J . Phys. Chem. 1991, 95, 9263-9266
9263
NMR Conformation Analysis. N M R spectra were recorded
assignment of this species is far from conclusive, the spectrum can be interpreted in terms of two different 31P hyperfine interactions. A likely candidate for this species is an intermediate of the conversion of a localized center into a PLP u* dimer radical cation.
on a Bruker AM400 spectrometer, at frequencies of 400.1, 162.0, and 100.6 M H z for 'H,31P,and I3C, respectively. In all N M R experiments we used CD2C12as solvent.
Acknowledgment. This investigation has been supported by The Netherlands Foundation for Chemical Research (SON) with financial aid from The Netherlands Organization for Scientific Research (NWO). We thank Dr. A. E. H. de Keijzer for performing some of the preliminary experiments in this field. Registry No. Ph2PCH2PPh2'+, 126435-46-9;(Z)-Ph2PCH= CHPPhZ.', 136655-40-8; (E)-Ph2PCH=CHPPh2+, 136655-41-9; Ph2P(R)-Ph2PCH(CHI)CH2PPhz.+l 136655-42(CH2)PPh{', 126575-31-3; 0; (S,S)-Ph2P(CH(CH3)2)PPh2'+, 136655-43-1 ; Ph2PC=CPPh2'+. 136546-98-0;Ph2P(CH2)2P(Ph)(CH2)2PPh2'+, 136546-99-1 ; Ph2P(CH2)3PPh2'+, 136547-00-7;Ph2P(CH2)4PPh2'+. 136547-01-8; Ph2PCH2CH(OC(CHj)20)CHCH2PPh2'+, 136655-45-3; Ph2P(CH2),PPh2'+, 136547-02-9;Ph2P(CH2)6PPh2'+, 136547-03-0; CH3PH2", 91391-14-9;MePH2, 593-54-4;(Z)-H2PCH==CHPH2'+, 136655-46-4; H*P(CH2)2PH;+, 136547-04-1 ; Ph,PCH2PPh2,207 1-20-7; (Z)-Ph,PCH=CHPPhz, 983-80-2;(E)-Ph2PCH=CHPPh2, 983-81-3; PhzP(CH2)2PPh2, 1663-45-2; (R)-Ph2PCH(CH,)CHZPPh,, 67884-32-6; (S)-Ph,PCH(CH,)CH(CH,)PPh2, 64896-28-2; Ph2PCECPPh2,5 1 1295-8;Ph2P(CH2)2P(Ph)(CH2)2PPh2, 23582-02-7;Ph2P(CH2)3PPhZ, 6737-42-4;Ph,P(CH2)4PPh2, 7688-25-7;Ph2PCH2CH(OC(CH3)20)CHCHzPPh2, 32305-98-9;Ph2P(CHz),PPhZ, 27721-02-4;Ph2P(CH2),PPh2, 19845-69-3; (R)-(+)-2,2'-bis(diphenylphosphino)- 1 ,l'-di(R)-(+)-2,2'-bis(diphenylphosphino)- 1,l'-binaphthyl'+, 136655-44-2;
Experimental Section Bis(dipheny1phosphine)s were obtained from Aldrich and were used as received. Dichloromethane was dried by passing over a basic alumina column. X-irradiation and ESR. Solutions of bis(diphenylphosphin0) derivatives in CH2CI2( 1 M) were degased by three consecutive freeze-pump-thaw cycles and subsequently frozen at 77 K in liquid nitrogen. The samples were X-irradiated at 77 K for 4 h using a Cu source,operating at 40 kV and 20 mA. X-band ESR spectra were recorded on a Bruker ER200D spectrometer, interfaced with a Bruker Aspect 3000 computer for digital storage. Typical spectra were recorded with 4K data points and a sweep width of 187.5 mT. Microwave power was 2 mW in most experiments. Temperature was controlled with the aid of a Bruker ER 4111 variable-temperature unit between 95 and 170 K. Hyperfine couplings and g values were determined from the spectra by using second-order corrections.20 (20)Weltner, W. Magnetic Atoms and Molecules; Scientific and Academic Editions: New York, 1983.
naphthyl, 76189-55-4.
