Ab initio periodic study of the conformational behavior of glycine helical homopeptides

Representative helicoidal conformations of polyglycine infinite chains have been investigated by using periodic boundary conditions, the B3LYP hybrid functional, and large basis sets, by means of the CRYSTAL code. The exploitation of the helix roto‐translational symmetry permits to optimize at a relatively low cost the structure of systems whose unit cell contains more than 300 atoms, much larger than the one investigated till now. In the present calculations, the helix symmetry is exploited at three levels. First, for the automatic generation of the structure. Second, for the calculation of the one‐ and two‐electron integrals that enter into the Fock matrix definition. Only the irreducible wedge of the Fock matrix is computed. Finally, for the diagonalization of the Fock matrix, where each irreducible representation is separately treated. The efficiency and accuracy of the computational scheme are documented, by considering cells containing up to 47 glycine residues. Results are compared with previous calculations and available experimental data. The role of hydrogen bonding in stabilizing polyglycine conformers is also addressed. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Melamine as an Effective Supramolecular Modifier and Stabilizer in a Nanotube‐Constituted Supergel

Self‐assembly of N‐fluorenyl‐9‐methoxycarbonyl glutamic acid (Fmoc‐Glu) in water generates metastable single‐wall nanotubes. These nanotubes entangle and bundle together to form unstable gels that shrink with time and finally result in lamellar crystalline precipitates. Melamine (Mm) was employed as a supramolecular modifier and stabilizer to improve the stability of the nanotubes. Mm interacts with the carboxyl‐rich surfaces of the nanotubes via H‐bonds and static electronic forces to diminish the high affinity of individual nanotubes and facilitate Fmoc‐Glu supergelation (critical gelation concentration <0.1 wt %). Although the basic process of nanotube formation is not disturbed, Mm inverts the supramolecular helicity of nanotubes from P to M.     

Boron‐Double‐Ring Sheet,Fullerene, and Nanotubes: Potential Hydrogen Storage Materials

Similar to carbon‐based graphene, fullerenes and carbon nanotubes, boron atoms can form sheets, fullerenes, and nanotubes. Here we investigate several of these novel boron structures all based on the boron double ring within the framework of density functional theory. The boron sheet is found to be metallic and flat in its ground state. The spherical boron cage containing 180 atoms is also stable and has I symmetry. Stable nanotubes are obtained by rolling up the boron sheet, and all are metallic. The hydrogen storage capacity of boron nanostructures is also explored, and it is found that Li‐decorated boron sheets and nanotubes are potential candidates for hydrogen storage. For Li‐decorated boron sheets, each Li atom can adsorb a maximum of 4 H₂ molecules with g_d=7.892 wt %. The hydrogen gravimetric density increases to g_d=12.309 wt % for the Li‐decorated (0,6) boron nanotube.     

Algebraic solutions for the octahedral group: Group chain O⊃C4

Using double‐induced representation and eigenfunction method, algebraic expressions are derived for irreducible matrices, projection operators, and symmetry‐adapted functions in the group chain O⊃C₄ for both single‐valued and double‐valued representations. The simplicity of these expressions lies in the fact that they are functions of the quantum numbers of the corresponding group chain (the analogy of j, m for the group chain SO₃⊃SO₂) instead of the irreducible matrix elements. The symmetries of the symmetry‐adapted functions are disclosed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 7–22, 1999     

Analytical irreducible representation bases of the single and double icosahedral groups and their applications

An equivalent basis of icosahedral molecules is introduced in which the basis functions can be transformed under the operations in the icosahedral group (I_h). In this equivalent basis, the irreducible representation basis (IRB) of I_h, including the double‐valued IRB of I, is deduced analytically based on the method introduced in the literature [J. Comput. Chem. 17 , 851 (1996)]. Therefore the concepts of symmetry‐matrix and symmetry‐supermatrix can be used in the single‐ and multiconfiguration self‐consistent field methods (including relativistic effects) to reduce the storage of two‐electron integrals and calculations of Fock matrix during iterations by a factor of ca. 10,000. In addition, the equivalent basis of I_h can also be used to reduce the calculations of atoms and representations of rank ≥ 2 tensors. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 615–624, 2000     

