九州大学大学院総合理工学府報告第 44 巻 第 1 号 1-11 頁 令和 4 年 9 月

Engineering Sciences Reports, Kyushu University
Vol. 44, No. 1, pp. 1-11, SEP, 2022

A Reinvestigation of Excitation Source of theCS2+(𝐀2u– 𝐗2g) Emission in the Ar Afterglow:
Both Ar+ and Ar2+ Ions Can Be Excitation Sources
Giving Significantly Different Spectral Features
Masaharu TSUJI*1,2† Minoru ENDOH*3 Tsuyoshi FUNATSU*3 Masafumi
NAKAMURA*3 Keiko UTO*1 Jun-Ichiro HAYASHI*1 and Takeshi TSUJI*4
E-mail of corresponding author: tsuji@cm.kyushu-u.ac.jp†(Received March 18, 2022, accepted April 18, 2022)
In 1984, we have reported that CS2+(A2u– X2g) visible emission in an Ar flowing afterglow arises
from the Ar2+ + CS2 charge-transfer (CT) reaction at thermal energy.1) In 1986, Upshulte et al.2) claimed
that Ar+ not Ar2+ is the responsible excitation source of the CS2+(A– X) emission in their flow-tube study.
Although more than 36 years have passed since these two-original flowing-afterglow studies, nodefinite conclusion has been obtained on the exact excitation source of the CS2+(A– X) emission in the
Ar afterglow. To confirm whether Ar2+ and/or Ar+ really contributes to the CS2+( A– X ) emission,
additional experiments were carried out in this flowing-afterglow study. Results show that theconclusion of Upshulte et al.2) is wrong and that both Ar+ and Ar2+ can be excitation sources ofCS2+(A– X) emissions, though spectral features are quite different between the two reactions. The Ar2+
+ CS2 reaction gives discrete CS2+(A– X) emission bands from low vibrational levels, whereas the Ar+ +CS2 reaction dominantly provides continuous CS2+(A– X) emission from high rovibrational levels. The
higher vibrational excitation of the CS2+(A) state than that expected from vertical Franck-Condon (FC)like ionization was confirmed by the re-examination of reported ion cyclotron resonance (ICR) data.
Key words: CS2+( 𝐴– 𝑋 ) emission, Flowing afterglow, Ar+ ion, Ar2+ ion, Charge-transfer reaction,
Franck-Condon factor, Energy-resonant requirement, Kinetic energy ICR

1.

Introduction

In 1984, we have reported an optical
spectroscopic study on the Ar afterglow
reactionofCS2.1)
A
strongvisible+22
CS2 (A u– X g) emission from low vibrational
levels were observed. Possible excitation
sources were Ar+, Ar2+, and Ar+*(metastableion) because this emission disappeared bytrapping ionic species using ion-collector grids
placed between the discharge section and thereaction zone. To determine the responsible
excitation source, the dependence of emission
intensity of CS2+(A– X) on the Ar pressure wascompared with that of OCS+( A– X ) emission
from the Ar+ + OCS reaction3) and CH(A–X)*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*4 Department of Materials Science, Shimane
University

emission from the Ar+* + CH3CN reaction.4)
The CS2+(A– X) emission increased its intensitywith increasing the Ar pressure from 0.3 to 4
Torr (1 Torr = 133.32 Pa), although the
OCS+(A– X) and CH(A–X) emissions gave peaks
at 0.5 and 0.4 Torr and rapidly decreased theirintensities with increasing the Ar pressure to 1
Torr. Based upon these facts, we concluded thatthe excitation source of CS2+(A– X) was not Ar+
or Ar+* but Ar2+.
After our flowing-afterglow study, two followup studies have been carried out by famousgroups in the fields of gas phase ion chemistry
in the world: Castleman’s group in Penn State2)and Bowers’s group in UC Santa Barbara.5)
Upshulte et al.2) carried out a flowing-afterglow
optical spectroscopic study on the CS2+( A– X )emission in 1986. Based on the disappearanceof this emission by ion trapping and variationsof emission intensity of the CS2+(A– X) emission
as a function of Ar pressure, flow velocity ofdischarge flow, or the glow discharge voltage,
they concluded that the excitation source was2

Re-investigation of excitation source of the CS2+(A2u-X2g) emission in the Ar afterglow

the thermal-energy Ar+ + CS2 CT reaction andnot the Ar2+ + CS2 CT reaction, we suggested.1)
Although they did not notice, there was asignificant difference in spectral features ofCS2+( A– X ) emission between their and ourspectra. Their CS2+(A– X ) emission was muchbroader than our spectrum due to an
appearance of strong continuous backgroundband.
After above two works, Rincon et al.5)
investigated the Ar+ + CS2 CT reaction atthermal and near thermal energies in 1988 byusing both tandem ICR spectroscopy andkinetic energy ICR. At thermal energy, the rate
constant was measured as 2.9  10-10 cm3
molecule-1 s-1, and branching ratios of S+ andCS2+ were determined to be 97 and 3%,
respectively.
Ar+ + CS2 → S+ + CS + Ar
→ CS2+ + Ar

(97%)
(3%)

(1a)
(1b)

Kinetic energy studies revealed that the CS2+
product is 90% formed in the A2u state with anear Franck-Condon (FC) vibrational state
distribution and 10% in the X2g state.
Ar+ + CS2 → CS2+(A2u) + Ar (90%)→ CS2+(X2g) + Ar (10%)

(2a)
(2b)

