J. Phys. Chem. 1994, 98, 768-770
768
Ab Initio Study of Argon-Nitrogen Positive Clusters Anne-Marie Sapse City University of New York, Graduate School and John Jay College, 445 W. 59th Street, New York, New York 10019 and Rockefeller University, New York 10021 Received: March 1 1 , 1993" Ab initio calculations up to the MP3 level of theory were performed for the Ar2N2+ and ArN4+ species. Both clusters are predicted to be linear. The ArN4+ complex features as its most stable conformation the conformation in which an argon is positioned between two nitrogen molecules, and the Ar2N2+ complex's most stable structure is the one in which the two argon atoms are bound to each other, and the nitrogen entity is bound to one of them.
Introduction Rare gas atoms and ions are known to form clusters which play an important role in the understanding of the transitions between the gas and the condensed phases, as well as in the stratosphere chemistry.'S2 The argon monoion dimers and trimers have been investigated in a number of experimental and theoretical studies.IJ Another small ionic cluster, the N4+ species, has also been studied with experimental and theoretical method^.^ Both the Ar2+ species and the N4+species have been reported to feature large binding energies, related to the electron delo~alization.~ A small ionic cluster formed by an argon atom and a nitrogen molecule and featuring a positive charge, the ArN2+ species, has been found equally stable in both theoretical and experimental ~ t u d i e sdue ,~ to the fact that the ionization potentials of Ar and N2 are almost the same. The electron delocalization is thus facilitated and contributes to the stability of the cluster. In contrast, monoion trimers of rare gases show a very small binding energy of the third atom to the positive dimer.6 Photodissociationspectra studies of complexes such as Ar2+, Ar3+, ArN2+, and N4+ have been reported in a number of studies;' however, the nature of the excited states and the structure of Ar had been the subject of debate.* Recently? Magnera and Michl reported a study of the photodissociation spectra of Arn-mN2m+ clusters, for n = 2 or 3 and m = 0 - n. The results reported by these authors show that, in contrast to N6+, the ArN4+ clusters are single molecules and not solvated dimers. The study also indicates that the UV excitation of these species leads to sequential decomposition,by generating a state analogous to the 22+ state of Ar3+. Information about the structure of the clusters is obtained in an indirect way, by a study of the thermal metastability products. Hiraoka et a1.l0 reported an experimental and theoretical study of the gas-phase solvation of N2+ with Ar atoms, using a pulsed electron beam mass spectrometer and ab initio calculations. They focused on the ArN2+ species, obtaining results similar to those previously reported by our group.5 In addition, they performed restricted Hartree-Fock calculations on the Ar2N2+and Ar3N2+species. In the paper presented here, ab initio calculationsare performed on both Ar2N2+ and ArN4+ species, using the unrestricted Hartree-Fock method, as suitable for open-shell systems, and taking into account the correlation energy effects by using the Moller-Plesset method, with and without geometry optimization. Method and Results The Gaussian 90 computer program' was used to perform ab initio calculations at unrestricted HartreeFock level of theory, using a triple-{set with polarization functions (6-3 1G*) in order 0
Abstract published in Advance ACS Abstracts, December 15, 1993.
la
lb Figure 1.
2a Figure 2.
TABLE 1: Geometrical Parameters of the Complexes (angstroms and degrees) structure l a parameter HF MP2 Arl-Ar2 Ar2-Nl Arl-Nl Nl-N2 N2-N3 Arl-N2
3.354 2.241
2.486 2.724
1.074
1.109
structure 2a
structure 2b
HF
MP2
HF
MP2
2.591 1.070
2.440 1.094
2.223 1.075 3.829
2.289 1.078 3.133
2.389
2.432
to determine the optimum geometries and the binding energies of the Ar2N2+ and ArN4+ complexes. The correlation energy effects were taken into account by using the Moller-Plesset method, of the MP2 order, performingcomplete geometry optimization (MP2/6-3 1 1G*). In addition, singlepoint energies of MP3 order were calculated, with Hartree-Fock optimized geometry. The theoretical values of equilibrium bond lengths and angles were obtained by the Berny optimization method, by locating the minima on the potential energy surface for various starting structures of different symmetry types for the ions in the ground state. The conformations of the complexes investigated are shown in Figure 1 (ArN2+) and Figure 2 (ArN4+). The optimized geometrical parameters of structures la, lb, and 2a are shown in Table 1. Table 2 shows the total energies of the optimized complexes, expressed in atomic units.
