Time-dependent density-functional and reduced density-matrix methods for few electrons: Exact versus adiabatic approximations

To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories.     

Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds

Symmetry can dramatically reduce the computational cost (running time and memory allocation) of Self-Consistent-Field ab initio calculations for crystalline systems. Crucial for running time is use of symmetry in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the SACO (Symmetry Adapted Crystalline Orbital) basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. We here illustrate the effectiveness of this scheme, following recent advancements in the CRYSTAL code, concerning memory allocation and direct basis set transformation. Quantitative examples are given for large unit cell systems, such as zeolites (all-silica faujasite and silicalite MFI) and garnets (pyrope). It is shown that the full SCF of 3D systems containing up to 576 atoms and 11136 Atomic Orbitals in the cell can be run with a hybrid functional on a single core PC with 500 MB RAM in about 8 h.     

Density functional calculations of large systems containing heavy elements by means of the regionalization algorithm

The compounds containing transition metals orother heavy elements play important roles in chemistry.They possess diverse properties which have been util-ized in numerous functional materials. Some of theseproperties are also involved in biological processes.However, it is very difficult to study these compoundsdeeply by means of quantum chemical methods, be-cause in these systems usually there are a large amountof electrons, the distribution of the frontier orbitals isdense, the correlation be…     

Density matrix structure for saturated molecules

Conclusion The existence of a common Hamiltonian matrix structure for saturated systems results in common structural properties of the density matrices for the whole class of molecules, such as the zero occupation of AO in the first approximation, the density matrix perturbations due to a heteroatom, etc. This fact can be taken as a quantum-mechanical foundation for viewing saturated molecules as a separate class of compounds. The endowment of this system with the transferability of electronic structure properties, relative to atoms and bonds, to high accuracy, within the framework of the effective Hamiltonian method follows from an analysis of the general expressions for the density matrix elements. The transferability of the saturated system Hamiltonian matrix elements requisite for this is supported by a comparison among the self-consistent Fock matrix elements of various hydrocarbons in a localized orbital basis [9]. Independently of the detailed structure of the actual molecules, the influence of a heteroatom on the electron density distribution in saturated systems dies off quickly with distance from the heteroatom. From an analysis of expressions for the nondiagonal elements of the density matrix corresponding to nonneighboring AO we establish a connection between the degree of electron localization in saturated systems and the size or certain Hamiltonian matrix elements.There is a consequent analogy between saturated and alternatively conjugated hydrocarbons, which, starting from the common structure of the Hamiltonians, also leads to common properties of the density matrices [14]. However, the study of the influence of heteroatoms on the density matrices in these systems by means of perturbation theory is complicated by the dependence of the matrix N(4) on the molecular structure, which makes it necessary to introduce highly simplified approaches for the solution of Eq. (2) [8]. Therefore, for alternating hydrocarbons we have succeeded in establishing only the sign of the orbital — orbital polarizability (alternating polarity theorem [14]), while, as for saturated systems, the equality N=1 permits an analytic expression for the polarizability.V. Kapsukas Vilnius State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 29, No. 5, pp. 3–8, September–October, 1988.     

Floquet-liouville super-matrix approach for multiphoton non-linear optical processes in intense laser fields

A practical non-perturbative approach is presented for the treatment of multiphoton non-linear optical processes in intense monochromatic or polychromatic field. By extending the many-mode Floquet theory recently developed by the authors, the time-dependent Liouville equation for the density matrix of atoms or molecules undergoing radiative and/or collisional relaxations can be transformed into an equivalent time-independent Floquet-Liouville super-matrix eigenvalue problem. The method is illustrated by a study of the multiphoton resonance fluorescence spectra of two-level systems.     

Eigenvalue independent partitioning and direct minimization in self-consistent field theory

It is pointed out that the matrix elements of a partitioning operator, f, introduced previously for constructing effective hamiltonians, provide natural sets of unconstrained and non-redundant variables in which to formulate self-consistent field theory. The elements of f are complementary to corresponding elements of the density matrix, the relation being essentially that between covariant and contravariant vectors. Some consequences for direct minimization SCF techniques are considered.     

On density function coordinate matrix

The present letter presents a short discussion about the misleading name associated to a matrix, connected to (first order) density functions defined in turn within the LCAO-MO framework, which is widespread in quantum chemistry. The author proposes to call such a matrix form with the logical name of: density function coordinate matrix.     

