PRESSURE BROADENING AND SHIFTING COEFFICIENTS AS TESTS OF H2(D2)-He POTENTIAL ENERGY SURFACES

HAL Id: hal-01263187

https://hal.archives-ouvertes.fr/hal-01263187

Submitted on 1 Feb 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

PRESSURE BROADENING AND SHIFTING COEFFICIENTS AS TESTS OF H2(D2)-He

POTENTIAL ENERGY SURFACES

Franck Thibault, P Wcislo, R Ciurylo

To cite this version:

Franck Thibault, P Wcislo, R Ciurylo. PRESSURE BROADENING AND SHIFTING COEFFI-

CIENTS AS TESTS OF H2(D2)-He POTENTIAL ENERGY SURFACES. The 24th Colloquium on

High Resolution Molecular Spectroscopy HRMS 2015, Aug 2015, Dijon, France. 2013. �hal-01263187�

PRESSURE BROADENING AND SHIFTING COEFFICIENTS AS TESTS OF H ₂ ‐He POTENTIAL ENERGY SURFACES

Franck THIBAULT

Institut de Physique de Rennes, UMR CNRS 6251, Université de Rennes I, F‐35042 Rennes, France

Piotr WCISLO, Roman Ciurylo

Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5/7, 87‐100 Torun, Poland

We have used the Schaefer and Köhler

¹

(SK),the modified Muchnick and Russek

²

(MR), the Boothroyd, Martin and Peterson

³

(BMP), and the Bakr, Smith and Patkowski

⁴

H

2

‐He potential energy surfaces in order to calculate, using the close coupling method, pressure broadening and shifting coefficients. The helium pressure broadening and shifting generalized cross sections of the isotropic raman Q(1) lines of the fundamental of D

2

and H

2

as well as the purely rotational Stokes S

0

(1) line of H

2

were computed. We have decomposed the pressure broadening cross‐sections in a purely inelastic and a purely dephasing, including a vibrational one for the Q lines, contributions. Such a decomposition allows us to better understand the main differences that exist between these potentials.

The old Schaefer and Köhler PES and the most recent one, namely the Bakr et al PES, give close results in quite good agreement with available experimental data.

1. PESs used

2. Pressure broadening and shifting cross‐sections and coefficients

3. Raman isotropic Q(1) line  of the fundamental band of D

₂

[1] J. Schaefer and W.E. Köhler, Physica A 129, 469 (1985) [2] P. Muchnick and A. Russek, J. Chem. Phys. 100, 4336 (1994) [3] A.I. Boothroyd, P.G. Martin, M.R. Peterson, J. Chem. Phys. 119, 3187 (2003) [4] B.W. Bakr, D.G.A. Smith, K. Patkowski, J. Chem. Phys. 139, 144305 (2013)

The modified MR PES shows the less differences in its isotropic parts in v=0 and v=1 while the SK PES shows the most differences.

The modMR PES differs significantly from the others at long range.

The BMP PES is the less anisotropic PES.

 

,vj ,vj' vj vj'

V_ ( R ) dr ( r )V ( r , R )_  ( r )

 

even

V ( r , R, ) V ( r , R )P (cos )_{ }



 

R (Å) 2.10 2.122.142.16 2.182.202.22 2.24 Vv(cm-1)

400 500 600 700 800 900

R (Å)

2.55 2.60 2.65 2.70 2.75

Vv(

cm-1)

40 60 80 100

R (Å)

3.0 3.2 3.4 3.6 3.8 4.0

Vv(cm -1)

-10 -9 -8 -7 -6 -5

R (Å)

7.0 7.2 7.4 7.6 7.8 8.0

Vv(cm -1)

-0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08

V00 Bakr V01 Bakr V00 SK V01 SK V00 mMR V01 mMR V00 BMP V01 BMP

R (Å)

1.8 2.0 2.2 2.4 2.6 2.8

± V2,v/V0,v

-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75

Bakr SK mMR BMP Bakr SK mMR BMP v = 0

v = 1

i f i f i f

( n ) ( n)

i f kin inelastic i f kin dephasing i f kin

(v j v j ;E ) (v j , v j ;E ) (v j , v j ;E )

    

i i f f

i f

' '

inelastic i f kin i i i i kin f f f f kin

j ' j j ' j

v v 1

( j , j ;E ) (v j v j ;E ) (v j v j ;E )

2

 

 

 

 

 



  



 

 

( n ) ( n )

PB

( ;E if

kin

) Re ( ;E if

kin

)

   ^{( n )PS}

( ;E if

kin

)



Im 

^{( n )}dephasing

( ;E if

kin

) 

2

b B

B

( n )

kin kin kin kin

v 1 d exp( / k T) if

i n



k T



E E



E ( ;E )