0022-3654/94/2098-0768$04.5Q/O 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98,No. 3, 1994 769
Argon-Nitrogen Positive Clusters TABLE 2
Total Energies of the Complexes (au)
structure l a structure 2a structure 26
1162.072 68 744.244 54 744.240 97
1162.631 47 745.159 52 745.148 67
TABLE 3: Binding Energies of the Complexes (kcal/mol) HF/ 6-311G*
MP2/ 6-311G*
MP3//HF/ 6-311G*
MP3//MP2/ 6-311G*
structure laa -0.56 -7.94 -1.71 4.89 structure 2ab -4.71 -8.91 -8.76 -1 1.4 " AE EWmpicx + EN*). - (EA,N,+ + EA,). AE = Ewmplcx - (EA,N~+ TABLE 4: Thermal Corrections (kcal/mol) and Entropies (cal/mol deg) structure thermal correction" entropy" la
8.5 13.8 6.3 4.8 1.5
2a
ArN2 N Ar
" HF//MP2/6-3
71.3 74.3 58.3 45.8b 37.0
1 lG* calculations. Experimental value.14
Table 3 shows the binding energies, expressed in kcal/mol, defined as the difference between the energy of the complex and the sum of the energies of the subsystems. The zero-point energies of the complexes and their subsystems have been calculated by using the structural parameters displayed in Table 1. Since HartreeFock vibrational frequencies tend to exceed experimental values, the calculated frequencies used to estimate the zero-point energies have been scaled by a factor of 0.89, as consistent with the recommendation of Pople et al.12 Table 4 shows the heat capacity corrections (H(298 K) - H(0 K) and the entropic differences, which were estimated by using the classical approximation for translation and rotation, assuming an ideal gas behavior at laboratory temperat~re.'~ Table 5 shows the net atomic charges of the atoms in the complexes, calculated via Mulliken population analysis. It also includes the Fermi contact analysis. Discussion of the Results The structures l a and 2a proved to be stationary points with all the eigenvalues of the second-derivativematrix positive. At the Hartree-Fock level, structure 2b is a stationary point with an imaginary frequency, proving it to be a transition state and not a real minimum. The nitrogen molecules are set at an acute angle to each other, so this structure is not linear. Its energy is higher than the energy of structure 2a. At the MP2 level, this complex is linear but features an energy higher by 6.7 kcal/mol than that of structure 2a. Structure l b is not a stationary point. Upon optimization it separates into N2+ and Ar2+. These results agree well with the experimental results of Magnera and M i ~ h lwho , ~ find that there is an equal probability to lose either N or Ar from the Ar2N2+ complex. Indeed, in this way there must be an argon atom and a nitrogen entity at the ends, as shown in structure la. For the ArN4+ complex, they find an exclusive loss of N2, as consistent with structure 2a, where TABLE 5
the argon is positioned between the two N2 entities and, as such, cannot be eliminated before the nitrogens. Both the experimental and theoretical results predict a linear structure for the complexes, except for structure 2b, at the HartreeFock level. As seen in Table 1, the distance between Nl and N2 is typical of an N2 molecule. The Ar-N distance of about 2.5 A is somewhat larger than the same distance in ArN2+.SThe bond lengths obtained through HartreeFock geometry optimization for structure l a are similar to those obtained by Hiraoka et al.1° However, when MP2/6-311G* geometry optimization is performed, the Ar-Ar and the Ar-N distances become much closer in length, leading to the description of a more symmetric complex. This is also the case for structure 2a, but the HartreG Fock and the MP2 predicted geometries are quite similar. The same pattern is observed for the binding energies: for structure 2a, the correlation energy increases the binding (almost doubles it), but there is no significant difference between the MP2 term calculated with Hartree-Fock geometry and the MP2 term obtained with geometry optimization. Structure la, however, shows a much smaller binding energy for the HF-optimized structure, while the MP2-optimized structure shows a large binding energy, 7.94 kcal/mol, more in agreement with the experiments of Hiraoka et a1.,I0 who report a binding energy stronger than 3.8 kcal/mol. When the MP2-optimized geometry is used to perform MP3 single-point calculations, in conjunction with the MP3/MP2/6-311G* energy