Spin-adapted density matrix renormalization group algorithms for quantum chemistry

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of S?(2), and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe(2)S(2), [Fe(2)S(2)(SCH(3))(4)](2-), and Cr(2) systems. In the case of Fe(2)S(2), the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe(2)S(2)(SCH(3))(4)](2-), we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr(2) we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.     

A Simple and Efficient One‐Pot Synthesis of Multifunctional 5‐Aryl‐5H‐thiazolo[3,2‐a]pyrimidines

One‐pot economical and efficient synthesis of multifunctional 5H‐thiazolo[3,2‐a]pyrimidines by the reaction of 4‐aryl dihydrothiopyrimidines with propargyl bromide in the presence of inorganic base has been reported in very short time.     

Indium triflate catalyzed one-pot multicomponent synthesis of spiro-hexahydropyrimidines explained by multiple covalent bond formation

A mild, efficient, and expeditious method has been developed for the synthesis of spiro-hexahydropyrimidine derivatives via a three-component, one-pot cyclocondensation reaction of aromatic amines, formaldehyde, and cyclic ketones in 4-6 h using In(OTf)₃ as Lewis acid catalyst for the first time. The reaction involving creation of six new covalent bonds was efficiently promoted by 10 mol % In(OTf)₃ and the catalyst could be recovered easily after the reaction and reused without any loss of its catalytic activity. The advantageous features of this methodology are high atom-economy, operational simplicity, shorter reaction time, and easy handling.     

Conductivity Study on PEO Based Polymer Electrolytes Containing Hexafluorophosphate Anion: Effect of Plasticizer

PEO based polymer electrolytes containing ammonium hexafluorophosphate (NH₄PF₆) and hexafluorophosphoric acid (HPF₆), both with PF anion have been studied. The effect of the addition of propylene carbonate (PC) to PEO-NH₄PF₆ and PEO-HPF₆ has been observed to increase in ionic conductivity which is attributed to an increase in free ion concentration due to the dissociation of ion aggregates present at higher acid/salt concentrations. The plasticized polymer electrolytes containing HPF₆ show relatively higher conductivity (σ_max = 1.02 × 10⁻⁴ S/cm at 10 wt% HPF₆) as compared to electrolytes containing NH₄PF₆ (σ_max = 1.09 × 10⁻⁵ S/cm at 10 wt% NH₄PF₆). Presence of free ions, ion aggregates and their dissociation with the addition of PC has been studied by Fourier Transform Infrared Spectroscopy (FTIR). The change in amorphous phase with PC content was also studied by X-Ray Diffraction (XRD). The variation of conductivity with temperature shows Vogel–Tammen–Fulcher (VTF) behavior, which is associated with the highly amorphous nature of electrolytes. ¹H Nuclear magnetic Resonance (NMR) spectra at different temperatures shows line narrowing and suggests the onset of long range ion diffusional motion. Change in surface morphology of polymer electrolytes with the addition of PC is also checked by Scanning Electron Microscopic (SEM) studies.     

Measurement of the neutron capture cross-section of 238U using the neutron activation technique

The ²³⁸U(n, ??)²³⁹U reaction cross-section at average neutron energy of 3.7?±?0.3?MeV from the ⁷Li(p, n)⁷Be reaction has been determined using activation and off-line ??-ray spectrometric technique. The ²³⁸U(n, ??)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections at average neutron energy of 9.85?±?0.38?MeV from the same ⁷Li(p, n)⁷Be reaction have been also determined using the above technique. The experimentally determined ²³⁸U(n, ??)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections were compared with the evaluated data of ENDF/B-VII, JENDL-4.0, JEFF-3.1 and CENDL-3.1. The experimental values were found to be in general agreement with the evaluated value based on ENDF/B-VII, and JENDL-4.0 but not with the JEFF-3.1 and CENDL-3.1. The present data along with literature data in a wide range of neutron energies were interpreted in terms of competition between different reaction channels including fission. The ²³⁸U(n, ??)²³⁹U and ²³⁸U(n, 2n)²³⁷U reaction cross-sections were also calculated theoretically using the TALYS 1.2 computer code and were also found to be in agreement experimental data.     

