J . Phys. Chem. 1987, 91,49-53 of the first origin-shift term in eq 16 (the second does not enter for a fixed bond origin) and the origin-shift term in eq 20. A particularly simple form of eq 22 is obtained if the bond origin is chosen to be one of the atoms of the bond. Choosing atom B to be this atom we obtain
where we have elected to use (dR,/aQ,)o instead of sAaand Rk,O becomes RB.0. If atom A is chosen to be the origin then RA and RB exchange roles in eq 23. This same result is obtained from the original bond-dipole expression provided in eq 14 (with the intrinsic contribution given in eq 1 l ) , demonstrating the equivalence of eq 14 and 22. An alternative derivation of eq 22 from 14 follows from substituting ( I ~ R , / ~ Q- ~(aRk/aQa)O )~ for (19p~~/aQ)~ thereby forcing the intrinsic term to contain s, vectors cancel and observing that the new negative terms in (~3Rk/aQ,)~ the inertial term. Therefore, eq 22 and 23 take no direct cognizance of whether the bond origin is fixed in space (and hence (dRk/aQu)Oare zero) or whether all terms in (aRk/aQ,)O cancel. Due to the simplicity of eq 23, it is particularly recommended for use in the computation of VCD intensity in the bond dipole model, when bond dipole moments and their derivatives are available. It is interesting to note that the two terms in eq 23 are of the form of an inertial term for one atom and a two group term for the other atom of the bond, with no intrinsic term, per se. Previous formulations of bond-dipole theories of VCD have included or mentioned the intrinsic terms, but none has given them an explicity form. We see from the present formulation that the intrinsic terms are vital to a complete description of the bond dipole model, at least at the level of equivalence to the charge flow model, as given in eq 14 and 22. In principle, additional kinds of intrinsic magnetic dipole contributions can be envisioned which involve the
49
circulation of local currents within a single bond. Here, currents are constrained (somewhat artificially) to flow along the bond axis, and the intrinsic magnetic dipole moment of the bond arises from a rocking motion of the bond.
Acknowledgment. L.A.N. and T.B.F. acknowledge support from the National Science Foundation (CHE 86-02854) and the National Institutes of Health (GM-23567) for financial support. J.R.E. acknowledges the support of a Fulbright Scholarship for postdoctoral study at Syracuse University.
Appendix We present here a few simple relations for the magnetic dipole moment operator that are consistent with the results of this paper. For the atom-centered formulation of m we can write
where .&,equals Inl, the current flowing along the bond line from n to 1. Taking the derivative of m with respect of Pu (which differs from zero only for the time varying quantities R, and .&,) gives eq 7. Similarly for the bond dipole theory we can write
Previous formulations6-’ of m at this level of simplicity have not included the term proportional to Pk X kk.Equation A2 leads directly to eq 14, after taking the derivative of both sides with respect to Pa. Finally, the magnetic moment expression associated with eq 22 is given by
for the bond origin at atom B.
Theoretical Investigation of the Structures and Electron Affinities of NCO and NCS Isomers, CH,NCH,, and CH,N Wolfram Koch Institut fur Organische Chemie, Technische Universitat Berlin, D - 1000 Berlin 12, West Germany
and Gernot Frenking* Molecular Research Institute, Palo Alto, California 94304 (Received: July 21, 1986)
The optimized geometries and vibrational frequenciesof neutral and anionic NCO and NCS isomers, CH2NCH2,and CHzN are reported at the SCF level employing the 6-31G* basis set. NCO, CNO, and CON are found as minima for the neutral NCO isomers. For the anions, only NCO- and CNO- are stable structures. In case of the NCS isomers, only NCS and CNS are minima for neutral and anionic species. The adiabatic electron affinities and vertical detachment energies are determined at the MP2/6-31+G*//6-31G* + ZPE level. The results are in excellent agreement with recent experimentally derived data reported for NCO, NCS, CH2NCH2,and CH2N.
Introduction In a recent investigation of the electron affinity of the azide radical N3,’ the theoretically predicted value for the vertical electron detachment energy of N3- (2.84 eV) was found to be in excellent agreement with the experimentally derived result (2.76 f 0.04 eV). This was somewhat surprising since this value was (1) Illenberger, E.; Comita, P. B.; Brauman, J. I.; Fenzlaff, H.-P.; Heni, M.; Heinrich, N.; Koch, W.; Frenking, G. Ber. Bunsenges. Phys. Ges. 1985, 89, 1026.
