第十一讲：现代电子结构计算方法
第十一讲：现代电子结构计算方法
N-Particle System ProblemRememberh222ethe good old days of theH山=E() =E(T)I-electron H-atom??2m4元E0They'reover!Nre2NNNh?"Z,e2h?ZZ12NX2H=N22m2MR-Ri1-1i-l i-i-ir1kinetic energy of ionskinetic energy of electronselectron-ion interactionpotential energy of ionselectron-electroninteractionMulti-Atom-Multi-Electron Schrodinger EquationH(R.,R.ri.r)(R....Rn,r....,)-EY(R....Rnir..,2
N-Particle System Problem 2
近似！：绝热近似Born-OppenheimerApproximation (skinless version)·mass of nuclei exceeds that of theelectrons bya factor of Iooo ormorewe can neglect the kinetic energyof thenucleitreatthejon-ioninteractionclassicallyBornOppenheimersignificantly simplifiestheThis term is just an external potentialV(r)Hamiltonianforthe electrons:N2h?"区1Z22Hr;2m-R-ri-l1i-1
3 近似I：绝热近似
近似Ⅲ：单电子近似InteractingNon-lnteracting体系Hamilton量简化九H=Zh>n2m;riu1h P, =6,单电子薛定方程分子轨道：+.4*非占据轨道O,为单电子波函数or分子轨道(MO)全同粒子本征值8.为对应的分子能级中中中泡利不相容原理占据轨道任何两个粒子不能有完全相同的量子数(n,l,m,s）其中s=±1/2自旋量子数
近似II：单电子近似 体系Hamilton量简化 单电子薛定谔方程 or 任何两个粒子不能有完全相同的量子数 (n, l, m, s) 其中s = ±1/2 自旋量子数
无相互作用多体波函数？Write wavefunction as a simple product of singleHartree积（HP多体波函数）particle states:Y(r1,...,rn) = P1(r1)P2(r2) ... Pn(rn)HardProduct of EasyTotal energyZE=8
无相互作用多体波函数？ Hartree 积 （HP多体波函数） Total energy