Systematic Study of Selected Diagonalization Methods for Configuration Interaction Matrices

Several modifications to the Davidson algorithm are systematically explored to establish their performance for an assortment of configuration interaction (CI) computations. The combination of a generalized Davidson method, a periodic two‐vector subspace collapse, and a blocked Davidson approach for multiple roots is determined to retain the convergence characteristics of the full subspace method. This approach permits the efficient computation of wave functions for large‐scale CI matrices by eliminating the need to ever store more than three expansion vectors ( b _i) and associated matrix‐vector products ( σ _i), thereby dramatically reducing the I/O requirements relative to the full subspace scheme. The minimal‐storage, single‐vector method of Olsen is found to be a reasonable alternative for obtaining energies of well‐behaved systems to within μE_h accuracy, although it typically requires around 50% more iterations and at times is too inefficient to yield high accuracy (ca. 10^?10 E_h) for very large CI problems. Several approximations to the diagonal elements of the CI Hamiltonian matrix are found to allow simple on‐the‐fly computation of the preconditioning matrix, to maintain the spin symmetry of the determinant‐based wave function, and to preserve the convergence characteristics of the diagonalization procedure. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1574–1589, 2001     

Elimination of the diagonalization bottleneck in parallel Direct-SCF methods

Summary It is shown that the matrix diagonalization bottleneck associated with thesequential O(N _BFN ³ ) diagonalization of the fock matrix within each iteration of the Direct-SCF procedure may be eliminated, and replaced instead with a combination ofparallel O(N _BFN ^<4 ) andsequential O(N _Sub ³ ) steps. For large basis sets, the relation N_Sub N_BFN between the dimension of the expansion subspace and the number of basis functions leads to a method of wave-function optimization in which the sequential bottleneck is eliminated. As a side benefit, the second-order iterative procedure on which this method is based displays superior convergence properties, and provides greater insight into the behavior of the energy with respect to orbital variations, than the traditional first-order, fixed-point, iterative approaches. The implementation of this method may be incorporated into essentially any existing Direct-SCF program with only minimal, and localized, changes.     

Symmetric‐group‐based methods in quantum chemistry

The eigenvalue problem of a Hamiltonian represented in a finite-dimensional model space being the N-electron subspace of the 2K-spinorbital Fock space is analyzed. It is pointed out that the permutation group S _N is a very convenient framework for this analysis. The resulting approach is known as the symmetric group approach to the N-electron problem. Its applications to construction of a basis in the model space, to the evaluation of matrix elements of spin‐independent and of spin‐dependent operators and, finally, to solution of the eigenvalue problem of the Hamiltonian are briefly reviewed. Recently developed applications of the symmetric group to studies of the Heisenberg Hamiltonian spectra and to evaluation of spectral density distribution moments are also dicussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the matching polynomials of graphs with small number of cycles of even length

Suppose that G is a simple graph. We prove that if G contains a small number of cycles of even length then the matching polynomial of G can be expressed in terms of the characteristic polynomials of the skew adjacency matrix A(G^e) of an arbitrary orientation G^e of G and the minors of A(G^e). In addition to a formula previously discovered by Godsil and Gutman, we obtain a different formula for the matching polynomial of a general graph. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

A comparative molecular similarity index analysis (CoMSIA) study identifies an HLA-A2 binding supermotif

The 3D-QSAR CoMSIA technique was applied to a set of 458 peptides binding to the five most widespread HLA-A2-like alleles: A^*0201, A^*0202, A^*0203, A^*0206 and A^*6802. Models comprising the main physicochemical properties (steric bulk, electron density, hydrophobicity and hydrogen-bond formation abilities) were obtained with acceptable predictivity (q ² ranged from 0.385 to 0.683). The use of coefficient contour maps allowed an A2-supermotif to be identified based on common favoured and disfavoured areas. The CoMSIA definition for the best HLA-A2 binder is as follows: hydrophobic aromatic amino acid at position 1; hydrophobic bulky side chains at positions 2, 6 and 9; non-hydrogen-bond-forming amino acids at position 3; small aliphatic hydrogen-bond donors at position 4; aliphatic amino acids at position 5; small aliphatic side chains at position 7; and small aliphatic hydrophilic and hydrogen-bond forming amino acids at position 8.     

