)2 [3]. The formation of fullerene-iridium complex is a reversible process and the reversible binding of IrCl(CO)(PPh3)2 to fullerenes can be used as a structural probe because the adducts can build ordered single crystals that are suitable for X-ray diffraction [4, 5]. Fullerene-iridium complexes that contain an enantiomeric phosphine ligand are used as solar photoelements [6]. One of the significant characteristics of fullerenes is that they are capable of encaging atoms, ions and small molecules to form endohedral complexes. Endohedral metallofullerenes (EMFs) are those that encapsulate metal atoms within a hollow carbon cage. Proft et al. theoretically studied the interactions between encapsulated monoatomic ions (Li+ to Rb+ and F to I) and C60 and its Si and Ge analogues [7] and found that, for these families, the interactions between Li+(Na+) and F(Cl) ions and C60 are strongest and exothermic, which confirms the possibility of the existence of these species. Recently, Li+@C60 was successfully synthesized and isolated by Watanabe et al. [8].

Understanding the strength and nature of metal-ligand bonding is crucial for the design of new fullerene-transition metal complexes because the structure and stability of various intermediates are important to the formation of organometallics [9]. In an earlier work by the authors [10], {η2-(X@C60)}ML2 complexes (M = Pt, Pd; X = 0, Li+, L = PPh3) were studied and it was found that there is a relationship between thermodynamic stability and π back-bonding; that is, the greater the π back-bonding, the greater is thermodynamic stability. This shows that thermodynamic stability can be modified by tuning the π back-bonding. As far as the authors are aware, π back-bonding could be affected by several factors, including the encapsulated ions, the metal fragments and the cage sizes. This study determines the importance of π back-bonding to the thermodynamic stability of {η2-(X@Cn)}ML2 complexes by using M = Pt, Pd; X = F, 0, Li+ and n = 60, 70, 76, 84, 90 and 96 to ascertain the role of these factors in π back-bonding. Since the system is very large, methyl-substituted N-heterocyclic carbenes (NHC) are used as a ligand (L), instead of PPh3. NHC is one of the frequently used and most powerful tools in organic chemistry [11]. In this work, the following reactions are studied:

ML2+X@Cnη2X@CnML2E1

2. Computational details

The following fullerenes that comply with the isolated pentagon rule are used to develop a correlation: Ih-C60, D5h-C70, D2-C76, D2d(23)-C84, D5h(1)-C90 and D3d(3)-C96. These are experimentally isolated and identified [12, 13, 14]. The symmetry and numbering scheme for fullerene isomers are in accordance with an approved classification [15]. Hückel molecular orbital calculations show that the 6:6 ring junctions at the poles of the molecules usually have highest π bond orders (B) and are expected to be the most reactive, so these are the sites of attack (see Scheme 1) [12, 16].

Scheme 1.

The sites of attack for addition to the fullerenes Ih-C60, D5h-C70, D2-C76, D2d(23)-C84, D5h(1)-C90 and D5h(1)-C96. The Hückel π bond orders (B) were calculated using the freeware program, HuLiS [16].

The geometry optimizations are performed without any symmetry restrictions by using the M06 [17]/LANL2DZ [18, 19] level of theory. The vibrational frequency calculations at 298.15 K and 1 atm use the same level of theory. The stationary points are confirmed by the absence of imaginary frequencies. The natural charges are obtained using NBO 5.9, as implemented in the Gaussian 09 program [20].

The interatomic interactions are determined using energy decomposition analysis (EDA). Two types of EDA are used in this work. The first is the basic EDA that was developed individually by Yang et al. [21] and by Ziegler and Rauk [22]. For this basic EDA, the bonding energy (∆E) is partitioned into two terms, ∆E = ∆E(DEF) + ∆E(INT). In this work, basic EDA is used for the optimized ML2X@Cn complexes, which are categorized into transition metal complexes (A), carbon cages (B) and metal ions (C) as shown in Scheme 2. The deformation energy (∆E(DEF)) is the sum of the deformation energy of A (∆E(DEF)A, which is defined as the energy of A in the product relative to the optimized isolated structure (A0) and B (∆E(DEF)B)). The interaction energy term, ∆E(INT)A(BC), is the interaction energy between A and (BC) for their respective optimized product structures.

