Molecular modeling of porous carbons using the hybrid reverse Monte Carlo method

We apply a simulation protocol based on the reverse Monte Carlo (RMC) method, which incorporates an energy constraint, to model porous carbons. This method is called hybrid reverse Monte Carlo (HRMC), since it combines the features of the Monte Carlo and reverse Monte Carlo methods. The use of the energy constraint term helps alleviate the problem of the presence of unrealistic features (such as three- and four-membered carbon rings), reported in previous RMC studies of carbons, and also correctly describes the local environment of carbon atoms. The HRMC protocol is used to develop molecular models of saccharose-based porous carbons in which hydrogen atoms are taken into account explicitly in addition to the carbon atoms. We find that the model reproduces the experimental pair correlation function with good accuracy. The local structure differs from that obtained with a previous model (Pikunic, J.; Clinard, C.; Cohaut, N.; Gubbins, K. E.; Guet, J. M.; Pellenq, R. J.-M.; Rannou, I.; Rouzaud, J. N. Langmuir 2003, 19 (20), 8565). We study the local structure by calculating the nearest neighbor distribution, bond angle distribution, and ring statistics.     

Evaluation of methods for determining the pore size distribution and pore-network connectivity of porous carbons

The pore size distribution (PSD) and the pore-network connectivity of a porous material determine its properties in applications such as gas storage, adsorptive separations, and catalysis. Methods for the characterization of the pore structure of porous carbons are widely used, but the relationship between the structural parameters measured and the real structure of the material is not yet clear. We have evaluated two widely used and powerful characterization methods based on adsorption measurements by applying the methods to a model carbon which captures the essential characteristics of real carbons but (unlike a real material) has a structure that is completely known. We used three species (CH4, CF4, and SF6) as adsorptives and analyzed the results using an intersecting capillaries model (ICM) which was modeled using a combination of Monte Carlo simulation and percolation theory to obtain the PSD and the pore-network connectivity. There was broad agreement between the PSDs measured using the ICM and the geometric PSD of the model carbon, as well as some systematic differences which are interpreted in terms of the pore structure of the carbon. The measured PSD and connectivity are shown to be able to predict adsorption in the model carbon, supporting the use of the ICM to characterize real porous carbons.     

The NMR spectra of porphyrins—19: 13C and proton NMR spectra of metal-free porphyrins with the Type-IX substituent orientation,and of their zinc(II) complexes

The ¹³C and proton NMR spectra of six porphyrins bearing the substituent orientation characteristic of the natural “Type-IX” arrangement are reported and assigned. Significant concentration effects in the spectra of the free base porphyrins, together with the broadening of the C_α (and occasionally C_β) carbon resonances due to NH tautomerism caused a significant loss of data in these spectra. However, the spectra of the corresponding zinc(II) porphyrins (with addition of excess pyrrolidine) show that both these extraneous effects are completely removed to give well-resolved spectra with accurately reproducible chemical shifts. These spectra are assigned and an analysis of the chemical shifts allows the deduction of substituent chemical shift (SCS) parameters for the peripheral substituents at the beta and meso carbons. There is no global effect of these beta substituents, the beta carbon SCS being confined to the immediate pyrrole ring, and the meso carbon SCS to the two adjacent pyrrole rings. The SCS parameters are analyzed and it is shown how they can be used to predict the peripheral and meso carbon chemical shifts of any porphyrin bearing the substituents discussed.     

Wetting phase connectivity and irreducible saturation in simple granular media

We present drainage simulations that allow trapping of wetting phase in a simple but nontrivial granular medium, a dense random packing of equal spheres. The basis for the simulations is a network model derived directly from the known locations and dimensions of pore space features. This provides a means of evaluating the morphology of trapped wetting phase. The possible morphologies depend on the assumed connectivity of the wetting phase. At one extreme, we assume that the entire wetting phase except for pendular rings is connected. At the opposite extreme, we illustrate a low level of connectivity by assuming that pendular rings are trapped as soon as the pores surrounding them are drained; any wetting phase not yet drained from pore throats connecting these pores is also assumed to be trapped. Finally we consider a set of criteria involving larger neighborhoods within the network, which allows trapping in individual pores. Irreducible wetting phase saturations obtained in the latter case agree with experimental data. The numbers of pendular rings and liquid bridges are also consistent with observations. Because the agreement does not involve adjustable parameters, we conclude that a relatively simple, local evaluation of trapping criteria can yield physically representative wetting phase configurations.     