Phase separation of polymer‐functionalized SWNTs within a PMMA/polystyrene blend

Phase separation of polystyrene (PS) and poly(methyl methacrylate) (PMMA) blends was used as a means to segregate PS‐ or PMMA‐functionalized single‐walled carbon nanotubes (SWNTs) in thin films. Dilute solutions (5 wt % in THF) of 1:1 PS/PMMA blends containing the functionalized nanotubes were spin cast and annealed at 180 °C for 12 h. Two different polymer molecular weights were used (M_n = 8000 or M_n = 22,000), and were of approximately equivalent molecular weight to those attached to the surface of the nanotubes. Nanotube functionalization was accomplished using the Cu(I)‐catalyzed [3 + 2] Huisgen cycloaddition, in which alkyne‐decorated nanotubes were coupled with azide‐terminated polymers, resulting in polymer‐SWNT conjugates that were soluble in THF. Characterization of the annealed films by scanning Raman spectroscopy, which utilized the unique Raman fingerprint of carbon nanotubes, enabled accurate mapping of the functionalized SWNTs within the films relative to the two phase‐separated polymers. It was found that nanotube localization within the phase‐separated polymer films was influenced by the type of polymer attached to the nanotube surface, as well as its molecular weight. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 450–458, 2009     

Ab initio study of organic mixed valency

A series of six radical cations of the type (D L D)⁺ was investigated at the ab initio unrestricted Hartree–Fock level. One localized and one delocalized conformation were systematically searched by full geometry optimization. At both nuclear arrangements, mostly found as being minima in the symmetry‐restrained Hartree–Fock framework, excitation energies were calculated through the expansion of the wave function on single electronic excitations of the Hartree–Fock fundamental determinant and at the unrestricted Hartree–Fock or at the multiconfigurational self consistent field levels. Few calculations were also performed by taking into account some part of the electronic correlation. Except for N,N,N′,N′‐tetramethyl p‐phenylenediamine, all the studied compounds are localized stable cations, at the symmetry‐restrained Hartree–Fock level. However, the reoptimization of their wave function changes this observation since only three of them seem to conserve a localized stable conformation. Most of the studied systems are characterized by one or two excited electronic states very close to the fundamental one and should thus present an unresolved broadened first absorption band in the near‐infrared region. These features are in agreement with the available experimental data. Strong Hartree–Fock instabilities are found for the delocalized structure and put in relation with the existence of the large nonadiabatic coupling in this conformational region. The solvent influence is discussed in the Onsager dipolar reaction field framework. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 552–573, 2000     

The effect of molecular weight on the separation of semiconducting single‐walled carbon nanotubes using poly(2,7‐carbazole)s

The use of selective interactions between conjugated polymers and single‐walled carbon nanotubes has emerged as a promising method for the separation of nanotubes by electronic type. Although much attention has been devoted to investigating polyfluorenes and their ability to disperse semiconducting carbon nanotubes under specific conditions, other polymer families, such as poly(2,7‐carbazole)s, have been relatively overlooked. Poly(2,7‐carbazole)s have been shown to also preferentially interact with semiconducting carbon nanotubes, however a detailed investigation of polymer parameters, such as molecular weight, has not been performed. We have prepared seven different molecular weights of a poly(2,7‐carbazole), from short chain oligomers to high molecular weight polymers, and have investigated their effectiveness at dispersing semiconducting single‐walled carbon nanotubes. Although all polymer chain lengths were able to efficiently exfoliate carbon nanotube bundles using a mild dispersion protocol, only polymers above a certain threshold molecular weight (M_n ～ 27 kDa) were found to exhibit complete selectivity for semiconducting nanotubes, with no observable signals from metallic species. Additionally, we found the quality of separation to be strongly dependent on the ratio of polymer to carbon nanotube. Contrary to previous reports, we have found that an excess of poly(2,7‐carbazole) leads to incomplete removal of metallic carbon nanotubes. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2510–2516     