Scheme 2.

Basic EDA for {η2-(Li+@Cn)}PtL2.

Advanced EDA unites the natural orbitals for chemical valence (NOCV), so it is possible to separate the total orbital interactions into pairwise contributions [23]. The advanced EDA (i.e., EDA-NOCV) further divides the interaction energy (∆E(INT)) into three main components: ∆E(INT) = ∆Eelstat + ∆EPauli + ∆Eorb. It is used for a quantitative study of π back-bonding to fullerene ligands that uses the M06/TZ2P level of theory with the ADF 2016 program package [24]. The relativistic effect is considered by applying a scalar zero-order regular approximation (ZORA) [25]. The interaction energy and its decomposition terms are obtained from a single-point calculation using the M06/TZ2P basis set from the Gaussian 09 optimized geometry.

3. Results and discussion

3.1. Geometric changes

The structures of {η2-(X@Cn)}ML2 complexes for M = Pt, Pd; X = F, 0, Li+ and n = 60, 70, 76, 84, 90 and 96 were fully optimized at the M06/LANL2DZ level of theory. The geometries that are obtained are illustrated in Figure 1. The key structural parameters of the stationary points are listed in Table 1 (the structural parameters for n = 70, 76, 84, 90 and 96 are presented elsewhere). For the Pt-C60 complex in the absence of encapsulated ions, the respective lengths of the metal-carbon bonds are 2.12 Å and 2.12 Å (Table 1). When the Li+ ion is encapsulated into the cage, the metal-carbon bonds remain unaltered and the respective distances between C1, C2 and Li+ are 2.29 Å and 2.29 Å. As the encapsulated ion is changed to F, the metal-carbon bonds remain almost unchanged (2.13 and 2.13 Å), but the distance between C1, C2 and encapsulated ions (F) increases (3.18 and 3.18 Å). The Li+ ion is located at a site that is close to the transition metals because of electrostatic interaction. The metal-coordinated carbon atoms of C60 are negatively charged because there is π back-donation from the metal center. For the Pt-C60 complex without encapsulated ions, the natural population analysis (NPA) shows that the atomic charges on the C1 (C2) atoms are −0.27 (−0.27). When the cage is encapsulated by a Li+ ion, the atomic charges on the C1 (C2) atoms are increased to −0.32 (−0.32) and the atomic charge on the Li atom is +0.86. Therefore, the encaged Li+ ion is attracted toward these negatively charged C atoms. However, as the encapsulated ion is changed to F, NPA shows that the atomic charges on C1 (C2) atoms are decreased to −0.23 (−0.23) and the atomic charge on the F atom is negative (−0.93), so the encaged F ion is repelled by the negatively charged C atoms. In terms of Pd-C60 complexes, it is worthy of note that the geometrical distances are generally similar to the corresponding distances for Pt-C60 complexes, but the charge distributions are different. Specifically, the encaged Li atom has a charge (+0.86) but the charges on C1 (C2) atoms are reduced to −0.27 (−0.27). The negative charges on metal-coordinated carbon atoms are also less for X = 0 and F. Similar geometric changes and charge distributions are seen for n = 70, 76, 84, 90 and 96 and are presented elsewhere.

Figure 1.

Optimized geometries for {η2-(X@C60)}ML2 (M = Pt, Pd; X = Li+, 0, F−).

Table 1.

Selected geometrical parameters (bond distances in Å) and the NPA atomic charge for optimized complexes ({η2-(X@C60)}ML2) at the M06/LANL2DZ level of theory.

