Browsing by Author "Zhu, Chaoyuan"

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A Density Functional Theory Study on Nonlinear Optical Properties of Double Cage Excess Electron Compounds: Theoretically Design M[Cu(Ag)@(NH3)(n)](M = Be, Mg and Ca; n=1-3)
(2019-04-05)
Liang, Yan Ying
;
Li, Bo
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Xu, Xuan
;
Gu, Feng Long
;
Zhu, Chaoyuan
In this work, we investigated the nonlinear optical (NLO) properties of excess electron electride molecules of M[Cu(Ag)@(NH3)(n)](M = Be, Mg and Ca; n = 1-3) using density functional theory (DFT). This electride molecules consist of an alkaline-earth (Be, Mg and Ca) together with transition metal (Cu and Ag) doped in NH3 cluster. The natural population analysis of charge and their highest occupied molecular orbital suggests that the M[Cu(Ag)@(NH3)(n)] compound has excess electron like alkaline-earth metal form double cage electrides molecules, which exhibit a large static first hyperpolarizability (beta(e)(0)) (electron contribution part) and one of which owns a peak value of beta(e)(0) 216,938 (a.u.) for Be [Ag@(NH3)(2)] and vibrational harmonic first hyperpolarizability [(beta(nr)(zzz)) (nuclear contribution part) values and the ratio of beta(nr)(zzz)/beta(e)(zzz'), namely, eta values from 0.02 for Be[Ag@(NH3)] to 0.757 for Mg [Ag@(NH3)(3)]. The electron density contribution in different regions on beta(e)(zzz) values mainly come from alkaline-earth and transition metal atoms by first hyperpolarizability density analysis, and also explains the reason why beta(e)(zzz) values are positive and negative. Moreover, the frequency-dependent values ss(-2 omega,omega,omega) are also estimated to make a comparison with experimental measures. (c) 2018 Wiley Periodicals, Inc.
A nonlinear optical switch induced by an external electric field: inorganic alkaline-earth alkalide
(2019-05-28)
Li, Bo
;
Peng, Daoling
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Gu, Feng Long
;
Zhu, Chaoyuan
;
應用化學系分子科學碩博班
Exploring a new type of nonlinear optical switch molecule with excess electron character is extremely important for promoting the application of excess electron compounds in the nonlinear optical (NLO) field. Here, we report external electric field (EEF) induced second-order NLO switch molecules of inorganic alkaline-earth alkalides, M(NH3) 6Na2 (M = Mg or Ca). The centrosymmetric structure of M(NH3) 6Na2 is destroyed in the presence of an EEF, and then a long-range charge transfer process occurs. It has been found that excess electrons are gradually transferred from one Na atom to the other Na atom through the inorganic metal cluster M(NH3) 6. Finally, the excess electrons are completely located on one of the two Na atoms. In particular, the electronic contribution of the static first hyperpolarizability (b e 0) for M(NH3) 6Na2 exhibits a large significant difference when the EEF is switched on. The b e 0 value of M(NH3) 6Na2 is 0 when EEF = 0, while the peak b e 0 values are 5.95 106 (a. u.) for Mg(NH3) 6Na2 (EEF = 58 10 4 (a. u.)) and 1.83 107 (a. u.) for Ca(NH3) 6Na2 (EEF = 53 10 4 (a. u.)). This work demonstrates that the compounds M(NH3) 6Na2 can serve as potential candidates for NLO switches.
A phenothiazine-based colorimetric chemodosimeter for the rapid detection of cyanide anions in organic and aqueous media
(2014)
Garg, Bhaskar
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Yan, Linyin
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Bisht, Tanuja
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Zhu, Chaoyuan
;
Ling, Yong-Chien
A novel, phenothiazine-based chemodosimeteric probe PCP 1 has been developed and studied as a cyanide selective indicator in organic and aqueous media. Complete colour bleaching was observed due to nucleophilic addition of cyanide to the tricyanovinyl moiety of PCP 1, which results in the disruption of the extended conjugate and turn-off the intramolecular charge transfer process.
A QUASICLASSICAL TRAJECTORY STUDY OF REACTIVE SCATTERING ON AN ANALYTICAL POTENTIAL ENERGY SURFACE FOR GeH(2) SYSTEM
(2011-04-01)
Zhang, Li
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Zhu, Chao-Yong
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Jiang, Gang
;
Zhu, Chaoyuan
;
Zhu, Z. H.
