1 60th International Symposium on Molecular Spectroscopy, Talk RG03, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution

160th International Symposium on Molecular Spectroscopy, Talk RG03, 23 June 2005, Ohio State University, Columbus, OH

Approved for Public Release; Distribution Unlimited. AAC/PA 05-03-05-170

Mario E. FajardoAFRL/MNME, Energetic Materials Branch, Ordnance Division,

U.S. Air Force Research Laboratory, 2306 Perimeter Road, Eglin AFB, FL 32542-5910. [email protected]

Takamasa MomoseDivision of Chemistry, Graduate School of Science, Kyoto University,

Kyoto 605-8502, Japan.

* Introduction to MIS in solid parahydrogen (pH2)

* IR absorption spectra of CO monomers in solid pH2

* Crystal Field Theory (CFT) analysis & assignments

* Summary

Crystal Field Theory Analysis of Rovibrational Spectra of CO Monomers in

Solid Parahydrogen



ortho- and para-hydrogen

I.F. Silvera, Rev. Mod. Phys. 52, 393 (1980). T. Oka, Fiz. Nizk. Temp. 22, 134 (1996).

Electrostatics:

Body fixed 00 = 0.484 ea02

oH2(J=1): = (2/5) 00

= 8.69x10-41 Cm2

40 r 4

3(r)

E

Rnn(pH2) 3.8Å

E(3.8Å) 108 V/m 1 MV/cm



Rapid vapor deposition of solid pH2

M.E. Fajardo and S. Tam, J. Chem. Phys. 108, 4237 (1998).S. Tam and M.E. Fajardo, Rev. Sci. Instrum. 70, 1926 (1999).S. Tam and M.E. Fajardo, J. Low Temp. Phys. 122, 345 (2001).

Deposition conditions: Tconv = 15 K

100 ppm oH2

Tconv = 19 K

1000 ppm oH2

npH2/t = 200 mmol/hr

x/t = 3.1 mm/hr Tsub = 2.4 K 2.9 K

TpH2 4.6 K

Result: mixed fcc/hcp microstructure in as-deposited samples;can anneal to pure hcp.



12C16O/pH2 IR absorptions

13 ppm 12C16O/pH2, d=2.9 mm,deposited in 60 min @ T=2.4K.

Assignments from CFT analysis.

", ||" polarization vs. hcp c-axis"" CO in metastable fcc sites

(c) T=2.4K, annealed.

(b) T=4.8K.

(a) T=2.4K, as deposited.

wavenumber (cm-1)

2135 2140 2145 2150

log 1

0(I

0/I)

(ab

s.)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

(c)

(b)

(a)

P(2)

P(1)

Q(1)CO-oH2

(CO)n

R(0)

R(1)

R(2)S(0)



Devonshire Crystal Field Theory

Physical assumptions:

(1) Molecular center-of-mass (C.M.) remains fixed at trapping site center.

(2) Rigid, undistorted trapping site.

Potential for diatomic rotor in Oh crystal field:

Vcry() = -K4 {P40(cos ) +

(1/168)P44(cos ) cos(4)}

A.F. Devonshire, Proc. Roy. Soc. (London) A153, 601 (1936).

4



CFT analysis of 12C16O in fcc pH2

For 12C16O in fcc pH2:

Beff(pH2) 0.79 Be(gas)

E(Eg - T2g) 0.56 Be(gas)

green: K4 +12Be, -19Be

red: K4 +1Be, -1Be

Pure CFT cannot explain both observations simultaneously!

Approach: use CFT for MJ splittings, treat Beff as an adjustable parameter.

Need alternative explanation for matrix effects on rotational constants.