0022-3654/87/2091-0049$01.50/0
obtained at a rather moderate (MP2/6-31G*//MP2/6-31G*) level of theory. Generally, a much higher level is considered to be necessary to predict electron affinities within an accuracy of 0.2 eV.2 However, it has been shown that computed electron affinities at the MP2 level, using a split-valence basis set augmented by diffuse functions, agree with experimental values within an error limit of C N O > CON. For the anions, only NCO- (1A) and CNO- (2A)were found as minima with nearly the same energy difference as for the neutral species, while CONdissociates without activation into CO- and N. This is in agreement with the experimentalz4 and theoretical25 finding that (23) Hout, R. F., Jr.; Levi, B. A.; Hehre, W. J. J . Comput. Chem. 1982, 3, 234. (24) (a) Smith, P. A. S . The Chemistry of Open-Chain Organic Nitrogen Compounds, Benjamin: New York, 1966; Vol. 1 and 2. (b) Grundmann, C.; Grunanger, P. The Nitrile Oxides; Springer-Verlag: West-Berlin, 197 1. (c)
Gay, R. G. The Chemistry of Cyanates and their Thio Derivatives, Patai, S., Ed.; New York, 1977; Part 11, p 819 f.
Figure 1. Schematicrepresentation of the degenerate 2a and 3a orbitals of linear ABC molecules, and the splitting into 2a", 3a", 6a', and 7a' MOs for bent ABC.
substituted NCO species (cyanates and isocyanates) are generally more stable compared to substituted CNO compounds (fulminates and formonitrile oxides). Theoretical studies of C H N O isomersI4 showed that HNCO and HOCN are clearly lower in energy than H C N O and HONC, and H N O C was found only as a weak complex of N H and C O with a very long N - 0 distance of 2.321 A (4-31G).14a However, a theoretical study of NCO+ cation^'^ showed an energy ordering of NCO' > CON' > CNO+. A reversal of the stability order when neutral and respective ionic species are compared has been reported for other systems and has been explained by the nature of the orbitals where electrons are added or taken from.26 Our computed geometries for NCO (1N) and NCO- (1A) agree quite well with previous theoretical results for the neutralI0J1 and anionic species (Chart I).13 Experimentally, the only available data is an upper limit for the sum of the bond lengths of 1N (C2.408 A),12a,b which is matched by our results. The C-N bond lengths predicted for NCO-, CNO, and CNO- indicate a carbon-nitrogen triple bond.z7 A slightly longer C-N bond length is found for NCO. The C-0 and N - 0 bond lengths in neutral and anionic N C O and C N O are intermediate between a single and double bond.27 Electron attachment to N C O and CNO leads to shorter C-N and longer C-0 and N - 0 bonds. The C-0 and N - O bonds in the least stable isomer CON (3N) are clearly longer than in the neutral and anionic isomers. The rather long and weak bonds of 3N indicate that it will be very difficult to observe CON experimentally. Fulminic acid HONC2*and substituted C N O compounds, i.e. fulminates and formonitrile oxides,24are experimentally known, and our results indicate that the strongly bound unsubstituted C N O and CNO- species should be detectable in the gas phase. The unpleasant tendency of fulminic acid and ~~
(25) Poppinger, D.; Radom, L. J . A m . Chem. SOC.1978,100, 3674, and
literature cited therein. (26) (a) Frenking, G.; Schwarz, H. Naturwissenschaften 1982,69, 446. (b) Frenking, G.; Heinrich, N.; Schmidt, J.; Schwarz, H. Z . Naturforsch. 1982,376, 1597. (c) Frenking, G.; Schwarz, H. Z . Nuturforsch. 1982,376, 1602. (d) Frenking, G.; Koch, W. Chem. Phys. Lett. 1984, 105, 659. (27) Pople, J. A.; Beveridge, D. L. Approximate Molecular Orbital Method; McGraw-Hill: New York, 1970; p 11 1. (28) Wentrup, C.; Gerecht, B.; Briehl, H. Angew. Chem. 1979, 91, 503, and cited literature therein.