A quasiclassical trajectory method was employed to study reaction Ge + H(2) (v = 0, j = 0) and reverse reaction H + GeH (v = 0, j = 0) on an analytical potential energy surface obtained from simplified many-body expansion method with fitting to B3P86/CC-pVTZ calculations around a global minimum and a long-range van de Waals well plus spectroscopy data for diatomic molecules GeH and H(2). Reaction probabilities from both reaction and reverse reaction were calculated. Dominant reaction is complex-forming reaction Ge + H(2) (v = 0, j = 0) -> GeH(2), and its cross section is 10 times bigger than that of complex-forming reaction from the reverse reaction. There is no threshold effect for complex-forming reaction and the cross sections for both complex-forming reactions decrease with the increase of collision energy. Life time of complex is shown to be decreasing with increase of collision energy. Dominant reverse reaction is reaction H + GeH (v = 0, j = 0) -> Ge + H(2); the reaction probability decreases with the increase of collision energy and differential cross section shows that this reverse reaction has almost equal angular distribution at low collision energy and mostly forward scattering at high collision energy.
A QUASICLASSICAL TRAJECTORY STUDY OF REACTIVE SCATTERING ON AN ANALYTICAL POTENTIAL ENERGY SURFACE FOR GeH2 SYSTEM
(2011-04-01)
Zhang, Li
;
Zhu, Chao-Yong
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Jiang, Gang
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Zhu, Chaoyuan
;
Zhu, Z. H.
A quasiclassical trajectory method was employed to study reaction Ge + H-2 (v = 0, j = 0) and reverse reaction H + GeH (v = 0, j = 0) on an analytical potential energy surface obtained from simplified many-body expansion method with fitting to B3P86/CC-pVTZ calculations around a global minimum and a long-range van de Waals well plus spectroscopy data for diatomic molecules GeH and H-2. Reaction probabilities from both reaction and reverse reaction were calculated. Dominant reaction is complex-forming reaction Ge + H-2 (v = 0, j = 0) -> GeH2, and its cross section is 10 times bigger than that of complex-forming reaction from the reverse reaction. There is no threshold effect for complex-forming reaction and the cross sections for both complex-forming reactions decrease with the increase of collision energy. Life time of complex is shown to be decreasing with increase of collision energy. Dominant reverse reaction is reaction H + GeH (v = 0, j = 0) -> Ge + H-2; the reaction probability decreases with the increase of collision energy and differential cross section shows that this reverse reaction has almost equal angular distribution at low collision energy and mostly forward scattering at high collision energy.
A TDDFT study on the excited-state double proton transfer reaction of 8-hydroxyquinoline along a hydrogen-bonded bridge
(2017-08-21)
Liu, Yu-Hui
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Wang, Shi-Ming
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Zhu, Chaoyuan
;
Lin, Sheng Hsien
;
應用化學系
The mechanism of the excited-state double proton transfer (ESDPT) reactions of 8-hydroxyquinoline (8HQ) along three types of hydrogen-bonded bridges-ammonia (NH3), water (H2O) and acetic acid (AcOH) has been investigated by using time-dependent density functional theory. Based on the analysis of hydrogen bond strengths and the excited-state potential energy surfaces (PES) along the proton transfer coordinates, it is concluded that the hydrogen bonds play the key role in the excited-state multiple proton transfer reaction. Moreover, three different concerted mechanisms have been found in 8HQ center dot NH3, 8HQ center dot H2O and 8HQ center dot AcOH complexes. Upon photoexcitation, the deprotonation of a hydroxyl group in 8HQ would occur first in 8HQ center dot NH3 due to the stronger hydrogen bond -OH center dot center dot center dot NH3. On the contrary, the hydrogen bond -OH center dot center dot center dot O-C-OH is much weaker in the 8HQ center dot AcOH complex, and this leads to a fast protonation of -N- in the 8HQ moiety. For the 8HQ center dot H2O complex, the hydrogen bond strengths are almost the same, so that both protons would transfer simultaneously in a symmetrical and concerted fashion.