Synthesis and Properties of Porphyrin Nanotubes

Discrete π‐conjugated zinc porphyrin nanotubes are investigated as molecular analogues of carbon nanotubes. These porphyrin nanotubes have a diameter of 2.4 nm (Zn–Zn distance) and lengths of up to 3.6 nm, measured to the van der Waals surfaces of the outer β‐pyrrole hydrogen atoms, or 4.5 nm measured to the para hydrogen atoms of the aryl groups. We explore three different strategies for synthesizing these nanotubes. The first two strategies use a template to achieve direct or sequential stave‐joining, respectively, and proceed via linear oligomers that pre‐define the length of the nanotube. These strategies are applied to synthesize porphyrin nanotubes containing 12‐ or 18‐porphyrin subunits, with ethynylene (C₂) or butadiynylene (C₄) links between the 6‐porphyrin nanorings. The third strategy involves the covalent stacking of pre‐formed 6‐porphyrin nanorings to form a 12‐porphyrin nanotube, without using a template to guide this coupling reaction. The nanotubes show strongly red‐shifted absorption spectra and low fluorescence quantum yields, indicating structural rigidity and extensive π‐conjugation.     

Unitary group approach to spin-adapted open-shell coupled cluster theory

We show that the irreducible tensor operators of the unitary group provide a natural operator basis for the exponential Ansatz which preserves the spin symmetry of the reference state, requires a minimal number of independent cluster amplitudes for each substitution order, and guarantees the invariance of the correlation energy under unitary transformations of core, open-shell, and virtual orbitals. When acting on the closed-shell reference state with n_c doubly occupied and n_v unoccupied (virtual) orbitals, the irreducible tensor operators of the group U(n_c) ? U(n_V) generate all Gelfand-Tsetlin (GT) states corresponding to appropriate irreducible representation of U(n_c + n_v). The tensor operators generating the M-tuply excited states are easily constructed by symmetrizing products of M unitary group generators with the Wigner operators of the symmetric group S_M. This provides an alternative to the Nagel-Moshinsky construction of the GT basis. Since the corresponding cluster amplitudes, which are also U(n_c) ? U(n_s) tensors, can be shown to be connected, the irreducible tensor operators of U(n_c) ? U(n_v) represent a convenient basis for a spin-adapted full coupled cluster calculation for closed-shell systems. For a high-spin reference determinant with n, singly occupied open-shell orbitals, the corresponding representation of U(n), n=n_c + n_v + n_s is not simply reducible under the group U(n_c) ? U(n_s) ? U(n_v). The multiplicity problem is resolved using the group chain U(n) ? U(n_c + n_v) ? U(n_s) ? U(n_c) ?U(n_s)? U(n_v) ? U(n_v). The labeling of the resulting configuration-state functions (which, in general, are not GT states when n_c > 1) by the irreducible representations of the intermediate group U(n_c + n_v) ?U(n_s) turns out to be equivalent to the classification based on the order of interaction with the reference state. The irreducible tensor operators defined by the above chain and corresponding to single, double, and triple substitutions from the first-, second-, and third-order interacting spaces are explicitly constructed from the U(n) generators. The connectedness of the corresponding cluster amplitudes and, consequently, the size extensivity of the resulting spin-adapted open-shell coupled cluster theory are proved using group theoretical arguments. The perturbation expansion of the resulting coupled cluster equations leads to an explicitly connected form of the spin-restricted open-shell many-body perturbation theory. Approximation schemes leading to manageable computational procedures are proposed and their relation to perturbation theory is discussed. © 1995 John Wiley & Sons, Inc.     