Complete one‐ and two‐center partitioning scheme for the total energy in the Hartree–Fock theory

We proposed a complete calculation scheme for attributing the total energy by the Hartree–Fock theory to atoms (E_A) and the region between two atoms (E_AB). It was pointed out that the conventional method using the Fock matrix includes a large amount of mutual contamination in both E_A and E_AB. The new scheme was derived from the basic expression of the total energy. Calculated results by the new scheme satisfy the theoretical requirements. The scaling effect on partitioned energies was also examined. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 35–46, 1999     

Polysulfonylamine. CLIV [1] Kristallstrukturen von Metall‐di(methansulfonyl)amiden. 7 [2] Ein dreidimensionales Koordinationspolymer aus Schichten und Pfeilern: Kristallstruktur von Ba[(CH3SO2)2N]2·2H2O

Polysulfonylamines. CLIV. Crystal Structures of Metal Di(methanesulfonyl)amides. 7. A Three‐Dimensional Coordination Polymer Built up from Layers and Pillars: Crystal Structure of Ba[(CH₃SO₂)₂N]₂·2H₂O The barium compound BaA₂·2H₂O, derived from HA = di(methanesulfonyl)amine, has been characterized by single crystal X‐ray diffraction at —95 °C (monoclinic, space group P2₁/n, Z = 4). Despite numerous metal‐ligand bonds, the independent anions A^— and A′^— retain the pseudo‐C₂ symmetric conformation that commonly occurs in organic onium salts BH⁺A^—. The large cation attains ninefold coordination via interactions with one (O, N)‐chelating A^—, three κ¹O‐bonding A^—, two κ¹O‐bonding A′^— and two monodentate water molecules; if a distinctly longer barium‐water distance is included, the coordination number may alternatively be viewed as 9 + 1 and one water molecule regarded as an asymmetrically μ₂‐bridging ligand. In contrast to the previously reported layer structures of SrA₂ and PbA₂, the present crystal displays a three‐dimensional coordination assembly consisting of layers formed by the cations, the water molecules and the pentadentate A^— ligands, and of interlayer pillars provided by the bidentate A′^— ligands; however, the Ba²⁺/A^— substructure turns out to be topologically and crystallographically congruent with the corresponding M²⁺/A^— substructures in SrA₂ and PbA₂. The crystal cohesion of the barium complex is reinforced by four O(W)—H···O=S hydrogen bonds and several non‐classical C—H···O=S hydrogen bonds.     

Use of atomic force microscopy and fractal geometry to characterize the roughness of nano-, micro-, and ultrafiltration membranes

Membrane surface roughness alters the surface area accessible to foulants and may influence macroscopic properties, such as zeta potential. It is usually quantified by atomic force microscopy (AFM) at a single scan size. This would be appropriate if roughness is independent of scale. This study shows that the root-mean-square roughness, R_RMS, is scale (or scan size, L × L) dependent through the power law R_RMS = AL^3−D. The coefficient, A, is the roughness at a scan size of 1² μm². D is the fractal dimension that relates the increase in roughness to the increase in scan size. Values for A and D were determined for a range of micro- and ultrafiltration membranes using an AFM scan series covering at least three orders of magnitude in L. They were also determined for nanofiltration membranes by re-analysis of data in the literature. The results suggest that using the power law expression allows potentially greater discrimination among membrane types and provides a way to quantify membrane roughness over a range of scales. It was further observed that the coefficients A and D of PVDF membranes showed positive and negative correlations, respectively, with the molecular weight cut-off. Additionally, zeta potentials of PVDF membranes measured by the tangential streaming potential method became more negative with increasing A and more positive with increasing D, suggesting possible significant influence of roughness on hydrodynamic transport of ions.     

基于NMR技术的溶菌酶在琼脂糖凝胶中的动力学研究

运用脉冲梯度场测量自扩散系数及自旋自旋弛豫时间测量核磁共振技术对鸡蛋清溶菌酶(HEWL)在琼脂糖凝胶中的动力学进行了研究.试验结果表明,HEWL在琼脂糖凝胶中的自扩散系数及自旋自旋弛豫时间较其在纯乙酸钠溶液中变小,说明琼脂糖凝胶的三维网状结构使HEWL分子整体运动及局部运动都受到阻碍.并且随着琼脂糖浓度的增大,凝胶网孔尺寸不断减小,HEWL分子运动受限程度加剧,从而蛋白质分子可以较长时间内停留在高浓度区,分子间更容易互相碰撞,发生反应,晶核生长得以促进.同时琼脂糖凝胶较小流体力学网孔尺寸抑制聚晶或沉淀的出现,晶体质量获得提高.     