3.2. Basic energy decomposition analysis (basic EDA)

In order to better understand the factors that govern the thermodynamic stability of {η2-(X@Cn)}ML2 complexes, basic EDA is performed on {η2-(X@Cn)}ML2 complexes (the basic EDA results for n = 70, 76, 84, 90 and 96 are presented elsewhere). The bonding energy (∆E) is defined as ∆E = E({η2-(X@Cn)}ML2) − E(X@Cn) − E(ML2), using Eq. (1). The Pt-C60 complex without encapsulated ions is initially considered. Basic EDA shows that both the metal fragment and the empty C60 fragment are distorted during the formation of the metal-carbon bond (Table 2). The metal fragment undergoes greater distortion (∆E(DEF)A = 52.1 kcal/mol) than C60 (∆E(DEF)B = 13.9 kcal/mol). The same results are obtained for X = Li+ or F. It is found that the encapsulation of the Li+ ion induces more distortion in fragments A and B of the Pt-Li+@C60 complex than those of the Pt-F@C60 complex (∆∆E(DEF)(X = Li+) = 8.0, ∆∆E(DEF)(X = F) = −14.8 kcal/mol). However, the interaction energy increases when the Li+ ion is encapsulated (∆∆E(INT)A(BC)(X = Li+) = −35.9, ∆∆E(INT)A(BC)(X = F) = +33.8 kcal/mol), which shows that the encapsulated Li+ ion induces a stronger interaction between the metal fragment and the X@C60 fragment, so {η2-(Li+@C60)}PtL2is more stable. The relative thermodynamic stability increases in the order: ∆E(X = F) < ∆E(X = 0) < ∆E(X = Li+), as shown in Table 2. In addition, |∆∆E(DEF)| is small and |∆∆E(INT)A(BC)| is large, so the latter must be responsible for an increase in thermodynamic stability. Similar results are obtained for Pd-C60 complexes, but, the distortion in fragments A or B is smaller than that for the Pt-C60 complex, as is the interaction energy, so the complex is less stable. For instance, ∆E(M = Pd, X = Li+) = −34.5 > ∆E(M = Pt, X = Li+) = −35.9 kcal/mol. When the cage size increases (n = 70, 76, 84, 90 and 96), the encapsulated Li+ ion still induces a stronger interaction between the metal fragment and the X@Cn fragment and |∆∆E(DEF)| is smaller than |∆∆E(INT)A(BC)|. Therefore, an increase in the cage size has no effect on the basic EDA results.

X∆E(DEF) (∆E(DEF)A, ∆E(DEF)B)∆∆E(DEF)c∆E(INT)A(BC)∆∆E(INT)A(BC)c∆Ed∆∆Ec,d
2-(X@C60)}PtL2
F51.2 (41.0, 10.2)−14.8−67.0+33.8−14.7+20.1
066.0 (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
2-(X@C60)}PdL2
F30.7 (25.9, 4.8)−12.6−45.829.0−13.9+17.6
043.3 (35.0, 8.3)−74.8−31.5
Li+51.1 (37.9, 13.2)7.8−109.3−34.5−59.2−27.7

Table 2.

Basic EDA for {η2-(X@C60)}ML2 (M = Pt, Pd) at M06/LANL2DZa,b.

Energies are given in kcal/mol.


A and B respectively represent the metal fragment and C60 cage.


The difference is relative to corresponding quantity at X = 0.


The reaction energy without zero-point energy (ZPE) correction for the product, relative to the corresponding reactants.


3.3. Advanced energy decomposition analysis (advanced EDA)

In an earlier study by the authors, structural parameters and spectral characteristics were used to estimate the strength of π back-bonding for {η2-(X@C60)}ML2 (M = Pt, Pd; X = 0, Li+, L = PPh3) complexes [10]. The changes in bond length (Δr/r0), bond angle (Δθav), vibrational frequency (Δν) and the chemical shift (Δδ) were used to describe the character of the π-complex s. In this study, the strength of the π back-bonding strength is estimated from an energetic viewpoint using an advanced EDA method. This analysis shows the effect of encapsulated ions, metal fragments and cage sizes on π back-bonding.

