Potential energy curves, spectroscopic parameters, vibrational levels and molecular constants for 37 low-lying electronic states of He2

International Journal of Chemistry, Mathematics and Physics (IJCMP)
[Vol-9, Issue-2, Apr-Jun, 2025]
https://dx.doi.org/10.22161/ijcmp.9.2.4
ISSN: 2456-866X
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Potential energy curves, spectroscopic parameters,
vibrational levels and molecular constants for 37 low-lying
electronic states of He2
Michel Douglas Epée Epée1
, Roland Kevin Douthio Mbayang2
1
Department of Physics, Faculty of Science, University of Douala, P. O. Box: 24157, Douala, Cameroon
2
Postgraduate Training Unit for Mathematics, Applied Computer Science and Pure Physics, University of Douala, Douala,
Cameroon
Corresponding author: epeemichel23@yahoo.fr
Received: 20 May 2025; Received in revised form: 18 Jun 2025; Accepted: 22 Jun 2025; Available online: 26 Jun 2025
©2025 The Author(s). Published by AI Publications. This is an open access article under the CC BY license
(https://creativecommons.org/licenses/by/4.0/)
Abstract— A manifold of singlet and triplet electronic states of He2 is characterized theoretically using the
R-matrix method. Potential energy curves have been calculated for u
+
1
, g
+
1
, u
1
, g
1
, u
+
3
, g
+
3
,
u
3
, g
3
electronic states. These potential curves are then fitted to analytical potential energy functions
(APEFs) using the Murrell-Sorbie potential function. The spectroscopic parameters, such as 𝐷𝑒, 𝜔𝑒, 𝜔𝑒𝑥𝑒 ,
𝐵𝑒, 𝛼𝑒 are determined using the obtained APEFs, and compared with theoretical and experimental data
available. A whole set of vibrational level 𝐺(𝑣) and inertial rotation constant 𝐵𝑣 predicted for these
electronic states by solving the ro-vibrational Schrödinger equation of nuclear motion using Numerov’s
method completes these characterization.
Keywords— Spectroscopic parameters, molecular constant, vibrational level.
I. INTRODUCTION
The properties of rare gases are of considerable interest
for the development of modelling and as standard values for
experiments. The interatomic potential is of fundamental
importance for understanding the dynamic and static
properties of gases, liquids, and solids. With only four
electrons, He2 belong to the limited class of molecular
system for which highly accurate ab-initio quantum
mechanical calculations are feasible. The potential energy
curve of the ground state of He2 is purely repulsive,
exhibiting a very shallow van-der-walls Minimum of 9.1
10-3
eV at 2.97 Å [1, 2]. The low-lying excited states of the
helium dimer He2 are more or less strongly covalently
bound [3, 4]. The occurrence of highly excited bound states
above a repulsive ground states suggests several important
applications. Since these molecular excited states are
generated in rare gas discharges, one can use the continuum
emissions from these states as light sources in the vacuum
ultraviolet [5, 6]. The existence of humps on nearly all
potential curves of bound excited states of He2 has caused
a great amount of theoretical studies, both in qualitative and
quantitative way. More than 60 electronic states are known
for He2 mainly through the extensive classical grating
measurements of Ginter et al [7]. The low-lying electronic
states of He2 have been the subject of theoretical and
experimental studies [8, 9] but have not been treated a whole;
with the exception of some states which have been studied
in context of particular problems such as the excited triplet
states which are important in the study of penning ionization
while the lowest triplet states are of interest in spectroscopy
and scattering studies and as potential means of energy
storage [10]. The first calculation of potential energy curves
of the excited states for He2 has been reported by
Buckingham and Dalgarno[11]. Subsequently, many
calculation of the low-lying electronic states were
performed. The lowest u
+
1
, g
+
3
and the first excited
g
+
1
states of He2 were computed by Browne [12]. The
lowest singlet 𝐴 u
+
1
excited state was calculated by
Mukamel and kadldor [13] and Komasa [14]. The diabatic

