Engineering Sciences Reports, Kyushu University
Vol. 45, No. 2, pp. 11-22, FEB, 2024

九州大学大学院総合理工学府報告第 45 巻 第 2 号 11-22 頁 令和 6 年 2 月

Emission Spectra of He2* Excimer Produced from
Ion-Ion Neutralization Reactions of He2+ with
C6F6- and C6F5Cl- in the He Flowing Afterglow
Masaharu TSUJI*1,2† and Erika Oda−Sako*3
E-mail of corresponding author: tsuji@cm.kyushu-u.ac.jp†(Received November 17, 2023, accepted December 1, 2023)
The ion-ion neutralization reactions of He2+ with C6F6- and C6F5Cl- were studied by observing He2*
excimer emissions in the 200–990 nm region. He2* excimer emissions from six triplet states and six orfive singlet states with excitation energies of 19.3−20.7 eV were identified in these two reactions. The
relative formation rate constant of an upper 𝑢 level of He2*, 𝑘 𝑢 , rapidly decreased with increasing
the excitation energy of He2*. Major triplet and singlet He2* states were the lowest observed c3g+ andC1g+ states, which occupied 70% and 21% of ∑ 𝑘 𝑢 , in the He2+/C6F6- reaction, and 69% and 18%
in the He2+/C6F5Cl- reaction, respectively. The total formation ratios of triplet and singlet states were
78:22 in the He2+/C6F6- reaction and 81:19 in the He2+/C6F5Cl- reaction. No vibrational excitation wasobserved for all observed He2* states. The rotational distributions of f 3u+(𝑣 =0), e3g 𝑣 =0), d3u+(𝑣 =0),c3g+(𝑣 =0), and C1g+(𝑣 =0) states were expressed by either single or double Boltzmann rotationaltemperatures of 310−1530 K. Rovibrational distributions of these excited states indicated that most ofexcess energies are not released as rovibrational energies of He2*, but they (90.4−97.2%) are deposited
into relative translational energies of products and rovibrational energies of C6F5X (X=F, Cl). The
observed vibrational and rotational distributions were compared with statistical ones assuming long
lived [He2–C6F5X]* intermediates.
Key words: He2+ ion, Ion-Ion neutralization, Flowing afterglow, He2* excimer emission,

Relative formation rate constant, Rotational temperature, Statistical prior distribution

1.

Introduction

Electron-ion and ion-ion recombination andneutralization processes are important loss
processes of charged particles in space andman-made plasmas because of their extremely
large cross sections due to long range
Coulombic attractive forces between positive
ions and electrons or negative ions.1-6) In a
preceding paper, we studied the formation of
He2* excimer by three-body collisionalradiative recombination (CRR) reaction (1) inthe He flowing afterglow (FA):7)
He2+ + e- + e- → He2* + e-.

*1

(1)

Institute for Materials Chemistry and Engineering,and Research and Education Center of GreenTechnology*2 Department of Molecular Science and Technology*3 Department of Molecular Science and Technology,
Graduate Student

Thirty triplet and twelve singlet transitions ofHe2* with excitation energies of 19.3–21.8 and
19.6–21.8 eV region, respectively, wereidentified. The relative formation rate constantof He2*, 𝑘 𝑢 , rapidly decreased withincreasing the excitation energy. Major triplet
and singlet product He2* states were the lowest
observed c3g+ and C1g+ states, which occupied
39.9% and 7.1% of ∑ 𝑘 𝑢 , respectively. The
total intensity ratio of triplet and singlet states
were 84:16 respectively. No vibrational
excitation was observed for all thirty-fourstates. The rotational distributions off3u+ 𝑣 =0), e3g 𝑣 =0), and d3u+(𝑣 =0) wereexpressed by double Boltzmann rotationaltemperatures, whereas that of c3g+(𝑣 =0) was
representedbyasingleBoltzmanntemperature. On the basis of observed
rovibrational distributions, most of the total
excess energy (95.2−98.5%) is deposited into
the relative translational energy of products.
The observed vibrational and rotational

12

Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

distributions were lower than those ofstatistical prior ones calculated assuming along lived [He2–e-]* intermediate. It was
concluded that He2* molecules are not formed
via long lived [He2–e-]* intermediate, where
excess energies are statistically distributed to
all degrees of freedom.
In the present study, the formation of He2*
excimer by the ion-ion neutralization reactionsof He2+ with C6F6- and C6F5Cl- are investigatedusing the He FA. The relative formation rate
constants and rotational distributions of fivetypical states are determined. The observed
vibrational and rotational distributions arecompared with statistical ones assuming long
lived [He2–C6F5X]* (X=F, Cl) intermediates.
Preliminary results of this paper have beencommunicated previously.5,8)2.

Experimental

The FA apparatus used in this study has
been previously described in detail.5,8) In brief,
He(23S), He+, and electrons were generated bya microwave discharge of high purity heliumgas (Nippon Sanso, purity >99.995%) in adischarge flow operated at 1.6–1.8 Torr. The
contribution of charged species to the observed
emissions was examined by using a pair of ioncollector grids placed between the discharge
section and the reaction zone.
The positive He2+ ions were formed by thethree-body reaction of He+ with 2He in a flow
tube:

k2

He+ + 2He → He2+ + He,（2)(k2 = 8.3 × 10-32 cm6 molecule-2 s-1 [Ref. 9]).
An electron attachment gas, C6F6 (Tokyo Kasei,
purity >99%) or C6F5Cl (Tokyo Kasei, >95%),
was added from the first gas inlet placed 10 cm
downstream from the center of microwave
discharge, where negative C6F6- or C6F5Cl- ion
was formed by a fast non-dissociative electron
attachment to these two gases:
C6F6 + e- → C6F6-,(k3 = 8.6 × 10-8 cm3 s-1 [Ref. 10]),(3)

C6F5Cl + e- → C6F5Cl-,(k4 = 1.0 × 10-7 cm3 s-1 [Ref. 11]).

