Objects for Introducing Communication, A.I based on a Territorial Intelligence Process

Yann Bertacchini

To cite this version:

Territorial Intelligence Hypotheses Proofreading assumptions: analysis of a STICA under territorial intelligence hypotheses.

  Yann Bertacchini1*, Paul Déprez and Paul Rasse.The Territorial Intelligence Process: The Informational Perimeter Study of a 21 Local Agenda for Building an Ecology System of Communication British Journal of Education, Society & Behavioural Science 9(4): 248-264, 2015, Article no.BJESBS.2015.143 ISSN: 2278-0998 SCIENCEDOMAIN international www.sciencedomain.org

	7 Objects for Introducing Communication, A.I based on a Territorial
		Intelligence Process
	Dr Yann Bertacchini (Emeritus & European Expert)
	y.bertacchini@gmail.com & http://www.yann-bertacchini.eu
	Gate 3 :Aeras of Communication, Components of a STICA & proof
		reading Assumptions
		Components of a STICA
	A: Area of social production	B: Area of social cooperation	C: Production area /
	cooperation / information exchange	production / Capture information,	networking, networking & skills
		Gain granted	transfer
	1: media product/ mediation vectors:	2: media product / mediation	3: media product / mediation
	technical 2017. sic_01835102 Dimension/exchanged information	vectors: Dimension Technical / Gain	vectors: Dimension technical / network creation and skills
			transfer

Yann Bertacchini. 7 Objects for Introducing Communication, A.I based on a Territorial Intelligence Process: Gate 3 :Aeras of Communication, Components of a STICA & proof reading Assumptions.


Asian Journal of Humanities and Social Studies

	7 Objects for Introducing Communication, A.I based on a Territorial
	Intelligence Process
	Dr Yann Bertacchini (Emeritus & European Expert)
	y.bertacchini@gmail.com & http://www.yann-bertacchini.eu
	Gate 2 : A Territorial Intelligence Definition seen through an Ecology
	Point of View of Communication
	A Territorial Intelligence Definition
	"an information and anthropological process, regular and continuous, initiated by local actors,
	group dispersed in
	such a territory ». "And stress it will be to achieve a description of transactional human
	activity, knowledge networks and systems."

physically present and / or distant, who intend to appropriate land resources by mobilizing and transforming the energy of the territorial system into a project capacity"

[7,p3], [7a]

.

Asian Journal of Computer and Information Systems

(ISSN: 2321 -5658),Volume 04-Issue 05, October 2016, Asian Online Journals (www.ajouronline.com) 155, Territorial Intelligence & Artificial Intelligence : On Discussion Ecology of Communication We will do it within relation of the proposal for a Ecology of Communication exposed and demonstrated by Abraham Moles (1995) in a book "Structural Theory of Communication & Society" whom we quote some extracts p.94 and following "Ecology Science communication is the relationships and interactions between different species of communications activities within a closed area such as the time available for individual or social (ISSN: 2321 -2799), Volume 04 -Issue

05, October 2016, Asian Online Journals (www.ajouronline.com) 353,

The Territorial Intelligence Process: A Humanistic Path and a Realistic Mediation for Development of Hybrid Territories


Djamal Rabli
email: djamal.rabli@gmail.com

Ronald Mccarroll
email: ronald_mccarroll@upmc.fr

Theoretical study of the low-lying adiabatic states of the NaLi + molecular ion

Keywords: model potential, NaLi +, ab-initio, adiabatic energies, molecular spectroscopic constant

, employing model potential methods, is showing a serious disagreement concerning several molecular states. In particular, the low-lying states 2 2 Σ + , 4 2 Σ + , 6 2 Σ + , 8 2 Σ + , 10 2 Σ + and 4 2 Π obtained by Magnier and Frécon, are found to be repulsive whereas they are attractive when ab-initio methods are used.

To clarify the origin of such a disagreement, in this work, the NaLi + cation is re-investigated within the framework of the model potential approach. Adiabatic energies and corresponding molecular spectroscopic constants of states dissociating up to the limit Li + +Na(4d) are computed. A good agreement with the previous ab-initio calculations is observed.

