15770
J. Phys. Chem. 1996, 100, 15770-15773
Structure and Stability of the Hypervalent Na2CN Molecule: An Experimental and ab Initio Study Masashi Hashimoto,† Keiichi Yokoyama,† and Hiroshi Kudo*,†,‡ AdVanced Science Research Center, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken 319-11, Japan, and Department of Chemistry, Graduate School of Science, Tohoku UniVersity, Sendai 980-77, Japan
C. H. Wu The NET Team, Max-Planck-Institute fu¨ r Plasmaphysik, Boltzmannstrasse 2, D-85748 Garching by Munich, Germany
Paul von Rague´ Schleyer Computer Chemistry Center, Institut fu¨ r Organische Chemie der UniVersita¨ t Erlangen-Nu¨ rnberg, Henkestrasse 42, D-91045 Erlangen, Germany ReceiVed: March 19, 1996; In Final Form: July 8, 1996X
The Na2CN molecule has been detected in the vapor over a mixture of sodium metal and sodium cyanide by means of Knudsen effusion mass spectrometry. The ionization potential, IP(Na2CN+) ) 4.9 ( 0.2 eV, and the energy of dissociation into NaCN and Na, D0°(NaCN-Na) ) 24.8 ( 1.6 kcal/mol, have been determined. The measured value of the dissociation energy indicates moderately strong bonding of sodium to the NaCN fragment, although theoretical calculations indicate a somewhat lower value of 17.4 kcal/mol. The experimental ionization potential agrees well with the theoretical value of 4.66 eV calculated for the vertical ionization. The lowest energy structures are planar with Cs symmetry. The two linear isomers are ca. 12 kcal/mol less stable and may be described as “electronomers” Na+(CN)-Na• and Na•(CN)-Na+. The molecule can be described as a salt of the Na2+ radical cation with the CN- anion, like the previously reported Li2CN molecule. The presence of the Na2+ unit justifies the term hypervalent for this system.
Introduction Wu1-5
as well as theoretical Experiments by Kudo and calculations by Schleyer’s and Marsden’s groups6-7 have provided evidence that polylithiated molecules such as Li3O, Li3S, and Li4P with 9 valence electrons and CLi6, Li4O, and Li4S with 10 valence electrons are thermodynamically stable, despite of their unusual stoichiometries. The stability of these molecules is ascribed to the Li-Li bond or “cage” formation arising from the excessive valence electrons. The study of the nature of bonding in these species, called hyperlithiated molecules, is a subject of continuing interest. In a previous paper,8 we have reported experimental characterization as well as a theoretical study of the thermodynamic stability of another type of hyperlithiated species, Li2CN, with more than one electronegative atom. The molecule exhibited a complex potential energy surface with several minima of comparable stability. The results of geometry optimization indicated that the two lowest energy structures of Li2CN had Cs symmetry; both isomers were best described as complexes of CN- with the Li2+ radical cation. Are similar molecules composed of other alkali metals possible? This paper reports the experimental detection of the Na2CN molecule and the measurement of its thermodynamical stability. The results of an ab initio study on the stability and isomeric structures of this newly found species are also reported. Theoretical Calculations The bond dissociation energy (D0°) and ionization energy (IP) of Na2CN were obtained by ab initio MRCI calculations.9 An * Author to whom correspondence should be addressed. † Japan Atomic Energy Research Institute. ‡ Tohoku University. X Abstract published in AdVance ACS Abstracts, September 1, 1996.
