Bo-Cheng Wang

Localized Gaussian type orbital-periodic boundary condition-density functional theory study of infinite-length single-walled carbon nanotubes with various tubular diameters.

The detailed geometrical structures of zigzag and armchair type single-walled carbon nanotubes (SWCNTs) with infinite tubular length were investigated using localized Gaussian type orbital-periodic boundary condition-density functional theory (LGTO-PBC-DFT) method. The structures of (n, 0) zigzag SWCNTs were optimized for n = 5-21, (n, n) armchair SWCNTs for n = 3-12. For comparison, the optimized geometry of a two-dimensional graphite sheet was also calculated. It was found that the optimized structures of the SWCNTs showed two C-C bond lengths that decrease with an increase in the tubular diameter. More specifically, the two bond lengths converged with those found in the two-dimensional graphite sheet. We also found a degeneracy in the highest occupied crystal orbitals if identical bond lengths were employed for the zigzag SWCNTs and the two-dimensional graphite sheet. This implies that the two different bond lengths found in the zigzag SWCNTs and the two-dimensional graphite sheet are probably due to the Jahn-Teller effect. The armchair SWCNTs show two slightly different bond lengths if the diameter is less than 12 A; otherwise they are almost identical, approaching the longer bond length of the two-dimensional graphite sheet. This can be due to the fact that the armchair SWCNTs do not have degeneracy in occupied crystal orbitals for identical C-C bond lengths. The crossing point of the conducting and valence bands of each armchair SWCNT were also calculated and show a diameter dependence in which the deviation from 2pi/3a decreases as diameter increases.

The free-OH stretching frequencies of 3-coordinated H2O in water clusters and on ice surfaces

Abstract The free-OH stretching of 3-coordinated H 2 O on ice and water surfaces typically resonates at 3690 cm −1 , but it blue-shifts to 3715 cm −1 in small- to medium-sized water clusters. This research attempts to account computationally for the frequency difference using ab initio calculations for a number of benchmark systems. Systematic investigations indicate that the 25 cm −1 difference is primarily due to the disparity in molecular structures between water clusters and crystalline ice. We attribute the blue-shifting in water clusters to the reduction of hydrogen bond directionality and the presence of nearby water molecules in the form of double proton donors that are absent in crystalline ice.

Theoretical investigation the electroluminescence characteristics of pyrene and its derivatives

The chromophore of pyrene molecule has been studied in detail by using ab initio (HF, DFT and MP2) and the semi-empirical methods (AM1, PM3 and ZINDO). For its molecular structure, HOMO, LUMO, molecular orbital energies and electronic spectra, the theoretical calculations using AM1 (for optimized structure) with ZINDO (for excitation energy) showed results consistent with experimental finding. Further investigation on 1-, 2- and 4-mono-substituted derivatives of pyrene with the effect of the substitution position and the substituents showed: (1) LUMO is decreased when the substituent is an electron acceptor group; (2) HOMO is increased when the substituent is an electron donor group. However, both electron donor and electron acceptor substituents are effective in reducing the energy gap between HOMO and LUMO in the mono-substituted pyrene. In terms of electronic spectra, the transition π→π∗ shows a larger red shift if the substitutions on the pyrene ring are in the 1- and 4-positions. The red shift is even larger if the substituents contain both electron donor and electron acceptor groups. Nevertheless, a slight blue shift would occur, since the substituents are large groups and distort the planar structure of the parent pyrene molecule. This decreases the overlap of the π orbital and hinders the electron transition from π to π∗. According to the above conclusion, semi-empirical AM1 and ZINDO methods in this work predict several electron luminescence materials among pyrene derivatives, and the results agree very well with the experimental findings. Presumably, the procedures of theoretical calculation employed in this study can be successfully applied to investigation on the electroluminescence characteristics of other materials, and further, to design novel materials for organic light emitting diode.

Structures and stabilities of C60(OH)6 and C60(OH)12 fullerenols

Abstract Recently, Chiangs group have prepared water-soluble polyhydroxylated C 60 derivatives (Fullerenols) in fuming sulfuric acid via hydrolysis of polycyclosulfated precursors. A suggested reaction mechanism is proposed. The calculation of different isomers of C 60 (OH) 6 and C 60 (OH) 12 fullerenols has been carried out using the semiempirical MNDO and MM2 methods with two different approaches: 1. (a) consideration of the geometries and thermodynamic stabilities; 2. (b) consideration of the cyclosulfation and hydrolysis reaction mechanisms. For (a), the double bonds in the pentagon lead to a decrease in the electron delocalization energy. Thus, the ΔH f O values of fullerenol are predicted to increase for each double bond placed in the pentagon for these fullerenols. According to the ΔH f o values, the most stable structures of C 60 (OH) 6 and C 60 (OH) 12 with externally bound hydroxyl groups have been generated, with C s and S 6 symmetries respectively. The ΔH f O values for these fullerenols are 503 kcal mol −1 (C 60 (OH) 6 ) and 131.8 kcal mol −1 (C 60 (OH) 12 ). According to the geometric structure of C 60 (OH) 6 and C 60 (OH) 12 fullerenol, multi-hydroxy additions follow 1,2- or 1,4- addition to a cyclohexatriene. For (b) the most likely products in this reaction are C 60 (OH) 6 ( C s ) and C 60 (OH) 12 ( S 6 ), whose ΔH f O values are 573 and 141.5 kcal mol −1 , respectively. These stable structures could contain exact hydroxyl group sites in C 60 , and they may be helpful in the investigation of the physical properties of polymers or other groups substituted onto fullerenols (called star-like polymers).

