DielsâAlder Cycloaddition of Cyclopentadiene and C60 at the Extreme

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Article

Diels-Alder Cycloaddition of Cyclopentadiene and C at the Extreme High Pressure 60

Tao Yang, Ryoichi Fukuda, Roberto Cammi, and Masahiro Ehara J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 16 May 2017 Downloaded from http://pubs.acs.org on May 17, 2017

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The Journal of Physical Chemistry

Diels-Alder Cycloaddition of Cyclopentadiene and C60 at the Extreme High Pressure

Tao Yang*,†,‡, Ryoichi Fukuda*,‡,ǁ, Roberto Cammi,*,§ and Masahiro Ehara*,†,‡,#

†

Institute for Molecular Science, Research Center for Computational Science, Myodaiji, Okazaki

444-8585, Japan ‡

Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-

8245, Japan ǁ

Department of Molecular Engineering, Graduate School of Engineering, Kyoto University,

Nishikyo-ku, Kyoto 615-8510, Japan §

Department of Chemical Science, Life Sciences, and Environmental Sustainability, University of

Parma, Parco Area delle Scienze 17/A, 43124 Parma, Italy #

SOKENDAI, the Graduate University for Advanced Studies, Myodaiji, Okazaki 444-8585, Japan

ABSTRACT: High-pressure Diels-Alder cycloaddition reaction of fullerenes is an important synthetic method for the thermally stable cycloadducts. The effects of high pressure on the potential energy surfaces of Diels-Alder cycloaddition of cyclopentadiene and C60 were studied with a recently developed approach, the polarizable continuum model for extreme pressure (XP-PCM). It is revealed that the high pressure reduces the activation energies and increases reaction energies drastically, making the DA reaction more favorable. The pressure effects on the reaction energetics may be divided into the cavitation and electronic contributions. For the activation energy, the cavitation contribution is significant in comparison with the electronic contribution. To assist future experiments, the activation volume and reaction volume were computed based on the relationship between activation energy or reaction energy with the pressure as a consequence of the fitting linear correlation between activation energy or reaction energy with the pressure.

1

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INTRODUCTION Fullerenes are carbon cages which consists of sp2-hybridized carbon atoms.1 C60 as well as C70 are two most representatives of the fullerene family.2 With chemical reactions, numerous fullerene derivatives have been synthesized up to date.3-8 In particular, exohedral cycloaddition reactions of fullerenes (especially C60) have been widely used to achieve the functionalization of fullerenes, including

Diels-Alder 21-24

cycloaddition.

(DA)

cycloaddition,9-17

1,3-dipolar

cycloaddition,18-20

and

[2+2]

2

Thanks to its electron-withdrawing nature and sp -hybridized carbon atoms, C60

as a reactive dienophile undergoes [4+2] DA cycloaddition reactions with various dienes such as cyclopentadiene, furan, and anthracene.9-15 DA cycloadducts might undergo facile cycloreversion upon heating and regenerate C60 and dienes.13-14, 25 On the other hand, thermally stable adducts are usually required for further characterizations. High-pressure DA reaction provides a way to thermally stable cycloadducts. Takeshita and coworkers studied the high-pressure (300 MPa) DA reaction of fullerene and several tropones and the adducts are thermally stable under 140 ºC.26-28 The same group also reported high-pressure DA reaction of C60 with 2,5-dioxaspiro-[4.4]non-6-ene and it was revealed that even at 150 ºC for 15 h, no cycloreversion of the adducts was observed experimentally.29 The high-pressure conditions can also make the least reactive dienes reactive in DA reaction with C60. For example, Matty revealed that the high pressure is necessary for DA reaction of C60 and 4,5-dimethylene-2,2-1,3-dioxolane.30 XP-PCM, the Polarizable Continuum Model for eXtreme Pressure, has been systemically developed by one of the present authors (Roberto Cammi). Starting from a basic version in 2008,31 the XP-PCM has been extended recently with applications for studying the effects of extreme high pressure on the equilibrium geometries,32 vibrational frequencies,33 and the electronic excitations of molecular systems.34 Very recently, this quantum chemical method has been further developed and applied to investigation of the potential energy surfaces of reactive molecular systems at extreme high pressures.35 In the present work, we theoretically studied the effect of the extreme high pressure (0.6-16 GPa) on DA cycloaddition of cyclopentadiene (CP) and C60 with the use of XP-PCM. DA cycloaddition of CP and C60 was chosen because it has been intensively investigated with theoretical and experimental methods.10, 12-14, 36-38 2


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COMPUTATIONAL METHODS In this section, we briefly address the computational method for calculating free energy under extreme pressure. For the details of the theory and implementation, the readers are referred to the original articles.31,35 In the XP-PCM method, a potential energy surface (PES) of chemical reactions is given by: , = , + ,

