Vibrational Levels Associated with Hydrogen Bonds

Alain Joye

Description

Vibrational Levels Associated with Hydrogen Bonds? Alain JOYE FOURIER INSTITUTfi ? Joint work with George HAGEDORN, (Virginia Tech, Blacksburg) Nice November 13 - 14th 2008 – p.1/19

• combes-duclos-seiler


• born-oppenheimer approximation


• klein-martinez-seiler-wang


• ∆xb ?


• tri-atomic molecule

Sujets

• Hagedorn
• Born?Oppenheimer approximation

Informations

• Publié par: pefav
• Nombre de lectures: 15
• Langue: English

Extrait

∗

Vibrational Levels Associated with Hydrogen Bonds

Joint work with

Alain JOYE

f UTSTIT FIRUO NI RE

George HAGEDORN, (Virginia Tech, Blacksburg)

NiceNovember 31 -

∗

1 t 4 h 2008 –p.1/19

Setup

Tri-atomic molecule

NucleiA,B,C molecular Hamiltonian

x A − 1 Δ− 1 x C +h e (x A  x B  x C ) − 2m 1 A Δ 2m B x B 2m C Δ

withh e (x A  x B  x C )theelectronic Hamiltonian

NiceNovember 31 - 1 t 4 h 0280 –p.2/91

Setup

Tri-atomic molecule

NucleiA,B,C molecular Hamiltonian

− 2m 1 A Δ x A − 2m 1 B Δ x B − 2m 1 C Δ x C +h e (x A  x B  x C )

withh e (x A  x B  x C )theelectronic Hamiltonian

Jacobi Coordinates Rtotal C.M.,x AB C.M. ofAandB W=x B −x A ,Z=x C −x AB ⇒

Mtotal mass,m AB =m A +m B ,

1m − − 2M Δ R 2m AB A m B Δ W − 2m A M B m C Δ Z +h e (W Z)

Bond states only⇒discard the K.E.− 1 2M Δ R of the C.M.

NcieNvomeber 13 - 1 t 4 h 2008 –.p/219