• Bulletin of the Korean Chemical Society
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• v.32 no.7
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• pp.2233-2236
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• 2011

We evaluate quantum-mechanical velocity autocorrelation functions from classical molecular dynamics simulations using quantum correction approaches. We apply recently developed approaches to supercritical argon and liquid neon. The results show that the methods provide a solution more efficient than previous methods to investigate quantum-mechanical dynamic behavior in condensed phases. Our numerical results are found to be in excellent agreement with the previous quantum-mechanical results.

• Interaction and multiscale mechanics
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• v.1 no.2
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• pp.303-315
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• 2008

In this paper, thermodynamical properties of crystalline silicon under strain are calculated using classical molecular dynamics (MD) simulations based on the Tersoff interatomic potential. The Helmholtz free energy of the silicon crystal under strain is calculated by using the ensemble method developed by Frenkel and Ladd (1984). To account for quantum corrections under strain in the classical MD simulations, we propose an approach where the quantum corrections to the internal energy and the Helmholtz free energy are obtained by using the corresponding energy deviation between the classical and quantum harmonic oscillators. We calculate the variation of thermodynamic properties with temperature and strain and compare them with results obtained by using the quasi-harmonic model in the reciprocal space.

• Bulletin of the Korean Chemical Society
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• v.35 no.3
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• pp.858-864
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• 2014

Recently, many researches have shown that even photosynthetic light-harvesting pigment-protein complexes can have quantum coherence in their excitonic energy transfer at cryogenic and physiological temperatures. Because the protein supplies such noisy environment around pigments that conventional wisdom expects very short lived quantum coherence, elucidating the mechanism and searching for an applicability of the coherence have become an interesting topic in both experiment and theory. We have previously studied the quantum coherence of a phycocyanin 645 complex in a marine algae harvesting light system, using Poisson mapping bracket equation (PBME). PBME is one of the applicable methods for solving quantum-classical Liouville equation, for following the dynamics of such pigment-protein complexes. However, it may suffer from many defects mostly from mapping quantum degrees of freedom into classical ones. To make improvements against such defects, benchmarking targets with more accurately described dynamics is highly needed. Here, we fall back to reduced hierarchical equation of motion (HEOM), for such a purpose. Even though HEOM is known to applicable only to simplified system that is coupled to a set of harmonic oscillators, it can provide ultimate accuracy within the regime of quantum-classical description, thus providing perfect benchmark targets for certain systems. We compare the evolution of the density matrix of pigment excited states by HEOM against the PBME results at physiological temperature, and observe more sophisticated changes of density matrix elements from HEOM. In PBME, the population of states with intermediate energies display only monotonically increasing behaviors. Most importantly, PBME suffers a serious issue of wrong population in the long time limit, likely generated by the zero-point energy leaking problem. Future prospects for developments are briefly discussed as a concluding remark.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.933-940
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• 2012

Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic lightharvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density.

• Rapid Communication in Photoscience
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• v.5 no.1
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• pp.8-10
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• 2016

The potential curves of OH bonds of liquid water are inhomogeneous because of a variety of interactions with other molecules and this leads to a wide distribution of vibrational frequency which hampers our understanding of the structure and dynamics of water molecules. Mixed quantum/classical (QM/CM) calculation methods are powerful theoretical techniques to help us analyze experimental data of various vibrational spectroscopies to study such inhomogeneous systems. In a type of those approaches, the interaction energy between OH bonds and other molecules is approximately represented by the interaction between the charges located at the appropriate interaction sites of water molecules. For this purpose, we re-calculated the values of charges by comparing the approximate interaction energies with quantum chemical interaction energies. We determined a set of charges at the TIP4P charge sites which better represents the quantum mechanical potential curve of OH bonds of liquid water.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.275-281
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• 2001

The trajectory of a classical dynamics is determined by the least action principle. As soon as we come to quantum dynamics, we have to consider all possible trajectories which are proposed to be a sum of the classical trajectory and Brownian fluctuation. Thus, the action involves the square of the derivative B(t) (white noise) of a Brownian motion B(t). The square is a typical example of a generalized white noise functional. The Feynman propagator should therefore be an average of a certain generalized white noise functional. This idea can be applied to a large class of dynamics with various kinds of Lagrangians.