Introduction

For the calculation of potential energy surfaces, most ab-initio techniques make use of Gaussian-type orbitals basis functions. In such a basis set, matrix elements involving the electron-electron repulsion terms in the electronic Hamiltonian can be calculated analytically. On the other hand, such matrix elements in a Slater-type basis involve a numerical integration. However, for certain types of problems, a Slater-type basis does have certain particular virtues for the description of long-range interactions involving excited Rydberg states. For such states, the passive electrons may be represented by a model potential, designed to reproduce the experimental energies of the interacting atoms or ions. Molecules having only effective active electron provide a way to test the effectiveness of model potential methods for the calculation of excited electronic states, for which a Slater-type basis is well adapted. Such methods have proved to be very successful in providing an accurate description of avoided crossings of energy curves of excited adiabatic states. In practice, there are two types of systems which are amenable to the use of model potential techniques, namely the alkali molecular ions and the alkali-rare gas systems, both of which involve one active electron . Typical homo-nuclear alkali molecular ions such as Li + 2 , Na + 2 , K + 2 ,. . . , and heteronuclear species such as LiNa + , NaK + , LiK + ,. . . , have been the subject of several extensive studies [3,4,5,6,7,8,[START_REF] Azizi | AIP Conference Proceedings[END_REF]. Typical alkali-rare gas, such as Na-He , Na-Ne , Na-Xe require a special treatment since in order to take account of the Pauli principle, it is necessary to preclude the active electron from the closed shell implicitly [START_REF] Valiron | [END_REF]11]. An extensive review of more recent work has been presented by Ben Salem et al. [12].

In this paper, we will be concerned with the LiNa + molecular ion. From the experimental prespective, direct measurements of crossed-beam reaction rate coefficients for the production of NaLi + ions, have been reported by Johnson et al. [13]. Several other experimental studies involving indirectly this molecular ion, have been motivated by the measurement of cross sections of charge transfer process which occurs in Li + /Na collisions [14,15,16,17,18]. From the theoretical point of view, besides computation of charge transfer cross sections which has motivated several studies [19,20,21,22,23], theoretical determination of the adiabatic energy curves of the NaLi + ion, has also received considerable attention. Indeed, the ground state X 2 Σ + of this system has been computed in Hartree-Fock approximation by Bertoncini et al. [24], while the first systematic calculation of both the ground and excited states was carried out by Magnier and Frécon [2] using a model potential originally proposed by Klapisch [25] to describe the interaction of the valence electron with the lithium and sodium cores. Results were presented of the first eighteen low-lying molecular states (ten Σ + , six Π and two ∆).

A little later, Berriche [1] developed a method combining ab-initio methods together with a non-empirical pseudo-potential to describe the Li + and Na + cores and taking into account the core-valence correlation as a correction. This method was used to calculate the adiabatic energies of the ground X 2 Σ + state and of all the excited molecular states dissociating up to the Na(4d)+Li + limit. Subsequently, Khelifi et al. [26], following the formalism of Foucrault et al. [27] reproduced the spectroscopic constants of both, the NaLi alkali dimer and the NaLi + cation. While different experimental and theoretical results show a global agreement for the X 2 Σ + ground state, the lack of experimental data for the excited states of the NaLi + system makes it difficult to reach a final conclusion. However, there are significant disagreements between some of the theoretical results. Comparison between the ab-initio data [1,26] and those of Magnier and Frécon [2] based on model potential techniques, exhibit a significant number of serious disagreement concerning several excited states. Some states are found to be repulsive by Magnier and Frécon [2] but attractive when ab initio techniques are used. According to the model potential results [2], the molecular states 2 2 Σ + , 4 2 Σ + , 6 2 Σ + , 8 2 Σ + , 10 2 Σ + and 4 2 Π states do not exhibit any energy minimum whereas a well pronounced energy minimum is observed for these states in the ab-initio approach [1].