3.3.1. The effect of encapsulated ions on π back-bonding

In an earlier discussion (Section 3.2), it was proven that thermodynamic stabilities increase in the order: ∆E(X = F) < ∆E(X = 0) < ∆E(X = Li+), because the interaction energy (∆E(INT)) is increased. The interaction between the metal fragment and X@Cn is now studied using advanced EDA, which further decomposes the interaction energy into electrostatic interaction (∆Eelstat), repulsive Pauli interaction (∆EPauli) and orbital interaction (∆Eorb) terms. The orbital interactions are the most important of these three and only the most important pairwise contributions to ΔEorb are considered. The advanced EDA method is used for {η2-(X@Cn)}ML2 complexes, as shown in Tables 3 and 4 (the results for n = 70, 76, 84, 90 and 96 are presented elsewhere). A plot of the deformation density and a qualitative drawing of the orbital interactions between the metal fragment and X@C60 are shown in Figure 2. In terms of the Pt-C60 complexes, Table 3 shows that both the electrostatic interaction (∆Eelstat) and the orbital interaction (∆Eorb) stabilize the complexes because they are negative terms, but the percentage of ∆Eorb increases in the order: ∆Eorb(X = F) < ∆Eorb(X = 0) < ∆Eorb(X = Li+). Therefore, the enhanced orbital interaction must be responsible for the increase in the thermodynamic stability. Table 3 also shows that ΔE1 contributes significantly to ΔEorb: 69.5% for X = F, 75.2% for X = 0 and 76.4% for X = Li+. The deformation densities show that these come from π back-donation from a filled d orbital of the metal to the π* orbitals of C60 (charge flow is yellow to green at the top of Figure 2c). The large contributions of ΔE1 to ΔEorb are in agreement with the results of previous studies. The metal-carbon bonds are principally formed by π back-donation [8]. It is also seen that the order of ΔE1 is |ΔE1(X = F)| = 94.4 < |ΔE1(X = 0)| = 118.6 < |ΔE1(X = Li+)| = 142.8 kcal/mol. Therefore, ΔE1 is increased when there is the encapsulated Li+ ion but decreased when there is a F ion. The second contribution of ΔE2 to ΔEorb is comparatively small: 18.0% for X = F, 13.1% for X = 0 and 10.0% for X = Li+. This results from σ-donation from a filled π orbital of C60 to the π* orbital of the metal (middle of Figure 2c). The computational results show that π back-bonding is crucial to the thermodynamic stability of Pt-C60 complexes and that an encapsulated Li+ ion increases π back-bonding but an encapsulated F has the opposite effect.

FragmentsL2Pt and F@C60L2Pt and C60L2Pt and Li+@C60
ΔEint−67.7−100.8−133.0
ΔEPauli257.2235.8227.6
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%)
ΔE1c−94.4 (69.5%)−118.6 (75.2%)−142.8 (76.4%)
ΔE2c−24.4 (18.0%)−20.6 (13.1%)−18.6 (10.0%)
ΔE3c−7.1 (5.2%)−5.7 (3.6%)−6.5 (3.5%)
ΔE4c−3.0 (2.2%)−3.8 (2.4%)−5.5 (3.0%)
ΔE5c−3.6 (2.7%)−4.2 (2.7%)−5.0 (2.7%)
ΔE6c−2.1 (1.1%)
ΔErestc−5.8 (4.3%)−6.3 (4.0%)−6.8 (3.6%)

Table 3.

The advanced EDA results for {η2-(X@C60)}PtL2a (X = F, 0, Li+) at the M06/TZ2P level of theory. The fragments are PtL2 and X@C60 in a singlet (S) electronic state. All energy values are in kcal/mol.

Optimized structures at the M06/LANL2DZ level of theory.


The values in parentheses give the percentage contribution to the total attractive interactions, ΔEelstat + ΔEorb.


The values in parentheses give the percentage contribution to the total orbital interactions, ΔEorb.


FragmentsL2Pd and F@C60L2Pd and C60L2Pd and Li+@C60
ΔEint−45.1−73.5−103.9
ΔEPauli188.9176.5176.4
ΔEelstatb−142.8 (61.0%)−137.0 (54.8%)−138.9 (49.6%)
ΔEorbb−91.2 (39.0%)−113.0 (45.2%)−141.3 (50.4%)
ΔE1c−71.9 (78.8%)−96.9 (85.8%)−121.0 (85.6%)
ΔE2c−15.5 (17.0%)−10.8 (9.6%)−9.4 (6.7%)
ΔE3c−4.9 (5.4%)−4.2 (3.7%)−4.6 (3.3%)
ΔE4c−2.1 (2.3%)−2.3 (2.0%)−3.6 (2.5%)
ΔE5c−2.0 (2.2%)−2.9 (2.6%)−3.6 (2.5%)
ΔErestc−2.7 (3.0%)−3.6 (3.2%)−6.5 (4.6%)

Table 4.

