The architecture and the Jones polynomial of polyhedral links

In this paper, we first recall some known architectures of polyhedral links (Qiu and Zhai in J Mol Struct (THEOCHEM) 756:163–166, 2005; Yang and Qiu in MATCH Commun Math Comput Chem 58:635–646, 2007; Qiu et al. in Sci China Ser B Chem 51:13–18, 2008; Hu et al. in J Math Chem 46:592–603, 2009; Cheng et al. in MATCH Commun Math Comput Chem 62:115–130, 2009; Cheng et al. in MATCH Commun Math Comput Chem 63:115–130, 2010; Liu et al. in J Math Chem 48:439–456 2010). Motivated by these architectures we introduce the notions of polyhedral links based on edge covering, vertex covering, and mixed edge and vertex covering, which include all polyhedral links in Qiu and Zhai (J Mol Struct (THEOCHEM) 756:163–166, 2005), Yang and Qiu (MATCH Commun Math Comput Chem 58:635–646, 2007), Qiu et al. (Sci China Ser B Chem 51:13–18, 2008), Hu et al. (J Math Chem 46:592–603, 2009), Cheng et al. (MATCH Commun Math Comput Chem 62:115–130, 2009), Cheng et al. (MATCH Commun Math Comput Chem 63:115–130, 2010), Liu et al. (J Math Chem 48:439–456, 2010) as special cases. The analysis of chirality of polyhedral links is very important in stereochemistry and the Jones polynomial is powerful in differentiating the chirality (Flapan in When topology meets chemistry. Cambridge Univ. Press, Cambridge, 2000). Then we give a detailed account of a result on the computation of the Jones polynomial of polyhedral links based on edge covering developed by Jin, Zhang, Dong and Tay (Electron. J. Comb. 17(1): R94, 2010) and, at the same time, by using this method we obtain some new computational results on polyhedral links of rational type and uniform polyhedral links with small edge covering units. These new computational results are helpful to judge the chirality of polyhedral links based on edge covering. Finally, we give some remarks and pose some problems for further study.     

Structure and Reactivity of the <Emphasis Type="BoldItalic">N</Emphasis>-Acetyl-Cysteine Radical Cation and Anion: Does Radical Migration Occur?

The structure and reactivity of the N-acetyl-cysteine radical cation and anion were studied using ion-molecule reactions, infrared multi-photon dissociation (IRMPD) spectroscopy, and density functional theory (DFT) calculations. The radical cation was generated by first nitrosylating the thiol of N-acetyl-cysteine followed by the homolytic cleavage of the S–NO bond in the gas phase. IRMPD spectroscopy coupled with DFT calculations revealed that for the radical cation the radical migrates from its initial position on the sulfur atom to the α-carbon position, which is 2.5 kJ mol^–1 lower in energy. The radical migration was confirmed by time-resolved ion-molecule reactions. These results are in contrast with our previous study on cysteine methyl ester radical cation (Osburn et al., Chem. Eur. J. 2011 , 17, 873–879) and the study by Sinha et al. for cysteine radical cation (Phys. Chem. Chem. Phys. 2010 , 12, 9794–9800) where the radical was found to stay on the sulfur atom as formed. A similar approach allowed us to form a hydrogen-deficient radical anion of N-acetyl-cysteine, (M – 2H) ^•– . IRMPD studies and ion-molecule reactions performed on the radical anion showed that the radical remains on the sulfur, which is the initial and more stable (by 63.6 kJ mol^–1) position, and does not rearrange.     

Three-propeller-blade-shaped electride: remarkable alkali-metal-doped effect on the first hyperpolarizability

Significant alkali-metal-doped effects on the structure and the first hyperpolarizability (β ₀) of effective multi-nitrogen complexant tris[(2-imidazolyl)methyl]amine (TIMA) are investigated. Three imidazoles of TIMA like three blades of propeller connect with methyls by the C–C single bonds. Because of the three C–C single-bond cooperative rotations, the TIMA behaves with great flexibility, and it is a high-performance multi-nitrogen complexant for the alkali metal doping. Thus, the new complexes A_m-TIMA (A_m = Li, Na, and K) with electride characteristic have diffuse excess electron than the reported electride-type system due to the strong interaction between the complexant TIMA and alkali metal. For the first hyperpolarizability, three engaging electrides A_m-TIMA with the diffuse excess electrons exhibit considerably large β ₀ values using the MP2 (full) method and the β ₀ values of new electrides are greatly larger (3,464–29,705 times) than that (338 au) of TIMA. Surprisingly, the K-TIMA sets a new record β ₀ value to be 1.00 × 10⁷ au which far exceeds than that (3,694–76,978 au) of the reported electride-type system Li@calix[4]pyrrole (J Am Chem Soc 127:10977–10981, 2005) and Li_n−H−(CF₂−CH₂)₃−H (n = 1, 2) (J Am Chem Soc 129:2967–2970, 2007) and 31,123 au of the organometallic system (J Am Chem Soc 121:4047–4053, 1999) Ru(trans-4,4′-diethylaminostyryl-2,2′-bipyridine)₃²⁺, as well as 1.23 × 10⁶ au of the large donor-CNT systems (Nano Lett 8:2814–2818, 2008). Clearly, the alkali-metal-doped effect on the first hyperpolarizability is very dramatic for the high-performance multi-nitrogen complexant TIMA. Considering simple possibility from molecule to material, the β ₀ values of optimized Li-TIMA-dimer and Li-TIMA-tetramer are investigated by BHandHLYP method. Interestingly, results show that the order of β ₀ value is Li-TIMA-monomer < Li-TIMA-dimer < Li-TIMA-tetramer. So the new three-propeller-blade-shaped electrides can be considered as candidates for high-performance nonlinear optical materials.     