Ab Initio Study of Argon and Nitrogen Ionic Clusters Vladimir Frecer,*Vt Department of Physiology and Biophysics, Mount Sinai School of Medicine of the City University of New York, 1 Gustave L. Levy Place, New York, New York 10029
Duli C . Jain, Natural Sciences Department, City University of New York, York College, Jamaica, New York, New York 11451
and Anne-Marie Sapse* Department of Chemistry, City University of New York, Graduate School, New York, New York, and John Jay College, 445 W 59th St., New York, New York 10019, and Rockefeller University, New York, New York 10021 (Received: March 28, 1991)
Ab initio calculations up to the MP4 level of theory were performed for the ArN2+,Ar2+,and (Nz)Z+,molecular ions. These species play an important role in the chemistry of the atmosphere. While the first two clusters are linear, the last is predicted to have a Z - shaped form. Calculated dissociation enthalpies of the clusters correspond well to experimentally observed binding energies. Theoretical reaction enthalpies and equilibrium constants were estimated for a set of reactions involved in the formation of these clusters.
Introduction Small ionic clusters, which play an important role in stratospheric chemistry,'S2 have formed the object of numerous experimenta1pi1*2628as well as theoretical12studies. Among these species, the ionic clusters ArN2+, Ar2+, or (N2)2+ have been experimentally shown to feature large binding energie~.~-*~ 1,z628 As far as the simple homoatomic cluster Ar2+ is concerned, the large binding energy typical for this category of homonuclear complexes, is related to the electron d e l o c a l i ~ a t i o n . ~ ~ The .'~.~~ ArN2+ complex also belongs to this category of clusters since the ionization potentials of Ar and N, are almost the s a ~ n e . ~ . ~ ~ 'Permanent address: Cancer Research Institute, Slovak Academy Sciences, CS-81232 Bratislava, Czechoslovakia.
0022-365419 112095-9263$02.50/0
Experimental observations have shown dissociation energies for the (N2),+ cluster ranging from 11.5 to 24.5 kcal mol-1.9J3.26827 (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 Cluster Ion Spectroscopy and Structure; Maier, J. P., Ed.; Elsevier: Amsterdam, 1989;p 241. ( 3 ) Lindinger, W . ;Dotan, I.; Albritton, D. L.; Fehsenfeld, F. C. J . Chem. Phys. 1978, 68,2607. (4)Arnold, F.; Krankowsky, D.; Marieu, K. J. Nature 1977, 267, 30. ( 5 ) Smith, D.; Adams, N. G.; Miller, T. M. J. Chem. fhys. 1978,69,308. (6)Jarrold, M. F.; Illies, A. J.; Bowers, M. T. J . Chem. Phys. 1983. 79,
6086;1984, 81,214;1985, 82, 1832. (7)Kim, H.S.; Bowers, M. T. J . Chem. Phys. 1990, 93,1159. (8) Mielke, Z.; Andrews, L. J . Phys. Chem. 1990, 94,3519. (9)Teng, H.W.;Conway, D. C. J. Chem. Phys. 1973, 59,2316.
0 1991 American Chemical Society
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The Journal of Physical Chemistry, Vol. 95, No. 23, 1991
Frecer et al.
