Xuezhuang Zhao

Study on chaos synchronization in the Belousov–Zhabotinsky chemical system

Abstract We presented the numerical investigation of the synchronization between two Belousov–Zhabotinsky (BZ) chemical chaotic systems by the Pecora–Carroll scheme. Both identical synchronization and two types of generalized synchronization were obtained under different conditions. Based on the reaction mechanism, the chemical background of efficiency by using different driving variables was discussed. The results indicated that in a real variable coupling BZ experimental system, Br − is the unique feasible variable to obtain synchronization.

SEMI-EMPIRICAL CALCULATIONS ON THE BN SUBSTITUTED FULLERENES C60-2X(BN)X (X = 1-3) : ISOELECTRONIC EQUIVALENTS OF C60

Abstract The equilibrium structures and relative stabilities of BN substituted fullerenes C60−2x(BN)x (x=1–3) have been studied using AM1 and MNDO semi-empirical methods. The calculation results obtained by both methods indicated that the BN substituted fullerenes are less stable than C60. The homo–lumo splitting and heat of formation suggests that the isomer of C58BN in which two neighboring carbon atoms between the six- and six- membered ring are substituted by BN units is the most stable species. The stabilities of C58BN decrease with increasing the distance between the heteroatoms. For C56(BN)2, the calculation results show that N–N and B–B bonds should be avoided and the smallest number of the C–X bonds is preferred for the stable isomer of C56(BN)2 and the isomer in which the B–N–B–N bond is formed has the lowest heat of formation, thus the most stable species. The structure of the most stable isomer of C54(BN)3 has been proposed based on the calculations on various isomers of C58BN and C56(BN)2, i.e. the most energetic favorable C54(BN)3 should have three BN units located in the same hexagon to form B–N–B–N–B–N ring. The BN substituted fullerenes C60−2x(BN)x have somewhat smaller ionization potentials and bigger affinity potentials compared with C60, which suggests that it is easier to oxidize and reduce C60−2x(BN)x relative to C60, thus the redox characteristics of C60 can be enhanced by doping. Based on the optimized geometries, the electronic spectra for these BN doped fullerenes have been calculated using INDO/CIS method

Calculations on all possible isomers of the substituted fullerenes C58X2 (X=N,B) using semiempirical methods

A systematic investigation on the molecular structures of all the possible isomers of C58N2 and C58B2 has been performed using the semiempirical methods AM1, PM3 and MNDO. The equilibrium geometrical structures, heats of formation, HOMO–LUMO gap energies, heats of atomization, ionization potentials and affinity potentials of C58X2 (X=N,B) have been studied. The calculation results obtained by all these semiempirical methods show that the heterofullerenes are less stable than C60, and that C58N2 should be more stable than the boron analog C58B2. All the empirical methods in this work indicate that isomer-7, which corresponds to 1,4-substitution in the cyclohexatriene unit, is the most stable isomer for C58X2 (X=N,B). The stability decreases with the increasing distance between the heteroatoms. The heterofullerenes C58X2 have smaller ionization potentials and bigger affinity potentials compared with C60, thus the redox characteristics of C60 can be enhanced by doping. Both C58N2 and C58B2 are expected to have significantly different chemical and physical properties from those of the fullerenes. We propose that the change of hybridization from s to s may be the underlying reason why 1,4-substitution is favored in both C58N2 and C58B2. The electronic spectra for these doped fullerenes have been calculated using the INDO/CIS method based on the optimized geometries.

Theoretical studies on the substituted fullerene C60−x−yBxNy(x+y=2)

Abstract The equilibrium structures, relative stabilities of substituted fullerenes C 58 B 2 , C 58 N 2 and C 58 BN have been studied at the AM1, PM3, MNDO and INDO level. The calculation results obtained by all these semi-emperical methods show that the substituted fullerenes are less stable than C 60 , 6–6 isomers are the most stable species for C 58 B 2 , C 58 N 2 and C 58 BN, the stabilities decrease with the increase of the distance between the heteroatoms. The calculation results also show that the stability of C 58 BN is considerably higher than that of C 58 N 2 , and the stability of C 58 N 2 is considerably higher than that of C 58 B 2 . Calculations on the C 58 B 2 -(NH 3 ) 2 adducts have been employed in this paper to evaluate Smallys proposition on the substitute preference of C 58 B 2 . The elctronic spectra for these doped fullerenes have been calculated using INDO/CIS method

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.

Theoretical studies on the BN substituted fullerenes C70−2x(BN)x (x=1–3)—isoelectronic equivalents of C70

Abstract The equilibrium structures and relative stabilities of BN-doped fullerenes C70−2x(BN)x (x=1–3) have been studied at the AM1 and MNDO level. The most stable isomers of C70−2x(BN)x have been found out and their electronic properties have been predicted. The calculation results show that the BN substituted fullerenes C70−2x(BN)x have considerable stabilities, though they are less stable than their all carbon analog. For C68BN, the isomers whose BN is located in the most chemically active bonds of C70 (namely B and A) are among the most stable species, of which B is predicted to be the ground state. The stabilities of C68BN decrease and the dipole moments increase with increasing the distance between the heteroatoms. For C66(BN)2, the lowest energy species is the isomer in which the B–N–B–N bond is formed; For C64(BN)3, the most stable species should have three BN units located in the same hexagon to form B–N–B–N–B–N ring. The ionization potentials and the affinity energies of the most stable species of BN-doped C70 are almost the same as those of C70 because of the isoelectronic relationship. The ionization potentials and affinity energies depend on the relative position of the heteroatoms in C68BN, the chemical reactivities of the isomers whose heteroatoms are well separated should differ significantly from their all carbon analog.

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.

Fuzzy symmetries of molecule and molecular orbital: characterization and simple application

A fuzzy point group has been constructed to describe imperfect molecular symmetry by using fuzzy set theory. Then the fuzzy symmetry of the molecular orbital has also been analyzed, and several concepts, such as fuzzy irreducible representation and fuzzy characters (fuzzy generalized parity) for molecular orbitals have been advanced. The results show that sometimes the symmetry of the molecule as a whole is not obvious, however, that of some molecular orbital may be obvious. Although oscillator strength in the electronic spectrum is not determined solely by fuzzy symmetry, it is obviously related to the fuzzy symmetry, which seems to be a fuzzy rule for the electronic spectrum.

Investigation of the kinetic properties for the forward and reverse WGS reaction by energetic analysis.

The kinetic properties of forward water gas shift reaction (CO þ H2O ! CO2 þ H2) and reverse water gas shift reaction (CO2 þ H2 ! CO þ H2O) over the copper surface have been analyzed by UBI-QEP approach. For the ‘surface redox’ mechanism, the energies analysis results show that the rate controlling step in FWGS is the dissociation of adsorbed H2O, and the dissociation of adsorbed CO2 is the rate controlling step of the RWGS reaction. The RWGS reaction is more structure sensitivity than that of FWGS reaction over the Cu single crystal surfaces. Both the activity of FWGS reaction and RWGS reaction over the Cu (111) surface are higher than that of in Au (111) surface. In the meantime, the reason why the FWGS reaction and RWGS reaction is easily poisoned by sulphur has been explained, namely, the activation barrier of rate controlling step increases with the increasing of the coverage of sulphur. q 2003 Elsevier B.V. All rights reserved.