• Proceedings of the Optical Society of Korea Conference
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• 2000.02a
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• pp.122-123
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• 2000

Fock-state is a highly non-classical radiation-field state. So if one can generate a Fock-state it is possible to study many interesting quantum-mechanical aspects. But in spite of its attraction, it is very difficult to generate a Fock-state experimentally although there have been many theoretical and experimental efforts to do it. Recently Chough et. al.$^{(1)}$ proposed a feasible scheme to achieve quasi number states. The key is to exploit the multi-photon resonances occurring in a driven Jaynes-Cummings system, so it is important to understand the processes at multi-photon resonances. In the present work we study the dynamics of multi-photon resonances in the driven Jaynes-Cummings system. (omitted)

• Journal of the Korean Chemical Society
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• v.52 no.1
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• pp.7-15
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• 2008

Molecular motion influencing the absorption spectrum of a chromophore in liquid is theoretically described by a quantum mechanical time correlation function. In the present paper, we developed a theoretical method to calculate such a quantum mechanical time-correlation function from a classical time-correlation function using semi-classical approximations. The calculated time-correlation function was combined with the second order cumulant expansion method to calculate the absorption spectrum of nile blue in acetonitrile. Reasonably good agreement with experimental spectrum was obtained. From the comparison with experimental spectrum, we concluded that the time scale of solvation dynamics of the system should be longer then 1ps and the first shell of solvent is the major contribution to the solvation dynamics.

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.885-892
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• 2012

Energy transfer dynamics of excited vibrational energy of OH stretching bonds in liquid water is theoretically studied. With time-dependent vibrational Hamiltonian obtained from a mixed quantum/classical calculation, we construct a master equation describing the energy transfer dynamics. Survival probability predicted by the master equation is compared with numerically exact one and we found that incoherent picture of energy transfer is reasonably valid for long-time population dynamics. Within the incoherent picture, we assess the validity of independent pair approximation (IPA) often introduced in the theoretical models utilized in the analysis of experimental data. Our results support that the IPA is almost perfectly valid as applied for the vibrational energy transfer in liquid water. However, proper incorporation of radial and orientational correlations between two OH bonds is found to be critical for a theory to be quantitatively valid. Consequently, it is suggested that the Forster model should be generalized by including the effects of the pair correlations in order to be applied for vibrational energy transfer in liquid water.

• Proceeding of EDISON Challenge
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• 2014.03a
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• pp.15-27
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• 2014

양자화학 (quantum chemistry)을 처음 접했을 때, 이전까지의 고전역학 (classical mechanics)에 익숙한 대다수의 학생들은 양자화학을 받아들이는 데 어려움을 겪는다. 모형계에 양자역학 (quantum mechanics)을 직접 적용하여 봄으로써 생소한 양자 개념에 대한 이해를 도울 수 있다. 본 논문에서는 양자동역학 (quantum dynamics)을 수치적으로 구현하는 계산 프로그램을 모형계에 적용하여 양자 개념을 설명할 수 있는 몇 가지 예를 보이고자 한다. 1 차원 시간의존 슈뢰딩거 방정식 (1-D time-dependent $Schr{\ddot{o}}dinger$ equation)의 해를 얻어 양자동역학을 구현하였으며, 그에 해당하는 고전동역학은 뉴턴 방정식 (Newton's equation)의 해로 얻어졌다. 조화 진동자 퍼텐셜 (harmonic oscillator potential), 모스 진동자 퍼텐셜 (Morse oscillator potential), 이중 우물 퍼텐셜 (double-well potential), 네모 퍼텐셜 장벽 (rectangular potential barrier), 그리고 에카트 퍼텐셜 (Eckart potential)에 대한 계산을 수행하였다. 두 가지 동역학을 비교하기 위하여 계산 결과의 시각화 (visualization)를 이용하고 동역학 특성의 차이를 비교하는 차별화 (differentiation)를 강조한다. 영점에너지 (zero-point energy), 위상어긋남 (dephasing), 터널링 (tunneling), 그리고 반사 (reflection) 현상과 같은 양자동역학의 특징을 고전동역학과 비교함으로써 직관적인 이해를 도울 수 있었다. 이러한 결과는 양자화학에 입문하는 학생들을 대상으로 쓰일 수 있는 효율적인 강의 모델을 제시할 것으로 기대한다.