(4)

The partial pressures of C6F6 and C6F5Cl in thereaction zone were 2−15 mTorr.
A reaction flame, observed around the C6F6
or C6F5Cl gas inlet was dispersed in the

200–1000 nm region with a Spex 1250M
monochromatorequippedwith a cooled
photomultiplier (Hamamatsu Photonics R376
or R316-02). The wavelength response of
monochromator and the optical detection
system were corrected using standard D2 andhalogen lamps.

3.

Results and Discussion

3.1
Emission spectra of He2* excimer
resulting from the He2+/C6F6- and He2+/C6F5Clion-ion neutralization reactions
Figure 1 shows typical emission spectra in
the 430–980 nm region resulting from theHe(23S)/C6F6,
He+,He2+/C6F6,
andHe+,He2+/C6F6- reactions. Figure 2 shows thecorresponding spectra for C6F5Cl reagent. Six
triplet and six or five singlet transitions of He2*
given in Table 1 are identified in the He2+/C6F6and He2+/C6F5Cl- reactions by referring toreported spectral data of He2*.12-15) In addition
to many He2* emissions, C6F6+( B– X ),16)
C6F5Cl+(B– X),17) He*,18) and H*18) emissions areobserved. Strong broad C6F6+( B– X ) andC6F5Cl+( B– X ) emissions result from
He(23S)/C6F5X
Penning
ionization
andHe2+/C6F5X charge-transfer reactions.19) He*
lines dominantly result from He+/C6F5Xneutralization reactions.19,20) H* lines arise
from reaction of He(23S) with residual H2O.21)
The observed He2* emissions, on which thepresent work focuses, disappeared whencharged species were removed from the He
afterglow on applying an electrostatic potential
to the grid. The formation of He2(c, d, e, f, C, D,
E, F) by the He2+/C6F6 and He2+/C6F5Cl chargetransfer reactions are highly endothermic,
Table 1. He2* emission systems produced
He2+/C6F6- and He2+/C6F5Cl- reactions in the
He FA.

a)

Triplet transitions

Singlet transition

f3Δu(3dδ)-b3Πg

F1Δu(3dδ)-B1Πgf3Πu(3dπ)-b3Πg

F1Πu(3dπ)-B1Πgf3Σu+(3dσ)-b3Πg

F1Σu+(3dσ)-B1Πg

e3Πg(3pπ)-a3Σu+

E1Πg(3pπ)-A1Σu+d3Σu+(3sσ)-b3Πg

D1Σu+(3sσ)-B1Πga)

c3Σg+(3pσ)-a3Σu+

C1Σg+(3pσ)-A1Σu+

Observed only in the He2+/C6F6- reaction.

令和 5 年度

九州大学大学院総合理工学報告◇**第 45 巻

第2号

*

*

d-b

*

f-b

*

e-a

13

*

E-A

◇

◇

F-B

*

f-b

*

E-A

F-B

d-b

◇

* e-a
450

500

550

600

450

650

500

550

600

650

c - a, C - A

*
○

*

d-b

*

*

c-a, C-A

○

*

d-b

◇

*

◇

650

700

750

800

850

900

650

950

700

750

800

850

900

950

Wavelength / nm

Wavelength / nm

Fig. 1. Emission spectra of He2* resulting
from the He2+/C6F6- reaction in the He FA at a
He gas pressure of 1.8 Torr. Lines marked by* and ◇ are He* and H* lines, respectively.

Fig. 2. Emission spectra of He2* resulting
from the He2+/C6F5Cl- reaction in the He FA at
a He gas pressure of 1.8 Torr. Lines marked
by * and ◇ are He* and H* lines, respectively.

because high energies are required for theionization of C6F6 (9.90 eV) and C6F5Cl (9.72
eV):22)energies of 21.2–21.8 eV disappeared. On theother hand, six triplet levels from c to f statesin the 19.3–20.7 eV region and six or five
singlet levels from C to F states in the 19.6–
21.3 eV region (Table 1 and Figs. 3 and 4)
remained after C6F6 or C6F5Cl addition. These
results indicate that electrons are completely
scavenged by C6F6 or C6F5Cl, so that thecontribution of CRR reaction (1) to the observed
He2* bands is negligible. Thus, remaining
processes for the formation of He2* are thefollowing ion-ion neutralization reactions:

He2+ + C6F6 → He2(c~f,C~F) + C6F6+− (7.0~8.4 eV),(5)

He2+ + C6F5Cl → He2(c~f,C~F) + C 6F5Cl+− (6.8~8.2 eV).
(6)
Therefore, these processes can be energetically
excluded from possible formation processes.
Figures 3 and 4 show energy-level diagramsof triplet and singlet states of He2*, whereobserved emitting levels are shown in red. The
excitation energies of He2* and therecombination energy of He2+ (22.223 eV) wereobtained from Ref. 12. We found that twentytwo triplet states and twelve singlet states ofHe2* in the 19.3–21.8 eV region are formed in
the He2+/2e- CRR reaction (1).7) By the C6F6 or
C6F5Cl addition to the He discharge flow,
several He2* bands with high excitation

He2+ + C6F6→ He2(c~f,C~F) + C6F6 + (0.97~2.4 eV), (7a)→ He2(c~f,C~F) + C6F5 + F− (2.7~4.1 eV), (7b)0

He2+ + C6F5Cl→ He2(c~f,C~F) + C6F5Cl + (0.75~2.2 eV), (8a)→ He2(c~f,C~F) + C6F5 + Cl
− (1.8~3.2 eV). (8b)0Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

14

He2+
np 3Σg+ ns 3Σu+ np 3Πg nd 3Σu+ nd 3Πu

nd 3Δu22.22
22.00
He2+/C6F6-

He2+/C6F5Cl-

10
6
5

21.00

Energy / eV

4

n
k’

6
5
4

k

10
6
5

h

4

d

3

o

p
l
i

6
5
4

q
m
j

6
5
4

q
m
j

6
5
4

g
3

e

3

f

3

f

3

q
m

He2*

j

f

20.00

3

c

processes. The observation of He2* states in
the 19.3–20.7 eV region is consistent with thefact that processes (7a) and (8a) areresponsible for the formation of He2*. Based on
above facts, it was concluded that He2* statesarise from neutralization reactions (7a) and(8a). The observed excited states in theHe2+/C6F5Cl- reaction were the same as thosein the He2+/C6F6- reaction except for theabsence of the D state. This indicates that thedifference in electron affinity between C6F6
and C6F5Cl does not affect the observed energy
levels of He2*.