Variable connectivity index for cycle-containing structures.

In the early applications of the connectivity index the index was empirically modified for some properties of cyclic structures by subtracting 1/2 from the computed value based solely on valence of vertices in the molecular graph. In this article we looked into the origin of this heuristic adjustment of the connectivity indices for cyclic structures. We have examined the relative role of carbon atoms in cycle-containing structures by differentiating carbon atoms making up a ring and carbon atoms in exocyclic bonds. We found in the case of the boiling points of cycloalkanes and alkylcycloalkanes that contributions of "cyclic" and "acyclic" atoms to molecular additivities differ somewhat.     

Core and peripheral connectivity based cluster analysis over PPI network

A number of methods have been proposed in the literature of protein–protein interaction (PPI) network analysis for detection of clusters in the network. Clusters are identified by these methods using various graph theoretic criteria. Most of these methods have been found time consuming due to involvement of preprocessing and post processing tasks. In addition, they do not achieve high precision and recall consistently and simultaneously. Moreover, the existing methods do not employ the idea of core-periphery structural pattern of protein complexes effectively to extract clusters. In this paper, we introduce a clustering method named CPCA based on a recent observation by researchers that a protein complex in a PPI network is arranged as a relatively dense core region and additional proteins weakly connected to the core. CPCA uses two connectivity criterion functions to identify core and peripheral regions of the cluster. To locate initial node of a cluster we introduce a measure called DNQ (Degree based Neighborhood Qualification) index that evaluates tendency of the node to be part of a cluster. CPCA performs well when compared with well-known counterparts. Along with protein complex gold standards, a co-localization dataset has also been used for validation of the results.     

Ionic liquids from Car-Parrinello simulations, part I: liquid AlCl3

The properties of isolated AlCl3 clusters and the bulk system are investigated by means of static and dynamic electronic structure methods. We find important structural motifs with the edge connectivity dominant in a dimer and the corner connectivity dominant in a trimer. Furthermore, the trimer cluster exhibits an interesting ring structure with large cooperative effects relative to the dimer. Comparing the found structural motifs in isolated molecule calculations with the structure of the liquid allows us to determine the dominance of edge connectivity in the liquid. The size of the clusters present in the liquid indicates indeed that the dimer is the most abundant species, but there are also trimers, tetramers, and pentamers present. From the local dipole analysis both for the isolated clusters as well as for the liquid, further proof for the edge connectivity is given. However, all results point to the fact that there is also some small percentage of corner connectivity present that might be attributed to the most stable corner-connected cluster, namely the trimer. Importantly, we find that energetic considerations of isolated (static) clusters only do not represent the findings in liquid phase. Instead, a quantum cluster equilibrium approach or simulations are needed.     

Complete set of Hopf bifurcation in an autocatalytic ring network

We investigate the Hopf bifurcation for a five species chemical ring network with an autocatalytic reaction. We show that the bifurcation hypersurface in the rate constants space is the boundary of a simply connected set. We use a numerical method to calculate this hypersurface.     

