Photo fragmentations, State Interactions and Energetics of
Rydberg and Ion-pair states: REMPI via E and V (B)
states of HCl and HBr
Jingming Long, Huasheng Wang and Ágúst Kvaran*
Supplemental Material
Content:
Intensity ratio analysis (text, formulas)...........................................................
1
Table SI (Typical experimental parameters for REMPI experiments.)...........
Table SII (Hamiltonian matrixes elements).....................................................
3
3
Fig. S1(Contour plots showing B´E as a function of WL and WH).....................
Fig. S2 (I(35Cl+)/I(H35Cl+) vs. J´ for H35Cl , E1+ (v’ = 0), H35Cl................
Fig. S3 (Fractional state mixing of E(0), V(10)) and V(11) for H35Cl)............
4
6
7
References........................................................................................................
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Intensity ratio analysis:
Intensity ratios vs. J´ have been expressed as a function of fractional contributions to
the state mixing, derived for two-level interactions.1 Assuming, to a first approximation, that
the ion intensity ratio is a sum of contributions due to interactions between a Rydberg state (1)
and two ion-pair (2) vibrational states (2H and 2L), such as those between the E1+(v´) (E(v´))
and the V1+(v´) states closest in energy (VH and VL), the following expression is derived,



I (iX  )
 H  c22H (1   H )
 L  c22L (1   L )
 H
L
I (iHX  )
(1  c22H )
(1  c22L )

(1a)
where c 22I (I = H,L) are the fractional contributions of the VI (I = H,L) states to the state
mixing
1
c22I 
(E J ´ (1,2 I )) 2  4(WI ) 2
1

; c12  1 c22I ; I  H , L
2
2 | E J ´ (1,2 I ) |
(1b)
and
I (i X  )   2 I c22I  1c12 ;
 I  2 I / 1 ;
I ( H iX  )  1c12   2 I c22I ;
 I  1 /  2 I ;
 I  I  1 / 1 ;
I  H, L
I  H, L
(1c)
(1d)
EJ´(1,2H) and EJ´(1,2L) are the energy spacings between levels with the same J´ quantum
numbers for the 1, 2H and 1,2L states respectively, easily derivable from energy levels. WH
and WL are the corresponding interaction strengths. 1, 1, 2I, 2I (I = H,L) are ionization
rate coefficients. γI and αIγI are measures of iX+ ion formations via dissociation of the
Rydberg state, relative to that of the formations of iX+ via exciations of the ion-pair state (γI)
and relative to that of the formations of HiX+ via excitation of the Rydberg state (αIγI). To a
first approximation WL = WH = W , L = H = and L = H =  is assumed,2

 

   c22H (1   )   c22L (1   ) 
I (iX  )
 


2
I ( i HX  )
(1  c22L ) 
 (1  c2 H )
(1e)
2
Fractional mixings of the three states, C12 , C22L and C 2H
are determined as,
C12 1 /(1  k L  k H )
C 22L  k L /(1  k L  k H )
(1f)
C 22H  k H /(1  k L  k H )
where
k L  c22L / c12 ;
k H  c22H / c12 ;
2
Table SI. Typical equipment / condition parameters for REMPI experiments.
Gas sample
HCl-Merck Schuchardt, Germany. Purity: 99.8%
HBr-Merck-Schuchardt; Purity >99.9%
Laser dye
C460, C480, C503
Frequency doubling crystal
BBO-2
Laser repetition rate
10Hz
Dye laser bandwidth
0.095 cm-1
Laser intensity used
0.1-0.3 mJ/pulse
Laser beam focal distance
30 cm
Nozzle size
500 m
Sample backing pressure:
2.0 – 2.5 bar
Pressure inside ionization chamber: 10-6 mbar
Nozzle opening time
150 - 200 s
Delay time for laser excitation
450-550 s
Excitation wavenumber step sizes
0.05 – 0.1 cm-1
Time of flight step sizes
10 ns
Table SII. Hamiltonian matrixes elements used to derive spectroscopic parameters (0, B´
and D´) by diagonalization (see text) a.
E(v')
VL
VH
0
E
WL
WH
VL
WL
0
VL
VH
WH
E(v ')
E
E
0
EVH
a
EE0   E0  BE' J ' ( J '1)  DE' J '2 ( J '1) 2 ;
EVI0   VI0  BVI' J ' ( J '1)  DVI' J '2 ( J '1) 2 ;
I = L, H
E(v´) is an E1+(v´) state and VL and VH are the lower and higher energy ion-pair states (V
 (v´) and (v´+1)) respectively (see text).  E0 and  VI0 are term values (band origins). B´E and
1 +
B´VI are the rotational constants. D´E and D´VI are the centrifugal distortion constants. WL and
WH are the interaction parameters. See for example reference 3 for comparison
3
Figure S1a
Figure S1b
4
Figure S1c
Fig. S1 Contour plots showing rotational constants for the E(v´) states (B´E) derived from
deperturbation calculations as a function of the interaction strengths, WL and WH, with the VL
and VH states respectively (see text for definition) for HCl, E1+ (v’ = 1) (a), HCl, E1+ (v’ =
0) (b) and HBr, E1+ (v’ = 0) (c). Red circles represent B´E ´s corresponding to 0 < D´E <
0.001 and WL  WH for integer values of WL and WH (see text). Filled dots refer to WL and
WH values used in the analysis of the intensity ratios. Broken lines represent points for WL =
WH.
5
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
35
+
35
+
I( Cl )/I(H Cl )
Experimental data
V(v'=10)
V(v'=11)
0.0
0.0
0
1
2
3
4
5
6
7
J'
Fig. S2 H35Cl: Relative ion signal intensities, I(35Cl+)/I(H35Cl+) vs. J´ derived from Q
rotational lines of REMPI spectra due to two-photon resonance excitations to the Rydberg
states E1+ (v’ = 0). Gray columns are experimental values. The black and white columns are
calculated values for the contributions due to the interactions of the E(v´) states with the
lower energy V states (VL) and the higher energy states(VH), respectively.
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C12, CL2, CH2
E(0)
V(10)
V(11)
J´
Fig. S3 H35Cl: Fractional contributions of the E1+ (v’ = 0) (C12) (E(0)), V1+ (v’ = 10) (CL2)
(V(10)) and V1+ (v’ = 11) (CH2) (V(11)) states in the state mixing derived from analysis of
the ion intensity ratios as a function of J´ (Fig. S2 and text above).
References
1
2
3
A. Kvaran, K. Matthiasson, and H. Wang, J. Chem. Phys 131, 044324 (2009).
K. Matthiasson, J. Long, H. Wang, and A. Kvaran, Journal of Chemical Physics 134,
164302 (2011).
T. C. Melville and J. A. Coxon, J. Phys. Chem. A 106, 8271 (2002).
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