自旋动力学第八章核自旋的哈密顿量.ppt

《自旋动力学第八章核自旋的哈密顿量.ppt》由会员分享，可在线阅读，更多相关《自旋动力学第八章核自旋的哈密顿量.ppt（35页珍藏版）》请在课桌文档上搜索。

1、第八章 核自旋的哈密顿量,Nuclear Spin Hamiltonian,核自旋的运动：Schrdinger equation,Hamiltonian（能量）,8 Nuclear Spin Hamiltonian,核自旋与外加磁场的相互作用,静磁场，Zeeman作用,射频磁场，操纵自旋,相互作用性质和类别：,相互作用的大小、时间尺度NMR谱，弛豫,能级修正或分裂，本征态混合（能级混合）NMR谱特征,核自旋哈密顿,性质，大小,8 Nuclear Spin Hamiltonian,8.1 Spin Hamiltonian Hypothesis,Interactions:核-外磁场作用（exter

2、nal magnetic field）核-核（nucleus-nucleus）核-电子（nucleus-electron）Full Hamiltonian and operator（完整H算符)包括所有上述粒子间相互作用,positions,velocities,and spin states of all the electrons and nuclei.,Nuclear spin Hamiltonian:,depending on the directions of the nuclear spin polarizations.,the magnetic and electrical in

3、fluences of the rapidly moving electrons:Average,and,Nuclear Spin Hamiltonian,掌握：相互作用性质和类别 能级修正或分裂，本征态混合（能级混合），弛豫,四极相互作用,电磁相互作用,8.2 Electromagnetic Interactions,核与环境的相互作用（The nucleus interacts with its environment）：与电场作用（it interacts with electric fields）与磁场作用（it(magnetic moment）interacts with magne

4、tic fields）,Anisotropic:electromagnetic Interactions,Orientation dependence of the nuclear energy,Quadrupolar interaction,(I 1/2),（电磁相互作用）,电场,磁场,8.2.1 Electric spin Hamiltonian,The electric energy depends on nucleus orientation with respect to the rest of the molecule.,完全电性相互作用核自旋算子？,电性质的自旋Helec,(I

5、1/2),四极核：非球形电荷分布,取向相关,(r),处于电势场(r)中核的电势能：,(r)-核的电荷密度,核中心处的电势,物理意义,点电荷-电势场的作用能量,电偶极矩-电场的作用能量,无偶极矩，但电荷分布不均？,位于电势场中核,张量,。,电场强度的梯度,电四极矩,电四极矩,电四极矩-电场梯度的作用能量,Qxx,Qyy,Qzz,Qxy,Qxz,QyzQyx,Qzx,Qzy,(r),核：中心对称的电荷分布,氢原子的轨道：,核-外电势场的相互作用：,核的电多极子:,外电势场,电场梯度,电场,电势,球形电荷,电偶极,电四极矩,完全静电库伦互作用核自旋算子？,8.2.1 Electric spin Ha

6、miltonian,电场梯度V(2)（核所处的环境）（the gradient of the electric field）,The electric energy depends on nucleus orientation with respect to the rest of the molecule.,完全静电库伦互作用核自旋算子？,作用于核处的电场梯度0（核周围电荷分布）非球称性,核：非球对称的电荷分布（核固有）,四极相互作用0，两个要素：,核-环境的电性作用,电四极矩（核固有电荷分布）,电四极矩：核,zz,核：非球对称的电荷分布（核固有）,四极相互作用 与作用于核处的电场梯度密切相

7、关（核周围电荷分布）,球或立方对称环境,非球对称电荷环境,电场梯度V(2)=0,电场梯度V(2)0,8.2.2 磁性的自旋相互作用Magnetic spin interactions,8.3.1 Spin interactions:summary,8.3 External and Internal Spin Interactions,8.4 External Magnetic Fields,1.Static magnetic field B0,2.The r.f.coil in the probe generates an r.f.oscillating field,BRF(t)时间变化,3.