Energetics and structure of the hydrated gaseous halide anions

Energetics and geometries for the hydrated gaseous halide anions have been computed from a simple model in which the molecular dipole of water was composed of two parts, one due to a lone pair on oxygen (60%) and the rest to formal charges on the nuclei. The calculations were made for both the symmetric and nonsymmetric structures. A variety of structures were used to compute potential energies and distances with up to six water molecules. The total energy consisted of a sum of electrostatic, polarization, dispersion, and repulsion terms. Various sets of repulsive potential parameters, ranging from those determined from molecular beam experiments to those determined using experimental ion–water distances or energies, have been employed to compute repulsive interaction energies. It was found that the range parameters play a significant role in deciding the magnitudes of the distances and energies, as the latter are most sensitive to them. It was also shown that with a simple correlation scheme the consistency of the experimental energies and distances can be tested separately without using repulsive potential parameters from other sources. It also suggests that a range of parameters can be used to compute repulsion energies. Despite the fact that the model is greatly simplified, the agreement of both the predicted ion-oxygen distances and energies with both experiment and other calculations is excellent. A detailed analysis of our calculation suggests that the negative ion clusters with one to three water molecules contain symmetric orientation of water molecules, while those with more than three may contain asymmetric orientations of water molecules or a mixture of both. From the log–log plots of hydration energies versus (R + radius of water molecule), we have proposed empirical expressions of the type ΔE_n?1,n = 10·0^x (R + 1.38)^?y with both Pauling's and Ladd's radii for univalent ions with which stepwise hydration energies of the latter can be predicted if we know thier radii. The values predicted for the alkali cations are in excellent agreement with the experimental and theoretical values, indicating the consistency of the simple model.     

Electron paramagnetic resonance study on Cu[(C6H11O)2PS2]2 complex single crystal

X-band EPR studies on Cu[(C₆H₁₁O)₂PS₂]₂ complex single crystal at room temperature were reported. The EPR spectrum shows that the hyperfine structure is produced by ⁶³Cu nuclei, and the ligand hyperfine structure by ³¹P nuclei. The spin-Hamiltonian parameters were rigorously calculated using a least-squares-fitting technique, specially adapted to noncoincident g and A tensors systems. The principal values of g tensor imply that Cu²⁺ occupies the site consisting of four ligands S, and is tetragonal symmetric, but the principal values of A tensor in Cu—S₄ plane reveal a large anisotropy caused by the presence of two ligands P. One of principal axes for g and A tensors is coincident, and they are perpendicular to the Cu—S₄ plane. It was found that the interaction between electron spin and ligands ³¹P nuclear spin is isotropic and the hyperfine-coupling constant A^P related ligands was obtained.     

Static light scattering from poly(ethylene oxide) in methanol

Static light scattering measurements were performed on dilute solutions of monodisperse poly(ethylene oxide) (PEO) in methanol at 25°C. PEOs of five different molecular weights ranging from nominal M_w = 8.6 × 10⁴ to 9.13 × 10⁵ were used. Linear Zimm plots were obtained for all the PEO samples: no downturn was observed at small angles, indicating that no large aggregates of PEO molecules exist in the solution. From the plots, values of the weight-average molecular weight, M_w, the radius gyration, R_G, and the second virial coefficient, A₂, were successfully determined for respective PEOs. Observed relationship between R_G and M_w indicates that methanol is certainly a good solvent for the polymer. © 1996 John Wiley & Sons, Inc.     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Membrane osmometer for use at moderate applied pressures

A membrane osmometer designed for use at pressures greater than 0.1 MPa and less than 6 MPa was employed to determine the pressure coefficient of the equilibrium osmotic pressure (?π/?P) of a dilute polystyrene/toluene solution. The pressure coefficient of the second virial coefficient (?A₂/?P), calculated from ?π/?P, was 6 (±4) × 10^?5 cm³ mol g^?2 MPa^?1, which was in reasonable agreement with the value obtained from pressure‐dependent light scattering. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3064–3069, 2003     