Bearing in mind that the disagreement between the ab-initio [1,26] and the model potential results [2] occurs for states for which the energy minimum occurs at large equilibrium distances (14 < R e < 44 a.u), where model potential methods are expected to provide an accurate description of the system, in the present work we re-investigate the NaLi + system using the model potential of Klapisch [25], previously employed by Magnier and Frécon [2]. We aim to clarify the origin of these existing disagreements: either due to a numerical artifact, or more seriously to some unknown limitation of either the ab-initio or model potential methods.

Except where stated, atomic units will be used throughout.

Theory

The interaction of the electron of valence with the closed shells, Li + (1s 2 ) and Na + (2p 6 ) cores, is described by model potentials V Na/Li model previously used in the work by Magnier and Frécon [2] and originally proposed by Klapisch [25] in the form:

V model (r) = - q r - Z -1 r (e -α 1 r + βre -α 2 r ), (1)
where r denotes the radial distance of the electron form the nucleus, q the ionic core charge and Z the atomic number. The set of parameters (α, β) shown in Tab. [25] has been optimised such that the eigenvalues of the model atomic Hamiltonian

H model = T + V model , ( 2
)
where T is the kinetic energy operator, reproduce the experimental energies of the ground and the first few excited states of the corresponding ion, Li + and Na + in the present study.

Fixing the lithium and sodium cores at A and B positions respectively as shown in Figure 1, the NaLi + molecular cation is then treated as a set of two closed shells Li + (1s 2 ) and Na + (2p 6 ) cores and a single active electron moving in the field created by the two ionic cores, whose position is described in the Born- Oppenheimer approximation [START_REF] Born | [END_REF], by the electronic Hamiltonian

e - t i E B( Na + ) A( Li + ) x x r A r B R
H e = T + V Li + model (r A ) + V Na + model (r B ) + U core , (3)
where T denotes the electronic kinetic energy operator, r A and r B the radial distances of the active electron from the cores Li + and Na + respectively. Since we are concerned with intermediate and large internuclear distances only (R ≥ 4 a.u), U core in previous equation ( 3), is mainly the nuclei repulsion modified by polarization terms namely:

U core = q Li .q Na R - α Li d + α Na d 2R 4 - α Li q + α Na q 2R 6 , (4)
where q Li = q Na =1 denotes the ionic core charge, α d and α q are dipole and quadrupolar polarizabilities, respectively. In the present study, as in the work by Magnier and Frécon [2], we have used α Li d = 0.1915 a.u [START_REF] Müller | [END_REF], α Li q = 0.0156 a.u [31] for lithium, and α Na d = 0.9965 a.u [32] , α Na q = 0.376 a.u [32] for sodium. The spectrum of the effective Hamiltonian H e defined in equation ( 3) is determined by conventional variational techniques, using a basis set of Slater-type orbitals f sto , expressed in prolate spheroidal coordinates

λ ∈ [1, ∞], µ ∈ [-1, 1] and , φ ∈ [0, 2π] where λ = 1 2R (r A + r B ), µ = 1 2R (r A -r B ), φ, (5)
is the azimuthal angle.

In this prolate spheroidal coordinates system, the basis functions of Slater-type orbitals take the form:

λ, µ, φ | f sto = A[(λ 2 -1)(1 -µ 2 )] Λ 2 λ l µ k e -R 2 ζ(λ+ µ) e imφ , (6)
where A denotes a normalisation factor, a parameter that takes the values ±1 depending on whether the orbital is centred on lithium or sodium cores, (l, k) integers, ζ a variational parameter describing the decay of the orbital, m the projection of the electronic angular momentum on the z-axis (coinciding with R) and Λ =| m |=0,1,2,. . . for Σ + , Π and ∆ molecular states respectively.