Epée and Mbayang International Journal of Chemistry, Mathematics and Physics (IJCMP), Vol-9, Issue-2 (2025)
and adiabatic potential energy curve for the u
+
3
, g
+
3
,
u
3
, g
3
, u
3
, g
3
was obtained by Cohen[8]. Sunil et
al. [15] used the Unitary Group multiconfiguration self-
consistent field (MCSCF) procedure to calculate the
potential energy curves of 𝐶 g
+
1
, 𝑐 g
+
3
, 𝐴 u
+
1
, 𝑎 u
+
3
. They
also produced spectroscopic constants and vibrational
energy levels and their spacing from these curves. The
potential energy curves, vibrational levels and their spacing
for the 𝐴 u
+
1
and 𝐶 g
+
1
states have been obtained by Jordan
[16] by combining scattering, spectroscopy and ab- initio
theory. The properties for 𝐴 u
+
1
, 𝐶 g
+
1
, 𝐵 g
1
, 𝑎 g
+
3
,
u
3
, 𝑏 g
3
excited states of He2 have also been calculated
by Yarkony [4]. As can be seen in the literature, these
studies mainly concentrated on the properties of 𝐴 u
+
1
,
𝐶 g
+
1
, 𝐵 g
1
, 𝑎 g
+
3
, u
3
, 𝑏 g
3
, excited states. The
properties of more electronic singlet and triplet excited
states still remain unknown.
The present work is devoted to an accurate
description of the 18 singlet and 19 triplet excited
electronic states of He2. The potential energy curve , the
spectroscopic constants 𝑅𝑒, 𝑇𝑒, 𝐷𝑒, 𝜔𝑒, 𝜔𝑒𝑥𝑒 , 𝐵𝑒, 𝛼𝑒 of
the corresponding u
+
1
, g
+
1
, u
1
, g
1
, u
+
3
, g
+
3
,
u
3
, g
3
electronic states have been investigated along
their vibrational levels and the inertial rotation constant 𝐵𝑣.
II. COMPUTATIONAL DETAILS
In this work, we use the R-Matrix method [17] as
implemented in the UKRMol codes [18]. The basis set
employed is the cc-pVTZ Gaussian basis set for He2
molecule. This set includes polarization functions. The
molecule is treated in a reduced 𝐷2ℎ symmetry in which
there are eight symmetries Ag, Au, B1g, B1u, B2g, B3g, B2u, B3u.
An initial set of molecular orbital was obtained by
performing Self-Consistent Field (SCF) calculations for the
𝑋 g
+
1
state of He2, although in practice the choice of
orbitals is not important in a full configuration interaction
(FCI) calculation. In the close coupling expansion of the
trial wave function of the He2 system, we include the ground
state 𝑋 g
+
1
and the eight lowest excited state 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
and 𝐹 u
1
, 𝑎 u
+
3
, 𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
.
Each state was represented by an FCI wave function. In our
CI model we have the occupied orbitals which are
augmented by the virtual molecular orbital up 11ag, 5b2u,
5b3u, 2b1g, 11b1u, 5b2g, 5b3g, 2au. To obtain potential energy
curves, Our FCI calculations were performed for several
bondlengths.
The potential curves obtained are then fitted to analytical
potential energy functions (APEFs) using the Murrell-
Sorbie potential function [19]. The general expression of the
Murrell potential function is:
𝑉(𝜌) = −𝐷𝑒(1 + ∑ 𝑎𝑖
𝑛
𝑖=1 𝜌𝑖
exp(−𝑎1𝜌)) (1)
where 𝜌 = 𝑅 − 𝑅𝑒 , 𝑅 is the inter-nuclear distance of
diatomic molecule, 𝑅𝑒 is it equilibrium inter-nuclear
distance and is regarded as a fixed parameter in the fitting
process. The parameters 𝐷𝑒 and 𝑎𝑖 (𝑖 = 1,2,3 … . . 𝑛) are
determined by fitting. The quadratic, cubic, and quartic
force constants 𝑓𝑛 (𝑓𝑛 =
𝑑𝑛𝑉
𝑑𝑅𝑛 , 𝑛 = 2, 3 and 4) could be
derived from function at the equilibrium position as
followed
𝑓2 = 𝐷𝑒(𝑎1
2
− 2𝑎2) (2)
𝑓3 = −6𝐷𝑒(𝑎3 − 𝑎1𝑎2 +
1
3
𝑎1
3
) (3)
𝑓4 = 𝐷𝑒(3𝑎1
4
− 12𝑎1
2
𝑎2 + 24𝑎1𝑎3) (4)
The expression relating the spectroscopic constants with the
force constants 𝑓2, 𝑓3 and 𝑓4 for diatomic molecules may be
found as
𝐵𝑒 =
ℎ
8𝜋𝑐𝜇𝑅𝑒
2 (5)
𝜔𝑒 = √
𝑓2
4𝜋2𝑚𝑐2 (6)
𝛼𝑒 = −
6𝐵𝑒
2
𝜔𝑒
(
𝑓3𝑅𝑒
3𝑓2
+ 1) (7)
𝜔𝑒𝑥𝑒 =
𝐵𝑒
8
[−
𝑓4𝑅𝑒
2
𝑓2
+ 15 (1 +
𝜔𝑒𝛼𝑒
6𝐵𝑒
2 )
2
] (8)
Based on the relationship equations among spectroscopic
parameters and force constants (6)-(8), the spectroscopic
data of diatomic molecule can be calculated. Using the
potential energy curves obtained at the MRCI/ cc-pV5Z
level of theory, the radial Schrödinger equation of nuclear
motion is numerically solved using the Numerov method
[20] to get the vibrational states when 𝐽 = 0. The complete
vibrational levels G(v), inertial rotation constant Bv are
calculated.
III. RESULTS AND DISCUSSION
The potential energy curves of 37 electronic states of He2
have been investigate, namely four u
+
1
, five u
1
, four
g
+
1
, five g
1
for singlet states and five u
+
3
, five u
3
,
four g
+
3
and five g
3
for triplet states. To obtain the
potential energy curves for the low-lying electronic states of

