A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.     

Vibrational contributions to the second-order nonlinear optical properties of π-conjugated structure acetoacetanilide

FT-Raman and IR spectra of the nonlinear optic (NLO) crystal, acetoacetanilide have been recorded and analyzed. The detailed interpretation of the vibrational spectra has been carried out with the aid of normal coordinate analysis (NCA) following the scaled quantum mechanical force field methodology. The various intramolecular interactions that is responsible for the stabilization of the molecule was revealed by natural bond orbital analysis. The Kurtz and Perry powder reflection technique appeared to be very effective in studies of second-order nonlinear optical properties of the molecule.     

Polymer additive analysis by pyrolysis-gas chromatography. I. Plasticizers

Plasticizers are widely used in thermoplastic polymers to modify their physical properties and processibility. Plasticizers as well as most of the other additives in the polymer can be qualitatively analyzed by pyrolysis-gas chromatography (Py-GC) simultaneously with the polymer composition. The key to the successful analysis of plasticizers not only requires a comprehensive understanding of commercial plasticizers but also requires knowledge of the polymer and its applications, as well as the Py-GC technique. In this study, several plasticizers in different polymeric systems were studied to demonstrate the utility of Py-GC as a good tool for the characterization of these systems. The advantages of using Py-GC for plasticizer analysis are also discussed.     

Parallelization of the deMon2k code

The parallelization of the LCGTO-KS-DFT code deMon2k is presented. The parallelization of the three-center electron repulsion integrals, the numerical integration using a direct grid algorithm and the matrix multiplication and diagonalization are described. The efficiency of the parallelization is analyzed by selected benchmark calculations. It is shown that geometry optimizations of systems with more than 8,000 basis functions are feasible on cluster architectures.     

A normal coordinate analysis of monomethylhydrazine and its bidentate nickel (II) chloride complex

A full normal coordinate analysis (NCA) has been carried out on monomethylhydrazine and N-deuterated monomethylhydrazine. The C_3ν symmetry of the methyl group is lost; nevertheless the concept of specific methyl group modes is still valuable. The NN stretching mode is relatively pure enabling it to be used as a criteria of coordination. An NCA has also been carried out for the bidentate nickel complex NiCl₂(NH₂NHCH₃)₂. Interesting effects are observed for the wagging and twisting modes of the NH₂ group on coordination.     

Six-dimensional vibrational analysis of coupled intermolecular vibrations in a binary cluster

We report on full- (six-) dimensional calculations of the intermolecular vibrations of a binary aromatic-solvent cluster. An exact Hamiltonian for this kind of interaction is modified in a general manner in order to perform calculations of molecules without symmetry. The binary cluster phenol(H2O)1 is used as a test case since its intermolecular vibrations are anharmonic and highly coupled. The formulation of the Schrodinger equation leads to a complex-valued eigenvalue problem with a dimension larger than two million, which is solved by filter diagonalization to obtain both eigenvalues and eigenvectors. With the knowledge of the eigenvectors, an interpretation of all eigenvalues is possible by a characterization with pseudoquantum numbers that are related to the widely used nomenclature of intermolecular normal motions in aromatic(solvent) clusters.     

A coherent discrete variable representation method for multidimensional systems in physics

A coherent discrete variable representation (ZDVR) is proposed for constructing a multidimensional potential-optimized DVR basis. The multidimensional quadrature pivots are obtained by diagonalizing a complex coordinate operator matrix in a finite basis set, which is spanned by the lowest eigenstates of a two-dimensional reference Hamiltonian. Here a c-norm condition is used in the diagonalization procedure. The orthonormal eigenvectors define a collocation matrix connecting the localized ZDVR basis functions and the finite basis set. The method is applied to two vibrational models for computing the lowest bound states. Results show that the ZDVR method provides exponential convergence and accurate energies. Finally, a zeroth-order approximation method is also derived.     