The S+ product in process (1a) is formed
exclusively in the ground S+(4S) state with the
maximum kinetic energy allowed by energy
and momentum conservation. These results
imply that the Ar+ + CS2 CT reaction takes
place via a long-range electron jump since no
momentum transfer occurs in most part. On theother hand, the formation of minor CS2+(A2u)state proceeds through short-range intimate
collision accompanying with substantial
momentum transfer. They reported that it isstill possible that Ar2+ is the source of theCS2+( A– X ) emission and that this reaction
preferentially populates low vibrational statesof A2u. However, this suggestion contradicted
the previous conclusion of Upshulte et al.2)
Although it takes more than 34 years after
these three-pioneering works on the CT
reactions of Ar+ and Ar2+ with CS2 leading toCS2+(A– X) emission,1,2,5) no definite conclusion
has been obtained until now on the exact
excitation source of CS2+(A) in the Ar flowing
afterglow. The objective of this work is todetermine whether Ar+ + CS2 and/or Ar2+ + CS2
CT reaction really participate in the formationof CS2+(A– X) emission based on new additional

experiments in the flowing afterglow. In theprevious two flowing-afterglow experiments,1,2)
only Ar afterglow was used for the study of ionmolecule reactions of CS2. A disadvantage of
the Ar afterglow experiment is that both Ar+
and Ar2+ can contribute to the CS2+( A– X )emission, which makes difficult to assign its
exact excitation source. In the present study,
the contribution of the Ar+ + CS2 CT reaction is
examined by using the He afterglow where only
Ar+ monomer ion is generated by the He(23S) +Ar Penning ionization. In this case, thecontribution of the Ar2+ + CS2 CT reaction iscompletely excluded. Then, the contribution of
the Ar2+ + CS2 reaction is examined bycomparing the CS2+( A– X ) emission spectrum
obtained from the Ar+ + CS2 CT reaction in the
He afterglow with that in the Ar afterglow at
various Ar pressures. Active ionic species
produced in the Ar afterglow are also monitored
using mass spectrometry to examine ionicspecies in the flow tube. The rovibrational
distribution of CS2+(A) by the thermal-energy
Ar+ + CS2 reaction is discussed based on
re-examination of kinetic energy ICR datareported by Rincon et al.5)

2.

Experimental

Figures 1(a) and 1(b) show Ar afterglow andHe afterglow apparatuses used in this study.
The Ar afterglow apparatus was the same asthat used previously.1) The Ar afterglow
apparatus was used for the study of the Ar+ +CS2 and Ar2+ + CS2 reactions, whereas the He
afterglow apparatus was employed for the
study of the Ar+ + CS2 CT reaction. In the Ar
afterglow experiment, CS2 gas was added fromthe first entry port in Fig. 1(a). Typical partialpressures of Ar (purity 99.9999%) and CS2 were0.5–1.5 Torr and 3 mTorr, respectively.
In the He afterglow, high purity He gas(99.995%) was passed through a flow tube
evacuated by a 10 000 L min-1 mechanicalbooster pump. Such He active species as
He(23S), He+, and He2+ were generated by a
2.45 GHz microwave discharge at a He
pressure of 0.60–0.70 Torr. The relative
concentrations of He(23S), He+, and He2+ at 0.65
Torr have been estimated to be 1.0:1.5:0.05,
respectively.6) On addition of Ar gas from thefirst entry port and a target CS2 gas from thesecond entry port, a conical reaction flame wasobserved around the second entry port. Typicalpartial pressures of He, Ar, and CS2 were 600–
700, 40, and 3 mTorr, respectively.
Green flames were observed in the Ar or He

令和 4 年度

九州大学大学院総合理工学報告
CS2

(a)
Flame
To mechanicalbooster pumpAr

Microwave
cavityQuartzwindow

Grids

CS2

Ar

(b)
Flame
He

Microwave
cavityGrids

To mechanicalbooster pump

Quartzwindows

Fig. 1. (a) Ar flowing-afterglow and (b) Heflowing-afterglow apparatuses used for thethermal-energy CT reactions of Ar+ and Ar2+
with CS2.
afterglow through a quartz window. Emission
spectra in the 450–600 nm region were
measured with a Jarrell Ash 1 m
monochromator equipped with an HTV R585
photomultiplier.
Mass spectra of Ar ionic species in the Ar
afterglow were measured using a similar
apparatus reported previously.7)

3.

Results and Discussion

3.1
Active species formed by microwave
discharge in Ar and He afterglows
By microwave discharge of Ar gas, Ar(3P0,2),
Ar+, Ar+M, and Ar2+ can be formed as active
species.
Frommassspectroscopic
measurements, we confirmed that Ar+ and Ar2+
ions are present in our conditions as ionicactive species. The [Ar2+]/[Ar+] ratio increases
with increasing the Ar gas pressure because
Ar2+ ions are formed by the termolecular
reaction.

k3

Ar+ + 2Ar → Ar2+ + Ar(3)
k3 = (2.7 ± 0.3)  10-31 cm6 molecule-2 s-l.8)
By microwave discharge of He gas, neutral
He(23S) atoms with an excitation energy of
19.82 eV, and He+ and He2+ ions withrecombination energies of 24.59 eV and 18.3–
20.3 eV, respectively, are generated as active
species. When He+ and He2+ ions were removed
from the discharge flow using the ion-collector

第 44 巻第1号

3

grids and the Ar gas was injected from the firstentry port in Fig. 1(b), only neutral He(23S)
atoms can go downstream along the flow tube
and arrive at the reaction zone. Then, thefollowing Penning ionization and associative
ionization occur around the first entry portwith a rate of 7.5 × 10-11 cm3 molecule-1 s-1.9)
He(23S) + Ar
→ Ar+(2P1/2,3/2) + He + e→ HeAr+ + e-

(87%)
(13%)

(4a)
(4b)

The branching ratio of (4a) and (4b) was
measured to be 0.87:0.13, respectively.10-12)
Reaction (4a) provides Ar+(2P1/2,3/2) ions andPenning electrons. The recombination energies
of Ar+(2P1/2) and Ar+(2P3/2) are 15.94 and 15.76
eV,
respectively.
The
initial[Ar+(2P1/2)]/[Ar+(2P3/2)] ratio in the He(23S) + Ar
Penning ionization has been measured to beabout 0.5 by using Penning ionization electron
spectroscopy.13) The [Ar+(2P1/2)]/[Ar+(2P3/2)] ratio
in the reaction zone was estimated by observing
ArF* excimer emission resulting from theAr+(2P1/2,3/2) + SF6- ionic recombination
reaction.14) On the basis of our optical
spectroscopic studies on the spin-orbit state
selective formation of rare gas monofluoride
excimers,14,15) the ArF(B-X,C-A) excimers are
selectively formed from the Ar+(2P3/2) + SF6reaction, while the ArF(D-X) excimer
preferentially results from the Ar+(2P1/2) + SF6reaction. Therefore, the intensity ratio of
ArF(D-X)/ArF(B-X,C-A)
reflects
the[Ar+(2P1/2)]/[Ar+(2P3/2)] ratio. The only ArF(BX,C-A) excimers were observed by addition of asmall amount of SF6 into the reaction zone,
when Ar+ was formed both by the He(23S) + Ar
Penning ionization and by a microwave
discharge of Ar. This suggests that the upperAr+(2P1/2) spin-orbit component relaxes to thelower Ar+(2P3/2) one by superelastic collisions
with electrons under our conditions.16)
Ar+(2P1/2) + e- → Ar+(2P3/2) + e-

