International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 STRUCTURE, DIPOLE MOMENTS, POLARIZABILITIES, AND MOLECULAR

International Symposium on Molecular Spectroscopy 62nd Meeting - Columbus- June 18-22, 2007

STRUCTURE, DIPOLE MOMENTS, POLARIZABILITIES, AND MOLECULAR SPIN ORBIT OF STRONG DIPOLAR

ALKALI DIATOMICSMireille Aymar, Olivier Dulieu

Laboratoire Aimé Cotton, CNRS and Université d’Orsay, France

PhD’s: Johannes Deiglmayr (U. Freiburg/ LAC Orsay), Andreas Gerdes (U. Hannover/ LAC Orsay), Sihem Azizi (U. Tlemcen) until 2005

Coll. with F. Spiegelman (Lab. de Physique et Chimie Quantiques , Toulouse)

Other members of the group: N. Bouloufa, A. Crubellier, R. Osseni, M. Raoult

COMOL HPRN-CT-2002-00290 Interferences and Quantum Aplications

French-GermanUniversity


MOTIVATIONS for such computations:

Guide or interpret cold atom photoassociation and cold molecule formation experiments, as well as standard laser spectroscopy (gas phase, He-clusters..)Discover new processes for cold molecule formation; calculation of rates

Alkali dimers: systems of choice experimentally

Numerous quantum chemistry results on potential curves for homo- and heteronuclear diatomics (Lyon, Beirut, Monastir, Temple U., Riga-Moscow, Kaiserslautern…)

Only few data on permanent or transition dipole moments, static polarisabilities, spin-orbit couplings

No systematic quantitative comparison on the accuracy/consistency between various methods


REVIEW of OUR RECENT WORK

New series of systematic calculations of electronic properties for ALL alkali pairs involving Li, Na, K, Rb, Cs: potential curves, permanent and transition dipole moments, static polarizabilities, spin-orbit couplings

New results for Francium compounds (Fr2, RbFr, CsFr)

Method based on the CIPSI package (Configuration Interaction by Perturbation of a multiconfiguration wave function Selected Iteratively, Laboratoire de Physique Quantique, Toulouse, France). (B. Huron et al., J. Chem. Phys. 58, 5745)

Spin-orbit calculations relying on a diabatization procedure with no adjusted parameter

Automated calculations and data treatment for ALL Pairs, ALL symmetries, ALL interatomic distances, ALL transitions

Convergence and accuracy checked against size of basis sets, and through detailed comparison with other methods


CALCULATION STEPS (in short) ATOM:

The ionic core described by an ℓ-dependent (large core) pseudopotentiel [1] Effective one-electron atom described by a Gaussian basis set. Pseudopotential parameters adjusted to reproduce energies and valence orbitals of an all-electron Hartree-Fock (HF) calculation. Fr: new pseudopotential with parameters adjusted to reproduce spin-averaged orbitals and energies of an all-electron relativistic Dirac-Fock (DF) calculation [2]. Core polarization: ℓ-dependent effective core polarization potential (ECPP) [3], involving (expt’l [4]) ion polarizabilities, and cut-off radii (fitted on atomic spectrum) to prevent divergence at short distances

MOLECULE: One-electron molecular orbitals (MO) determined via Restricted Hartree-Fock calculation, including ECPP’s: potential curves for molecular ions Full (2 electron) configuration interaction (CI): potential curves, permanent and transition dipole moments. Computation in an external electric field: static polarizabilities

[1] P. Durand and J.C. Barthelat, Theor. chim. Acta, 38, 283 (1975)[2] J.P. Desclaux, Comp. Phys. Comm., 9, 31 (1975)[3] M. Foucrault, P. Millié, and J.P. Daudey, J. Chem. Phys. 96, 1257 (1992)[4] J.N. Wilson and R.M. Curtis, J. Chem. Phys. 74, 187 (1970)


RESULTS: POTENTIAL CURVES

excellent overall agreement with previous work from Lyon group and coll. (same parameters, same basis)

Core-core interaction

Extended basis: improved description of atomic energies. Example for Cs : [7s4p5d1f]/[6s4p4d1f] extended to [9s6p6d4f].

Potential wells deeper by about 20cm-1 for molecular ions, 70-200cm-1 for neutrals.

Corresponds to the limits of accuracy for such calculations (core-core interaction,…)

5s+6s

5s+6p

5p+6s


R (a.u.)