Formation of the imide [Ta(NMe2)3(μ-NSiMe3)]2 through an unprecedented α-SiMe3 abstraction by an amide ligand

Ta(NMe(2))(4)[N(SiMe(3))(2)] (1) undergoes the elimination of Me(3)Si-NMe(2) (2), converting the -N(SiMe(3))(2) ligand to the ═NSiMe(3) ligand, to give the imide "Ta(NMe(2))(3)(═NSiMe(3))" (3) observed as its dimer 4. CyN═C═NCy captures 3 to yield guanidinates Ta(NMe(2))(3-n)(═NSiMe(3))[CyNC(NMe(2))NCy](n) [n = 1 (5), 2 (6)]. The kinetic study of α-SiMe(3) abstraction in 1 gives ΔH(?) = 21.3(1.0) kcal/mol and ΔS(?) = -17(2) eu.     

The t-analog of the level one string function for twisted affine Kac–Moody algebras

We study Lusztig?s t-analog of weight multiplicities, or affine Kostka–Foulkes polynomials, associated to level one representations of twisted affine Kac–Moody algebras. We obtain an explicit closed form expression for the unique t-string function, using constant term identities of Macdonald and Cherednik. This extends previous work on t-string functions for the untwisted simply-laced affine Kac–Moody algebras.     

Cognitive learning in differential evolution and its application to model order reduction problem for single-input single-output systems

Differential evolution (DE) is a well known and simple population based probabilistic approach for global optimization over continuous spaces. It has reportedly outperformed a few evolutionary algorithms and other search heuristics like the particle swarm optimization when tested over both benchmark and real world problems. DE, like other probabilistic optimization algorithms, has inherent drawback of premature convergence and stagnation. Therefore, in order to find a trade-off between exploration and exploitation capability of DE algorithm, a new parameter namely, cognitive learning factor (CLF) is introduced in the mutation process. Cognitive learning is a powerful mechanism that adjust the current position of individuals by the means of some specified knowledge (previous experience of individuals). The proposed strategy is named as cognitive learning in differential evolution (CLDE). To prove the efficiency of various approaches of CLF in DE,?CLDE is tested over 25 benchmark problems. Further, to establish the wide applicability of CLF,?CLDE is applied to two advanced DE variants. CLDE is also applied to solve a well known electrical engineering problem called model order reduction problem for single input single output systems.     

Fitness based Differential Evolution

Differential Evolution (DE) is a well known and simple population based probabilistic approach for global optimization. It has reportedly outperformed a few Evolutionary Algorithms and other search heuristics like Particle Swarm Optimization when tested over both benchmark and real world problems. But, DE, like other probabilistic optimization algorithms, sometimes exhibits premature convergence and stagnates at suboptimal point. In order to avoid stagnation behavior while maintaining a good convergence speed, a new position update process is introduced, named fitness based position update process in DE. In the proposed strategy, position of the solutions are updated in two phases. In the first phase all the solutions update their positions using the basic DE and in the second phase, all the solutions update their positions based on their fitness. In this way, a better solution participates more times in the position update process. The position update equation is inspired from the Artificial Bee Colony algorithm. The proposed strategy is named as Fitness Based Differential Evolution ( $FBDE$ ). To prove efficiency and efficacy of $FBDE$ , it is tested over 22 benchmark optimization problems. A comparative analysis has also been carried out among proposed FBDE, basic DE, Simulated Annealing Differential Evolution and Scale Factor Local Search Differential Evolution. Further, $FBDE$ is also applied to solve a well known electrical engineering problem called Model Order Reduction problem for Single Input Single Output Systems.