(5)

HeAr+(X2+) produced from reaction (4b) has asmall dissociation energy of D0 = 207 cm-1.17)
This binding energy is smaller than the kinetic
energy of He buffer gas at 300 K (39 mV = 313
cm-1). Therefore, HeAr+(X2+) heterodimer
cluster ions dissociate into He + Ar+ by collision
with He buffer gas.18)
HeAr+(X2+) + He → Ar+ + 2He

(6)

4

Re-investigation of excitation source of the CS2+(A2u-X2g) emission in the Ar afterglow

The most important point in the He afterglow
experiment is that Ar partial pressure (40mTorr) is too low to generate Ar2+. The only
presence of Ar+ and the absence of Ar2+ andHeAr+ in the present He afterglow experiments
were confirmed by the mass spectroscopic
measurement of product ions.
3.2 CS2+(𝐀2u– 𝐗2g) emissions resulting from
Ar2+ + CS2 CT reaction in the Ar afterglow andAr+ + CS2 CT reaction in the He afterglow
Figure 2(a) shows a typical emission
spectrum of the CS2+( A 2u – X 2g) transition
obtained in the Ar afterglow at a high Ar gas
pressure of 1.3 Torr. This emission was similar
to that observed at a higher Ar pressure of 2.6
Torr in our previous study.1) Besides strong
CS2+( A– X ) emissions from the groundvibrational 00 = (0,0,0) levels, weak CS2+(A– X)
emissions from such low vibrational levels as 11= (1,0,0) and 22 = (0,2,0) are identified in bothtwo Ω =1/2 and 3/2 spin-orbit components.
Besides the principal (0,0,0)–(𝑣 ″,0,0) bands for𝑣 ″= 0–2 and (0,0,0)–(𝑣 ″–1,2,0) Fermi resonantbands for 𝑣 ″ = 1 and 2, weak (1,0,0)–(0,0,0),(0,2,0)–(0,0,0), and (0,2,0)–(0,2,0) bands fromthe excited 𝑣 ′ = 1 and 𝑣 ′ = 2 levels are
identified.1,19) We concluded that this CS2+(A– X)
emission arises from the Ar2+ + CS2 CT reaction
at thermal energy in our previous study.1)
Figure 2(b) shows a typical emission
spectrum obtained from the Ar+ + CS2 CT

Fig. 2.
CS2+( A 2u – X 2g) emissions
resulting from (a) the thermal-energy Ar2+
CS2 CT reaction in the Ar afterglow and (b)the thermal-energy Ar+ + CS2 CT reaction in
the He afterglow.

reaction using the He afterglow apparatus
shown in Fig. 1(b). It should be noted thatspectral features are quite different from thoseof the Ar2+ + CS2 reaction (Fig. 2(a)). In Fig. 2(b),a strong continuous band is observed, asreported by Upschlte et al. under low spectral
resolution.2) In addition, some weak discrete
bands, which are ascribed to CS2+( A– X )emissions from the (0,0,0), (1,0,0), and (0,2,0)
levels, are found over strong continuous bands.
The relative intensities of the CS2+( A– X )emissions from the excited (1,0,0) + (0,2,0)
levels to those from the ground (0,0,0)
vibrational levels in Fig. 2(b) are stronger thanthose in Fig. 1(a) by a factor of about 3. This
result shows that CS2+(A– X ) emission in Fig.
2(b) is more vibrationally excited than that inFig. 2(a).
Similar unidentified continuous emissions
have been observed from CS2 in the UV-visible
region as background emission of the discreteCS2+( A– X ) bands under fast electron-impact
excitation,20,21) He(23S), He(21S), and Ne(3P0,2)
Penning ionization,22-25) and CO+ + CS2 CT
reaction at thermal energy.21) The mostoutstanding features of the continuous
emission in the Ar+ + CS2 reaction are that its
relative intensity to the discrete CS2+( A– X )bands is much higher than those observed inother ionization processes described above.20-25)
The continuous emission with nearly
constant intensity appears in the whole
wavelength range of 460–515 nm including theshorter wavelength region of the 0 originbands of Ω= 3/2 and 1/2 components at 474
and 480 nm, respectively. The observation ofstrong continuous emission below the 0bands indicates that vibrationally excitedstates of CS2+(A) are formed in the Ar+ + CS2 CT
reaction. Although Upschlte et al.2) assigned tothis continuous emission to CS2+(A– X) emission
from high vibrational levels, they did not
discuss exact reason why the CS2+( A– X )emission from high vibrational levels gives
such a broad emission.
Figure 3 shows potential energy curves of
CS2 and CS2+( X, A, B ) and recombinationenergies of Ar+ and Ar2+. The internuclear
distances of the CS2(X), CS2+(X ), and CS2+(A )states are 1.5545, 1.5542, and 1.615 Å,
respectively.19,26,27) Although the internuclear
distances of the CS2(X) and CS2+(X) states arenearly the same, that of the CS2+(A ) state islarger than that of the CS2(X) state by 0.06 Å.
Therefore, Franck-Condon factors (FCFs) forCS2(X) → CS2+(A ) ionization obtained by HeI

