A numerical method for computing dispersion constants

We reformulate and discuss a previously proposed variational numerical technique for the computation of dispersion coefficients. The method extends the Full CI idea to the perturbation equation for the intermolecular interaction, by expanding the perturbative solution in a small number of tensor products of suitably chosen Full CI vectors. Some new expansion vectors are proposed and their convergence properties are tested by performing computations on HF and H₂O. Last, a natural state analysis of the solution is performed via an orthogonal transformation of the original expansion vectors and it is found that a single couple of natural states strongly dominates the expansion.     

An efficient data compression method for the Davidson subspace diagonalization scheme

Summary A flexible and efficient compression scheme for the expansion and product vectors Hamiltonian matrix times expansion vectors is presented within the Davidson diagonalization method. Our approach is based on an error analysis of the energy in terms of the aforementioned vectors and on a compression scheme for representing floating point numbers with a variable length mantissa. For a selection of typical quantum chemical test cases total saving factors of up to ten are reported. The method is expected to work especially well for extended multi-reference CI and full CI cases. As a general outcome of our analysis we obtain limits of possible sizes of a CI expansion within the Davidson procedure in relation to the energy and the desired accuracy of the energy assuming the usual IEEE floating point standard.     

A data compression method applicable to first-order convergent iterative procedures

A data compression method is presented that is generally applicable to first-order convergent iterative procedures that employ subspace expansions or extrapolations based on successive correction vectors. This method is based on the truncation of insignificant information in successive correction vectors. Although the correction vectors themselves may be severely truncated with the proposed approach, the final solution vector may be represented to arbitrary accuracy. A feature of the proposed method is that more slowly convergent iterative procedures allow the correction vectors to be more severely truncated without affecting the overall convergence rate. The method is implemented and applied to the iterative Davidson diagonalization method. If the compressed representation of the expansion vectors can be held in main computer memory, then a significant reduction in the I/O requirements is achieved.     

基于三维荧光光谱的乳制品脂氧化判别方法

为快速、无损判别乳制品脂氧化程度,提出了利用乳制品三维荧光光谱的氧化水平进行判别的方法。该方法用平行因子分析对荧光矩阵进行分解,用载荷向量组确定脂氧化过程中的光敏成分,用不同成分得分向量对样本进行聚类,并建立了不同氧化水平样本的偏最小二乘判别模型。实验采集不同存储环境下氧化程度各异的酸奶样本,找出了核黄素等荧光团在脂氧化过程中的变化规律,选取得分向量建立偏最小二乘判别模型对不同存储阶段氧化程度各异的样本判别分类,其特异度和灵敏度达88.9%以上,验证了该法对评判乳制品脂氧化水平的有效性。     

Quantum and electromagnetic propagation with the conjugate symmetric Lanczos method

The conjugate symmetric Lanczos (CSL) method is introduced for the solution of the time-dependent Schrodinger equation. This remarkably simple and efficient time-domain algorithm is a low-order polynomial expansion of the quantum propagator for time-independent Hamiltonians and derives from the time-reversal symmetry of the Schrodinger equation. The CSL algorithm gives forward solutions by simply complex conjugating backward polynomial expansion coefficients. Interestingly, the expansion coefficients are the same for each uniform time step, a fact that is only spoiled by basis incompleteness and finite precision. This is true for the Krylov basis and, with further investigation, is also found to be true for the Lanczos basis, important for efficient orthogonal projection-based algorithms. The CSL method errors roughly track those of the short iterative Lanczos method while requiring fewer matrix-vector products than the Chebyshev method. With the CSL method, only a few vectors need to be stored at a time, there is no need to estimate the Hamiltonian spectral range, and only matrix-vector and vector-vector products are required. Applications using localized wavelet bases are made to harmonic oscillator and anharmonic Morse oscillator systems as well as electrodynamic pulse propagation using the Hamiltonian form of Maxwell's equations. For gold with a Drude dielectric function, the latter is non-Hermitian, requiring consideration of corrections to the CSL algorithm.     

Spectral density calculation by using the Chebyshev expansion

A method to calculate the spectral density of any state vectors with respect to a set of eigenstates of a Hamiltonian is presented. A spectral density operator, whose expectation value on the state vector gives the spectral density, is evaluated indirectly by using the Chebyshev expansion method. A spectral transformation function is introduced to improve resolution at the low energy region, at the expense of the one at the higher region. The predissociation spectrum of CO+ is calculated to demonstrate the method.     

Polymers in gene therapy technology

There are several barriers to gene delivery. One of the biggest challenges is the design of appropriate vectors. Currently, nonviral vectors have received significant attention because of low toxicity, potential for tissue specificity, stability during storage, lack of immunogenicity, and relatively low production cost. Despite the high efficiency of viral vectors, they show limited clinical applications because of potentially fatal adverse effects and because of the likelihood of the immune response shutting down the transgene expression system. Nonviral technologies comprise plasmid‐based expression systems harboring a gene that encodes a therapeutic protein along with a synthetic gene delivery system. This review provides a broad perspective on recent improvements in the development of four kinds of nonviral vectors that are based on polymers, peptides, lipids, and DNA and discusses the cytotoxicity associated with gene therapy. Copyright © 2014 John Wiley & Sons, Ltd.     