He2 our calculation were repeated for 130 bondlengths in
the range 𝑅 = 1.0 to 13.0 a.u. Figure 1 and 2 display,
respectively, singlet u
+
1
, u
1
, g
+
1
, g
1
and triplet
u
+
3
, u
3
, g
+
3
, g
3
electronic states as function of
internuclear distance. From Figures 1 and 2, one can see the
existence of humps at about 2-3 Å on nearly all the potential
energy curves of the excited states computed in the present
work . It is seen in these figure that the general profile of
singlet 𝐴 u
+
1
, 𝐶 g
+
1
, 𝐵 g
1
and triplet 𝑎 u
+
3
, 𝑐 g
+
3
, 𝑏 g
3
potential curves is similar to the ones described by Sunil et
al [15] and Yarkony[4] and are in satisfactory agreement.
The spectroscopic parameters such as the equilibrium
distance 𝑅𝑒 , the dissociation energy 𝐷𝑒, The adiabatic
excitation energies 𝑇𝑒, the vibrational harmonic constant
𝜔𝑒, the anharmonic frequencies 𝜔𝑒𝑥𝑒 , the rotational
constant 𝐵𝑒 for the 37 electronic states obtained in this
work are presented in Table 1 for u
+
1
and u
1
, Table 2
for g
+
1
and g
1
, Table 3 for u
+
3
and u
3
, and Table 4
for g
+
3
and g
3
along with the experimental and
theoretical results available.
The lowest excited singlet states of He2 are 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
and 𝐹 u
1
.
For the 𝐴 u
+
1
state, the Re value obtained in this
work is 1.0419 Å that compares favorably with the 1.0404
Å and 1.0406 Å experimental results of Huber and
Herzberg [9] and Focsa [22]. The theoretical Re obtained by
Wasilewki et al. [23], Sunil et al [15] and Yarkony [4] are
slightly higher than the experimental results and our
calculation. In the case of the spectroscopic constants (𝜔𝑒,
𝜔𝑒𝑥𝑒 , 𝛼𝑒 , 𝐵𝑒 ), our results (1838.45 cm-1
, 33.39 cm-1
,
7.7024 cm-1
, 0,2227 cm-1
) are reasonably in good
agreement with the theoretical results of Wasilewki et al.
[23] and Sunil et al [15] and the experimental results of
Huber and Herzberg[9], and Focsa[22] as shown in Table 1.
The 𝐵 g
1
electronic state, with a dissociation
energy of 20271.92 cm-1
, is located at 150351 cm-1
(Te)
above the 𝑋 g
+
1
state. Our results for 𝜔𝑒 =
1752.974 𝑐𝑚−1
, 𝜔𝑒𝑥𝑒 =36.7169 𝑐𝑚−1
, 𝐵𝑒 =7.37848
𝑐𝑚−1
𝛼𝑒=0.2337 𝑐𝑚−1
are in good agreement with those
obtained by Huber and Herzberg [9] (1.0667 cm-1
, 1765.76
cm-1
, 7.4030 cm-1
, 0.2160 cm-1
) respectively.
The C g
+
1
state equilibrium inter-nuclear distance
Re, dissociation energy De, vibrational harmonic constant,
anharmonic frequencies 𝜔𝑒 and rotational constant 𝐵𝑒
computed to be respectively 1.0930 Å , 1654.643 cm-1
,
43.0382 cm-1
and 7.0286 cm-1
are in reasonably good
agreement with the theoretical MCSCF calculations of
Sunil et al.[15] and the experimental data of Huber and
Herzberg [9](see Table 2).
The F u
1
state located at 165971 cm-1
above
𝑋 g
+
1
state with a dissociation energy of 4862.95 cm-1
, the
equilibrium inter-nuclear distance Re = 1.0822 Å, 𝜔𝑒 =
1681.95 cm-1
compares well with the experimental results
of Huber and Herzberg [9].
The lowest triplet electronic states are 𝑎 u
+
3
,
𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
. The lowest-lying electronic state of
He2 is the 𝑎 u
+
3
, 𝑇𝑒 = 144 192 𝑐𝑚−1
, 𝑅𝑒 = 1.0459 Å,
𝜔𝑒 = 1781.862 𝑐𝑚−1
, 𝜔𝑒𝑥𝑒 = 42.3944 𝑐𝑚−1
and 𝐵𝑒 =
7.6981 𝑐𝑚−1
. Beside the 𝑎 u
+
3
state, there is another
excited state that correlates with the first dissociation
channel He(1s2 1
S)+He(2s 3
S): the 𝑐 g
+
3
state 𝑇𝑒 =
155 183 𝑐𝑚−1
, 𝑅𝑒 = 1.0974 Å , 𝜔𝑒 = 1570.776 𝑐𝑚−1
,
𝜔𝑒𝑥𝑒 = 55.46 𝑐𝑚−1
and 𝐵𝑒 = 6.9990 𝑐𝑚−1
. The 𝑏 g
3
state, 𝑇𝑒 = 149 171 𝑐𝑚−1
, 𝑅𝑒 = 1.0640 Å , 𝜔𝑒 =
1769.593 𝑐𝑚−1
, 𝜔𝑒𝑥𝑒 = 40.4618 𝑐𝑚−1
and 𝐵𝑒 =
7.4389 𝑐𝑚−1
dissociating in the same channel He(1s2
1
S)+He(2p 3
S) with 𝑓 u
3
is the second lowest triplet
excited state. From Table 3 and 4, it is not difficult to find
that our calculated bond lengths are in good agreement with
the experimental values of Huber and Herzberg [9]. The
dissociation energy for 𝑎 u
+
3
and 𝑐 g
+
3
are 150-650 cm-1
closer to theoretical and experimental values available. For
𝜔𝑒 and 𝐵𝑒 the agreement between our results, the
theoretical data computed by Sunil et al [15] and
experimental values of Huber and Herzberg [9], and Focsa
[22] is reasonably good. Our results for 𝜔𝑒𝑥𝑒 shows a slight
gap in comparison with other theory and experiments.
For the other singlet u
+
1
, u
1
, g
+
1
, g
1
and
triplet u
+
3
, g
3
, g
+
3
, u
3
electronic states, From Table
1-4 the comparisons of our calculated data with the
experimental values of Huber and Herzberg [9], one can
find that an excellent agreement is obtained for the values
of the equilibrium interatomic separation Re with the
relative difference 0.061 % <
∆𝑅𝑒
𝑅𝑒
< 1.54% and a very
good agreement for the values of Be with the relative
difference 1.01. 10−5
% <
∆𝐵𝑒
𝐵𝑒
< 1.6% . The values of 𝜔𝑒
are in good accordance with the experimental data. A slight
deviation can be observed between our results for 𝜔𝑒𝑥𝑒 and
the experiment.
Vibrational energy level for singlet u
+
1
, u
1
,
g
+
1
, g
1
and triplet u
+
3
, u
3
, g
+
3
, g
3
electronic
states was calculated by solving the radial Schrödinger

equation numerically. We have obtained the maximum
vibrational levels to be: 25 for 𝐴 u
+
1
, 22 for 𝐷 u
+
1
, 17 for
𝐹 u
+
1
, 21 for 𝐽 u
+
1
; 21 for 𝐵 g
1
, 22 for 𝐸 g
1
, 20 for
𝐼 g
1
and 21 for 𝐿 g
1
; 19 for 𝐹 u
1
, 20 for 𝐽 u
1
, 21 for
𝑀 u
1
and 23 for 𝑄 u
1
; 16 for 𝐶 g
+
1
, 17 for 2 g
+
1
, 19 for
𝐺 g
+
1
and 20 for 𝐾′ g
+
1
; 27 for 𝑎 u
+
3
, 19 for 𝑑 u
+
3
, 20 for
ℎ u
+
3
, 21 for 𝑘 u
+
3
, 22 for 𝑜 u
+
3
; 23 for 𝑏 g
3
, 22 for
𝑒 g
3
, 𝑖 g
3
, 𝑙 g
3
, 20 for 𝑝 g
3
; 17 for 𝑐 g
+
3
, 22 for
𝑔 g
+
3
, 21 for 𝑘′ g
+
3
, 𝑛 g
+
3
; 19 for 𝑓 u
3
, 22 for 𝑗 u
3
, 21
for m u
3
, 22 for 𝑞 u
3
.
The vibrational levels spacing 𝐺(𝑣 + 1) −
𝐺(𝑣) between the adjacent vibrational states for the 37
electronic states have been calculated. The first six (𝑣 =
0 − 5) are collected in Table 5 for singlet states u
+
1
, u
1
,
g
+
1
, g
1
and Table 6 for triplet u
+
3
, u
3
, g
+
3
, g
3
states; the remaining ones are available upon request. For
the lowest singlet 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
and 𝐹 u
1
states
and triplet u
+
3
, 𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
states, as can be seen
from Tables 5 and 6, the present results are in excellent
agreement with the experimental data of Brown [25], the
MCSCF calculation of Sunil et al.[14], the MCSCF/CI
calculation of Yarkony[4] and the CI results of Jordan[16]
with the deviations less than 0.18% , 0.048%, 0.45% ,
0.38% , 0.06% and 0.28% when 𝑣 = 0, 1, 2, 3, 4, 5
respectively. The present data of 𝐵𝑣 are reported in Tables
7 and 8 respectively for the singlet 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
Fig.1: Potential energy curves of the lowest-lying singlet states of the molecule He2 molecule. The symmetry of
each electronic states is indicated in the panel. Present calculation: continuous curves. Black dash and dotted
curves in the u
+
1
, g
+
1
and g
1
figures; Yarkony [4] and Sunil et al. [15]