(1)

where , is the electronic quantum mechanical (QM) energy functional of the XP-PCM,31

and , is the cavitation free energy required for the formation of the cavity hosting the

molecular solute into the solvent39 at the given condition of pressure p. The cavitation free energy is computed according to the scaled particle theory40 as modified for the molecular cavities made by the union of van der Waals sphere. See Ref. [35] for further details. The XP-PCM computational protocol exploits the variations of the volume Vc of the molecular cavity used for the calculation of the free-energy functional Ger to gauge the pressure p acting on the system. The physical parameters describing the solute-solvent interaction, the dielectric permittivity of the external medium and its numeral density ns, and the Pauli step barrier potential V0, are also considered to depend on variations of the cavity volume Vc. In PCM calculations at the standard condition of pressure, the molecular cavity used for the calculation of the free-energy functional Ger is constructed starting from a set of primary atomic spheres centered on the nuclei of the constituting atoms. Each atomic sphere has radii Ri that is equal to the corresponding atomic van der Waals radii times a scaling factor f, that is, Ri = RvdW × f, which is assumed to be fixed at f = f0 = 1.2. Additional spheres are introduced to account for the space nonaccessible to the solvent molecules. The resulting cavity is a Solvent Excluding Surface (SES) cavity.39 In XP-PCM, the SES cavity is shrunk by varying the cavity scaling factor f that is suitably decreased with respect to the reference scaling factor f0. Numerical tests show that the range of values for the scaling factor f = 1.2-0.90 allows one to span an increase of the pressure p from approximately 1–16 GPa. The physical parameters describing the solute-solvent interactions are the dielectric permittivity ε, the numeral density ns of the external medium, and the Pauli repulsion step barrier V0. These 3



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physical parameters are considered to be functions of the scaling factor f used to reduce the volume of the cavity. This dependence is based on the assumption that for a given scaling of the volume of molecular cavity, the external medium also experiences a parallel scaling of its volume. In the computational protocol, for each selected scaling factor f of the cavity, the environment is subjected to a scaling s of its linear dimensions defined in terms of the ratio between the volume of the cavity Vc(f) and the cavity volume V(f0) corresponding to the reference scaling factor f0:

= 1/3 .

(2)

Correspondingly, the entire volume of the environment is scaled by s3 and its corresponding numeral density ns(s) is given by: =

(3)

where is the numeral density of the medium at the standard condition of pressure. To this variation of the numeral density ns corresponds a variation of the dielectric permittivity34 ε(s) determined by: = 1 +

!

(4)

where ε0 is the dielectric permittivity of the medium at the standard pressure condition, and a variation on the energy barrier potential V0 as well:

" = #$

(5)

where V0 is the step barrier at the standard condition of pressure41 and η is a semiempirical parameter used to gauges the strength of the solute-solvent Pauli repulsion, as a higher value of the hardness parameter η is indicative of a harder Pauli barrier potential of the medium. The range of values of

parameter η can be estimated from a comparison of the equation of state of the pressure p as a function of the cavity volume Vc with the macroscopic equation of state p – V of several solvents.3234

4


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For each of the selected values of the scaling factor f for the SES molecular cavity, the free-energy functional Ger(R) is computed using the values of the physical parameter dielectric permittivity ε(s) and the Pauli repulsion barrier V0(s) obtained from the previous eqs. (2–5). The pressure p associated with each value of the cavity scaling factor f is computed by differentiation of the free-energy functional Ger with respect to the cavity volume Vc(f): &'

= − &().

(6)

It is convenient to perform an analytical fitting of the free-energy functional Ger as a function of the cavity volume Vc using the following expression34 " = " + * × " ,-

!

-

+ 1. + / × " !

(7)

and the compute the pressure p by direct analytical differentiation: 0 =

&'()

&

= * × ,

− 1. − /.

(8)

The cavitation energy Gcav(p) is evaluated for each of the selected values of eq. (1) of the pressure p obtained from eq. (8) according to the protocol of Ref. 35. For each value of the pressure p, the PES Gtot(p, R) is computed according to Eq. (1) by summing up the corresponding values of the free-energy functional Ger(p, R) and the cavitation energy Gcav(p, R). All the DFT calculations were performed using the M06-2X42 functional with 6-31G(d) in Gaussian09 program Rev. B.01.43 Subsequent frequency calculations at the same level of theory confirmed those molecular structures are local minima or transition states (TSs). Argon (ε0 = 1.430, ρ = 1.3954 g/cm3 at standard thermodynamic conditions) was used as the external medium. Osuna, Swart, and Solà revealed that the dispersion effect is important and a stable reactant complex forms between C60 and CP before TS.36 Since the XP-PCM calculations of bimolecular complexes may show numerical instabilities due to the complexity of the cavity topology, the effects of high pressure on transition states and products will be discussed in the present work. Both η = 6 and 3 were chosen as the gauge parameters for the Pauli barrier repulsion. Here, the results using η = 6 are presented and the results for η = 3 are collected in the Supporting Information. In cavitation, we 5



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removed the unnecessary PCM cavity inside the C60 fullerene, which was generated by the standard PCM procedure.

