Theoretical Study on the Reactivity and Regioselectivity of the Diels

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A Theoretical Study on the Reactivity and Regioselectivity of Diels-Alder Reaction of Fullerene: Effects of Charges and Encapsulated Lanthanum on the Bis-Functionalization of C 70

Cheng-Xing Cui, Ya-Jun Liu, Yuping Zhang, Ling-Bo Qu, and Zhao-Pei Zhang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b10231 • Publication Date (Web): 23 Dec 2016 Downloaded from http://pubs.acs.org on December 25, 2016

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The Journal of Physical Chemistry

1 2 3 4

A Theoretical Study on the Reactivity and Regioselectivity of Diels-Alder Reaction of Fullerene: Effects of Charges and Encapsulated Lanthanum on the Bis-functionalization of C70

5 6 7 8 9 10 11

Cheng-Xing Cui*, †, §, Ya-Jun Liu *, ‡, Yu-Ping Zhang †, Ling-Bo Qu §, Zhao-Pei Zhang † † Postdoctoral Research Base, School of Chemistry and Chemical Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China § Henan University of Technology, Zhengzhou 450001, China ‡ Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China

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ABSTRACT: Bis-adducts of fullerenes are important for both material and biological

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science. The first added substituent greatly impacts the reactivity and regioselectivity of

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fullerene. What determines the bond reactivity and how to control the regioselectivity are

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two crucial questions in synthesizing bis-adduct of C70. Recently, unexpected 12 o’clock

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isomer of anthracene bis-adduct of C70 was prepared with high yield by the Diels-Alder

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(DA) reaction although three possible isomers (12, 2, and 5 o’clock isomers) may be

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formed. In the current study, the beneath mechanism is systematically investigated by

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density functional theory methods. Moreover, effects of charges and encapsulated

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lanthanum atom on the regioselectivity are reported. The computational results

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successfully rationalize experimental observations by Venkata et al. A possible way to

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change the regioselectivity of DA reaction is put forward. The kinetical promotion effect

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of encapsulated La atom on 12 o’clock reaction is elucidated.


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1. INTRODUCTION

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Oligo-adducts of fullerenes have potential biological applications in molecular

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recognition and polymer solar cells.1,

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compounds have become hot topics for a long time. Very recently, Cerón and Echegoyen

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gave an excellent review for new development in the regiochemical control of

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bis-functionalization of C60, C70, and some endohedral cluster fullerenes.4 A pure

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cis-isomer of bis-adduct of fullerene was synthesized and isolated, which was good

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electron-acceptor in solar cells.3 Encapsulated metal fullerenes were successfully

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functionalized

by

region-isomeric

2, 3

Synthesis and characterization of such

bis-additions

with

the

tether-controlled

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multi-functionalization method.5 The cyclopentadienyl-type adducts at the pole pentagon

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of D5h-C70 (written as C70 for convenience) were prepared and characterized with

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multi-amination reactions.6 Conventional methods for fullerene functionalization such as

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addition-elimination of halogenated malonates and 1,3-dipolar cycloadditions of ylides

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always produce multiple isomeric bis- and tris-adducts that are relatively difficult to

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separate.7, 8 So how to control the regioselectivity in the synthesis stage is crucial to

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further development of the application of such materials. There is only one kind of carbon

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atom and two kinds of carbon bonds (6-6 and 6-5 bonds) in C60, so the regioselectivity is

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low.9 The bis-adduct of C60 was prepared with high regio-specific reaction on

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mono-adduct of C60.10, 11 The number of possible isomers for bis-adduct of C70 greatly



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increases because there are five types of carbon atoms (a, b, c, d, and e) and eight kinds

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of bonds (a-a, a-b, b-c, c-c, c-d, d-d, d-e, and e-e bonds) in C70 (see the bottom right of

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Figure 1).12 The eight different bonds in C70 can be collected into two groups: a-b, c-c,

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d-e, and e-e bonds belong to 6-6 ring junction; a-a, b-c, c-d, and d-d bonds belong to 6-5

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ring junction. It has been demonstrated that a-b bond is the most reactive one by both

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experimental and theoretical methods.13,

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usually taken place on two a-b bonds (opposite top-ends) of C70 with very few

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exceptions.7, 16 There isn’t a systematic way to define C70 bis-adducts till now, but a

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simple nomenclature was introduced as shown in Figure 1, i.e. 12, 2, or 5 o’clock

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isomer.16 As shown in Figure 1, they are all adducts on a-b bond and the bonds are

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correspondingly labeled as a1-b1, a2-b2, and a3-b3 bonds, respectively. The presence of the

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first substituent has significant influence on the chemical reactivity and the

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regioselectivity of C70 cage. In the addition of Ir(CO)Cl(PPhMe2)2 to C70 and preparation