and 𝐹 u
1
states and triplet u
+
3
, 𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
state. For convenient comparison with the present results for
𝐴 u
+
1
, 𝐶 g
+
1
, 𝑎 u
+
3
, 𝑏 g
3
and 𝑐 g
+
3
electronic states , we
also tabulate in Tables 7 and 8 the values from theories and
experiments for these states. From Tables 7-8, it is not
difficult to find the excellent agreement between the present
results, theoretical values of Yarkony[4], Sunil et al.[14],
Jordan[16] and experimental data of Brown and Ginter [25]
and Focsa et al. [22] with the errors 0.058 𝑐𝑚−1
,
0.012 𝑐𝑚−1
, 0.023 𝑐𝑚−1
, 0.072 𝑐𝑚−1
, 0.041 𝑐𝑚−1
and
0.029 𝑐𝑚−1
for 𝑣 = 0, 1, 2, 3, 4, 5 respectively.
Unfortunately, no theoretical results, no experiments can be
found in the literature about 𝐺(𝑣) and 𝐵𝑣 for other excited
states of He2 than the singlet 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
and
𝐹 u
1
states and triplet 𝑎 u
+
3
, 𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
. We
cannot make any direct comparison. According to the
excellent agreement between the present spectroscopic
parameters, vibrational levels spacing, the inertial rotation
constant 𝐵𝑣 and the available theoretical and experimental
results, we have reasons to believe that the results presented
in Tables 1-8 4 are accurate and must be reliable.
IV. CONCLUSION
In the present work, the study for the 37 low-lying
singlet u
+
1
, u
1
, g
+
1
, g
1
and triplet u
+
3
,
Fig.2: Potential energy curves of the lowest-lying singlet states of the molecule He2 molecule. The symmetry of each
electronic states is indicated in the panel. Present calculation: continuous curves. Black dash and dotted curves in the
u
+
3
, g
+
3
and g
3
figures; Yarkony [4] and Sunil et al.[15]

u
3
, g
+
3
, g
3
electronic states of He2 molecule
has been performed using the UK R-Matrix molecular codes.
The potential energy curves and the spectroscopic constant
have been determined for the lowest-lying states. The
comparison of our results, for different states, with
theoretical data and experiment shows an excellent
agreement. For excited states other than 𝐴 u
+
1
𝐵 g
1
, 𝐶 g
+
1
, 𝐶 g
+
1
, 𝐹 u
1
, u
+
3
, 𝑏 g
3
, 𝑐 g
+
3
, 𝑓 u
3
,
Vibrational states have been predicted for the first time. For
each vibrational state, the vibrational levels
Table 1 : Spectroscopic constants of He2 singlet u
+
1
, u
1
electronic states
State 𝑹𝒆(Å) 𝑫𝒆(𝒄𝒎−𝟏
) 𝑻𝒆(𝒄𝒎−𝟏
) 𝝎𝒆(𝒄𝒎−𝟏
) 𝝎𝒆𝒙𝒆(𝒄𝒎−𝟏
) 𝑩𝒆(𝒄𝒎−𝟏
) 𝜶𝒆(𝒄𝒎−𝟏
)
2𝑠𝜎 𝐴 u
+
1
This work 1.0419 19185.8442 146 545 1838.45 33.39 7.7024 0.2227
CEPAa
1.0457 19324.0742 1846.33 33.78
MCSCFb
1.0457 19453.4843 1848.10 34.20 7.7030 0.2155
MCSCF/CIc
1.0440 19804 146 120 1860.30
ECGd
19996 146 390 1863.10
Experimente
1.0406 146 365 1861.33 35.28 7.7789 0.2166
Experimentf
1.0404 1861.30 35.20 7.7814 0.2197
3𝑠𝜎 𝐷 u
+
1
This work 1.0671 5607.1225 165 002 1712.55 35.86 7.3905 0.2811
Experimente
1.0694 165 085 1746.43 35.54 7.3650 0.2180
3𝑑𝜎 𝐹 u
+
1
This work 1.0797 4966.1907 165 643 1718.18 42.49 7.2616 0.2479
Experimente
1.0894 165 813 1564.25 40.00 7.0980 0.2460
4𝑠𝜎 𝐻 u
+
1
This work 1.0789 13488.2263 170 850 16691.12 42.72 7.2358 0.2216
Experimente
1.0770 171 951 7.2600 0.2300
4𝑑𝜎 𝐽 u
+
1
This work 1.0790 1323.1801 172 222 1707.89 34.79 7.1980 0.2178
5𝑠𝜎 u
+
1
This work 1.0774 12026.4901 173 548 1708.16 41.05 7.2553 0.2357
5𝑑𝜎 𝑀 u
+
1
This work 1.0797 10656.204 173 667 1712.75 35.81 7.2221 0.2229
Experiment 1.0910 174 748
u
1
3𝑑𝜋 𝐹 u
1
This work 1.0822 4862.95 165 745 1681.95 48.77 7.1920 0.2498
Experimentd
1.0849 5162.4133 165 971 1670.57 40.03 7.1560 0.2350
4𝑑𝜋 𝐽 u
1
This work 1.0817 14502.17 171 181 1691.52 40.32 7.1974 0.2325
Experimentd
1.0908 172 290 7.080
5𝑑𝜋 𝑀 u
1
This work 1.0805 17261.05 173 706 1702.67 37.8620 7.2144 0.2299
Experimentd
1.0910 174 788 7.0700
6𝑑𝜋 u
1
This work 1.0806 18349.05 175 065 1698.76 34.4075 7.2131 0.2283
7𝑑𝜋 u
1
This work 1.0807 18866.41 175 882 1703.47 29.9749 7.2116 0.2215
a
CEPA calculations of Wasilewsli et al [23]
b
MCSCF calculations of Sunil et al [15]
c
MCSCF/CI calculation of yarkony [4]
d
ECG calculation of Komasa [14]
e
Experiment from Huber and Herzberg [9]
f
Experiment from Focsa et al. [22]