Theoretical studies of C60/C70 fullerene derivatives: C60O and C70O

Abstract A semiempirical (AM1) calculation on the structures and stabilities of isomers of the fullerene derivatives C 60 O and C 70 O is carried out. The ozonolysis reaction mechanism and the thermodynamics of the compounds are studied. The two isomers of C 60 O (56 bond and 66 bond) formed by an oxygen atom bridging across a C-C bond have an epoxide-like or an annulene-like structure. According to the ozonolysis reaction mechanism and kinetic factor analysis, the possible products of this ozonolysis reaction are C 60 O with oxygen bridging over the 66 bond ( C 2 v ) as an epoxide-like isomer and that with oxygen bridging over the 56 bond ( C s ) as an annulene-like isomer. Further, the sixteen isomers of C 70 O (both epoxide-like and annulene-like structures) have been studied with respect to the same reaction mechanism. The most possible product in this ozonolysis reaction contains oxygen bridging across in the upper part (66 bond in C 70 O-2 or C 70 O-4) as an epoxide-like structure. The other possible product is C 70 O-8 (annulene-like structure), in which oxygen bridges across an broken equatorial CC bond in C 70 ( D 5 h ). The vibrational frequency analysis and the electronic structure of the selected C 60 O and C 70 O isomers are generated for experimental characterisation. The experimental results indicate that C 60 O and C 70 O may decompose into the odd number fullerenes C 59 and C 69 . We therefore studied the structures of C 59 and C 69 also.

Symmetry and isomeric structures of giant fullerenes and polyhedral clusters

Abstract In order to illustrate the extension of cage cluster of given symmetry to a possible larger giant cluster of the same symmetry type, we have designed methods for drawing Schlegel (or quasi-Schlegel) diagrams that show clearly all (or almost all) the faces, vertices and edges of a three-dimensional cluster in a two-dimensional plane. The symmetries and structural details were used to select unit cells which serve as “abbreviations” for huge (fullerene) clusters, and these unit cells were then used as basis to derive mathematical principles for extending the structures up to infinitely large clusters. Possible isomers and various fullerene clusters (up to C150 of D5h symmetry) of different point-group symmetries are presented (the point groups involved for different sizes are Ih, D6d, D5d, D3d, D6h, D5h, D3h, D3, Td, C3, C3v, and D6). Simple illustrations are given to show how such clearly visible detailed structures can be used to derive the possible magic numbers of (van der Waals) clusters and to formulate the mechanism and reaction coordinates of isomeric transformations. For mixed clusters with different sets of atoms (molecules), the common (minimum) subgroup symmetry is illustrated, which can be used to determine the total structures. An example of A8B12 (e.g. Ti8C+12) is given to show the possibility of Th or D3d symmetry.

Structural and optical properties of passivated silicon nanoclusters with different shapes: a theoretical investigation.

Optimized geometries and electronic structures of hydrogenated silicon nanoclusters, which include the Td and Ih symmetries, have been generated by using the semiempirical AM1 and PM3 methods, the density functional theory (DFT) B3LYP method with the 6-31G(d) and LANL2DZ basis sets from the Gaussian 03 package, and the local density functional approximation (LDA), which is implemented in the SIESTA package. The calculated diameters for these Td symmetric hydrogenated silicon nanoclusters are in the range from 6.61 A (Si5H12) to 23.24 A (Si281H172). For the Ih symmetry, we calculated Si20H20 and Si100H60 nanoclusters only. Theoretically, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is size dependent. The calculated energy gap decreases (Si5H12: 7.65 eV to Si281H172: 3.06 eV) while the diameter of silicon nanocluster increases. By comparing different calculated results, we concluded that the calculated energy gap by B3LYP/6-31G(d)//LDA/SIESTA is close to that from experiment and that the LDA/SIESTA result underestimates the experimental value. On the contrary, the AM1 and PM3 results overestimate the experimental results. For investigation of the optical properties of Si nanoclusters as a function of surface passivation, we carried out a B3LYP/6-31G(d)//LDA/SIESTA calculation of the Si35 and Si47 core clusters with full alkyl-, OH-, NH2-, CH2NH2-, OCH3-, SH-, C3H6SH-, and CN- passivations. The calculated optical properties of alkyl passivated Si35 nanoclusters (Si35(CH3)36, Si35(C2H5)36, and Si35(C3H7)36) are close to one another and are higher than those of oxide, nitride, and sulfide passivated Si 35 clusters. In conclusion, the alkyl passivant affects weakly the calculated optical gaps, and the electron-withdrawing passivants generate a red-shift in the energy gap of silicon nanoclusters. A size-dependent effect is also observed for these passivated Si nanoclusters.