RESULTS AND DISCUSSION DA reaction of C60 and CP in the gas phase C60 has two different carbon-carbon bonds, [5,6] and [6,6] bonds, whose experimentally observed bond lengths are 1.458 and 1.401 Å, respectively.44-45 As presented in Figure 1, the calculations at the M06-2X/6-31G(d) level predicted their bond lengths as 1.451 and 1.387 Å, respectively, close to the experimental values. Previous experimental and theoretical investigations revealed that the [6,6] bond is shorter and has a larger π-electron density, resulting in its higher reactivity than the [5,6] bond.9-15, 36-38,46 DA cycloaddition of C60 prefers to take place on the [6,6] bond without the bond scission. Due to the configuration of CP, there are two possible DA cycloadditions of CP with the [5,6] bond of C60. Here, all the three possible cycloadditions of C60 and CP are considered, including 66, 56-1 and 56-2.

Figure 1. Molecular structures of C60 (left) and cyclopentadiene (CP, right). The [5,6] and [6,6] bonds are represented in red and blue, respectively.

In the previous experimental works, the activation energy for the DA reaction of cyclopentadiene and C60 was found to be 6.9 kcal/mol by Pang and Wilson.13 On the other hand, Giovane and coworkers reported an activation energy of 26.7 ± 2.2 kcal/mol for the retro-DA cycloaddition of cyclopentadiene and C60.14 Based on these two values, it’s reasonable to estimate that the reaction 6


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energy is 19.8 ± 2.2 kcal/mol.36 By using DFT with dispersion corrections, Solà and coworkers theoretically predicted the activation energy and reaction energy to be 9.1 and -23.3 kcal/mol, respectively.36 Figure 2 depicts the transition states and products with their corresponding energies relative to those of isolated C60 and CP (reactants). The DA reaction on the [6,6] bond has the lowest activation energy (6.5 kcal/mol) and the largest reaction energy (-27.1 kcal/mol), which agrees with previous experimental and theoretical results.47 Furthermore, the calculated distance between C60 and CP in TS66 is 2.22 Å, also close to the results by Solà et al.36-37 On the other hand, two DA reactions on the [5,6] bond have almost similar activation energies about 20 kcal/mol with asymmetric structure at TS and reaction energies about -5 kcal/mol. In the following calculations on the effect of the pressure, the configurations of the reactants, transition states, and adducts in the gas phase for all of these three mechanisms were fixed. There are two reasons: (a) the formulation and implementation of analytical first and second derivatives of the total free energy for the automatic determination of the critical point is under development; (b) it is convenient to reduce the number of variables to a minimum in comparing the high-pressure calculations to those without pressure.

Figure 2. Transition states and products with their corresponding electronic energies relative to 7



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those of isolated C60 and CP. The important distances are also shown.

Physical Parameters of the External Medium as Function of the Cavity Scaling Factor f In this section, we discussed the correlation between scaling factor f and the physical properties of the external medium. Table 1 presents the values of the scaling factor s for the external medium associated with the scaling factor f of the molecular cavity of the reactive system, including all the reactants, transition states, and the final products of the three cycloaddition reactions of CP and C60. First, it is shown that the values of the scaling factor s slightly depend on the target molecular system. Interestingly, all the TSs or products have the same s values, regardless of the cycloaddition type. Second, the scaling factor s of the external medium of CP changes much more than other C60involving systems. In order to define a representative value of the scaling parameter s for all the three reaction paths, we adopted the following procedure. First, the average value of reactants (CP + C60), TS, and product for each reaction path was computed as (X) (X = 66, 56-1, and 56-2). Then,

a mean value over all the eight structures has been calculated,48 which is regarded as the

representative scaling factor and are listed in Table 1. With the representative scaling factor , the physical parameters (i.e., dielectric permittivity ε, density ρ, and molar volume Vmol) of the external medium have been further calculated, as presented in Table 2. These values of the external medium parameters have been used together with two values of the parameter η = 6 and 3 to calculate the free-energy functional Ger as a function of the cavity scaling factor f.

Table 1. Scaling Factor s for the External Medium as a Function of the Scaling Factor f of the Atomic Spheres of the Molecular Cavities for DA Cycloaddition of CP and C60. The Mean Value of Scaling Factor for Reaction X s (X) and s are Defined in Ref. 48. f

CP

C60

TS66

P66

(66)

TS56-1

P56-1

(56-1)

TS56-2

P56-2

(56-2)