S0022-3654(96)00829-5 CCC: $12.00
atomic natural orbital (ANO) basis set10 of (14s9p4d3f) for N and C atoms contracted to [4s3p2d1f] was used, while that of (17s12p5d4f) or Na contracted to [5s4p2d1f] was employed. Reference wave functions were obtained from complete active space (CAS) self-consistent field (SCF) procedures. Active spaces considered in the CASSCF were 11 electrons in 10 orbitals and 10 electrons in 9 orbitals for Na2CN and NaCN, respectively. All configurations with an absolute CI coefficient |ci| greater than 0.05 were used as the reference configurations in the subsequent MRCI calculations. Total energies were taken from estimated full CI energies with Davidson’s correction.11 The MRCI calculations were carried out using MOLCAS2.12 Geometry optimizations, performed with the Gaussian92 program13 at the MP2(FU)/6-31+G* level, located the Na2CN minima. Table 1 lists the geometric parameters and vibrational frequencies of four isomers, two nonlinear planar structures (1, 2) and two linear structures (3, 4) shown in Figure 1. The C-N bond lengths of all of the isomers are short enough to indicate the triple bond between the carbon and nitrogen atoms. The most stable structure is 1, although 2 has almost the same stability (only 0.4 kcal/mol higher than 1). The potential energy of the linear structures 3 and 4 are 11.7 and 12.0 kcal/mol higher than 1, respectively. Vertical ionization energies, which are calculated as the MRCI total energy of the neutral molecule relative to the singly charged molecular ions at the geometry of the neutral, are listed in Table 2, together with detailed results of the CI calculation. The calculated bond dissociation energy of Na2CN to liberate one Na atom, D0°(NaCN-Na), was 17.4 kcal/mol, the MRCI energy of Na2CN relative to a supermolecule, NaCN + Na, separated by 30 Å. The vibrational correction was accounted for using MP2(FU)/6-31+G* frequencies. © 1996 American Chemical Society
Hypervalent Na2CN Molecule
J. Phys. Chem., Vol. 100, No. 39, 1996 15771
TABLE 1: Vibrational Frequencies of NanCN Molecules Calculated at the MP(FU)/6-31+G* Level
a
molecule
point group
ZPEa (kcal/mol)
freq/cm-1
Bb/GHz
NaCN Na2CN 1 Na2CN 2 Na2CN 3 Na2CN 4
Cs Cs Cs C∞ C∞
3.59 4.25 4.33 4.83 4.64
162,362, 1987 126, 140, 151, 242, 305, 2021 123, 136, 157, 251, 302, 2072 81, 81, 212, 253, 253, 392, 2116 72, 72, 167, 218, 218, 416, 2091
5.52, 8.08, 3.35 7.46, 3.77, 2.51 7.36, 3.49, 2.37 1.30 1.27
Zero-point vibrational energy. b Rotational constant.
eters listed in Table 1. The free energy functions of NaCN(g) and Na2CN(g) are given in Table 3. Results and Discussion
Figure 1. Equilibrium geometries of Na2CN calculated at the MP2(FU)/6-31+G* level (bond distances in angstroms).
Experimental Section The detailed Knudsen effusion mass spectrometry experiments were described in the previous paper.2c,4 A mixture of sodium metal and 5 wt % NaCN crystals loaded in a molybdenum Knudsen cell was heated by a radio frequency (rf) generator, the temperature being controlled within (5 K. The sample temperature was measured both with a thermocouple (R-type) and a pyrometer, calibrated in situ at the triple points of Al and Ag. Identification of the gaseous species effusing from the cell was achieved from their mass to charge ratio, isotopic abundance, ionization energy, and shutterability. The proportionally constant, necessary for converting the ion intensities into partial pressures, was determined from comparison of the ion intensity ratio, I(Na+)2/I(Na2+), with the equilibrium constant for the Na2(g) ) 2Na(g) process reported in the literature.14 The molecular ionization cross section was calculated by taking the sum of Mann’s atomic cross sections.15 All of the molecular species but NaCN effusing from the Knudsen cell were ionized by electron impact at 10 eV. The NaCN species, the ionization energy of which was about 5 eV higher than the other species of current interest, was ionized at 15 eV. To evaluate the thermochemical values, the equilibrium partial pressures of gaseous species for the following processes were obtained:
Na2CN(g) f NaCN(g) + Na(g)
(1)
Na2CN(g) + Na(g) f NaCN(g) + Na2(g)
(2)
The third-law enthalpies of reactions 1 and 2 were calculated from the equation -∆H298°/T ) R ln Kp + ∆[(GT° - H298°/T] where R, Kp, and ∆[(GT° - H298°)/T] represent the gas constant, the equilibrium constant, and the change in free energy functions for the corresponding reactions, respectively. The free energy functions of Na(g) and Na2(g) were taken from JANAF tables,14 while those of NaCN(g) and Na2CN(g) were calculated by a statistical themodynamical method using the molecular param-
Figure 2 shows a typical mass spectrum observed at 709 K for the molecular beam effusing from the Knudsen cell containing a mixture of sodium metal and sodium cyanide. The signals for Na+, Na2+, NaCN+, and Na2CN+ were detected only when the shutter was open. The mass peaks at m/z ) 72 and 73 must be the signals for different isotopic combinations in Na2CN; i.e., m/z ) 72 for [23Na212C14N]+ and m/z ) 73 for [23Na213C14N]+ and [23Na212C15N]+. The observed pattern coefficients of 1 and 0.02 for m/z ) 72 and 73, respectively, agree with that calculated for a Na2CN molecule with the natural isotopic abundances of constituent elements (100% 23Na, 98.9% 12C, 1.1% 13C, 99.6% 14N, and 0.4% 15N). Figure 3 shows the ionization efficiency curves of Na+, Na2+, NaCN+, and Na2CN+. The ionization energies of NaCN(g) and Na2CN(g) were evaluated by the extrapolated voltage difference method16 referring to the ionization energies of 5.139 eV for Na(g) and 4.889 eV for Na2(g).17 Three determinations gave the ionization energies IP(NaCN+) ) 8.70 ( 0.20 eV and IP(Na2CN+) ) 4.92 ( 0.20 eV. These values agreed well with the theoretically calculated vertical ionization energies 8.99 eV for NaCN(g) and 4.66 eV for Na2CN(g). The partial pressures of gaseous species in the equilibrium vapor over the mixture of sodium metal and sodium cyanide are shown in Figure 4 as a function of the reciprocal of temperatures. The equilibrium constants of reactions 1 and 2 obtained from the measured partial pressures were listed in Tables 4 and 5. For the dissociation of Na2CN to liberate one Na atom, the energy was determined directly from the enthalpy of reaction 1 as D0°(NaCN-Na) ) 25.0 ( 1.1 kcal/mol. The third-law enthalpy of reaction 2 was obtained as ∆H0° ) 6.5 ( 1.2 kcal/mol. Combining this value with D0°(Na2) ) 18.2 kcal/ mol of the atomization energy for Na2, we can obtain the dissociation energy of Na2CN as D0°(NaCN-Na) ) 24.6 ( 1.2 kcal/mol. The average of these two dissociation energies is D0°(NaCN-Na) ) 24.8 ( 1.6 kcal/mol. The experimental and theoretical values of the dissociation energy of Na2CN are summarized in Table 2, together with the ionization energies of Na2CN and NaCN. The experimental value of the dissociation energy was somewhat larger than the theoretical value, D0°(NaCN-Na) ) 17.4 kcal/mol, calculated by the MRCI method for the Cs symmetry form of Na2CN. In the absence of experimental data, theoretical calculations provide useful information about the molecular structure. The bond lengths between the carbon and nitrogen atoms calculated for all of the isomeric Na2CN 1-4 are short (1.19 Å) and correspond to triple bonds. This implies that Na2CN is a hypervalent molecule, NaCN with an “extra” Na. The planar structure 1 is the global minimum at the MP2(FC)/6-31+G* level. The other planar structure 2 is nearly as stable as 1, and the calculated total energy of 2 is actually 0.1 kcal/mol lower than that of 1 at the MRCI level. At the B3LYP/6-31+G* level, the total energy of 2 is 0.27 kcal/mol higher than that of 1.
15772 J. Phys. Chem., Vol. 100, No. 39, 1996
Hashimoto et al.