令和 4 年度

九州大学大学院総合理工学報告

17

~
B2S +

CS+ + S~

CS+ + Su15.76 eV RE Ar+
14.5

Potential energy (eV)14.46 eV RE Ar2+

A2Pu

CS2+
12.7–13.5 eV

12.7

~

X2Pg
10.1

CS + S

4.0

CS2
X1S+

CS2

r (C-S) distanceFig. 3. Potential energy curves of CS2 andCS2+ and recombination energies of Ar+ andAr2+(adiabatic value).
photoelectron spectrum (PES) have a broad
distribution in the range of CS2+( A :(0,0,0) –(7,0,0)) levels with a broad peak at 𝑣 ′=1–3:(0,0,0) – (7,0,0) = 0.10 : 0.20 : 0.24 : 0.19 : 0.13 :0.09 : 0.05 : 0.02.28) Although CS2+( A– X )emissions from CS2+(A: 𝑣 ′=0–7) are expected tobe observed on the basis of FCFs for ionization
given above, only CS2+( A– X ) emissions from𝑣 ′=0–3 or 𝑣 ′=0–4 and their Fermi-resonancelevels were observed in vacuum ultraviolet(VUV) photoionization (= 92.3 nm),29) fastelectron-impact ionization,30) and He(23S)
Penning
ionization.23)
Under
VUV
photoionization where ionization proceeds
through vertical FC-like ionization, dominant
CS2+(A– X ) emissions occur from 𝑣 ′=0–2 andthose from 𝑣 ′ = 3 and 4 are weaker than
expected from FCFs. Wu et al.29) attributed theabsence of emissions from 𝑣 ′ = 5 and 6 to small
FCFs for the CS2+(A– X) transition.
If an excess energy released in the thermalenergy CT reaction is not favorably converted
to translational energies of products, nearresonant internal-energy states will be formed
dominantly. Although the CS2+(A– X) emission
from 𝑣 ′ > 4 level has not been observed, highvibrationally excited states with small FCFs forionization will be formed in the Ar+ + CS2 CT
reaction
becauseenergy-resonancerequirement may take part in the reaction.

第 44 巻第1号

5High vibrational states of CS2+(A) has beenstudied by Liu et al.31) using high resolution
pulsed field ionization-photoelectron (PFI-PE)
spectroscopy. CS2+( A ) peaks from (0,0,0) to(6,0,0) and (5,2,0) levels have been identified in
the 12.69–13.13 eV region. In the energy region
above 13.13 eV, the intensity of PFI-PE bands
decreases significantly. Their calculations
indicated that most of the PFI-PE bands in thehigher energy region are strongly mixed due toanharmonic and Fermi resonances and polyads
interactions so that the assignment of thevibrational quantum numbers is not possible.
Thus, it is expected emissions from such highvibrationally excited states as 𝑣 ′ > 6 consist of
many complicated energy levels. Thus, if
emission occurs from high vibrational levels,
complicated emissions providing continuous
emission will occur. The formation ofcomplicated high vibrational levels due toFermi resonance and Renner-Teller effects asobserved by PFI-PE and laser induced
fluorescence spectra32,33) is one reason for theappearance of the continuous CS2+( A– X )emission from high vibrational levels.
In our previous optical spectroscopic studies
on the Ar flowing-afterglow reaction of
OCS,34,35) OCS+( A 2 – X 2:  = 1/2, 3/2)
emission resulting from the thermal-energy Ar++ OCS CT reaction was observed.
Ar+(2P3/2) + OCS→ OCS+(A:(0,0,0)) + Ar + 0.68 eV. (7)The emission band widths of each OCS+(A– X)
emission were much broader than thoseobtained by He(23S) and Ne(3P0,2) Penningionization because of high rotational excitationof OCS+( A ). The fluorescence channel in the
OCS+(A: 0,0,0) level was found to be open for
rotationally excited levels up to J ≈ 170 (≈ 5500
cm-1).
The
rotational
distribution
of
OCS+(A23/2:0,0,0) could be characterized by aBoltzmann temperature of 4300±500 K,
indicating that 55±7% of the excess energy isdeposited into the rotation of OCS+(A ). Since
the excess energy of the Ar+ + CS2 →CS2+(A: 0,0,0) + Ar CT reaction, 3.1 eV, is muchhigher than that in the Ar+(2P3/2) + OCS →OCS+( A :(0,0,0)) + Ar CT reaction, 0.68 eV,
similar or much higher rotational excitation is
expected for many vibrational CS2+(A ) states
formed in the Ar+ + CS2 CT reaction. A highrotational excitation of CS2+(A) will be the otherreason for the appearance of continuous bandin the CS2+(A– X) emission from the Ar+ + CS2

6

Re-investigation of excitation source of the CS2+(A2u-X2g) emission in the Ar afterglow

CT reaction.
We concluded that strong unresolved
backgroundband
arisesfromheavy
overlapping of many emissions from highvibrational and rotational excited states ofCS2+(A ). They are major product channels in
the Ar+ + CS2 CT reaction leading to the CS2+(A)state.
Ar+ + CS2 → CS2+(A: high vibrational levels:
𝑣 ′ >4) + Ar (major product)(8a)
Weak discrete bands are attributed toCS2+(A– X) emission from such low vibrational
states as (0,0,0), (1,0,0), and (0,2,0). They areminor product channels in the Ar+ + CS2 CT
reaction.
Ar+ + CS2 → CS2+(A: low vibrational levels:
𝑣 ′ =0,1 and 𝑣 ″=2) + Ar (minor product)(8b)
Based on our previous study,24) collisional
relaxation from high vibrational levels of
CS2+(A ) to low vibrational ones occurs in theflowing afterglow. It is therefore reasonable toassume that not only direct formation but also
collisional relaxation from high rovibrational
levels to low rovibrational levels participates in
the formation of low vibrational levels of
CS2+(A).
It should be noted that our conclusion thathighly rovibrationally excited states are
dominant product states in the Ar+ + CS2 CT
reaction is inconsistent with the ICR study by
Rincon et al.5) They predicted that thevibrational distribution of CS2+(A) is essentiallyFC-like one on the basis of kinetic energy ICR
data of CS2+ ions. If the CT reaction occurs by a
rapid electron jump at large internuclear
separation, the transfer process is expected to
be governed primarily by FCFs for vertical
ionization. It has been known that CS2+(A– X)
emissions observed by VUV photoionizationand He(23S) Penning ionization of CS2 proceed
through FC-type vertical ionization,23,29) so that
CS2+(A– X ) emissions from 𝑣 ′ = 0–4 and 0–3
were observed, respectively. If CS2+( A– X )emission observed from the thermal-energy Ar++ CS2 CT reaction proceeds also through FCtype vertical ionization, as predicted by Rincon
et al.,5) its spectral features should be similar to
those observed by VUV photoionization andHe(23S) Penning ionization of CS2.23,29)
However, the observed spectral features ofCS2+( A– X ) emission from the Ar+ + CS2 CT

reaction are significantly different from those
by VUV photoionization and He(23S) Penningionization of CS2, where strong continuous
emission was not observed. This finding also
supports our conclusion that vibrational
distribution of CS2+(A ) in the thermal-energy
Ar+ + CS2 reaction is non-FC-type one.
3.3 A re-examination of ICR data of Rincon etal.5) for the Ar+ + CS2 → CS2+(𝐀2u) + Ar CT
reaction
In order to obtain information on the reason
for the discrepancy between the present optical
study and ICR measurements, ICR datareported by Rincon et al.5) was re-examined.
Figure 4(a) shows plot of the percentage of CS2+
ions trapped versus the square of the trapping
voltage for the thermal-energy Ar+(2P3/2) + CS2
CT reaction leading to CS2+ parent ions. In
general, ion kinetic energies can be determinedin the ICR experiments by measuring thedependence of the fraction of the ions trappedon the trapped voltage.5,36) When theelectrostatic trapping well employed in the ICR
is sufficiently deep, all of the ions are trappedin the ICR cell. However, as the well depth isdecreased, kinetically excited ions will escapefrom the trap. For a positive singly charged ion,plots of the fraction of the ions trapped, f (%),
versus the square root of the trapping potential,(V T)1/2, are expected to give two distinct linear
regions described by

f = 100;

