自旋动力学第八章核自旋的哈密顿量.ppt

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（external 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 influences 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 magnetic 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 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 Hamiltonian,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.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 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 by 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,？,neglected,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 rotations,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.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 the 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 assume,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 usually 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 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 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 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-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,