1.200

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.000

1.175

0.986

0.992

0.992

0.992

0.991

0.992

0.992

0.991

0.992

0.992

0.991

0.992

1.150

0.972

0.985

0.985

0.985

0.982

0.985

0.985

0.982

0.985

0.985

0.982

0.983

8


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1.125

0.958

0.977

0.977

0.977

0.972

0.977

0.977

0.972

0.977

0.977

0.972

0.975

1.100

0.944

0.969

0.970

0.970

0.963

0.970

0.970

0.963

0.970

0.970

0.963

0.967

1.075

0.930

0.961

0.962

0.962

0.954

0.962

0.962

0.954

0.962

0.962

0.954

0.958

1.050

0.916

0.954

0.954

0.955

0.945

0.954

0.954

0.945

0.954

0.955

0.945

0.950

1.025

0.902

0.946

0.947

0.947

0.935

0.947

0.947

0.935

0.947

0.947

0.935

0.941

1.000

0.888

0.938

0.939

0.939

0.926

0.939

0.939

0.926

0.939

0.939

0.926

0.933

Table 2. Values of the Physical Parameters Dielectric of the External Medium: Permittivity ε, Density ρ (g/cm3), and Molar Volume Vmol (cm3/mol) as Functions of the Cavity Scaling Factor f and of Corresponding Linear Scaling of the Medium. f

ε

ρ

Vmol

1.200

1.000

1.4300

1.395

22.41

1.175

0.992

1.4411

1.431

21.85

1.150

0.983

1.4524

1.468

21.30

1.125

0.975

1.4642

1.506

20.76

1.100

0.967

1.4762

1.545

20.23

1.075

0.958

1.4890

1.587

19.70

1.050

0.950

1.5021

1.630

19.19

1.025

0.941

1.5159

1.674

18.68

1.000

0.933

1.5302

1.721

18.18

Free-Energy Functional Ger and Pressure p as a Function of the Cavity Scaling Factor f Table 3 presents the free-energy functional Ger as a function of the cavity scaling factor f for the reactants, transition states, and cycloadducts of three cycloaddition pathways. It is evident that as the cavity scaling factor f of the cavity reduces, Ger increases monotonically, which is ascribed to the higher solute-solvent Pauli repulsion. The decrease of the cavity scaling factor f represents the reduction of the cavity volume used to host the molecular solute. This will further increases the amount of the electronic charge of the solute that is exposed to the overlap with the electronic distribution of the medium, resulting in an increase of the repulsive Pauli interaction. Because Pauli parameter η indicates the strength of the repulsive interaction; the larger the η, the stronger the solute-solvent interaction. Consequently, the values of the free-energy functional Ger computed using

9



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the Pauli parameter η = 6 are higher than the corresponding value computed using Pauli parameter η = 3 (See Table S4). The free-energy functional Ger values of Table 3 have been fitted as a function of the cavity volume Vc with a Murnaghan-like analytical expression (7), and the resulting fitting parameters a, b, c are reported in Table S3. The free-energy functional Ger computed with the Pauli parameter η = 6 gives higher values of the Murnaghan parameters a and b, reflecting a more repulsive Pauli solute-solvent interaction.

Table 3. Free-Energy Functional Ger (in a.u.) as a Function of the Molecular Cavity Scaling Factor f for DA Cycloaddition of CP and C60. The Values Are Given Relative to -193.0 (CP), -2285.0 (C60) and -2479.0 (TS and P) a.u. The Results Refer to the Pauli Exponential Parameter η = 6. f

CP

C60

TS66

P66

TS56-1

P56-1

TS56-2

P56-2

1.200

-1.0017

-0.4506

-0.4433

-0.4965

-0.4172

-0.4611

-0.4220

-0.4603

1.175

-1.0005

-0.4478

-0.4398

-0.4931

-0.4140

-0.4576

-0.4187

-0.4567

1.150

-0.9988

-0.4437

-0.4347

-0.4885

-0.4092

-0.4529

-0.4131

-0.4522

1.125

-0.9964

-0.4379

-0.4275

-0.4814

-0.4019

-0.4455

-0.4064

-0.4447

1.100

-0.9928

-0.4294

-0.4178

-0.4712

-0.3924

-0.4346

-0.3960

-0.4343

1.075

-0.9879

-0.4170

-0.4013

-0.4559

-0.3772

-0.4190

-0.3810

-0.4187

1.050

-0.9806

-0.3989

-0.3799

-0.4297

-0.3531

-0.3979

-0.3580

-0.3945

1.025

-0.9710

-0.3726

-0.3498

-0.4027

-0.3229

-0.3655

-0.3256

-0.3675

1.000

-0.9568

-0.3341

-0.3017

-0.3527

-0.2732

-0.3212

-0.2812

-0.3167

Based on the analytical differentiation of the Murnaghan-like analytical fitting of the free-energy functional Ger with the fitting parameters in Table S3, the value of the pressure p as a function of the cavity scaling factor f were calculated, as presented in Table 4. It is revealed that with a given scaling factor f, the pressure p slightly depends on the target molecular system, especially those C60invloving systems. For each reaction path, we have computed a mean value (X) (X = 66, 56-1, and

56-2) of the pressure p at a given cavity scaling factor f and found that is nearly the same for all

three cycloaddition paths. Then, a further average of the pressure over all the eight structures is

calculated48 and the corresponding values are reported in the last column of Table 4, which are regarded as the unique value of the pressure p. The pressure ranges from 0.8 to 16.1 GPa for η = 6

10


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and from 0.6 to 7.5 GPa for η = 3 (Table S5).