Ab initio studies of excited electronic state S(2) of pyrazine and Franck-Condon simulation of its absorption spectrum
(2009-07-07)
He, Rongxing
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Zhu, Chaoyuan
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Chin, Chih-Hao
;
Lin, Sheng Hsien
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應用化學系分子科學碩博班
The equilibrium geometry and 24 vibrational-normal-mode frequencies of the excited state S(2)((1)B(2u))of pyrazine are calculated and characterized using the complete active space self-consistent field method in the adiabatic representation. The displaced harmonic oscillator approximation is used to simulate the absorption spectrum of the S(2)((1)B(2u)) state along with the Franck-Condon approximation. It is found that the totally symmetric mode v(1) plays the most important role and this exactly agrees with the experimental observations. The simulated absorption spectrum agrees well with those experimentally observed. This indicates that the present S(2)((1)B(2u)) state calculated in the adiabatic representation effectively includes contribution from the diabatic vibronic coupling through the conical intersection. (C) 2009 Elsevier B.V. All rights reserved.
Ab initio studies of excited electronic state S-2 of pyrazine and Franck-Condon simulation of its absorption spectrum
(2009-07-07)
He, Rongxing
;
Zhu, Chaoyuan
;
Chin, Chih-Hao
;
Lin, Sheng Hsien
;
應用化學系分子科學碩博班
The equilibrium geometry and 24 vibrational-normal-mode frequencies of the excited state S-2(B-1(2u))of pyrazine are calculated and characterized using the complete active space self-consistent field method in the adiabatic representation. The displaced harmonic oscillator approximation is used to simulate the absorption spectrum of the S-2(B-1(2u)) state along with the Franck-Condon approximation. It is found that the totally symmetric mode v(1) plays the most important role and this exactly agrees with the experimental observations. The simulated absorption spectrum agrees well with those experimentally observed. This indicates that the present S-2(B-1(2u)) state calculated in the adiabatic representation effectively includes contribution from the diabatic vibronic coupling through the conical intersection. (C) 2009 Elsevier B.V. All rights reserved.
Absorption and fluorescence spectra of the neutral and anionic green fluorescent protein chromophore: Franck-Condon simulation
(2012-07-10)
Huang, Tsung-wei
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Yang, Ling
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Zhu, Chaoyuan
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Lin, Sheng Hsien
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應用化學系分子科學碩博班
Absorption and fluorescence spectra of the neutral and anionic green fluorescent protein (GFP) chromophore, namely p-hydroxybenzylideneimidazolidinone (p-HBDI), have been simulated using the Franck-Condon factors including inhomogeneous broadening of solvent effect. Ground and the first excited states were calculated by time dependent density functional theory with and without the polarizable continuum model environment. Simulated peak of the neutral/anionic p-HBDI at 380 nm (423 nm)/421 nm agrees with experiment value 370 nm (434 nm)/419 nm for absorption (fluorescence) spectrum. Simulated width of the neutral/anionic p-HBDI at 0.51 eV (0.54 eV)/0.57 eV agrees with experiment value 0.54 eV (0.66 eV)/0.56 eV for absorption (fluorescence) spectrum. (C) 2012 Elsevier B. V. All rights reserved.
Algorithmic decoherence time for decay-of-mixing non-Born-Oppenheimer dynamics
(2008-07-14)
Cheng, Shu Chun
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Zhu, Chaoyuan
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Liang, Kuo Kan
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Lin, Sheng Hsien
;
Truhlar, Donald G.
The performance of an analytical expression for algorithmic decoherence time is investigated for non-Born-Oppenheimer molecular dynamics. There are two terms in the function that represents the dependence of the decoherence time on the system parameters; one represents decoherence due to the quantum time-energy uncertainty principle and the other represents a back reaction from the decoherent force on the classical trajectory. We particularly examine the question of whether the first term should dominate. Five one-dimensional two-state model systems that represent limits of multidimensional nonadiabatic dynamics are designed for testing mixed quantum-classical methods and for comparing semiclassical calculations with exact quantum calculations. Simulations are carried out with the semiclassical Ehrenfest method (SE), Tully's fewest switch version (TFS) of the trajectory surface hopping method, and the decay-of-mixing method with natural switching, coherent switching (CSDM), and coherent switching with reinitiation (CSDM-D). The CSDM method is demonstrated to be the most accurate method, and it has several desirable features: (i) It behaves like the representation-independent SE method in the strong nonadiabatic coupling regions; (ii) it behaves physically like the TFS method in noninteractive region; and (iii) the trajectories are continuous with continuous momenta. The CSDM method is also demonstrated to balance coherence well with decoherence, and the results are nearly independent of whether one uses the adiabatic or diabatic representation. The present results provide new insight into the formulation of a physically correct decoherence time to be used with the CSDM method for non-Born-Oppenheimer molecular dynamic simulations. (c) 2008 American Institute of Physics.