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of Bingel adducts of C70, 2 o’clock isomer is favored (12 : 2 : 5 o’clock adduct = 2.8 : 6.8:

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1.0).16 In a recent study on the Diels-Alder (DA) reaction between anthracene and C70,

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mono- and bis-adducts were both separated and characterized in the absence of solvent

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(molten).7 Interestingly, 12 o’clock isomer was abundant, but not 2 o’clock isomer as in

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other bis-cycloaddition reactions of C70.7 This indicated that the reactivity of a1-b1 bond

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was more enhanced than other two a-b bonds by the first anthracene addition, although all

14, 15

The addends in bis-adducts of C70 are


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a-b bonds had the same reactivity in unsubstituted C70. The beneath mechanism wasn’t

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put forward till now and it is worthy of a thorough investigation.

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A fascinating property of fullerene is its ability to accommodate atoms, ions, or

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clusters in its empty inner space to form the so-called encapsulated metallic fullerenes

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(EMFs).17 C70 is one of the most abundant members among fullerene family. The signal

Figure 1. Three possible locations of the second anthracene, three types of a-b bond in ACMA, and five types of atoms and eight types of bonds in C70. 44

of lanthanum encapsulated fullerene (La@C70) was detected before three decades, but its

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structure remains unresolved up to now because of its much high reactivity under ambient

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conditions and insolubility in organic solvents.17 Fortunately, the first example of rare

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metal EMFs of C70, i.e. La@C70(CF3)3, was recently separated and characterized by



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X-ray crystallographic because the reactivity of La@C70 was stabilized by CF3 groups,

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where three electrons were proposed to transfer from La to C70 cage in pristine [email protected]

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Fullerenes are good electron acceptors. Stepwise electro-generation of stable C70n- (n = 1

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to 4) anions were fulfilled in benzonitrile.19 C705- and C706- were prepared at even 25 °C.20

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The reactivity and regioselectivity of EMFs are largely influenced by the formal charge

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transfer of encapsulated species to fullerene cage.21, 22 So the negatively charged empty

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fullerene is good chemical model for understanding the reactivity of EMFs.23 Based on

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this idea, the negatively charged anthracene-C70-mono-adduct on a-b bond of C70

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(ACMAn- (n=0 to 3), Figure 1) may be suitable for understanding the reactivity of bond

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and regioselectivity of mono-adducted La@C70. It was proven that the regioselectivity of

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the DA, 1,3-dipolar, and carbene cycloadditions changed from usual 6-6 attack in neutral

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(C60) to 6-5 attack in high negative charged species (C606-).23 But little attention was

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previously devoted to the effect of charges on the reactivity and regioselectivity about

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bis-DA reactions of C70.

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Theoretical methods, especially density functional theory (DFT), have been regular

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way in understanding and prediction of reactivity of fullerenes and mechanisms of DA

64

reaction. With DFT calculations, it was found that the interplay between the activation

65

strain energy and the transition-state interaction governed the DA reactivity of different

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bowl-shaped polycyclic aromatic hydrocarbons.24 DFT calculations proved that [2+2]


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cycloaddition of benzene to two types of EMFs followed a biradical rather than a carbine

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mechanism and the formation of the biradical intermediate was the rate-determining

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step.25 We pointed out based on theoretical calculations that a-b bond in C70 was the

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highest reactive one, which was consistent with experimental results.26, 27, 28 In the current

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study, the DA reactions between ACMAn- (n = 0 to 3) or La@ACMA and anthracene

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were systematically investigated. The following things were made clear and predicted: (1)

73

why 12 o’clock isomer is more plentiful in experimental investigation; (2) whether the

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reactivity and regioselectivity change when charges are exerted on ACMA; (3) the

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solvent effect on the bis-DA reaction of ACMAn- (n = 0 to 3); (4) the influence of

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encapsulated lanthanum atom on the reactivity and regioselectivity of bi-addition of C70.

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2. COMPUTATIONAL METHODS

78

Geometries of reactant (R), reactant complex (RC), transition state (TS), and product (P)

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were optimized without any restrictions using Truhlar’s M06-2X functional.29 M06-2X is

80

reliable for thermodynamics of C-C bond-forming reactions30. This functional always

81

yields reasonable energetics of cycloaddition reactions.31,

82

polarized basis set (6-31G(d)) was used for C, O, and H atoms. The effective core

83

potential-based LANL2DZ basis set was adopted for La. The calculated activation

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energies for DA reactions of empty C60 and Li+@C60 at the M06-2X/6-31G(d) theoretical

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level agreed well with the experimentally obtained values.34 Harmonic vibrational


32, 33

A valence double-zeta


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frequency calculations were performed to verify stationary points and to get zero-point

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vibrational energies (ZPVE) and thermodynamics data at standard state (298.15 K and 1