Table 4. Pressure (GPa) as a Function of the Cavity Scaling Factor f for DA Cycloaddition of CP and C60. The Mean Value of Pressure for Reaction X p (X) and p are Defined in Ref. 48. The Results Refer to the Pauli Exponential Parameter η = 6. f

CP

C60

TS66

P66

(66)

TS56-1

P56-1

(56-1)

TS56-2

P56-2

(56-2)

1.200

1.2

0.7

0.8

0.8

0.8

0.7

0.8

0.8

0.8

0.8

0.8

0.8

1.175

1.6

0.9

1.1

1.1

1.2

1.0

1.1

1.2

1.1

1.1

1.2

1.1

1.150

2.2

1.4

1.5

1.6

1.7

1.5

1.6

1.7

1.6

1.6

1.7

1.6

1.125

3.1

2.0

2.2

2.3

2.4

2.2

2.3

2.4

2.3

2.3

2.4

2.3

1.100

4.5

2.9

3.2

3.3

3.5

3.2

3.3

3.5

3.3

3.3

3.5

3.4

1.075

6.5

4.3

4.7

4.9

5.1

4.7

4.9

5.1

4.7

4.9

5.1

5.0

1.050

9.5

6.4

6.9

7.2

7.5

7.1

7.0

7.5

7.0

7.1

7.5

7.3

1.025

14.0

9.6

10.2

10.7

11.1

10.6

10.3

11.1

10.2

10.6

11.1

10.8

1.000

20.8

14.3

15.3

16.0

16.6

16.0

15.2

16.6

15.1

15.8

16.5

16.1

Cavitation Free-Energy Gcav as a Function of the Pressure Table 5 reports the values of the cavitation free-energy Gcav as a function of the pressure p for the three cycloaddition reaction mechanisms, including 66, 56-1, and 56-2, of cyclopentadiene and C60 (Table S6 for η = 3). From Table 5, it is found that the numerical values of Gcav decreases slowly in passing from the reactants (CP + C60) to the transition states and products of the cyclopentadiene reactions reflecting the decrement of the system size. Moreover, the value slightly depends on the cycloaddition sites. With a given pressure p, the Gcav of all three TSs (or adducts) are quite similar.

Table 5. Cavitation Free-Energy Gcav (in kcal/mol) as a Function of the Pressure (GPa) of DA Cycloaddition of CP and C60. The Results Refer to the Pauli Exponential Parameter η = 6.

CP

C60

TS66

P66

TS56-1

P56-1

TS56-2

P56-2

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

11



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0.8

14.3

79.5

92.0

91.1

91.9

91.3

91.8

91.2

1.1

18.8

109.9

126.6

125.4

126.5

125.6

126.3

125.6

1.6

25.2

153.2

175.8

174.2

175.6

174.4

175.4

174.4

2.3

34.6

217.1

248.3

246.1

248.1

246.5

247.8

246.4

3.4

47.9

309.5

353.1

350.0

352.8

350.5

352.4

350.4

5.0

68.1

449.6

511.9

507.5

511.6

508.2

511.0

508.1

7.3

98.0

656.3

746.3

739.9

745.8

741.0

744.9

740.7

10.8

143.9

971.9

1104.2

1094.8

1103.5

1096.3

1102.2

1096.0

16.1

216.1

1458.0

1656.1

1642.0

1655.0

1644.2

1653.0

1643.7

Effect of Extreme High Pressure on the Reaction Energy Profile The combination of the free-energy functional Ger and cavitation free-energy Gcav gives birth to the values of the total free-energy Gtot as a function of the pressure for three cycloaddition reactions, which are presented in Table 6. The corresponding activation and reaction free energies are shown in Figure 4 with data in Table S2. The data for η = 3 are collected in Tables S7 and S8. The free energy profiles at the pressure 2.3 GPa (η = 6) and 2.1 GPa (η = 3) are compared to those without pressure in Figure 3 and Figure S1, respectively. For all the three cycloaddition reactions, Figure 3 reveals a dramatic effect of the pressure on the activation energy and the reaction free-energy, which are responsible for the kinetic effect and thermodynamic effect, respectively. As the pressure increases, the activation energy of 66 reaction which is 6.5 kcal/mol in the gas phase (0 GPa) decreases monotonically and becomes to be negative at 3.4 GPa for η = 6 (2.1 GPa for

η = 3), suggesting that the reaction is barrier-less. The 66 reaction is exothermic (-27.1 kcal/mol) in the gas phase (0 GPa). With the increase of the pressure, it becomes more exothermic. For example, the reaction energy rises to 45.8 kcal/mol (η = 6) at 7 GPa (57.1 kcal/mol for η = 3). The cycloaddition reactions on the [5,6]-bond (56-1 and 56-2) which have higher activation energy about 20 kcal/mol in the gas phase (0 GPa). As the pressure increases, the activation energy of those two reactions also reduces monotonically. When the pressure increases above 16.1 GPa for