Results

We have computed the adiabatic potential energies of the attractive ground state dissociating into a sodium ion Na + and a lithium atom in its ground state Li(2s), and of the manifold of excited states correlated in the asymptotic region to Na + +Li(1s 2 ,nl), nl=2p, 3s, 3p, 3d, 4s, 4d and Li + +Na(2p 6 ,nl), nl=3s, 3p, 4s, 3d, 4p, 5s, 4d. 3.1. Σ + states Graphics showing our adiabatic potential energies curves for the 2 Σ + states, are presented in Fig. 2, for internuclear separations up to 50 a.u while comparison of the obtained spectroscopic constants with available values resulting from different approaches is shown in Table 3.

For the X 2 Σ + ground state, present calculations yield a dissociation energy D e =8331 cm -1 and an equilibrium distance R e =6.26 a.u. These values may be compared to the ab-initio results of Berriche [1], D e =8061 cm -1 and R e =6.37 a.u, and to those of Khelifi et al. [26], D e =8155 cm -1 and R e =6.29 a.u. Our vibration constants ω e =194.88 cm -1 and ω e χ e = 1.14 cm -1 , also compare well to the ab-initio ones [1], ω e =192.98 cm -1 and ω e χ e =1.11 cm -1 , however due to the nonavailability of the experimental values, we simply mention that our dissociation energy which is slightly greater than other available theoretical values, compares favourably to the experimental value [START_REF] Huber | Molecular Spectra and Molecular Structure[END_REF] predicted in the range D e =7985±242cm -1 .

On the other hand, our potential energy curve relative to the 2 2 Σ + state exhibits an energy minimum occurring at an equilibrium internuclear distance R e =14.83 a.u, with a corresponding dissociation energy D e =307 cm -1 and vibration constants ω e =36.984 cm -1 and ω e χ e =1.115 cm -1 . Therefore, contrary to the conclusion of Magnier and Frécon [2], and as predicted by previous ab-initio methods [1,26], present study confirms the attractive behaviour of the 2 2 Σ + state.

For the 3 2 Σ + state, our calculations give a dissociation energy D e =1488 cm -1 , an equilibrium distance R e = 13.65 a.u and vibration constants ω e =57.961 cm -1 and ω e χ e =0.564 cm -1 . As shown in Table 3, these values are in good agreement with those of Berriche [1] resulting from an ab-initio calculation.

On the other hand, for the 4 2 Σ + state, contrary to the conclusion of Magnier and Frécon [2], the present study clearly indicates that a such state is attractive with a dissociation energy D e =867 cm -1 , an equilibrium distance R e =18.90 a.u and vibration constants ω e = 38.139 cm -1 and ω e χ e = 0.419 cm -1 . While those new results agree with the ab-initio ones of Berriche [1], our vertical excitation T e = 26476 cm -1 , remains about 300 cm -1 greater than the ab-initio value. This is due to our ground state which seems to be about 300 cm -1 deeper than the value predicted by ab-initio methods.

For the 5 2 Σ + state which has also been generated in the present work, our results show that this state has an equilibrium distance R e =22.43 a.u and a dissociation energy D e =2289 cm -1 . As shown in Table 3, those values compare well to the ab-initio results of Berriche [1], D e =2262 cm -1 , R e =22.41 a.u and to the ones of Khelifi et al. [26], D e =2194 cm -1 and R e =22.47 a.u.

As previously mentioned, the 6 2 Σ + state has been a subject of disagreement when comparing ab-initio [1] and model potential results [2], contrary to the claims of Magnier and Frécon [2], present results show that the 6 2 Σ + state is attractive with a dissociation energy D e =270 cm -1 and an internuclear equilibrium distance R e =34.16 a.u. Those values may be compared to the ab-initio ones of Berriche [1], D e =265 cm -1 , R e =34.24 a.u and to the ones of Khelifi et al. [26], D e =165 cm -1 and R e =34.72 a.u.

Equally, the analysis of our potential energy curves shows that the 7 2 Σ + state correlated to Na + +Li(3p) in the asymptotic limit, has a well pronounced energy minimum occurring at an equilibrium distance R e = 31.35 a.u with a dissociation energy D e =1490 cm -1 . According to the ab-initio results of Kheliifi et al. [26] this state is also attractive with D e =980 cm -1 , while according to results of Berriche [1] and those of [2] the 7 2 Σ + state is purely repulsive.

