J . Phys. Chem. 1990, 94, 526-528
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ARTICLES The N, Molecule and Its Metastability Michelle M. Francl*,’ Department of Chemistry, Bryn Mawr College, Bryn Mawr, Pennsylvania 1901 0
and John P. Chesick*,’ Department of Chemistry, Haverford College, Haverford, Pennsylvania 19041 (Received: October 1 7 , 1988; In Final Form: July 18, 1989)
Ab initio calculations have been used to locate optimal structures for the ground states of N2,tetrahedral N4, and the probable transition state for the dissociationof N, to two N, using a variety of basis sets and Moller-Plesset perturbation theory through fourth order. The energy of formation of N4 from two N, is calculated to be 814 kJ/mol, and the barrier for the dissociation of N4 through a transition state of DZdsymmetry is found to be 315 kJ/mol.
Introduction Tetrahedral P4 has long been known as the form of white phosphorus, dissociating to P2 at high temperature. The extraordinary stability of the triple bond in N, is usually the explanation given for this as the only form of nitrogen having a significant lifetime. N4 has, however, been the subject of a number of published theoretical studies starting with the calculation of Guest, Hillier, and Saunders2 using an STO-3G minimum basis set, with optimization of the bond length for the tetrahedral structure. Wright3 reported the results of using single- and double-{ STO basis sets with geometry optimization. Venanzi and Schulman, have provided essentially the only calculations and N4 discussion of the potential energy surface for the 2N2 reaction, using a double-{ contracted Gaussian basis set. From a force constant analysis of results for N4 they concluded that this molecule had a local energy minimum with Td symmetry, as assumed by previous workers. Similar arguments suggested that a symmetrical distortion of DZdsymmetry was the lowest energy path to the N, dissociation products. N4 with a DZddistortion has a ground-state configuration in which the highest occupied molecular orbital (HOMO) is Ib,, correlating with a corresponding excited state for two N, of the same symmetry. Conversely, the assembly of two molecules of Nz with DZdsymmetry has a ground-state configuration in which the HOMO is 4b2. (The HOMO is doubly occupied in all cases.) The transition state for the N, dissociation was taken to be at the lowest energy point on the ridge of intersection of these two energy surfaces. Venanzi and Schulman reported this saddle point on the intersection ridge to be about 0.064 au (167 kJ/mol) above the equilibrium energy for N4. A 2 X 2 CI calculation using the (lb,), and (4b2), configurations reduced this dissociation barrier to 125 kJ/mol, but no C1 calculations were performed for the reference state of N4. Some estimates were made of the relative size of correlation energy effects based on semiempirical results. Novarro and Castillo5 repeated the calculations for the ground states of N, and N4 using the 4-3 1 G split-valence set, with essentially the same results as those of Wright and Venanzi-Schulman for the calculated N4dissociation energy. Trinquier, Malrieu, and Daudey6
included d orbitals in an “ab initio pseudopotential calculation” and reported that the inclusion of these orbitals changed the energetics of the N, dissociation reaction by a significant amount, 220 kJ/mol. The size of the barrier for decomposition of N, is obviously related to the possibility of its preparation as a metastable species. It is now possible to explore the approach to the Hartree-Fock limit using a variety of basis sets for these closed-shell systems. Both the ground states of these molecules and the energy surface for the Dzd symmetry deformation can be studied and the effects of correlation energy using various orders of M0lIer-Plesset7** (MP) perturbation theory explored. The results of such an investigation are reported here.
( I ) Correspondence may be addressed to this author. (2) Guest, M. F.; Hillier, 1. H.; Saunders, V. R. J . Chem. Soc., Faraday Trans. 2 1972, 68, 2070. (3) Wright, .I.J . Am. Chem. SOC.1974, 96, 4753. (4) Venanzi. T. J.; Schulman, J. M. Mol. Phys. 1975, 30, 281. ( 5 ) Novarro. 0.: Castillo. S . Int. J . Quantum Chem. 1984, 26, 41 1.
80, 552.