19.00

2
18.00

3.2 Relative formation rate constants of He2*
in the He2+/C6F6- and He2+/C6F5Cl- reactionsb

2 aFig. 3. Energy-level diagram of triplet statesof He2*. Observed emitting levels in theHe2+/C6F6- and He2+/C6F5Cl- reactions areshown in red.
He2+
np 3Σg+ ns 3Σu+ np 3Πg nd 3Σu+ nd 3Πu

nd 3Δu22.22
22.00
He2+/C6F6He2+/C6F5Cl-

10
6
5

21.00

Energy / eV

4

n
k’

6
5
4

k

10
6
5

h

4

d

3

o

p
l
i

6
5
4

q
m
j

6
5
4

q
m
j

6
5
4

g
3

e

3

f

3

f

3

q
m

He2*

j

f

20.00

3

c

Radiative lifetimes of the f, e, and d states
have been measured as 19±5 ns, 25±5 ns, and,57±10 ns, respectively.24) Although theradiative lifetimes of the c, F, E, D, and C statesobserved in this study are unknown, they may
be the same order as the above states.
Radiative lifetimes of excited He2* molecules
are short enough to emit radiation within theobservation region. It is therefore reasonable toassume that the relative emission intensities
are proportional to their formation rate
constants.
In general, the overall rate constant of the
production of an upper state of He2*, 𝑘 𝑢 , isgiven by summation of direct formation rate
constant, 𝑘 𝑢 , and the contribution ofradiative
cascadefrom
upperstates,𝑘 𝑢: cascade ,

19.00

𝑘 𝑢
2
18.00

𝑘 𝑢

𝑘 𝑢: cascade .

(9)

b

2 a

Fig. 4. Energy-level diagram of singlet statesof He2*. Observed emitting levels in theHe2+/C6F6- and He2+/C6F5Cl- reactions areshown in red.
In processes (7a) and (8a), parent C6F5X
molecules are formed as products, whereas
C6F5 + X fragments are generated in processes(7b) and (8b). Electron affinities of C6F6 andC6F5Cl are 0.53 eV and 0.75 eV,22) anddissociation energies of D(C6F5-F) and D((C6F5Cl) are 5.03 eV and 3.97 eV, respectively.23) By
using these thermochemical data, -Ho values
for the formation of He2(c~f,C~F) in processes(7a), (7b), (8a), and (8b) were estimated. Since
the reactions (7b) and (8b) are endoergic, they
can be excluded from possible reaction

Radiative cascade does not contributes to theformation of all excited levels (Table 1).
Therefore, the relation 𝑘 𝑢
𝑘 𝑢 holds inthe formation of 12 or 11 excited states in theHe2+/C6F6andHe2+/C6F5Clreactions,
respectively.
Table 2 shows excitation energies of observed
He2* states 𝑇
and 𝑘 𝑢 values in theHe2+/C6F6- and He2+/C6F5Cl- reactions. The
dependence of 𝑘 𝑢 on the energy of He2*
state in the He2+/C6F6- and He2+/C6F5Clreactions is shown in Figs. 5 and 6, respectively.
value rapidly decreases withThe 𝑘 𝑢increasing the excitation energy of He2*. A
similar tendency was observed for He* in the
He+/C6F5X-(X=F, Cl) neutralization reaction,19)
indicating that ion-ion neutralization dynamics
is similar between atomic He+ and molecular
He2+ ions. Major triplet and singlet He2* states令和 5 年度

九州大学大学院総合理工学報告

He2+/C6F6-

He2+/C6F5Cl-

(eV)

𝑘 𝑢

𝑅 (Å)

𝑘 𝑢

𝑅 (Å)

f3Δu(3dδ)

20.7

1.1

14.9

4.0

14.9

f3Πu(3dπ)

20.7

1.8

14.0

2.8

14.2

3

+

f Σu (3dσ)

20.6

1.7

13.7

2.8

13.9

e3Πg(3pπ)

20.6

1.0

13.6

1.7

14.2

3

+

d Σu (3sσ)

20.5

5.4

12.1

6.7

12.9

3

+

19.3

100

6.1

100

6.9

F Δu(3dδ)

20.7

0.3

19.2

0.6

19.2

F1Πu(3dπ)

20.7

0.2

17.9

0.6

18.2

F1Σu+(3dσ)

20.7

0.3

17.3

0.6

17.6

E1Πg(3pπ)

20.7

0.1

17.2

0.4

18.1

D1Σu+(3sσ)

20.6

0.2

14.8

0.0

16.0

C1Σg+(3pσ)

19.6

30.7

6.7

25.5

7.8

c Σg (3pσ)
1were the lowest observed c3g+ and C1g+ states,
which occupied 70% and 21% of ∑ 𝑘 𝑢 , in theHe2+/C6F6- reaction, and 69% and 18% in theHe2+/C6F5Cl- reaction, respectively. The 𝑘 𝑢values of higher d, e, f, D, E, and F states in theHe2+/C6F6- and He2+/C6F5Cl- reactions are
smaller than 6.7%, indicating that theformation of these high energy states areunfavorable. The ∑ 𝑘 𝑢 value of highenergy d, e, f, E, and F states in theHe2+/C6F5Cl- reaction (20.2%) is larger than d,e, f, D, E, and F states (12.1%) in the He2+/C6F6reaction by a factor of 67%. This suggests thatthe formation of high energy d, e, f, E, and F
states is more favorable in the He2+/C6F5Clreaction. The total formation ratio of thetriplet/singlet states was about 3.5 and 4.3 inthe He2+/C6F6- and He2+/C6F5Cl- reactions,
respectively, which were slightly larger than astatistical ratio of 3.0.
3.3
Vibrational distribution of He2* androtational distributions of He2(f, e, d, c, C:𝒗𝟎 ) in the He2+/C6F6- and He2+/C6F5Clreactions
Only (0,0) bands were observed for all theHe2* systems, so that no vibrational excitation
was observed. Rotational populations of He2*

Relative formation rate constant (k0(u)) / %

𝐸

State

第2号

15

100

80

Triplet state
Singlet state

60

40

20

0
19.2

19.4

19.6

19.8

20.0

20.2

20.4

20.6

20.8

Energy of He2* / eV

Fig. 5. The dependence of 𝑘 𝑢 on theenergy of He2* state in the He2+/C6F6reaction.