TABLE I: HF/&31C(d) Equilibrium Geometries and Unscaled Harmonic Frequencies for the Ionic Clusters and Molecules Studied cluster sYm bond length, A bond angle,' deg freq, cm-' ArN2' (a) C ,, N N , 1.084 ArNN, 180.0 212 (n),208 (Eg), 2414 ( 2 , )
ArN2' (b)
ClL
(N2)2+ (d)
D-h
(Nd2' (e)
c2,
(N212'
c2,
(f)
(N2)2+ (g)
cs
Ar2
C,, C." C, C,,
Ar2'
N2 N 2+
ArN, 2.224 NN, 1.093 ArN, 3.451 ArY*, 3.407 NIN2, 1.090 N2N3, 1.940 NjN4, 1.090 NIN2, 1.086 N2X*, 2.146 NINA. 1.110
NNN. 180.0
N;N;: I ,102
NNN, 90.0
NArN, 18.23 ArY*N, 90.0 315 (nu), 381 (nJ,484 (EB), 1869 (ZJ, 2045 C(),
N,N?X*, 180.0 N,X*NS, 90.0
N2N3, 2.375 NIN2, 1.102 N2N3, 1.893 N?Na, 1.089 A;A;, 4.412 ArAr, 2.515 NN, 1.078 NN, 1.094
126 (A'), 208 (A'), 215 (A"), 452 (A'), 2229 (A'), 2314 (A')
NINZN,, 117.29 N2N,N,, 174.18
OX* is the center of the N3N4bond in cluster (N2)2C(d) collinear with the N , N 2 bond. Y* is the center of the N , N 2 bond in ArN2* (b) structure; see Figure I for the cluster numbering. This fact was recently supported also by a b initio calculations'2 resulting in high dissociation energy value over 30 kcal mol-' at the Hartree-Fock level. Teng and Conway9 have studied the stability of Ar2+and (N2)2+complexes. They found values of the dissociation energy close to 26 and 24 kcal mol-', respectively, for both structures. Munson et al.Is presented experimental evidence of a large dissociation energy for the ArN2+complex. Kaul and Fuchs16 reported a lower limit of the dissociation energy of about 15 kcal mol-' for the same complex. However, Curran" suggested a lower limit of 24.5 kcal mol-' using electron impact appearance potential of the ion. The latter value is supported by Teng and Conway? who have used mass spectroscopy techniques. Collision-induced dissociation experiments of ArN2+=showed that the cluster ion is decaying by metastable decomposition. A more recent study, reported by Kim and Bowers,' based on photodissociation experiments in a mass spectrometer, dealt with equilibrium constant measurements of the reaction
+
(N2)2+ Ar
-
ArN2+ + N 2
(IO) Tichy, M.; Twidly, N. D.; Wareing, D. P.; Adams, N. G.;Smiths, D. Int. J . Mass Spectrom. Ion Processes 1987, 81, 235. ( I 1) Miller, T. M.; Ling, J. H.; Saxon, R. P.; Moseley, J. T. Phys. Reu.
1976, A13. 2171. (12) de Casto. S.C.; Schaefer 111, H. F.; Pitzer, R. M. J. Chem. Phys. 1981, 74, 550. (13) Payzant. J. D.; Kebarle, P. J . Chem. Phys. 1970, 53,4723. (14) Conway, D. C.; Nesbitt, L. E. J . Chem. Phys. 1968, 48, 509. ( 1 5 ) Munson, M. S.;Field, F. H.; Franklin, J. L. J . Chem. Phys. 1%2. 37. (16) Kaul, W.; Fuchs, R. 2.Naturforsch. 1960, 15, 326 (17) Curran, R. K. J . Chem. Phys. 1963, 38, 2974.
Ar ....
t
111
NI .....Ar .....N2
t
N'
NI
.. . ,. N2
Ill
Ill
N3
...,.,..
i
NI E5 N2 N 3 z N4 +
pw
IfICl"
(1)
Kim and Bowers' investigated the energetics and kinetics of the photodissociation of the ArN2+ ion to form either the Ar/N2+ or the Ar+/N2 pair. Direction of this equilibrium is still a topic of dispute in the literat~re.'*~,'~ These authors also point out the fact that more information about the nature of this species could be obtained from a b initio calculations. In this paper we apply a b initio quantum chemical methods to calcualte dissociation energies for ArN2+,Ar2+,and (NJ2+ ionic complexes as well as in theoretical estimates of reaction heats and equilibrium constants for reaction 1 and for the formation and dissociation of the molecular ions shown in Figure 1. A uniform theoretical approach is taken for all the systems to derive their equilibrium structures, harmonic frequencies, and bond dissociation energies. These are then used to predict thermodynamic functions for cluster ground states. Results of these theoretical considerations are compared with available experimental data.