52 The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
fulminates to e ~ p l o d e ~may ~ * be ~ *a reason that no experimental investigations of 2N and 2A are reported in the literature. Our theoretically determined vibrational frequencies (Table 11) also indicate weaker bonds in the C O N isomer compared to 1N and 2N. The only experimentally derived frequencies exist for the cyanate radical 1N.12 The most recently reported values obtained for NCO in solid argon]” are 529.5, 1272, and 1923 cm-I. Thus, our predicted frequencies shown in Table I1 are consistently too low, especially for u3. The highest occupied molecular orbital (HOMO) of the linear C, N, 0 isomers is the doubly degenerate 2 a orbital shown in Figure 1. In the neutral structures this orbital is occupied by three electrons and thus the molecules are subject to the Renner-Teller effect.29 While distortion from linearity leads to an energy increase for 1N and 2N, two electronic states, A’ and A”, have to be considered for the bent molecules CON (3N). We found the A” state to be 10.4 kcal/mol lower in energy (MP2/ 6-31+G*//6-31G*) than the A’ state which also has a bent geometry (rc-o = 1.299 A; rO-N = 1.310 A; LCON = 133.0’; 6-3 lG*). The C, N, 0 and C, N, 0- species are 15 and 16 valence electron molecules, respectively. The Walsh rules30,31predict that triatomic molecules with 15 or 16 valence electrons should have a linear geometry in their ground states. Obviously, CON (3N) violates the Walsh rules. How can this be explained? The Walsh rules are based on the observations that the shapes of molecules in a class are determined by the frontier orbitals.30 The rules can be considered as the summaries of M O angular correlation diagrams indicating qualitatively if a molecule is linear or benL3Ox3I Triatomic molecules ABC with 13-16 valence electrons should be linear because the degenerate 2 a H O M O increases in energy if the molecule is bent (Figure 1). It is customary to demonstrate Walsh rules using symmetrical molecules AB2 for which the coefficient of the 2 a orbital (which is the la, orbital) at the central atom is zero by symmetry (Figure l).31 For unsymmetrical molecules ABC, this coefficient may be small, but is bonding either to A or B. However, this is probably not the reason that N O C (3N) is found with a strongly bent geometry. We calculated N O C with enforced linear geometry and compared the HOMO with the respective orbitals of bent 3N. It was found that crossing of orbital levels has occurred, and that the highest lying doubly occupied M O of the bent structure actually is the 7a’ orbital depicted in Figure 1 which corresponds to the 3 a M O of the linear structure (Figure 1). In a strongly bent geometry such as calculated for 3N, this orbital may become bonding between atoms A, B, and C. The 7a’ orbital is even stabilized relative to the 2a” M O (Figure 1) which is indicated by the result that the A” state is lower in energy than the A’ state. In electron detachment spectroscopy, the photodetachment threshold is measured for the vertical transition of an anionic species to a corresponding neutral molecule: A- -k hu
+
A
+ e-
The energy necessary for electron detachment (ED) for this process is not strictly equal to the electron affinity (EA) of the neutral species defined as the adiabatic energy difference between A- and A. However, if the Franck-Condon factor is large enough, the adiabatic onset can be seen in the spectrum. In particular, when the geometries of A and A- are very similar vertical and adiabatic transitions may have nearly the same energies, as was found for N3-.’ Table 111 shows that our theoretical study predicts an electron affinity of 3.74 eV for N C O ( l N ) , which agrees well with the latest experimental results of 3.6 0.24aand >3.54 eV.4b Thus, the results of earlier s t u d i e ~are ~ . ~probably wrong. Note that the theoretically predicted value for the vertical transition, i.e. the detachment energy of NCO- ( l A ) , is 4.04 eV. The dif-
*
(29) (a) Herzberg, G.; Teller, E. Z . Phys. Chem. B 1933, 21, 410. (b) Renner, R. Z . Phys. 1934, 92, 172. (30) Walsh, A. D. J. Chem. SOC.1953, 2260, 2266, 2288, 2296, 2301, 2306, 2318, 2321, 2325, 2330. (31) Gimarc, B. M. Molecular Structure and Bonding: The Qualitatice Molecular Orbital Approach; Academic Press: New York, 1979.
