Proton formation in 2+1 resonance enhanced multiphoton excitation
of HCl and HBr via ( Rydberg and ion-pair states
Constantin Romanescu and Hans-Peter Loock1
Department of Chemistry, Queen’s University, Kingston, ON K7L 3N6, Canada
Supporting Information (EPAPS)
The attached file contains a detailed analysis of the pathways by which excited hydrogen atoms,
H*(n=2), may be formed through resonance enhanced 2+1 photon excitation of HCl through a
variety of intermediate states.
1
To whom correspondence should be addressed: HPLoock@chem.queensu.ca
1-613-533-2621
1
In the following paragraphs we provide support for the proposed mechanism by which
H*(n=2) is formed from HCl following excitation of the V 1+) [v = 9, 11-13, 15], or E 1+)
[v=0] states through either the Q(0) or Q(1) lines.
Following the Wigner-Witmer rules1, the lowest HCl+ electronic states that correlate to
H+ are the bound A2+14*0) and the unbound (2)213*1) states. Assuming that the
superexcited states that dissociate into H* are Rydberg-type states converging to these two ionic
limits, Chichinin et al.2 devised a correlation diagram, which we use in what follows.
The diagram shows that the unbound [(2)2..4s state correlates to H*(2S1/2) and
spin-orbit excited Cl(2P1/2) while the bound [A2+..4s1,3 states correlate to H*(2S1/2) +
Cl(2P3/2). Similarly, the unbound [(2)2..4p state correlates to H*(2P1/2) and spin-orbit
excited Cl(2P1/2) while the bound [A2+..4p1,3 states correlate to H*(2P1/2) + Cl(2P3/2). 2 As
the excitation process is found to be largely parallel, contributions from the and 1
states are assumed to be dominant. Perpendicular excitation of, e.g. the [A2+..4s 3 state
also produces ground state chlorine atoms whereas the correlation limit of the unbound
[(2)2..4s  or states depends on their respective ordering.2
In order to discuss the assignment of the electronic states responsible for the dissociation
of HCl and the formation of the H*(n=2) photofragments we will first discuss the angular
distribution of the protons.
Proton angular distributions
The angular distribution of the protons formed by dissociation of superexcited HCl**
(channel 2) changes with the excitation energy. This is unlike the angular distribution of the
2
protons formed via the ion-pair dissociation channel discussed in the main text. Moreover, for
the same excitation energy (intermediate state) the angular distributions of the protons formed in
coincidence with different spin-orbit state of chlorine atoms are different. To explain the
differences in the angular distributions one should consider the incoherent excitation of
dissociative electronic states with different symmetries,   0 , 1 .
The experimental values of the anisotropy parameters and the branching ratios between
the two channels, as well as the M (0) values derived from the 2 and 4 values are shown in
2
EPAPS Table 1.
Similar spatial anisotropy parameters on the (2+1) REMPI of HCl were reported recently
by Chichinin et al. 2 3 They studied the Q(0) and the Q(1) transitions to the E 1(0+) [v=0] and V
(0+) [v=12] intermediate states by using a 3D ion imaging technique. The image resolution did
1
not allow measuring the fine structure of the proton images, and consequently they provided
anisotropy parameter values which were averaged separately for all “slow” and “fast” protons. In
order to compare our spatial anisotropy parameters with those published by Chichinin et al.
2,3
we integrated the angular distribution, e.g. in Figure 1(a), over the velocities for all “slow”
protons. Following this procedure we found for the Q(0) line 2 = 0.98(5), which compares well
with the two previous values obtained 2 = 1.00(16) 3 and 2 = 0.9(2) 2. Similarly, for the Q(1)
line we find 2 = 0.35(5) and 4 = -0.40(5) in good agreement with 2 = 0.28(8) and 4 = 0.57(25) previously obtained. 3
As noted by Chichinin et al. 2, their previous values are high estimates of the spatial
anisotropy parameters, because the analysis included the protons formed in coincidence with Cl-,
for which a near-limiting value of  2  2 was found (see main text). Our more detailed analysis
3
EPAPS Table 1: Anisotropy parameters (2, 4) and branching fractions (BF) for dissociation of HCl into excited hydrogen
atoms. The uncertainties for 2, 4 and BF’s were obtained from a fit to the proton kinetic energy release spectra and are not
corrected for artifacts due to proton recoil. The branching fractions are defined as BF = [Cl(2P1/2)]/ [Cl(2P1/2)+ Cl(2P3/2)].