TABLE 2: Total Energies of NanCN at the MRCI Level ∆H0°/(kcal/mol)
IP/eV molecule
(Eh)
n
CSF
∑ci2
Na2CN 1 Na2CN 2 Na2CN 3 Na2CN 4 NaCN NaCN + Na Na2CN+ 1 NaCN+
-416.470 426 -416.470 562 -416.452 766 -416.452 003 -254.583 565 -416.441 684 -416.299 141 -254.253 322
4 4 4 4 5
1426 906 1448 761 1448 761 1722 590 484 133
0.92 0.92 0.91 0.92 0.92
5 8
891 966 958 217
0.92 0.91
theory
4.66 8.99
expt
ZPE/(kcal/mol)
theory
4.3 4.3 4.8 4.6
0.0 -0.02 11.7 12.0
3.6
17.4
expt
24.8(1.6
4.92(0.20 8.70(0.20
TABLE 3: Free Energy Functions -(GT° - H298°)/T and Heat Content Functions -(HT° - H298°)/T for Na2CN Molecule Calculated by a Statistical Thermodynamical Methoda
a
T/K
-(GT° - H298°)/T/ (cal/(mol K))
-(HT° - H298°)/T/ (cal/(mol K))
0 298.15 400 500 600 700 800
infinite 79.067 79.747 81.038 82.497 83.970 85.402
-4.190 0 1.767 3.534 5.327 7.146 8.986
The molecular parameters are listed in Table 1.
Figure 3. Ionization efficiency curves of Na+, Na2+, NaCN+, and Na2CN+ observed at 747 K.
Figure 2. Typical mass spectrum for the vapor over a mixture of Na and NaCN observed at 709 K.
Hence, there are no distinguishable differences between structures 1 and 2. The valence molecular orbitals of Na2CN 1 and 2 are described as (11a′)2(12a′)2(13a′)2(2a′′)2(14a′)2(15a′)1. The 15a′ singly occupied orbital corresponds to the Na2+ radical cation MO and contributes to Na-Na bonding. The other electons are distributed around the CN moiety. The in-plane valence electron density of Na2CN 1, depicted in Figure 5, shows the interaction between the Na2+ and CN- units. The theoretical calculations suggest the existence of an Na2+ unit in the planar Na2CN molecule. This molecule can be considered to be a salt of Na2+ and CN-, similar to Li2CN.8 The MP2(FU)/6-31+G* Na-Na bond length (3.276 Å) in Na2CN is shorter than that in the Na2+ cation (3.653 Å) but longer than in the Na2 molecule (3.152 Å). The valence molecular orbitals of the linear isomers (3, 4) with C∞ symmetry are (9σ)2(10σ)2(3π)4(11σ)2(12σ)1, and the extra valence electron is localized on either of the Na atoms. The linear NaCNNa structure 3 is a minimum, but 3 is 11.7 kcal/mol higher in energy than 1. The extra valence electron of 3 is localized on the Na atom near the N atom. The energy
Figure 4. Equilibrium vapor pressures of gaseous species over a mixture of Na and NaCN as a function of reciprocal of temperatures. The vapor pressures of Na2CN are indicated by open squares.
of 4 is 12.0 kcal/mol higher than that of 1. The extra valence electron of 4 is localized on the Na atom near the C atom. Hence, these “electronomers”18 can be described as Na+(CN)-Na• (3) and Na•(CN)-Na+ (4). The geometries of the Na2CN isomers are quite similar to those of the four Li2CN isomers (two planar and two linear structures), although there are differences in bond lengths.8 The thermodynamic stability of Na2CN is somewhat lower than that of Li2CN; e.g., D0°(LiCN-Li) ) 32.7 ( 3.3 kcal/mol for the most stable structure. The difference in experimental dissociation energies for metal atom loss between Na2CN and Li2CN is 7.9 ( 2.6 kcal/mol. The difference in the theoretical values is 7.4 kcal/mol at the MRCI level. This value coincides with the 7.7 ( 0.6 kcal/mol14 difference in the atomization energies between the Na2 and Li2 molecules.