K4 (Bgas)

-25 -20 -15 -10 -5 0 5 10 15 20 25

ener

gy le

vels

(B

ga

s)

-6

-4

-2

0

2

4

6

8

10Eg

T2g

T1u

A1g

K4 (Bgas)

-25 -20 -15 -10 -5 0 5 10 15 20 25

tran

sitio

n en

ergi

es (

Bg

as)

0

2

4

6

8

10

R(1)

R(1)

R(0)

R(1)

R(0)



Diatomic rotor in D3h crystal field

cryrv VHH

)1()1()1(),( 212

21 JJvJJDJJBvJvE eeeerv

)()()( CO3,3CO3,33CO0,22 CCCVcry

)(12

4)(

2

1

lmlm Y

lC

six adjustable fitting parameters:vibration: e

rotation: Be, De, e

crystal field: 2, 3



CFT analysis of 12C16O in hcp pH2

constant 12C16O values (cm-1)

0 2140.295(2)b [2143.2711]c

Be 1.577(1) [1.9313]

De 0.0271(1) [0.00000612]

e d 0.0129(6) [0.01750]

2 1.026(4)

3 2.523(7)a Values in parentheses are the standard deviation (1) of the least squares fitting for the last digit.b Values in square brackets are those in the gas phase. [J.A. Coxon and P.G. Hajigeorgiou, J. Chem. Phys. 121, 2992 (2004).]c The band origin of the gas phase is calculated by e-2exe+(13/4)eye.d The ground state rotational constant is B0=Be-(1/2)e and that in the excited state is Bv=Be-(3/2)e. e Fit limited to J=0, 1, & 2 levels.

82%

4400x!

~Be



Fitting results: 12C16O in hcp pH2

obs (cm-1) calc (cm-1) obs.-calc. assignment (J',M') (J",M") pol.

2134.551 2134.552 -0.001 P(2) hcp (1,1)(2,2)

2135.204 2135.204 0.000 P(2) hcp (1,0) (2,1)

2136.741 2136.743 -0.002 P(1) hcp (0,0) (1,0) //

2137.607 2137.606 0.001 P(1) hcp (0,0) (1,1)

2140.268 2140.266 0.002 Q(1) hcp (1,1) (1,1)

2142.953 2142.953 0.000 R(0) hcp (1,1) (0,0)

2143.818 2143.818 0.000 R(0) hcp (1,0) (0,0)

2145.282 2145.279 0.003 R(1) hcp (2,1) (1,0)

2145.931 2145.930 0.001 R(1) hcp (2,2) (1,1)

2146.14 2146.142 -0.002 R(1) hcp (2,1) (1,1)

2147.12 R(2) hcp ?

2148.615 2148.617 -0.002 S(0) hcp (2,2) (0,0)

J=3 levels not included



Energy levels: 12C16O in hcp pH2

8.73 calc

?



CFT for CO isotopomers in pH2

Annealed samples at T = 2.4 K.

Spectra shifted by subtracting gas-phase R(0) line.

relative wavenumber (cm-1)

-15 -10 -5 0 5

log

10(I

0/I)

(ab

s.)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

12C16O

(x2)13C18O

13C16O

(c)

(b)

(a)

12C18O

(d)

isotopomer Beff(pH2)(cm-1)

Bgas

(cm-1)

Beff/Bgas

12C16O 1.577 1.9313 0.8165

13C16O 1.538 1.8462 0.8331

12C18O 1.469 1.8391 0.7988

13C18O 1.437 1.7540 0.8193

Matrix effect on rotational constant Be

depends on CO isotopic composition!(see companion talk RG04).



Summary

* CO monomers exist as hindered rotors in solid pH2.

* Detailed spectroscopic assignments accomplished using Crystal Field Theory for diatomic in D3h field.

* Obtained excellent fits to experimental data.(six parameters vs. ten energy levels) 2, 3 ~ Be

Beff(pH2) 0.8 Be(gas)De(pH2) 4400 De(gas)

* Matrix effect on rotational constant Be depends on CO isotopomer! (subject of companion talk RG04...)

Documents

1 60th International Symposium on Molecular Spectroscopy, Talk RG03, 23 June 2005, Ohio State University, Columbus, OH Approved for Public Release; Distribution