Solution characterization of poly(isobornyl methacrylate) in tetrahydrofuran

Thermodynamic and hydrodynamic properties of dilute solutions of poly (isobornyl methacrylate) (PIMA) in tetrahydrofuran (THF) were characterized by using viscosity, static, and dynamic light scattering measurements. PIMA samples with different molecular weight were obtained by fractional precipitation of PIMA solution. Chain dimension parameters (R_g and R_H), together with second virial coefficient A₂ and intrinsic viscosity [η], were used to calculate various solution parameters characterizing polymer chains in polymer solutions. The experimental results are compared with calculation, indicating that PIMA behaves as a flexible coil in THF. © 1994 John Wiley & Sons, Inc.     

Synthesis of nonsymmetric chain end functionalized polyisobutylenes

We present the synthesis of nonsymmetric α‐ω‐functionalized polyisobutylenes (PIBs) bearing different functional moieties on their chain ends. Thus, on one chain end either, a short tri‐ethylene oxide chain (TEO) or a phosphine oxide ligand is attached, whereas the other chain end is substituted by hydrogen bonding moieties (thymine/2,6‐diaminotriazine). The nonsymmetric PIBs were synthesized via living cationic polymerization using methyl‐styrene epoxide as initiator, followed by quenching reaction with 3‐bromopropyl‐benzene. Subsequent bromide/azide exchange and the use of the azide/alkyne click reaction allowed the synthesis of (a) (α)‐TEO‐(ω)‐thymine‐telechelic PIB ( 7a ), (b) (α)‐triethyleneoxide‐(ω)‐triazine telechelic PIB ( 7b ), and (c) (α)‐phosphinoxide‐(ω)‐thymine‐telechelic PIB ( 13 ) with molecular weights M_n ～ 4000 g mol^?1 and low polydispersities (M_w/M_n = 1.3). The chemical identity of the final structures was proven by extensive ¹H NMR investigations and matrix‐assisted laser desorption/ionization‐mass spectroscopy (MALDI). The presented method for the first time offers a simple and highly versatile approach toward supramolecular nonsymmetric α‐ω‐functionalized PIB. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

INVESTIGATION ON THE RELATIONSHIP BETWEEN INTRINSIC VISCOSITY AND MOLECULAR WEIGHT OF POLY (VINYL CHLORIDE-DIETHYL MALEATE)

A poly (vinyichloride-diethyl maleate) copolymer has been fractionated by repeated precipitation method. All fractions and the unfractionated sample have been characterized by viscometry, dynamic osmometry, Zimm static osmometry, light scattering and gel permeation chromatography. After correction for polydispersity, a [η]～M relationship for monodisperse polymer solutions has been obtained:[η]=1.99×10~(-3)M~(0.87) (ml/g, at 25℃, in cyclohcxanone)For the copolymer solution in THF, the second virial coefficient A_2 decreases as the molecular weight increases. The relationship isA_2=2 slope ((?)_n RT)~(-1/2).     

Polar anchoring strengths of nematic liquid crystal on high-density polymer brush surfaces

ABSTRACT

Herein, the polar anchoring energy coefficient (A_θ) of nematic liquid crystal (NLC) was examined for high-density polymer brushes via capacitance measurements. The A_θ is 10^?4 J m^?2 for the brushes of poly(methyl methacrylate), poly(ethyl methacrylate) and poly(styrene). The value decreases to 10^?5 J m^?2 for poly(n-butyl methacrylate) and poly(hexyl methacrylate) with lower glass transition temperatures. However, each polymer brush displays a constant A_θ value over a temperature range of ?15°C to 90°C, which is hardly affected by the graft density and brush thickness. At 25°C, A_θ is 10 times greater than the corresponding azimuthal anchoring energy coefficient (A_φ); therefore, NLCs on polymer brushes can be preferentially aligned along the in-plane component of the applied field.     

Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators

The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T^? = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ? should be stable under complex conjugation, so that ?* = ?α. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H^?, in which the effective Hamiltonian H_eff (1) may have complex eigenvalues ε_k. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.