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atm). As shown in Figure S1, we considered different electronic states of ACMA1-,

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ACMA2-, and ACMA3- and found the ground states of ACMA1-, ACMA2-, and ACMA3-

90

are doublet, singlet, and doublet, respectively. The intrinsic reaction coordinate (IRC)

91

calculation was performed for each TS to ensure that they connected the right local

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minimums. The energies of RC, TS, and P are relative to the total energy of ACMAn- (n=

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0 to 3) or La@ACMA and anthracene. The activation barrier from RC to P and the

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reaction energy in Gibbs free energy were denoted by ∆G‡ and ∆Gr, respectively. ∆G‡ is

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defined as ∆G‡ = GTS - GRC. The relative entropy and enthalpy values were defined with a

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similar way.

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Houk’s distortion/interaction model divided the electronic activation barrier into two

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imaginary categories: distortion energy concerning geometric changes and interaction

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energy between distorted reactants.35, 36, 37 The distortion process is unfavorable, but the

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electronic interaction is favorable. This model was usually adopted in understanding

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reactivity of fullerenes and cycloaddition reactions.38, 39 The electronic activation barrier

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of current system was dissected as: ∆E‡ = ∆E‡d1 (ACMAn- or La@ACMA)) + ∆E‡d2

103

(anthracene) + ∆E‡i, where ∆E‡d denoted the distortion energy, and ∆E‡i denoted the

104

interaction energy. The solvent effect of toluene (nonpolar solvent) was modeled using


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the polarizable continuum model (PCM) with a dielectric constant of 2.374,40 while that

106

of CH3CN (polar solvent) was modeled using the conductor-like polarizable continuum

107

model (CPCM) with a dielectric constant of 35.688.41, 42 Geometries of stationary points

108

were fully optimized in solvents at the same theoretical level as in gas phase. The UV

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spectrum was calculated based on time-dependent DFT (TDDFT) method. All theoretical

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calculations were performed with the Gaussian 09 suite of programs.43

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3. RESULTS AND DISCUSSION

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Geometric Changes The main geometric parameters of stationary points along the

113

potential energy curves (PECs) were listed in Table 1. Those of 12 o’clock reaction were

114

also labelled in Figure 2. In neutral 12 o’clock reaction, the distance between two

115

attacked carbon atoms of ACMA (ri) is 1.389 Å. The electrostatic potential surfaces

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(EPS) of anthracene and ACMA were shown in Figure S2. The face of anthracene has a

117

negative electrostatic potential, while the sites of a1-b1, a2-b2, and a3-b3 bonds have

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positive electrostatic potential. So just as previous theoretical investigations on the single

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cycloaddition reactions of fullerenes, RC was trapped.28, 44 The currently used M06-2X

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functional introduces some dispersion corrections,45 which is crucial to locating the RC in

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DA reaction of fullerene.46 The length of ri is shortened by 0.002 Å from R to RC, but

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gradually elongated to 1.450 Å in TS and 1.599 Å in P, which is in line with the crystal

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X-ray diffraction result (1.601 Å in P).7 With the elongation of a1-b1 bond from RC to TS,



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the π-characteristic stability is slowly broken (the decreases of the initial stability)

125

because of the introducing of σ-characteristic. The lengths of r1 and r2 are 3.092 and

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3.112 Å in RC and gradually decrease to 1.584 and 1.587 Å in P, respectively, which are

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consistent with experimental values (r1=1.586 and r2=1.590 Å).7 The lengths of two

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forming bonds are nearly equal in TS and no intermediate is located between RC and P,

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so neutral 12 o’clock reaction is concerted and synchronous. The spin density of ACMA1-

130

(Figure S3) was calculated to locate the position of its unpaired electron, where the more

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reactive carbon atom may be included. It can be found that the unpaired electron is

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mainly located on C70 moiety of ACMA1-. Moreover, the spin density mainly disperses in

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the semi-sphere of C70 where the first anthracene added. The reactivity of carbon bonds in

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this region are strengthened. However, it cannot be concluded which one of a1-b1, a2-b2,

135

and a3-b3 bonds is more strengthened only based on the spin density, because the

136

reactivity is also affected by the gap of frontier orbitals and other factors. In reactions of

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ACMA1- or ACMA2-, all ris are slightly smaller in RC than in R as in neutral ones, except

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for 12 o’clock reaction (from 1.387 Å in R to 1.388 Å in RC) of ACMA1-. The two newly

139

forming C-C bonds are of nearly equal length. The differences between r1 and r2 become

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large when the charge on ACMA changes from 0 to -3, which indicates that the reaction

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tends to be asynchronous. Especially, the difference between r1 and r2 is 0.502 Å in 2

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o’clock reaction and 0.542 Å in 5 o’clock one. This obvious asynchronous characteristic


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has large effect on the reactivity and corresponding regioselectivity of the cycloaddition,

144

which will be discussed in the following sections.



