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ICAMM 2014, Nantes, France, 08/07/2014
Non-adiabatic effects in the 1D optical spectra of H
2
+ and H2
Alison CrawfordNano-Bio Spectroscopy Group and ETSF Scientific Development Center,
Departamento de Física de Materiales,Centro de Física de Materiales CSIC-UPV/EHU-MPC and DIPC,
Universidad del País Vasco UPV/EHU, Avenida de Tolosa 72, E-20018, San Sebastián, Spain
http://nano-bio.ehu.es/users/alison
Outline● Motivations
● Model systems: H2
+ charged and H2 neutral in 1D
● Configurations in 1D
● Optical spectra: theory
● Results: classical fixed/moving vs quantum ions
● Conclusions
Motivations● Optical absorption spectra
● Quantum (feasible in 1D for one- and two-electron systems)
● See effects of quantum ions vs classical fixed/moving ions
● Adiabatic approximations → decouple electron-ion
– Born Oppenheimer Approximation (BOA)
● Electron: ● Ion:
not in 1D
Classical negligible if >
Model systems: H2
+ and H2
in 1D
● H2
+ (centre of mass) → simplify to 2 variable problem in 1D
● H2 (centre of mass) → simplify to 3 variable problem in 1D
Change only mass→ → assess electron-ion coupling
M me
X=X 2−X 1
ξ=x−X1+X 2
2
H internal(X , x ,ξ)=−1M
∂2
∂X 2−
1+M4M
∂2
∂ξ2− ∂2
∂ x2−
1
√( X2 +x2+ξ)
2
+ΔIe2
−1
√( X2 +x2−ξ)
2
+ΔIe2
−1
√( X2 −x2+ξ)
2
+ΔIe2
−1
√( X2 −x2−ξ)
2
+ΔIe2
+1
√x2+Δee2+
1
√X 2+ΔII2
x=x2−x1
ξ=x1+x2
2−X 1+X 2
2
M H 2+ ;M D2
+ ;M Li2+ ;M K2
+
H internal(X ,ξ)=−1M
∂2
∂ X 2−
2M+14M
∂2
∂ξ2−
1
√( X2 +ξ)2
+ΔIe2
−1
√( X2 −ξ)2
+ΔIe ²
+1
√X 2+ΔII2
Configurations in 1D→ 2D and 3D bare Coulomb→ Particles confined in 1D trajectories separated by → Classical geometrical interpretation
Δ
Optical spectra → theory● Kicked initial state in the dipole approximation
● Dipole moment
● Optical spectra
d (t)=⟨ψ∣ξ∣ψ ⟩
σ(ω)=limK→∞
4 παω
Kℑ[∫
0
∞
dt e−iω t (d (t )−d (0))]
ψ(X ,ξ ,t )≈ψgse−iεgs t
2 +iK∑k>0
e−iεk t
2 ⟨ψk∣(2M+22M+1
)ξ∣ψgs⟩ψk
V ext=eiK ξ≈(1+iK ξ)
ψ(X , x ,ξ , t )≈ψgse−iεgs t
2 +iK∑k>0
e−iεk t
2 ⟨ψk∣−2(2M+1)+2M(M+1)(2M+1)(M+1)
ξ∣ψgs⟩ψkODD !! EVEN
ODD
Optical spectra H2
+: classic vs quantum
Overall shape and Xeq
G. Sansone et al. Nature, Vol. 465, 2010 E0(X
eq) → E
i(X
eq) electronic
Even to odd splitting Asymmetry (repulsion)
Fix X (no t) Quantum vs fixed Xeq
(with t)
Optical spectra H2
+: classic move/fix
Ionic motion peak
Vanishes MFixed/moving not capture
quantum non-adiabatic effects
↑
d(t)
t
Optical spectra H2
+: classic vs quantum
Even to Odd splits Positronium first peak
Larger M third/fifth peak Width/Lifetime → ele to ion M (not elastic)↓
d(t)
t
Optical spectra H2: classic vs quantum
Overall PES shape and equilibrium geometry
ee repulsion dissociate 2H
G. Sansone et al. Nature, Vol. 465, 2010 Weaker effects
Repulsion (asymmetry)
Optical spectra H2: classic vs quantum
Symmetry x (even) (odd)
Gs → 2Ex Gs → 6Ex
Gs → 10 Ex
x
ξ
Planar alsoGs → 3Ex
both odd ??
ξ
Conclusions● Non adiabatic electron-ion effects
– Splitting + asymmetry (non-elastic)
– Stronger for charged H2
+
– Configuration → repulsive interionic potential
– Vanish as mass increases (relative strengths)
● Range of applicability of ED and BOA
● Compare 1D vs 3D optical spectra (only PES)
● Analytical interpretation of the non-adiabatic features
ICAMM 2014, Nantes, France, 08/07/2014
Non-adiabatic effects in the 1D optical spectra of H
2
+ and H2
Alison CrawfordNano-Bio Spectroscopy Group and ETSF Scientific Development Center,
Departamento de Física de Materiales,Centro de Física de Materiales CSIC-UPV/EHU-MPC and DIPC,
Universidad del País Vasco UPV/EHU, Avenida de Tolosa 72, E-20018, San Sebastián, Spain
http://nano-bio.ehu.es/users/alison
THANK YOU
1st approach ● BOA analysis (ion dark coupling)
?
i ℏ ∂∂ t
χi(R , t )=(−ℏ
2
2μ I∂
2
∂R2−F i(R−Ri)+εi(Ri))χi(R ,t )
E0 χ0(R)=(−ℏ
2
2μ I∂
2
∂R2−12K (R−R0)
2+ε0(R0))χ0(R)
d (t )∝∫ dRci(t )χ0*(R)χ i(R ,t)
2nd approach ● Two-level system (ion bonding/antibonding)
belowabove
Eele
Eion E
ion
Eele