Stability, spectroscopic constants, and dissociation of CO2+: A theoretical study

Stability, Spectroscopic Constants, andDissociation of CO2�: A TheoreticalStudy

BHASKAR MONDAL, NARAYAN C. BERA, ABHIJIT K. DASDepartment of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur,Kolkata 700 032, India

Received 7 May 2008; accepted 11 June 2008Published online 18 September 2008 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.21847

ABSTRACT: Stability, spectroscopic constants, and dissociation of CO2� have beenstudied in detail using ab initio MP2, CCSD and CCSD(T) methods, and densityfunctional B3LYP method. The stability and the ambiguity between the ground andmetastable state of the molecular dication have been discussed. The spectroscopicconstants of the molecular dication have been compared with the experimental andtheoretical values wherever available. Various charge symmetric and charge asymmetricdissociation pathways of CO2� have been investigated. After dissociation, thefragmented atoms and ions are considered to be either in their ground or in theirmetastable state. Interesting results have been obtained for the charge symmetric andcharge asymmetric dissociation of the diatomic dication. © 2008 Wiley Periodicals, Inc.Int J Quantum Chem 109: 469–476, 2009

Key words: stability; spectroscopic constants; dissociation; CO2� dication; ab initio;B3LYP study

Introduction

M olecular dications are most easily formed bythe double ionization of neutral molecules.

The chemical bonds become considerably weaker ifthe two electrons are ionized from the valence shellof a molecule. The Coulomb repulsion between thetwo nuclei can no longer be compensated by chem-ical bonding and consequently the molecule disso-

ciates into atoms and ions. However, in some mol-ecules when both electrons are removed from thenonbonding orbitals, or when the molecules havemultiple-bond structure, the molecular dicationsare still stable or quasi-stable with respect to disso-ciation. In such diatomic molecular dications, thechemical bonding is sufficient to overcome the Cou-lomb repulsion and create potential well. Thesestable or quasi-stable dications play an importantrole in plasma occurred in the ionosphere and ininterstellar medium. Molecular dications are alsohighly chemically reactive due to long-range inter-Correspondence to: A. K. Das; e-mail: [email protected]

International Journal of Quantum Chemistry, Vol 109, 469–476 (2009)© 2008 Wiley Periodicals, Inc.

action with neutral species. Many experimentaltechniques have been applied to study CO2�. Putt-ner et al. [1] determined the potential energy curvesof the quasi-stable states of CO2� using Auger spec-troscopy. They calculated equilibrium bond length,harmonic frequency, and anharmonicity constantsfor the quasi-stable states. Guo [2] studied the dis-sociation of CO2� and showed that doubly ionizedCO, once produced, will dissociate into chargesymmetric and charge asymmetric fragments. Vinciet al. [3] measured the dissociative recombinationrate of CO2�. They also studied the potential energycurves for the first seven electronic states of CO2�.Eland et al. [4] tested the accuracy of the potentialsby a synthesis of the available vibrationally re-solved threshold photoelectrons in coincidence(TPEsCO) and time of flight photoelectron photo-electron coincidence (TOF-PEPECO) spectra ofCO2�. Ab initio calculations have also been under-taken for the potential energy curves of CO2�. Fu-ruhashi et al. [5] studied doubly charged molecularions of N2 and CO using a double charge transfer(DCT) spectrometer capable of resolving vibra-tional levels. They calculated Franck-Condon (FC)profiles using CASSCF and MRCI methods to re-produce the observed spectra. Hochlaf et al. [6]recorded the threshold photoelectron coincidence(TPEsCO) spectra of N2

2� and CO2� with improvedresolution to resolve the lowest three vibrationalprogressions in each species. The molecular con-stants of ground and metastable states of thesedications have been calculated. Mathur and Rajgara[7] reported the result of a translation energy spec-trometric study of state-selected electron capturereaction between metastable CO2� ion and di-atomic molecules and ions. The experimental datawere interpreted within the framework of recent abinitio calculation of the potential energy curves oflow-lying electronic states. In their work 1�� isreported to be the ground state of CO2� and 3� isits metastable state. The theoretical works on CO2�

are very limited. Polak [8] calculated low-lying elec-tronic states of the dication of carbon monoxideusing the classical valence bond and atoms-in-mol-ecules approaches. Larsson et al. [9] studied thepotential energy curves for a number of electronicstates of the doubly charged CO2� applying com-plete active space SCF (CASSCF) and multirefer-ence contracted CI (MRCCI) methods with a one-particle basis set of medium size (3s 6p 2d).Wetmore et al. [10] calculated the equilibrium geo-metrical parameters for both ground and metasta-ble states of the dication using SCF/MRCI method.

