• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Bulletin of the Korean Chemical Society
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• v.30 no.11
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• pp.2617-2620
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• 2009

Using Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices the series expansion formulae in terms of multicenter overlap integrals of three complete orthonormal sets of ${\psi}^{\alpha}$‒exponential type orbitals and linear combination coefficients of molecular orbitals are established for the potential of electrostatic field produced by the charges of molecule, where $\alpha$ = 1, 0, ‒1, ‒2,${\cdots}$. The formulae obtained can be useful for the study of interaction between atomic--molecular systems containing any number of closed and open shells when the ${\psi}^{\alpha}$‒exponential type basis functions and Coulomb-Yukawa like correlated interaction potentials are used in the Hartree-Fock-Roothaan and explicitly correlated approximations. The final results are valid for the arbitrary values of parameters of correlated interaction potentials and orbitals. As an example of application, the calculations have been performed for the potential energy of interaction between electron and molecule $H_2O$ using combined Hartree-Fock-Roothaan equations suggested by the author.

• Journal of the Korean Chemical Society
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• v.29 no.1
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• pp.3-8
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• 1985

Molecular electronegativity (EN) values are calculated employing the density functional definition of EN: the negative of the chemical potential in the density functional theory. Calculations are limited to the use of valence electrons (valence electron approximation). Our formula for the EN is given in terms of Hartree-Fock(HF) orbital energies. Resulting EN values for molecules as well as atoms exhibit a remarkable correlation with other existing scales. For molecules, we have achieved electronegativity equalization principle (Sanderson's principle).

• Journal of Electrical Engineering and Technology
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• v.9 no.5
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• pp.1670-1676
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• 2014

This paper presents the modeling of Single Electron Transistor (SET) based on Physical model of a device and its equivalent circuit. The physical model is derived from Schrodinger equation. The wave function of the electrode is calculated using Hartree-Fock method and the quantum dot calculation is obtained from WKB approximation. The resulting wave functions are used to compute tunneling rates. From the tunneling rate the current is calculated. The equivalent circuit model discuss about the effect of capacitance on tunneling probability and free energy change. The parameters of equivalent circuit are extracted and optimized using genetic algorithm. The effect of tunneling probability, temperature variation effect on tunneling rate, coulomb blockade effect and current voltage characteristics are discussed.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.953-957
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• 1994

Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${\AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.

• Journal of the Korean Chemical Society
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• v.40 no.8
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• pp.579-584
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• 1996

The HOMO-LUMO gap, and static and dynamic third-order polarizabilities for the polyenes are evaluated by means of the time-dependent Hartree Fock(TDHF) semiempirical PM3, AM1, MNDO, and MINDO/3 calculations. All calculations have performed on the series $C_2H_4$ to $C_{32}H_{34}$. The HOMO-LUMO gap increases in the order: MINDO/3> MNDO> PM3> AM1 levels. THG, DC-EFISHG, IDRI, and OKE for the various calculations show the order: AM1 > MNDO > PM3 levels. The various third-order effects for the polyenes have the following order: THG> DC-EFISHG> IDRI> OKE.

• Journal of the Korean Chemical Society
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• v.40 no.5
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• pp.317-326
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• 1996

The frequency dependent longitudinal polarizabilities ${\alpha}zz(\omega)$ and the second hyper-polarizabilities ${\gamma}zzzz(\omega)$ of the linear polyenes, $C_4H_6\;to\;C_{30}H_{32}$, have been evaluated using the ab initio time-dependent coupled perturbed Hartree-Fock (TDCPHF) theory with the 6-31G basis set. The ratios of the dynamic properties to the static values have been examined to illustrate the relative dispersion effect and extrapolated to the infinite polymer limit. Also the effect of interchain interaction for linear and nonlinear optical properties has been investigated for $C_4H_6$ and the theoretical discussion has been described to overcome the limitation of ab initio TDHF method in the resonance region.

• Journal of the Korean Chemical Society
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• v.42 no.4
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• pp.391-397
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• 1998

The geometry of furan, relevant to the binding of bis-furan lexitropsin that contains this ring to the base pair of minor groove of DNA, is optimized by semiempirical (MNDO) and ab initio (Hartree-Fock) methods. The proton affinity and electronic structure are evaluated at the 6-31G and $6-31G^{\ast}$ level of theory for the optimized geometry. The proton affinities are also studied for various substituted furans with the electrondonating and -withdrawing groups to estimate the substituent effect on the proton affinity of furans. It has been found that the electron-donating substituents increase the proton affinity of furan, whereas the electron-withdrawing substituents decrease it. This result can be explained with atomic charge and electron density at oxygen of substituted furans.

• 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.

• Proceeding of EDISON Challenge
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• 2017.03a
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• pp.11-15
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• 2017

We present a study of transition metal compounds using density functional theory (DFT), and density-corrected density functional theory(DC-DFT). By replacing the self-consistent density with that obtained from Hartree-Fock calculation, i.e., HF-DFT, the abnormality driven by self-interaction error is removed in several important cases. We discuss when and how HF-DFT works by examining 3d orbital dimers using approximate functionals and by comparing the results from self-consistent-DFT and HF-DFT with experimental values.