H*(n=2) + Cl(2P1/2)
State
V(v=9)
g (v=0)
E(v=0)
V(v=11)
V(v=12)
V(v=13)
V(v=15)
Line
2
H*(n=2) + Cl(2P3/2)
BF
|M(0)|2
4
2
|M(0)|2
4
Q(0) 0.30 (5)
0.61
0.01(7)
0.16(7)
0.56
0.0(1)
Q(1) -0.08(3)
0.74
-0.11(3) -0.18(2)
0.71
-0.03(2)
0.8(2)
0.76(5)
Q(0)
(a)
Q(1)
1.29(2)
1.00
-0.63(3)
1.14(5)
0.97
n/a
Q(0)
1.28(2)
0.86
-0.18(3)
0.74(3)
0.83
-0.14(4)
Q(1)
1.04(2)
0.95
-0.57(3) -0.82(3)
0.41
-0.09(4)
Q(0)
1.29(2)
0.86
-0.08(3)
1.08(3)
0.82
-0.03(4)
Q(1)
0.33(2)
0.84
-0.46(2)
0.62(2)
0.89
-0.40(3)
Q(0)
0.46(2)
0.66
-0.08(2)
0.97(2)
0.79
-0.09(2)
Q(1) -0.13(1)
0.73
-0.29(1)
0.19(2)
0.81
Q(0)
1.01(4)
0.80
-0.13(5)
1.35(4)
0.88
-0.36(2) 0.61(24)
-0.10(6)
Q(1)
0.40(2)
0.85
-0.45(2)
0.59(2)
0.88
-0.44(3) 0.62(20)
Q(0)
1.71(2)
0.95
0.08(3)
Q(1)
1.53(2)
1.06
-0.13(3)
0.92(8)
0.68(6)
(b)
(a) Proton image had poor resolution
(b) H* + Cl(2P3/2) channel is overlapped with the HCl+  H+ + Cl- channels
distinguishes between these contributions and leads to considerably lower spatial anisotropy
parameters for both H*(n=2) formation channels (Table 1 in main paper and EPAPS Table 1).
A minor disagreement was found when comparing spatial anisotropy parameters for the E
(0+) [v=0] intermediate state. This was unexpected because the three photon dissociation via
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the E 1(0+) state shows only a very small contribution of the H+ + Cl- channel and leads almost
exclusively to the formation of H*(n=2) + Cl(2P1/2). It was expected that the 2 values reported
by Chichinin et al. 2,3 are similar to our averaged values. The difference is larger for the Q(1) line
4
for which they found 2 = 0.42(12) and 4 = -0.76(17) while we found 2 = 0.88(5) and 4 = 0.51(5) when averaging the contributions form both Cl spin-orbit components. A previous
analysis by our group gave 2 = 0.9 and 4 = -0.67 for the dominant H* + Cl (2P1/2) channel.4 The
reason for the discrepancy is not apparent. We note that good agreement exists between the
values obtained for the Q(0) line.
H*(2s) + Cl(2P1/2) dissociation channel
Depending on the intermediate state, 61-92% of the excited hydrogen atoms are formed
in coincidence with spin-orbit excited chlorine atoms. Of those, 50-90% are formed in a parallel
excitation process. Earlier assignments by de Beer et al.5 and by Manzhos et al.4 proposed that
the dissociative [A 24s] 1+ superexcited state6 forms H*(2S) + Cl(2P1/2). On the other hand
Chichinin et al.2 assigned the dissociative state to the [(2)2..4p] 1state (channel 8a in ref.
2
) and consequently predicted that the hydrogen atoms have a 2P electronic configuration. The
second scenario appears more likely, since according to the correlation diagram (Figure 5) the
superexcited electronic states that form H*(2S, 2P) in coincidence with spin-orbit excited chlorine
atoms are Rydberg states converging to the unbound (2)2 ionic state2. While the predicted
formation of H*(n=2, 2P) appears not to be consistent with the observed photoelectron angular
distribution ( 2  1.1  1.3 ) or the observed proton recoil reported in ref. 6, we note that l and 
cannot be well-defined in the laser field and the H*(2S) and (2P) photofragment states are
strongly mixed. It may therefore be more accurate to express the process as
X1(0)  1(0)  [(2)2..4l] 3(0) or 1(0)  H*(2P,2S) + Cl(2P1/2)
5
Here, we resist the temptation to assign the dissociative state to the [(2)24s]
3
superexcited state, which in a field-free environment would correlate to H*(2S) + Cl(2P1/2).
The potential energy curves relevant for the excitation of the intermediate states of HCl and the
formation of H*(n=2) are shown in Figure 5 in the main text.
An alternative explanation for the formation of H*(n=2) + Cl(2P1/2) is the predissociation
of bound [A 2+..nl] 1+ superexcited states with 5s, 4d or 5p Rydberg electrons by the same
=0 unbound [(2)2..4l] Rydberg state via spin-orbit coupling. These bound superexcited
states are the same states that lead to the ion-pair dissociation (see main text). The interaction
does not have an equivalent in the potential energy curves of HCl+ since the A 2 and the (2)2
states of the ion do not cross. An interaction between the Rydberg states converging to these
states is however feasible, since the superexcited states differ by only two spin-orbitals and
previous studies proved that l mixing between superexcited Rydberg states plays an crucial role
in the dissociation of HCl.2 For example, Lefebvre-Brion et al.7 found that the [2..3d] 10)
state is predissociated by the [4..4s] 30) state that dissociates into H + Cl*(4s) due to the s-d
mixing of the bound state. Strong mixing was also found between superexcited states with p and
d Rydberg electrons.