Approach for the calculation of high‐order connectivity indices of polymers and its application

A method for the calculation of connectivity indices of polymers was developed that can be used to calculate any order connectivity indices of polymers in a consistent and unambiguous manner without any truncation errors. The proposed method makes it possible to correlate the physical properties of polymers in terms of connectivity indices of higher than first order, which may not only improve the correlation and prediction accuracy but also possibly eliminate the normally required atomic and group correction terms to develop more general correlations with reliable predictive capability. As an example, two correlations with connectivity indices up to the third order are proposed to correlate the thermal conductivities at room temperature for 20 amorphous polymers. The two proposed correlations give comparable or even better accuracy than the existing one, which requires connectivity indices up to the first order and an atomic correction term. Because only connectivity indices were used in the newly proposed correlations, they are general models with better predictive capability. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 401–407, 2002; DOI 10.1002/polb.10104     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.     

Comparative conformational studies of cyclic derivatives by 13C NMR spectroscopy

The ¹³C chemical shift of the substituted or functionalized carbon of various medium and large rings is plotted against ring size (6–15 carbons). The curves thus obtained allow a conformational analysis of the corresponding derivatives.     

改进的分子连接性方法

通过用Mulliken键级来加权分子连接性指数中的点价,使分子轨道理论与分子连接性指数有机地结合起来,将分子连接性指数改进成为一种量子拓扑指数。对比发现,分子连接性指数的点价与Mulliken键级具有相近的物理意义,而Mulliken键级更具有独特的优越性。利用改进的分子连接性指数对几种具有代表性的烃类与其体积、疏水常数以及热力学性质进行了关联,得到了满意的结果。     

Theory of the PCP effect and related phenomena

Recent studies of cyclic conjugation in the five-membered ring of acenaphthylene and fluoranthene congeners revealed some peculiar regularities, of which the so-called PCP effect attracted the greatest attention. The PCP effect is a significant increase in the magnitude of cyclic conjugation in the five-membered ring caused by the six-membered rings separated from the five-membered ring by a single carbon–carbon bond. We now present the mathematical formalism of a general theory capable of treating cyclic–conjugation phenomena of this kind, of which the PCP effect is just a special case. Namely we calculate the influence of any cycle present in a polycyclic conjugated molecule on the energy effect of cyclic conjugation of any other cycle.     

Structure and stability of the defect fullerene clusters of C60: C59, C58, and C57

We have performed density functional calculations for the structures and stabilities of various isomers of the defect fullerene clusters of C(60): C(59), C(58), and C(57). The C(59_)5-8, C(58_)5-5-7, and C(57_)4-5-9 clusters were calculated to be the most stable isomers of the C(59), C(58), and C(57) clusters, respectively. There are obvious relationships between structure and stability of the defect fullerene clusters. First, an unsaturated carbon atom favors being located at a 6-membered ring rather than a 5-membered ring. Second, the most stable isomers prefer to have newly formed 5-membered rings, rather than newly formed 4-membered rings.     

Optical response of small carbon clusters

We apply the time-dependent local density approximation (TDLDA) to calculate dipole excitations in small carbon clusters. A strong low-frequency mode is found which agrees well with observation for clusters C_n with n in the range 7–15. The size dependence of the mode may be understood simply as the classical resonance of electrons in a conducting needle. For a ring geometry, the lowest collective mode occurs at about twice the frequency of the collective mode in the linear chain, and this may also be understood in simple terms.     

NMR assignment methods for the aromatic ring resonances of phenylalanine and tyrosine residues in proteins

The unambiguous assignment of the aromatic ring resonances in proteins has been severely hampered by the inherently poor sensitivities of the currently available methodologies developed for uniformly 13C/15N-labeled proteins. Especially, the small chemical shift differences between aromatic ring carbons and protons for phenylalanine residues in proteins have prevented the selective observation and unambiguous assignment of each signal. We have solved all of the difficulties due to the tightly coupled spin systems by preparing regio-/stereoselectively 13C/2H/15N-labeled phenylalanine (Phe) and tyrosine (Tyr) to avoid the presence of directly connected 13C-1H pairs in the aromatic rings. The superiority of the new labeling schemes for the assignment of aromatic ring signals is clearly demonstrated for a 17 kDa calcium binding protein, calmodulin.     