1790.
N2
Ar .....N E N i t
lgl 6
Figure I . Structures of the studied molecular ions
Theoretical Methods and Results Studies on the equilibrium geometries of the ionic clusters were made at the unrestricted Hartree-Fock level of theory using a split-valence basis set with polarization functions 6-3 1G(d).I8 The theoretical values of equilibrium bond lengths and bond angles were obtained by the Berny optimization method implemented in the GAuSSIANBB and GAUSSIAN~Oprogram package^'^^^^ by locating the minima on the potential energy surface for various starting structures of all possible symmetry types for the ion ground states. The structural data, summarized in Table I, was used for the calculation of theoretical moments of inertia and harmonic vibrational frequencies listed in Table I for the structures representing the local minimum at each potential energy surface. Since theoretical Hartree-Fock frequencies tend to exceed known experimental values, the calculated frequencies were scaled by a factor of 0.89 when used to derive zero-point vibrational energies (18) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 3973, 28, 213. (19) GAUSSIANBB, Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius. C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.;Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1988. (20) GAUSSIAN go, Revision H; Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.;Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J . A. Gaussian, Inc., Pittsburgh, PA, 1990.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9265
Argon and Nitrogen Ionic Clusters
TABLE 11: HF and MP/631C(d) Total Energies (hartrees) for HF/631C(d) Equilibrium Geometries" cluster HF MP2 MP3 -635.634 17 -635.644 33 ArN2+ (a) -635.203 85 -63 5.1 40 73 -217.373 86 -21 7.356 5 1 -217.34222 -217.36485 -1053.54750 -1053.02682 -108.943 95 -108.36602 -526.773 74 -526.235 04 -54.245 78 -53.747 12
-635.61 141 -217.94448 -217.94058 -217.93347 -217.94779 -1 053.296 40 -1 053.296 40 -109.248 20 -108.698 29 -526.91 105 -526.347 1 1 -54.328 57 -53.818 17
MP4 -635.673 63 -635.643 6 1 -2 1 7.999 94 -217.992 82 -217.981 90 -218.001 IO -1053.326 71 -1053.326 71 -1 09.266 49 -108.717 1 1 -526.92444 -526.364 56 -54.351 32 -53.845 88
-635.597 19 -217.946 12 -217.964 02 -217.93266 -217.94768 -1053.322 18 -1053.322 18 -109.245 34 -108.672 27 -526.923 06 -526.362 17 -54.346 22 -53.838 29
'See Figure 1 for the cluster numbering. TABLE III: Scaled Zero-Point Vibrational Energies (kcal mol-'), Thermal Corrections (kcal mot'), and Entropies (cal mot1 K-l)O cluster ZPE HO(298 K) - Ho(OK) SO(298 K) 4.0 3.3 7.3 7.0 6.3 7.1 0.0 0.3 3.5 3.3
3.1 2.9 3.3 3.4 3.2 3.7 2.6 2.4 2.1 2.1 1.5 1.5 1.5 1.5
62.7 67.4 61.4 67.1 66.6 70.8 65.1 57.4 45.7 47.1 37.v 37.0b 36.6b 36.6b
'See Figure 1 for the cluster numbering. bExperimental value.24 (ZPE) and thermochemical corrections. This is consistent with the recommendation of Pople et aL2I The heat capacity corrections [HO(298 K) - HO(OK)] and the entropic corrections were estimated by using the scaled theoretical frequencies for vibrations and the classical approximation for translation and rotation assuming an ideal gas behavior at laboratory temperature.22 The electronic energies of molecular ions were computed by using single-point calculations that included electron correlation employing fourth-order Maller-Plesset perturbation theory (MP4), the 6-31G(d) basis set, and for the UHF/6-31G(d) equilibrium geometries. Electron correlation was included only for valence electrons in the space of single, double, triple, and quadruple excitations (MP4SDTQ). The reaction enthalpies at 298.1 5 K [AH0,(298 K)] for the molecular ions' dissociation reactions and for reaction 1 were derived from the theoretical energies following the approach described by Pople et al.23 In this approach, the reaction enthalpies