Applications of cold polar moleculesGerrit C. Groenenboom

Institute of Theoretical Chemistry

University of Nijmegen

The Netherlands

Missoula, May 2006 – p. 1/35

Collaborators

Nijmegen, NetherlandsAd van der AvoirdGuillaume DhontMark van der LooGerrit Groenenboom

ITAMP, HarvardAlex DalgarnoBalakrishnanRoman KremsXi Chu

UtrechtJoop van Lenthe

Berlin, GermanyGerard MeijerBas van de MeerakkerSteven HoekstraJoop GilijamseNicolas Vanhaecke

Missoula, May 2006 – p. 2/35

Introduction

Buffer gas cooling and magnetic trapping3He+CaH(2Σ+), cooling+trapping, Doyle group, 19983He+NH(3Σ−), cooling, Doyle group, 20043He+OH(2Π3/2)

Stark deceleration

Radiative lifetime of trapped OH(v = 1)

Collisions of Xe with Stark controlled OH(2Π3/2f )

NH(3Σ−)+NH(3Σ−) potentials, bound states.Chemistry?

Missoula, May 2006 – p. 3/35

Ab initio calculations

RCCSD(T) method (MOLPRO)

One electron basis:

CaH(2Σ+)–He d-aug-cc-pVTZ; Ca: 6-311G++(3df)NH(3Σ−)–He aug-cc-pVQZOH(2Π)–He aug-cc-pVTZ (A′ and A′′ PES)OH(2Π)–Xe aug-cc-pVQZ (A′ and A′′ PES) [256 orbitals]

+ bond orbitals

Xe: ECP28MDF_AVQZ, Kirk Peterson et al. JCP (2003)

Xe: (5s)2(5p)6 in CCSD(T), polarizability within 1%

Missoula, May 2006 – p. 4/35

Jacobi coordinates

Θ

R

rHCa

He

Missoula, May 2006 – p. 5/35

He-CaH (2Σ+) potential (cm−1)

R (a0)

−1

−2−4−6−8

−10

−2

8

1632

6410

020

0

500

500 100

θ (d

eg)

6 8 10 12 140

30

60

90

120

150

180

G. C. Groenenboom and N. Balakrishnan, J. Chem. Phys., 118, 7380 (2003)

Missoula, May 2006 – p. 6/35

He–NH (3Σ−) potential (cm−1)

5 6 7 8 9 10 11 120

30

60

90

120

150

180

θ (d

egre

es)

R (a0)

−1

−3−5

−7−9

−11

−13−15

−17

−19

−15

−11

020

6010

0

H. Cybulski, R. V. Krems, H. R. Sadeghpour, A. Dalgarno, J. Klos, G. C. Groenenboom, A.

van der Avoird, D. Zgid, and G. Chalasinski, J. Chem. Phys., 122, 094307 (2005) Missoula, May 2006 – p. 7/35

He–OH(2Π) potentials (cm−1)

4 5 6 7 8 9 100

30

60

90

120

150

180

−27

−24

−21

−21

−18

−18

−15

−15−12

−12

−9 −9

−6

−6

−3

−3

0

50

100

150200

250

300

350

400

450

500

R (a0)

θ (d

egre

es)

He−OH (A’)

4 5 6 7 8 9 100

30

60

90

120

150

180

−24

−21

−21

−18

−18

−15

−15

−12

−12

−9

−9

−6

−6

−3

−3

0

50100

150200

250

300350

400450

500

R (a0)

θ (d

egre

es)

He−OH (A’’)

H.-S. Lee, A. McCoy, R. Toczyłowski, and S. M. Cybulski, J. Chem. Phys. 113, 5736 (2000)

Missoula, May 2006 – p. 8/35

Xe–OH(2Π) potentials (cm−1)

4 6 8 10 120

30

60

90

120

150

180

R (a0)

θ (d

egre

es)

Xe−OH (A’)

−200−175

−150−

125−

100−

75

−50

−25

1450

450

850

650

50

5 6 7 8 9 10 11 120

30

60

90

120

150

180

R (a0)

θ (d

egre

es)

Xe−OH (A’’)

−200

−175−150

−125−100

−100

−75

−50

−25

−75

50

1450

450850

Missoula, May 2006 – p. 9/35

Zeeman interaction (2Σ)

0 1 2 3 4−2

−1

0

1

2

B/tesla

Ene

rgy/

cm−

1

|S,MS> = |1/2, 1/2>

|S,MS> = |1/2, −1/2>

σinelastic

(Spin−flipping)

HZeeman = −µ ·B

µ = − e2m(L + geS)

state |µ|

CaH 2Σ+ 1µB

NH 3Σ− 2µB

OH 2Π3/2 1.4µB

Elastic momentum transfer cross section:

σtr(E) = 2π

∫ π

0

dσ(E)

d cos χ(1− cos χ)d cos χ

Missoula, May 2006 – p. 10/35

He–CaH: coupled channel calculation

Hamiltonian:

H = −~

2

2µR

d2

dR2R +

l2

2µR2+

N2

2µCaHr2+ V (R, re, θ) + VSR

Spin-rotation term:

VSR = γN · S (γ = 0.0415 cm−1)

Channel basis:|NMN 〉|SMS〉|lml〉

Missoula, May 2006 – p. 11/35

He–CaH: modified potential

Spherically averaged potential

8 12 16 20R (a0)

−5

0

5

Ene

rgy

(cm−

1 )

Original potentialModified potential (f=0.15)

V = V CCSD(T) + f × (V CCSD(T) − V CCSD)

f = 0.15: van der Waals minimum 3% more attractive

Missoula, May 2006 – p. 12/35

3He–CaH(N=0): elastic cross sections

10−3

10−2

10−1

100

101

Kinetic energy (cm−1

)

102

103

104

105

Cro

ss s

ectio

n (1

0−16

cm

2 )originalmodified (f=0.1)modified (f=0.15)

Missoula, May 2006 – p. 13/35

3He–CaH: comparison with experimentThermal averaged elastic momentum transfer cross section

0.0 0.2 0.4 0.6 0.8 1.0Temperature (K)

10−14

10−13

Theory (modified potential)TheoryExperiment

Cro

ss s

ectio

n (c

m2 )

σtr(E) = 2π

∫ 2π

0

dσ(E)

d cos χ(1− cos χ)d cos χ

Experiment: J. D. Weinstein et al., Nature 395, 148 (1998)

Missoula, May 2006 – p. 14/35

3He+CaH: Spin-flipping

VSR = γN · S

1/2j =

N = 1

0N =

j = 3/2

j = 1/2

Phys. Rev. A, 67, 060703 (2003)

Missoula, May 2006 – p. 15/35

3He+CaH(N = 0): spin flip cross sections

10−6

10−5

10−4

10−3

10−2

10−1

100

Collision energy (cm−1

)

10−15

10−12

10−9

10−6

10−3

100

103

Cro

ss s

ectio

n (Å

2 )

k(T = 0.4K) = 〈σv〉 = 1.65×10−14 cm3s−1 (with resonance)

1.20×10−17 cm3s−1 (modified potential)

Experiment: k(0.4K) ≈ 10−17 cm3 s−1

Missoula, May 2006 – p. 16/35

3He-NH(3Σ−): (in)elastic cross sections

(B = 100 G = 0.01 T)

10−6

10−4

10−2

100

102

Collision energy (cm−1

)

10−11

10−9

10−7

10−5

10−3

10−1

101

103

Cro

ss s

ectio

n (Å

2 )

← elastic

← inelastic

← without the N = 2 level

Effect of omitting γN · S is negligible

Missoula, May 2006 – p. 17/35

3He+OH(2Π3/2): (in)elastic cross sections

10−6

10−5

10−4

10−3

10−2

10−1

100

101

10−10

10−8

10−6

10−4

10−2

100

102

104

Collision energy (cm−1)

Cro

ss s

ectio

n (A

ng2 )

3He+OH

Elastic, B=0 T

B=0 T

B=2 T

B=0.5 T

B=0.01 T

B=0.1 T

Missoula, May 2006 – p. 18/35

3He+OH(2Π3/2): (in)elastic cross sections

10−1

100

100

101

102

103

E (cm−1)

σ (Å

2 )

B=0 T

B=0.1 T

B=2 T

Missoula, May 2006 – p. 19/35

Stark decelerator

H.L. Bethlem, G. Berden, and G. Meijer, Phys. Rev. Lett. 83, 1558 (1999).

Missoula, May 2006 – p. 20/35

Stark decelerator

Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin

Missoula, May 2006 – p. 21/35

Missoula, May 2006 – p. 22/35

Radiative lifetime of OH[X2Π3/2(v = 1)]

S. van de Meerakker, N. Vanhaecke, M. van der Loo, G. Groenenboom, and G. Meijer, Phys.

Rev. Lett., 95, 013003 (2005)

Missoula, May 2006 – p. 23/35

Calculation

0.5 1 1.5 2 2.5

−5

0

5

10

Pot

entia

l Ene

rgy

(eV

)

O−H distance (Å)

v=0v=1

⟨µz⟩

OH(X2Π)

0.5 1 1.5 2 2.5

−1

−0.5

0

0.5

1

1.5

2

Dip

ole

Mom

ent (

Deb

ye)