100
Relative formation rate constant (k0(u)) / %Table 2. Observed triplet and singlet excitedstates, energies (𝐸), relative formation rate
constants (𝑘 𝑢 ), and equilibrium internuclear
distance (𝑟 ) of He2* excimer.

第 45 巻

80

Triplet state
Singlet state

60

40

20

0
19.2

19.4

19.6

19.8

20.0

20.2

20.4

20.6

20.8

Energy of He2* / eV

Fig. 6. The dependence of 𝑘 𝑢 on theenergy of He2* state in the He2+/C6F5Clreaction.
were estimated for five band systems, for whichrotational structures are well resolved. Figures
7a–7d and 8a–8d show expanded emission
spectra of the f 3u+-b3Πg, e 3g-a3u+, d3u+-b3Πg,
and c 3g+-a3u+ + C 1g+-A1u+ systems of He2* inthe He2+/C6F6- and He2+/C6F5Cl- reactions,
respectively. In 4He, the nuclear spin is zeroand due to the symmetry rules for homonuclear
molecules all even or odd numbered rotational
levels are missing.13-15,25) Therefore, only odd oreven levels of P, Q, or R branches are observedin the above five transitions.
00Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

16Q(c) d3Σu+-b3Πg (0,0)(c) d3Σu+-b3Πg (0,0)

Q

P4
P2

P6
P8

R4
R8R6 R
2

R10
625

630

635

R
R8R6 4
R2
R

P10
P12
P14P16
P18P20
640

645

650

655

P2 P4

P5 P7

R5
R3

P9

625

P10P12 P P18
P14 16 P

630

635

640

R9 R7

C1Σg+-A1Σu+ (0,0)

R5
R3

900

910

P3

P7

R7

P1

920

P17

P13

930

940

950

P19

960

970

650

655

C1Σg+-A1Σu+ (0,0)

P7 P9
P11

P3

P15
5

P5

R5
R3

P11

P3

R1 P

645

20

(d) c3Σg+-a3Σu+ (0,0)

P13
R7

P8

10

(d) c3Σg+-a3Σu+ (0,0)
R9 R7

P6

980

Wavelength / nm

Fig. 7. Rotational structures of the (0,0)
bands of He2(f-b,e-a,d-b,c-a,C-A) systems
resulting from the He2+/C6F6- reaction in the
He FA at a He gas pressure of 1.8 Torr.

900

P13

R1
P1

R5
R3
R1

P3

910

920

P7
P13

P5

930

940

P15

P15

950

P17

960

970

980

Wavelength / nm

Fig. 8. Rotational structures of the (0,0)
bands of He2(f-b,e-a,d-b,c-a,C-A) systems
resulting from the He2+/C6F5Cl- reaction in
the He FA at a He gas pressure of 1.8 Torr.

九州大学大学院総合理工学報告

Rotational distributions of the f, e, d, c, andC states in the ground vibrational levels were
determined from relative intensities of Q or P
branch. Rotational levels of He2* which belong
to Hund’s case (b) are represented by thequantum number 𝑁′. The band intensity(photons s-1) of a transition from a 𝑣 𝑁 levelto a 𝑣′′ 𝑁′′ level is expressed as
𝐼 ′ ′ ′′ ′′ ∝ 𝑁 ′ ′ 𝑅𝑒

第 45 巻

第2号

17

2.0

(a) f3Σu+(v’=0)

1.0ln(IN'N"/SN'N"N'N"3)

令和 5 年度

0.0
-1.0
-2.0
-3.0

𝑟̄ ′ ′′ 𝑞 ′ ′′ 𝜈 ′ ′ ′′ ′′ 𝑆 ′ ′′ 𝑔 ′ , (10)

0

50

100

150

200

250

300

350

N'(N'+1)

2.5(b) e3Πg(v’=0)

2.0
1.5ln(IN'N"/SN'N"N'N"3)

where 𝑁 ′ ′ is the rotational population in agiven vibrational level, 𝑅𝑒 𝑟̄ ′ ′′ the electronictransition moment, 𝑞 ′ ′′ the Franck-Condon
factor (FCF), 𝜈 ′ ′ ′′ ′′ the transition frequency,
𝑆 ′ ′′ the rotational line strength, and 𝑔 ′2𝑁1.25) When a fixed 𝑣 , 𝑣" band, 𝑅𝑒 𝑟̄ ′ ′′and 𝑞 ′ ′′ values are constant. Assuming a
Boltzmann distribution, Boltzmann rotationaltemperature is obtained from the following
relation:

1.0
0.5
0.0
-0.5
-1.0
0

50

100

, (11)

where 𝑘 and 𝑇
are the Boltzmann constantand the Boltzmann rotational temperature,
respectively.25) In Figs. 9a–9e and 10a–10e,
⁄𝜈
ln 𝐼
𝑆
values are plottedagainst 𝑁′ 𝑁
1 for the 𝑣
0 levels of thef, e, d, c, and C states in the He2+/C6F6- andHe2+/C6F5Cl- reactions, respectively. Results
show that plots can be fitted by either single or
double Boltzmann temperatures. From theslopes, ℎ𝑐𝐵 /𝑘𝑇 , the effective rotationaltemperatures, 𝑇 , are estimated for eachstate. Results obtained are shown in Table 4.
For comparison corresponding data for theHe2+/2e- CRR reaction7) are also shown. The
rotational temperature of the f state in theHe2+/C6F5Cl- reaction is lower than that in theHe2+/C6F6- reaction. On the other hand,rotational temperatures of the e, d, c, and C
states in the He2+/C6F5Cl- reaction are higher
than or about the same as those in theHe2+/C6F6- reaction. Rotational temperatures ofthe f, e, d, and c states in the He2+/C6F5X- (X=F,
Cl) reactions are higher than those in theHe2+/2e- CRR reaction.7)
From
theobserved
rovibrational
distributions of He2(f, e, d, c, C) in the He2+/C6F6and He2+/C6F5Cl- reactions, we estimated theaverage vibrational and rotational energies ofeach state, denoted as <Ev> and <Er>, and theaverage yields of total available energy into
these degrees of freedom, denoted as <fv> and<fr>, respectively. Here, the total available
00000

250

300

(c) d3Σu+(v’=0)

1.0ln(IN'N"/SN'N"N'N"3)

1 /𝑘𝑇

0.0
-1.0
-2.0
-3.0
-4.0
-5.0
0

100

200

300

400

500

N'(N'+1)
5.0(d) c3Σg+(v’=0)

4.0ln(IN'N"/SN'N"N'N"3)ℎ𝑐𝐵 𝑁′ 𝑁′

3.0
2.0
1.0
0.0
-1.0
-2.0
0

100

200

300

400

500

N'(N'+1)
2.0(e) C1Σg+(v’=0)

1.5
1.0ln(IN'N"/SN'N"N'N"3)∝ 𝑐𝑜𝑛𝑠𝑡

200

3.0
2.0

ln

150
N'(N'+1)

0.5
0.0
-0.5
-1.0
-1.5
-2.0
0

50

100

150

200

250

300

N'(N'+1)

Fig. 9. Estimation of effective rotationaltemperaturesfromtheslopes⁄𝜈of ln 𝐼𝑆
against 𝑁′ 𝑁
1for the He2(f:𝑣 =0), He2(e:𝑣 =0), He2(d:𝑣 =0),He2(c:𝑣 =0), and He2(C:𝑣 =0) states in theHe2+/C6F6- reaction.

18

Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

3.0(a) f3Σu+(v’=0)ln(IN'N"/SN'N"N'N"3)

2.0
1.0
0.0
-1.0
-2.0
0

50

100

150

200

N'(N'+1)

2.5(b) e3Πg(v’=0)

2.0ln(IN'N"/SN'N"N'N"3)

1.5
1.0
0.5
0.0
-0.5
-1.0
0

50

100

150

200

250

300

N'(N'+1)ln(IN'N"/SN'N"N'N"3)

1.0(c) d3Σu+(v’=0)

0.0
-1.0
-2.0
-3.0
0

50

100

150

200

250

N'(N'+1)
4.0(d) c3Σg+(v’=0)ln(IN'N"/SN'N"N'N"3)

3.0
2.0
1.0

3.3 Reaction dynamics of the He2+/C6F6- andHe2+/C6F5Cl- neutralization reactions

0.0
-1.0
-2.0
0

50

100

150

200

250

300

N'(N'+1)
0.5(e) C1Σg+(v’=0)0.0ln(IN'N"/SN'N"N'N"3)energies for the formation of each He2* state
were
calculatedfromtherelation:𝐸= -H0o ＋ 4RT at 300 K. From the <Ev>,<Er>, <fv>, and <fr> values, the sum of therelative translational energy and internalenergy of C6F5X, <Et> + <𝐸 C F X >, and its
fraction of the total energy, <𝑓 > + <𝑓 C F X >,were determined. Results obtained aresummarized in Table 5. The <fr> values in theHe2+/C6F6- and He2+/C6F5Cl- reactions are
2.8–9.6% and 3.1–9.6%, respectively. The <𝑓 >values are zero for both reactions. Although the
𝐸 values for the low energy c and C states arelarger than those of higher f, e, and d states,
their <Er> values are similar to those of theupper three states. Therefore, the <𝑓 > valuesof the c and C states are smaller than those of
upper three states. Thus, <𝑓 > + <𝑓 C F X >values of the c and C states are slightly larger
than those of upper states. On the basis of<𝑓 > + <𝑓 C F X > values, most of the total
available energies (90.4–97.2%) are deposited
into relative translational energies ofHe2* + C6F5X (X=F, Cl) products and internalenergies of C6F5X. Among three internal energy(electronic,
vibrational,
androtationalenergies), electronic energy can be excluded
from an acceptor mode of excess energies,
because the energies of C6F5X* (S1) states(>4 eV)22,26) are higher than excess energies
released in processes (7a) and (8a). Therefore,
C6F5X accepts excess energies as theirvibrational and rotational energies in the
ground electronic states.

Since the formation of He2* takes place via
strongly attractive ion–pair potentials, a long
lived [He2–C6F5X]* complex can be postulated:
He2+ + C6F5X→ [He2–C6F5X]* → He2* + C6F5X.

-0.5
-1.0

(8)

According to a simple statistical theory,27–29)
the vibrational and rotational prior populationsof a given He2* level are given by the relations:

-1.5
-2.0
-2.5
0

50

100

150

200

250

N'(N'+1)

Fig. 10. Estimation of effective rotationaltemperaturesfromtheslopes⁄𝜈of ln 𝐼𝑆
against 𝑁′ 𝑁
1for the He2(f:𝑣 =0), He2(e:𝑣 =0), He2(d:𝑣 =0),He2(c:𝑣 =0), and He2(C:𝑣 =0) states in theHe2+/C6F5Cl- reaction.

𝑃 𝑣

∝ 𝐸

𝐸

𝑃 𝑁

∝ 2𝑁

1 𝐸

(9)

,
𝐸

.