In all these works the potential energy curves andthe spectroscopic constants have been determined,but no experimental and theoretical attempts havebeen made so far to investigate its dissociation. In arecent paper [11], we elaborately studied the disso-ciation of molecules taking into account that thefragmented atoms are either in their ground state orin their metastable states. This new idea is utilizedin this work. In this article we have studied in detailthe charge symmetric and charge asymmetric dis-sociation of CO2�. After dissociation the moleculardication as well as the fragmented atoms and ionsare considered to be either in their ground state orin their metastable states. The stability, potentialenergy curves, and the spectroscopic constants ofthe dication are studied along with it.

Computational Details

In this article we have studied the stability, spec-troscopic constants and charge symmetric andcharge asymmetric dissociation of CO2� using abinitio MP2, CCSD, CCSD(T) methods [12–17] anddensity functional B3LYP method [18, 19]. The hy-brid B3LYP functional, among all DFT functionals,is well tested and is very successful for calculatingthe properties of small as well as big molecules. Inboth charge symmetric and charge asymmetric dis-sociation processes the molecular dication and thefragmented atoms and ions have been consideredto be either in their ground state or in their meta-stable state. The electron correlation effects havebeen taken into account via Moller–Plesset pertur-bation (MP) theory and coupled cluster techniques.The conventional ab initio methods applied to thiswork are second order Moller–Plesset perturbation(MP2) theory and the coupled cluster CCSD andCCSD(T) methods. The CCSD(T) method includessingle and double excitations and an estimate of

TABLE I ______________________________________Ionization potential (IP) of constituent atoms.

Ionizationpotential(eV)

Basis setCBSlimit

Expt.valuescc-pVTZ cc-pVQZ cc-pV5Z

IP1(C) 11.16 11.20 11.21 11.21 11.26a

IP2(C) 24.22 24.27 24.29 24.30 24.37a

IP1(O) 13.31 13.48 13.53 13.55 13.61a

a Ref. [26].

MONDAL, BERA, AND DAS

470 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 109, NO. 3

triple excitations by a perturbation treatment,whereas the CCSD method incorporates only singleand double excitations. The Gaussian 98 suite of thequantum chemistry programs [20, 21] have beenused to perform B3LYP, MP2, CCSD, and CCSD(T)calculations. The frozen core (FC) approximation isused for all ab initio calculations. The correlatedconsistent cc-pVTZ basis set [22] has been used forC and O. The basis set superposition error (BSSE)has been taken into account in the calculation usingthe method of Boys and Bernardi [23].

Results and Discussion

It is known that for a diatomic dication, theidentities of the dissociation products are deter-mined by the relative magnitudes of the atomicionization energies. For most light molecular dica-

tions, such as CO2�, the molecule will dissociate togive two charged fragments provided that the sumof the first two ionization energies of one atom[IP1(C) � IP2 (C)] is greater than the sum of the firstionization energies of the two different atoms [IP1(C) � IP1 (O)] where IP1 and IP2 are the first andsecond ionization potential of an atom. In Table I,the first and second ionization potential of carbonand the first ionization potential of oxygen are cal-culated using correlation consistent basis set im-proved from cc-pVTZ to cc-pV5Z [24]. The calcu-lated ionization potential is then extrapolated to the

TABLE II _____________________________________Energy and zero point energy (ZPVE) of CO2�.

Method

3� 1��

Energy (a.u.)ZPVE(eV) Energy (a.u.)

ZPVE(eV)

B3LYP �111.837546 0.09 �111.803775 0.12MP2 �111.615730 0.09 �111.636078 0.15CCSD �111.633972 0.09 �111.607906 0.12CCSD(T) �111.649456 0.08 �111.642281 0.12

FIGURE 1. Potential energy curve for CO2� at B3LYPlevel.

FIGURE 2. Potential energy curve for CO2� at MP2level.

FIGURE 3. Potential energy curve for CO2� at CCSDlevel.

THEORETICAL STUDY OF CO2�

VOL. 109, NO. 3 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 471

complete basis set (CBS) limit using the function asdiscussed by Peterson et al. [25]. The calculatedionization potentials agree very well with the ex-perimental values of Moore [26]. From the table it isobserved that [IP1(C) � IP2(C)] � [IP1(C) � IP1(O)].Therefore, the molecule can dissociate into twocharged fragments.