A computational approach to linear conjugacy in a class of power law kinetic systems

This paper studies linear conjugacy of PL-RDK systems, which are kinetic systems with power law rate functions whose kinetic orders are identical for branching reactions, i.e. reactions with the same reactant complex. Mass action kinetics (MAK) systems are the best known examples of such systems with reactant-determined kinetic orders (RDK). We specify their kinetics with their rate vector and T matrix. The T matrix is formed from the kinetic order matrix by replacing the reactions with their reactant complexes as row indices (thus compressing identical rows of branching reactions of a reactant complex to one) and taking the transpose of the resulting matrix. The T matrix is hence the kinetic analogue of the network’s matrix of complexes Y with the latter’s columns of non-reactant complexes truncated away. For MAK systems, the T matrix and the truncated Y matrix are identical. We show that, on non-branching networks, a necessary condition for linear conjugacy of MAK systems and, more generally, of PL-FSK (power law factor span surjective kinetics) systems, i.e. those whose T matrix columns are pairwise different, is \(T = T'\), i.e. equality of their T matrices. This motivated our inclusion of the condition \(T = T'\) in exploring extension of results from MAK to PL-RDK systems. We extend the Johnston–Siegel Criterion for linear conjugacy from MAK to PL-RDK systems satisfying the additional assumption of \(T = T'\) and adapt the MILP algorithms of Johnston et al. and Szederkenyi to search for linear conjugates of such systems. We conclude by illustrating the results with several examples and an outlook on further research.     

Comparison of two genres for linear scaling in density functional theory: purification and density matrix minimization methods

Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.     

Some difficulties in the application of the concept of density of states

The problem of defining N(E), the density of states, for molecular systems is discussed. It is shown that a numeric evaluation of N(E) is often only approximate, even for continuous data, and is not well defined for quantized systems. The application of the concept of density of states is discussed, particularly with regard to the RRKM theory of unimolecular reactions. The sum of states, W(E), and density of states curves are evaluated for several harmonic and anharmonic model systems and the results discussed in order to illustrate the foregoing considerations.     

Quantitative nanomechanical property mapping of epoxy thermosetting system modified with poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) triblock copolymer

An epoxy based thermosetting matrix was modified with poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) triblock copolymer, obtaining cured nanostructured thermosetting systems. Resulting systems were investigated using a novel atomic force microscopy (AFM) imaging mode, known as PeakForce quantitative nanomechanical property mapping (PeakForce QNM), that allows for the quantitative mapping of the local mechanical properties, such as adhesion and elastic modulus, together with the topography. It was demonstrated the capacity of this quantitative nanomechanical mapping to provide information on the local distribution of the elastic modulus, being able to distinguish between the mechanical properties of the two phases present in the analyzed thermosetting systems.     

Temperature dependence of the spin-lattice relaxation rates in the triplet state of pyrazine at low temperatures

The electron spin-Lattice relaxation, (SLR) rate constants have been measured for the triplet state at pyrazine-d₄ in a cyclohexane matrix from 1 to 8 K by resolving the phosphorescent decay curve into three exponential components. A matrix kinetics is presented that gives the relationship between the SLR rate constants and the observed decay component rate constants and the decay component intensities of the three zero-field levels. An exact numerical procedure based on the Newton-Raphson technique is described in detail for systems of two and three coupled levels. This procedure was used to find the SLR rate constants starting from either the decay component rate constants or the decay component intensities. Both the matrix kinetics and the numerical procedure should be useful in many other studies involving multilevel systems whose sublevels are connected by some combination of SLR and microwaves. The observed SLR rate constants are best explained as a function of temperature as the sum of a direct process (linear in T) and a Raman process (T² dependence). Their relative magnitudes indicate that the Raman process is probably antharmonic. Vancus mechanisms for SLR in this system are examined, and a short review of SLR theory and experiment is given. The nature of the zero-field sublevels in pyrazine-J₄ is also discussed as is the effect of the choice of matrix solvent upon SLR rate constants and the phosphorescent spectrum.     

Towards an order-N DFT method

One of the most important steps in a Kohn-Sham (KS) type density functional theory calculation is the construction of the matrix of the KS operator (the “Fock” matrix). It is desirable to develop an algorithm for this step that scales linearly with system size. We discuss attempts to achieve linear scaling for the calculation of the matrix elements of the exchange-correlation and Coulomb potentials within a particular implementation (the Amsterdam density functional, ADF, code) of the KS method. In the ADF scheme the matrix elements are completely determined by 3D numerical integration, the value of the potentials in each grid point being determined with the help of an auxiliary function representation of the electronic density. Nearly linear scaling for building the total Fock matrix is demonstrated for systems of intermediate size (in the order of 1000 atoms). For larger systems further development is desirable for the treatment of the Coulomb potential. Received: 30 March 1998 / Accepted: 6 July 1998 / Published online: 15 September 1998     

Interaction of antitumoral drug erlotinib with biodegradable triblock copolymers: a molecular modeling study