Edge-termination and core-modification effects of hexagonal nanosheet graphene.

Optimized geometries and electronic structures of two different hexagonal grapheme nanosheets (HGNSs), with armchair (n-A-HGNS, n = 3–11) and zigzag (n-Z-HGNS, n = 1–8) edges have been calculated by using the GGA/PBE method implemented in the SIESTA package, with the DZP basis set, where n represents the number of peripheral rings. The computed HOMO-LUMO energy gap (Eg = ELUMO − EHOMO) decreases for fully H-terminated A- and Z-HGNSs with increasing n, i.e., with increasing nanosheet size and pπ-orbitals being widely delocalized over the sheet surface. The full terminations, calculated with various functional groups, including the electron-withdrawing (F-, Cl-, and CN-) and -donating (OH-, and SH-) substitutions, were addressed. Significant lowering of EHOMO and ELUMO was obtained for CN-terminated HGNS as compared to those for H-terminated ones due to the mesomeric effect. The calculated Eg value decreases with increasing n for all terminations, whereby for the SH-termination in HGNS, the termination effect becomes less significant with increasing n. Further, the calculation results for stabilities of HGNS oxides support the tendency toward the oxidative reactivity at the edge site of the sheet, which shows most pronounced C-C bond length alternation, by chemical modification. Physical properties of HGNSs with various numbers of the core-defects, which can be obtained by strong oxidation, were also investigated. Their structures can change drastically from planar to saddle-like shapes. These conformations could be used as stationary phases with controlled interaction in the separation methods such as HPLC and the other chemical analysis techniques.

Theoretical studies of C70(OH)n (n=14, 16, 18 and 20) fullerenols

The experimental results indicated that polyhydroxylated C70 fullerene may generate water soluble C70(OH)n fullerenols with n=14, 16, 18 and 20. The plausible reaction mechanism has been proposed with the consideration of cyclosulfation and hydrolysis. According to the experimental results, the number of hydroxyl substitutes in C70(OH)n fullerenols should be even. Random subroutine in MS FORTRAN 5.0 program library and reaction-mechanism consideration were first used to generate the structure of possible isomers for C70(OH)14, C70(OH)16, C70(OH)18 and C70(OH)20 fullerenols and reaction precursors C70(SO4)7, C70(SO4)8, C70(SO4)9 and C70(SO4)10. The heats of formation, relative stability and optimized structures have been generated by semi-empirical PM3 calculation. Among the possible structures, the electronic structures of these having higher symmetry were then computed. According to the structure analysis, the relative stability of fullerenols depends on the number of hydroxy addends in the equatorial belt region. The 2D Schlegel diagrams of C70(OH)n fullerenols were presented for the geometrically optimized structure by PM3 calculations and contained exact positions of hydroxy addend in C70. These diagrams may be helpful in the investigation of the physical properties of starburst polymers or other groups substituted onto fullerenols. This theoretical computational procedure for searching possible isomers may be a helpful tool for isomer study with symmetry consideration.

Structural symmetry analysis of possible addition/elimination and isomeric rearrangement mechanisms of fullerenes

Abstract This work displays two-dimensional planar diagrams of three-dimensional fullerene cage clusters to clearly visualize the symmetrical arrangements of the complete number of vertices (carbon atoms), edges (bonds) and faces (carbon rings) and to search for the possible isomeric rearrangement and addition/elimination reaction mechanisms. The reactionary symmetry correlation is based on the choice of the common subgroup symmetry for the total reaction coordinate — the latter comes from the combination of multiple sets of local reaction coordinates over the periodic surface of the fullerene cage. The symmetric analysis also involves the determination of the number of symmetry-equivalent ways for such combinations to generate the total reaction coordinate. The symmetry investigation also involves the hypothetical mechanisms for the addition (and elimination) of two (diatomic) carbon atoms to (and from) the reactant fullerene cage, to be followed by subsequent cooperative cage surface rearrangements over the cyclic boundaries to reach the structural symmetry of the final-product fullerene cage. The diagrams and isomeric rearrangement mechanisms elaborated are C60(Ih, D6h, C3v, C3, D5), C76(Td, D2, C3) and C84(Td, C3, C3v). The additions and eliminations elaborated are C26(D3h) ← C28(Td) → C30(D5h), C60(Ih) → C58(C3v), and C76(D2) → C78(C2v, D3h) ← C80(D5d)b.