for ArN2+, the binding energy of structure l a becomes 4.89 kcal/mol, a value similar to the experimental one obtained by Hiraoka et al.1° The scaled vibrational zero-point energies of structures l a (HartreeFock geometry) and 2a are 4.7 kcal/mol and 8.1 kcal/ mol, respectively, as calculated at the Hartree-Fock level, using the 6-31 1G* basis set and the MP2 geometry. Since the zeropoint energy at the same calculational level of ArN2+ is 3.7 kcal/ mol, the binding energy of structure l a has been corrected by 1.O kcal/mol. The zero-point energy of N2 is calculated to be 3.5 kcal/mol, so the binding energy of structure 2a has to be reduced by 0.9 kcal/mol. The nonscaled stretching frequency of the N-N bonds is 2478.8 cm-I in structure la. In ArN2+, it takes a value of 2447.2 cm-I, while in structure 2a there are two frequencies for the two N2 entities, one of 2670.3 and the other of 2730.2 cm-'. These last are closer than the others to the theoretically calculatedvibrational frequency of N2 which is 2740.6 cm-I. These results are not surprising, since in structure 2a the net atomic charge on the nitrogens is very small, while in structure l a there are charges of .081 and .158 eu on N1 and N2 respectively, making the N2 entity acquire more of an N2+ character. It can be seen from Table 5 that in structure 2a almost all of the positive charge is on the argon. For the Hartree-Fock geometry, in structure la, the charge is more delocalized on the nitrogens, but still the argon is more positive. The repartition of charges in structure l a is similar to that in ArN2+ with Arl featuring a negligible charge (0.17 eu). For the MP2 geometry, both argons are positively charged. These results are in agreement with the photodissociation mechanism proposed by Magnera and Michl? which shows the decomposition of structure 2a to occur via an adiabatic process resulting in the formation of ArN2+ and
Net Atomic Charges and Fermi Contact Analysis structure 2a
structure la HF/6-311G*
Ar 1 Ar2 N1 N2 N3 N4
0.0 17 0.743 0.081 0.158
0.01 1 0.223 0.868 -0.043
MP2/6-3 1 lG* 0.348 0.628 -0.045 0.079
0.199 0.151 0.128 -0.016
HF/6-311G*
MP2/611G*
0.835
0.189
0.831
0.181
0.078 0.127 0.01 1 0.103
-0.010 0.218 0.488 -0.022
0.102 -0.021 -0.017 0.105
-0.028 0.373 0.399 -0.030
770 The Journal of Physical Chemistry, Vol. 98, No. 3, 1994 Nz. The ab initio-obtained energies of Nz, Nz+, Ar, Ar+, and ArN2+ confirm these results. The thermal correction to thedissociationreactions of structure l a into Ar and ArNz+ is of .7 kcal/mol, while for the dissociation of structure 2a into ArNZ+ and Nz it is of 2.1 kcal/mol. The entropy differencesfor the two reactions are -24 cal/mol deg and -32 kcal/mol deg, respectively. In consequence, using the MP3/ 6-31 16*//MP2/6-311G* binding energies, the free energy of binding AG(298 K) will be positive for both structures l a (4 kcal/mol) and 2a (5.8 kcal/mol). It can be concluded that structure l a will be more stable at lower temperatures and it will require a temperature as low as 130 K to bring AG to zero. This result is in agreement with the results of Hiraoka et al.,1° who observe the presence of Ar2N2+ only below 150 K. Structure 2a would be thus stable only below 106 K, when the Hartree-Fock geometry is considered. At MP2 geometry,structure 2a features an uncorrected binding energy of 11.4 kcal/mol, when MP3 single point energy calculations are performed. When the entropy, zeropoint energy, and thermal corrections are computed at this geometry, structure 2a is predicted to be stable below 237 K. As far as the spin distribution is concerned, examining Table 5, one notices that, at the Hartree-Fock geometry, the highest spin is set on N1 in structure la, with some on N2, while at the MP2 geometry it is distributed between Arl, Ar2, and N1. In structure 2a the spin is shared by argon and the two nitrogens close to it, especially in the more symmetricalstructure described by the MP2 optimization. It can be concluded that for a theoretical description which would agree with the experimental results, a geometry optimization which takes into account correlation energy effects is
Sapse necessary. Such calculationspredict more symmetricaland more stable complexes that can be considered molecules and not just solvated dimers.