Table II summarizes the energy and the zeropoint vibrational energy (ZPVE) of CO2� in its 3�and 1�� state. It is important to note that the energyof the 3� state calculated by B3LYP, CCSD, andCCSD(T) methods is lower than that of 1�� state,whereas in MP2 method 1�� is energetically lowerthan 3� state. The potential energy obtained byB3LYP method has been plotted in Figure 1. Thefigure shows that there is a crossing between 1��

and 3� states at around 1Å and 3� is the groundstate of CO2�. The MP2 potential energy curves forthe singlet and triplet states are shown in Figure 2.The 3� state is energetically higher than the 1��

state. This situation is opposite to rest of the three

TABLE III ____________________________________________________________________________________________Spectroscopic constants of CO2� in the X3� and 1�� state calculated using cc-pVTZ basis set.

State Parameters B3LYP MP2 CCSD CCSD (T)

Other values

Expt. Theor.

X 3� Re (Å) 1.23 1.23 1.23 1.25 1.25a,b 1.26c, 1.18d

�e (cm�1) 1557.6 1581.5 1555.3 1396.3 1453a, 1435b, 1363e 1392c, 2049d

� (eV) 1.77 4.05 1.97 1.65�exe (cm-1) 42.41 19.13 37.95 36.49 24.6b, 17.75e 31.7c, 56.5d

�eye (cm�1) 2.04 0.41 1.64 1.70 0.15b

Be (cm�1) 1.61 1.61 1.60 1.56 1.58b 1.56c

De (10�6 cm�1) 6.95 6.74 6.97 7.85�e (cm�1) 0.04 0.02 0.04 0.04 0.03b 0.034c

�e (10�7 cm�1) �4.38 �0.86 �3.64 �4.37�e (10�4 cm�1) �5.44 �0.90 �4.31 �4.78

1�� Re (Å) 1.13 1.20 1.14 1.16 1.16a, 1.16b 1.17c, 1.13d

�e (cm�1) 2082.4 2468.3 1969.5 1949.6 1907a, 1921b, 1613e 1899c, 2323d

� (eV) 5.15 7.75 5.51 4.00�exe (cm�1) 26.11 24.37 21.80 30.14 16.7b 18.7c,16.1d

�eye (cm�1) 0.58 0.43 0.43 0.82 0.37b

Be (cm�1) 1.91 1.70 1.88 1.82 1.83b 1.81c

De (10�6 cm�1) 6.47 3.21 6.86 6.30�e (cm�1) 0.028 0.020 0.026 0.031 0.021b 0.022c

�e (10�7 cm�1) �1.04 �0.50 �0.80 �1.54�e (10�4 cm�1) �1.19 �0.70 �0.87 �1.81

a Ref. [1].b Ref. [4].c Ref. [9].d Ref. [10].e Ref. [6].

FIGURE 4. Potential energy curve for CO2� atCCSD(T) level.



calculations. According to CCSD and CCSD(T) cal-culations, 3� is the ground state and 1�� is a meta-stable state of CO2�, and it is reflected from thepotential energy curves plotted in Figures 3 and 4.In the translational energy spectroscopy of CO2�,Mathur and Rajgara [7] determined the spectro-scopic data from the potential curve of CO2� thatshows 1�� is the ground state and 3� is a metasta-ble state, whereas both CCSD and CCSD(T) calcu-lations confirm that 3� is the ground state. Thedifference of energy between 1�� and 3� statesdecreases from CCSD to CCSD(T) and a crossingbetween the singlet and triplet states appears ataround 1.2 Å. It should be mentioned here that thepotential energy curves and the calculation of spec-troscopic constants have been performed using cc-pVTZ basis set. The CO2� dication becomes unsta-ble if the basis set is being improved further. Itimplies that with the improvement of basis set thedication becomes more bound and simultaneouslythe Coulomb repulsion increases that break thechemical bonding between the two atomic systemsof the dication. This phenomenon is independent ofmethods used in this calculation.