and the inertial rotation constants are determined. As a
whole, comparison of our potential energy curves,
spectroscopic constants, vibrational levels and inertial
rotation constants with the available experiments and
theories shows that the present results are both accurate and
reliable. The new excited electronic states may provide a
reliable theoretical basis and information for the
experimental spectral properties related to the electronic
structure for He2 molecule and the potential curves will be
a useful guide for the experimentalist to properly assign the
transitions resulting from the highly dense set of excited
states.
Table 2 : Spectroscopic constants of singlet g
+
1
, g
1
electronic states
)
g
+
1
2𝑝𝜎 𝐶 g
+
1
This work 1.0930 8680.967 157 669 1654.643 43.0382 7.0286 0.2489
CEPAa
1.0970 8380.178 1652.43 28.74
MCSCFb
1.0953 8729.935 1652.90 40.40 7.0202 0.2300
MCSCF/CIc
1.0960 8819 157 108 1655.60
Experimente
1.0917 8862842 157 415 1653.43 41.04 7.0520 0.2150
Experimentf
1.0915 1571.809 7.07067 0.2470
3𝑝𝜎 g
+
1
This work 1.0811 2375.710 1694.27 49.3427 7.2061 0.2590
4𝑝𝜎 𝐺 g
+
1
This work 1.0808 12019.30 168 233 1697.35 47.3762 7.2088 0.2260
5𝑝𝜎 𝐾′ g
+
1
This work 1.0798 11277.42 172 319 1705.64 46.7682 7.2236 0.2291
g
1
2𝑝𝜋 𝐵 g
1
This work 1.0686 20271.92 150 351 1752.974 36.7169 7.37848 0.2337
CEPA 1.0726 20355.86 1744.76 32.59
MCSCF/CI 1.0710 20925 150 012 1764.3
Experimente
1.0667 21219.76 149 914 1765.76 34.39 7.4030 0.2160
Experimentf
1.0672 1766.151 34.586 7.3955 0.2156
3𝑝𝜋 𝐸 g
1
This work 1.0791 14392.23 165 791 1705.918 32.1155 7.2329 0.2270
Experimente
1.0764 165 911 1721.19 34.76 7.2705 0.2156
4𝑝𝜋 𝐼 g
1
This work 1.0804 17227.48 171 186 1699.204 33.2736 7.2151 0.2224
Experimente
1.078 172 266 7.242 0.223
5𝑝𝜋 𝐿 g
1
This work 1.0791 173 692 1705
Experimente
1.079 174 794 7.23 0.222
6𝑝𝜋 𝑃 g
1
This work 1.0808 18364.31 175 027 1709.67 35.4396 7.2096 0.2140
Experimente
1.080 176 160 7.23 0.222
a
CEPA calculations of Wasilewsli et al. [23]
b
MCSCF calculations of Sunil et al. [15]
c
d
e
f

Table 3 : Spectroscopic constants of He2 triplet u
+
3
, u
3
electronic states
State 𝑅𝑒(Å) 𝐷𝑒(𝑐𝑚−1
) 𝑇𝑒(𝑐𝑚−1
) 𝜔𝑒(𝑐𝑚−1
) 𝜔𝑒𝑥𝑒(𝑐𝑚−1
) 𝐵𝑒(𝑐𝑚−1
) 𝛼𝑒(𝑐𝑚−1
)
u
+
3
2𝑠𝜎 𝑎 u
+
3
This work 1.0459 15151.723 144 192 1787.862 42.3944 7.6981 0.2467
CEPAa
1.0483 15057.039 1816.00 34.50
MCSCFb
1.0504 15312.362 1794.50 36.40 7.6342 0.2291
MCSCF/CIc
1.0500 15751 143 907 1808.2 38.89
Experimente
1.0457 15805.519 144 048 1808.56 38.21 7.7036 0.228
Experimentf
1.0454 1808.50 37.812 7.7076 0.2340
3𝑠𝜎 𝑑 u
+
3
This work 1.0705 12822.321 164 278 1744.252 34.9554 7.3498 0.2206
Experimente
1.0712 164 479 1728.01 36.13 7.3412 0.2244
3𝑑𝜎 𝑓 u
+
3
This work 1.0749 1713.78 37.6847
Experimente
1.0914 165 685 1635.77 44.41 7.071 0.246
4𝑠𝜎 ℎ u
+
3
This work 1.0754 4282.231 170 628 1720.027 38.7203 7.2828 0.2347
Experimente
1.077 180884 1637.9 7.264 0.23
4𝑑𝜎 𝑗 u
+
3
This work 1.0846 170 628
Experimente
171323
5𝑠𝜎 𝑘 u
+
3
This work 1.0766 11611.005 173 427 1716.256 38.8348 7.2670 0.2370
Experimente
1.079 173698 1635.3 7.232 0.23
5𝑑𝜎 𝑚 u
+
3
This work 1.0815
Experimente
1.091 173730
u
3
3𝑑𝜋 𝑓 u
3
This work 1.0891 2886.745 165 674 1656.729 46.3226 7.1948 0.2482
Experimente
1.0865 165 877 1661.48 44.79 7.136 0.235
4𝑑𝜋 𝑗 u
3
This work 1.0849 13840.001 171 198 1654.725 7.1557 0.2361
Experimente
1.0827 171 402 1680.94 40.81 7.1860 0.2296
5𝑑𝜋 𝑚 u
3
This work 1.0818 17017.051 173 674 1692.115 7.1972 0.2287
Experimente
1.091 174 778 7.07
6𝑑𝜋 𝑞 u
3
This work 1.0809 18226.804 175 047 1701.809 7.2074 0.2241
Experimente
1.0898 176 169 7.092
7𝑑𝜋 u
3
This work 1.0804 18818.942 175 848 1709.569 7.2146 0.2196
a
b
c
d
e
f

Table 4 : Spectroscopic constants of He2 triplet g
+
3
, g
3
electronic states
)
g
+
3
2𝑝𝜎 𝑐 g
+
3
This work 1.0974 4158.907 155 183 1570.776 55.46 6.9990 0.3061
CEPAa
1.0980 4015.210 1644.85 35.04
MCSCFb
1.1004 4606.30 1582.60 52.50 6.9322 0.2560
MCSCF/CIc
1.1030 4858 154 703 1589.5
Experimentd
1.0977 4802.16 155 053 1583.85 52.74 7.0048 0.3105
Experimente
1588.34 54.16 6.9900 0.2638
3𝑝𝜎 g
+
3
This work 1.0825 1064.052 1676.084 55.53 7.1877 0.2616
Experimentd
4𝑝𝜎 𝑔 g
+
3
This work 1.0814 10738.52 1694.519 44.24 7.2016 0.2378
Experimentd
1.0801 1589.92 41 7.2207 0.2478
5𝑝𝜎 𝑘′ g
+
3
This work 1.0811 10924.47 1700.933 44.16 7.2067 0.2234
Experimentd
1.0684 1686.90 38.10 7.379 0.349
g
3
2𝑝𝜋 𝑏 g
3
This work 1.0640 19403.571 149 171 1769.593 40.4618 7.4389 0.2508
CEPAa
1.0689 19341.562 1756 33.22
MCSCF/CIc
1.0681 19947 148 943
Experimentd
1.0635 20250.93 148 835 1769.07 35.02 7.4473 0.2196
Experimente
1.0645 35.249 7.4334 0.2191
3𝑝𝜋 𝑒 g
3
This work 1.0758 20343.64 164 695 1732.021 35.0069 7.2776 0.2162
Experimentd
1.0754 165 598 1721.22 34.970 7.2838 0.2215
4𝑝𝜋 𝑖 g
3
This work 1.0807 20626.07 170 065 1703.236 34.5463 7.2114 0.2163
Experimentd
1.0785 171 290 1637.94 35.25 7.242 0.223
5𝑝𝜋 𝑙 g
3
This work 1.0817 20721.44 172 553 1701.272 33.8314 7.1979 0.2128
Experimentd
1.0797 173 884 1633.96 35.25 7.226 0.222
6𝑝𝜋 𝑞 g
3
This work 1.0811 20729.43 173 937 1705.911 31.3335 7.2058 0.2115
Experimentd
1.0801 175 281 1701.18 35.35 7.220 0.224
a
b
c
d
e

