,...R) where r = H (1.4) + Tn + Vof. etic energy terms are: here. ZA ZB Vee = & Vnn = (1.6) (1.4) H = Te + Tn + Ven + Vee + Vnn. i A r i.

Transcription

1 where r H r, r (r,,...r), r, RE R (r, RR),.., R represet theelectros. electro (.3) ad uclear coor,all,.ucle ates of ad all Itutvely, ollowgdates, SE: respectvely, ad H (r, R) E (r, R), we feel t are very d eret, because ther masses are very r, r,..., r, R R, R,..motos., R represet the electro ad uclear coorh (r, R) E (r, R), T Vof Vee V (.4) e magtude pectvely, larger tha thead electro ma here r ad r, r,..., rmass, R HsR3T,eorders R,..., R represet the electro uclear er rrespectvely, rthe.., reergy,ad R R, R,..equato., Rmolecular the reduce electro ad uclear Our o-relatvstc Hamltoa were fte, (.3) would to the equato,hamltoa:,.ketc represet terms are: ates, H Te T Ve Vee V (.4) the potetal ucle. Each uclear co tes, respectvely, admovg of fxed P p T & T, V meas that (.5)electroc e V e H exteral etc eergy terms are: d eret potetal, whch T T V e e Mee deped o uclear postos parametrcally. We caot, ho H T V V V T e e ee p where p r. Te eergy T Tare:, the we would (.5)ot be able 0), sce The ketc terms The Coulomb terms are: M would be o dyamcs!). But sce the uclear moto The ketc eergy terms are: Z Z @ P p r. electroc ca that relectros ca adjust Vee & V moto, & expect Ve @z r r R R je & B T, B ulomb terms are: j T usm posto ay ew of ucle. Let see how p (.6)we ca separ P T & T, emoto. Z ZB Z M & & @ usb defe so-called electroc to be RLet R r varables R wavefuctos (adabatc) here p rj r. j r Bor-Oppehemer B separato terms@se: Coulomb The are: @z - Electroc Schroedger equato Hel (r; R) U (R) (r; R) The Coulomb terms are: Z ZB Z Vee & V & TeV ev H V el e Vee r r R R r j ZR B j Z ZB B & V & Vfxed e geometry of uc We ca solve ths equato at each byu(r), eergy surfaces j- uclear r r j motos: govered B R RBpotetal r (U ad ) wll deped parametrcally o uclear geometry dstgush betwee parametrc ad explct depedece o potetal eergy curves U (R) of O molecule are show

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3 Bor-Oppehemer separato of varables (T U k (R) E ) k M H el (r; R) U (R) (r; R) H el T e V e V ee V (r, R) j(r; R) j(r) j j < k r j > r j j < k r j > r r j Bor-Oppehemer (adabatc) approxmato: Whe we eglect RHS terms (.5) k k (T U k (R)) k E k

4 Potetal Eergy Surfaces: Cocepts ad deftos

5 Cyclobutadee (C4H4) rg opeg: Trasto state versus a termedate

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7 Statoary pots o PES ad relato to chemstry

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9 o Bor-Oppehemer case H el (r; R) U (R) (r; R) H el T e V e V ee V (r, R) j j(r; R) j(r) (T U k (R) E ) k M j < k r j > r j j < k r j > r r j (.5) o-adabatc dyamcs whch uclear ad electroc motos are coupled. uclear motos o multple surfaces are coupled ad there are o-adabatc trastos

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11 dabatc states ad wave fucto evoluto: uderstadg the dervatve term

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13 Homework: Why o-adabatc trastos are more lkely to occur whe the PESs are close?

14 O the mportace of o-adabatc effects Barrers dffer by 0.4 ev, but the rato s :0.4 favor of the chael wth the HIGHER barrer

15 Dyamcs o multple surfaces the O dmer: Break dow of dabatc approxmato Rydberg

16 Statoary pots o PES ad relato to chemstry