Energy 0.02%

Dipole 0.7%

aug-cc-pV6Z, µz withaug-cc-pVQZ

1σ − 5σ, 1π − 2π CASSCF

Internally contractedSD-MRCI

Special relativistic effects atDouglas-Kroll one-electronlevel

Λ-type doubling, spin-orbit,spin-rotation,rotation-vibration

Field induced parity mixing

Missoula, May 2006 – p. 24/35

Radiative lifetime of OH[X2Π3/2(v = 1)]

τ−1 =∑

f Afi

Method Afi τ (ms) ε(τ) (ms)

HITRAN Q(T )

e−βEi−e−βEf

ω2

Iaπ2c2gfSfi 56.6 ±5.6 · · · ± 11.3

Decay in trap 59.0 ±2

Calculation 4αω3

fi

3c2e2 |〈f |µ|i〉|2 58.0 ±1

Missoula, May 2006 – p. 25/35

Xe+OH(2Π3/2f ) collision experiment

pulsed valve

hexapole

skimmer

Stark decelerator

LIF zone

PMT

photodissociation

laser (193 nm)

detection laser

(282 nm)

Xe

cooled -70o C

Bas van de Meerakker, Steven Hoekstra, Joop Gilijamse, Gerard Meijer (Berlin)

Missoula, May 2006 – p. 26/35

OH energy levels

0

50

100

150

200

250

1 3/2

2 5/2

3 7/2

1 1/2

2 3/2

N J

N J

cm-1

ef

ef

ef

ef

ef

+-

+- +

-

-+

-+

ε p

ε p

F1, X 2Π3/2

F2, X 2Π1/2

Missoula, May 2006 – p. 27/35

Xe-OH energy dependent cross sections

Xe-OH 2Π3/2(J′ = 3/2, f)→ Xe-OH 2Π3/2,1/2(J, e/f)

0 200 400 600 800

100

101

102

103

3/2f

3/2e

5/2e

5/2f

1/2e

E (cm−1)

σ (a

02 )

Xe−OH

Missoula, May 2006 – p. 28/35

Xe+OH, relative cross section

Missoula, May 2006 – p. 29/35

Xe+OH cross sections at 130 cm−1

Xe-OH 2Π3/2(J′ = 3/2, f)→ Xe-OH 2Π3/2,1/2(J, ǫ)

J, ǫ experiment (%) calculation (%)3/2, e 59± 4 61.55/2, e 26± 2 24.35/2, f 11± 2 13.41/2, e 1.5± 0.5 0.311/2, f 1.5± 0.5 0.44

Missoula, May 2006 – p. 30/35

NH(3Σ−)–NH(3Σ−)

SA = 1 and SB = 1⇒ S = 0, 1, 2

S = 0: chemically stable molecule

S = 1: idem, in triplet excited state H

H

N N

Ab initio calculations

S = 2 potential by RCCSD(T) method

Differences between S = 1 and S = 0 potentials andS = 2 potential by CAS-PT2 or CAS-PT3

G. S. F. Dhont, J. H. van Lenthe, G. C. Groenenboom, and A. van der Avoird,

J. Chem. Phys., 123, 184302 (2005)

Missoula, May 2006 – p. 31/35

N2H2 (diimide, diazene) chemistry

0

20

40

60

80

100

120

kcal

/mol +

+

+

C.-H. Lai et al., J. Phys. Chem., 107, 2700 (2003)

Missoula, May 2006 – p. 32/35

NH–NH potential, all three angles optimized

5.5 6 6.5 7 7.5 8 8.5 9−1000

−900

−800

−700

−600

−500

−400

−300

R (a0)

Pot

entia

l (cm

−1 )

S = 2

S = 1

S = 0

θA = θB = 0◦

θA, θB ≈ 90◦

Missoula, May 2006 – p. 33/35

NH–NH bound levels onS = 2 potential

0 1 2 3 0 1 2 3−400

−350

−300

−250

−200

A1

B1

A1

B1

B1

A1

B1

A1

0, 0, 0

1, 0, 00, 1, 0

0, 1,−12, 0, 01, 1, 0

0, 1, 1 + 0, 2, 00, 1, 0

0, 1, 0

1, 1, 00, 1, 1 + 0, 2, 00, 1, 0

J J

Ene

rgy

(cm

−1 )

Label : vs, k

A, k

B

Missoula, May 2006 – p. 34/35

Summary

buffer gas cooling

He+CaH(2Σ+): well understoodHe+NH(3Σ−): predicted favorableHe+OH(2Π3/2): predicted unfavorable

Stark decelerationOH (v = 1) life time: reduced error barXe+OH(2Π): high energy resolution scattering

NH(3Σ−)+NH(3Σ−): ultracold chemistry ?

Missoula, May 2006 – p. 35/35