Dip

ole

mom

ent (

Deb

ye)

RESULTS: PERMANENT DIPOLE MOMENTS

X1+

LiCs

KRb

JCP, 122, 204302 (2005)

+-light heavy

•R-dependence, v-dependence•Less than 1% variation with basis size •Most of these results were not available elsewhere

This work

Park et al (2000)

X1+

a3+

Kotochigova et al 2004)

This work

Kotochigova et al, PRA 68, 022501 (2003)Park et al, Chem. Phys, 257, 135 (2000)

KRb


Permanent dipole moments

-+light heavy

+-

Cs Fr

Rb Cs

Rb Fr

Ground state

Metastable triplet state

RESULTS: FRANCIUM COMPOUNDS

Aymar, Dulieu, Spiegelman JPB, 39, S905 (2006)


RESULTS: TRANSITION DIPOLE MOMENTS

Comparison with:Multi-partitioning perturbation theory, Zaitsevskii et al, PRA 63, 052504 (2001)

NaRb

Mol. Phys., in press (NaK, NaRb, NaCs)

Accurate check of the consistency of electronic wave functions among various methods


RESULTS: STATIC POLARIZABILITIES (1)

Homonuclear alkali pairs

Heteronuclear alkali pairs

RbCs

KCs

LiCs

KRb


RESULTS: STATIC POLARIZABILITIES (2)

5 10 15 20 250

100

200

300

400

500

600

700

800

900

Po

lari

zab

ility

[a

u]

R [a0]

LiNa LiCs NaCs KRb RbCs

Average polarizability

Anisotropy

5 10 15 20 250

200

400

600

800

1000

An

iso

tro

py

[au

]

R [a0]

LiNa LiCs NaCs KRb RbCs

LiCs


• important contribution for heavy alkalis

• Mainly included with effective (*** system-dependent ***) operators

• Published potential curves available for LiCs, NaCs, KCs, KRb, RbCs, Cs2.

• Almost no data on R-dependent SO couplings for dynamics purpose

MOLECULAR SPIN-ORBIT

•Calculate potential curves without spin-orbit operator

•Define states at large internuclear distance as reference basis

•Calculate unitary transformation to represent molecular states in

this

reference basis effective Hamiltonian in „atomic“ basis

•Add spin-orbit coupling in this basis (asymptotic fine structure)

•Rediagonalize Hamiltonian provides adiabatic curves

•OR rotate back to molecular basis provides coupling matrix

elements

•Same procedure for all systems , for an arbitrary number of

asymptotes

OUR IDEA


10 15 20 25

0.04

0.05

0.06

0.07

0.08

E a

bove

6s6

s [a

u]

R [a0]

Spiess90 our work

10 15 20 25

0.04

0.05

0.06

0.07

0.08

Ene

rgy

abov

e 6s

+6s

[au

]

R [a0]

First results for Cs2

states correlated to the 6s+6p and 6s+5d asymptotes

No spin-orbit interaction With spin-orbit interaction(rediagonalization)


R-dependent spin-orbit matrix elements(after rotation back to molecular basis)

Comparison with Spies’ data (1990) for 0g- (3g

+-3g) symmetry

10 15 20 25 30-3

-2

-1

0

1

2

3

4

5

(2,1)

(1,2)

(2,2)

(1,1)

cou

plin

g [

104 a

u]

R [a0]

(i) 3+

g H

SO (j) 3

g

Spiess90 our work

10 15 20 25 30-2

0

2

4

6

(1,2)

(2,2)

(1,1)

mat

rixe

lem

en

t [1

04 au]

R [a0]

(i) 3g H

SO (j) 3

g

Spiess90 our work


Cs2 0g-


Perspectives of this work:• Spin-orbit couplings for all alkali pairs (LiRb, LiCs, RbCs, Rb2,…).

• Mixed alkali/alkaline-earth ions… and neutrals…• Triatomic alkali ions… and neutrals…

• Dynamics… atom/molecule photoassociation…

• …and hopefully interaction with experimentalists…

• There « could be » possibilities for PhD/postdoc positions…

Today’s published results from our group:NaK, NaRb, NaCs: M. Aymar and O. Dulieu, submitted to Molecular Physics (2007)

Rb2: J. Lozeille et al (Orsay+ Pise + Storrs) Eur. Phys. J. D 39, 261 (2006); V. Horvatic

et al (Orsay+ Zagreb), Phys. Rev. A, 75, 032512 (2007).

KRb: Beuc et al (Zagreb+Orsay), J. Phys. B, 39, S1191 (2006)

Fr2, RbFr, CsFr: Aymar, Dulieu, Spiegelman J. Phys. B, 39, S905 (2006)

All other systems in preparation (including alkali hydrides)

Documents

International Symposium on Molecular Spectroscopy 62 nd Meeting - Columbus- June 18-22, 2007 STRUCTURE, DIPOLE MOMENTS, POLARIZABILITIES, AND MOLECULAR