C library for topological study of the electronic charge density

The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid‐based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton–Raphson method (to find the critical points, where the gradient is null) and the Cash–Karp Runge–Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three‐dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. © 2012 Wiley Periodicals, Inc.     

Semiempirical vibrational and electronic structures of C60 and C70

The electronic and vibrational structures of C₆₀ and C₇₀ have been calculated at the PM3 semiempirical level. C₆₀ has a partially delocalized structure, while C₇₀ has both a localized set and a delocalized set of MOs. As with AM1 and MNDO, PM3 predicts the heat of formation of C₇₀ to be greater than that of C₆₀, and that C₇₀ is the thermodynamically more stable species. Calculation of the normal modes was accelerated over 40 times by limited use of symmetry theory.     

Valence electronic structure of benzo-2,1,3-chalcogenadiazoles studied by photoelectron spectroscopy and density functional theory

The He I photoelectron spectra of benzo-2,1,3-thia-, selena-, and telluradiazole were measured, and the observed ionization bands were assigned by comparison with the results of DFT calculations. Whereas the B3LYP exchange-correlation functional provided orbital energies that permitted a preliminary assignment by application of Koopman's theorem, a more-accurate interpretation was established by calculation of the vertical ionization energies with the PW91 functional and analysis of the correlation of energy levels along the homologous series. This strategy clarified earlier disagreements in the assignment of the spectrum of benzo-2,1,3-thiadiazole.     

Microscopic structure of collective density oscillations C60 and C70

The microscopic structure of the photo-excited plasmon excitation in C₆₀ and C₇₀ is investigated using linear response theory. One finds that Landau damping provides the main contribution to the lineshape and the linewidth of the Mie-type plasmon being able, in the case of C₇₀, to mask the deformation splitting effect associated with the low equilibrium symmetry (D_5h) of this fullerene. Furthermore, it is found that the coupling of the plasmon to the normal modes of vibration of the fullerenes provides a sizeable contribution to the lineshape, without significantly affecting the linewidth. This coupling is found to be active already atT=0, exhibiting a weak temperature dependence.We would like to dedicate this work to Michael Hansen, who actively participated in most of the work and studies carried out in this paper, and who is not among us anymore     

The crystal structure of the 2D polymerized tetragonal phase of C60

Single crystals of the 2D polymerized tetragonal phase of C₆₀ without orientational domains were obtained under high pressure and high temperature. The crystal structure of this phase was resolved using single crystal X-ray diffraction data. The cell parameters are a=9.064(3) and c=15.039(8) Å with the space group P4₂/mmc and Z=2. A structural model of this phase proposed early was confirmed and refined to final R=0.075. The structure is slightly disordered. It consists of a random combination of the P4₂/mmc layers (84%) and of the Immm layers (16%), along the c-axis.     

Efficient charge separation in C60-based dyads: triazolino

Triazoline[4,5][60]fullerenes are strong electron acceptors that form with tetrathiafulvalene (TTF), a novel type of donor-acceptor dyad exhibiting efficient improved electron-transfer dynamics. In particular, a rapid photoinduced intramolecular electron transfer, forming a charge-separated state, is followed by a slow charge recombination to generate the fullerene triplet excited state in moderate quantum yields.     

Structure and electronic properties of highly charged C60 and C58 fullerenes

We present a theoretical study of the structure and electronic properties of positively charged C60(q+) and C58(q+) fullerenes (q = 0-14). Electronic energies and optimum geometries have been obtained using density-functional theory with the B3LYP functional for exchange and correlation. We have found that closed- and semiclosed-shell C60(q+) ions (q = 0, 5, and 10) preserve the original icosahedral symmetry of neutral C60. For other charges, significant distortions have been obtained. The C58(q+) fullerenes are, in general, less symmetric, being C58(8+) the closest to the spherical shape. Most C60(q+) fullerenes follow Hund's rule for spin multiplicity, while most C58(q+) fullerenes are more stable with the lowest spin multiplicity. The calculated ionization potentials for both kinds of fullerenes increase almost linearly with charge, except in the vicinity of C60(10+) and C58(8+). We have also explored the region of the potential-energy surface of C60(q+) that leads to asymmetric fission. Minima and transition states corresponding to the last steps of the fission process have been obtained. This has led us to conclude that, for 3 < or = q < or = 8, C2(+) emission is the preferred fragmentation channel, whereas, for higher q values, emission of two charged atomic fragments is more favorable. The corresponding fission barrier vanishes for q > 14.     