VT ≥ ET(9a)f = (V T /E T)1/2 ×100; V T < E T(9b)where E T is the kinetic energy of the ions. Fora reaction in which the products have only asingle value of E T, a plot of f versus V T1/2 isconstant at f = 100 until V T = E T, at which pointa break occurs and then linearly decreases tozero with decreasing V T1/2 to zero. The kinetic
energy of the ions can be determined from thebreak between these two linear regions. In areal reaction system, a distribution oftranslational energies would be observed due tothe vibrational and rotational distributions in
the products. Consequently, instead of a sharp
break, curvature will occur around the breakpoint.
If the kinetic energy of CS2+ ion has aconstant value, f should increase linearly until
VT = E T and then it keeps 100% at higher
trapping voltage. Although f linearly increases
from zero to VT1/2= 0.87 V1/2, it increases

令和 4 年度

九州大学大学院総合理工学報告(a)nonlinearly
from 0.87 V1/2 to 1.02 V1/2, and then
s
120
hown
% CS2+ trapped

100

80

n

CS2+( : =0)=6 4 2 060

CS2+( )

40

CS2+(

)

20
0
0.0

0.5

1.0

1.5

2.0

(VT)1/2,/ volts1/2

(b)
100

第1号

7

nonlinearly from 0.87 V1/2 to 1.02 V1/2, and thenit becomes nearly constant above 1.02 V1/2, asshown in Fig. 4(a). This indicates that the
kinetic energy of CS2+ ions is not constant, but
it has a distribution in the V T1/2 = 0.87–1.02 V1/2
range. Momentum conservation requires thecorresponding minimum and maximum total
kinetic energy release to be TKEmin = E T(CS2+)
× [(39.95 + 76.14)/39.95] = 2.2 eV and TKEmax =3.0 eV in the CS2+ + Ar products. The ionizationenergies for CS2+, IP(CS2+), at V T1/2 = 1.021,
0.958, and 0.875 V1/2 states are estimated to be
12.73, 13.09, and 13.54 eV, respectively fromthe following relation.
IP(CS2+) = IP0(CS2+) + IE(CS2+)= RE(Ar+:15.76 eV) – TKE(CS2+,Ar) (10)80

% CS2+ trapped

第 44 巻60
ICR data

40

FCF Ref. 5
FCF Tsuji (Tsuji work)
No vibrational excitation

20

Best fit data

0
0

0.2

0.4

0.6

0.8

1

1.2

(VT)1/2 / volt1/2(c)Franck-Condon factors or
rovibrational distribution

0.40
0.35

● Best fit distribution

0.30

2

0.25

1

0.20

3
4

0.15
0.10

■ FCF

=0

5
6

0.05
0
12.6

12.8

13.0

13.2

13.4

13.6

Ionization potential / eV

Fig. 4. (a) and (b) Plots of the percentage ofCS2+ ions trapped versus the square root of thetrapping voltage for the Ar+(2P3/2) + CS2
reaction to yield CS2+ product ions. ICR dataof Ref. 5 are plotted as filled red circles. The
threshold energies for the formation of the X,
A 𝑣 ′=0–6), and B states of CS2+ are shown in(a). The arrows in (a) are bracketing the nonlinear part of the curve, thus indicating theapproximate position and width of the kinetic
energy distribution. In (b), observed %CS2+
ions trapped versus V T1/2 is compared withthose expected from FC-type vertical
ionization (Ref. 5 and this work), no
vibrational and rotational excitation, and best
fit distribution. (c) detailed values of FCFs andbest fit distribution used in (b).

Here,
IP0(CS2+),
IE(CS2+),RE,and
TKE(CS2+,Ar) are the ionization potential for
CS2+(X ), internal (electronic, vibrational, androtational) energy of CS2+, the recombinationenergy of Ar+(2P3/2), and the total kinetic energy
released to CS2+ and Ar, respectively. Since theionization energies for CS2+( A : 𝑣 = 0–6) are
12.69–13.13 eV, besides these low energy states,
higher energy CS2+( A : 𝑣 > 6) states in the13.13–13.54 eV region are expected to beformed in the Ar+(2P3/2) + CS2 CT reaction (Fig.
3). Such high energy states will be a source ofcontinuous CS2+(A– X) emission.
In Fig. 4(b) are compared the observed f vs
VT1/2 function in ICR experiments with thosepredicted from no vibrational and rotational
excitation and from FC-type vertical
ionization.5) The f values obtained by assuming
no vibrational and rotational excitation in theCS2+( A ) state are smaller than the observed
ones. This discrepancy suggests that CS2+(A )ions are vibrationally and/or rotationallyexcited. Then, we compared the observed f vs
VT1/2 function with that expected from FC-type
vertical ionization. Figure 4(b) shows two
calculated data for FC-type ionization. One isreported data by Rincon et al.5) and the other isour data obtained using reliable FCFs (Fig.
4(c)).28) We obtained smaller f values than thosereported by Rincon et al.5) below V T1/2 = 1 V1/2
(Fig. 4(b). We do not know the reason why thediscrepancy is observed between our
calculation and their results, because detailed
FCFs for ionization they used were not reported.
Rincon et al.5) reported in Ref. 21 in their paperthat “The vibrational distribution in the A2ustate formed by 2.1-eV photons is peaked at
𝑣 = 3 and covers a broad distribution from 𝑣 =8Re-investigation of excitation source of the CS2+(A2u-X2g) emission in the Ar afterglow

