量子化学与群论基础 6.pptVIP

* * n =1,2,3… l = 0,1,2…n-1 m = 0, ? 1,?2 ?l… ms=? 1/2 Energy Magnitude of orbital angular momentum z-component of orbital angular momentum z-component of spin angular momentum n ? 1 0 ? l ? n -l ? m ? l ? 1/2 n l m ms Quantized quantity Integer values Quantum number ⑶ The states of the single-electron atoms 6.3 Many-electron atoms 1 The Schr?dinger equation of many-electron atoms （Born-Oppenheimer Approximation） Unfortunately, precise solutions are not available through the Schr?dinger equation, even for the simplest many-electron, helium, because ⑴ Independent particle model The Schr?dinger equation Separation of variables ⑵ Mean field model An electron at a distance r from the nucleus experiences a Coulombic repulsion from all the electrons within a sphere of radius r and which is equivalent to a point negative charge located on the nucleus. ， n =1,2,3,…… Symmetric, Bosons Antisymmetric, Fermions ⑵ The Pauli principle All electronic wavefunctions must be antisymmetric under the interchange of any two electrons. 2 Identical particles and the Pauli principle ⑴ Identical particles Identical particles cannot be distinguished by means of any intrinsic properties. ⑶ Slater determinant — Normalization constant (i) (ii) No two electrons in an atom can have the same values for all four quantum numbers. 4 Electron configurations ⑴ The Pauli exclusion principle No two electrons in an atom can have the same values for all four quantum numbers. ⑵Ground state electron configuration — Aufbau principle ⑶ Hund’s rule Electrons occupy the orbitals of a subshell singly until each orbital has one electron. p6 , d10, f14 p3 , d5 , f7 p0 , d0 , f0 ⑵ Atomic units 1a.u mass=the mass of electron m = 9.109×1028g 1a.u charge = the charge of proton e =1.602×10-19C 1a.u length =Bohr radius 1a.u energy = e2/a0 = 27.2eV The H2+ has two protons and one electron and can be described using the Schr?dinger equation 5 Molecules 5.1 Hydrogen?Molecu