A novel two‐dimensional nickel(II) coordination polymer with 1,4‐bis(1,2,4‐triazol‐1‐ylmethyl)benzene and azide ligands

The coordination geometry of the Ni^II atom in the title complex, poly[diazidobis[μ‐1,4‐bis(1,2,4‐triazol‐1‐ylmethyl)benzene‐κ²N⁴:N^4′]nickel(II)], [Ni(N₃)₂(C₁₂H₁₂N₆)₂]_n, is a distorted octahedron, in which the Ni^II atom lies on an inversion centre and is coordinated by four N atoms from the triazole rings of two symmetry‐related pairs of 1,4‐bis(1,2,4‐triazol‐1‐ylmethyl)benzene (bbtz) ligands and two N atoms from two symmetry‐related monodentate azide ligands. The Ni^II atoms are bridged by four bbtz ligands to form a two‐dimensional (4,4)‐network.     

On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

The symmetry properties of the mono- and bielectronic terms contributing to the Fock matrix in the ab initio Hartree–Fock treatment of periodic systems are discussed. A computational scheme which takes full advantage of the point symmetry is presented; in this respect, it represents a generalization of the scheme proposed in Int. J. Quantum Chem. 17 , 501 (1980). Computational details and numerical examples are reported; it is shown that with respect to two of the bottlenecks of this kind of calculation, namely, computer time and backing storage required for the bielectronic integrals, it is possible to obtain saving factors as large as h and h², respectively, where h is the order of the point group. Preliminary tests are reported which indicate that the study of relatively complicated systems, like quartz or corundum (9 and 10 atoms in the unit cell, respectively) at an ab initio Hartree–Fock level is now within reach.     

The Fock Matrix Analysis for Atomic Orbitals in Molecular Orbitals II. The Electronic Structure of N2 Molecules

Weinhold's natural hybrid orbitals can be chosen as the molecular adapted atomic orbitals to build the canonical molecular orbitals of N₂ molecules. The molecular Fock matrix expanded in the natural hybrid orbitals can reveal deeper insight of the electronic structure and reaction of the N₂ molecule. For example, the magnitude of F_ab can signify the bonding character of the paired electrons as well as the diradical character of the unpaired electrons for both σ‐ and π‐types. Discarding the concept of the overlap between non‐orthogonal atomic orbitals, the different orbitals for different spins in the unrestricted Hartree‐Fock wavefunction reveal that there are three pairs of opposite spin density flows between two atoms, which proceed until the bonding molecular orbitals form.     

Complete TDA and RPA Calculations on the Electronic Transitions of Fullerene‐C60 in the CNDO/S and INDO/S Approximations*

Complete single‐excitation mixing calculations on the electronic transitions of the icosahedral C₆₀ molecule have been carried out with the Tamm–Dancoff approximation (TDA) and random‐phase approximation (RPA) schemes in the CNDO/S and INDO/S approximations. The complete space of 14,400 (1p–1h) pairs is partitioned into subspaces classified according to the irreducible representations of the Ih group. For this purpose, matrix representations of the group generators are obtained on a fixed set of basis functions and are used to construct the projection operators. Degenerate molecular orbitals in each energy level are symmetry‐adapted to these projection operators. Degenerate (1p–1h) pairs or singly excited configuration wave functions are similarly symmetrized. In addition, the Clebsch–Gordan coefficients are obtained and listed in an Appendix. The TDA and RPA equations are then solved for each irreducible representation separately. Both schemes with the projection operators and with the Clebsch–Gordan coefficients gave the same results as expected, indicating that the calculations were correctly done. The transition energies from the ground state 1¹A_g to low‐lying singlet and triplet excited states and the oscillator strengths for the allowed transitions (n¹T_1u–1¹A_g) are given in tables. A proper way to normalize is discussed for the eigenvectors of the RPA‐type matrix equation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Algebraic solutions for point groups: The octahedral group for the group chain O⊃T⊃C3

Using the right‐induced technique and the eigenfunction method, concise algebraic expressions of the projection operators for both single‐valued and double‐valued representations are found for the group chain O?T?C₃ in terms of the projection operators of T?C₃. Extremely simple relations are discovered between the symmetry adapted functions (SAFs) of the groups T and O; namely the SAFs of the subgroup T which have proper symmetry are the SAFs of the group O. The projection operators and SAFs are functions of only the quantum numbers of the group chain [the analogy of ( j,m) for the group chain SO₃?SO₂], without involving any irreducible matrix elements. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 259–270, 2001     