Hypervalent Na2CN Molecule
J. Phys. Chem., Vol. 100, No. 39, 1996 15773
TABLE 4: Third-Law Enthalpies for the Reaction Na2CN(g) f NaCN(g) + Na(g)a T/K
-R ln (Kp)/ (cal/(mol K))
-∆[(GT° - H298°)/T]/ (cal/(mol K))
∆H298°/ (kcal/mol)
623.2 639.1 645.0 649.6 653.1 654.0 672.8 673.0 673.2 684.3 691.3 693.2 695.0 709.5
20.767 16.979 18.210 15.195 15.930 15.840 14.420 19.269 14.702 14.274 16.640 14.160 12.331 11.178
22.227 22.215 22.211 22.207 22.205 22.204 22.192 22.190 22.190 22.182 22.176 22.174 22.163 22.163
26.79 25.05 26.07 24.29 24.90 24.88 24.63 27.90 24.83 24.94 28.83 25.19 23.98 23.65 av: 25.2 ( 1.1 ∆H0°: 25.0 ( 1.1
a
Second-law values: ∆H0° ) 35.3 ( 8.6 kcal/mol.
TABLE 5: Third-Law Enthalpies for the Reaction Na2CN(g) + Na(g) f NaCN(g) + Na2(g)a T/K
-R ln Kp/ (cal/(mol K))
-∆[(GT° - H298°)/T]/ (cal/(mol K))
∆H298°/ (kcal/mol)
623.2 639.1 645.0 649.6 653.1 653.2 654.0 672.8 673.0 673.2 684.3 691.3 693.2 695.0 709.5
8.804 5.305 6.953 4.951 5.725 6.445 6.522 5.141 5.720 5.177 5.263 9.363 6.687 5.968 6.914
3.484 3.463 3.453 3.446 3.440 3.440 3.439 3.409 3.408 3.408 3.390 3.379 3.376 3.373 3.350
7.65 5.59 6.72 5.45 6.00 6.45 6.50 5.76 6.14 5.78 5.93 8.82 6.98 6.50 7.31 av: 6.7 ( 1.2 ∆H0°: 6.5 ( 1.2
a Second-law values: ∆H ° ) -0.24 ( 6.60 kcal/mol (D °(NaCN0 0 Na) ) 18.0 ( 6.6 kcal/mol).
Figure 5. Contour plot of the density population of valence electrons in the molecular plane of Na2CN 1.
Conclusion The existence of hypervalent Na2CN species has been demonstrated by mass spectrometric observations as well as
ab initio calculations. The dissociation of one Na atom from Na2CN was 24.8 ( 3.2 kcal/mol. The theoretical value calculated by the MRCI method was 17.4 kcal/mol. The dissociation energy determined for Na2CN was smaller than that of the previously reported Li2CN molecule, D0°(LiCN-Li) ) 32.7 ( 3.3 kcal/mol. The observed ionization energy, IP(Na2CN+) ) 4.92 ( 0.20 eV, agreed well with the theoretical value, 4.66 eV, calculated for the vertical ionization. Four stable structural isomers (two planar and two linear minima) have been obtained for the Na2CN molecule by the theoretical calculations. The Cs symmetry isomers are more stable than the linear electronomers. From the presence of a Na2+ unit in planar Na2CN, the molecule is described as a complex of the CNanion with the Na2+ radical cation, similar to Li2CN. References and Notes (1) (a) Kudo, H.; Wu, C. H.; Ihle, H. R. J. Nucl. Mater. 1978, 78, 380. (b) Wu, C. H.; Kudo, H.; Ihle, H. R. J. Chem. Phys. 1979, 70, 1815. (c) Wu, C. H. Chem. Phys. Lett. 1987, 139, 357. (2) (a) Kudo, H. Chem. Lett. 1986, 1611. (b) Kudo, H. Nature 1992, 355, 432. (c) Kudo, H.; Wu, C. H. J. Nucl. Mater. 1993, 201, 261. (3) (a) Kudo, H.; Wu, C. H. Chem. Express 1990, 5, 633. (b) Kudo, H.; Yokoyama, K.; Wu, C. H. J. Chem. Phys. 1994, 101, 4190. (4) Kudo, H.; Zmbov, K. F. Chem. Phys. Lett. 1991, 187, 77. (5) Kudo, H. J. Mass Spectrom. Soc. Jpn. 1993, 41, 317. (6) (a) Schleyer, P. v. R.; Wu¨rthwein, E.