Combination of molecular dynamics simulations and miscibility calculations was used to investigate erlotinib drug delivery systems based on poly-ε-caprolactone–polyethylene glycol–poly-ε-caprolactone (PCL–PEG–PCL) and poly-ε-caprolactone–polyglycolic acid–poly-ε-caprolactone (PCL–PGA–PCL) biodegradable copolymers. The molecular modeling strategy involving visual observation of models, concentration profile analysis, Flory–Huggins χ parameter, cohesive energy density, and mean square displacement calculations reproduced experimental evidence of erlotinib release from PCL–PEG–PCL matrix successfully. Increasing portion of PCL in PCL–PEG–PCL copolymer led to dissolution of erlotinib aggregates recorded in visual and concentration profile analyses. Higher portion of PCL led to higher cohesive energy density and lower mean square displacement values. Success of this strategy in reproduction of experimental data made an opportunity to utilize the same modeling design in prediction of erlotinib release from similar but not yet experimentally tested PCL–PGA–PCL matrix. In this case, agglomeration of erlotinib molecules and stronger cohesive energy density values were observed.     

Thermal stability of CR/CSM rubber blends filled with nano- and micro-silica particles

The properties of filled polymers depend on the properties of the matrix and the filler, the concentration of the components and their interactions. In this research we investigated the rheological and mechanical properties and thermal stability of polychloroprene/chlorosulfonated polyethylene (CR/CSM) rubber blends filled with nano- and micro-silica particles. The density of the nano-silica filled CR/CSM rubber blends was lower than that of the micro-silica filled samples but the tensile strength and elongation at break were much higher. The nano-silica filled CR/CSM rubber blend has higher V _r0/V _rf values than micro-silica composites and show better polymer–filler interaction according to Kraus equation. The nano-silica filled CR/CSM rubber blends were transparent at all filler concentration, and have higher glass transition values than micro-silica filled compounds. The higher values of the glass transition temperatures for the nano- than the micro-filled cross-linked systems are indicated by DMA analysis. The nano-filled cross-linked systems have a larger number of SiO–C links than micro-filled cross-linked systems and hence increased stability.     

Measurements of the density and refractive index for 1-n-butyl-3-methylimidazolium-based ionic liquids

Correlations between density and refractive index of pure systems of ionic liquids were examined in this work. To this end, the density and refractive index of four 1-n-butyl-3-imidazolium-based ionic liquids were measured at atmospheric pressure and temperature up to 353.2 K. Densities and refractive indices of the ionic liquids investigated are presented as a function of temperature. A group contribution-based equation was modified to calculate the density as a function of temperature. An empirical equation was used to study the temperature-dependence of refractive index. The Lorentz–Lorenz, Dale–Gladstone, Eykman, Oster, Arago–Biot, and Newton equations, as well as a modified Eykman were used to correlate the relation between the densities and refractive indices of the different ionic liquid systems. The correlations give satisfactory results. The results of this study can add to the newly organized database for ionic liquids and can also be used for various process design calculations.     

On the relationship of the X-ray form factor to the 1-matrix in momentum space

The X-ray form factor F(μ) is shown to be proportional to the convolution of the momentum space charge density matrix.     

Synthesis of natural rubber-g-maleic anhydride and its use as a compatibilizer in natural rubber/short nylon fiber composites

Natural rubber grafted maleic anhydride (NR-g-MAH) was synthesized by mixing maleic anhydride (MAH) and natural rubber (NR) in solid state in a torque rheometer using dicumyl peroxide (DCP) as initiator. Then the self-prepared NR-g-MAH was used as a compatibilizer in the natural rubber/short nylon fiber composites. Both the functionalization of NR with MAH and the reaction between the modified rubber and the nylon fiber were confirmed by Fourier transform infrared spectroscopy (FTIR). Composites with different nylon short fiber loadings (0, 5, 10, 15 and 20 phr) were compounded on a two-roll mill, and the effects of the NR-g-MAH on the tensile and thermal properties, fiber-rubber interaction, as well as the morphology of the natural rubber/short nylon fiber composites were investigated. At equal fiber loading, the NR-g-MAH compatibilized NR/short nylon fiber composites showed improved tensile properties, especially the tensile modulus at 100% strain which was about 1.5 times that of the corresponding un-compatibilized ones. The equilibrium swelling tests proved that the incorporation of NR-g-MAH increased the interaction between the nylon fibers and the NR matrix. The crosslink density measured with NMR techniques showed that the NR-g-MAH compatiblized composites had lower total crosslink density. The glass transition temperatures of the compatibilized composites were about 1 K higher than that of the corresponding un-compabilized ones. Morphology analysis of the NR/short nylon fiber composites confirmed NR-g-MAH improved interfacial bonding between the NR matrix and the nylon fibers. All these results signified that the NR-g-MAH could act as a good compatilizer of NR/short nylon fiber composites and had a potential for wide use considering its easy to be prepared and compounded with the composites.