**3. Results and discussion**

#### **3.1. Geometric changes**

The structures of {η<sup>2</sup> -(X@Cn)}ML2 complexes for M = Pt, Pd; X = F<sup>−</sup> , 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<sup>+</sup> ion is encapsulated into the cage, the metal-carbon bonds remain unaltered and the respective distances between

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?... http://dx.doi.org/10.5772/intechopen.70068 115

**Figure 1.** Optimized geometries for {η<sup>2</sup> -(X@C60)}ML2 (M = Pt, Pd; X = Li+ , 0, F<sup>−</sup> ).

is the sum of the deformation energy of A (∆E(DEF)A, which is defined as the energy of A in

tion energy term, ∆E(INT)A(BC), is the interaction energy between A and (BC) for their respec-

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 singlepoint calculation using the M06/TZ2P basis set from the Gaussian 09 optimized geometry.

complexes for M = Pt, Pd; X = F<sup>−</sup>

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

into the cage, the metal-carbon bonds remain unaltered and the respective distances between

of the metal-carbon bonds are 2.12 Å and 2.12 Å (**Table 1**). When the Li<sup>+</sup>

) and B (∆E(DEF)B)). The interac-

, 0, Li+

and n = 60, 70, 76, 84,

ion is encapsulated

the product relative to the optimized isolated structure (A0

@Cn)}PtL2 .


114 Fullerenes and Relative Materials - Properties and Applications

tive optimized product structures.

**Scheme 2.** Basic EDA for {η<sup>2</sup>

**3. Results and discussion**


**3.1. Geometric changes**

The structures of {η<sup>2</sup>

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<sup>−</sup> ) increases (3.18 and 3.18 Å). The Li<sup>+</sup> 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 C<sup>1</sup> (C2 ) atoms are −0.27 (−0.27). When the cage is encapsulated by a Li+ ion, the atomic charges on the C<sup>1</sup> (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 C<sup>1</sup> (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<sup>−</sup> . Similar geometric changes and charge distributions are seen for n = 70, 76, 84, 90 and 96 and are presented elsewhere.


is more stable. The relative thermodynamic stability increases in the order: ∆E(X = F−

(M = Pt, Pd) at M06/LANL2DZa,<sup>b</sup>

F<sup>−</sup> 51.2 (41.0, 10.2) −14.8 −67.0 +33.8 −14.7 +20.1 0 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

F<sup>−</sup> 30.7 (25.9, 4.8) −12.6 −45.8 29.0 −13.9 +17.6 0 43.3 (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

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.

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

) = −34.5 > ∆E(M = Pt, X = Li<sup>+</sup>

action 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.

In an earlier study by the authors, structural parameters and spectral characteristics were

quency (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

In an earlier discussion (Section 3.2), it was proven that thermodynamic stabilities increase

), as shown in **Table 2**. In addition, |∆∆E(DEF)| is small and |∆∆E(INT)A(BC)|

.

**∆∆E(DEF)<sup>c</sup> ∆E(INT)A(BC) ∆∆E(INT)A(BC)**

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?...


(X = 0) < ∆E(X = Li<sup>+</sup>

**Table 2.** Basic EDA for {η<sup>2</sup>

**X ∆E(DEF)** 

Energies are given in kcal/mol.

{η<sup>2</sup>

{η<sup>2</sup>

a

b

c



**(∆E(DEF)A, ∆E(DEF)B)**

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


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

= PPh3

in the order: ∆E(X = F−

For instance, ∆E(M = Pd, X = Li<sup>+</sup>

size increases (n = 70, 76, 84, 90 and 96), the encapsulated Li+

**3.3. Advanced energy decomposition analysis (advanced EDA)**

) complexes [10]. The changes in bond length (Δr/r<sup>0</sup>

) < ∆E(X = 0) < ∆E(X = Li<sup>+</sup>

used to estimate the strength of π back-bonding for {η<sup>2</sup>

ions, metal fragments and cage sizes on π back-bonding.