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Methods The calculations were performed using the GAUSSIAN 82 suite of program^.^ Restricted Hartree-Fock calculations were made for N2 and tetrahedral N4 using the seven basis sets listed in Table I with optimization of the N-N bond lengths to give the equilibrium energy for each of these basis sets. Table I also shows the results obtained from single-point MP/6-31 lG* and MP/63 1 I++G* calculations using the HF/6-31 lG* optimized geometry. The M P corrections were obtained to second, third, and fourth order using the frozen core approximation. Fourth-order corrections include single, double, and quadruple substitutions (MP4SQD). In some cases (when feasible), triple substitutions were included in the correction (MP4SDTQ). Note that while M P theory is derived from nondegenerate perturbation theory and that some of the states examined here are in fact degenerate, the zero-order wave function for Merller-Plesset is not the Hartree-Fock wave function, but the Hartree product wave function. The Hartree product wave functions for the states in question are nondegenerate. Also, since the individual terms of the M P energy expansion are not variational, there is no guarantee that the series is convergent. In the cases considered here, the magnitude of the E(,) term is always greater than that of E(3)while the fourth-order term (excluding triple substitutions) is smaller than or of the same magnitude as (6) Trinquier, G.; Malrieu, J. P.; Daudey, J. P. Chem. Phys. Lett. 1981, (7) M~ller,C.; Plesset, M. S.Phys. Reu. 1934, 46, 618. (8) Binkley, J. S.; Pople, J. A. In?. J . Quantum Chem. 1975, 9, 229. (9) Binkley, J. S.; Frisch, M.; Krishnan, R.; DeFrees, D. J.; Schlegel, H. B.; Whiteside, R.;Fluder, E.; Seeger, R.; Pople. J. A. Carnegie-Mellon University, 1982, rev. H.
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The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 521
The N4 Molecule and Its Metastability TABLE I: Effects of Basis Set and Perturbation OrdeP N2
N4
method/basis set
RN-N
energy
HF/STO-3G HF/3-21 G HF/6-21G HF/6-311G HF/6-3 1G* HF/6-31 lG* HF/6-311++G* MP2/6-31 IG* MP3/6-31 IG* MP4SDQ/6-3IlG* MP2/6-31 I++G* MP3/6-31 I++G* MP4SDQ/6-3 I 1++G*
1.134' 1.083" 1.084' 1.086' 1.078' 1 .070a 1.070' 1.070 1.070 1.070 1.070 1.070 1.070
-107.5006 -1 08.301 0 -108.77 10 -108.8946 -109.9439 -108.97 19 -108.9741 -109.2906 - 109.2853 -109.2943 -109.2951 -109.2891 -109.2985
RN-N 1.489" 1.54P 1S45' 1.444' 1.395' 1.391" 1.388" 1.391 1.391 1.391 1.391 1.391 1.391
energy
formation energy
-214.7684 -21 6.1924 -21 5.1260 -215.3589 -217.5338 -217.5851 -217.5882 -21 8.2816 -2 18.2666 -218.2763 -218.2895 -218.2732 -218.2835
0.233 0.410 0.416 0.430 0.354 0.359 0.360 0.300 0.304 0.3 12 0.301 0.305 0.314
"Optimized. bRN..Nis in angstroms and energies are in hartrees. TABLE 11: Eauilibrium Bond Lengths and Enereies, 6-311++G* BasisC
NZ energy
RN-N 1.070 1.120 1.095 1.107 1.120 1.065b 1.097d
method HF MP2 MP3 MP4SDQ MP4SDTQ HF limit
expt
-108.9741 -109.3016 -109.2911 -109.3024 -109.3312 -108.9971'
N4
- E)' 0.0000 0.0065 0.0020 0.0039 0.0064
(E,,070
RN-N 1.388 1.469 1.440 1.419
energy -21 7.5882 -218.3060 -218.2807 -218.291 1
- E)' -0.0001 0.0165 0.0075 0.0076
(E1.391
a Difference between energy at HF bond length specified and energy at equilibrium bond length. bSee ref 10 in text. 'Hariharan, P. C.; Pople, J. A. Theor. Chim.Acra 1973, 28, 21 3. Lofthus, A.; Krupenie, P. H. J . Phys. Chem. Ref. Data 1977, 6, 113. R N - N is in angstroms and energies are in hartrees.
N
I
Figure 1. Coordinates for DM symmetry N4.