The advanced EDA results for {η2-(X@C60)}PdL2a (X = F, 0, Li+) at the M06/TZ2P level of theory. The fragments are PdL2 and X@C60 in the singlet (S) electronic state. All energy values are in kcal/mol.

Optimized structures at the M06/LANL2DZ level of theory.


The values in parentheses give the percentage contribution to the total attractive interactions, ΔEelstat + ΔEorb.


The values in parentheses give the percentage contribution to the total orbital interactions, ΔEorb.


Figure 2.

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

3.3.2. The effect of metal fragments on π back-bonding

Pd-C60 complexes appear to be similar to Pt-C60 complexes, but a comparison of the results in Tables 3 and 4 shows that the value ΔE1 for a Pd-C60 complex is smaller than the corresponding value for a Pt-C60 complex, which demonstrates that the π back-bonding for a palladium center is weaker than that for a platinum center. For example, |ΔE1(M = Pd, X = Li+)| = 121.0 < |ΔE1(M = Pt, X = Li+)| = 142.8 kcal/mol. This is consistent with the earlier results that were obtained using structural parameters and spectral characteristics [10].

3.3.3. The effect of cage sizes on π back-bonding

Figure 3 shows a plot of the ΔE1 values versus cage sizes that are calculated for {η2-(X@Cn)}PtL2 complexes (n = 60, 70, 76, 84, 90 and 96). It is seen that there is no linear relationship and there is one obvious peak for each X at n = 84 [26]. This demonstrates the effect of a difference in size of the carbon clusters on π back-bonding for a metal center, but the correlation is not simply monotonic. Therefore, a larger (smaller) cage size does not necessarily imply that there is stronger (weaker) π back-bonding, which results in greater (lower) thermodynamic stability.

Figure 3.

The correlation between ΔE1 and cage sizes for {η2-(X@Cn)}PtL2 (n = 60, 70, 76, 84, 90 and 96) complexes. The blue, red and black lines indicate the ΔE1 for X = Li+, 0 and F−, respectively.

4. Conclusion

This computational study uses density functional theory to determine the thermodynamic stability of {η2-(X@Cn)}ML2 complexes (M = Pt, Pd; X = F, 0, Li+ and n = 60, 70, 76, 84, 90 and 96). The calculations show the reaction is more stable when the Li+ ion is encapsulated within Cn but the complex becomes unstable if there is a F ion. Basic EDA shows that there is an increase in the interaction between the metal fragment and Cn if there is an encapsulated Li+ ion but F ion has the opposite effect.

The advanced EDA results show that π back-bonding is crucial to thermodynamic stability and that thermodynamic stability is increased by the presence of a Li+ ion but the presence of a F ion has the opposite effect. These computations also show that a platinum center results in stronger π back-bonding than a palladium center and that there is no linear relationship between cage size and π back-bonding.

Acknowledgments

The authors would like to thank the National Center for High-Performance Computing in Taiwan for the donation of generous amounts of computing time. The authors are also grateful for financial support from the Ministry of Science and Technology of Taiwan.

© 2017 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite and reference

Link to this chapter Copy to clipboard

Cite this chapter Copy to clipboard

Ming-Chung Yang and Ming-Der Su (December 20th 2017). How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes? Role of Cage Sizes, Encapsulated Ions and Metal Ligands, Fullerenes and Relative Materials - Properties and Applications, Natalia V. Kamanina, IntechOpen, DOI: 10.5772/intechopen.70068. Available from:

chapter statistics

234total chapter downloads

1Crossref citations

More statistics for editors and authors

Login to your personal dashboard for more detailed statistics on your publications.

Access personal reporting

Related Content

This Book

Next chapter

Fullerene as Spin Converter

By Elif Okutan

Related Book

First chapter

Polyimides Bearing Long-Chain Alkyl Groups and Their Application for Liquid Crystal Alignment Layer and Printed Electronics

By Yusuke Tsuda

We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities.

More About Us