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Table 1. The dominant optimized geometrical parameters of Rs, RCs, TSs, and Ps of the bis-additions of anthracene to ACMAn- (n=0 to 3) with DA reaction calculated at the M06-2X/6-31G(d) level in gas phase, together with the only one imaginary frequency of TSs. (Unit: Å and cm-1. See Figure 1 for type of reaction.) R

RC

ria

ri d

r1b

TS r2b

ri

r1

r2

P r2-r1

vc

ri

r1

419i 0.050 1.599 1.584 419i 1.600 1.584 0.068 427i 1.601 1.584 0.076 429i 1.595 1.585 0.037 426i 1.592 1.590 0.039 -1 5 o’clock 1.395 1.394 3.193 3.370 1.454 2.161 2.222 440i 1.600 1.585 0.061 12 o’clock 1.385 1.383 3.049 3.321 1.440 2.199 2.253 401i 1.591 1.586 0.054 -2 2 o’clock 1.396 1.395 3.394 3.803 1.446 2.206 2.228 406i 1.592 1.586 0.022 423i 1.595 1.587 5 o’clock 1.398 1.397 3.337 3.852 1.455 2.158 2.240 0.082 12 o’clock 1.387 1.387 3.178 3.443 1.444 2.164 2.318 378i 1.590 1.590 0.154 -3 427i 1.592 1.590 2 o’clock 1.411 1.398 3.291 3.564 1.550 1.610 2.112 0.502 5 o’clock 1.403 1.393 3.223 3.542 1.546 1.614 2.156 443i 1.595 1.591 0.542 a. ri is the C-C distance of two attacked atoms of ACMA. b. r1 and r2 are the lengths of two forming C-C single bonds cycloaddition. c. v is the imaginary frequency of the saddle point. d. The data in bold face are explicitly discussed in the text. 0

12 o’clock 2 o’clock 5 o’clock 12 o’clock 2 o’clock

1.389 1.389 1.391 1.387 1.395

1.387 1.386 1.390 1.388 1.391

3.092 3.109 3.233 3.148 3.147

3.112 3.140 3.235 3.340 3.225

1.450 1.451 1.453 1.449 1.448

2.178 2.167 2.157 2.185 2.185

2.228 2.235 2.233 2.222 2.224

145 146 147 148


r2 1.587 1.588 1.587 1.587 1.591 1.587 1.587 1.588 1.588 1.590 1.591 1.592 in the

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149

Figure 2. The main geometric parameters (Å) of stationary points on the PEC of 12 o’clock reaction and relative enthalpies (kcal mol-1) and Gibbs free energies (kcal mol-1) calculated at the M06-2X/6-31G(d) level in gas phase.

150 151 152 153



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Thermochemistry Analysis The thermochemistry data were archived in Table 2. Those

155

of 12 o’clock reaction were also shown in Figure 2. The entropy changes were listed in

156

Table S1. In 12 o’clock reaction, the entropy decreases by 41.9 cal K-1 mol-1 from two Rs

157

to RC because of the restriction on vibrational movement and the resulting reduction of

158

degrees of freedom. The enthalpy decreases by -6.4 kcal mol-1 and the Gibbs free

159

increases by 6.1 kcal mol-1. From RC to P, the movement of participating molecules is

160

further restricted and the entropy becomes more negative. The change of Gibbs free

161

energy determines the position of equilibrium between different states of compounds.

162

The total process from two isolated reactants to final P releases a Gibbs free energy (△Gr)

163

of -4.7 kcal mol-1. This suggests that addition of the second anthracene to ACMA is a

164

spontaneous process. Of course, the reaction needs to overcome an energy barrier of 18.4

165

kcal mol-1. Although △Gr of 2 (-4.6 kcal mol-1) and 5 (-4.5 kcal mol-1) o’clock reactions

166

are nearly the same as 12 o’clock, but their activation barriers (△G‡) are higher (20.1 kcal

167

mol-1 for 2 o’clock reaction and 19.1 kcal mol-1 for 5 o’clock reaction). The order of the

168

activation barriers on the three sites are 12 o’clock < 5 o’clock < 2 o’clock. The 12

169

o’clock reaction has the lowest reaction barrier and is the most favorable one, which

170

agrees with high yield (68%) of 12 o’clock isomer in experimental investigation.7 The

171

UV-vis spectra of 12 o’clock isomer calculated with TDDFT method found a strong

172

absorption maximum near 413 nm, which is consistent with experimental one (442 nm).7


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173

In 12 o’clock reaction, the activation barriers are 18.5, 18.3, and 22.0 kcal mol-1 for

