Zhenfeng Shang

Systematic investigation of the molecular behaviors of heterofullerenes C48X2 (X=B, N)

Abstract A systematic investigation on all possible substituted fullerene isomers of C 48 B 2 and C 48 N 2 has been performed using the semiempirical methods AM1 and MNDO. The equilibrium geometrical structures, heats of formation, strain, aromaticity, HOMO–LUMO energy gaps, ionization potentials, electronic affinities, the absolute hardness and electronegativity have been studied. The results indicate that the isomer-78, which corresponds to 1,4-substitution in the six-membered ring located on the equator, is the most stable isomer for both C 48 B 2 and C 48 N 2 . The driving force governing the stabilities of the present studied C 48 X 2 (X=B, N) isomers is the strain being inherent in the C 50 cage. The contribution of the conjugation effect to the stabilization is not able to compete with that of the strain. From an application of the HSAB principle, the absolute hardness of the more stable isomers of both C 48 B 2 and C 48 N 2 are larger than that of C 50 , and the direction of electron flow for forming a complex among them may be C 48 N 2 →C 50 →C 48 B 2 according to the calculated absolute electronegativity. The more stable C 48 X 2 isomers have larger ionization potentials and smaller electronic affinities compared with C 50 , which suggests that it is more difficult to oxidize and reduce C 48 X 2 , i.e., the redox characteristics of C 50 can be weakened by doping. The vibrational spectra and electronic absorption spectra of these substituted fullerenes have been calculated, which could serve as a framework to interpret future experimental results. The computed nucleus independent chemical shifts (NICS) values also provide a basis for the possible characterization of these C 48 X 2 isomers.

Fuzzy Symmetry Characteristics of Propadine Molecule

Abstract The fuzzy symmetry characteristics for the internal-rotation of propadine were analyzed using the fuzzy symmetry theory for molecule and molecular orbital (MO). In the process of rotation, three different symmetry point groups D2h, D2d, and D2 were considered. Using the D4h point group, which is the minimal point group including all symmetry elements of D2h, D2d, and D2, we can analyze the fuzzy symmetry for this process. The elements included in D4h point group can be classified to four subsets: (i) G0—it includes all the elements in D2 point group, also belongs to all the above three point groups of D2h, D2d, and D2; (ii) G1—it includes the elements in D2h point group, but not in D2d point group; (iii) G2—it includes the elements in D2d point group, but not in D2h point group; (iv) G3—it includes the elements in D4h point group, but not in D2h or D2d point group. On the basis of the above four subsets, we analyzed the membership functions and the regularity of variation in MOs for the internal-rotation of propadine.

A systematic investigation on the molecular behaviors of substituted fullerenes C34X2 (X=N, B)

Abstract A systematic investigation on the molecular behaviors of all the possible isomers of C 34 B 2 and C 34 N 2 formed from the initial C 36 fullerene with C 6 v and C 6 h symmetries have been performed using the semi-empirical AM1 and MNDO methods. The equilibrium geometrical structures, heats of formation, HOMO–LUMO gap energies, heats of atomization, ionization potentials (IP) and affinity potentials (AP), conjugate effect and deformation energies of C 34 X 2 (X=N, B) have been studied. The calculation results show that the heterofullerenes are less stable than C 36 , and the C 34 N 2 should be more stable than the boron analog C 34 B 2 . Both empirical methods in this work indicate that the most stable isomer of C 34 X 2 (X=N, B) corresponds to 1,4-substitution in the cyclohexatriene unit which locating at the equatorial belt of the C 36 cage. Generally speaking, the C 34 X 2 (X=N, B) isomers with the doped atoms near the equatorial belt are more stable that the rest. The heterofullerenes C 34 X 2 have bigger IP and smaller AP compared with C 36 , thus the redox activity of C 36 can be reduced by doping. The results of π-orbital axis vector analysis show that replacements of carbon atoms with either nitrogen or boron can notably release the strains in local part of the cage. Both C 34 N 2 and C 34 B 2 are expected to have significantly different chemical and physical properties from those of the fullerenes.

Ab initio study on the structures and stabilities of C36O: oxide of fullerene C36 (D6h)

Abstract Total of six possible isomers of C 36 O, oxide of fullerene C 36 ( D 6 h ), have been investigated by ab initio calculations. An insight into the relationship between structures and stabilities of these isomers are presented. The results show that the c -open structure is the ground state of C 36 O and the stabilities of the isomers are determined by conjugate effect and tension jointly. Energy difference among the isomers is not very large, hence it can be expected that some isomers will co-exist in a mixture once C 36 O is synthesized. The infrared and Raman spectra have been calculated, which could serve as a framework to interpret future experimental results.

Theoretical investigation on the hydrogenation of armchair single-walled carbon nanotubes

Abstract Two hydrogen atoms added on armchair single-walled carbon nanotubes (ASWCNTs) was considered for semiempirical quantum chemical calculations at the level of AM1(RHF). The isomers with the addition type of 1, n- where n is even were found to be more stable than the isomers with n odd. The calculation also shown that the C–H binding energy of the addition isomers of ASWCNTs decreases with the increasing diameter of the nanotubes.