 

   





E_kin (cm^-1)

0 500 1000 1500 2000

Re() (Å2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

total PBXS Bakr total PBXS SK total PBXS mMR total PBXS BMP isotropic Bakr isotropic SK isotropic mMR isotropic BMP

inel Bakr

inel SK

inel mMR

inel BMP

deph Bakr

deph SK

deph mMR

deph BMP

j=3 open

Ekin (cm^-1)

0 500 1000 1500 2000

Im() (Å2)

-2 -1 0 1 2 3 4 5

total PSXS Bakr total PSXS SK total PSXS mMR total PSXS BMP

iso Bakr

iso SK

_iso mMR

iso BMP j=3 open

Contributions to the cross‐sections widths: 

total inelastic elastic dephasing

vibrational dephasing (V

iso

) 

shifts:

total vibrational dephasing (V

iso

)

T / K

0 100 200 400 500 600 700 800 900 1000

 (mK/amg)

0 2 4 6 8

 Bakr

 SK

 mMR

 BMP

_isoBakr

isoSK

_isomMR

_isoBMP

inelBakr

_inelSK

_inelmMR

inelBMP

 exp. Fakhr

 exp. Smyth

T / K

0 100 200 400 500 600 700 800 900 1000

 (mK/amg)

0 5 10 15 20

 Bakr

 SK

 mMR

 BMP

_iso Bakr

iso SK

_iso mMR

_iso BMP

 exp. Fakhr

 exp. Smyth

Pressure  shifting coefficients of the Q(1)  of D

₂

in He

At low T most of the broadening and  shifting arise from the isotropic parts  but as T increases the effects of the  anisotropy and related  inelastic  collisions increase.

4. Raman isotropic Q(1) line  of the fundamental band of H

2 

in He

T / K

0 500 1000 1500 2000 2500 3000

 (mK/amg)

0 2 4 6 8 10 12 14 16 18 20 22 24 26

 Bakr

 SK

iso Bakr

iso SK

_inel Bakr

inel SK

 exp. Forsman

0 100 200 300 400 500

0 1 2

T / K

0 500 1000 1500 2000 2500 3000

 (mK/amg)

0 10 20 30 40

50  Bakr

 SK

iso Bakr

iso SK

 exp. Forsman

0 100 200 300 400

0 2 4 6 8 10 12 14

Pressure  broadening coefficients of the Q(1)  of H

₂

in He Pressure  shifting coefficients of the Q(1)  of H

2

in He

The SK PES gives better agreement  with the experimental

⁷

PB coefficients  while the Bakr PES provides better  agreement for the PS coefficients.

5. Stokes S

0

(1) line of H

2 

in He

T / K

0 200 400 600 800 1000

(T) (mk/amg)

0 1 2 3 4 5

 Bakr

 SK

 FIT Michaut

 exp. Michaut

 exp. Hermans

T / K

0 200 400 600 800 1000

(T) (mk/amg)

0 1 2 3 4 5

 Bakr

 SK

 FIT Michaut

 exp. Michaut

 exp. Hermans

Comparison of the ratio of the first  anisotropic Component to the isotropic one in v=0 and v=1:

Comparison of the isotropic components in v=0 and in v=1  (j=j’=0, no centrifugal distortion):

Pressure  broadening coefficients of the Q(1)  of D

₂

in He

The modMR and BMP PESs are rejected.

Pressure shifting coefficients

In this case it is important to take  into account the centrifugal  distortion especially for the shifts.

The SK and Bakr et al PESs lead to  very close results in good  agreement with the experimental  values

^8,9

over the full range of T.

[5] S.H. Fakhr‐Eslam, G.D. Sheldon, P.M. Sinclair, J.R. Drummond, A.D. May, J.Q.S.R.T. 68, 377 (2001) [6] K.C. Smyth, G.J. Rosasco, W.S. Hurst, J. Chem. Phys. 87, 1001 (1987)

[7] J.W. Forsman, J. Bonamy, D. Robert, J.‐Ph. Berger, R. Saint‐Loup, H. Berger, Phys. Rev. A. 52, 2652 (1995) [8] P.W. Hermans, A. Van Die, H.F.P. Knaap, J.J.M. Beenakker, Physica A 122, 233 (1985) 

[9] X. Michaut, R. Saint‐Loup, H. Berger, M.‐L. Dubernet, J. Bonamy, D. Robert, J. Chem. Phys. 109, 951 (1998) 

Pressure broadening coefficients

Work in progress proves that the relative differences between PB coefficients  derived with the SK and Bakr PESs are  smaller than relative differences between coefficients taking into account inhomogeneous broadening or not. 

Including the inhomogeneous mechanism leads to much better agreement with observed widths.