174

the cycloaddition of anthracene to AMCA1-, AMCA2-, and AMCA3-, respectively. For 2

175

or 5 o’clock reactions, the barrier changes little when charges on ACMA are -1 or -2, but

176

the barrier apparently decreases when charges on ACMA changes to -3. Thus, the order

177

of activation barriers is 12 o’clock > 5 o’clock > 2 o’clock. That is, 12 o’clock reaction

Figure 3. The pyracylenic units in three reactions and corresponding bonds. 178

has the highest barrier for the cycloaddition of anthracene to AMCA3-. It has been

179

demonstrated that the regioselectivity of DA, 1,3-dipolar, and carbene additions changes

180

from the usual 6-6 bond to 6-5 bond as the number of electrons added to C60 cage

181

increases from 1 to 6.23 In the current reactions, the bond distances and pyramidalization

182

angles in the reaction center of ACMA don’t have obvious difference when charges

183

change for 0 to -3. So the geometric strain is not the underlying force for the

184

regioselectivity. In previous studies, it has been demonstrated that the aromaticity largely

185

impacts the bond reactivity of C60n- (n = 0 - 6).23 As shown in Figure 3, the electron



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186

charge transfer is mainly taken place on the pyracylenic unit in ACMA for these reactions.

187

Herein, the harmonic oscillator model of aromaticity (HOMA) index was employed as a

188

structural based measure of aromaticity and calculated as the following formula: ௡

a ଶ ‫ = ܣܯܱܪ‬1 − ෍൫ܴ௢௣௧ − ܴ௜ ൯ ݊ ௜ୀଵ

189

where n is the number of bonds in consideration; a is an empirical constant and equals to

190

257.7 for C-C bond; Ropt equals to 1.388 Å; Ri represents the bond length of the ith

191

bond.47, 48 The HOMA values of three pyracylenic units in ACMA were listed in Table 2.

192

The system with larger HOMA value has higher aromaticity, which implies more

193

resistance towards an attack over one of its bonds because the addition destroys the

194

favorable conjugation in the system. The HOMA values are 0.363, 0.370, 0.365 for 12, 2,

195

and 5 o’clock reactions of ACMA, but change to 0.366, 0.303, and 0.347 in AMCA3-,

196

respectively. The HOMA value of 12 o’clock reaction is the smallest among three

197

ACMA reactions but the biggest among three ACMA3- reactions. Changes in the

198

regioselectivity of the reaction were interpreted by the changes of aromaticity. It can be

199

predicted that the bond among the highest initial local aromaticity of the pyracylenic unit

200

has the largest stability in three bonds of ACMA. But 2 and 5 o’clock reactions are not in

201

accord with this rule.


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202 203

Table 2. The HOMA values of three pyracylenic units in ACMA, and △H and △G of Diels-Alder cycloaddition of anthracene to ACMAn- (n=0 to 3) calculated at the M06-2X/6-31G(d) level in gas phase. (Unit: kcal mol-1 for △H and △G) R HOMA of

RC

Activation Barrier

P

△GRC

△HTS

△GTS

△H

△G

‡

△Hr

△Gr

-6.4 6.1 0.363a 0 -6.9 4.3 0.370 2 o’clock -7.1 5.6 0.365 5 o’clock -2.7 9.7 0.393 12 o’clock -1 -4.4 6.2 0.323 2 o’clock -4.9 7.4 0.344 5 o’clock -4.5 9.1 0.364 12 o’clock -2 -4.6 5.7 0.317 2 o’clock -4.0 6.1 0.348 5 o’clock -9.8 1.5 12 o’clock 0.366 -3 -10.7 2.3 0.303 2 o’clock -2.0 2.6 0.347 5 o’clock a. The data in bold face are explicitly discussed in the text.

10.1 10.2 10.5 14.1 14.1 14.7 13.1 13.6 14.7 9.8 -1.0 0.4

24.5 24.4 24.6 28.2 28.2 28.9 27.4 27.5 28.6 23.5 14.0 15.4

16.5 17.1 17.6 16.8 18.5 19.6 17.6 18.2 18.7 19.6 9.7 2.4

18.4 20.1 19.0 18.5 22.0 21.5 18.3 21.8 22.5 22.0 11.7 12.8

-20.6 -20.1 -19.9 -17.8 -12.0 -15.7 -18.4 -17.1 -15.2 -19.4 -15.0 -15.9

-4.7 -4.6 -4.5 -1.8 3.7 -0.5 -2.3 -1.6 -0.3 -3.3 -0.5 -0.8

ACMA

12 o’clock

△HRC

TS


‡


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

Energy

Model

and

Frontier

Page 18 of 32

Distortion/Interaction

205

distortion/interaction model was adopted to understand the kinetics of these reactions.35

206

The calculated distortion/interaction energies were summarized in Table 3. The energies

207

of frontier orbitals in the reaction between ACMA and anthracene, along with

208

distributions of the highest occupied molecular orbital (HOMO) of anthracene and the

209

lowest unoccupied molecular orbital (LUMO) of ACMA were depicted in Figure 4.