at 0 K (calculated from electronic energies [EeI(OK)] and corrected for the zero-point vibrational energies) are supplemented with the thermal corrections giving the reaction heats at laboratory temperature: AHor(298 K) = [E,I(O K) + ZPE]pr,,,j - [Eel(OK) + ZPE],,, + [H0(298 K) - Ho(OK)]p,d - [H0(298 K) - H0(OK)],, (2) The electronic energies are listed in Table 11. The theoretical zero-point vibrational energies, thermal corrections, and entropies are summarized in Table 111. Data for the comparison between the theoretical and experimental thermal corrections and entropies S0(298K) are available only for Nz, where the agreement is ~
Pople. J. A.; Schlegel, H. B.;Krishnan, R.; DeFrees, D. J.; Binkley, J. S.;Frisch, M. J.; Whiteside, R. A.; Hout, R. J.; Hehre, W. J. Int. J . (21)
Quantum Chem. Symp. 1981, SIS,269. (22) Hehre, W. J.; Radom, L.;Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (23) Pople, J. A.; Luke, B. T.; Frisch, M. J.; Binkley, J. S. J. Phys. Chem. 1985, 89, 2198.
TABLE I V Atomic Charges from Mullikan Population Analysis on HF Wave Functions in 631C(d) Basis Set0 atomic charges cluster N, N, N, N4 Ar ArN,' (a) 0.156 0.121 0.722 ArN2+ (b) 0.469 0.469 0.009 (N2)2+(d) (N&+ (e) (N2)2' (f) (N2)2+ (g)
0.197 0.187 0.250 0.326
0.302 0.181 0.250 0.190
0.302 0.316 0.282 0.282
0.197 0.316 0.202 0.202
'See Figure 1 for the cluster numbering. excellent. The difference is less then 0.01 kcal mol-l for the thermal correction and less then 0.1 cal mol-' K-'for the entropy" (that is, less than 0.5% in both cases). The values in Table 111 were rounded off to one decimal. Reaction entropies [AS0(298 K)] were calculated in the usual way; Le., the difference between the theoretical entropies of the products and reactants.
Discussion The equilibrium geometry and electronic structure of the (N2)2+ ionic cluster was studied at Hartree-Fock level of theory by de Casto et al.lz using an extended Huzinaga-Dunning basis set. These authors have found the collinear structure (Figure Id), to be the most stable, followed by structures e and f with the dissociation energies between 30.4 and 19.9 kcal mol-'. Our calculations using the 6-31G(d) basis set show a similar trend. At the Hartree-Fock level, the highest dissociation energy can be assigned to the collinear Dmhcomplex d (40.1 kcal mol-I). The next most strongly bound cluster, not considered by de Casto et al., is the Z-shaped structure g having C, symmetry (34.4 kcal mol-I) followed by the T-shaped C, structure e (29.2 kcal mol-') and finally the trapezoid of C, structure f (20.2 kcal mol-I). The tetrahedral form of the (N2)z+complex was shown to be unstable. Since there are six possible low-lying electronic states of various symmetry for the (N2)2+cluster,l2 the single-determinant Hartree-Fock approximation is inadequate for describing the equilibrium geometry of the ion. It is therefore not surprising that the inclusion of correlation energy at MP4 level changes the order of stability of studied (Nz)z+ clusters. The effect of electron correlation results in significant reduction of stability for all the considered structures that is approximately proportional to the distance between the Nz fragments. Consequently, at the MP4 level the most stable (N2)2+molecular structure is that with the shortest distance between the fragments: namely, the structure g with dissociation energy of 11.0 kcal mol-' followed by structures d with 10.6 kcal mol-' and e with 5.8 kcal mol-'. The regular trapezoid-shaped cluster f, which has the largest interfragment distance (2.375 A) is unstable, having an energy of 1.1 kcal mol-l above the dissociated products. Since (N&+ dissociates into two unsymmetrical species (N2+ N2+)a Dmhcollinear structure with two pairs of equivalent atoms (and their equal contribution to the (24) CODATA Task Group, J. Chem. Thermodyn. 1978, 10. 903.