The spectroscopic constants of CO2� in its 3�and 1�� states are listed in Table III along with theexisting theoretical and experimental values. Asstated earlier, according to B3LYP, CCSD, andCCSD(T) methods the 3� state is the ground stateand 1�� is the metastable state, but the MP2 calcu-lation gives the opposite result. For the X3� groundstate, the equilibrium bond length calculated byCCSD(T) method agrees very well with the exper-imental values of Puttner et al. [1] and Eland et al.[4] who supported their experimental values byhigh level ab initio calculation. The harmonic fre-

quency is little lower than the experimental values,one of these two, namely the experimental value ofPuttner et al. is about 20 cm�1 higher than that ofEland et al. The experimental value of Hochlaf et al.[6] is much lower compared to the other two exper-imental values. Our calculated CCSD(T) harmonicfrequency is very close to that reported by Larssonet al. [9] using MRCCI method combined withCASSCF. Their basis set is smaller than our cc-pVTZ basis set. The spectroscopic constants havebeen calculated using the relations in Morse poten-tial deduced from the general expressions of Dun-ham [27] for molecules in a potential. The depth (�)of the potential well is used to calculate the spec-troscopic constants. The spectroscopic constantssuch as anharmonicity constant (�exe), rotationalconstant (Be), centrifugal distortion constant (De),and �e agree very well with the experimental valueof Eland et al. [4] and also with the theoreticalvalues of Larsson et al. The SCF/MRCI value ofWetmore et al. [10] for the equilibrium bond length

TABLE IV ____________________________________________________________________________________________Spectroscopic constants of CO2� for both 1�� and 3� state calculated using aug-cc-pVTZ basis.

State Parameters B3LYP MP2 CCSD CCSD(T)

X3� E (a.u) �111.838539 �111.619626 �111.637641 �111.653317Re (Å) 1.23 1.23 1.23 1.25�e (cm-1) 1551.90 1570.29 1550.19 1392.40Be (cm-1) 1.61 1.61 1.61 1.56De (10-6 cm-1) 7.00 6.84 7.01 7.89

1�� E (a.u) �111.804547 �111.640183 �111.611517 �111.646667Re (Å) 1.13 1.20 1.14 1.16�e (cm-1) 2077.20 2467.98 1966.11 1944.02Be (cm-1) 1.91 1.69 1.88 1.81De (10-6 cm-1) 6.50 3.21 6.88 6.34

TABLE V _____________________________________Dissociation energy (eV) for the charge symmetricdissociation of CO2� from X3� state.

Method

Dissociation channels

C�(2P) � O�(4S) C�(2P) � O�(2D/2P)

B3LYP �4.76 �0.88MP2 �5.49 �1.00CCSD �6.05 �2.15CCSD(T) �5.70 �2.04Other value �4.72a

a Ref. [28].



is lower than the experimental values and also thanthat of ours and the values for the spectroscopicconstants is much higher.

For the 1�� metastable state, the equilibriumbond length, anharmonicity constant, rotationalconstant, centrifugal distortion constant, and �e cal-culated by CCSD(T) method agree very well withthe experimental values of Puttner et al. [1] andEland et al. [4]. Our calculated harmonic frequencysupports the experimental value of Eland et al. Theexperimental value of Puttner et al. [1] is lower thanour value and also than the experimental value ofEland et al. [4]. The experimental value of Hochlafet al. [6] is about 300 cm�1 lower than the other twoexperimental values and also than our value.Among existing theoretical data, the spectroscopicconstants calculated by Larsson et al. [9] usingMRCCI method are in very good agreement withour CCSD(T) values but the equilibrium bondlength and harmonic frequency reported by Wet-more et al. [10] using SCF/MRCI method are lowerand higher than our respective value.

In Table IV, the energy, equilibrium bond length(Re), harmonic frequency (�e), and two spectro-scopic constants that depend on Re and �e are cal-culated using aug-cc-pVTZ basis set employing thegeometry optimized at cc-pVTZ basis set. At the

CCSD(T) level of calculation, the equilibrium bondlength, the rotational constant (Be), and the centrif-ugal distortion constant (De) remain almost un-changed but harmonic frequency decreases verylittle, about 6–8 cm�1.