An excited-state Wolff rearrangement reaction of 5-diazo Meldrum's acid: an ab initio on-the-fly nonadiabatic dynamics simulation
(2018-09-21)
Xu, Chao
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Gu, Feng Long
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Zhu, Chaoyuan
;
交大名義發表
;
應用化學系
A global switching on-the-fly trajectory surface hopping dynamics simulation at the 3SA-CASSCF(12,11)/6-31G* quantum level has been employed to probe the photo-induced Wolff rearrangement (WR) reaction of 5-diazo Meldrum's acid (DMA) within three low-lying electronic excited states. The present simulation predicted that the branching ratios for relaxing back to the ground state, isomerizing to diazirine, and reaction to ketene I via carbene I are 69% +/- 0.1, 3% +/- 0.4, and 28% +/- 0.1, which are in excellent agreement with those obtained by the femtosecond spectroscopy experiment, 67%, 3% and 30%, respectively. In particular, the present simulation revealed that the major WR reaction to ketene I pathway is stepwise via the excited-state to carbene I (17.8% +/- 0.2) and via the ground-state to carbene I (8.7% +/- 0.2), and the minor pathway is concerted synchronous (1.5% +/- 0.6). The photo-induced WR reaction of DMA has been quantitatively interpreted in terms of the distribution of extended seam surfaces as a function of CN dissociation bonds for two important conical intersections within three low-lying electronic excited states. Ultrafast dynamic time constants have been estimated to be about 500 fs +/- 120 fs and 180 fs +/- 80 fs for the stepwise and the concerted WR reaction to ketene I which are also in good agreement with those determined by the experiment. Therefore, the photo-induced excited-state WR reaction mechanism has been quantitatively revealed by the present real-time dynamics simulation.
Analytical semiclassical theory for general non-adiabatic transition and tunneling
(2009-10-01)
Zhu, Chaoyuan
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應用化學系分子科學碩博班
;
Institute of Molecular science
A semiclassical solution of general two-state non-adiabatic transition and tunneling is found analytically within the Wentzel-Kramers-Brillouin (WKB) semiclassical framework associated with the Stokes phenomenon in mathematics. The non-adiabatic scattering matrix is determined by a complex quantity called the Stokes constant, which can be directly connected to the complex transition points of the WKB solution. An accurate and compact analytical solution is found for this Stokes constant which is a function of three parameters, one of which corresponds to the diabatic-to-adiabatic transformation angle that is interpreted as a type of non-adiabatic transition. Numerical examples demonstrate that the present unified analytical semiclassical theory works very well for both non-adiabatic transition and non-adiabatic tunneling. The present analytical semiclassical method can be a very powerful tool for application to multidimensional non-adiabatic dynamic processes.
Anharmonic Franck-Condon Simulation of the Absorption and Fluorescence Spectra for the Low-Lying S(1) and S(2) Excited States of Pyridine
(2009-12-31)
Wang, Huan
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Zhu, Chaoyuan
;
Yu, Jian-Guo
;
Lin, Sheng Hsien
;
應用化學系分子科學碩博班
Anharmonic effects of the absorption and fluorescence spectra of pyridine molecule are studied and analyzed for the two-low lying singlet excited states S(1)((1)B(1)) and S(2)((1)B(2)). The complete active space self-consistent field (CASSCF) method is utilized to compute equilibrium geometries and all 27 vibrational normal-mode frequencies for the ground state and the two excited states. The present calculations show that the frequency differences between the ground and two excited states are small for the ten totally symmetric vibrational modes so that the displaced oscillator approximation can be used for spectrum Simulations. The Franck-Condon factors within harmonic approximation basically grasp the main features of molecular spectra, but simulated 0-0 transition energy position and spectrum band shapes are not satisfactorily good for S(1)((1)B(1)) absorption and fluorescence spectra in comparison with experiment observation. As the first-order anharmonic correction added to Franck-Condon factors, both spectrum positions and band shapes can be simultaneously improved for both absorption and fluorescence spectra. It is concluded that the present anharmonic correction produces a significant dynamic shifts for spectrum positions and improves spectrum band shapes as well. The detailed structures of absorption spectrum of S(2)((1)B(2)) state observed from experiment can be also reproduced with anharmonic Franck-Condon simulation, and these were not shown in the harmonic Franck-Condon simulation with either distorted or Duschinsky effects in the literature.