Rearrangement Pathways of the <Emphasis Type="BoldItalic">a</Emphasis><Subscript><Emphasis Type="BoldItalic">4</Emphasis></Subscript> Ion of Protonated YGGFL Characterized by IR Spectroscopy and Modeling

The structure of the a ₄ ion from protonated YGGFL was studied in a quadrupole ion trap mass spectrometer by ‘action’ infrared spectroscopy in the 1000–2000 cm^–1 (‘fingerprint’) range using the CLIO Free Electron Laser. The potential energy surface (PES) of this ion was characterized by detailed molecular dynamics scans and density functional theory calculations exploring a large number of isomers and protonation sites. IR and theory indicate the a ₄ ion population is primarily populated by the rearranged, linear structure proposed recently (Bythell et al., J. Am. Chem. Soc. 2010, 132, 14766). This structure contains an imine group at the N- terminus and an amide group –CO–NH₂ at the C-terminus. Our data also indicate that the originally proposed N-terminally protonated linear structure and macrocyclic structures (Polfer et al., J. Am. Chem. Soc. 2007, 129, 5887) are also present as minor populations. The clear differences between the present and previous IR spectra are discussed in detail. This mixture of gas-phase structures is also in agreement with the ion mobility spectrum published by Clemmer and co-workers recently (J. Phys. Chem. A 2008, 112, 1286). Additionally, the calculated cross-sections for the rearranged structures indicate these correspond to the most abundant (and previously unassigned) feature in Clemmer’s work.     

Solid state kinetics of Cu(II) complex of [2-(1,2,3,4-thiatriazole-5-yliminomethyl)-phenol] from thermo gravimetric analysis

The ligand [2-(1,2,3,4-thiatriazole-5-yliminomethyl)-phenol] (L) is a schiff base derived from condensation reaction of 1,2,3,4-thiatriazole-5-ylamine and Salicylaldehyde. Synthesis of the ligand (L) and the complex [Cu(II)(L)₂]·2H₂O have been studied in our previous work (Bharti et al., Asian J Chem 23(2):773–776, 2011). Thermal decomposition behavior of synthesized Cu(II) complex has been investigated by thermo gravimetric (TG) analysis at heating rate of 10 °C min⁻¹ under nitrogen atmosphere. The mechanism of decomposition of Cu(II) complex has been established from TG data. Kinetic parameters such as order of reaction (n), activation energy (E _a), frequency factor (Z) and entropy of activation (∆S ^≠) were calculated by using Freeman and Carroll (J Phys Chem 62:394–397, 1958) as well as Doyle’s methods as modified by Zsako (J Phys Chem 72(7):2406–2411, 1968).     

Long cycles in fullerene graphs

It is conjectured that every fullerene graph is hamiltonian. Jendrol’ and Owens proved [J. Math. Chem. 18 (1995), pp. 83–90] that every fullerene graph on n vertices has a cycle of length at least 4n/5. In this paper we, improve this bound to 5n/6 − 2/3.     

Kinetics for tautomerizations and dissociations of triglycine radical cations

Fragmentations of tautomers of the α-centered radical triglycine radical cation, [GGG^•]⁺, [GG^•G]⁺, and [G^•GG]⁺, are charge-driven, giving b-type ions; these are processes that are facilitated by a mobile proton, as in the fragmentation of protonated triglycine (Rodriquez, C. F. et al. J. Am. Chem. Soc. 2001, 123, 3006–3012). By contrast, radical centers are less mobile. Two mechanisms have been examined theoretically utilizing density functional theory and Rice-Ramsperger-Kassel-Marcus modeling: (1) a direct hydrogen-atom migration between two α-carbons, and (2) a two-step proton migration involving canonical [GGG]^•+ as an intermediate. Predictions employing the latter mechanism are in good agreement with results of recent CID experiments (Chu, I. K. et al. J. Am. Chem. Soc. 2008, 130, 7862–7872).     

Comparison of Reliability of log P Values Calculated from a Group Contribution Approach and from the Autocorrelation Method

Abstract

The values of log P (n-octanol/water partition coefficient) for 1449 chemicals were calculated from the fragmental/regression model of Klopman and co-workers (J. Chem. Inf. Comput. Sci. 1994, 34, 752-781) and from the autocorrelation/backpropagation neural network model implemented in AUTOLOGP_TM (Version 4.0). Both models provided good simulation results but the superiority of the latter was demonstrated.     

Numbers of faces in disordered patches

It has been shown that the boundary structure of patches with all faces of the same size k, all interior vertices of the same degree m and all boundary vertices of degree at most m determines the number of faces of the patch (Brinkmann et al., Graphs and discovery, 2005; Guo et al., Discrete Appl Math 118(3):209–222, 2002). In case of at least two defective faces, that is faces with degree k′ ≠ k, it is well known that this is not the case. The most famous example for this is the Endo–Kroto C ₂-insertion (Endo and Kroto, J Phys Chem 96:6941–6944, 1992). Patches with alimited amount of disorder are especially interesting for the case k = 6, m = 3 and k′ = 5. This case corresponds to polycyclic hydrocarbons with a limited number of pentagons and to subgraphs of fullerenes. The last open question was the case of exactly one defective face or vertex. In this paper we generalize the results of Brinkmann et al. (2005) and Guo et al. (2002) and in some cases corresponding to Euclidean lattices also deal with patches that have vertices of degree larger than m on the boundary, have sequences of degrees on the boundary that are identical only modulo m and have vertex and face degrees in the interior that are multiples of m, resp. k. Furthermore we prove that in case of at most one defective face with a degree that is not a multiple of k the number of faces of a patch is determined by the boundary. This result implies that fullerenes cannot grow by replacing patches of a restricted size.