(2,2′‐Biquinoline‐κ2N,N′)dichloropalladium(II), ‐copper(II) and ‐zinc(II)

In the three title complexes, namely (2,2′‐biquinoline‐κ²N,N′)dichloro­palladium(II), [PdCl₂(C₁₈H₁₂N₂)], (I), and the corresponding copper(II), [CuCl₂(C₁₈H₁₂N₂)], (II), and zinc(II) complexes, [ZnCl₂(C₁₈H₁₂N₂)], (III), each metal atom is four‐coordinate and bonded by two N atoms of a 2,2′‐biquinoline molecule and two Cl atoms. The Pd^II atom has a distorted cis‐square‐planar coordination geometry, whereas the Cu^II and Zn^II atoms both have a distorted tetra­hedral geometry. The dihedral angles between the N—M—N and Cl—M—Cl planes are 14.53 (13), 65.42 (15) and 85.19 (9)° for (I), (II) and (III), respectively. The structure of (II) has twofold imposed symmetry.     

The infinite double‐stranded chain polymer catena‐poly­[[bis­(dicyan­amido)­zinc(II)]‐di‐μ‐1,2‐bis(1,2,4‐triazol‐1‐yl)­ethane‐κ4N4:N4′]

The coordination geometry of the Zn^II atom in the title complex, [Zn(C₂N₃)₂(C₆H₈N₆)₂]_n or [Zn(dca)₂(bte)₂]_n, where bte is μ‐1,2‐bis(1,2,4‐triazol‐1‐yl)­ethane and dca is dicyan­amide, is distorted compressed octahedral, in which the Zn^II atom lies on an inversion center and coordinates four N atoms from the triazole rings of four symmetry‐related bte ligands and two N atoms from two symmetry‐related monodentate dca ligands. The structure is polymeric, with 18‐membered spiro‐fused rings extending in the b direction and each 18‐membered ring involving two inversion‐related bte mol­ecules.     

The role of the medium in electrochemical functionalization and dispersion of carbon nanotubes

An electrochemical method for dispersion of single-walled carbon nanotubes (SWNTs) is described. The technique is based on grafting of oxygen-containing functional groups to the nanotube surface during electrolysis in aqueous and nonaqueous potassium bromide solutions. A dependence of the degree of functionalization of nanotubes on the solvent was revealed experimentally. Nanotubes treated in DMSO have about 14 carbon atoms per oxygen atom from functional groups (cf. nearly four C atoms per oxygen atom in the nanotubes treated in aqueous solutions). The corresponding maximum specific capacities of the electrodes are nearly 10 and 60 F g⁻¹. The samples treated in solutions of KBr in DMSO have about 300 carbon atoms per bromine atom on the nanotube surface (cf. only 30 carbon atoms in the samples treated in aqueous solution). A mechanism of electrochemical modification of SWNTs is proposed. Its key step is production of atomic oxygen that oxidizes the nanotube surface with the formation of functional groups.     

The layered compound poly[μ2‐4,4′‐bipyridyl‐di‐μ2‐chlorido‐mercury(II)]

The title compound, [HgCl₂(C₁₀H₈N₂)]_n, features two‐dimensional [HgCl₂(4,4′‐bipy)]_n neutral networks (4,4′‐bipy is 4,4′‐bipyridine), based on an octahedral Hg atom coordinated by four μ₂‐Cl atoms and two μ₂‐4,4′‐bipy ligands in trans positions, yielding a HgCl₄N₂ octahedron. The structure has mmm symmetry about the Hg atoms, with most of the atoms on at least one mirror plane, but the unsubstituted C atoms of the 4,4′‐bipy rings are disordered across a mirror plane. Photoluminescent investigations reveal that the title compound displays a strong emission in the green region, which probably originates from a ligand‐to‐ligand charge‐transfer transition.