210

ACMA is electrophilic and anthracene is the electron donor. It can be found that the

211

symmetry is favorable for all three neutral reactions. For 12 o’clock cycloaddition

212

reaction of neutral ACMA, the distortion energies of ACMA and anthracene are 6.6 and

213

18.4 kcal mol-1, respectively. The total distortion energy is 25.0 kcal mol-1. The HOMO

214

of anthracene in RC is -6.44 eV and the LUMO of ACMA is -2.52 eV. As the reaction

215

preceding, the LUMO of ACMA decreases but the HOMO of anthracene increases

216

because of the geometric distortion, which makes the gap between them changes from

217

3.92 to 3.64 eV. Correspondingly, the interaction between them is more favorable in TS

218

than in RC, which decreases the activation barrier by 8.1 kcal mol-1. The final activation

219

barrier is 16.9 kcal mol-1. The distortion energy of 5 o’clock reaction is larger than 12 and

220

2 o’clock reactions and has the highest barrier. Although the total distortion energy of 12

221

o’clock is the same as 2 o’clock reaction, but its interaction energy is larger. The

222

HOMO-LUMO gap of 12 o’clock is the smallest one. The distortion and interaction


Orbital

Analysis

The

204

Page 19 of 32

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223

energies of DA addition of anthracene to AMCAn- (n = 1 or 2) are similar to three neutral

224

ACMA reactions. But in AMCA3- reactions, the distortion energy of 2 and 5 o’clock

225

reactions are very higher, which is the results of the asynchronous characteristic and the

Figure 4. Energies (eV) of HOMOs of distorted anthracene and LUMOs of distorted ACMA in RCs and TSs of 12 (black), 2 (pink), and 5 (green) o’clock reactions calculated at M06-2X/6-31G(d) level in gas phase. 226

larger deviation from the balanced geometries in TS than in RC. The interaction energies

227

of 2 and 5 o’clock are also larger (-30.0 and -28.0 kcal mol-1) compared to 12 o’clock

228

(-3.3 kcal mol-1) reaction. This can be understood from the energies and distributions of

229

interacting orbitals in TSs as shown in Figure S4. According to the Woodward-Hoffmann



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Page 20 of 32

230

rule, the electron transfers are from HOMO-5, HOMO-1, and HOMO of ACMA3- to

231

LUMO+4 of anthracene in 12, 2, and 5

232

o’clock reactions, respectively. The HOMO-5 of ACMA3- is lower than LUMO+4 of

233

anthracene by 1.44 eV for 12 o’clock reaction, but the HOMO-1 and HOMO of ACMA3Table 3. The distortion energy of ACMAn- (n = 0 to 3) (∆E‡d1) and anthracene (∆E‡d2), and the interaction energy (∆E‡i) of Diels-Alder cycloaddition of anthracene to ACMAn- (n = 0 to 3) calculated at the M06-2X/6-31G(d) level in gas phase, where ∆E‡total is the total distortion energy and ∆E‡ is the electronic barrier. (Unit: kcal mol-1)

∆E‡d1

∆E‡d2

6.6a 18.4 0 6.8 18.2 2 o’clock 6.9 18.9 5 o’clock 12 o’clock 6.0 19.0 -1 5.9 19.1 2 o’clock 6.2 19.9 5 o’clock 12 o’clock 5.1 19.0 -2 5.4 19.5 2 o’clock 5.7 20.5 5 o’clock 12 o’clock 5.2 17.3 -3 14.3 23.3 2 o’clock 15.5 20.8 5 o’clock a. The data in bold face are explicitly discussed in the text. 12 o’clock

∆E‡total

∆E‡i

∆E‡

25.0 25.0 25.8 25.0 25.0 26.1 24.1 24.9 26.2 22.5 37.6 36.3

-8.1 -6.9 -8.0 -6.1 -5.4 -6.1 -5.6 -6.9 -6.4 -3.3 -30.1 -28.0

16.9 18.1 17.8 18.9 19.6 20.0 18.5 18.0 19.8 19.2 7.5 8.3

234

are higher than LUMO+4 of anthracene by 1.22 and 1.49 eV for 2 and 5 o’clock

235

reactions, respectively. Therefore, the electron transfers are easier and the interaction

236

energies are larger in 2 and 5 o’clock reactions. The final barrier of 2 o’clock reaction is

237

the smallest (7.5 kcal mol-1), so 2 o’clock reaction is the most favorable one in the DA

238

cycloaddition of anthracene to AMCA3-. The distortion/interaction model along with the


Page 21 of 32

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239

orbital symmetry character perfectly interprets the chemical kinetics data and

240

experimental observations.