For the 8 2 Σ + correlated in the asymptotic limit to Li + +Na(3d) and which also has been subject of disagreement when comparing previous ab-initio [1] and model potential [2] results, contrary to the conclusion of Magnier and Frécon [2], our 8 2 Σ + is an attractive molecular state with an equilibrium distance R e = 41.18 a.u and a dissociation energy D e = 444 cm -1 . Those new values may be compared to the ab-initio ones of Berriche [1] D e =375 cm -1 and R e =37.47 a.u and to those of Khelifi et al. [26], D e =112 cm -1 and R e =40.76 a.u. On the other hand, for the 9 2 Σ + state, correlated to Li(3d)+Na + in the asymptotic limit, as predicted by previous works [1,2,26] our study indicates that the 9 2 Σ + state is purely repulsive.

While previous model potential results [2] concluded that the 10 2 Σ + state is repulsive, our work shows that this state has an attractive behaviour with an equilibrium distance R e = 45.14 a.u and a corresponding dissociation energy D e =138 cm -1 . As shown in Table 3, those new values are in agreement when they are compared to the ones issued from an ab-initio study [1], D e =127 cm -1 and R e = 44.95 a.u.

The set of excited states 11 2 Σ + , 12 2 Σ + , 13 2 Σ + and 14 2 Σ + have not been included in the previous work by Magnier and Frécon [2] and are generated for the first time in a study based on a model potential approach. For the 11 2 Σ + , our study yields an equilibrium distance R e = 47.33 a.u with a corresponding dissociation energy D e =1243 cm -1 , however a such state has been found repulsive in the ab-initio study of Berrihe [1], but attractive R e = 42.99 a.u in the work of Khelifi et al. [26].

On the other hand, the present study shows that the 12 2 Σ + state correlated to Li + +Na(5s) in the dissociation limit has a well pronounced minimum of 230 cm -1 occurring at an equilibrium distance R e = 62.64 a.u. Those values are compared to the ab-initio results [1], D e =201 cm -1 and R e = 62.05 a.u. Equally, our our vibration constants ω e =6.375 cm -1 and ω e χ e =0.044cm -1 compare favourably to the ab-initio values [1], ω e =6.97 cm -1 and ω e χ e =0.03cm -1 .

Our study also shows that the potential energy curve for the 13 2 Σ + state, has a minimum occurring at an equilibrium distance R e = 46.19 a.u, and a dissociation energy 1048 cm -1 . Since those values remain different from the ab-initio results [1], R e = 33.91 a.u and D e =488 cm -1 , it is not obvious to reach an accurate conclusion and certainly an experimental investigation focusing on a such state will be of great interest.

Finally, as shown in Table 3, our 14 2 Σ + state exhibits an energy minimum occurring at a very large equilibrium distance R e =68.71 a.u with a corresponding dissociation energy D e =501 cm -1 , whereas a such state has been found attractive when ab-initio methods [1,26] The obtained adiabatic potential energies curves for the 2 Π states, are plotted in Fig. 3 for internuclear separations up to 50 a.u, while comparison of the corresponding spectroscopic constants with available values resulting from different approaches is shown in Table 4.

For the 1 2 Π state correlated in the dissociation limit to Na + +Li(2p), present study yields a dissociation energy D e =663 cm -1 and an equilibrium distance R e = 8.46 a.u. Those may be compared to values issued from an ab-initio approach [1], D e =496 cm -1 and R e = 8.53 a.u and to those exploiting model potential approach [2] D e =614 cm -1 and R e = 8.56 a.u. As indicated in Table 4, our vibration constants ω e = 67.271 cm -1 and ω e χ e =1.704 cm -1 , also compare favourably to the ab-initio values [1], ω e = 68.70 cm -1 and ω e χ e =1.40 cm -1 .