Table 5 : Vibrational energy levels spacing 𝐸𝑣+1 − 𝐸𝑣 (c𝑚−1
) for u
+
1
, g
1
, g
+
1
and u
1
singlet States of He2
State 𝑣 0 1 2 3 4 5
2𝑠𝜎 𝐴 u
+
1
This work 1788.2443 1718.0851 1657.9791 1597.9264 1507.9269 1427.9807
MCSCFa
1779.20 1708.85 1637.75 1566.17 1492.43 1417.30
MCSCF/CIb
1789.76 1719.25 1648.46 1577.17 1503.93 1429.25
ECGc
1791.56 1720.38 1648.05 1575.23 1501.73 1426.82
Experimentf
1790.76 1719.69 1647.98 1575..40 1501.90
3𝑠𝜎 𝐷 u
+
1 This work 1620.0748 1529.4481 1440.7501 1353.9809 1269.1405 1186.2289
3𝑑𝜎 𝐹 u
+
1 This work 1633.8730 1550.7592 1468.8867 1388.2556 1308.8658 1230.7173
4𝑠𝜎 𝐻 u
+
1 This work 1624.3542 1553.9856 1479.8557 1401.9646 1320.3123 1234.8988
4𝑑𝜎 𝐽 u
+
1 This work 1637.6142 1566.1002 1493.2963 1419.2026 1343.8191 1267.1456
5𝑠𝜎 u
+
1 This work 1632.0840 1555.6589 1478.8686 1401.7133 1324.1929 1246.3074
5𝑑𝜎 𝑀 u
+
1 This work 1640.6387 1567.6437 1493.7295 1418.8960 1343.1433 1266.4773
g
1
2𝑝𝜋 𝐵 g
1 This work 1640.2003 1677.8059 1514.3799 1449.9221 1384.4325 1317.9112
3𝑝𝜋 𝐸 g
1 This work 1659.7599 1587.8686 1514.8809 1440.7968 1365.6162 1289.3392
4𝑝𝜋 𝐼 g
1 This work 1634.9500 1566.0122 1496.3942 1426.0959 1355.1173 1283.4585
4𝑓𝜋 g
1 This work 1632.8916 1563.1812 1492.3829 1420.4965 1347.5222 1273.4598
5𝑝𝜋 𝐿 g
1 This work 1630.3919 1560.4173 1489.2295 1416.8287 1343.2148 1268.3878
5𝑓𝜋 g
1 This work 1636.8370 1565.9909 1494.0392 1420.9818 1346.8188 1271.5501
6𝑝𝜋 𝑃 g
1 This work 1641.2428 1571.8551 1501.4703 1430.0884 1357.7094 1284.3334
6𝑓𝜋 g
1 This work 1635.0122 1566.2296 1496.4363 1425.6324 1353.8178 1280.9925
g
+
1
2𝑝𝜎 𝐶 g
+
1
This work 1579.1033 1494.1395 1404.7647 1305.9818 1198.7898 1070.1888
MCSCFa
1572.60 1491.13 1405.44 1311.47 1206.55 1081.32
VBPAd
1573.11 1488.02 1400.14 1307.73 1203.24 1070.4
Experimentf
1571.82 1489.26 1402.11 1308.17 1202.33
3𝑝𝜎 g
+
1 This work 1603.2510 1511.4271 1418.7640 1325.2617 1230.9203 1135.2617
4𝑝𝜎 g
+
1 This work 1627.9266 1556.6480 1483.4340 1408.2845 1331.1997 1252.1795
4𝑓𝜎 𝐶 g
+
1 This work 1639.9846 1566.8975 1492.5799 1416.7319 1339.6535 1261.2446
5𝑝𝜎 𝐶 g
+
1 This work 1632.6517 1558.4528 1482.9929 1406.2721 1328.2904 1249.0477
5𝑓𝜎 𝐶 g
+
1 This work 1636.2473 1562.3533 1487.5834 1411.9375 1335.4156 1258.0177
u
1
3𝑑𝜋 𝐹 u
1
This work 1598.2935 1514.1571 1429.5253 1344.3982 1258.7758 1172.6581
CIe
1604 1516 1334
4𝑑𝜋 𝐽 u
1 This work 1616.1537 1540.2523 1463.7894 1386.7650 1309.1791 1231.0317
5𝑑𝜋 𝑀 u
1 This work 1627.7894 1552.6459 1476.8672 1400.5718 1323.7596 1246.4307
6𝑑𝜋 u
1 This work 1627.0210 1555.1979 1483.2895 1411.2958 1339.2169 1267.0527
7𝑑𝜋 u
1 This work 1633.2980 1562.0982 1489.8304 1416.4947 1342.0912 1266.6197
a
b
MCSCF/CI calculation of yarkony[4]
c
d
Valence Bond pseudopotential approcach (VBPA) of Jordan [16]
e
CI Method of Chabalowski [24]
f
Experiment of Brown et Ginter[26]

