• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.809-811
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• 2003

This brief review contains surveys of both four-component and two-component relativistic molecular theories. First the four-component relativistic approach is reviewed. Emphasis is placed on efficient computational schemes for the four-component Dirac-Hartree-Fock and Dirac-Kohn-Sham methods. Next, in the twocomponent relativistic framework, two relativistic Hamiltonians, RESC and higher-order Douglas-Kroll (DK), are introduced. An illustrative application is shown for the relativistic study on valence photoelectron spectrum of OsO₄. The developing four-component relativistic and approximate quasi-relativistic methods have been packed in a program suite named REL4D.

• Bulletin of the Korean Space Science Society
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• 2009.10a
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• pp.34.2-34.2
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• 2009

The relativistic Weibel instability has drawn attention as a main mechanism of the magnetic generation in the core of galaxies or in the formation of universe. The Weibel instability is not yet fully understood in the relativistic region. We investigated nonlinear saturation and decay of the relativistic Weibel instability. It is found that the early phase of the instability is in excellent agreement with the linear theory. But, an analysis based on an alternative magnetic trapping saturation theory reveals that a substantial discrepancy between the theory and simulation is revealed in the relativistic regime in contrast to an excellent agreement in the non-relativistic regime. The analysis of the Weibel instability beyond the quasilinear saturation stage shows an inverse cascade process via a nonlinear decay instability involving electrostatic fluctuation.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.193-196
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• 2002

The relativistic theory has not been properly taken up by the marine hydrodynamicists. To take on a relativistic view, we confine ourselves to a simple vector case of a wave train in spacetime, to be shown to represent a sound wave or a surface wave, and bring in an observer who is travelling on another platform. We are interested in relative position of each event on these two worldlines. It, then, will be shown that the velocity, the acceleration, the encounter frequency, the group velocity, and the time and the space distance between the wave and the observer on the worldlines should all be derivable in principle. This is interpreted to mean that we really have the relativistic events taking place with different values of time dilation in the sense of 'spacetime', and that the well-known ${\lceil}special Theory of Relativity{\rfloor}$ applies just as well in hydrodynamic waves.

• Bulletin of the Korean Chemical Society
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• v.34 no.1
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• pp.179-187
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• 2013

We describe newly developed software named KPACK for relativistic electronic structure computation of molecules containing heavy elements that enables the two-component ab initio calculations in Kramers restricted and unrestricted formalisms in the framework of the relativistic effective core potential (RECP). The spin-orbit coupling as relativistic effect enters into the calculation at the Hartree-Fock (HF) stage and hence, is treated in a variational manner to generate two-component molecular spinors as one-electron wavefunctions for use in the correlated methods. As correlated methods, KPACK currently provides the two-component second-order M${\o}$ller-Plesset perturbation theory (MP2), configuration interaction (CI) and complete-active-space self-consistent field (CASSCF) methods. Test calculations were performed for the ground states of group-14 elements, for which the spin-orbit coupling greatly influences the determination of term symbols. A categorization of three procedures is suggested for the two-component methods on the basis of spin-orbit coupling manifested in the HF level.

• Bulletin of the Korean Chemical Society
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• v.24 no.6
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• pp.728-730
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• 2003

Bond lengths, harmonic vibrational frequencies and dissociation energies of TlAt are calculated at ab initio molecular orbital and density functional theory using effective spin-orbit operator and relativistic effective core potentials. Spin-orbit effects estimated from density functional theory are in good agreement with those from ab initio calculations, implying that density functional theory with effective core potentials can be an efficient and reliable methods for spin-orbit interactions. The estimated $R_e$, $ω_e$ and $D_e$ values are 2.937 ${\AA}$, 120 $cm^{-1}$, 1.96 eV for TlAt. Spin-orbit effects generally cause the bond contraction in Group 13 elements and the bond elongation in the Group 17 elements, and spin-orbit effects on Re of TlAt are almost cancelled out. The spinorbit effects on $D_e$ of TlAt are roughly the sum of spin-orbit effects on $D_e$ of the corresponding element hydrides. Electron correlations and spin-orbit effects are almost additive in the TlAt molecule.