On the other hand, as shown in Fig. 4, the analysis of the potential energy curve of the 1 2 Π state at intermediate internuclear separations, indicates the existence of a potential barrier, located at an internuclear distance around 18 a.u with a maximum height of 62.55 cm -1 . Theory [26] For the 2 2 Π state, correlated to Li + + Na(3p) in the asymptotic limit, our potential energy curve is shown in Fig. 5. Present results indicate that this state has a very weak energy minimum of 26.95 cm -1 occurring at an equilibrium distance of 17.98 a.u, while according to previous studies employing both methods, ab-initio and model potential [2,1], the 2 2 Π state is purely repulsive.

For the 3 2 Π state, present study shows that the potential energy curve relative to this state has an energy minimum occurring at an equilibrium distance R e = 19.09 a.u with a corresponding dissociation energy D e =2864 cm -1 and vibration constants ω e = 38.264 cm -1 and ω e χ e =0.129 cm -1 Those values to be compared to the ab-initio results [1], R e = 19.35 a.u D e =2667 cm -1 , ω e = 37.27 cm -1 and ω e χ e =0.139 cm -1 .

On the other hand, our 4 2 Π state which has been a subject of disagreement when comparison of previous ab-initio results [1] and model potential ones [2] is made, contrary to the claims of Magnier and Frécon [2], a such state is attractive with a dissociation energy D e =423 cm -1 , and an equilibrium distance R e =34.64 a.u. These results are in agreement with what have been predicted by previous abinitio studies [1], giving for dissociation energy D e = 398 cm -1 and for equilibrium distance R e =34.76 a.u.

For the 5 2 Π and 6 2 Π states, the analysis of our potential energies curves does not show any energy minimum therefore, these states are repulsive, as predicted by other studies based on ab-initio methods [1,26] and model potential approach [2], as well.

Finally we mention that our excited molecular states 7 2 Π and 8 2 Π computed in the present study, have been found to be attractive as predicted by ab-initio methods [1]. However, as shown in Table 4, values of our spectroscopic constants remind different from the ab-initio ones.

∆ states

Our potential energy curves for the 2 ∆ symmetry are plotted in Fig. 6 for different internuclear distances up to 50 a.u, and the corresponding spectroscopic constants are compared to available data issued from different methods in Table 5.

The 1 2 ∆ state, correlated in the asymptotic limit to Li + +Na(3d), exhibits an energy minimum at an equilibrium distance R e =17.89 a.u, with a corresponding dissociation energy D e = 307 cm -1 . These values, as shown in Table 5, compare well to those of Magnier and Frécon [2], but a difference around 250 cm -1 in dissociation energy is observed when comparison is made with ab-initio results [1]. From Table 5, it is also easy to see that our frequencies ω e =21.572 cm -1 and ω e χ e =0.386 cm -1 and vertical excitation energy T e =39252 cm -1 , compare favourably to the ab-initio results [1] ω e =18.48 cm -1 , ω e χ e =0.35 cm -1 and T e =39216 cm -1 .

On the other hand, our study shows that the 2 2 ∆ state correlated in the asymptotic region to Na + +Li(3d), is a repulsive state, as predicted by previous studies of Magnier and Frécon [2] based on model potential and those of Berriche and Khelifi [1,26] using an ab-initio approach.

For the 3 2 ∆ state correlated to Li + +Na(4d), present calculations yield a dissociation energy D e =912 cm -1 and an equilibrium distance R e = 31.75 a.u. Those values may be compared to the ab-initio ones [1] D e =522 cm -1 and R e = 31.10 a.u. If both calculations are giving a large equilibrium distance around 31 a.u, our dissociation energy well is about 400 cm -1 deeper.

Avoided crossing

A simple analysis of our potential energy curves shows the presence of an important number of avoided crossings between adjacent adiabatic states belonging to the same molecular symmetry. It is well known that the internuclear distance R c of the pseudo-crossing and the corresponding energy gap ∆E c are relevant to charge transfer process, and can be used to estimate cross sections via Landau-Zener approximation [35].