Koch and Frenking ference between the vertical and adiabatic values is larger for NCO (0.30 eV) compared to N3 (0.12 eV1). This can be explained by the larger geometry alterations between the neutral and anionic structure for NCO/NCO- compared to N3/N3-. For the latter, the N-N bonds were stretched only slightly from 1.186 to 1.219 A,‘ while the C - 0 bond in NCO- is considerably longer (1.241 A) compared to N C O (1.166 A). The results in Table 111 show that the detachment energy of CNO- (2A) and electron affinity of C N O (2N) are only slightly lower compared to 1A and l N , respectively. Here, the two data differ less (0.10 eV) compared to 1 (0.30 eV) and the detachment energy of the CNO- anion can more readily be taken as electron affinity of CNO. As with N3/N3-, the geometry alterations for 2N resulting from electron attachment, yielding 2A, are smaller compared to l N / l A . NCS Isomers. Only the neutral and anionic NCS (4N, 4A) and CNS (5N, 5A) isomers are found as minima on the potential energy surfaces. Neither CSN (6N) nor CSN- (6A) could be located as stable structures. The energy differences between the two isomers, thiocyanate 4 and thiofulminate 5, are substantially lower for the neutral and anionic molecules compared to the oxygen-containing analogues. There are very few reference data to compare our optimized geometries with. For NCS- a 4-31G optimized value has been published (rCN= 1.158 A, rcs = 1.719 A),17cand an experimental geometry for the NaSCN crystal is available (rcN = 1.170 A, rcs = 1.643 A) which shows a slightly bent structure for SCN-.32 Our results show that electron attachment to both, N C S and CNS, has very little effect upon the geometry. In fact, all four structures 4N, 4A, 5N, and 5A have nearly the same C-N bond length, indicating a triple bond. The C-S bond in 4N and 4A is intermediate between a single and double bond,33while the N-S bond in 5N and 5A corresponds to a single bond.34 Thus, the bond orders for the C-S and N-S bonds in the neutral and anionic CNS isomers are, as to be expected, lower compared to the C-0 and N - 0 bonds in the oxygen-containing analogues, while the C-N bonds are very strong and comparable in magnitude. The theoretically determined values for the electron detachment energies and electron affinities (Table 111) allow an evaluation of the experimentally derived data for NCS. There is excellent agreement between the experimental value of 3.51 eVS and the computed results of 3.47 and 3.48 eV. Earlier experimental data7,* should be considered as dubious. Due to the minimal geometry change, the EA and ED values are nearly identical. Like the oxygen-containing molecules, the EA and ED values for the CNS and CNS- isomers are lower compared to 4N and 4A. 2-Azallyl Radical CH2NCH2and Methanimine Radical CH2N. The 2-azallyl radical 7N is isoelectronic with the allyl radical, and the geometries (planar C2J and electronic structures (2A2) are very similar. It is not a trivial result that a C20geometry for 7N is predicted at the H F level. For example, the restricted Hartree-Fock (RHF) method shows the allyl radical to have C, symmetry with one short and one long C-C b ~ n d . ’ ~This ,~~ “doublet instability” p r ~ b l e m ’ *is~ caused ~ ~ - ~ by ~ the result that R H F theory usually overestimates the stability of asymmetric structures for three-center, three a-electron systems. This can (32) Bats, J. W.; Coppens, P.; Kvick, A. Acta Crystallogr.,Sect. B 1977, 33, 1534. (33) For a carbon-sulfur single bond, suggested values are 1.80-1.83 A, and for a double bond (from CSJ 1.555 A: Tables oflnteratomic Distances and Bond Lengths, Supplement; The Chemical Society: London, 1965. (34) The S-N bond length in S4N4H4is 1.67 & 0.01 A: Sass, R. L.; Donohue, J. Acta Crystallogr. 1958, 11, 491. (35) Paldus, J.; Veillard, A. Mol. Phys. 1978, 35, 445, and references cited therein. (36) (a) Feller, D.; Davidson, E. R.; Borden, W. T. J. A m . Chem. SOC. 1984, 106, 2513. (b) Huyser, E. S.; Feller, D.; Borden, W. T.; Davidson, E. R. J. Am. Chem. SOC.1982, 104, 2956. (c) Feller, D.; Huyser, E. S.; Borden, W. T.; Davidson, E. R. J . Am. Chem. SOC.1983, 105, 1459. (d) Borden, W. T.; Davidson, E. R. Tetrahedron 1982, 38, 737. (37) (a) Bouma, W. J.; MacLeod, J. K.; Radom, L. J . A m . Chem. Soc. 1979, 101, 5540. (b) Bouma, W. J.; MacLeod, J. K.; Radom, L. Nouc. J . Chim 1978, 2, 439. (c) Bouma, W. J.; Poppinger, D.; Saebo, S.; MacLeod, J . K.; Radom, L. Chem. Phys. Lett. 1984, 104, 198.