(10)

The prior vibrational distributions of 𝑣 =0–3
levels of He2(f, e, d, c, C) states were calculated
as follow:

令和 5 年度

九州大学大学院総合理工学報告第 45 巻第2号

19

Table 4. Rotational temperatures of He2(f, e, d, c, C) produced from the He2+/C6F6- andHe2+/C6F5Cl- reactions and He2+/2e- CRR reaction.

Emitting species

He2+/C6F6𝑇 /K

He2+/C6F5Cl𝑇 /K

He2+/2e-a)
𝑇 /K

He2(f 3u+: 𝑣′=0)1020±201170±30530±30620±30350±502150
800±201530±110470±40580±20 (𝑁′=5–13)
310±70 (𝑁′=1–5)
990±190 (𝑁′=10–16)500±20 (𝑁′=2–10)830±20 (𝑁′=7–17)440±50 (𝑁′=1–7)

He2(e 3Πg: 𝑣′=0)770±60He2(d 3u+: 𝑣′=0)
He2(c 3Σg+: 𝑣′=0)1080±1101090±180720±140 (𝑁′=0–12)

He2(C 1Σg+: 𝑣′=0)940±301110±120a) Ref. 7.
Table 5. Total available energy, average vibrational and rotational energies deposited intoHe2(f, e, d, c, C), and average fractions of vibrational and rotational energies of He2(f, e, d, c, C)
and relative translational energies + internal energies of C6F5X deposited in the He2+/C6F5X(X=F, Cl) reactions.

Reaction-He2+/C6F6

He2+/C6F5Cl

𝐸

<𝐸 >

<𝐸 >

<𝑓 >

<𝑓 >

<𝑓 > + <𝑓 >

(eV)

(eV)

(eV)

(%)

(%)

(%)

(%)

f 3u+

1.15

0.11

0.0

9.6

0.0

9.6

90.4

e 3Πg

1.16

0.07

0.0

6.0

0.0

6.0

94.0

d 3u+

1.30

0.07

0.0

5.4

0.0

5.4

94.6

c 3g+

2.48

0.07

0.0

2.8

0.0

2.8

97.2

C 1g+

2.18

0.08

0.0

3.7

0.0

3.7

96.3

f 3u+

0.93

0.04

0.0

4.3

0.0

4.3

95.7

e 3Πg

0.94

0.09

0.0

9.6

0.0

9.6

90.4

d u

+

1.08

0.06

0.0

5.6

0.0

5.6

94.4

c 3g+

2.26

0.07

0.0

3.1

0.0

3.1

96.9

C g

1.96

0.08

0.0

4.1

0.0

4.1

95.9

State

-

3

1

+

He2+/C6F6He2(f: 𝑣 =0–2) = 1.0 : 2.5(-03) : 2.6(-06),
He2(e: 𝑣 =0–2) = 1.0 : 1.6(-03) : 8.3(-07),
He2(d: 𝑣 =0–2) = 1.0 : 2.0(-03) : 2.9(-06),
He2(c: 𝑣 =0–2) = 1.0 : 7.9(-02) : 6.2(-03),
He2(C: 𝑣 =0–2) = 1.0 : 4.5(-02) : 1.8(-03),
He2+/C6F5ClHe2(f: 𝑣 =0–2) = 1.0 : 5.1(-04) : 5.1(-08),
He2(e: 𝑣 =0–2) = 1.0 : 3.0(-04) : 1.1(-08),
He2(d: 𝑣 =0–2) = 1.0 : 9.4(-04) : 2.1(-07),
He2(c: 𝑣 =0–2) = 1.0 : 6.1(-02) : 3.6(-03),
He2(C: 𝑣 =0–2) = 1.0 : 3.1(-02) : 8.2(-04),<𝑓 > + <𝑓

C F X >

where (n) is power of 10 multiplying the entry.
The prior vibrational distributions predict low
vibrational excitation, which is consistent withthe experimental observations.
Figures 11a–11e and 12a–12e show observed
and prior rotational distributions of the f, e, d, c,and C states in the He2+/C6F6- and He2+/C6F5Clreactions, respectively. Observed rotational
distributions of f 3u+(𝑣 =0) and e3g 𝑣 =0) in theHe2+/C6F6- reaction and e3g 𝑣 =0) andC1g+( 𝑣 =0) in the He2+/C6F5Cl- reaction are
higher than prior ones. On the other hand,Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

Rotational distribution of He2(f:v'=0)

0.6

￥
0.4
0.2

0

2

4

6

8

10

12

14

Obs.

Prior

0.4
0.2

4

8

12

0

0.8
0.6

Obs.

Prior

0.2

8

12

Rotational distribution of He2(c:v'=0)(d) c3Σg+ :v’=0)
1.0
0.8

Obs.
0.6

Prior
0.4
0.2

0.6

10

15

0.2

0.8

Obs.

0.4
0.2

5

10

12

16

(c) d3Σu+ :v’=0)

0.8

Obs.

0.6

Prior

0.4
0.2

0

2

4

6

8

10

12

14

N'

(d) c3Σg+ :v’=0)

1.0
0.8

Prior

0.6

Obs.

0.4
0.2

0

5

10

15

20

15

20

N'

Fig. 11. Observed and statistical priorrotational distributions of the He2(f: 𝑣 =0),He2(e: 𝑣 =0), He2(d: 𝑣 =0), He2(c: 𝑣 =0), andHe2(C:𝑣 =0) states in the He2+/C6F6- reaction.

(e) C1Σg+ :v’=0)

Prior

1.0
0.8

Obs.

0.6
0.4
0.2
0.0
-0.2

0

8

N'

Rotational distribution of He2(C:v'=0)

1.0

Prior

4

1.2

(e) C1Σg+ :v’=0)

0.6

0

1.0

20

N'

1.2

14

0.4

0.0

5

12

Prior

1.2

1.2

0

10

Obs.

0.8

16

N'

0.0

8

(b) e3Πg :v’=0)

0.0

4

6

1.2

1.0

0

4

N'

N'

0.4

2

1.0

16

(c) d3Σu+ :v’=0)

0.0

Rotational distribution of He2(c:v'=0)

0.2

0.0

0

1.2

Rotational distribution of He2(C:v'=0)

Obs.