Our avoided crossing parameters obtained in the present study, are compared with values issued from different methods in Table 6. Good agreement with previous model potential and ab-initio [1,2] results is observed. Our crossing radius for 5/6 2 Σ + and 6/7 2 Σ + crossings which have been omitted in the study of Magnier and Frécon [2], also compare favourably to the ab-initio results [1]. However a difference in R c values, between our results and ab-initio ones [1] seems to become more important for crossings involving excited states.

Conclusion

We have investigated the NaLi + cation using a model potential approach to compute the adiabatic potential energies and the molecular spectroscopic constants for the first low-lying, fourteen 2 Σ + , eight 2 Π and three 2 ∆ states, dissociating up to the Li + +Na(4d) limit.

A good agreement between the present results based on model potential approach and those issued from ab initio methods is observed. This is an indication that the model potential method remains efficient in providing accurate description of molecular systems involving one single active electron.

Figure 1 :

 1 Figure 1: Relative coordinates for the active electron.

Figure 2 :

 2 Figure2: NaLi + potential energy curves of the 2 Σ + states, given with respect to the ground state dissociation limit.

Figure 3 :

 3 Figure3: NaLi + potential energy curves of the 2 Π states, given with respect to the ground state dissociation limit.

Figure 4 :

 4 Figure4: Shape of the potential barrier in the 1 2 Π state. Energies are given with respect to the ground state dissociation limit.

Figure 5 :

 5 Figure5: NaLi + potential energy curves of the 2 2 Π state. Energies are given with respect to the ground state dissociation limit.

Figure 6 :

 6 Figure6: NaLi + potential energy curves of the 2 ∆ states, given with respect to the ground state dissociation limit.

Table 1 :

 1 Comparison of calculated and experimental energy levels of the Na atom in a.u.

	2,

Table 2 : Klapisch model potential parameters

 2

Table 3 :

 3 Spectroscopic constants for 2 Σ + states, R e in a.u, D e , ω e , ω e χ e , B e and T e in cm -1 .

	State	R e	D e	T e	ω e	ω e χ e	B e	Reference
	X 2 Σ + 6.26	8331		194.88 1.140	0.286	Present work
		6.37	8061		192.98 1.11 0.278607 Theory [1]
		6.35	7988		192.04			Theory [2]
		6.29	8155					Theory [26]
		6.35	8115		193	1.09	0.277	Theory [30]
			7985±242					Exp [33]
	2 2 Σ + 14.83	307	10061 37.009 1.116	0.051	Present work
		14.90	294	9805 36.39 1.51 0.050840 Theory [1]
			Repulsive					Theory [2]
		14.94	295					Theory [26]
	3 2 Σ + 13.65	1488	21745 57.961 0.564	0.060	Present work
		13.65	1423	21543 58.14 0.21 0.060663 Theory [1]
								Theory [2]
		13.57	1414					Theory [26]
	4 2 Σ + 18.90	867	26476 38.139 0.419	0.031	Present work
		18.94	847	26219 32.54 13.76 0.031677 Theory [1]
			Repulsive					Theory [2]
		19.12	806					Theory [26]
	5 2 Σ + 22.43	2289	33215 39.814 0.173	0.022	Present work
		22.41	2262	33011 41.12 0.33 0.022492 Theory [1]
		22.43	2300	32879 40.00			Theory [2]
		22.47	2194					Theory [26]
	6 2 Σ + 34.16	270	35812 14.637 0.198	0.010	Present work
		34.24	265	35575 13.59 4.09 0.009606 Theory [1]
			Repulsive					Theory [2]
		34.72	165					Theory [26]
	7 2 Σ + 31.35	1490	37741 17.135 0.050	0.011	Present work
			Repulsive					Theory [1]
			Repulsive					Theory [2]
		30.32	980					Theory [26]
	8 2 Σ + 41.18	444	39091 11.410 0.073	0.007	Present work
		37.47	375	38896 43.29 13.00 0.008025 Theory [1]
			Repulsive					Theory [2]

Table 4 :

