4762
J . Phys. Chem. 1990, 94, 4762-4163
Structures and Properties of Double-Rydberg Anions J . V. Ortiz Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131 (Received: March 16, 1990) Double-Rydberg anions consist of a closed-shell cation core and two Rydberg-like,diffuse electrons. Ground-state geometry optimizations disclose stable minima for OH3-, NH4-, and PHI- but not for SH,-, FH2-, and CIH;. An alternative PH4structure with Cb symmetry, based on valence shell electron pair repulsion theory, is a more stable minimum than its double-Rydberg counterpart. Vibrational frequenciesof the minima are reported. Other optimizations of alternative structures based on valence shell electron pair repulsion theory converge either to double-Rydberg minima or to transition states. Electron propagator calculations yield ionization energies for the minima.
Introduction Double-Rydberg anions consist of a closed-shell cationic core plus two diffuse, Rydberg-like electrons. Tetrahedral NH,-,I a stable minimum structure, is 0.42 eV less stable than a H-(NH3) complex. Electron propagator calculations of the ionization energies of both isomers agree closely with spectral features observed in recent photoelectron experiment^.^^^ Computational studies of the barrier to dissociation into H- and N H 3 indicate kinetic stability of the tetrahedral anion.4 Pyramidal, C3, is also a stable minimum according to a recent study of structures, vibrational frequencies, and ionization energies. Ground-state optimizations have previously been performed on FH2-, OH3-, NH4-, and CH5-,6 but it is not certain whether these structures are true minima. Electronic stability of H3CH2-, NH4-, OH), FH2-, and NeH- relative to the corresponding neutrals has been demonstrated through configuration interaction calculations at the geometries of the corresponding cation cores.’ In this work, the search for stable double-Rydberg anions FH
,
cation’s electron configuration plus two electrons in an orbital that transforms according to the totally symmetric irreducible representation of the relevant point group. For all double-Rydberg species, the chief component of the highest occupied molecular orbital is a totally symmetric combination of diffuse hydrogen s functions. Diffuse s functions on the heavy atom are the next largest components; these functions have the opposite phase as the diffuse hydrogen s functions. Electron Propagator Theory. Electron propagator theory is a direct method for calculating electron binding energies without final-state wave functions or total energies.I0 Questions of variational balance between initial- and final-state wave functions and energies are circumvented by calculating systematic corrections to Koopmans’s theorem.I3 Electron binding energies incorporating relaxation and correlation corrections are obtained by solving the following form of the Dyson equation G-I(E) = Go-I(E) - Z(E) Poles of the matrix G are electron binding energies. One seeks values of E such that C-l has a zero eigenvalue. In the canonical molecular orbital basis IGo-’(E)li, = ( E - t,)6, where t, is the ith canonical molecular orbital energy. Neglect of Z(E), the self-energy matrix, in the Dyson equation produces poles at the Koopmans’s theorem values. Perturbative forms of the self-energy matrix are calculated through second, third, and partial fourth order^.'^.'^ Nondiagonal elements of the self-energy matrix are neglected. Eigenvectors corresponding to the poles produce linear combinations of canonical molecular orbitals, the Feynman-Dyson (or generalized overlap) amplitudes. In the case of an ionization energy, such a one-electron funqion, +(xi), corresponds to an overlap between the N-electron reference state and an (.V - I)-electron final state
where x, is the space-spin coordinate of the ith electron. Making the diagonal approximation forces to be a canonical molecular orbital. Iterations with respect to E are performed until the pole is discovered. Closed-shell Hartree-Fock anionic reference states are employed. Only core molecular orbitals are omitted from the diagrammatic summations that constitute the self-energy matrix elements. Electron propagator codes are written as links to accompany GAUSSIAN82’6 and GAUSSIAN88.”