Anharmonic Franck-Condon Simulation of the Absorption and Fluorescence Spectra for the Low-Lying S-1 and S-2 Excited States of Pyridine
(2009-12-31)
Wang, Huan
;
Zhu, Chaoyuan
;
Yu, Jian-Guo
;
Lin, Sheng Hsien
;
應用化學系分子科學碩博班
Anharmonic effects of the absorption and fluorescence spectra of pyridine molecule are studied and analyzed for the two-low lying singlet excited states S-1(B-1(1)) and S-2(B-1(2)). The complete active space self-consistent field (CASSCF) method is utilized to compute equilibrium geometries and all 27 vibrational normal-mode frequencies for the ground state and the two excited states. The present calculations show that the frequency differences between the ground and two excited states are small for the ten totally symmetric vibrational modes so that the displaced oscillator approximation can be used for spectrum Simulations. The Franck-Condon factors within harmonic approximation basically grasp the main features of molecular spectra, but simulated 0-0 transition energy position and spectrum band shapes are not satisfactorily good for S-1(B-1(1)) absorption and fluorescence spectra in comparison with experiment observation. As the first-order anharmonic correction added to Franck-Condon factors, both spectrum positions and band shapes can be simultaneously improved for both absorption and fluorescence spectra. It is concluded that the present anharmonic correction produces a significant dynamic shifts for spectrum positions and improves spectrum band shapes as well. The detailed structures of absorption spectrum of S-2(B-1(2)) state observed from experiment can be also reproduced with anharmonic Franck-Condon simulation, and these were not shown in the harmonic Franck-Condon simulation with either distorted or Duschinsky effects in the literature.
Anharmonic Franck-Condon simulation of the absorption and fluorescence spectra for the low-lying S-1 and S-2 excited states of pyrimidine
(2012-05-25)
Yang, Ling
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Zhu, Chaoyuan
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Yu, Jianguo
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Lin, Sheng Hsien
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應用化學系分子科學碩博班
Intensities and profiles of vibronic spectra of the low-lying singlet excited states were investigated with anharmonic and harmonic Franck-Condon simulations for pyrimidine. The first-order anharmonic correction shows dynamic shift of spectra that is exactly same as difference of reorganization energy between ground and excited states. The first-order correction show intensity enhancement of absorption and intensity weakening of fluorescence for S-1 state, and dynamic shift is also significant. On the other hand, the first-order correction is negligible for S-2 state. The main spectral progressions are well described by totally symmetry modes v(6a), v(1) and v(12). One mode from non-total symmetry v(16a) contributes to the weak band at 16a(2) transition for S-1 state. Four ab initio methods were employed in simulation; CASSCF, CASPT2, DFT and TD-DFT, and coupled-cluster singles-doubles (CCSD) and the equation-of-motion (EOM-CCSD) methods. They all work well, but CASSCF method show the best agreement with experiment for the weak-band intensities. (C) 2012 Elsevier B.V. All rights reserved.
Benchmark Performance of Global Switching versus Local Switching for Trajectory Surface Hopping Molecular Dynamics Simulation: Cis <-> Trans Azobenzene Photoisomerization
(2017-05-19)
Yue, Ling
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Yu, Le
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Xu, Chao
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Lei, Yibo
;
Liu, Yajun
A newly developed global switching algorithm that does not require calculation of nonadiabatic coupling vectors reduces computational costs significantly. However, the accuracy of this simplest nonadiabatic molecular dynamic method has not been extensively compared with the conventional Tully's fewest switches. It is necessary to demonstrate the accuracy of this global switching algorithm. An extensive comparison between local and global switching on-the-fly trajectory surface hopping molecular dynamics is performed for cis-to-trans (800 sampling trajectories) and trans-to-cis (600 sampling trajectories) azobenzene photoisomerization at the OM2/MRCI level. The global switching algorithm is coded into the Newton-X program package. Excellent agreement between the two switching algorithms is obtained not only for highly averaged quantities of quantum yields and lifetimes, but also for detailed contour patterns of product distributions, hopping spot distributions and hopping directions in terms of conical intersections between ground and the first excited states. Therefore, the global switching trajectory surface hopping method can be applied to larger complex systems in which nonadiabatic coupling is not available for excited-state molecular dynamic simulations.