0.4

1.2

0.6

0.0

0.6

N'

(b) e3Πg :v’=0)
0.8

Prior

0.8

0.0

16

1.0

0.0

(a) f3Σu+ :v’=0)
1.0

N'

1.2
Rotational disribution of He2(e:v'=0)

Obs.

Prior

0.8

0.0

Rotational distribution of He2(d:v'=0)

1.2(a) f3Σu+ :v’=0)

1.0

Rotational distribution of He2(e:v'=0)

Rotational distribution of He2(f:v'=0)

1.2
observed000

Rotational distribution of He2(d:v'=0)

20

0

5

10

15

N'

Fig. 12. Observed and statistical priorrotational distributions of the He2(f: 𝑣 =0),He2(e: 𝑣 =0), He2(d: 𝑣 =0), He2(c: 𝑣 =0), andHe2(C: 𝑣 =0) states in the He2+/C6F5Clreaction.

令和 5 年度

九州大学大学院総合理工学報告

observed rotational distributions are in
reasonable agreement with the prior ones ford3u+(𝑣 =0), c3g+(𝑣 =0), and C1g+(𝑣 =0) in theHe2+/C6F6- reaction and f3u+(𝑣 =0), d3u+(𝑣 =0),and c3g+( 𝑣 =0) in the He2+/C6F5Cl- reaction.
Therefore,
long-lived[He2–C6F5X]*
intermediates take part in the formation ofmany He2* states in the He2+/C6F6- andHe2+/C6F5Cl- reactions.
The ion–ion neutralization reactions studied
here proceed through strongly attractive
V[He2+,C6F5X-] ion-pair potentials. He2* arises
from diversion of trajectories from the entrance
V[He2+,C6F5X-]
potential
to
the
exit
V[He2*,C6F5X] potentials due to a strong
coupling between the two potentials. Thus theelectronic state distribution of He2* reflects thedifferent crossing point of the strongly
attractive ion-pair entrance potentials andrather flat covalent exit potentials at thecrossing points and the coupling between eachpair of states. The He2+–C6F5X- separations at
crossing points Rc are calculated from therelation:

Rc = e2/(IP–EA) = 14.40/(IP–EA),(11)

where IP is the ionization potential of He2* andEA is the electron affinity of C6F5X. The Rc
values for the formation of each He2* state arecalculated for each reaction. The results are
given in Table 2.
The ion–ion neutralization reactions proceed
through an approach of the He2+ and C6F5X- ionpair under their mutual Coulombic field
followed by an electron transfer from C6F5X- to
He2+.
Since
the
Born–Oppenheimer
approximation holds during a fast electrontransfer, the relative motion of an ion pair isunchanged after the neutralization. Therefore,a large kinetic energy resulting from the strong
mutual Coulombic force is conserved at the
instant of electron transfer. The electrontransfer
occursat
relatively
largeintermolecular separations of 6.1–19.2 Å,
where interactions between neutral He2* andC6F5X molecules are small. Thus, a large
amount of the kinetic energy will remain in theneutral products.
Under
the
Born–Oppenheimer
approximation, the internuclear separations of
He2+ ions are unchanged just after theneutralization. Since the equilibrium nuclear
separation of He2+ (X2u+:1.081 Å) is close to
those of He2*(1.068–1.097 Å for f, e, d, c, F, E, D,
and C states),12) the formation of He2* with the

第 45 巻第2号

21

largest FCFs for the He2+(X: 𝑣
0) → He2*(f,e, d, c, and C: : 𝑣
0 ) neutralization will bemost favorable, as evaluated in the previous
paper.7) This prediction is consistent with thepreferential formation of He2*(f, e, d, c, and C) inthe 𝑣
0 levels."
Just after the neutralization the geometriesof C6F5X- (X= F, Cl) anions are also reserved.
Structural information on the geometries of
C6F5X has been obtained from theoretical
calculations by Miller et al.10,11) using the
GAUSSIAN-03 program.30) According to theircalculations, aromatic neutral C6F6 molecule isobviously completely planar with D6h symmetry.
On the other hand, the calculated C6F6- anion
structure is non-planar with C2v symmetry,
where two opposite F atoms protrude above theaverage carbon plane by about 23◦. The C atoms
to which these two F atoms are bound lie veryslightly below the plane in which the remaining
four C atoms lie, with a dihedral angle of −0.5◦.
The remaining four F atoms lie in a plane of
their own, slightly below that of the four planar
C atoms. A symmetry change is also observed
between C6F5Cl and its anion from C2v to Cs,
resulting in a change in the rotational
symmetry number from 2 to 1. C6F5Cl is aplanar molecule, whereas C6F5Cl- is a nonplanar anion where Cl atom protrudes above
the average carbon plane by about 21.3o(B3LYP/6-311+G(3df) optimizations) or 37.1o(G3(MP2) calculation).
Since the equilibrium geometries of C6F5Xare significantly different from those of C6F5X,
some energy will be released as the vibrationalenergy of C6F5X after the neutralization
reaction. Consequently, most of excess energies
will be transformed into the vibrational energyof C6F5X and the relative kinetic energy of theneutralproducts
intheHe2+/C6F5Xneutralization reactions.

4.