241 242 243

Solvent Effects on ACMAn- (n = 0, 1, 2, and 3) Reactions The experimental research

244

was performed in molten anthracene.7 Herein, the effects of toluene and CH3CN were

245

explored at the same theoretical level as in gas phase. The calculated results of ACMA

246

were listed in Table 4, and those of ACMA1-, ACMA2-, and ACMA3- were listed in Table

247

S2. The Cartesian coordinates of the fully optimized stationary points were collected in

248

Supplementary Information. There is only one TS and distances of two forming C-C Table 4. The △H and △G of Diels-Alder cycloaddition of anthracene to ACMA with Diels-Alder cycloaddition calculated at the M06-2X/6-31G(d) level in toluene and CH3CN. (Unit: kcal mol-1 for △H and △G)

RC

12 o’clock toluene

2 o’clock 5 o’clock 12 o’clock

CH3CN

2 o’clock 5 o’clock

Activation Barrier

TS

△HRC

△GRC

△HTS

△GTS

△H‡

△G‡

△Hr

△Gr

-6.3 -6.7 -6.9 -6.0 -6.2 -6.5

5.4 3.6 4.9 5.4 3.7 5.2

10.0 10.1 10.4 10.0 10.2 10.5

23.7 23.4 23.9 23.7 23.6 24.0

16.3 16.8 17.2 16.0 16.4 17.0

18.2 19.8 18.9 18.3 19.9 18.8

-20.7 -20.1 -19.8 -20.7 -20.1 -19.7

-5.4 -5.5 -5.2 -5.6 -5.4 -5.1

a

a. The data in bold face are explicitly discussed in the text. 249

P

bonds



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

250

are nearly equal, so the reaction is of concerted synchronous mechanism just as in gas

251

phase. For reactions between AMCA and anthracene, both solvents stabilize the

252

stationary points more or less. For example, RCs of 12 o’clock reaction in the two

253

solvents are stabilized by 0.7 kcal mol-1, but △G‡ remains nearly unchanged. This

254

indicates that both polar and nonpolar solvents have barely influence to the current

255

reactions, which is a typical characteristic of the Diels-Alder reaction as our previous

256

studies.

257

toluene but destabilized by CH3CN. The activation barriers of 12 o’clock reaction is the

258

highest in ACMA1- and ACMA2- reactions, but the lowest in ACMA3- reactions, which is

259

the same as that in gas phase. Generally, solvents don’t change the order of bond

260

reactivity.

261

The Role of La Insertion The dominant optimized geometrical parameters and

262

thermochemistry data of RCs, TSs, and Ps of the DA cycloaddition of anthracene to

263

La@ACMA in gas phase were depicted in Figure 5, where the energies are relative to the

264

two Rs. For 12 o’clock reaction, the two new bonds in RC are 3.031 and 3.084 Å,

265

respectively. The distance between two Rs is relatively large, so that the interaction

266

between them is weak. The La atom is 2.782 and 2.675 Å apart from the two attacked

267

carbon atoms. From Rs to RC, the Gibbs free energy change is 9.6 kcal mol-1. The two

268

reactants approach each other gradually. The two new bonds shortened to 2.093 and

26, 27, 28, 44

In ACMAn- (n = 1, 2, and 3) reactions, the RCs are stabilized by


Page 22 of 32

Page 23 of 32

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269

3.168 Å, respectively. We can find that the distances between La atom and two attacked

270

carbon atoms are much different (2.452 and 2.918 Å), which may be the main reason of

271

asynchronous characteristic. Interestingly, two newly formed C-C bonds in P are nearly

272

equal (1.585 and 1.582 Å). The location of La atom remains unchanged from RC to TS,

273

but gradually approaches to the center of C70 moiety when the reaction proceeds to P. The



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

274

process from R to P is endergonic by 4.0 kcal mol-1, which isn’t a spontaneous change

275

from thermodynamics viewpoint. The reaction barrier of 12 o’clock reaction is 12.4 kcal

Figure 5. The dominant optimized geometrical parameters, relative enthalpies, and Gibbs free energies of RCs, TSs, and Ps, the charges (red number near La) on La in RCs, TSs, and Ps, and the only one imaginary frequency of the TSs of the DA cycloaddition of anthracene to La@ACMA calculated at the M06-2X/6-31G(d) level in gas phase. (Unit: Å and cm-1. See Figure 1 for type of reaction.)