Tensor decomposition in post-Hartree-Fock methods. I. Two-electron integrals and MP2

A new approximation for post-Hartree-Fock (HF) methods is presented applying tensor decomposition techniques in the canonical product tensor format. In this ansatz, multidimensional tensors like integrals or wavefunction parameters are processed as an expansion in one-dimensional representing vectors. This approach has the potential to decrease the computational effort and the storage requirements of conventional algorithms drastically while allowing for rigorous truncation and error estimation. For post-HF ab initio methods, for example, storage is reduced to O(d·R·n) with d being the number of dimensions of the full tensor, R being the expansion length (rank) of the tensor decomposition, and n being the number of entries in each dimension (i.e., the orbital index). If all tensors are expressed in the canonical format, the computational effort for any subsequent tensor contraction can be reduced to O(R(2)·n). We discuss details of the implementation, especially the decomposition of the two-electron integrals, the AO-MO transformation, the M?ller-Plesset perturbation theory (MP2) energy expression and the perspective for coupled cluster methods. An algorithm for rank reduction is presented that parallelizes trivially. For a set of representative examples, the scaling of the decomposition rank with system and basis set size is found to be O(N(1.8)) for the AO integrals, O(N(1.4)) for the MO integrals, and O(N(1.2)) for the MP2 t(2)-amplitudes (N denotes a measure of system size) if the upper bound of the error in the l(2)-norm is chosen as ε = 10(-2). This leads to an error in the MP2 energy in the order of mHartree.     

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     

Stationary states of the surface stabilized ferroelectric liquid crystal layers in electric field

Stationary states of surface stabilized ferroelectric liquid crystal layers in an electric field are analysed by use of the Taylor expansion method based on catastrophe theory. Two kinds of director distribution within the flat smectic layers are taken into account: the uniform and the presplayed one. The butterfly catastrophe describes the properties of the cells correctly. The results have a qualitative character. Two categories of transitions can be predicted: switching between stable states characterized by opposite uniform orientations of the polarization vectors, and deformation of the director field which relaxes after removing the field. The threshold field strengths are found and the role of the system parameters is investigated.     

A sparse matrix based full-configuration interaction algorithm

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers.     

Generation of genealogical spin eigenfunctions

A method is given for generating the Yamanouchi-Kotani genealogical spin eigenfunctions which requires neither storage of eigenfunctions for smaller numbers of electrons, nor summations of large order, nor explicit use of results from the theory of representations of the symmetric group. An explicit formula is given for the coefficients of expansion in terms of spin products.     

A new Lanczos-based algorithm for simulating high-frequency two-dimensional electron spin resonance spectra

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method: we incorporate QMR into the LA to monitor the convergence of the Lanczos projections in the reduction of large sparse matrices. We demonstrate that the combined approach of the LA and QMR can be utilized efficiently for the orthogonal transformation of large, but sparse, complex, symmetric matrices, such as are encountered in the simulation of slow-motional 1D- and 2D-electron spin resonance (ESR) spectra. Especially in the 2D-ESR simulations, it is essential that we store all of the Lanczos vectors obtained in the course of the LA recursions and maintain their orthogonality. In the LA-QMR application, the QMR weight matrix mitigates the problem that the Lanczos vectors lose orthogonality after many LA projections. This enables substantially more Lanczos projections, as required to achieve convergence for the more challenging ESR simulations. It, therefore, provides better accuracy for the eigenvectors and the eigenvalues of the large sparse matrices originating in 2D-ESR simulations than does the previously employed method, which is a combined approach of the LA and the conjugate-gradient (CG) methods, as evidenced by the quality and convergence of the 2D-ESR simulations. Our results show that very slow-motional 2D-ESR spectra at W-band (95 GHz) can be reliably simulated using the LA-QMR method, whereas the LA-CG consistently fails. The improvements due to the LA-QMR are of critical importance in enabling the simulation of high-frequency 2D-ESR spectra, which are characterized by their very high resolution to molecular orientation.     

The latest research progress on the prevention of storage pests by natural products: Species,mechanisms, and sources of inspiration

The quality of grains is influenced by storage pests, which are not only spoilers of stored grain, but also vectors of human and animal diseases. Chemical pesticides play an essential role in the cultivation and storage of cereals, however, due to the low degradability and residual toxicity of synthetic pesticides on the environment and non-target organisms, as well as the increasing resistance of target organisms to them, consideration should be given to the development of alternative pest control agents. Compounds isolated from natural sources have emerged as preferred targets for the development of novel insecticidal agents because of their eco-friendliness, safety, and effectiveness. In this review, we primarily focus on the natural product (NPs) control of storage pests. The effective monomer components of NPs and their anti-insect mechanisms were discussed, and natural sources of inspiration and models for insect repellents are described. This review aimed to provide guidelines for the exploitation and utilization of green and efficient natural insecticides.     