Metal complexes of allyl derivatives of C60 fullerene: molecular and electronic structure prediction from density functional calculations

The problem of existence of ³—-complexes of C₆₀ fullerene with transition metal atoms is discussed. The complexes C₆₀R₃Co(CO)₃ (R = H, F, Cl, Br), C₆₀H₃NiCp, and C₆₀H₃Fe(CO)Cp, where C₆₀R₃ is an allyl derivative of C₆₀ fullerene, were shown to be sufficiently stable. In these complexes the metal atoms are ³—-bound to the fullerene cage. In contrast to this, the metal atoms in the C₆₀H₃Li and C₆₀H₃FeCp complexes are ⁵—-coordinated to the carbon cage. Density functional calculations were carried out with the Perdew—Burke—Ernzerhof exchange-correlation potential (PBE). It was concluded that the type of bonding in the complexes of allyl derivatives of C₆₀ fullerene depends on the nature of the species attached. Among the systems studied, the maximum energy of the ³—-bond was obtained for the C₆₀H₃NiCp complex. The results obtained can be useful in the design of synthesis of new fullerene derivatives with the ³—-coordination of the transition metal atoms to the carbon cage.     

X-ray spectra and electronic structure of K x C60

Highly resolved CK_α spectra of the compounds K₃C₆₀ and K₆C₆₀ synthesized by thermal decomposition of potassium azide in a vacuum chamber of an X-ray tube were obtained. The possibility of monitoring the extent of intercalation of fullerenes by the CK_α spectra is demonstrated. The results are compared with the MNDO calculations for K₆C₆₀. The data are used to construct a diagram of the structure of the highest occupied and C1s levels in the series C₆₀−K₃C₆₀−K₆C₆₀. Deceased. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 3, pp. 514–519, May–June, 1996.     

Spectra of optical phonons and low-energy electronic transitions in C60/TMPD and C60/TPA single crystals

Single Crystals of C₆₀/TMPD and C₆₀/TPA have been grown from a chlorobenzene solution. Optical transmission spectra of single crystals of fullerene complexes withN,N,N,N-tetramethyl-p-phenylenediamine (TMPD) and triphenylamine (TPA) are studied in the spectral range from 600 to 16000 cm^–1. Splitting of the intramolecular vibration of C₆₀ is observed at 1428 cm^–1, which is likely caused by freezing of the rotation of the C₆₀ molecules due to their interaction with amines. Single crystals of C₆₀/TMPD differ from those of C₆₀/TPA by a decrease in the vibration frequency at 1428 cm^–1, vibrations of the C-C bonds of the TMPD molecule, and the redistribution of the forces of the oscillators of the vibrations of the C-N bonds. These peculiarities are interpreted to be the result of partial electron transfer from TMPD to C₆₀ in the C₆₀/TMPD single crystals. The electron transfer in the C₆₀/TPA system is less pronounced.Translated fromIzvestiya akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1459–1464, June, 1996     

Some electronic correlation effects in the topological analysis of the Laplacian of the electronic charge density in C-n-butonium cations

In this work, we present a topological study of the Laplacian of the electronic density using a 6-311++G basis set, at Hartree-Fock (HF) and second-order M?ller-Plesset (MP2) (full-electron and frozen-core) levels of theory, for the carbocations 2-C-n-butonium generated upon the insertion of a proton into the secondary C-C bond during the protonation of n-butane. The charge concentration, CC, critical points of the Laplacian distribution at each valence shell, VS, of carbon atoms, and the charge concentration closer to hydrogen atoms are studied. Also, the bonding critical points of the electronic density are analyzed. We analyze some effects that Coulomb correlation has on topological features of the electronic distribution. It is shown that they are mainly reflected in a decreasing of the charge concentrations at the VS and in a contraction of the VS to the nuclei. They are more pronounced over C-C bonds than in C-H bonds. The sensitivity of some parameters derived from this topological analysis to the correlation effect of core electrons and subtle effects related to hyperconjugative interactions are shown. Some consequences of different schemes (double and triple split-valence basis set with diffuse and polarization functions) in the definition of subtle VS charge concentrations at 3c-2e bond paths are presented. It is also demonstrated here how the facts that allow us to understand the MP2 stability order found in the carbocationic species 2-C-n-butonium > 1-C-n-butonium > 2-H-n-butonium > 1-H-n-butonium are similarly depicted at correlated and uncorrelated levels of calculation.     

Probing charge separation in structurally different C60/exTTF ensembles

The scope of the present work is to highlight the effects stemming from different C60/exTTF linkages (exTTF = 9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracene)-either via an anthracene unit or a dithiole ring. Particular emphasis is placed on photoinduced electron-transfer features. Therefore, we devised a new series of C60-exTTF ensembles, synthesized via 1,3-dipolar cycloaddition and Diels-Alder cycloaddition reactions, in which exTTF units are separated from C60 by two single bonds (3a-c, 4), one vinylene unit (5a), or two vinylene units (5b). The cyclic voltammetry reveals an amphoteric redox behavior with remarkably strong electron-donor ability of the trimethyl-substituted exTTF moiety in 4 and 5a,b. Steady-state and time-resolved photolytic techniques show that the fullerene singlet excited state in (3a-c, 4, and 5a,b) is subject to a rapid electron-transfer quenching. The resulting charge-separated states, that is C60*(-)-exTTF*+, were identified by transient absorption spectroscopy. We determined radical pair lifetimes of the order of 200 ns in benzonitrile. This suggests (i) that the positive charge of the exTTF*+ is delocalized over the entire donor rather than localized on one of the 1,3-dithiole rings and (ii) that linking exTTF via the anthracene or 1,3-dithiole ring has no appreciable influence. Increasing the donor-acceptor separation via implementing one or two vinylene units as spacers led to improved radical pair lifetimes (5a: tau = 725 ns; 5b: tau = 1465 ns).     