Table 6 : Vibrational energy levels spacing 𝐸𝑣+1 − 𝐸𝑣 (c𝑚−1
) for u
+
3
, g
3
, g
+
3
and u
3
Triplet States of He2
State 𝑣 0 1 2 3 4 5
2𝑠𝜎 𝑎 u
+
3
This work 1714.1754 1650.6992 1589.6591 1531.0552 1474.8874 1421.1559
MCSCFa
1720.38 1643.05 1563.88 1482.53 1397.10 1308.21
MCSCF/CIb
1731.05 1653.95 1576.24 1496.09 1409.44 1321.50
CIc
1736 1655 1577 1506 1412 1312
Experimentd
1732.14 1654.31 1574.31 1492.76 1408.11
3𝑠𝜎 𝑑 u
+
3 This work 1673.2273 1600.2297 1525.1740 1448.0604 1368.8889 1287.6594
3𝑑𝜎 𝑓 u
+
3 This work 1584.7543 1528.9654 1500.8587 1500.4343
4𝑠𝜎 ℎ u
+
3 This work 1642.3289 15841737 1485.5422 1406.4343 1326.8501 1246.7896
4𝑑𝜎 𝑗 u
+
3 This work 1605.1672 2537.6206 1470.5430 1403.9345 1337.7949 1272.1243
5𝑠𝜎 𝑘 u
+
3 This work 1638.3830 1560.1509 1481.5437 1402.5616 1323.2043 1243.4721
5𝑑𝜎 𝑚 u
+
3 This work 1629.2474 1557.1552 1484.3147 1410.7258 1336.3887 1261.3032
6𝑠𝜎 𝑜 u
+
3 This work 1630.3698 1557.1924 1483.7196 1409.9512 1335.8874 1261.5281
6𝑑𝜎 𝑑 u
+
3 This work 1626.1563 1562.3987 1494.6169 1422.8108 1346.9805 1267.1260
g
3
2𝑝𝜋 𝑏 g
3
This work 1682.7091 1596.7356 1511.7126 1427.6401 1344.518 1262.3468
MCSCF/CIb
1696.50 1625.17 1550.60 1478.25 1410.12 1334
CIc
1697 1629 1558 1485 1416 1342
Experimentd
1698.87 1628.25 1557.62
3𝑝𝜋 𝑒 g
3 This work 1662.1265 1591.4575 1519.9808 1447.6964 1374.6043 1300.7046
4𝑝𝜋 𝑖 g
3 This work 1634.9500 1566.0122 1496.3942 1426.0959 1355.1173 1283.4585
4𝑓𝜋 g
3 This work 1634.8957 1568.3629 1500.9208 1432.5693 1363.3083 1293.1380
5𝑝𝜋 𝑙 g
3 This work 1634.4627 1566.7118 1497.9783 1428.2623 1357.5637 1285.8826
5𝑓𝜋 g
3 This work 1641.5362 1569.5846 1496.7210 1422.9454 1348.2578 1272.6582
6𝑝𝜋 𝑝 g
3 This work 1638.9041 1570.2252 1499.8019 1427.6341 1353.7218 1278.0651
g
+
3
2𝑝𝜎 𝑐 g
+
3
This work 1477.7705 1367.983 1240.5562 1096.0440 934.2619 785.2097
MCSCFa
1479.39 1371.63 1247.23 1093.80 872.54
Experimentd
1480.02 1371.72 1247.56 1095.84 882.30
3𝑝𝜎 g
+
3 This work 1590.3228 1505.4479 1421.4982 1338.4736 1256.3742 1175.2000
4𝑝𝜎 𝑔 g
+
3 This work 1620.4046 1545.8592 1470.8643 1395.4199 1319.5261 1243.1827
4𝑓𝜎 g
+
3 This work 1638.2468 1562.4306 1486.3166 1409.9047 1333.1949 1256.1873
+
3 This work 1630.3905 1558.9147 1486.4653 1413.0425 1338.6462 1262.2763
5𝑓𝜎 g
+
3 This work 1639.9878 1565.7257 1490.5378 1414.4240 1337.3845 1259.4191
u
3
3𝑑𝜋 𝑓 u
3 This work 1559.9702 1464.5234 1370.4452 1277.7355 1186.3944 1096.4219
4𝑑𝜋 𝑗 u
3 This work 1583.7719 1512.5752 1441.1247 1369.4203 1297.4620 1225.2499
5𝑑𝜋 𝑚 u
3 This work 1618.3158 1543.9267 1468.9215 1393.3004 1317.0633 1240.2103
6𝑑𝜋 𝑞 u
3 This work 1629.9540 1558.1398 1486.3683 1414.6395 1342.9324 1271.3099
7𝑑𝜋 u
3 This work 1638.4887 15566.2396 1492.7709 1418.0824 1342.1744 1265.0467
a
b
MCSCF/CI calculation of yarkony[4]
c
CI Method of Chabalowski [24]
d
Experiment of Brown et Ginter[26],

Table 7 : Rotational constant 𝐵𝑣 (c𝑚−1
) for u
+
1
, g
1
, g
+
1
and u
1
singlet States of He2
State 𝑣 0 1 2 3 4 5
2𝑠𝜎 𝐴 u
+
1
This work 7.64806 7.43851 7.24214 7.05895 6.78895 6.53212
ECGa
7.67010 7.44750 7.2128 6.9857 6.7505 6.5096
VBPAb
7.66800 7.44420 7.2174 6.9876 6.753 6.510
Experimentc
7.70600 7.44670 7.2194 6.9870 6.748 6.503
Experimentd
7.67101 7.44692
3𝑠𝜎 𝐷 u
+
1 This work 7.25567 6.97204 6.68584 6.39706 6.10571 5.81179
3𝑑𝜎 𝐹 u
+
1 This work 7.13717 6.88501 6.62862 6.35799 6.10313 5.83402
4𝑠𝜎 𝐻 u
+
1 This work 7.12522 6.90513 6.68654 6.46945 6.25346 6.03976
4𝑑𝜎 𝐽 u
+
1 This work 7.08861 6.86699 6.64156 6.41232 6.17927 5.94241
5𝑠𝜎 u
+
1 This work 7.13709 6.89545 6.65699 6.41263 6.16539 5.91526
5𝑑𝜎 𝑀 u
+
1 This work 7.11024 6.88379 6.65378 6.42023 6.18312 5.94246
g
1
2𝑝𝜋 𝐵 g
1 This work 7.19654 6.986111 6.77652 6.56775 6.35982 6.15273
3𝑝𝜋 𝐸 g
1 This work 7.16980 6.94564 6.71769 6.48594 6.25040 6.01106
4𝑝𝜋 𝐼 g
1 This work 7.11919 6.89042 6.65987 6.42754 6.19344 5.95755
4𝑓𝜋 g
1 This work 7.10497 6.88256 6.65964 6.43623 6.21231 5.98789
5𝑝𝜋 𝐿 g
1 This work 7.10413 6.88391 6.66587 6.45001 6.23633 6.02484
5𝑓𝜋 g
1 This work 7.10794 6.88610 6.66283 6.43813 6.21200 5.98443
6𝑝𝜋 𝑃 g
1 This work 7.10216 6.88431 6.66257 6.43695 6.20744 5.97405
6𝑓𝜋 g
1 This work 7.09528 6.87739 6.65680 6.43350 6.20749 5.97877
g
+
1
2𝑝𝜎 𝐶 g
+
1
This work 6.97163 6.71222 6.43761 6.14780 5.84280 5.52259
VBPAb
6.9463 6.6967 6.4364 6.1632 5.8690 5.5240
Experimente
6.9450 6.7000 6.4410 6.1670 5.8670 5.5300
3𝑝𝜎 2 g
+
1 This work 7.07548 6.80743 6.53032 6.24414 5.94888 5.62456
4𝑝𝜎 𝐺 g
+
1 This work 7.09580 6.86991 6.64415 6.41850 6.19297 5.96756
4𝑓𝜎 g
+
1 This work 7.11355 6.88806 6.65772 6.42253 6.18248 5.93759
5𝑝𝜎 𝐾′ g
+
1 This work 7.10877 6.87735 6.64363 6.40763 6.16934 5.92877
5𝑓𝜎 g
+
1 This work 7.11878 6.88729 6.65355 6.41758 6.17938 5.93894
u
1
3𝑑𝜋 𝐹 u
1 This work 7.06636 6.81065 6.54907 6.28160 6.00826 5.72904
4𝑑𝜋 𝐽 u
1 This work 7.08064 6.84441 6.60442 6.36069 6.11321 5.86199
5𝑑𝜋 𝑀 u
1 This work 7.09908 6.86620 6.63041 6.39171 6.15009 5.90556
6𝑑𝜋 u
1 This work 7.09900 6.87128 6.64414 6.41760 6.19165 5.96629
7𝑑𝜋 u
1 This work 7.10096 6.88043 6.66092 6.44242 6.22493 6.00846
a
b
Valence Bond pseudopotential approcach (VBPA) of Jordan [16]
c
Experiment of Brown et Ginter[26]
d
e
Experiment from Ginter [25]