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

) < ∆E

, L

) = −35.9 kcal/mol. When the cage

**<sup>c</sup> ∆E<sup>d</sup> ∆∆Ec,d**

117

http://dx.doi.org/10.5772/intechopen.70068

ion still induces a stronger inter-

(M = Pt, Pd; X = 0, Li+

), bond angle (Δθav), vibrational fre-

), because the interaction energy (∆E(INT))

**Table 1.** Selected geometrical parameters (bond distances in Å) and the NPA atomic charge for optimized complexes ({η<sup>2</sup> -(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 {η<sup>2</sup> -(X@Cn)} ML2 complexes, basic EDA is performed on {η<sup>2</sup> -(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({η<sup>2</sup> -(X@Cn)}ML2 ) − E(X@Cn) − E(ML<sup>2</sup> ), 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<sup>+</sup> or F<sup>−</sup> . It is found that the encapsulation of the Li<sup>+</sup> ion induces more distortion in fragments A and B of the Pt-Li+ @C60 complex than those of the Pt-F<sup>−</sup> @C60 complex (∆∆E(DEF)(X = Li<sup>+</sup> ) = 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<sup>−</sup> ) = +33.8 kcal/mol), which shows that the encapsulated Li<sup>+</sup> ion induces a stronger interaction between the metal fragment and the X@C60 fragment, so {η<sup>2</sup> -(Li+ @C60)}PtL2

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?... http://dx.doi.org/10.5772/intechopen.70068 117


a Energies are given in kcal/mol.

**3.2. Basic energy decomposition analysis (basic EDA)**

) at the M06/LANL2DZ level of theory.

) − E(X@Cn) − E(ML<sup>2</sup>

**System Geometrical parameters NPA atomic charge**

116 Fullerenes and Relative Materials - Properties and Applications

ion induces more distortion in fragments A and B of the Pt-Li+

complexes, basic EDA is performed on {η<sup>2</sup>

ML2

Pt-F<sup>−</sup>

∆∆E(INT)A(BC)(X = F<sup>−</sup>

∆E= E({η<sup>2</sup>

M = Pt; X = Li+

M = Pt; X = 0

M = Pt; X = F<sup>−</sup>

M = Pd; X = Li+

M = Pd; X = 0

M = Pd; X = F<sup>−</sup>


ML2

ML2

ML2

ML2

ML2

ML2

({η<sup>2</sup>


The same results are obtained for X = Li<sup>+</sup>

@C60 complex (∆∆E(DEF)(X = Li<sup>+</sup>

interaction energy increases when the Li+

In order to better understand the factors that govern the thermodynamic stability of {η<sup>2</sup>

for n = 70, 76, 84, 90 and 96 are presented elsewhere). The bonding energy (∆E) is defined as

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).

or F<sup>−</sup>

stronger interaction between the metal fragment and the X@C60 fragment, so {η<sup>2</sup>

) = 8.0, ∆∆E(DEF)(X = F−

) = +33.8 kcal/mol), which shows that the encapsulated Li<sup>+</sup>


**M-C1 M-C2 X-C1 X-C2 M C1 C2 X**

X@C60 2.12 2.12 2.29 2.29 +0.48 −0.32 −0.32 +0.86

X@C60 2.12 2.12 – – +0.46 −0.27 −0.27 –

X@C60 2.13 2.13 3.18 3.18 +0.43 −0.23 −0.23 −0.93

X@C60 2.12 2.12 2.28 2.28 +0.44 −0.27 −0.27 +0.86

X@C60 2.13 2.13 – – +0.40 −0.21 −0.21 –

X@C60 2.15 2.15 3.15 3.15 +0.34 −0.16 −0.16 −0.93

**Table 1.** Selected geometrical parameters (bond distances in Å) and the NPA atomic charge for optimized complexes


) = −35.9,

@C60)}PtL2

ion induces a

complexes (the basic EDA results

@C60 complex than those of the


) = −14.8 kcal/mol). However, the

), using Eq. (1). The Pt-C60 complex without encapsulated

ion is encapsulated (∆∆E(INT)A(BC)(X = Li+

. It is found that the encapsulation of the Li<sup>+</sup>

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

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

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

**Table 2.** Basic EDA for {η<sup>2</sup> -(X@C60)}ML2 (M = Pt, Pd) at M06/LANL2DZa,<sup>b</sup> .

is more stable. The relative thermodynamic stability increases in the order: ∆E(X = F− ) < ∆E (X = 0) < ∆E(X = Li<sup>+</sup> ), 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<sup>+</sup> ) = −34.5 > ∆E(M = Pt, X = Li<sup>+</sup> ) = −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.

