• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.43-46
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• 2005

Reaction energies were determined for reductive ring-opening reactions of Li$^+$-coordinated ethylene carbonate (EC) and vinylene carbonate (VC) by a density functional method. We have also explored the ring-opening of Li$^+$-EC and Li$^+$-VC by reaction with a nucleophile (CH$_3$O$^-$.) thermodynamically. Our thermodynamic calculations led us to conclude that the possible reaction products are CH$_3$OCH$_2$CH$_2$OCO$_2$Li (O$_2$-C$_3$ cleavage) for Li$^+$-EC +CH$_3$O$^-$., and CH$_3$OCHCHOCO$_2$Li (O$_2$-C$_3$ cleavage) and CH$_3$OCO$_2$CHCHOLi (C$_1$-O$_2$ cleavage) for Li$^+$-VC +CH$_3$O$^-$.. The opening of VC would occur at the C$_1$-O$_2$ side by a kinetic reason, although the opening at the O$_2$-C$_3$ side is more favorable thermodynamically.

• Bulletin of the Korean Chemical Society
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• v.32 no.7
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• pp.2358-2368
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• 2011

Density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations, employing the B3LYP method and the LANL2DZ, 6-31G$^*$(LANL2DZ for Tc), 6-31G$^*$(cc-pVDZ-pp for Tc) and DGDZVP basis sets, have been performed to investigate the electronic structures and absorption spectra of the technetium-99m-labeled methylenediphosphonate ($^{99m}Tc$-MDP) complex of the simplest diphosphonate ligand. The bonding situations and natural bond orbital compositions were studied by the Mulliken population analysis (MPA) and natural bond orbital (NBO) analysis. The results indicate that the ${\sigma}$ and ${\pi}$ contributions to the Tc-O bonds are strongly polarized towards the oxygen atoms and the ionic contribution to the Tc-O bonding is larger than the covalent contribution. The electronic transitions investigated by TDDFT calculations and molecular orbital analyses show that the origin of all absorption bands is ascribed to the ligand-to-metal charge transfer (LMCT) character. The solvent effect on the electronic structures and absorption spectra has also been studied by performing DFT and TDDFT calculations at the B3LYP/6-31G$^*$(cc-pVDZ-pp for Tc) level with the integral equation formalism polarized continuum model (IEFPCM) in different media. It is found that the absorption spectra display blue shift in different extents with the increase of solvent polarity.

• Journal of the Korean Magnetics Society
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• v.26 no.4
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• pp.119-123
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• 2016

We have studied electronic and magnetic structure of cubane-type Cu magnetic molecule using density functional method. The calculated density of states show that Cu has 3d $x^2-y^2$ hole orbital because of short distances between Cu atom and in-plane 4 ligand atoms. The calculated total energy with in-plane antiferromagnetic spin configuration is lower than those of ferromagnetic configurations. The calculated exchange interaction J between in-plane Cu atoms is much larger than those between out-plane Cu atoms, since the $x^2-y^2$ hole orbital ordering of Cu 3d orbitals induces strong super-exchange interaction between in-plane Cu atoms.

• Journal of the Korean Magnetics Society
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• v.27 no.4
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• pp.140-144
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• 2017

We have studied electronic and magnetic structure of cubane-type Co magnetic molecule using density functional method. The calculated density of states show $Co^{+2}$ ionic state and high-spin state because of large exchange interaction between inside Co 3d electrons. The exchange interaction J between Co atoms depends Co-O-Co angle. The calculated J is ferromagnetic with right angles. On the other hand J is antiferromagnetic with large angles since super-exchange interactions between $Co^{+2}$ atoms. It induces that Co cubane has a antiferromagnetic spin structure of AFM1 = [${\uparrow}{\uparrow}{\downarrow}{\downarrow}$]

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.1
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• pp.88-93
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• 1994

This study is concerned with an analytic derivation of the probability density function applicable for wave heights in finite water depth using two different methods. As the first method of the study, a probability density function is developed by applying a series of polynomials which is orthogonal with respect to Rayleigh probability density function. The newly derived probability density function is compared with the histogram constructed from wave data obtained in finite water depth which indicate strong non-Gaussian characteristics. Although the probability density represents the histogram very well. it has negative density at large values. Although the magnitude of the negative density is small. it negates the use of the distribution function fer estimating extreme values. As the second method of the study, a probability density function of wave height is developed by applying the maximum entropy method. The probability density function thusly derived agrees very well with the wave height distribution in shallow water, and appears to be useful in estimating extreme values and statistical properties of wave heights in finite water depth. However, a functional relationship between the probability distribution and the non-Gaussian characteristics of the data cannot be obtained by applying the maximum entropy method.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.149-161
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• 2020

In this paper we extend the functional principal component analysis for real-valued random functions to the case of Hilbert-space-valued functional random objects. For this, we introduce an autocovariance operator acting on the space of real-valued functions. We establish an eigendecomposition of the autocovariance operator and a Karuhnen-Loève expansion. We propose the estimators of the eigenfunctions and the functional principal component scores, and investigate the rates of convergence of the estimators to their targets. We detail the implementation of the methodology for the cases of compositional vectors and density functions, and illustrate the method by analyzing time-varying population composition data. We also discuss an extension of the methodology to multivariate cases and develop the corresponding theory.

• Communications of the Korean Mathematical Society
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• v.14 no.3
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• Bulletin of the Korean Chemical Society
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• v.32 no.9
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• pp.3372-3376
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• 2011

We have studied the relative stability and atomic structures of five $C_{20}X_2$ regioisomers obtained as diadducts of a $C_{20}$ cage (X = H, F, Cl, Br, and OH). All the regioisomers are geometric isomers, i.e., they differ in their spatial arrangement. Full-geometry optimizations of the regioisomers have been performed using the hybrid density-functional (B3LYP/6-31G(d, p)) method. Our results suggest that the cis-1 regioisomer (the 1,2-diadduct) is the most stable and that the second most stable is the trans-2 (1,13-diadduct) regioisomer, implying that the long-range interaction between the two adducts and the resonance effect are more pronounced than the diadduct-induced strain in the $C_{20}$ cage. The HOMO and LUMO characteristics of each regioisomer with the same symmetry of structural regioisomers except $C_{20}(OH)_2$ are topologically same. This suggests that by using an entirely different set of characteristic chemical reactions for each regioisomer, we can distinguish between the five regioisomers for each $C_{20}$ diadduct derivative.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.9
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• pp.1161-1166
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• 1999

Delay testing has become highlighted in the field of digital circuits as the speed and the density of the circuits improve greatly. However, delay faults in sequential circuits cannot be detected easily due to the existence of state registers. To overcome this difficulty a new scan filp-flop is devised which can be used for both stuck-at testing and delay testing. In addition, the new scan flip-flop can be applied to both the existing functional justification method and the newly-developed reverse functional justification method which uses scan flip-flops as storing the second test patterns rather than the first test patterns. Experimental results on ISCAS 89 benchmark circuits show that the number of testable paths can be increased by about 10% on the average.