REFERENCES
[1] A. I. J. Burgmans, J. M. Farrar, and Y. T. Lee, J. Chem. Phys.,
Vol. 64, pp. 1345, 1976.
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[3] K. Huber and G. Herzberg, in Molecular Spectra, Molecular
structure, Vol. 4. Constants of diatomic Molecules, Van
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[4] D. R. Yarkony “ On the quenching of helium 2 2
S: Potential
energy curves for, and nonadiabatic, relativistic, and
radiative coupling between, the a 
3
u
+
, A 
1
u
+
, 𝐵 g
3
,
Table 8 : Rotational constant 𝐵𝑣 (c𝑚−1
) for u
+
3
, g
3
, g
+
3
and u
3
triplet States of He2
State 𝑣 0 1 2 3 4 5
2𝑠𝜎 𝑎 u
+
3 This work 7.57637 7.34312 7.12337 6.91710 6.72433 6.54506
Experimenta
7.58914 7.34874 7.10175
3𝑠𝜎 𝑑 u
+
3 This work 7.23884 7.01339 6.78313 6.54806 6.30819 6.06352
3𝑑𝜎 𝑓 u
+
3 This work 7.12114 6.82764 6.59118 6.41176 6.28938 6.22404
4𝑠𝜎 ℎ u
+
3 This work 7.16484 6.92540 6.68124 6.43235 6.17875 5.92042
4𝑑𝜎 𝑗 u
+
3 This work 7.04669 6.82075 6.59602 6.37250 6.15019 5.92910
5𝑠𝜎 𝑘 u
+
3 This work 7.14804 6.90736 6.66298 6.41489 6.16311 5.90763
5𝑑𝜎 𝑚 u
+
3 This work 7.08884 6.86226 6.63254 6.39970 6.16372 5.92462
6𝑠𝜎 𝑜 u
+
3 This work 7.12082 6.88906 6.65652 6.42320 6.18909 5.95420
6𝑑𝜎 𝑑 u
+
3 This work 7.06020 6.85960 6.65572 6.44856 6.23813 6.02443
g
3
2𝑝𝜋 𝑏 g
3 This work 7.31282 7.05678 6.79555 6.52913 6.25753 5.98073
Experimenta
7.32343 7.10061
3𝑝𝜋 𝑒 g
3 This work 7.16903 6.94914 6.72558 6.49835 6.26745 6.03287
4𝑝𝜋 𝑖 g
3 This work 7.10281 6.88334 6.66077 6.43511 6.20635 5.97451
4𝑓𝜋 g
3 This work 7.09250 6.87799 6.66103 6.44163 6.21977 5.99546
5𝑝𝜋 𝑙 g
3 This work 7.09112 6.87523 6.65629 6.43430 6.20925 5.98116
5𝑓𝜋 g
3 This work 7.11389 6.89183 6.66766 6.44137 6.21296 5.98244
6𝑝𝜋 𝑝 g
3 This work 7.09974 6.88553 6.66856 6.44883 6.22634 6.00110
6𝑓𝜋 g
3 This work 7.07616 6.78037 6.47305 6.15420 5.82381 5.12845
g
+
3
2𝑝𝜎 𝑐 g
+
3 This work 6.84315 6.51479 6.16414 5.79121 5.39600 4.97850
Experimenta
6.85395 6.55682 6.22636
3𝑝𝜎 2 g
+
3 This work 7.05653 6.79180 6.52393 6.25293 5.97878 5.70150
4𝑝𝜎 𝑔 g
+
3 This work 7.08536 6.85084 6.61357 6.37355 6.13079 5.88527
4𝑓𝜎 g
+
3 This work 7.12159 6.88490 6.64707 6.40809 6.16798 5.92672
+
3 This work 7.094472 6.86879 6.64031 6.40928 6.17572 5.93960
5𝑓𝜎 g
+
3 This work 7.11295 6.88359 6.65055 6.41381 6.17339 5.92928
u
3
3𝑑𝜋 𝑓 u
3 This work 7.05120 6.75975 6.46272 6.16011 5.85191 5.53813
4𝑑𝜋 𝑗 u
3 This work 7.03778 6.80277 6.56892 6.33621 6.10465 5.87425
5𝑑𝜋 𝑚 u
3 This work 7.08244 6.84993 6.61370 6.37372 6.13001 5.88257
6𝑑𝜋 𝑞 u
3 This work 7.09602 6.86846 6.63745 6.40298 6.16506 5.92368
7𝑑𝜋 u
3 This work 7.10442 6.88154 6.65545 6.42613 6.19358 5.71882
a
Experiment of Focsa et al. [22]

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Potential energy curves, spectroscopic parameters, vibrational levels and molecular constants for 37 low-lying electronic states of He2

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Potential energy curves, spectroscopic parameters, vibrational levels and molecular constants for 37 low-lying electronic states of He2