The molecular orbital (MO)(7.18)is a linear combination of atomic orbitals,an LCAO-MO.(Exponential parameter-effective nuclear charge) For the trial function(7.18),the secular equation is H-WS.H-WS=0 Hba-WSba Hob-WSpb (7.20) The integrals Haa and Hob are Hnm=∫4nH4ndk,Hb=∫4ibH4dy(I.21)） These two integrals are called Coulomb integrals.Since the H2'is a homonuclear diatomic system,Han=Hob.We have Hb=∫gaH4bdy,Ha=∫4bH4dy(7.22) Since is Hermitian and the functions in these integrals are real,we conclude that Hab=Hpa.The integral Hab,is called a resonance (or bond) integral.Sinceand are normalized and real.We have Sa=<4La|中a>=pi中1adh=1=Sb Sab=∫gin中i6dr=Sba (7.23) The secular equation(7.20)becomes H-W Ha-WS.=0 Hab -WSab Hoo-W (7.24) Hoo -W=(Hob-SabW) (7.25) 所-月tH4,所-二H 1+Sab 1-Sh (7.26) These two roots are upper bounds for the energies of the ground and the first excited electronic states of H2 The molecular orbital (MO) (7.18) is a linear combination of atomic orbitals, an LCAO-MO. (Exponential parameter—effective nuclear charge) For the trial function (7.18), the secular equation is = 0 − − − − ba ba bb bb aa aa ab ab H WS H WS H WS H WS (7.20) The integrals Haa and Hbb are Haa φ sa Hφ sadν Hbb φ sb Hφ1sbdν * 1 1 * 1 , ∫ ∫ ∧ ∧ = = (7.21) These two integrals are called Coulomb integrals. Since the H2 + is a homonuclear diatomic system, Haa = Hbb. We have Hab φ sa Hφ sbdν Hba φ sb Hφ1sadν * 1 1 * 1 , ∫ ∫ ∧ ∧ = = (7.22) Since ∧ H is Hermitian and the functions in these integrals are real, we conclude that Hab = Hba. The integral Hab is called a resonance (or bond) integral. Since φ1sa and φ1sb are normalized and real. We have ab sa sb ba aa sa sa sa sa bb S dv S S dv S = = =< >= = = ∫ ∫ 1 * 1 1 * 1 | 1 1 1 φ φ φ φ φ φ (7.23) The secular equation (7.20) becomes = 0 − − − − H WS H W H W H WS ab ab aa aa ab ab (7.24) H W (H S W ) aa − = ± ab − ab (7.25) ab aa ab ab aa ab S H H W S H H W − − = + + = 1 , 1 1 2 (7.26) These two roots are upper bounds for the energies of the ground and the first excited electronic states of H2 +