We have studied the charge symmetric andcharge asymmetric dissociation of CO2� using abinitio and density functional methods. After disso-ciation of CO2�, the fragmented atom and ion areconsidered to be either in their ground state or intheir metastable state. The dissociation of CO2� hasbeen investigated both from its X3� ground stateand also from its 1�� metasatble state. In Tables Vand VI, the charge symmetric dissociations of CO2�

have been considered from its X3� ground state andfrom its 1�� metastable state respectively. For allthe charge symmetric dissociation channels, the dis-sociation energy is negative whether the moleculardication and the fragmented ions are either in theirground state or in their metastable state. The neg-ative dissociation energy is obtained for all themethods applied to this system. The negative dis-sociation energy is also supported by the calcula-tion of Janoschek [28]. Interestingly, the dissocia-tion energy for all the charge asymmetricdissociation channels is positive. In Table VII,among six possible charge asymmetric dissociationa channel, lowest dissociation energy has been cal-culated for the C2� (1S) � O (3P) channel whereboth C2� and O are in their ground state. Thisdissociation channel is the most probable one. Thehighest dissociation energy has been estimated forthe C (1D/1S) � O2� (1D/1S) channel where both Cand O2� are in their metastable state; O2� is iso-electronic with C atom. The next probable channelis C2� (1S) � O (1D/1S) where C2�, which is iso-electronic with B atom, is in its ground state and Ois in its metastable state. It is important to note thatthe dissociation energy for the charge asymmetricdissociation channels where C is in its dication form

TABLE VI ____________________________________Dissociation energy (eV) for the charge symmetricdissociation of CO2� from 1�� state.

Method


C�(2P) � O�(4S) C�(2P) � O�(2D/2P)

B3LYP �5.71 �1.84MP2 �4.98 �0.50CCSD �6.79 �0.44CCSD(T) �5.91 �2.27

TABLE VII ____________________________________________________________________________________________Dissociation energy (eV) for the charge asymmetric dissociation of CO2� from X3� state.

Method


C(3P)�O2�(3P)

C(3P)�O2�(1D/1S)

C(1D/1S)�O2�(3P)

C(1D/1S)�O2�(1D/1S)

C2�(1S)�O(3P)

C2�(1S)�O(1D/1S)

B3LYP 18.91 22.43 20.70 24.21 6.11 10.59MP2 18.38 22.03 20.28 23.94 5.56 8.44CCSD 17.74 20.59 19.25 22.08 4.81 7.21CCSD(T) 18.08 20.81 19.50 22.25 5.15 7.36



is much lower than that for the channels where C isin its neutral form. Among four possible dissocia-tion channels when C is in its neutral form, theminimum dissociation energy has been obtainedfor the C (3P) � O2� (3P) channel where both C andO2� are in the ground state. The dissociation energyincreases for the rest three channels.

Table VIII shows the various charge asymmetricdissociation pathways of CO2� from its 1�� meta-stable state. As seen from the table, the dissociationenergy of a channel is lower than its correspondingchannel when the dication dissociates from its X3�ground state. The lowest dissociation energy hasbeen obtained for the C2�(1S) � O(3P) channelwhere C2� and O both are in the ground state. Thehighest dissociation energy has been calculated forthe C (1D/1S) � O2� (1D/1S) channel where both Cand O2� are in the metastable state. This situation issimilar to what we observed in Table VII for thedissociation of CO2� for its X3� ground state. Theimportant point to be noted here is that dissociationenergy of a dissociation channel from 1�� state ofCO2� decreases uniformly, about 0.2 eV, from thecorresponding dissociation channel of CO2� whenit dissociates from its 3� ground state.

Conclusion

Stability, spectroscopic constants and dissocia-tion pathways of CO2� has been studied in detailusing ab initio and density functional methods. Themolecular dication CO2� becomes unstable if thebasis set is improved further after cc-pVTZ. Thecalculated spectroscopic constants agree well withthe existing theoretical and experimental values.Both charge symmetric and charge asymmetric dis-sociation of CO2� have been investigated. Afterdissociation of the dication the fragmented atomsand ions are considered to be either in the ground

state or in the metastable states. The dissociationenergy of all charge symmetric dissociation chan-nels is negative irrespective of the state of the frag-mented ions and molecular dication. The dissocia-tion energy for the entire charge asymmetricdissociation channels is positive. The lowest disso-ciation energy is obtained when both C2� and O arein the ground state and highest dissociation energyis estimated when both C and O2� are in the meta-stable state. For all the dissociation channels ofCO2� from its X3� ground state, the dissociationenergy is uniformly higher than the correspondingchannel when dissociation takes place from its 1��

metastable state.

References

1. Puttner, R.; Liu, X. J.; Fukuzawa, H.; Tanaka, T.; Hoshino,M.; Tanaka, H.; Harries, J.; Tamenori, Y.; Carravetta, V.;Ueda, K. Chem Phys Lett 2007, 445, 6.