0 to 𝑣 = 8.” Based on the standard PES data
by Turner et al.37) and Frost et al.,28) thissentence should be revised as “The vibrational
distribution in the A2u state formed by 21.21eV photons is peaked at 𝑣 = 2 and covers abroad distribution from 𝑣 = 0 to 𝑣 = 7.” Thus,
it seems that they did not use correct FCFs intheir simulation. Anyway, there are still
discrepancies between the observed f vs V T1/2
function and those calculated assuming FCtype ionization in the V T1/2 = 0.87–1.02 V1/2
region, although Rincon et al.5) reported thatthe vibrational distribution of the A2u state isa near FC-type one. When the f vs VT1/2 function
was simulated assuming various internal(vibrationalandrotational)
energydistributions in the V T1/2 = 0.87–1.02 V1/2 region,a reasonable agreement between the observedand calculated functions was obtained using
the following distribution (Fig. 4(c)): 40%, 30%,
and 30% for IP(CS2+)=12.73, 13.09, and 13.54
eV, respectively. The internal energy
distribution in the 13.1–13.5 eV region also
supports the formation of high energy states
above CS2+(A: 𝑣 = 6), which will be responsible
for the appearance of continuous CS2+( A– X )emission in the Ar+ + CS2 CT reaction.
Parent et al.38) performed a systematic study
on the thermal-energy CT reactions of Ar+ withsuch triatomic molecules as H2O, N2O, and CO2
using an ICR spectrometer. From the measured
ion kinetic energy, the percentage of the excessenergy, which is in internal energy (%TIE), wasdetermined to be 48–70% for H2O+, 48–79% for
N2O+, and 69–77% for CO2+. The mean %TIE
values for H2O+, N2O+, and CO2+ are 59, 63.5,
and 73%, respectively. On the basis of nonlinear part in the kinetic energy distribution(Fig. 4(a)), we estimate the lower and upper
limits of %TIE values for CS2+ to be TIEmin =47% and TIEmax = 61%, respectively. The
mean %TIE value is 54%. The internal energy
distribution of CS2 is narrower than those of
H2O, N2O and CO2, and its mean value issmaller than those of the three triatomic
molecules.
3.4 CS2+(𝐀2u-𝐗2g) emissions from thermalenergy Ar2+ + CS2 and Ar+ + CS2 reactions in
the Ar afterglow
In section 3.2, we can obtain CS2+( A X )emission resulting solely from the Ar+ + CS2 CT
reaction. Taking this result into consideration,
we have re-investigated CS2+(A– X) emission in
the Ar afterglow. In our previous work,1) wemeasured CS2+( A– X ) emission at a high Ar

Fig. 5.
CS2+( A 2u – X 2g) emissions
resulting from the Ar afterglow reaction of
CS2 at (a) 1.3 Torr, (b) 1.0 Torr, and (c) 0.75
Torr.
pressure of 2.6 Torr, where the concentration of
Ar+ is negligibly low. In this work, we measured
CS2+( A– X ) emissions at three typical Ar
pressures of 1.3, 1.0, and 0.75 Torr. Results
obtained are shown in Figs. 5(a)–5(c). It isnoteworthy that significant changes in spectralfeatures are observed. The spectrum at 1.3 Torrconsists of only discrete bands without
continuous background band, which agrees
with our previous report.1) With decreasing the
Ar pressure from 1.3 to 1.0 Torr, the intensityof discrete bands decreases, and undergroundcontinuous band appears. With further
decreasing the Ar gas pressure from 1.0 Torr to
0.75 Torr, the relative intensity of the discrete
bands to the continuous band becomes small
and the spectral features become similar to
those observed in the Ar+ + CS2 reaction in the
He afterglow (Fig. 2(b)). It is therefore
reasonable to assume that major excitation
source is Ar+ monomer ion at the Ar pressure of
0.75 Torr. These results led us to conclude that
CS2+(A– X) emission in the Ar afterglow consistof two components. One is only discrete bands
without
undergroundcontinuum
band
resulting from the Ar2+ + CS2 CT reaction andthe other is the weak discrete and strong
underground continuum band resulting from

九州大学大学院総合理工学報告

the Ar+ + CS2 CT reaction. The intensity ratioof resolved bands to underground continuousband of CS2+( A– X ) emission depends on the[Ar2+]/[Ar+] ratio in each experimental
condition. At high Ar pressures (e.g., 1.3 Torr),the former reaction is dominant, whereas thelatter reaction occupies major part at low Ar
pressures (e.g. 0.75 Torr). At intermediate Ar
pressures (e.g. 1.0 Torr), both components areoverlapped with each other.
On the basis of present results, theconclusion by Upshulte et al.2) on the excitation
source of CS2+( A– X ) should be revised. They
identified excitation source of CS2+( A– X )assuming that it is either Ar+ or Ar2+ ion andthe possibility of the contribution of both Ar+
and Ar2+ ions was excluded. This made themwrong conclusion that only Ar+ is the excitation
source of CS2+(A– X).
We re-examined their reported CS2+( A– X )spectra observed at various experimental
conditions.2) With increasing the Ar pressure,decreasing the bulk flow velocity, anddecreasing negative voltage, the intensity ratio
of weak discrete bands to strong undergroundcontinuous bands increases (Figs. 3–5 in Ref. 2).
These results can be explained by the increasein the [Ar2+]/[Ar+] ratio in their conditions. In
our experiments, continuous background band
nearly disappears at an Ar pressure above 1
Torr. However, in their experiments, weakcontinuous components remain even at high Ar
pressures of 1.50 and 1.75 Torr. These results
imply that the [Ar+]/[Ar2+] ratio in theirexperiments using glow discharge plasma washigher than that in our experiments using
microwave discharge. Another reason for theappearance of background continuous bands intheir experiments at high Ar pressures may be
the observation region of emission spectra.
Based on their flow-tube apparatus equippedwith optical detection system (Fig. 2 in Ref. 2),
they observed downstream emission spectra of
the CS2 gas inlet using an optical fiber. It seems
that they did not detect emission directly
around the CS2 gas inlet, whose exit was facingin the opposite direction of the discharge flow.
Therefore, they observed downstream emission
from the CS2 gas inlet. It has been known thatthe total reaction rate constant of the Ar2+ +CS2 at thermal energy (8.8  10-10 cm3
molecule-1 s-1) is 3.4 times larger than that of
the Ar+ + CS2 reaction at thermal energy (2.9 
10-10 cm3 molecule-1 s-1).5,39) It is therefore
reasonable to assume that the [Ar+]/[Ar2+] ratio
becomes large with increasing the distance of