η = 6 (7.5 GPa for η = 3), both of them become barrier-less. The 66 reaction is exothermic (-27.1 12


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kcal/mol) in the gas phase (0 GPa) and becomes more exothermic with the increase of the pressure. At 7 GPa, the reaction energies for 56-1 and 56-2 reactions increase to 24.9 and 22.9 kcal/mol for η = 6, respectively. However, the order of 56-1 and 56-2 does not change. With an increase of the pressure, the cycloaddition reaction on the [6,6] bond is still always preferred thermodynamically and kinetically. Interestingly, since the pressure is above 16.1 GPa (η = 6) or 7.5 GPa (η = 3), all three DA cycloaddition reactions of cyclopentadiene and C60 become barrier-less, indicating the possibility of the generation of the [5,6] cycloadduct.

Table 6. Total Free-Energy Functional Gtot (in a.u.) as a Function of the Pressure (GPa) of DA Cycloaddition of CP and C60. The Values Are Given Relative to -193.0 (CP), -2284.0 (C60) and 2476.0 (TS and P) a.u. The Results Refer to the Pauli Exponential Parameter η = 6.

CP

C60

TS66

P66

TS56-1

P56-1

TS56-2

P56-2

0.0

-1.0047

-1.4567

-3.4511

-3.5046

-3.4251

-3.4692

-3.4299

-3.4684

0.8

-0.9789

-1.3238

-3.2967

-3.3513

-3.2707

-3.3156

-3.2757

-3.3149

1.1

-0.9705

-1.2726

-3.2381

-3.2933

-3.2125

-3.2575

-3.2174

-3.2567

1.6

-0.9586

-1.1996

-3.1546

-3.2109

-3.1293

-3.1749

-3.1336

-3.1743

2.3

-0.9413

-1.0919

-3.0318

-3.0892

-3.0065

-3.0527

-3.0114

-3.0521

3.4

-0.9164

-0.9362

-2.8552

-2.9134

-2.8301

-2.8760

-2.8344

-2.8759

5.0

-0.8793

-0.7005

-2.5855

-2.6471

-2.5620

-2.6091

-2.5667

-2.6090

7.3

-0.8245

-0.3530

-2.1906

-2.2505

-2.1646

-2.2171

-2.1709

-2.2140

10.8

-0.7418

-0.8238

-1.5901

-1.6580

-1.5644

-1.6184

-1.5692

-1.6209

16.1

-0.6125

-0.0107

-0.6625

-0.7361

-0.6359

-0.7010

-0.6469

-0.6972

According to chemical thermodynamics49-55 and the thermodynamic formulation of transition state theory,56 the effects of pressure on the chemical kinetics and chemical equilibrium are described in terms of the pressure dependence of the corresponding activation and reaction free-energies. These dependences are reflected by the activation volume ∆V† and by the reaction volume ∆Vrxn, 3 4 respectively.35 Figure 4 shows the computed activation energy 2 and reaction energy 2 ,

3 4 respectively, as a function of the pressure. Both 2 and 2 present a good linear correlation

and the linear correlation coefficients correspond to the activation volume ∆V† and the reaction volume ∆Vrxn, respectively. The computed activation and reaction volumes for three cycloaddition

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

reactions are shown in Table 7. It is revealed that the computed activation volume for the 66 reaction are -8.0 cm3/mol (η = 6) or -12.5 cm3/mol (η = 3) while the reaction volume of -11.1 cm3/mol (η = 6) or -16.2 cm3/mol (η = 3). These calculated results would provide further comparison to the future experimental observation. The volume of a single molecule may be defined with using its electron density distribution. The molecular volume can be estimated conveniently using Gaussian 09 program. This density-based volume is compared to the thermodynamic-based volume computed by the XP-PCM. The densitybased molecular volume is defined as the volume inside a contour of 0.001 electrons/Bohr3 density. Molecular volume was evaluated by Monte-Carlo method with the number of points sets to 10000/Bohr3. The averaged values of ten trials are given in Table 8. The estimated ∆V values by the electron density agree well with the values obtained by the XP-PCM free energies using η = 3. Considering the error of Monte-Carlo integration, the activation volumes ∆V† are around −12.0 cm3· mol−1, and the reaction volumes ∆Vrxn are around −15.5 cm3· mol−1. The values are almost constant among the three reactions. The absolute values of molecular volume and ∆V† depend on the contour value or hardness parameter. Although the contour value of 0.001 electrons/Bohr3 has provided reasonable molecule volumes,57 the density-based volumes calculated with other contour values are given in Table S11. We found that the relative activation and reaction volumes among the three reactions do not depend on the choice of the contour value and hardness parameter (Figure S4). These findings verify the validity and accuracy of the present method at least for relative volume changes. Moreover, the XP-PCM is useful to discuss the activation and reaction volumes of complicated systems in which accurate Monte-Carlo integration cannot be easily performed.