Hypercoordinated carbon in C-doped boron fullerenes: a quantum chemical study

The structures and stability of C-doped boron fullerenes with the three-dimensional arrangement of non-classical pentacoordinated quasi-flat carbon centers were studied using the density functional theory (DFT) B3LYP/6-311+G(d,p) method. The doping with carbon atoms in apical positions above the five-membered rings stabilizes the spherical boron fullerene forms due to multicenter interactions of p_z-orbitals of the carbons and adjacent boron atoms. Increasing in the size of the fullerene cluster is accompanied by change in the bonding pattern and by flattening of the hypercoordinated carbon centers. Endohedral metal atoms significantly affect on the structure and stability of the fullerene systems with hypercoordinated carbon centers.     

Photodissociation of noble metal-doped carbon clusters

Noble metal carbide cluster cations (MC(n)(+), M = Cu, Au) are produced by laser vaporization in a pulsed molecular beam and detected with time-of-flight mass spectrometry. Copper favors the formation of carbides with an odd number of carbon atoms, while gold shows marked drops in ion intensity after clusters with 3, 6, 9, and 12 carbons. These clusters are mass selected and photodissociated at 355 nm. Copper carbides with an odd number of carbons fragment by eliminating the metal from the cluster; for the small species it is eliminated as Cu(+) and for the larger species it is lost as neutral Cu. Copper carbides with an even number of carbons also lose the metal, but in addition to this they eliminate neutral C(3). This even-odd alternation, with the even clusters having mixed fragments, holds true for clusters as large as CuC(30)(+). No loss of C(2) is observed for even the largest clusters studied, indicating that fullerene formation does not occur. The gold carbide photodissociation data closely parallel that of copper, with even clusters losing primarily C(3) and odd ones losing gold. Comparisons to known carbon cluster ionization potentials give some insight into the structures of carbon photofragments. DFT calculations performed on CuC(3-11)(+) allow comparisons of the energetics of isomers likely present in our experiment, and metal-carbon dissociation energies help explain the even-odd alternation in the fragmentation channels. The simplest picture of these metal-doped carbides consistent with all the data is that the small species have linear chain structures with the metal attached at the end, whereas the larger species have cyclic structures with the metal attached externally to a single carbon.     

Four-membered rings family in the Si–O extended rocking IR band from quantum chemistry calculations

We calculate the vibrational modes of four-membered rings family in the Si–O extended rocking infrared for vitreous SiO₂ materials. In particular these species are obtained in the early stages of the sol–gel process. We have performed high quality quantum-mechanical calculations based on cluster models and gradient corrected density functional theory, (GC-DFT). Three possible configurations were obtained, a regular planar, a slightly deformed or quasi-planar, and a deformed ring. According to our result, the more probable one is the slightly deformed configuration. The calculated vibrational frequencies are compared with experimental IR and Raman results obtaining very good agreement. Also, we calculated geometries and vibrational frecuencies for three-membered rings. We found that 3- and 4-fold rings show evidence of decoupled vibrational modes, those modes are compared with a Raman spectrum obtaining very good coincidence.     

CCSD calculations on C(14), C(18), and C(22) carbon clusters

The structure and energetics of the ring isomers of C(4n+2) (n=3-5) carbon clusters were studied by using coupled-cluster singles and doubles excitation theory to overcome the vast differences existing in the literature. The results obtained in the present study clearly indicate that C(14), C(18), and C(22) carbon rings have bond-length and bond-angle alternated acetylenic minimum energy structures. Contrarily, density functional theory calculations were unable to predict these acetylenic-type structures and they ended up with the cumulenic structures. It is found from the coupled-cluster studies that the lowest-energy ring isomer for the first two members of C(4n+2) series is a bond-angle alternated cumulenic D((2n+1)h) symmetry structure while the same for the remaining members is a bond-length and bond-angle alternated C((2n+1)h) symmetry structure. In C(4n+2) carbon rings, Peierls-type distortion, transformation from bond-angle alternated to bond-length alternated minimum energy structures, occurs at C(14) carbon ring.