E(3). The sign of the terms oscillates from negative to positive; one would expect that the oscillation will eventually dampen and approach zero. It is well-known that Hartree-Fock bond lengths are generally shorter than the experimental valuesk0 Use of the M P correction should give calculated equilibrium bond lengths that are longer and thus in better accord with experimental values. It was practical for N z and for tetrahedral N4 to perform the full array of Mdler-Plesset calculations using the 6-31 1++G* basis set at different bond lengths. From this, the equilibrium bond lengths and corresponding energies were obtained for the various orders of perturbation theory employed. Table I1 shows these results as well as the difference in energy between the H F structure and the minimum-energy structure for the M P calculation performed. The full energy surface for N4 of arbitrary geometry involves six independent internal coordinates. Venanzi and Schulman4 presented some reasonable arguments for restricting the distortions to those with D2,, symmetry, and we have followed their lead in this work. This reduces the number of independent internal coordinates from six to two. Figure 1 shows the two independent lengths LI and L2 used in defining the structure of N 4 with Dzd symmetry. The 6-31 1G basis set was first used to map the (Ll,L2) vs E surface. Equality of total energy for the two states having either the 1 b, or the 4b2 orbital as the H O M O defined a "ridge line" in the (LI,L2) plane. The corresponding ridge line was then located for the 6-31 IG* basis. Energy values on each ridge line were then used to locate the saddle points given in Table I11 for the basis sets used. The saddle point obtained by using the 6(10) Cade, P.
E.;Sales, K.D.; Wahl, A. C. J. Chem. Phys. 1966,44,1973.
TABLE 111: D M Symmetry Transition for N, Dissociation saddle point parameters N4 dissociation method/basis set Ll' L2' energy" barrieP 0.063 1.571 1.264 -2 17.295 5 HF/6-311G 0.129 1.534 1.21 1 -21 7.4565 HF/6-311G* 0.1 12 1.534 1.211 -21 8.1696 MP2/6-311G* 0.130 1.534 1.211 -21 8.1365 MP3/6-311G* 0.1 19 1.534 1.211 -2 18.1573 MP4SDQ/6-31 lG* 0.984' 1.391" -21 8.2763 MP4SDQ/6-31 lG* 1.534 1.215 -217.4626 0.126 HF/6-311++G* 0.108 1.534 1.215 -21 8.1814 MP2/6-3 11++G* 0.127 1.534 1.215 -21 8.1464 MP3/6-311++G* 0.1 16 MP4SDQ/6-311++G* 1.534 1.215 -21 8.1679 MP4SDQ/6-3 1 1++G* O.98lb 1.388b -2 17.5882
'Parameters for tetrahedral N4 with R N - N = 1.391 A. bParameters for tetrahedral N, with RN-N = 1.388 A. 'In angstroms. hartrees. 31 1G* basis was 0.065 8, away in this (Ll,L2) coordinate plane from the saddle point for the 6-311G basis. Use of the 631 l++G* basis set moved the saddle about another 0.003 A from the 6-31 1G* saddle point. For comparison, this saddle point was 0.58 A away in the (Ll,L2) coordinate plane from the point defining the equilibrium structure of tetrahedral N4. The coordinates and energy for the equilibrium tetrahedral N4 structure are also included in Table I11 for comparison.
Results and Discussion Table I shows the effect of basis set improvement on the total energies of N, and N,. The energy difference shown in the last column illustrates the relatively large effect of the added d orbitals on the N, bonding in comparison to N2. The 6-3 1 1++G* basis set gives an energy that is within 0.023 hartree of the HartreeFock limit for N,, and the energy of N4 calculated with the same basis set should be similarly close to the corresponding limit. The value of 0.360 hartree (946 kJ/mol) in the last column of Table I is probably close to the Hartree-Fock energy difference for the formation of N, from two N2. The bond length for N, differs insignificantly from the Hartree-Fock limiting value, and the value of 1.388 8, should correspond to the Hartree-Fock limit for the
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J . Phys. Chem. 1990, 94, 528-531
N-N bond length in N4. The values in Table I for the cruder basis sets reproduce the bond lengths and dissociation energies in the previously cited works. Using the geometries optimized at the Hartree-Fock level, the MP calculations give energies that undergo oscillations about an average value with increase in order of perturbation theory. However, the energy differences in the last columns of Tables I and I11 are comfortingly constant for the different perturbation orders for each basis set. The perturbation theory calculations show that the energy of formation of N4 is in the range of 0.300-0.3 14 hartree, or 788-824 kJ/mol, and that the correlation energy for this molecule is at least 0.050 hartree larger than that of two N2. This is in contrast to the estimate of 21 kJ/mol made by Venanzi and Schulman, for this correlation energy difference. The dissociation energy barrier, found in the last column of Table 111, is probably close to 315 kJ/mol, averaging