276

mol-1, which is lower than neutral hollow reaction (18.4 kcal mol-1) by 6.0 kcal mol-1. The

277

encapsulation of metal cations (Li+ or Na+) reduces the activation barrier of the

278

Diels-Alder reaction of C60.34, 44 But for metal encapsulated fullerene, charge transfer


Page 24 of 32

Page 25 of 32

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279

from metal to carbon cage normally reduces the reactivity of fullerene cage by making it

280

less electrophilic.49,

281

La@ACMA can be understood from Figure S5. The interaction orbitals are HOMO of

282

anthracene and LUMO of La@ACMA like in hollow neutral reactions (anthracene +

283

ACMA). The energy of LUMO decreases from -2.61 eV in hollow ACMA to -3.00 eV

284

after encapsulation of La. The HOMO-LUMO gap is 3.64 eV in 12 o’clock reaction of

285

ACMA, and decreases to 3.33 eV in 12 o’clock reaction of La@ACMA. This is favorable

286

for the electron transfer process. Totally speaking, 12 o’clock reaction is kinetically

287

enhanced by the encapsulated La atom.

50

The reduction of activation energy in 12 o’clock reaction of

288

The processes and geometric characteristics of stationary points in 5 and 2 o’clock

289

reactions are alike to 12 o’clock reaction. The processes from R to P aren’t spontaneous

290

change like 12 o’clock reaction. Based on previous investigation, three electrons to C70 in

291

pristine La@C70 transfer from La to C70 and La@C70 may be have a form of

292

[email protected] Similarly, La@ACMA should have a form of La3+@AMCA3-. Then the

293

DA reaction between La3+@AMCA3- and anthracene should have similar reactivity and

294

regioselectivity to AMCA3- reactions in previous section and the order of the three

295

reactions should be 2 > 5 > 12 o’clock. But as shown in Figure 5, the reaction barriers are

296

22.3 and 23.3 kcal mol-1 for 5 and 2 o’clock reactions, respectively, which is larger than

297

12 o’clock reaction. So when La atom is encapsulated into ACMA, the order of the



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

298

reactivity is: 12 > 2 > 5 o’clock reaction. The distortion and interaction energies of

299

La@ACMA reactions were listed in Table S3. It can be found that the total distortion

300

energy is 17.0 kcal mol-1, and the interaction energies of 12 o’clock reaction is -5.4 kcal

301

mol-1. The distortion energies of 2 and 5 o’clock reactions are larger than 12 o’clock

302

reaction, and the final barrier is higher. The Mulliken charges on La of all the stationary

303

points (RCs, TSs, and Ps) were shown in Figure 5. The Mulliken charge on La is 1.5, so

304

the form of La@ACMA is [email protected]. The charges on La of RCs, TSs, and Ps are

305

all not 3 but near 1.5. That is, the DA reaction of anthracene to La@ACMA should be

306

similar to the reaction of AMCA1- or AMCA2-. It can be found from Table 2 that 12

307

o’clock reaction has the highest reactivity in AMCA1- and AMCA2-, which is the same as

308

La@ACMA reaction. The regioselectivity don’t change because the charges transferred

309

from La to ACMA is not enough. The 12 o’clock reaction is still the most favorable one.

310

Conclusion

311

The reactivity and regioselectivity of bis-DA cycloaddition of anthracene to C70 were

312

elucidated by DFT method. We found that 12 o’clock reaction has the lowest barrier

313

among three possible reaction sites for the reaction of anthracene and neutral ACMA,

314

which helps to understand the experimental observations. The influences of charges

315

exerted on ACMA were systematically considered, which is difficult for experimental

316

methods. We found that the regioselectivity may change from 12 to 2 o’clock when the


Page 26 of 32

Page 27 of 32

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317

exerted charges increase to -3. Solvents have little effect on these reactions. The

318

bis-addition of La@C70 were predicted because there are no experimental results till now.

319

We found that La insertion can increase the reactivity of the bonds but cannot change the

320

regioselectivity because the charges transferred from La to ACMA cage is not enough.

321 322

ASSOCIATED CONTENT

323

Supporting Information

324

The Cartesian coordinates of optimized structures, the detailed thermochemical data in

325

gas phase and solvents, the distortion/interaction energies of DA reaction between

326

anthracene and La@DCMA, and the electrostatic potential surfaces of anthracene and

327

neutral ACMA have been collected in the Supporting Information. This material is

328

available free of charge via the Internet at http://pubs.acs.org/.

329 330

AUTHOR INFORMATION

331

Corresponding Author

332

*E-mail: [email protected]

333

*E-mail: [email protected]

334 335

Notes



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

336

The authors declare no competing financial interest.

337 338

ACKNOWLEDGMENTS

339

This study was supported by grants from the National Nature Science Foundation of

340

China (Grant Nos. 21273021, 21325312 and 21421003) and start-up research grant and

341

postdoctoral research funding from Henan Institute of Science and Technology.

342 343

Reference

344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364

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Theoretical Study on the Reactivity and Regioselectivity of the Diels

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