亚洲免费av电影一区二区三区,日韩爱爱视频,51精品视频一区二区三区,91视频爱爱,日韩欧美在线播放视频,中文字幕少妇AV,亚洲电影中文字幕,久久久久亚洲av成人网址,久久综合视频网站,国产在线不卡免费播放

        ?

        Application of Connection in Molecular Dynamics

        2018-05-14 01:05:14XinSun孫鑫
        Communications in Theoretical Physics 2018年3期

        Xin Sun(孫鑫)

        Department of Physics and State Key Laboratory of Surface Physics,Fudan University,Shanghai 200433,China

        Collaborative Innovation Center of Advanced Microstructure,Nanjing 210093,China

        1 Introduction

        In molecule,since nuclei are much heavier than electrons,they are considered as classical particle,this is semi-quantum molecular dynamics.The electronic states in molecule are time-dependent superpositions of all the eigenstates,and the electron distribution is changing with the time,this is dynamical evolution.At the same time,the nuclear motion makes the base vectors of the eigenstates continuously varying,and it indirectly induces additional evolution,it is kinematical evolution.

        Recent years,the semi-quantum molecular dynamics,especially the Ehrenfest dynamics,have got further progress,[1?4]where the dynamical evolution can be expressed analytically,and its calculation is transparent.However,the kinematical one depends on complicated numerical calculation,[5?7]which causes some confusions.It is needed to establish an analytic formula to express the kinematical evolution,then all the results become de finite.This paper will provide one approach based on the connection in the geometry to derive such an expression.

        A molecule consists ofNnuclei andMelectrons,the coordinates of nuclei areand that of electrons are.Rdetermines the con figuration and shape of the molecule.

        The electronic Hamiltonian is Hilbert space.

        2 Formulation

        The time-dependent Schr?dinger equation is

        By solving the combined equations of Schr?dinger Eq.(3)and Newtonian Eq.(7),both the electronic statesand nuclear motioncan be obtained.Since nuclear motion is much slower than that of electrons,a practical method to solve these combined equations is the iteration approach step by step,each step takes a short time interval ?t. In solving the Schr?dinger Eq.(3),withincan be fixed and Eq.(3)becomes equation,it is the dynamical evolution caused by the phase change. The second partcomes from the transformation of base vectorit is the kinematic evolution.

        The rest problem is how to calculate the matrixA primary method is numerical calculation,and such method needs a lot of computer work.As usual,heavy numerical calculation may cause uncertainty,one is energy shift. If we can derive an analytic expression for the kinematic evolutionit is desirable.This goal can be achieved by using the connection of fiber bundle.The details are presented in the following.

        3 Connection of Fiber Bundle

        The change from con figurationis a deformation operatorwhich includes unit elementinverse elementD?1(i,j)=D(j,i),multiplicationassociativity of productsHere,the multiplication has a restriction:two operators can multiply only they are connected.With such multiplication,the deformation operators form a special group,and the deformation groupD(i,j)can be represented in terms of matrix,based on the Hamiltonian(1).

        In base spaceR,at any point,a linear Hilbert space with the base vectorscan be attached,it is a fiber bundle.

        During the deformation fromthe bases are transformed fromSinceare complete set,can be expanded in terms of

        The change rate of the transformation matrixin the componentRαis

        In geometry,this ratedemonstrates the orientation correlation between neighboring base vectors of fiber bundles.Here,in the molecule,it is the connection of deformation.In base spaceR,is a vector with the component indexα.In the Hilbert space of fiber bundle,is a tensor with the indexes(n,m).

        By the way,in algebra,is the in finitesimal generator of the representation

        By using the perturbation theory,we can get

        is the vector itself with 3Ncomponents(α=1,2,...,3N).is the connection of molecule deformation.It is notable that the main part of the connectionis the gradient matrixwhich has been got in Newtonian Eq.(7).

        By usingfrom Eq.(17),we can get

        In Eq.(23),the last termis the kinematic evolution,which has been analytically expressed by the connection(Eq.(20))of the fiber bundle,and original heavy numerical calculation is avoided.If neglecting the connection the electronic state would not be able to spread over different eigenfunctions,that is the BOA.

        Finally,by solving combined equations(7)and(23),the evolutions of electronic stateand the nuclear con figurationR(t)can be determined.

        Polymers are chain-like molecules.Since they are onedimensional systems,the polymers have prominent selftrapping,which is a typical deformation effect.The selftrapping produces many novel phenomena in polymers,such as photoinduced spin- fl ipping of charge carries and charge- fl ipping of spin carries.The Ehrenfest dynamics has been used to study these processes.[6?7]But these works have a problem,that their numerical calculations are very heavy,even getting some uncertainty.The connection of fibre bundle can be used to reduce the numerical calculation and make results transparent.

        4 Conclusion

        Molecule is a physical model of the fiber bundle,which can be used to build analytic expression for molecular dynamics and simplify numerical calculation.

        Acknowledgements

        The author would like to thank Professor R.B.Tao,Professor Y.S.Wu,Mr.Y.S.Zhang and Mr.D.Y.Jiang for their helpful discussions.

        [1]S.Stafstr?m,Chem.Soc.Rev.39(2010)2484.

        [2]A.P.Hors field,et al.,J.Phys.Condens.Matter.16(2004)3609.

        [3]A.Johansson and S.Stafstr?m,Phys.Rev.Lett.86(2001)3602.

        [4]Z.An,C.Q.Wu,and X.Sun,Phys.Rev.Lett.93(2004)216407.

        [5]Z.Sun and S.Stafstr?m,J.Chem.Phys.135(2011)074902.

        [6]J.Dong,W.Si,and C.Q.Wu,J.Chem.Phys.144(2016)144905.

        [7]B.Di,S.Yang,Y.Zhang,et al.,J.Phys.Chem.C 117(2013)18675.

        [8]X.Sun,Chin.Phys.Lett.33(2016)123601.

        三年片免费观看大全国语| 91精品人妻一区二区三区水蜜桃 | 亚洲欧美日韩人成在线播放| 免费毛片性天堂| 中文字幕久久熟女人妻av免费| 亚洲中文字幕久久精品一区| 精品无码无人网站免费视频| 蜜臀av一区二区| 国产V亚洲V天堂A无码| 久久一区二区三区老熟女| 精品视频无码一区二区三区| 亚洲国产欧美在线成人| 精品丝袜一区二区三区性色| 亚洲av人片在线观看| 亚洲熟妇无码一区二区三区导航| 丝袜AV在线一区二区三区| 最新亚洲av日韩av二区一区| 精品久久久少妇一区二区| 亚洲av永久精品爱情岛论坛| 亚洲日韩图片专区小说专区| 高清少妇一区二区三区| 四虎影在永久在线观看| 女人扒开下面无遮挡| 久久精品国产只有精品96| 国产精品一区二区偷拍| 色欲av蜜桃一区二区三| 免费AV一区二区三区无码| 亚洲天堂av中文字幕| 狠狠色丁香婷婷综合潮喷| 日本午夜免费福利视频| 亚洲精品综合在线影院| 激情五月我也去也色婷婷| 伊人久久久精品区aaa片 | 成人看片黄a免费看那个网址 | 亚洲av一二三四又爽又色又色| 久久综合噜噜激激的五月天| 国产午夜亚洲精品午夜鲁丝片 | 东京热日本道免费高清| 亚洲国产精品成人精品无码区在线| 老少交欧美另类| 久久狠狠爱亚洲综合影院|