#### **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 {η<sup>2</sup> -(X@C60)}ML2 (M = Pt, Pd; X = 0, Li+ , L = PPh3 ) complexes [10]. The changes in bond length (Δr/r<sup>0</sup> ), 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<sup>+</sup> ), 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 {η<sup>2</sup> -(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<sup>−</sup> ) < ∆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<sup>−</sup> , 75.2% for X = 0 and 76.4% for X = Li+ . The deformation densities show that these come from π backdonation 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 backdonation [8]. It is also seen that the order of ΔE1 is |ΔE1 (X = F<sup>−</sup> )| = 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 ΔE<sup>2</sup> to ΔEorb is comparatively small: 18.0% for X = F− , 13.1% for X = 0 and 10.0% for X = Li<sup>+</sup> . 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

, 0, Li+

Pd-C60 complexes appear to be similar to Pt-C60 complexes, but a comparison of the results in

ing value for a Pt-C60 complex, which demonstrates that the π back-bonding for a palladium

 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

ion increases π back-bonding but an encapsu-

) at the M06/TZ2P level of theory. The fragments

for a Pd-C60 complex is smaller than the correspond-

)| = 142.8 kcal/mol. This is consistent with the earlier results that were

**Pd and C60 L2**

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?...

**Pd and Li+**

http://dx.doi.org/10.5772/intechopen.70068

**@C60**

119

values versus cage sizes that are calculated for {η<sup>2</sup>

(M = Pd, X = Li+

)| = 121.0


Pt-C60 complexes and that an encapsulated Li+

Optimized structures at the M06/LANL2DZ level of theory.

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

center is weaker than that for a platinum center. For example, |ΔE1

obtained using structural parameters and spectral characteristics [10].

has the opposite effect.

**Table 4.** The advanced EDA results for {η<sup>2</sup>

**Tables 3** and **4** shows that the value ΔE1

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

(M = Pt, X = Li+

**Figure 3** shows a plot of the ΔE1

lated F<sup>−</sup>

are PdL2

**Fragments L2**

ΔEelstat

ΔEorb

ΔE1

ΔE<sup>2</sup>

ΔE<sup>3</sup>

ΔE<sup>4</sup>

ΔE<sup>5</sup>

ΔErest

a

b

c

**Pd and F<sup>−</sup>**

**@C60 L2**

<sup>b</sup> −142.8 (61.0%) −137.0 (54.8%) −138.9 (49.6%)

<sup>b</sup> −91.2 (39.0%) −113.0 (45.2%) −141.3 (50.4%)

<sup>c</sup> −71.9 (78.8%) −96.9 (85.8%) −121.0 (85.6%)

<sup>c</sup> −15.5 (17.0%) −10.8 (9.6%) −9.4 (6.7%)

<sup>c</sup> −4.9 (5.4%) −4.2 (3.7%) −4.6 (3.3%)

<sup>c</sup> −2.1 (2.3%) −2.3 (2.0%) −3.6 (2.5%)

<sup>c</sup> −2.0 (2.2%) −2.9 (2.6%) −3.6 (2.5%)

<sup>c</sup> −2.7 (3.0%) −3.6 (3.2%) −6.5 (4.6%)

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


and X@C60 in the singlet (S) electronic state. All energy values are in kcal/mol.

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

a (X = F<sup>−</sup>

ΔEint −45.1 −73.5 −103.9 ΔEPauli 188.9 176.5 176.4

< |ΔE1

PtL2

stability.

a Optimized structures at the M06/LANL2DZ level of theory.

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

**Table 3.** The advanced EDA results for {η<sup>2</sup> -(X@C60)}PtL2 a (X = F<sup>−</sup> , 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.

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?... http://dx.doi.org/10.5772/intechopen.70068 119


a Optimized structures at the M06/LANL2DZ level of theory.

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 {η<sup>2</sup>

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

the enhanced orbital interaction must be responsible for the increase in the thermodynamic

donation from a filled *d* orbital of the metal to the π\* orbitals of C60 (charge flow is yellow to

the results of previous studies. The metal-carbon bonds are principally formed by π back-

is |ΔE1

, 13.1% for X = 0 and 10.0% for X = Li<sup>+</sup>

percentage of ∆Eorb increases in the order: ∆Eorb(X = F<sup>−</sup>

118 Fullerenes and Relative Materials - Properties and Applications

donation [8]. It is also seen that the order of ΔE1

**Pt and F<sup>−</sup>**

Optimized structures at the M06/LANL2DZ level of theory.