14


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Figure 3. The energetics of reactant, transition state and product of three DA cycloadditions of CP and C60 at 0 and 2.3 GPa. The results refer to the Pauli exponential parameter η = 6.

3 4 Figure 4. Correlation between the activation energy 2 , reaction energy 2 and the pressure

for three DA cycloadditions of CP and C60. The results refer to the Pauli exponential parameter η = 6. 3 4 Table 7. Activation ∆V† = 52 /dp (cm3/mol) and Reaction ∆Vrxn = 52 /dp (cm3/mol)

Volumes for Three DA Cycloadditions of CP and C60. reaction

∆V†

∆Vrxn

66

-8.0

-11.1

56-1

-7.8

-11.0

56-2

-8.6

-10.8

15



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Page 16 of 26

Table 8. Molecular volume (V) and its variation (∆V) during the reactions calculated by the electron density and Monte-Carlo integration by Gaussian 09. V/cm3·mol−1 [SD/SEa]

∆V/cm3·mol−1

Reactant (CP + C60)

438.6 [1.5/0.5]

0.0

(CP)

(61.4) [0.2/0.1]

–

(C60)

(377.3) [1.5/0.5]

–

TS66

426.8 [1.6/0.5]

−11.8

TS56-1

426.1 [0.7/0.2]

−12.6

TS56-2

426.2 [1.4/0.5]

−12.5

P66

423.1 [1.5/0.5]

−15.6

P56-1

423.6 [1.4/0.4]

−15.1

P56-2

423.1 [1.2/0.4]

−15.6

a

Standard deviation (SD) and standard error (SE) of Monte-Carlo integration.

An Analysis of the Effect of the Pressure on the Activation Energy According to eq. (1), the effect of the pressure on the PES can be analyzed in terms of the two components of the potential energy Gtot, the electronic contribution Ger, and the cavitation Gcav 3 of three contributions. Here, the effect of the pressure on the activation energy ∆

cycloaddition reactions of CP and C60 will be discussed. 3 is given by: The shift induced by the pressure on the activation energy ∆ 3 3 3 = ∆ − ∆ 0 ∆∆

(9)

3 0 denotes the activation energy in the gas phase. By introducing eq. (1) into eq. (9), where ∆

we can write the shift induced by the pressure as: 3 3 3 = ∆ + ∆∆ 0 ∆∆

(10)

3 is a cavitation contribution: where ∆ 3 = 89, − :; + : 3GPa) with the decrease of the relative contribution of the cavitation term 3 . Taking the cycloaddition on the [6,6] bond with the Pauli parameter η = 6 as an example, ∆

at 0.8 GPa, the cavitation term (-1.8 kcal/mol) and the electronic term (-0.9 kcal/mol) contributes 66.7% and 33.3%, respectively, to the total shift. In contrast, when the pressure rises to 7.3 GPa, the cavitation term (-7.9 kcal/mol) contributes 53.7% to the total shift and the electronic term (-6.8 kcal/mol) contributes 46.3%. This is because the electronic contribution originating from the shortrange Pauli repulsion interaction with the external medium increases more rapidly with the pressure 3 for three cycloaddition than the cavitation contribution. Moreover, the cavitation term ∆

reactions always follows the order of TS66 < TS56-1 < TS56-2, despite the increase of the pressure. The order of this contribution in the different channel of a reaction mainly depends on the corresponding order of variation of the volumes used for the calculation of the cavitation energy, which was also observed in the previous work.28 On the other hand, the order of the relative values of the electronic term depends strongly on the pressure. For example, at 1.6 GPa, the order of the electronic contributions are TS56-2 (-1.3 kcal/mol) < TS66 (-1.5 kcal/mol) < TS56-1 (-1.8 kcal/mol). In contrast, on moving to the 10.8 GPa, the order changes to TS56-2 (-8.5 kcal/mol) < TS56-1 (-9.8 kcal/mol) < TS66 (-10.4 kcal/mol). This order depends on ancillary details of the cavity used for the calculation of the electronic contribution. These details, that is the cavity surface and volume, the number of the surface elements used for the numerical integration in the calculation of the Pauli

17



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Page 18 of 26

repulsion etc., may change with the pressure as the cavity used for the calculation of the pressure is shrunk (i.e. it is not fixed) to increase the pressure. 3 3 Table 9. Electronic, 22 (kcal/mol) and Cavitation, 2 (kcal/mol), Components of the Shift, 3 2 (kcal/mol), Induced by the Pressure on the Activation Free-Energy for DA Cycloaddition of

CP and C60. The Results Refer to the Pauli Exponential Parameter η = 6.