• Publications of The Korean Astronomical Society
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• v.26 no.2
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• pp.55-70
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• 2011

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

• Bulletin of the Korean Chemical Society
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• v.22 no.9
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• pp.969-974
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• 2001

Model calculations for small molecules Li2, F2, LiF and BF have been performed at the Dirac-Fock level of theory using Dirac-Coulomb and Dirac-Coulomb-Magnetic Hamiltonians with various basis sets. In order to understand what may happen when the relativity becomes significant, the value of c, speed of light, is varied from the true value of 137.036 a.u. to 105 (nonrelativistic case) and also to 50 and 20 a.u. (exaggerated relativistic cases). Qualitative trends are discussed with special emphasis on the effect of the magnetic part of the Breit interaction term. The known relativistic effects on bonding such as the bond length contraction or expansion are demonstrated in this model study. Total energy, $\pi-orbital$ splitting, bond length, bond dissociation energy and dipole moment are calculated, and shown to be modified in a uniform direction by the effect of the magnetic term. Inclusion of the magnetic term raises the total energy, increases the bond length, reduces the $\pi-orbital$ splitting, increases the bond dissociation energy, and mitigates the changes in dipole moment caused by the Dirac term.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.775-782
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• 2014

The importance of including spin-orbit interactions for the correct description of structures and vibrational frequencies of haloiodomethanes is demonstrated by density functional theory calculations with spin-orbit relativistic effective core potentials (SO-DFT). The vibrational frequencies and the molecular geometries obtained by SO-DFT calculations do not match with the experimental results as well as for other cations without significant relativistic effects. In this sense, the present data can be considered as a guideline in the development of the relativistic quantum chemical methods. The influence of spin-orbit effects on the bending frequency of the cation could well be recognized by comparing the experimental and calculated results for $CH_2BrI$ and $CH_2ClI$ cations. Spin-orbit effects on the geometries and vibrational frequencies of $CH_2XI$ (X=F, Cl, Br, and I) neutral are negligible except that C-I bond lengths of haloiodomethane neutral is slightly increased by the inclusion of spin-orbit effects. The $^2A^{\prime}$ and $^2A^{{\prime}{\prime}}$ states were found in the cations of haloiodomethanes and mix due to the spin-orbit interactions and generate two $^2E_{1/2}$ fine-structure states. The geometries of $CH_2XI^+$ (X=F and Cl) from SO-DFT calculations are roughly in the middle of two cation geometries from DFT calculations since two cation states of $CH_2XI$ (X=F and Cl) from DFT calculations are energetically close enough to mix two cation states. The geometries of $CH_2XI^+$ (X=Br and I) from SO-DFT calculations are close to that of the most stable cation from DFT calculations since two cation states of $CH_2XI$(X=Br and I) from DFT calculations are energetically well separated near the fine-structure state minimum.

• Journal of Astronomy and Space Sciences
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• v.36 no.2
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• pp.45-60
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• 2019

The Earth's outer radiation belt has long received considerable attention mainly because the MeV electron flux in the belt varies often dramatically and at various time scales. It is now widely accepted that the wave-particle interaction is one of the major mechanisms responsible for such flux variations. The wave-particle interaction can accelerate electrons to MeV energies, explaining the observed flux increase events, and can also scatter the electrons' motion into the loss cone, resulting in atmospheric precipitation and thus contributing to flux dropouts. In this paper, we provide a review of the current state of research on relativistic electron scattering and precipitation due to the interaction with electromagnetic ion cyclotron (EMIC) waves in the inner magnetosphere. The review is intended to cover progress made over the last ~15 years in the theory and simulations of various issues, including quasilinear resonance diffusion, nonlinear interactions, nonresonant interactions, effects of finite normal angle on pitch angle scattering, effects due to rising tone emission, and ways to scatter near-equatorial pitch angle electrons. The review concludes with suggestions of a few promising topics for future research.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.60.1-60.1
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• 2013

We study tidal disruption and subsequent mass fallback process for stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that the mass fallback rate decays with the expected -5/3 power of time for parabolic orbits, albeit with a slight deviation due to the self-gravity of the stellar debris. For eccentric orbits, however, there is a critical value of the orbital eccentricity, significantly below which all of the stellar debris is bound to the supermassive black hole. All the mass therefore falls back to the supermassive black hole in a much shorter time than in the standard, parabolic case. The resultant mass fallback rate considerably exceeds the Eddington accretion rate and substantially differs from the -5/3 power of time. We also show that general relativistic precession is crucial for accretion disk formation via circularization of stellar debris from stars on moderately eccentric orbits.