**Table 3.** The advanced EDA results for {η<sup>2</sup>

ion but decreased when there is a F−

paratively small: 18.0% for X = F−

green at the top of **Figure 2c**). The large contributions of ΔE1

)| = 142.8 kcal/mol. Therefore, ΔE1

**@C60 L2**

ΔEint −67.7 −100.8 −133.0 ΔEPauli 257.2 235.8 227.6

<sup>b</sup> −189.0 (58.2%) −178.8 (53.1%) −173.8 (48.2%)

<sup>b</sup> −135.8 (41.8%) −157.7 (46.9%) −186.9 (51.8%)

<sup>c</sup> −94.4 (69.5%) −118.6 (75.2%) −142.8 (76.4%)

<sup>c</sup> −24.4 (18.0%) −20.6 (13.1%) −18.6 (10.0%)

<sup>c</sup> −7.1 (5.2%) −5.7 (3.6%) −6.5 (3.5%)

<sup>c</sup> −3.0 (2.2%) −3.8 (2.4%) −5.5 (3.0%)

<sup>c</sup> −3.6 (2.7%) −4.2 (2.7%) −5.0 (2.7%)

<sup>c</sup> – – −2.1 (1.1%)

<sup>c</sup> −5.8 (4.3%) −6.3 (4.0%) −6.8 (3.6%)

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

a (X = F<sup>−</sup>

, 0, Li+

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


and X@C60 in a singlet (S) electronic state. All energy values are in kcal/mol.

stability. **Table 3** also shows that ΔE1

for X = 0 and 76.4% for X = Li+

complexes, as shown in **Tables 3** and **4** (the results for n = 70, 76, 84, 90 and 96 are

) < ∆Eorb(X = 0) < ∆Eorb(X = Li+

)| = 94.4 < |ΔE1

is increased when there is the encapsulated

**Pt and Li+**

) at the M06/TZ2P level of theory. The fragments

contributes significantly to ΔEorb: 69.5% for X = F<sup>−</sup>

. The deformation densities show that these come from π back-

(X = F<sup>−</sup>

ion. The second contribution of ΔE<sup>2</sup>

**Pt and C60 L2**

Cn)}ML2

< |ΔE1

Li+

ΔEelstat

ΔEorb

ΔE1

ΔE<sup>2</sup>

ΔE<sup>3</sup>

ΔE<sup>4</sup>

ΔE<sup>5</sup>

ΔE<sup>6</sup>

ΔErest

a

b

c

are PtL2

(X = Li+

**Fragments L2**


). Therefore,

(X = 0)| = 118.6

to ΔEorb is com-

. This results from

**@C60**

to ΔEorb are in agreement with

, 75.2%

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

**Table 4.** The advanced EDA results for {η<sup>2</sup> -(X@C60)}PdL2 a (X = F<sup>−</sup> , 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.

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<sup>−</sup> has the opposite effect.

#### *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 {η<sup>2</sup> -(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.

**4. Conclusion**

stability of {η<sup>2</sup>

F−

a F<sup>−</sup>


between cage size and π back-bonding.

ion has the opposite effect.

**Figure 3.** The correlation between ΔE1

blue, red and black lines indicate the ΔE1

**Acknowledgements**

but the complex becomes unstable if there is a F−

This computational study uses density functional theory to determine the thermodynamic


How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?...

, respectively.

The advanced EDA results show that π back-bonding is crucial to thermodynamic stability

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 grate-

ful for financial support from the Ministry of Science and Technology of Taiwan.

 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

, 0, Li+

and n = 60, 70, 76, 84, 90 and 96).

(n = 60, 70, 76, 84, 90 and 96) complexes. The

http://dx.doi.org/10.5772/intechopen.70068

121

ion is encapsulated within Cn

ion but the presence of

ion but

ion. Basic EDA shows that there is an increase

complexes (M = Pt, Pd; X = F<sup>−</sup>

and cage sizes for {η<sup>2</sup>

, 0 and F<sup>−</sup>

for X = Li+

in the interaction between the metal fragment and Cn if there is an encapsulated Li+

The calculations show the reaction is more stable when the Li<sup>+</sup>

and that thermodynamic stability is increased by the presence of a Li<sup>+</sup>

**Figure 2.** (a) A qualitative drawing of the orbital interactions between the metal fragment and Li<sup>+</sup> @C60; (b) the shape of the most important interacting occupied and vacant orbitals of the metal fragments and Li<sup>+</sup> @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.

How Important is Metal-Carbon Back-Bonding for the Stability of Fullerene-Transition Metal Complexes?... http://dx.doi.org/10.5772/intechopen.70068 121

**Figure 3.** The correlation between ΔE1 and cage sizes for {η<sup>2</sup> -(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<sup>−</sup> , respectively.