 4 Spectroscopic constants for 2 Π states, R e in a.u, D e , ω e , ω e χ e , B e and T e in cm -1 .

	State	R e	D e	T e	ω e	ω e χ e	B e	Reference
	1 2 Π	8.46	663	22572 67.271 1.704	0.156	Present work
		8.53	496	22471 68.70	1.40 0.155188 Theory [1]
		8.56	614	22282 58.24			Theory [2]
		8.50	519.3					Theory [26]
	2 2 Π	17.98	-26.95 27366 10.479 -1.018	0.0346 Present work
		Repulsive						Theory [1]
		Repulsive						Theory [2]
		Repulsive						Theory [26]
	3 2 Π	19.09	2864 36370 38.264 0.129	0.0307 Present work
		19.35	2667 36319 37.27	0.13 0.030175 Theory [1]
		19.09	2863 36020 38.34			Theory [2]
		19.20	2432.8					Theory [26]
	4 2 Π	34.64	423	39106 12.927 0.098	0.009	Present work
		34.76	398	38872 7.12	42.57 0.009550 Theory [1]
		41.28	422	38849 6.76	42.57 0.009550 Theory [1]
		Repulsive						Theory [2]

Table 5 :

 5 Spectroscopic constants for 2 ∆ states, R e in a.u, D e , ω e , ω e χ e , B e and T e in cm -1 .

	State	R e	D e	T e	ω e	ω e χ e	B e	Reference
	1 2 ∆	17.89	307 39252 21.752 0.386	0.035	Present work
		19.59	57	39216 18.48 0.35 0.029415 Theory [1]
		17.97	340 38900 22.0			Theory [2]
		20.3	110.8					Theory [26]
	2 2 ∆ Repulsive						Present work
		Repulsive						Theory [1]
		Repulsive						Theory [2]
		Repulsive						Theory [26]
	3 2 ∆	31.75	912 43477 17.123 0.080	0.011	Present work
		31.10	522 44110 14.15 8.43 0.011596 Theory [1]
		29.8	234					Theory [26]

Table 6 :

 6 Avoided crossing parameters (R c , ∆E c ) Σ + -9 2 Σ + 7.15 10 -4 25.06 24.59 25 9 2 Σ + -10 2 Σ + 5.80 10 -3 10.92 10.82 10 2 Σ + -11 2 Σ + 6.71 10 -4 6.66 6.7 10 2 Σ + -11 2 Σ + 4.52 10 -3 20.44 20.19 11 2 Σ + -12 2 Σ + 7.51 10 -4 13.27 10.26 11 2 Σ + -12 2 Σ + 3.23 10 -3 35.89 33.50 12 2 Σ + -13 2 Σ + 6.11 10 -3 10.71 16.00 12 2 Σ + -13 2 Σ + 7.64 10 -4 25.58 22.25 13 2 Σ + -14 2 Σ +

		Present work		Ab-initio[1]	Model potential [2]
	Avoided crossing ∆E c (a.u) R c (a.u)	R c (a.u)	R c (a.u)
	4 2 Σ + -5 2 Σ +	4.60 10 -3	7.75	7.73	7.75
	5 2 Σ + -6 2 Σ +	4.32 10 -3	4.18	4.29	4.25
	5 2 Σ + -6 2 Σ +	1.83 10 -2 15.77	15.61
	6 2 Σ + -7 2 Σ +	7.42 10 -3	8.07	7.86
	6 2 Σ + -7 2 Σ +	1.09 10 -4 16.73	16.02	16.5
	7 2 Σ + -8 2 Σ +	1.27 10 -2 11.20	11.4
	8 2 Σ + -9 2 Σ +	10 -3	7.54	7.52	7.5
	8 2 9.03 10 -4 15.13	14.51
	3 2 Π + -4 2 Π +	3.52 10 -3	8.27	8.18	8.25
	4 2 Π + -5 2 Π +	2.18 10 -3 20.01	19.59	20
	5 2 Π + -6 2 Π +	3.78 10 -3 18.11	18.19	18.25
	6 2 Π + -7 2 Π +	6.06 10 -4	8.69	8.34
	7 2 Π + -8 2 Π +	8.36 10 -4 25.51	29.75