In conclusion, while the experimental data allows us to identify the dissociative state
[(2)2..4l] 3(0), 1(0) as responsible for the formation of H*(n=2) + Cl(2P1/2), it remains
unclear if the dissociation proceeds in a single step or is mediated by the excitation and
subsequent fast predissociation of a 1+ bound superexcited state.
6
H*(2S) + Cl(2P3/2) dissociation channel
The H*(2S) + Cl(2P3/2) dissociation represents a minor process and is associated with a
Δ = 0 excitation to the dissociating state, i.e. M (0)  0.8 for all intermediate states, except V
2
0+) [v = 9] and E 10+) [v = 0].
1
According to the correlation diagrams by Chichinin et al., the H*(n=2) + Cl(2P3/2)
photofragments may be formed in a parallel process via excitation of the bound [A24l] 1+
Rydberg state above the dissociation limit.2 This pathway is deemed unlikely due to poor
Franck-Condon overlap with all intermediate states.
The excitation of a different   0 state with a dissociation limit below H*(n=2) +
Cl(2P3/2) can also form H*(n=2) at an avoided crossing with the [A(2+)..4l 1+ state. Such a
state is the repulsive [44s] 3 state that fragments into H  Cl * (4 s, 2 P1 / 2 ) .6 The 3
superexcited state has a dissociation limit at 109974.05 cm-1, lying 8033.1 cm-1 below the
dissociation limit of the H *(n  2)  Cl ( 2 P3/ 2 ) channel, and crosses the 1+ state at around
2.45Ǻ (Figure 5 in main text). Excitation of [44s] 3 state was proposed to lead to
formation of Cl*(4s) in a direct dissociation process and is the dominant pathway of Cl*
formation in the 2+1 excitation of the E 10+) intermediate state.7 H  Cl * (4 s, 2 P1 / 2 ) . Also the
same [4..4s] 30+) superexcited state has been identified as a possible gateway state in the
autoionization dynamics, thence responsible for the large number of vibrational states of HCl+.6
The matrix element for the spin-orbit interaction between the corresponding 4and
A(2+) ionic states was calculated by Raferty and Richards8 as ASO = 520 cm-1. A Landau-Zener
type calculation can then be used to estimate the fraction of H *(n  2)  Cl ( 2 P3/ 2 ) fragments
formed through an adiabatic passage through this avoided crossing. The calculation shows that
7
following parallel excitation of the [44s] 3state and at excitation energies used in this
study about 5 – 10 % of the excited molecules will adiabatically couple to the [A 2+..4s] 1+
state and proceed to form H *(n  2)  Cl ( 2 P3/ 2 ) .9 The potential parameters that were needed for
the Landau-Zener estimate were obtained from the ab initio ionic curves by Pradhan et al.10
With the exception of the V 10+) [v=13] intermediate state, the branching fractions [H*
+ Cl(2P3/2)] / ([H* + Cl(2P3/2)] + [H + Cl*(4s)]) calculated from the Landau-Zener model are
consistent with the branching fractions obtained from photoelectron intensities. 6,11 The deviation
observed in the case of photoexcitation of V 10+) [v=13] intermediate state is probably due to
the overlap of the H*(n=2) + Cl(2P3/2) peak with the proton peaks arising from the dissociation of
HCl+[v+=5] (see also Figure 2 in main text).
Reference List
1. G. Herzberg, Molecular Spectra and Molecular Structure I. Spectra of Diatomic
Molecules,2nd Edition (Van Nostrand, New York, 1950).
2. Chichinin, A. I., Maul, C., and Gericke, K. H., J.Chem.Phys. 124(22), (2006).
3. Chichinin, A. I., Shternin, P. S., Godecke, N., Kauczok, S., Maul, C., Vasyutinskii, O. S.,
and Gericke, K. H., J.Chem.Phys. 125(3), (2006).
4. Manzhos, S., Romanescu, C., Loock, H.-P., and Underwood, J. G., J.Chem.Phys. 121(23),
11802 (2004).
5. de Beer, E., Buma, W. J., and de Lange, C. A., J.Chem.Phys. 99(5), 3252 (1993).
8
6. Romanescu, C., Manzhos, S., Boldovsky, D., Clarke, J, and Loock, H.-P., J.Chem.Phys.
120(2), 767 (2004).
7. Lefebvre-Brion, H. and Keller, F., J.Chem.Phys. 90(12), 7176 (6-15-1989).
8. Raferty, J and Richards, W.G., J.Phys.B. 6, 1301 (1973).
9. Zener, C., Comm.Proc.Royal Soc.London 137, 696 (1932).
10. Pradhan, A. D., Kirby, K. P., and Dalgarno, A., J.Chem.Phys. 95(12), 9009 (1991).
11. Romanescu, C., Ph.D . Dissertation, Queen's University, Kingston, ON, Canada, 2007.
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