References and Notes (1) Ferguson, E.E.In Kinetics of Ion-Molecule Reactions; Ausloos, P., Ed.; Plenum Press: New York, 1979. (2) Bowers, M. T. In Ion and ClusterSpectroscopy andstructure; Maier, J. P., Ed.; Elsevier: Amsterdam, 1989. (3) (a) Teng, H. W.; Conway, D. C. J. Chem. Phys. 1973,59,2316.(b) Payzant, J. D.; Kebarle, P. J . Chem. Phys. 1968,48,509. (c) Varney, R.N. J. Chem. Phys. 1959,31, 1314. (d) de Casto, S. C.; Scbaefer, H. F., 111; Pitzer, R. M. J . Chem. Phys. 1981,74,550. (4) (a) Conway, D.C.; Nesbitt, L.E. J. Chem. Phys. 1968,48,509.(b) Stephan, K.;Mark, T. D. Chem. Phys. Lett. 1982,87,226. ( 5 ) Freccr, V.;Jain, D.C.; Sapse, A. M. J. Phys. Chem. 1991,95,9263. (6) (a) Wadt, W. R. Appl. Phys. Lett. 1981,38,1030.(b) Sapse, A. M. To be published. (7) (a)Lee,L.C.;Smith,G.P.Phys.Reu.A l979,19,2329,andrefcrences therein. (b) Deluca.M. J.: Johnson. M. A. Chem. Phvs. Lett. 1989.162.445. (c) Kim,H. S.; Bowers, M.T. J. Chem. Phys. 1991,-93,1158. (d) Nagata, T.; Kondow, T. Z . Phys. D 1991,20,153. ( e ) Chen, Z.Y.; Albertoni, C. R.; Hasigawa, M.; Kuhn, R.; Castleman, A. W. J. Chem. Phys. 1989,91,4019. ( 8 ) (a) Nagata, T.; Hirokawa, J.; Kondow, T. Chem. Phys. Lett. 1991, 176,526.(b) Gadea, F. X . Z . Phys. D 1991,20,25.(c) Hirapka, K.; Mori, T. J. Chem. Phys. 1989,90,7143. (9) Magnera, T. F.;Michl, J. Chem. Phys. Left. 1992,192,99. (10)Hiraoka, K.; Mori, T.; Yamabe, S . Chem. Phys. Leu. 1992,189,1, 7. (11) Frisch, M. J. et al. Gaussian 90; Gaussian Inc.: Pittsburgh, PA, 1990. (12) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees. D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R.; Hehre, W. J. Int. J . Quantum Chem. Symp. 1981,S15,269. (13) Poplc, J. A.; Luke, B. T.; Frisch, M. J.; Binkley, J. S. J. Phys. Chem. 1985,89,2198. (14) CODATA Task Group. J. Chem. Thermodyn. 1978,10,903.