9266
The Journal of Physical Chemistry, Vol. 95, No. 23, I991
molecular orbitals) may become a serious constraint. We can assume that the dissociation energy will be more adequately approximate by the (N2),+ structure g, which has the lowest C, geometrical symmetry of all the models as well as the lowest symmetry in electronic structure (Table IV). A more precise description of the structure of the Z-shaped form can be obtained by geometry optimization using second-order Moller-Plesset perturbation theory with inclusion of all electrons into the second-order correlation correction calculation using more flexible triple {basis set with polarization functions 6-3 1 1G(d).2S This method partly restores the broken symmetry of the (N2)2+ g form. It leads to a nonplanar Z-shaped structure with the bond lengths NlN2, 1.108 A, N2N3 1.854 A, N3N4 1.108 A, bond angles N I N 2 N 3 136.4', N2N3N4 136.4', and dihedral angle 188.0', which is closer to C, type symmetry than the Z-shaped structure obtained at the Hartree-Fock level. Using a MP4/6-311G(d)//MP2/6-31 lG(d) level approximation the Z-shaped structure is shown to be 14.0 kcal mol-' more stable than the collinear form. Reaction enthalpies at MP4/6-3 lG(d)//HF/6-3 1G(d) level for the dissociation of (N2)2+ionic cluster at 298.15 K, calculated via eq 2 and using the thermal correction factors from Table 111, lead to a value of AH0,(298 K) 10.6 kcal mol-', which is at the lower limit of the experimentally observed binding energies, which range from 11.5 to 24.5 kcal mol-1.9J3926-27 It conforms well with the theoretical values of de Casto et al.I2 predicted for the regular trapezoid structure f and the T-shaped cluster e relative to their lowest calculated dissociation limit as 4.3 and 13.4 kcal mol-I, respectively. Reaction entropies, Gibbs free energies, and equilibrium constants for these dissociation reactions are given in Table V . These theoretical thermodynamic quantities agree with the observed high dissociation energy of this molecular ion and indicate that the equilibrium favors the dissociation products N 2 and N2+. Along with the (N2)2+ionic cluster dissociation, we have also studied the structure and dissociation of ArN2+ molecular ion. Three possible limiting structures depicted in Figure 1 were considered: collinear Cmo structure a, T-shaped C2, structure b, and a collinear D,,,complex c with the argon atom between two nitrogens. Structure c has proven to be highly unstable. Geometrical parameters for HF/6-3 1G(d) equilibrium geometries of a and b forms are given in Table I and electronic energies are shown in Table 11. The data suggest that, at the Hartree-Fock level of theory, the linear C,, form of ArN2+ cluster is 39.6 kcal mol-' more stable than the T-shaped C2, structure. At the MP4 level this value is reduced to 18.8 kcal mo1-I. This result is in agreement with the work of Kim and Bowers,7who made the same qualitative conclusion from a dynamical impulsive model of the ArN2+ photodissociation mechanism. Kim and Bowers7 also suggested that ArN2+is formed from N2+and Ar via the reactions Ar+ + N, N2+ + Ar (3)
+
- -
N2+ Ar (ArN2+)* ArN2+ (4) and degrades to ground-state photodissociation products via ArN2'
+
hv