TS66

TS56-1

TS56-2

3 22

3 2

3 22

3 22

3 2

3 22

3 22

3 2

3 22

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.8

-2.7

-1.8

-0.9

-2.7

-1.9

-0.8

-2.8

-2.0

-0.8

1.1

-3.4

-2.2

-1.2

-3.6

-2.3

-1.3

-3.7

-2.4

-1.2

1.6

-4.2

-2.7

-1.5

-4.7

-2.8

-1.8

-4.3

-3.0

-1.3

2.3

-5.6

-3.4

-2.2

-6.1

-3.5

-2.5

-6.1

-3.9

-2.3

3.4

-8.1

-4.3

-3.8

-8.7

-4.6

-4.1

-8.4

-5.0

-3.4

5.0

-10.0

-5.8

-4.3

-11.6

-6.1

-5.4

-11.6

-6.7

-4.8

7.3

-14.7

-7.9

-6.8

-14.7

-8.5

-6.3

-15.6

-9.3

-6.3

10.8

-21.9

-11.5

-10.4

-22.1

-12.3

-9.8

-22.0

-13.6

-8.5

16.1

-31.1

-17.9

-13.2

-30.7

-19.1

-11.6

-34.7

-21.0

-13.6

3 3 Figure 5. Correlation between activation energy shift 22 , cavitation contribution 2 , and

3 electronic contribution 22 with the pressure for DA cycloadditions of CP and the [6,6]-bond of

C60. The results refer to the Pauli exponential parameter η = 6.

18


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CONCLUSIONS By using the XP-PCM method, the effects of high pressure (1~16 GPa) on the PES of DA cycloaddition reaction of cyclopentadiene and both [5,6] and [6,6] bonds of fullerene C60 have been studied for the first time. Although the [6,6] bond is always preferred over the [5,6] bond thermodynamically and kinetically, the high pressure leads to the large reduction of the activation energy and increase of the exothermicity, making the DA reaction more favorable. More interestingly, under extreme high pressure (16.1 and 7.5 GPa for η = 6 and 3, respectively) conditions, three cycloaddition reactions become barrier-less, suggesting the possibility of the synthesis of both 66- and 56-cycloadducts. Further analysis revealed that the cavitation contribution has a larger influence on the activation energy shift than the electronic contribution. Both the activation and reaction volumes have been computed, which will assist the future experiments.

ASSOCIATED CONTENT Supporting Information 3 4 Volume Vc of the SES molecular cavity, activation energy 2 and reaction energy 2 ,

parameters of eq. (17) for the analytical fitting of the free-energy functional Ger, results with the Pauli exponential parameter η = 3, Density-based volumes calculated with several contour values, and Cartesian coordinates of all the optimized molecular structures. The Supporting Information is available free of charge on the ACS Publications website at xxx.

AUTHOR INFORMATION Corresponding Authors *Email: [email protected] (T. Yang); [email protected] (R. Fukuda); [email protected] (R. Cammi); [email protected] (M. Ehara) Notes

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The authors declare no competing financial interest.

ACKNOWLEDEMENT This work was supported by a MEXT (Ministry of Education Culture, Sports, Science and Technology in Japan) program "Elements Strategy Initiative to Form Core Research Center". M. E. acknowledge the financial support from a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS), JP16H04104, JP16H06511. The computations were partially performed at the Research Center for Computational Science, Okazaki, Japan.

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s (X) = [ s(CP) + s(C60 ) + s(TSX) + s(PX)] 4

and

the

totally

averaged

value

s

is

by

s =  s (CP) + s (C 60 ) + ∑ X=66, 56-1, 56-2 {s (TSX) + s (PX)} 8 . In the same manner, the averaged values of   the pressure for each reaction X, p(X) = [ p(CP) + p(C60 ) + p(TSX) + p(PX)] 4 and the total averaged value p is by p =  p (CP) + p (C 60 ) + ∑ X=66, 56-1, 56-2 { p (TSX) + p (PX)} 8 .  

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49. Hamann, S. D. Physico-Chemical Effects of Pressure. Butterwoth and Co. Ltd: London, 1957. 50. Le Noble, W. J. Organic High Pressure Chemistry. Elsevier: Amsterdam, 1988. 51. van Eldik, R.; Kläner, F.-G. High Pressure Chemistry. Wiley: New York, 2008. 52. Bini, R.; Schettino, V. Materials Under Extreme Conditions. World Scientific: Singapore, 2014. 53. Asano, T.; Le Noble, W. J. Activation and Reaction Volumes in Solution. Chem. Rev. 1978, 78, 407489. 54. Van Eldik, R.; Asano, T.; Le Noble, W. J. Activation and Reaction Volumes in Solution. 2. Chem. Rev. 1989, 89, 549-688. 55. Drljaca, A.; Hubbard, C. D.; van Eldik, R.; Asano, T.; Basilevsky, M. V.; Le Noble, W. J., Activation and Reaction Volumes in Solution. 3. Chem. Rev. 1998, 98, 2167-2290. 56. Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes. McGraw-Hill: New York, 1940. 57. Parsons, D. F.; Ninham, B. W. Ab Initio Molar Volumes and Gaussian Radii. J. Phys. Chem. A 2009, 113, 1141–1150.

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DielsâAlder Cycloaddition of Cyclopentadiene and C60 at the Extreme

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DielsâAlder Cycloaddition of Cyclopentadiene and C60 at the Extreme