Theoretical predictions of the structures and electronic spectra of C60NH with comparisons with the isoelectronic molecules C60O and C60CH2

Intermediate neglect of differential overlap (INDO ) calculations were used to study two structures of C₆₀NH: one of C_2ν, geometry with a bridging NH across the bond between two fused six-membered rings in C₆₀ and the other of C_s geometry with a bridging NH across the bond between a five- and a six-membered ring. We calculated the most stable isomer of C₆₀NH to be of C_2ν, symmetry. It was found that the C_2ν isomer has a protonated aziridine structure with a bridging C? C bond length of 0.1520 nm. The electronic spectra of both isomers of C₆₀NH were calculated. Comparisons were made with the isoelectronic molecules C₆₀O and C₆₀CH₂, cases in which the calculated electronic spectra for the most stable isomers C₆₀O (C_2ν) and C₆₀CH₂ (C_2ν) are in good agreement with recent experimental results. © 1995 John Wiley & Sons, Inc.     

Chain transfer constants for vinyl monomers polymerized in methyl oleate and methyl stearate

Chain transfer constants were obtained for styrene, methyl methacrylate, methyl acrylate and vinyl acetate, polymerized in methyl oleate and methyl stearate at 60°C. Transfer constants increased in the order: methyl methacrylate < styrene < methyl acrylate ? vinyl acetate in both solvents. Average values of the transfer parameters were: for methyl oleate, Q_tr = 2.04 × 10^?4, e_tr = 1.08; for methyl stearate, Q_tr = 0.373 × 10^?4, e_tr = 1.01. Indication that polar species predominate in the transition state is supported by the observed order of reactivity. The usual rate dependence appeared to be followed by all of the monomers except vinyl acetate, which was retarded, severely in methyl oleate. Transfer in methyl oleate was about 5.8 times greater than that found in methyl stearate for these four monomers. The internal allylic double bond of methyl oleate had about the same reactivity in transfer as had the terminal unsaturation in N-allylstearamide at 90°C. Rough estimates were obtained of the monomer transfer constants for the long side-chain homologs of these four monomers from the respective monomer transfer constants and the experimental transfer constants, corrected for transfer to the labile groups of the solvent. It was concluded that the rate of polymerization would determine in large measure the degree of polymerization for the reactive 18-carbon homologs but that the molecular weight of poly(vinyl stearate) and (oleate) will be regulated primarily by transfer to monomer.     

Multiphoton photodetachment of C60-

A model delta-function potential is considered for simulating the interaction of the attached electron in C(60) (-) with the fullerene environment. The analytical expressions for the energy eigenstates, and the Green's function, are used to deduce the one-, two-, and three-photon photodetachment probabilities for C(60) (-). Particularly interesting is the observation that the three-photon photodetachment is greatly enhanced by the bound states with energies close to the energies for resonant absorption of one and two photons, and a resonance in the l=3 state.     

Molecular view of charge exchange in ion–C60 collisions

We present a theoretical study of charge transfer in H⁺+C₆₀ and He²⁺+C₆₀ collisions using an extension of the molecular time‐dependent method of ion–atom collisions. Energy‐correlation diagrams have been evaluated for the corresponding (C₆₀–H)⁺ and (C₆₀–He)²⁺ quasi‐molecules. Single and double charge‐transfer cross sections in C₆₀+He²⁺ collisions are reported for the first time. The results show that double charge‐transfer cross sections are only one order of magnitude smaller than single charge‐transfer cross sections. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Analysis of the electronic structure of C60 doped withp-elements

The electronic structure of C₆₀ doped with thep-elements B-F, Al-Cl and Ga-Br located at the centre of the cage has been analyzed within the local density approximation using the von Barth-Hedin exchange correlation potential. The calculations show the existence ofn- andp-type doped Buckminsterfullerene, where a partly occupied level occurs in the band gap, similar to the donor or acceptor levels in traditionally doped semiconductors.     

Broken inter-C60 bonds as the cause of magnetism in polymeric C60: a density functional study using C60 dimers

Bond breaking in C60-C60 dimeric units is believed to play an important role in the onset of magnetism in 2D polymeric C60. On the basis of density-functional theory, the calculations we present here provide further insight into this mechanism through a quantitative characterization of the bond-breaking processes in the isolated dumbbell-shaped C60 dimer. In particular, the analysis of the calculated potential energy surfaces for the low-lying singlet and triplet states identifies and locates the S0-T2 crossing point, which is crucial for the transition to a magnetic state to take place under thermal conditions. These results also suggest a possible new approach to the production of magnetic polymeric C60.