Transition-metal-catalyzed dehydrocoupling: a convenient route to bonds between main-group elements

The development of transition-metal-catalyzed dehydrocoupling reactions as a synthetic method for the formation of main-group element-element bonds provides an increasingly attractive and convenient alternative to traditional routes such as salt metathesis/elimination-type reactions. Since the first reported examples in the early 1980s, there has been a rapid expansion of this field, with extensions to a wide variety of metal-mediated homonuclear and heteronuclear bond-forming processes. Applications of this new chemistry in molecular and polymer synthesis, materials science, hydrogen storage and the transfer hydrogenation of organic substrates are attracting growing attention. An overview of this emerging area is presented in this Concepts article with a focus on recent results.     

Analysis of molecular orbital wave functions in terms of valence bond functions for molecular fragments. I. Theory

A method of expansion of molecular orbital wave functions into valence bond (VB ) functions is extended to molecular fragments. The wave function is projected onto a basis of mixed determinants, involving molecular orbitals as well as fragment atomic orbitals, and is further expressed as a linear combination of VB functions, characteristic of structural formulas of the fragment but whose remaining bonds are frozen. Structural weights for the fragment are deduced from this expression. Delocalized molecular orbitals are used as a startpoint, as they are after an ordinary SCF calculation. Wave functions of medium-sized molecules may be analyzed with reasonable storage requirements in a computer.     

Lossless compression of chemical fingerprints using integer entropy codes improves storage and retrieval

Many modern chemoinformatics systems for small molecules rely on large fingerprint vector representations, where the components of the vector record the presence or number of occurrences in the molecular graphs of particular combinatorial features, such as labeled paths or labeled trees. These large fingerprint vectors are often compressed to much shorter fingerprint vectors using a lossy compression scheme based on a simple modulo procedure. Here, we combine statistical models of fingerprints with integer entropy codes, such as Golomb and Elias codes, to encode the indices or the run lengths of the fingerprints. After reordering the fingerprint components by decreasing frequency order, the indices are monotone-increasing and the run lengths are quasi-monotone-increasing, and both exhibit power-law distribution trends. We take advantage of these statistical properties to derive new efficient, lossless, compression algorithms for monotone integer sequences: monotone value (MOV) coding and monotone length (MOL) coding. In contrast to lossy systems that use 1024 or more bits of storage per molecule, we can achieve lossless compression of long chemical fingerprints based on circular substructures in slightly over 300 bits per molecule, close to the Shannon entropy limit, using a MOL Elias Gamma code for run lengths. The improvement in storage comes at a modest computational cost. Furthermore, because the compression is lossless, uncompressed similarity (e.g., Tanimoto) between molecules can be computed exactly from their compressed representations, leading to significant improvements in retrival performance, as shown on six benchmark data sets of druglike molecules.     

A vector grouping algorithm for liquid crystal tensor field visualization

Tensor fields are at the heart of many science and engineering disciplines. Many tensor visualization methods separate the tensor into component eigenvectors and visualize those instead. Eigenvectors are normally ordered according to their eigenvalues: the eigenvectors corresponding to the smallest, median, or largest eigenvalues are in their corresponding groups. We show that this ordering strategy is undesirable for liquid crystal systems and propose a new approach, where the vectors are grouped to minimize some local energy. The grouping process is reminiscent of the epitaxial expansion in the anchoring of liquid crystals on a surface. The new algorithm is successfully applied to a liquid crystal system to study the biaxiality structure near a defect.     

On multireference superdirect configuration interaction in third order

The superdirect configuration interaction (Sup-CI ) method has the usual versatility and stability of the CI methods with computational efficiency typical to that of the many-body methods, such as the many-body perturbation theory (MBPT ). The Hamilton operator is projected into a space of a few trial vectors, such as Krylov, Nesbet, or Møller–Plesset correction vectors. In this space, Hamiltonian matrix elements may be directly computed in the many-body fashion, as weighted sums of integral products over orbital indices. The variation-perturbation method based on the first-order wave function is equivalent to the Sup-CI method with a single correction vector of the Møller–Plesset type. Different points of view on the superdirect CI method are discussed and a version in which third-order contributions are computed for a relatively small (10–100) space of reference and correction vectors is tested. Selection of the best “effective first-order spaces” and size-extensivity corrections in Sup-CI are briefly discussed. Møoller–Plesset, Epstein–Nesbet, and other correction vectors are included in the model calculations on the symmetric stretch of bonds in water, acetylene, and the NH₂ molecule. Errors are almost independent of molecular geometry and the method appears to be superior than the multireference second-order perturbation methods. © 1994 John Wiley & Sons, Inc.