Summary and Conclusion

The ion-ion neutralization reactions of He2+
with C6F6- and C6F5Cl- were studied byobserving He2* excimer emissions in the He FA.
Six triplet and six or five singlet transitions ofHe2* with excitation energies of 19.3–20.7 eV
were identified. Major triplet and singlet He2*
states were the lowest observed c3g+ and C1g+states, which occupied 70% and 21% of∑ 𝑘 𝑢 , in the He2+/C6F6- reaction, and 69%
and 18% in the He2+/C6F5Cl- reactions,
respectively. Thus the 𝑘 (c3g+) + 𝑘 (C1g+)values occupy 91% and 87% of ∑ 𝑘 𝑢 in theHe2+/C6F6andHe2+/C6F5Clreactions,22

Formation of He2* from neutralization reactions of He2+ with C6F6- and C6F5Cl- in the He flowing afterglow

respectively. The total formation ratio of thetriplet/singlet states was about 3.5 and 4.3 inthe He2+/C6F6- and He2+/C6F5Cl- reactions,which were slightly larger than a statisticalratio of 3.0. No vibrational excitation wasobserved for all observed He2* states because oflarge FCFs for He2+(X: 𝑣
0) → He2*(f, e, d, c,and C : 𝑣
0 ) neutralization. The rotational
distributions of f3u+ 𝑣 = 0), e3g 𝑣 = 0),d3u+(𝑣 =0), c3g+(𝑣 =0), and C1g+(𝑣 =0) states
were expressed by either single or double
Boltzmannrotationaltemperaturesof
310–1530 K. Rovibrational distributions ofthese excited states indicated that most ofexcess energies are not released as
rovibrational energies of He2* but they
(90.4–97.2%) are deposited into rovibrationalenergies of C6F5X (X=F, Cl) and relativetranslational energies of products. Equilibrium
molecular structures of C6F5X are planer,whereas those of C6F5X- anions are non-planer.
Therefore, vibrational energies of C6F5X are themost important internal energy of C6F5X. The
observedvibrationalandrotational
distributions were compared with statisticalones assuming long lived [He2–C6F5X]*
intermediates. In many cases, a reasonableagreement between observed and priorvibrational and rotational distributions were
found. Therefore it was concluded that long
lived [He2–C6F5X]* intermediates take part inmost of the neutralization reactions.
Acknowledgments
The authors acknowledge Prof. Kenji
Furuya of Kyushu University for his carefulreading of our manuscript. This work has
been supported by the Mitsubishi
foundation (1996).
References
1)
2)
3)

D. R. Bates, A. E. Kingston, and R. W. P. McWhirter,
Proc. R. Soc., Ser. A, 267, 297 (1962).
M. R. Flannery, Adv. At, Mol. Opt. Phys., 32, 117(1994).
M. R. Flannery, in “Handbook of Atomic, Molecular,
and Optical Physics ”, 800, Edited by G. Drake,
Springer, New York (2006).

4)
5)

6)
7)
8)

N. G. Adams, V. Poterya, and L. M. Babcock, Mass
Spectrom. Rev., 25, 798 (2006).
M. Tsuji, in “Advances in Gas-Phase Ion Chemistry ”
Vol. 4., Edited by N. G. Adams and L. M. Babcock,Elsevier, 137 (2001).
Z. Liu, M. Roy, N. J. DeYonker, and R.
Gopalakrishnan, J. Chem. Phys., 159, 114111 (2023).
M. Tsuji and E. Oda-Sako, Eng. Sci. Rep. Kyushu
Univ., 45, 1 (2024).

M. Tsuji, E. Oda, M. Tanaka, M. Nakamura, and Y.
Nishimura, Chem. Lett., 26, 465 (1997).

9)

Y. Ikezoe, S. Matsuoka, M. Takebe, and A. Viggiano,“Gas Phase Ion-Molecule Reaction Rate Constants
through 1986 ”, Maruzen, Tokyo (1987).
10) T. M. Miller, J. M. Van Doren, A. A. Viggiano, Int. J.
Mass Spectrom., 233, 67 (2004).
11) T. M. Miller and A. A. Viggiano, Phys. Rev. A, 71,
012702 (2005).
12) K. P. Huber and G. Herzberg, “Molecular Spectra andMolecular Structure, IV. Constants of Diatomic
Molecules ”, Van Nostrand Reinhold, New York (1979).
13) M. L. Ginter, J. Chem. Phys., 42, 561 (1965).
14) M. L. Ginter, J. Mol. Spectrosc., 18, 321 (1965).
15) C. M. Brown and M. L. Ginter, J. Mol. Spectrosc., 40,
302 (1971).
16) M. Allan and J.P. Maier, Chem. Phys. Lett., 34, 442(1975).
17) J. P. Maier, O. Marthaler, M. Mohraz, and R. H. Shiley,Chem. Phys., 47 295 (1980).
18) Atomic Spectra Database, NIST Standard Reference
Database, 78, Ver. 5.9. Oct. (2021).
19) M. Tsuji, M. Nakamura, Y. Nishimura, E. Oda, H.
Oota, and M. Hisano, J. Chem. Phys., 110, 2903 (1999).
20) M. Tsuji, M. Nakamura, and Y. Nishimura, Chem.
Lett., 26, 259 (1997).
21) S. Yamaguchi, M. Tsuji, and Y. Nishimura, J. Chem.
Phys., 88, 3111 (1988).
22) NIST Chemistry WebBook, NIST Standard Reference
Database,
Number69(2023)
https://doi.org/10.18434/T4D303.
23) Y.-R. Luo, “Bond Dissociation Energies ”, Number 69
in CRC Handbook of Chemistry and Physics, 81th Ed.,
CRC Press, Boca Raton (2000).
24) S. Neeser, R. Tietz, M. Schulz, and H. Langhoff, Z.
Phys. D., 31, 61 (1994).
25) G. Herzberg, “Molecular Spectra and Molecular
Structure: I. Spectra of Diatomic Molecules ”, 2nd ed.
Van Nostrand Reinhold, New York (1950).
26) M. Z. Zgierski, T. Fujiwara, and E. C. Lim, J. Chem.
Phys., 122, 144312 (2005).
27) R. D. Levine, Annu. Rev. Phys. Chem., 29, 59 (1978).
28) R. D. Levine and J. L. Kinsey, in “Atom–Molecule
Collision Theory ”, Edited by R. B. Bernstein, Plenum,
New York, (1979).
29) E. Zamir and R. D. Levine, Chem. Phys., 52, 253(1980).
30) M. J. Frisch et al., “GAUSSIAN 03 ”, Revision B.02,
Gaussian, Inc., Pittsburgh, (2003).