New algorithms for iterative matrix‐free eigensolvers in quantum chemistry

New algorithms for iterative diagonalization procedures that solve for a small set of eigen‐states of a large matrix are described. The performance of the algorithms is illustrated by calculations of low and high‐lying ionized and electronically excited states using equation‐of‐motion coupled‐cluster methods with single and double substitutions (EOM‐IP‐CCSD and EOM‐EE‐CCSD). We present two algorithms suitable for calculating excited states that are close to a specified energy shift (interior eigenvalues). One solver is based on the Davidson algorithm, a diagonalization procedure commonly used in quantum‐chemical calculations. The second is a recently developed solver, called the “Generalized Preconditioned Locally Harmonic Residual (GPLHR) method.” We also present a modification of the Davidson procedure that allows one to solve for a specific transition. The details of the algorithms, their computational scaling, and memory requirements are described. The new algorithms are implemented within the EOM‐CC suite of methods in the Q‐Chem electronic structure program. © 2014 Wiley Periodicals, Inc.     

The structure of water in polymer systems as revealed by Raman spectroscopy

A review on the structure of water in aqueous polymer systems as revealed by Raman spectroscopy is presented. Various interpretations and analysis procedures for Raman bands of liquid water which have been proposed are introduced. The structure and hydrogen-bonding properties of water which exist in aqueous polymer solutions and gels are described. Effects of chemical properties of polymer chains and size of water domains surrounded by polymer chains on the structure of water are discussed.     

Numerical generation of hyperspherical harmonics for tetra-atomic systems

A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates-a hyper-radius and eight angles-is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles. The remaining two-angle harmonics defined in kinematic invariant space are expanded in a basis of trigonometric functions, and the diagonalization of the kinetic energy operator in this basis provides highly accurate harmonics. This trigonometric basis is chosen to provide a mathematically exact and finite expansion for the harmonics. Individually, each basis function does not satisfy appropriate boundary conditions at the poles of the kinetic energy operator; however, the numerically generated linear combination of these functions which constitutes the harmonic does. The size of this basis is minimized using the symmetries of the system, in particular, internal symmetries, involving different sets of coordinates in nine-dimensional space corresponding to the same physical configuration.     

Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules

The use of energy selected bases (ESB) with iterative diagonalization of the Hamiltonian matrix is described for vibrations of tetra-atomic systems. The performance of the method is tested by computing vibrational states of HOOH below 10,000 cm(-1) (1296 A+ symmetry states) and H(2)CO below 13,500 cm(-1) (729 A(1) symmetry states). For iterative solutions, we tested both the implicitly restarted Lanczos method (IRLM) and the standard (nonreorthogonalizing) Lanczos approach. Comparison with other contracted basis approach as well as direct product grid representation shows superior performance of the ESB/IRLM approach. Of the two systems, H(2)CO is found to be more challenging than HOOH since it has much stronger couplings among vibrational modes, which leads to a drastically larger primitive basis set. For H(2)CO we also discuss some interesting behavior of the molecule in the high internal energy regime.     

The molecular dynamics problem in multiphoton excitation

While the molecular dynamics for weakly coupled, harmonic oscillators undergoing infinitesimal amplitude displacements are well described by normal modes, and the other extreme — strongly coupled anharmonic, large amplitude oscillating units can be treated as though they are ergodic systems, so that only state densities are needed, intermediate cases are very difficult to analyze. Here we propose that some intermediate cases, wherein we seek relative rates for reaction induced by specific frequency excitation (three-center displacement reactions or dissociation), may be approximately estimated from a normal mode analysis by calculating increment in root mean square amplitudes for a suitable internal coordinate, upon specific multiple photon absorption. A test case is presented as an illustration.     

On subspectral problem—benzenoid hydrocarbons with common eigenvalues ±1

Summary The method for the contraction and expansion of graphs is used to treat the subspectrality of benzenoid hydrocarbons in relation to eigenvalues ±1. Counts of benzenoid hydrocarbons together with degeneracies of eigenvalues have been carried out for all species having h 7 hexagons. In addition, twelve homologous series are evaluated, and the closed results for the distribution of eigenvalues ± 1 and degeneracies in terms of the number of repeated units are tabulated. This method is universal and applicable to cases sharing other eigenvalues and to nonbenzenoid systems.Also known as Yuan-sun Kiang     

Application of the Sakurai-Sugiura projection method to core-excited-state calculation by time-dependent density functional theory

