1. Introduction:
Since its discovery, buckminsterfullerene[1 ] has been considered as an important precursor for several chemical compounds which have wide-scale applications [2-7 ], ranging from material science to biological sciences [8-10 ]. The functionalization of the fullerene cages including polymeric derivatives has sorted out some of the problems associated with low solubility and miscibility of corresponding C60 systems[11 ].In the past decades, a large number of fullerene derivatives have been synthesized and characterized with desirable applications [12-15 ], such as photoelectric conversion [16 ], magnetic resonance imaging [17 ], cancer therapy[18 ] and so on. Among the experimental and theoretical methods implemented for fullerene modifications, Diels-Alder cycloaddition reaction[19-23 ] on the fullerene surface and encapsulation of atom/metal cluster/small molecules into the hollow cage of fullerene [24-27 ] are drawing great scientific attention. In this aspect, selective encapsulation of fullerene cages is also observed to offer one of the key techniques in their purification [28 ]. On the Ih-symmetric C60, mainly two kinds of C–C bond connectivity [29 ] have been observed, namely [6, 6] and [6, 5]. The [6, 6] bond of fullerene (C60) is found to exhibit much higher reactivity towards Diels-Alder reactions with dienes[30, 31 ] than that of [6, 5] bond[32-35 ].
In recent decades, extensive studies on the chemical reactivity of endohedral-metallofullerenes (EMFs) have got a new dimension. The EMFs show enhanced reactivity not only towards Diels-Alder[36] but also to other essential reactions necessary for varied utilization[37] . In this regard, Li+ encapsulated fullerenes (Li+@C60)[38, 39 ] are of great interest for both experimentalists as well as theoreticians. According to the studies done by Ueno et al. [40 ], a lesser HOMO-LUMO gap in Li+@C60 compared to neutral C60 is the principal reason for facilitating [4+2] cycloaddition reaction, inducing significant changes in the frontier orbitals. As a result, the Diels-Alder reaction of Li+@C60 is 2400-fold faster than neutral C60. However, the effect of counter anion in Li+-encapsulated C60 during the Diels-Alder reaction has also been explored[41 ].
Cui et al. [42 ] showed the thermodynamic feasibility of cycloaddition reactions between CpH and Ca2+@C60 as well as M+@C60 (M = Li, Na, K, Rb, and Cs). Their computational study inferred that encapsulated cations facilitate DA reactions by altering distortion and interaction energies. García-Rodeja and co-workers[43 ] also explored the influence of varied ion-encapsulation (Li+, Na+, K+, Be2+, Mg2+, Al3+) on the reactivity of the DA reaction between corresponding encapsulated fullerene and 1,3-cyclohexadiene by employing Density Functional Theory (DFT). Osuna et al. [44 ] reported about the modulated reactivity and regio-selectivity in Diels-Alder reaction of noble-gas-encapsulated fullerene systems. Recently, Wuet al. [45 ] observed that [6,5] bond of calcium-encapsulated C60 molecule can be successfully activated in the course of DA reaction based on charge transfer from the metal atom to fullerene cage.
After reviewing these earlier reported works, it is quite evident that the investigation of the reactivity of the EMFs in the context of Diels-Alder (DA) reaction is a challenging field of exploration both in terms of the experiment as well as theory. In our previous study[46 ], we have successfully explored the energetics related to neutral C60 as well as mono- and di-cation encapsulated EMFs towards DA reaction with 1,3-butadiene, resulting in mono-functionalized products. But to the best of our knowledge, the reactivity of neutral C60 as well as encapsulated C60 towards Multi-Diels-Alder (MDA) reaction beyond bis-functionalization[45 ] is yet to be revealed computationally. Under these circumstances, we are going to investigate the sequential MDA reactions on C60 fullerene surface with 1, 3-butadiene computationally by employing DFT. Moreover, in the present venture, we have extended our exploration to the titled reaction procedure for Li+@C60 also to check the effect of metal ion encapsulation on the reactivity of each step of the MDA reaction. In order to get a clear idea about the bond selectivity, both [6, 6] and [6, 5] connectivities on neutral as well as charged EMF surfaces (Figure 1 ) are considered separately for MDA reactions. Overall, our objective is to provide a fundamental understanding of the reactivity of neutral C60 towards MDA reactions and to enquire about the effect of Li+-encapsulation in the reactions, as mentioned earlier.