-U.; Pople, J. A. J. Am. Chem. Soc. 1982, 104, 5839. (b) Schleyer, P. v. R.; Wu¨rthwein, E.-U.; Jaufmann, E.; Clark, T.; Pople, J. A. J. Am. Chem. Soc. 1983, 105, 5930. (c) Schleyer, P. v. R. In New Horizons of Quantum Chemistry; Lo¨wdin, P.-O., Pullman, B., Eds.; Reidel: Dortrecht, The Netherlands, 1983; p 95. (d) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. In Ab initio Molecular Orbital Theory; Wiley: New York, 1986; p 425. (e) Schleyer, P. v. R.: Reed, A. E. J. Am. Chem. Soc. 1988, 110, 4553. (f) Rehm, E.; Boldyrev, A. I.; Schleyer, P. v. R. Inorg. Chem. 1992, 31, 4834. (7) (a) Gutsev, G. L.; Boldyrev, A. I. Chem. Phys. Lett. 1982, 92, 262. (b) Boldyrev, A. I.; Schleyer, P. v. R. J. Am. Chem. Soc. 1991, 113, 9045. (c) Boldyrev, A. I.; Shamovsky, I. L.; Schleyer, P. v. R. J. Am. Chem. Soc. 1992, 114, 6469. (d) Zakrewski, V. G.; von Niessen, W.; Boldyrev, A. I.; Schleyer, P. v. R. Chem. Phys. Lett. 1992, 197, 195. (e) Zakrewski, V. G.; von Niessen, W.; Boldyrev, A. I.; Schleyer, P. v. R. Chem. Phys. Lett. 1993, 174, 167. (f) Marsden, C. J. J. Chem. Soc., Chem. Commun. 1989, 1356. (g) Ivanic, J.; Marsden, C. J. J. Am. Chem. Soc. 1993, 115, 7503. (h) Ivanic, J.; Marsden, C. J.; Hassett, D. M. J. Chem. Soc., Chem. Commun. 1993, 822. (i) Gutovski, M.; Simons, J. J. Phys. Chem. 1994, 98, 8326. (j) Shi, Z.; Wang, J.; Boyd, R. J. J. Phys. Chem. 1995, 99, 4941. (8) Kudo, H.; Hashimoto, M.; Yokoyama, K.; Wu, C. H.; Dorigo, A. E.; Bickelhaupt, F. M.; Schleyer, P. v. R. J. Phys. Chem. 1995, 99, 6477. (9) Schaefer, H. F., III. In Methods of Electronic Structure Theory; Roos, B. O.; Siegbahn, P. E. M., Eds.; Plenum Press: New York, 1977; p 277. (10) Widmark, P.-O.; Malmqvist, P.-A° .; Roos, B. O. Theor. Chim. Acta 1990, 77, 291. (11) Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8, 61. (12) Anderson, K.; Blomberg, M. R. A.; Fu¨lscher, M. P.; Kello¨, Y.; Lindh, R.; Malmqvist, P.-A° .; Noga, J.; Olsen, J.; Roos, B. O.; Sadlej, A. J.; Siegbahn, P. E. M.; Urvan, M.; Widmark, P.-O. MOLCAS, Version 2; University of Lund: Lund, Sweden, 1991. (13) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision C.4; Gaussian Inc.: Pittsburg, PA, 1992. (14) Chaser, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Fruip, D. J.; McDonald, R. A.; Syverund, A. N. JANAF Thermochemical Tables, 3rd ed. J. Phys. Chem. Ref. Data 1985, 14, (15) Mann, J. B. J. Chem. Phys. 1967, 46, 1646. (16) Hildenbrand, D. L. Int. J. Mass Spectrom. Ion Phys. 1970, 4, 75. (17) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holms, J. L.; Levine, J. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17. (18) (a) Dorigo, A.; Schleyer, P. v. R. Chem. Phys. Lett. 1991, 186, 363. (b) Dorigo, A.; Schleyer, P. v. R.; Hobza, P. J. Comput. Chem. 1994, 15, 322.
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