The Sakurai-Sugiura projection (SS) method was implemented and numerically assessed for diagonalization of the Hamiltonian in time-dependent density functional theory (TDDFT). Since the SS method can be used to specify the range in which the eigenvalues are computed, it may be an efficient tool for use with eigenvalues in a particular range. In this article, the SS method is applied to core excited calculations for which the eigenvalues are located within a particular range, since the eigenvalues are unique to atomic species in molecules. The numerical assessment of formaldehyde molecule by TDDFT with core-valence Becke's three-parameter exchange (B3) plus Lee-Yang-Parr (LYP) correlation (CV-B3LYP) functional demonstrates that the SS method can be used to selectively obtain highly accurate eigenvalues and eigenvectors. Thus, the SS method is a new and powerful alternative for calculating core-excitation energies without high computation costs.     

Synthesis,characterization and recent developments of liquid crystalline polymers

Recent developments of polymer liquid crystals (PLCs) are reviewed. The virial expansion method of Onsager and the lattice model used by Flory to appreciate the most relevant parameters in establishing mesomorphic behavior in polymeric systems are presented. These and other theoretical predictions are confirmed by numerous experiments. Both lyotropic (polymer solutions) and thermotropic (polymer melts) types of PLCs are considered with emphasis placed on the latter. The general properties of mesophases formed by such polymers are surveyed and some chemical structures capable of producing mesophases are classified in relation to their ability to form lyotropic and thermotropic systems. The synthetic routes, the effects of polymer structure on physical properties, and applications of two major classes of lyotropic systems (polypeptides, polyamides) and of a range of potentially important thermotropic polymers are discussed.     

微流控技术在外泌体分离分析中的研究进展

外泌体是一类由细胞分泌的含有脂质、蛋白、核酸等多种物质的纳米级囊泡,主要参与细胞间的物质交换及信息传导,与多种疾病的发生发展密切相关。对外泌体进行深入研究,理解其生物学功能,对疾病诊断与治疗具有重要意义。由于外泌体尺寸较小且密度和体液接近,想要对复杂生物样本中的外泌体进行分离与分析十分困难。传统的外泌体分离方法如超速离心、超滤等大都需要借助大型仪器设备,且耗时长、操作复杂。因此迫切需要开发高效、便捷的外泌体分离检测手段。微流控技术因其微型化、高通量、可集成等特点,为外泌体的分离分析提供了一个新的平台。该文主要对近年来微流控技术在外泌体分离分析相关领域的研究进展进行了综述。重点从外泌体物理特性和生化特性两个角度出发,介绍了微流控芯片技术用于外泌体分离领域的主要原理、策略和方法。此外,还介绍了微流控技术与荧光、电化学传感、表面等离子体共振等多模态检测方法结合,实现外泌体一体化分析的新进展。最后,该文分析了目前微流控技术用于外泌体分离检测存在的挑战,并对其发展趋势和前景进行了展望。随着微流控外泌体分离分析装置的不断微型化、集成化、自动化,微流控芯片技术将在外泌体分离、生化检测、机制研究等方面将发挥越来越重要的作用。     

Polymerization of N-carboxy–amino acid anhydrides in the solid state. II. Relation between polymerizability and molecular arrangement in L-leucine NCA and L-alanine NCA crystals

The polymerizability of N-carboxy–amino acid anhydrides (NCAs) of L -leucine and L -alanine was examined in the solid state and in solution. L -leucine NCA shows much higher reactivity in the solid state (when immersed in hexane) than in solution (in acetonitrile), but the opposite is true for L -alanine NCA. However, the two NCAs give similar values of apparent activation energy in each polymerization system. Rather high-molecular-weight polypeptides were obtained in the polymerization of L -leucine NCA in the solid state compared with those obtained in solution, while the molecular weight of polymers obtained from L -alanine NCA was higher in solution than in the solid state. IR spectra showed that α helices form mainly in the polymerization of both L -leucine NCA and L -alanine NCA in the solid state; a small amount of the β structure forms in the latter polymerization. X-ray diffraction and electron microscopy revealed that L -leucine NCA polymerizes predominantly along the c axis in the crystal, while the polymer chains grow in random directions in the crystal of L -alanine NCA. The difference can be explained by the molecular arrangement in the crystal. There are two requirements for high reactivity in the solid state: the five-membered rings of the monomer must form a layer structure and the polymer must occupy nearly the same space as the reacting monomer.