N C O and N C S Isomers, CH2NCH2,and C H 2 N
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
be corrected by inclusion of correlation energy.18,35,36-37c It has been shown that substitution of an electronegative atom for the central CH group in the allyl radical leads to a more facile distortion from c, symmetry: the potential energy surface of H2C-O-CH2+, another molecule being isoelectronic with 7N, was found to be very flat when the C-C bond lengths are asymmetrically d i ~ t o r t e d . ~ "Thus, , ~ ~ ~ the predicted C, syfnmetric structure for 7 N indicates that U H F is better suited for this kind of problem than RHF. The same conclusion has been drawn from the results obtained for the ring-opened ethylene oxide cation H2COCH2+.37C The nonbonding ?r M O is singly occupied in 7N and doubly occupied in 7A. The C-N bond length is rather short in 7N and corresponds to a double bond.27 A partial geometry optimization of 7N at the STO-3G C I levells also predicts a C geometry, but the C-N bonds are supposed to be longer (1 -38 Because the C-O bond length in the H2COCH2+cation at the 6-31G* level (1.293 A)37cwas also found to be shorter compared to the MCSCF/3-21G value (1.327 A36a),our predicted C-N bond length for 7N is probably too short. Because of charge repulsion, the C N C bond angle is larger in the anion (127') compared to the neutral structure (119.1'). The latter result is in good agreement with the value of 115' found at STO-3G CL1* At the same time the C-N bond is slightly shorter in the anion since hybridization at nitrogen changes from sp2 toward sp. A C,, geometry has also been found as minimum structure for the allyl anion.38 Because of the small geometry differences between the neutral and anionic 2-azallyl molecules, the theoretically predicted electron affinity of 7 N (0.47 eV) is not very different from the detachment energy of 7A (0.53 eV). A comparison with the recently published experimental value for the electron affinity of the 2-azallyl radical (0.8 f 0.3 eV)9 suggests that the exact value is probably at the lower end of the error bar. Our result agrees with the finding9 that the electron affinity of 7 N is larger than the allyl anion (0.357 eV).39 We finally studied the methanimine radical SN and anion SA. Our optimized geometry for 8N (Chart I) is nearly identical with the results obtained by at the H F / D Z level (rCN= 1.263 A, rCH= 1.078 A, LHCH = 118.2'). The HF/DZ+P results of Hinchliffe (rCN = 1.24 A, rCH = 1.14 A, LHCH = 119°)19bshow
a somewhat long C-H bond, but otherwise they are very similar to our data. Due to negative h y p e r c o n j ~ g a t i o nthe ~ ~C-N bond in the anion is shorter and the C-H bonds are substantially longer. Our predicted electron affinity for CHzN (0.52 eV, Table 111) agrees perfectly with the experimental value of 0.5 f 0.1 eV.9 The predicted detachment energy for the anion CH2N- (0.56 eV) differs only slightly.
+
f).
+
(38)(a) Pross, A.; DeFrees, D. J.; Levi, B. A,; Pollack, S. K.;Radom, L.; Hehre, W. J. J. Org. Chem. 1981,46, 1693. (b) Boerth, D.W.; Streitwieser, A. J. A m . Chem. SOC.1978, 100, 750. (39)Oaks, J. M.;Ellison, G. B. J. A m . Chem. SOC.,in press, referred to in ref 5 .
53
Summary Strongly bound neutral and anionic NCO, CNO, NCS, and C N S are predicted by our theoretical investigation, and all four species should be observable in the gas phase. Although C O N was found as a minima on the 6-31G* potential energy surface, the bond lengths are much longer, especially for the 0-N bond, and it seems rather unlikely to observe C O N experimentally. However, CON is theoretically interesting because it is the only NCX isomer found in our study which is not linear and thus it violates Walsh rules. Our theoretically predicted electron affinities and detachment energies agree with recently reported experimentally derived data for C N 0 4 and CNS,S respectively. The 2-azallyl radical 7N was found by our study to have a C, geometry with rather short C-N bonds. The computed electron affinity of 7N (0.47 eV) suggests that the true value is probably at the lower error bar of the experimental value of 0.8 f 0.3 eV.9 A perfect agreement is found for the electron affinity of CH2N between theory (0.52 eV) and experiment (0.5 f 0.1 eV).9 A final remark shall be made concerning the accuracy of the theoretically determined electron affinities reported here. It was shown in ref 1-3 that electron affinities computed at the MP2/6-31+G* level are in remarkable agreement with experiment. As mentioned before, this is due to fortuitous error cancellation at this level. The results presented here are further examples for this. However, it should be kept in mind that the range where this approach yields reliable results is not known. Our results are especially important for larger molecules where the theoretical level is limited for computational reasons. Note Added in Proof. Various levels of theory have been examined and the electron affinities of NCO have been calculated after this paper was submitted.41
Acknowledgment. G.E. thanks Dr. Brian T. Luke for his help in preparing the manuscript. (40) Schleyer, P. v. R.; Kos,A. Tetrahedron 1983,39, 1141. (41)Baker, J.; Nobes, R. H.; Radom, L. J. Comput. Chem. 1986,7,349.