2. Guo, C. Phys Rev A 2006, 73, 41401.3. Vinci, N.; de Ruette, N.; Waffeu Tamo, F. O.; Motapon, O.;

Fifirig, M.; Crumeyrolle, O.; Urbain, X.; Tennyson, J.; Schnei-der, I. F. J Phys C 2005, 4, 162.

4. Eland, H. D. J.; Hochlaf, M.; King, G. C.; Kreynin, P. S.; LeRoy, R. J.; McNab, I. R.; Robbe, J. M. J Phys B Atom Mol OptPhys 2004, 37, 3197.

5. Furuhashi, O.; Kinugawa, T.; Masuda, S.; Yamada, C.;Ohtani, S. Chem Phys Lett 2001, 337, 97.

6. Hochlaf, M.; Hall, R. I.; Pentent, F.; Kjeldsen, H.; Lablanquie,P.; Lavolle, M.; Eland, J. H. D. Chem Phys 1996, 207, 159.

7. Mathur, D.; Rajgara, F. A. Phys Rev A 1990, 41, 4824.8. Polak, R. Chem Phys 1998, 232, 25.9. Larsson, M.; Olsson, B. J.; Sigary, P. Chem Phys 1989, 139,

457.10. Wetmore, R. W.; Le Roy, R. J.; Boyd, R. K. J Phys Chem 1984,

88, 6318.11. Bhattacharyya, I.; Bera, N. C.; Das, A. K. Int J Quantum

Chem 2008, 108, 447.12. Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry;

McGraw-Hill: New York, 1998 (and references therein).

TABLE VIII ___________________________________________________________________________________________Dissociation energy (eV) for the charge asymmetric dissociation of CO2� from 1�� state.

Method


C(3P)�O2�(3P)

C(3P)�O2�(1D/1S)

C(1D/1S)�O2�(3P)

C(1D/1S)�O2�(1D/1S)

C2�(1S)�O(3P)

C2�(1S)�O(1D/1S)

B3LYP 17.96 21.48 19.74 23.25 5.16 7.86MP2 18.86 22.52 20.75 25.43 6.04 8.93CCSD 16.99 19.83 18.59 21.33 4.06 6.47CCSD(T) 17.85 20.58 19.28 22.01 4.93 7.14



13. Bartlett, R. J. Ann Rev Phys Chem 1981, 32, 359.14. Cizek, J. Adv Chem Phys 1969, 14, 35.15. Purvis, G. D., III; Bartlett, R. J. J Chem Phys 1982, 1910, 76.16. Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F., III. J Chem

Phys 1988, 89, 7382.17. Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J Chem

Phys 1987, 87, 5968.18. Becke, A. D. J Chem Phys 1993, 98, 5648.19. Stephens, P. J.; Devlin, F. J.; Frisch, M. J.; Chabalowski, C. F.

J Phys Chem 1994, 98, 11623.20. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;

Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgom-ery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Mil-lam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas,O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci,B.; Pomelli, C.; Adamo, C.; Clifford, S. J.; Ochterski, G.;Peterson, A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick,D. K.; Rabuck, A.; Raghavachari, K.; Foresman, J. B.; Ci-oslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,

A.; Piskorz, P.; Komaromi, L.; Gompets, R.; Matirt, R. L.; Fox,D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara,A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson,B. G.; Chen, W.; Wong, M. W.; Andres, L.; Head-Gordon, M.;Replogle, E. S.; Pople, J. A. Gaussian 98; Gaussian: Pitts-burgh, PA, 1998.

21. Forseman, J. B.; Frisch, M. J. Exploring Chemistry with Elec-tronic Structure Methods; Gaussian: Pittsburgh, PA, 1996.

22. Dunning, T.H., Jr. J Chem Phys 1989, 90, 1007.

23. Boys, S. F.; Bernardi, F. Mol Phys 1970, 19, 553.

24. Paterson, K. A.; Dunning, T. H., Jr. J Chem Phys 2002, 117,20548.

25. Peterson, K. A.; Woon, D. E.; Dunning, T. H., Jr. J Chem Phys1994, 100, 7410.

26. Moore, C. E. Atomic Energy Levels, NSRDS-NBS (U.S.) 35,Vol. I, 1971.

27. Dunham, J. L. Phys Rev 1932, 41, 721.

28. Janoschek, R. IUPAC Pure Appl Chem 2001, 73, 1521.



Documents

Stability, spectroscopic constants, and dissociation of CO2+: A theoretical study