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.

        白浆国产精品一区二区| 国产精品美女AV免费观看| 婷婷成人亚洲综合国产| 人妻经典中文字幕av| 欧美日韩在线视频一区| 国产成人vr精品a视频| 国产精品一区二区三区精品| 国产在线观看黄片视频免费| 亚洲av无码一区东京热久久| 国产精品成年片在线观看| 亚洲一区区| 中文字幕乱码一区在线观看| 国产色系视频在线观看| 国产微拍精品一区二区| 国产盗摄XXXX视频XXXX| 日本加勒比精品一区二区视频| 国产电影一区二区三区| 国产人妻黑人一区二区三区| 素人系列免费在线观看| 日韩美女亚洲性一区二区| 亚洲色欲色欲大片www无码| 伊人网在线视频观看| 久久综合老鸭窝色综合久久 | 人与人性恔配视频免费| 中文字幕日本最新乱码视频| 国产69精品一区二区三区| 91精品国产九色综合久久香蕉| 天堂网www资源在线| 欧美午夜刺激影院| 午夜日本理论片最新片| 风韵丰满熟妇啪啪区老老熟妇| 欧美亚洲日本国产综合在线| 一区二区三区国产美女在线播放| 加勒比久久综合久久伊人爱| 国产午夜精品一区二区| av一区无码不卡毛片| 亚洲粉嫩视频在线观看| 亚洲日韩国产av无码无码精品| 中文字幕av在线一二三区| 日本视频一区二区二区| 日韩精品人成在线播放|