第 44 巻第1号

9

the observation region from the CS2 gas inlet,
leading to an enhancement of continuous
CS2+(A– X) emission from the Ar+ + CS2 reaction.
The rate constant for the formation of CS2+(A)from the Ar+ + CS2 reaction is estimated to be
7.8  10-12 cm3 molecule-1 s-1 using a reported
total reaction rate constant in a flow tube andthe branching ratio for the formation of CS2+(A)(2.7%) obtained in the ICR experiment.5) On theother hand, no information on the branchingratios of CS2+( A ) and CS2+( X ) have beenobtained. Therefore, only the maximum value
for the formation of CS2+(A ), 8.8  10-10 cm3
molecule-1 s-1, can be obtained assuming thatthe branching ratio of CS2+(A ) is 100%. Thisvalue is larger than that in the Ar+ + CS2
reaction by two orders of magnitude.
Figure 6 shows potential energy curves of theground Ar2+(A2 Σ / ) and Ar2(X1 Σ ) states.
The
adiabatic
ionization
potentialof
Ar2+(A2 Σ / : 𝑣" 0 ) has been measured as
14.46 eV.40,42) Although Ar2+ has a boundpotential with a short equilibrium internuclear
distance of 2.392 Å and a binding energy of 1.31
eV, Ar2(X1 Σ ) potential has a weakly boundpotential with a long equilibrium internuclear
distance of 3.755 Å and a small binding energyof 0.01 eV.40-42) Therefore, Ar2(X1Σ ) potential isrepulsive in the FC width of Ar2+(A2Σ / : 𝑣"
0 as shown in Fig. 6. We have previously
estimated the effective recombination energy of20+

Ar2+(A21/2u)

15
Potential energy / eV

令和 4 年度

Ar+(2P3/2) + Ar″=0

15.76 eV
14.46 eV1012.0 eV
13.0 eV5+

Ar2 (X1g)

0

2.0

2.5

3.0

3.5

4.0

Internuclear distance / A

Fig. 6.
Potential energy curves ofAr2+(A2Σ / ) and Ar2(X1Σ ). Morse potentialof Ar2+(A) was calculated by using molecularconstants in Ref. 40, whereas the repulsive
potential of Ar2(X) was calculated using afunction reported in Ref. 41.

10Re-investigation of excitation source of the CS2+(A2u-X2g) emission in the Ar afterglow

Ar2+(A2Σ / : 𝑣" 0) to be 12.6–13.5 eV1) using
reported
molecular
constantsof
Ar2+(A2Σ / )43) and potential energy functionof Ar2(X1 Σ ).41) In this study, the effective
recombination energy of Ar2+(A2Σ / : 𝑣" 0)
was re-evaluated to be 12.0–13.0 eV using more
precise molecular constants of Ar2+(A2Σ / ).40)
The result obtained is shown in Fig. 6.
The ionization energy of CS2+( A : 𝑣 ′=0) is
12.69 eV and those of CS2+(A: 𝑣 ′=4,5) are 12.99
and 13.06 eV, respectively.31) Thus, theCS2+(A : 𝑣 ′>4) levels cannot be formed by theAr2+ + CS2 reaction energetically. In the Ar2+ +CS2 reaction, low vibrational levels of CS2+(A)are preferentially formed and no continuous
CS2+( A– X ) emission can be observed. One
reason for the absence of the continuous
CS2+(A– X) emission is the endothermicity of theformation of high energy levels. The otherreason is lower rotational excitation of CS2+(A).

4.

Summary and Conclusion

We have previously observed CS2+( A– X )emission in an Ar flowing afterglow.1) Although
we attributed its excitation source to Ar2+, alater flow-tube study by Upshulte et al.2)
indicated that Ar+ not Ar2+ is the responsible
excitation source. Additional experiments inthis flowing-afterglow study led us to conclude
that our previous assignment of the excitation
source is correct and strong discrete CS2+(A– X)
emissions from low vibrationally excited states
really arise from the Ar2+ + CS2 reaction at highAr pressures above ≈1 Torr. We separately
studied the thermal-energy Ar+ + CS2 reaction
using the He afterglow where the contribution
from Ar2+ was excluded completely. Then, weak
discrete CS2+( A– X ) emissions from low
vibrationally excited states were observed overstrong continuous background emission, which
was consistent with the previous observation ofUpshulte et al.2) The present results clearlyshow that both Ar+ and Ar2+ ions can be
excitation sources of CS2+(A– X) emission in the
Ar afterglow with significantly different
spectral features. The Ar2+ + CS2 reaction wasits dominant source at high Ar pressure above≈1 Torr, whereas the Ar+ + CS2 reaction was
responsible for the CS2+(A– X) emission at a low
Ar pressure of 0.75 Torr. At intermediatepressure range of Ar, both Ar+ and Ar2+ ionscontributed to the CS2+(A– X) emission. Basedon the present findings, both Ar+ and Ar2+ ionswere excitation sources of low-resolution
CS2+(A– X ) emissions obtained in the Ar flow-

tube experiments by Upshulte et al.,2) although
the relative contribution of Ar+ and Ar2+ ionsdepended on various experimental parameters
they used.
Rincon et al.5) reported that vibrational
distribution of CS2+(A ) in the thermal-energy
Ar+ + CS2 reaction is essentially FC-like fromthemeasurementsofkinetic
energydistribution of CS2+ using ICR spectrometer.
However, the spectral features of the observed
CS2+(A– X) emission from the Ar+ + CS2 reaction
was completely different from those of VUVphotoionization and Penning ionization, which
proceed via vertical FC-like ionization. It wastherefore concluded that the Ar+ + CS2 reaction
takes place through non-FC-like ionization.
The product ions were expected to be morevibrationally excited than those expected from
FCFs for ionization. The formation of highly
vibrationally and rotationally excited stateswith complicated band structures due toanharmonic and Fermi resonances and polyads
interactions will be responsible for theappearance of strong continuous CS2+( A– X )emission. Re-examination of kinetic energy
distribution of CS2+ obtained by Rincon et al.
using ICR technique5) suggested that internal(vibrational and rotational) energy distributionof CS2+(A) is more excited than FC-like vertical
ionization. This result supported the formationof high rovibrationally excited states which
provide strong continuous emission in the Ar++ CS2 reaction.
Acknowledgments
This paper is dedicated to one of the coauthors Dr. Minoru Endoh who was working at
Hitachi Metals, Ltd. and deceased in 2015.
References
1)
2)

3)
4)
5)
6)
7)
8)
9)

M. Endoh, M. Tsuji, and Y. Nishimura, Chem. Phys.

Lett., 109, 35 (1984).