Benchmarking calculations of spectral densities for the diagonal and nondiagonal exciton-phonon coupling of tetracene crystal
(2017-08-01)
Zhang, Jin
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Zhu, Chaoyuan
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Liang, WanZhen
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應用化學系
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Department of Applied Chemistry
The spectral densities of diagonal and nondiagonal exciton-phonon (e-p) coupling for tetracene crystal have been calculated by the harmonic oscillator (HO) model and ground-state MD-based approaches. We find that classical MD-based approaches overestimate the coupling of exciton with high-frequency vibrational modes and predict the strongest e-p coupling appeared above 1500 cm(-1) whereas HO model and AIMD-based approach predict it appeared at similar to 1400 cm(-1). Additionally, the calculated spectral densities of nondiagonal e-p coupling for three different dimers show that they are continuously distributed in the range of 0-150 cm(-1) and are 2-3 order of magnitude smaller than the maxima of diagonal e-p coupling. (C) 2017 Elsevier B.V. All rights reserved.
C/B codoping effect on band gap narrowing and optical performance of TiO2 photocatalyst: a spin-polarized DFT study
(2013)
Lin, Yanming
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Jiang, Zhenyi
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Zhu, Chaoyuan
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Hu, Xiaoyun
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Zhang, Xiaodong
The electronic and optical properties of several possible C/B-codoped models of anatase and rutile TiO2 have been investigated systematically using spin-polarized density functional theory calculations. Our calculated results show that the synergistic effect of C/B codoping can induce some hybridized energy states appearing in the forbidden gap and the band gap has a narrowing in anatase and rutile TiO2, which can lead to a decrease of the photon excitation energy and an obvious red-shift of the optical absorption edge. These results lead to an excellent photocatalytic activity in C/B-codoped TiO2. Moreover, with the increase of C and B impurities' concentration in anatase and rutile TiO2, we find that the intensity of impurity states has a strengthening in the band gap, the position of impurity states changes, and the visible-light absorption performance improves gradually.
Chiral conversion and periodical decay in bridged-azobenzene photoisomerization: an ab initio on-the-fly nonadiabatic dynamics simulation
(2016-01-01)
Gao, Wanqing
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Yu, Le
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Zheng, Xiaolei
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Lei, Yibo
;
Zhu, Chaoyuan
With the implementation of global nonadiabatic switching probability algorithm based on the Zhu-Nakamura theory, we performed on-the-fly trajectory surface hopping simulations at the CASSCF level to analyze the cis <-> trans photoisomerization mechanism of bridged-azobenzene upon S-1 excitation. The cis-to-trans isomerization process was initiated by the pedal-like twist of -N=N- moiety and observed hopping to S-0 mainly via the cis-form conical intersection region. While, the trans-to-cis process is induced by the nonsymmetrical torsion motion toward the central eight-membered ring and encountered surface hopping through another conical region lying in the middle of the isomerization pathway. In cis-to-trans photoisomerization, we also observed a particular chiral conversion pathway with surface hopping occurs at CI-trans conical region. The trajectories followed this pathway possess relative longer excited state lifetimes as the similar to 40 fs initial stage oscillation in the cis Franck-Condon region. Moreover, the periodical population decay pattern of S-1 state in trans-to-cis process was observed with an interval of similar to 16 fs.
Constraint Trajectory Surface-Hopping Molecular Dynamics Simulation of the Photoisomerization of Stilbene
(2014)
Lei, Yibo
;
Wu, Shaomei
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Zhu, Chaoyuan
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Wen, Zhenyi
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Lin, Sheng-Hsien
Combining trajectory surface hopping (TSH) method with constraint molecular dynamics, we have extended TSH method from full to flexible dimensional potential energy surfaces. Classical trajectories are carried out in Cartesian coordinates with constraints in internal coordinates, while nonadiabatic switching probabilities are calculated separately in free internal coordinates by Landau-Zener and Zhu-Nakamura formulas along the seam. Two-dimensional potential energy surfaces of ground S-0 and excited S-1 states are constructed analytically in terms of torsion angle and one dihedral angle around the central ethylenic C-C bond, and the other internal coordinates are all fixed at configuration of the conical intersection. At this conical intersection, the branching ratio from the present simulation is 48 : 52 (33 : 67) initially starting from trans(cis)-Stilbene in comparison with experimental value 50 : 50. Quantum yield for trans-to-cis isomerization is estimated as 49% in very good agreement with experimental value of 55%, while quantum yield for cis-to-trans isomerization is estimated as 47% in comparison with experimental value of 35%.