the results of the highest order perturbation theory calculations. This energy difference is seen to be close to the value calculated by using the simple Hartree-Fock method, and thus the transition state and the tetrahedral form of N, seem to have essentially the same correlation energy. Inclusion of correlation through use of the M P perturbation theory leads to longer equilibrium bond lengths than are obtained with just the H F calculations. Table I1 shows the equilibrium internuclear distance found for each of four levels of M P perturbation theory using the 6-31 l++G* basis set. Here we see that the equilibrium bond length in tetrahedral N, is 0.08-0.03 8, longer than the Hartree-Fock value, depending on the order of M P theory employed. Also shown in Table I1 are the equilibrium energy at given bond length and the difference between this energy and the energy at the HF bond length for each perturbation order. The energy of formation calculated and displayed
in Table I for the H F structures must be corrected for the nonequilibrium bond lengths used. These geometry corrections amount to respectively -0.0035, -0.0035, and 0.0002 hartree for the MP2, MP3, and MP4SDQ calculations of the energy of formation of N, given in Table I for the 6-31 l++G* basis set. The errors incurred by the use of H F bond lengths then largely cancel, and the value of 0.310 hartree for the overall energy of formation of N, shown in the last entries of Table I stands as essentially correct. However, a structure that is on a saddle point for a transition state at the Hartree-Fock calculational level is expected to be off the saddle point in a less predictable way when perturbation theory or configuration interaction methods are used to include electron correlation effects. This could result in an energy either higher or lower than the Hartree-Fock saddle point energy for the transition state. A more refined search for the transition-state saddle point using energy values from the M P theory corrected energies would be required to eliminate corresponding errors of about 16 kJ/mol in the N4 decomposition activation energy bamer.
Conclusion Although the calculated value of 8 14 kJ/mol for the energy of formation of N4 shows that this molecule is clearly unstable with respect to dissociation to N2, the barrier of 315 kJ/mol calculated for its decomposition is large enough to suggest a significant lifetime and metastability if N, could be made and trapped. Prolonged irradiation of liquid nitrogen with radiation of wavelength less than 140 nm might yield evidence of N4 formation, using mass spectrometric sampling of carefully vaporized product mixture or through the IR absorption spectrum of the liquid product mixture. Registry No. N4, 12596-63-3.
Collective Proton Motion and Proton Polarizability of the Hydrogen-Bonded System in Disubstituted Protonated Mannich Bases Bogumil Brzezinski, Hanna Maciejewska, Department of Chemistry, A. Mickiewicz University, 60- 780 Poznaii, Poland
Georg Zundel,* and Rainer Kramer Institute of Physical Chemistry, University of Munich, 0 - 8 0 0 0 Munich 2, FRC (Received: January 4, 1989; In Final Form: June 23, 1989)
Nine 2-mono- and 2,6-disubstituted Mannich bases with different 3- and 4-substituents as well as the monoperchlorates of the protonated disubstituted compounds were studied by Fourier-transform infrared spectroscopy. In the case of the monoand disubstituted Mannich bases the intensity of an infrared (IR) continuum increases with increasing acidity of the phenolic group indicating increasing proton polarizability of the intramolecular OH-N F= O--.H+N hydrogen bonds. In the case of the monoperchlorates of the disubstituted Mannich bases with increasing acidity of the phenolic group the intensity of the 1R continuum first increases indicating collective proton fluctuation and proton polarizability of the N+H-OH.-N + N-HO-H+N system. If the acidity increases further, a third proton limiting structure N+H-O--.H+N yields weight. The I R continuum indicates now collective proton motion and proton polarizability in the N+H-OH.-N + N+H-.O--H+N + N-HO-.H+N system. With further increasing acidity of the phenolic group, the intensity of the continuum decreases. This result indicates that the proton polarizability decreases again. Finally, the protons are localized at the N atoms; i.e., only the proton limiting structure N+H-.O--H+N is realized.
( I ) Kurkovskaja, L.N.; Kuliev, A. M.;Shapetko, N. N. Dokl. Akad. Nauk SSSR 1971, 197, 842. (2) Schreiber, V. M.; Koll, A.; Sobczyk, L. Buff.Acad. Pol. Sci., Ser. Sci. Chim. 1978, 24, 651.
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(3) Koll, A.; Rospenk, M.; Sobczyk, L. J . Chem. SOC.,Faraday Trans. f 1981, 77, 2309.
(4) Rospenk, M.; Ruminskaya. T. G.: Schreiber. V. M. Zh. Prikfad.
Spektrosk. 1982, 36,156.
0 1990 American Chemical Society