B. L. Upshulte, R. J. Shul, R. Passarella, R. E.
Leuchtner, R. G. Keesee, and A. W. Castleman, Jr., J.
Phys. Chem., 90, 100 (1986).
H. Sekiya, M. Tsuji, and Y. Nishimura, Chem. Phys.
Lett., 100, 494 (1983).
K. Suzuki and K. Kuchitsu, Bull. Chem. Soc. Jpn., 50,
1905 (1977).
M. E. Rincon, J. Pearson, and M. T. Bowers, J. Phys.
Chem., 92, 4290 (1988).
M. Endoh, PhD thesis, Graduate Schools of Eng. Sci.,
Kyushu Univ. (1984).
M. Tsuji, T. Funatsu, H. Kouno, Y. Nishimura, and H.
Obase, J. Chem. Phys., 96, 3649 (1992).
R. Johnsen, A. Chen, and M. A. Biondi, J. Chem. Phys.,
73, 1717 (1980).
F. W. Lee and C. B. Collins, J. Chem. Phys., 65, 5189
(1976).

令和 4 年度

九州大学大学院総合理工学報告

10) H. Hotop, A. Niehaus, and A. Schmeltekopf, Z. Phys.,229, 1 (1969).
11) J. A. Herce, K. D. Foster, and E. E. Muschlitz, Jr., Bull.
Am. Phys. Soc., 13, 206 (1968).
12) W. P. West, T. B. Cook, F. B. Dunning, R. D. Rundel,
and R. F. Stebbings, J. Chem. Phys., 63, 1237 (1975).
13) C. E. Brion, C. A. McDowell, and W. B. Stewart, J.
Electron Spectrosc., 1, 113 (1972/73).
14) M. Tsuji, M. Furusawa, and Y. Nishimura, Chem.
Phys. Lett., 166, 363 (1990).
15) M. Tsuji, M. Furusawa, and Y. Nishimura, J. Chem.
Phys., 92, 6502 (1990).
16) N. G. Adams, D. K. Bohme, D. B. Dunkin, and F. C.
Fehsenfeld, J. Chem. Phys., 52, 1951 (1970).
17) I. Dabrowski, G. Herzberg, and K. Yoshino, J. Mol.
Spectrosc., 89, 491 (1981).
18) H. L. Kramer, J. A. Herce, and E. E. Muschlitz, Jr., J.
Chem. Phys., 56, 4166 (1972).
19) W. J. Balfour, Can. J. Phys., 54, 1969 (1976).
20) M. Toyoda, T. Ogawa, and N. Ishibashi, Bull. Chem.
Soc. Jpn., 47, 95 (1974).
21) M. Tsuji, K. Mizukami, H. Sekiya, H. Obase, S.
Shimada, and Y. Nishimura, Chem. Phys. Lett., 107,389 (1984).
22) A. J. Yencha and K. T. Wu, Chem. Phys., 49, 127(1980).
23) A. Benz, O. Leisin, H. Morgner, H. Seiberle, and J.
Stegmaier, Z. Phys. A, 320, 11 (1985).
24) M. Tsuji and J. P. Maier, Chem. Phys., 126, 435 (1988).
25) I. Tokue, T. Kudo, M. Kobayashi, and K. Yamasaki,
Bull. Chem. Soc. Jpn., 70, 71 (1997).
26) J. H. Callomon, Proc. Roy. Soc. London A, 244, 220(1958).
27) G. Herzberg, “Molecular Spectra and Molecular

Structure III, Electronic Spectra and Electronic
Structure of Polyatomic Molecules”, Krieger: Malabar,

FL (1991).

第 44 巻第1号

1128) D. C. Frost, S. T. Lee, and C. A. McDowell, J. Chem.
Phys., 59, 5484 (1973).
29) C. Y. Wu, T. S. Yih, and D. L. Judge, Int. J. Mass
Spectrom. Ion Process., 68, 303 (1986).
30) I. Tokue, H. Shimada, A. Masuda, Y. Ito, and H. Kume,
J. Chem. Phys., 93, 4812 (1990).
31) J. Liu, M. Hochlaf, G. Chambaud, P. Rosmus, and C.
Y. Ng, J. Phys. Chem. A, 105, 2183 (2001).
32) C.-C. Zen and Y.-P. Lee, Chem. Phys. Lett., 244, 177(1995).
33) S.-G. He and D. J. Clouthiera, J. Chem. Phys., 124,
084312 (2006).
34) H. Sekiya, M. Tsuji, and Y. Nishimura, Chem. Phys.
Lett., 100, 494 (1983).
35) M. Tsuji, J. P. Maier, H. Obase, H. Sekiya, and Y.
Nishimura, Chem. Phys. Lett., 137, 421 (1987).
36) G. Mauclaire, R. Derai, S. Fenistein, and R. Marx, J.
Chem. Phys., 70, 4017 (1979).
37) D. W. Turner, C. Baker, A. D. Baker, and C. R.
Brundle, “Molecular Photoelectron Spectroscopy ”,
Wiley-Interscience, New York (1970).
38) D. C. Parent, R. Derai, G. Mauclaire, M. Heninger, R.
Marx, M. E. Rincon, A. O'Keefe, and M. T. Bowers,
Chem. Phys. Lett., 117, 127 (1985).
39) R. J. Shul, R. Passarella, X. L. Yang, R. G. Keesee, andA. W. Castleman, Jr., J. Chem. Phys., 87, 1630 (1987).
40) P. Rupper and F. Merkt, J. Chem. Phys., 117, 4264
(2002).
41) L. Mattera, C. Salvo, S. Terreni, and F. Tommasini, J.
Chem. Phys., 72, 6815 (1980).
42) K.-M. Weitzel and J. Mähnert, Int. J. Mass Spectrom.,
214, 175 (2002).
43) P. A. Christiansen, K. S. Pitzer, Y. S. Lee, J. H. Yates,
W. C. Ermler, and N. W. Winter, J. Chem. Phys., 75,
5410 (1981).