Study on dichlorocarbene cycloaddition isomers of armchair single-walled carbon nanotubes

Abstract Armchair single-walled carbon nanotubes with the various length and diameter, along with their dichlorocarbene cycloaddition isomers were optimized by AM1 and PM3 methods. Nanotube with larger diameter has less strain force and a relatively strong π-conjugated interaction. For short carbon nanotubes and the edge region of the long carbon nanotubes, dichlorocarbene cycloaddition can form both open and closed isomers on the horizontal and slopy C–C bond, respectively. In the middle of the relatively long nanotubes, dichlorocarbene cycloaddition can only form Horizontal-open and Slopy-closed isomers. The Horizontal-open isomer is more stable than other isomers thermodynamically in any case. The calculated infrared spectra are useful to determine whether the reaction between carbon nanotube and dichlorocarbene has taken place.

A systematic investigation on the molecular behaviors of boron- or nitrogen-doped C40 cluster

A systematic investigation on all possible substituted fullerene isomers of C38B2, C38N2 and C38BN has been performed using the semiempirical methods AM1 and MNDO. The heat of formation, stabilization energy, HOMO–LUMO gap, the strain, the absolute hardness and electronegativity have been studied. The calculations show that the order of stability is C40 > C38B2 > C38BN > C38N2, which is similar to heterofullerenes C36 though somewhat different from the hetero-C60 cluster. The strain in C38XY rises relative to the C40 cluster according to POAV analysis, and the absolute hardness and the electronegativity of C40 is larger from an application of the HSAB principle. The selectivity of the substitution positions is commonly determined by the conjugative effect and tension. The vibration spectra for the doped fullerenes have been calculated, which could serve as a framework to interpret future experimental results.

Theoretical study of C60O2 molecular properties

Abstract The equilibrium geometries and heats of formation of oxidized fullerene derivatives C60O and C60O2 were computed using MNDO, AM1 and PM3 methods. The most stable isomer of C60O2 is that with two oxygen atoms positioned over two 6:6 ring junctions on a common six-membered face of the carbon cage, which is in agreement with the experimental results. Using the optimized geometries, the electronic spectra of C60O2 were calculated by the INDO/CI method.

Systematic investigation of the molecular behavior of C50X2(X=H,F): An echo of the H/F parallels on structures and energetics among their derivatives

A systematic investigation of all possible C50H2 and C50F2 isomers has been performed using the semiempirical methods AM1 and PM3. The equilibrium geometrical structures, heats of formation, HOMO–LUMO energy gaps, ionization potentials, electronic affinities, strain and aromaticity have been studied. The results indicate that isomer-78, which corresponds to 1,4-addition in the six-membered ring located on the equator, is the most stable isomer for both C50H2 and C50F2. The driving force governing the stabilities of the presently studied C50X2 (X=H,F) isomers is the strain inherent in the C50 cage. The contribution of the conjugation effect to the stabilization is not able to compete with that of the strain. The relatively more stable C50X2 isomers have larger ionization potentials and smaller electronic affinities than C50, which suggests that it is more difficult to oxidize and reduce C50X2, i.e., the redox characteristics of C50 are weakened by hydrogenation and fluorination. The vibrational spectra and electronic absorption spectra of the hydrogenated and fluorinated fullerenes have been calculated, which could serve as a framework to interpret future experimental results. The computed nucleus independent chemical shifts (NICS) values also provide a basis for the possible characterization of these C50X2 isomers. Isostructural C50H2 and C50F2 molecules are predicted to have a constant energy difference. The phenomenon of H/F parallels on structures and energetics among derivatives of some fullerenes has been echoed.

Molecular torus group

Generally speaking, the highest symmetry of Möbius cyclacene molecule possesses the C2 symmetry based on the theory of point group according to the previous works. However, based on the topology principle, the fundamental group of Möbuis strip is an infinite continuous cyclic group and its border is made up of twice of the generator. Of course, the Möbius strip-like molecule is associated with a finite discrete cyclic symmetry group. For the cyclacene isomers constructed by several (n) benzene rings, these isomers include: the common cylinder Hückel cyclacene (HC-[n]) molecules, the Möbius cyclacene (MC-[n]) molecules by twisting the linear precursor one time (180°), and the multi-twisted Möbius strip-like cyclacene (MmC−[n]) molecules by twisting the linear precursor m times (m × 180°). The relevant results suggest that in addition to the point symmetry, there is a new kind of symmetry called the torus screw rotation (denoted as TSR). In this article, we take the MmC−[n] molecules as examples to discuss their TSR group and point group symmetry, and the relative symmetry adaptive atom sets as well as their atomic orbital (AO) sets. Here, the Cartesian coordinates is not quite fit for the investigation of these AOs, so it is replaced by either the torus orthogonal curvilinear coordinates (for MmC−[n] molecule) or the cylinder orthogonal curvilinear coordinates (for HC-[n] molecule). According to the features of cyclic group, the character table of the irreducible representation of the TSR group could be constructed easily. Some other relevant point-group symmetries maybe also belong to the molecule, so its symmetry maybe called as the torus group symmetry. For multi-twisted Möbius strip-like molecule, there are some correlations in topology characteristics.