8、The magnetic field gradient field:Bgrad(r,t)空间、时间变化,BRF(t)，B grad(r,t)B0,Total H:,8.4.2 Radio-frequency field,1 200 kHz,横向,纵向,横向,BRF,共振分量,非共振分量,固体NMR,8.4.3 梯度磁场 Gradient field,Bz(x,y,z),8.4.4 External spin interactions:summary,核自旋与外磁场相互作用,改变共振频率,自旋操控,纵向磁场,横向（交变）磁场,8.5 Internal Spin Hamiltonian,8.5.1

9、 The internal spin interactions,Chemical shift terms:the 间接磁相互作用 of the external magnetic field and the nuclear spins,through the involvement of the electrons:,2.Quadrupolar couplings:electric interactions of spin 1/2 nuclei with the surrounding electric fields,Quadrupolar coupling,Chemical shift,化学

10、位移,内部相互作用,3.Direct dipoledipole couplings:直接磁相互作用 of nuclear spins with each other,dipoledipole,4.J-couplings:间接磁相互作用 of nuclear spins with each other,through the involvement of the electrons,分子内,分子内，间,5.Spinrotation interactions：the interactions of the nuclear spins with magnetic fields generated b

11、y rotational motion of the molecules:,8.5.2 Simplification of the internal Hamiltonian,(i)the very strong external magnetic field：,久期近似(Secular approximation)：,对易近似,(与外磁场）,（内部作用）,对易绝断近似（一级近似）,内部哈密顿量简化,例1.对易绝断近似（一级近似）,对易绝断近似,梯度磁场,横向磁场影响：,（H对角）,Secular Approximation,例2.久期近似,横向作用不能忽,保留靠近对角元素,？,neglecte

12、d,NMR谱,弛豫,内部哈密顿量简化,久期近似,运动平均,非久期项,(ii)the rapid molecular motion in liquids and gases,and in some solids,motional averaging：,分子无规运动的“频率”相互作用强度（频率）,(a),分子转动 zz-xx(Hz),NMR谱,弛豫,8.6 Motional Averaging,8.6.1 Modes of molecular motion,internal molecular motions:translation and rotations.,8.6.2 Molecular r

13、otations,the probability density of the molecule having a certain orientation,空间取向参量,时间平均用取向平均来代替,P()=1/4,平动和转动,转动,各向同性无规转动：,the probability density of the molecule having a certain orientation,In gases and isotropic liquids,all orientations are equally likely,isotropic average,单位立体角取向几率,各向同性液体、气体,2

14、.In an anisotropic liquid:there is considerable molecular motion,but all orientations are not equallyProbable-liquid crystal,3.In a solid:the atomic motion is usually heavily restricted.Each internal spin Hamiltonian term is different from its isotropic value depends strongly on the orientation of t

15、he solid with respect to the magneticfield,各向异性液体,部分平均,内部自旋 Hamiltonian仍然依赖于相对于磁场的取向,分子运动严重受限，内部自旋 Hamiltonian强烈依赖于相对于磁场的取向,8.6.3 Molecular translations,1.In gases,diffusion is extremely fast and easily extends to the physical boundaries of the sample on the time-scale of an NMR experiment.We may as

16、sume,therefore,that the positions of all molecules in a gas are exchanged during an NMR pulse sequence,2.In liquids,diffusion is much slower,depending on the molecular size and on the viscosity.It is possible to imagine a diffusion sphere,3.In solids,the diffusional motion of the molecules is usuall

17、y insignificant on the NMR time-scale.,10 m,扩散球,平动,8.6.4 Intramolecular and intermolecular spin interactions,dipoledipole couplings,分子内和分子间相互作用,long-range and short-range intermolecular interactions:Short-range:interacting molecules share the same diffusion sphere.Long-range:Interacting molecules do

18、 not share the same diffusion sphere,长程和短程分子间作用,0,0,8.6.5 Summary of motional averaging,In a gas,rapid and complete rotational and translational motion isotropic intramolecular spin interactions zero intermolecular interactions,2.In an isotropic liquid,Rapid rotation average:isotropic intramolecular

19、 spin interactions,Diffusion average:zero short-range intermolecular interactionsbut unable to average out long-range intermolecular interactions.,3.In an anisotropic liquid,Rotation partially averages all intramolecular spin interactions-anisotropic values.Diffusion completely averages short-range

20、intermolecular interactions-zero long-range intermolecular interactions survive,4.In most solids,the atomic motion is highly restricted and there is little averaging of the internal spin interactions except by the restricted motions of some molecular groups:CH3 rotation,5.In certain molecular solids

21、-plastic crystals Unusual situation:fixed centres of gravity of the molecules with respect to the crystal lattice,but the molecules themselves rotate rapidly about their lattice sites,in many cases isotropically-C60,the rapid molecular rotation:isotropic intramolecular interactions whereas the incomplete averaging of the intermolecular interactions,金刚丸13C质子去偶,