+
(13) Koopmans, T. Physica 1933, I , 104. (14) Ortiz, J. V. J . Chem. Phys. 1988, 89, 6348. ( 1 5 ) Ortiz, J. V. Int. J . Quantum Chem. Symp. 1988, 22, 431. (16) GAUSSIANB~Release A: Binkley, J. S.; DeFrees, D.; Frisch, M.; Fluder. E.; Pople, J. A.; Ragavachari, K.; Schlegel, H. B.; Seeger, R.; Whiteside, R. Carnegie-Mellon University: Pittsburgh, PA, 1982. (17) GAUSSIANBB: Frisch, M. J.; Head-Gordon, M.; Schlegel, H.B.; Ragavachari, K . ; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.: Stewart, J. J. P.; Fluder, E. M.: Topiol, S.; Pople, J. A. Gaussian, Inc.: Pittsburgh. PA, 1988.
0 1990 American Chemical Society
Letters
Basis Sets. Standard programsI6J7are employed to calculate equilibrium geometries with second-order many-body perturbation theory.Is The 6-31 l++G(d,p)l* basis is used for anions with second period atoms, while the 6-31++G(d,p) basis is used for anions with third-period atoms. At the optimum geometry, vibrational frequencies are evaluated, partly to determine whether the structure is a true minimum in the potential energy surface. In the electron propagator calculations, basis sets with multiple diffuse and polarization functions are used. It is necessary to augment the usual diffuse functions12with extra diffuse functions whose exponents are smaller by a multiplicative factor of 0.3. This generates a double diffuse basis, (2+,2+). Applying a factor of 0.09 to the original diffuse exponents generates additional functions for a triple diffuse basis, (3+,3+). The final basis set, designated 6-3 1 1(3+,3+)G(2d,2p), was successfully employed in calculations on NH4- and OH3-.195 Results and Discussion FH,. Although the initial geometric guess has C2, symmetry with bond lengths of 0.961 8, and a bond angle of 113.8', the optimized anion structure has Dmhsymmetry with bond lengths of 1.252 8,. There is one imaginary frequency corresponding to a uu mode. This structure is a transition state. C1H2-. Another D m h transition state is obtained with bond lengths of 1.6355 8,. The cation structure used as an initial guess has bond lengths of 1.286 8, and a bond angle of 97.3'. OH3-. The results of a recent study5 of this anion are summarized as follows. A C3,minimum with bond lengths of 1.030 A and bond angles of 107.2' has vibrational frequencies of 2754, 25 13, 1302, and 896 cm-I. There is little difference between the partial fourth order electron propagator vertical ionization energy, 0.432 eV, and the adiabatic ionization energy, 0.42 eV, where the OH, Rydberg molecule is the final state. A similar D3, structure is a transition state. SH). From an initial, C3, guess with bond lengths of 1.330 8, and bond angles of 96.9', the anion optimization converges to a D,, structure with bond lengths of 1.554 8,. There are two imaginary frequencies with e' symmetry. Following one of these modes leads to a dissociation of H- from H2S along the latter's C, axis. This result and the predictions of VSEPR theory suggest that there may be a T-shaped isomer with C2,symmetry. Such an optimized structure has one bond length of 1.3 18 8, and two bond lengths of 1.657 A. In VSEPR theory, the two latter hydrogens occupy the axial sites of a trigonal bipyramid. The bond angle about the S nucleus involving the axial and equatorial H's is 85.1'. This structure is also a transition state with an imaginary frequency having b2 symmetry. Distortion along this mode correlates with dissociation into H- and H2S. NH4-. A recent paper on this tetrahedral anion] presented evidence for its presence in photoelectron experiment^.^,) Results obtained by using the methods discussed above have not yet appeared, however. The bond length is 1.045 8,. Vibrational frequencies are as follows: 1323 (T2), 1579 (E), 2971 (A,), and 31 12 (T2) cm-l. The partial fourth order electron propagator result ( 1 8) Bartlett, R. J. Annu. Reo. Phys. Chem. 1981,32, 359, and references therein.
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 4163 for the vertical ionization energy is 0.424 eV, in close agreement with previous results. Calculations on the tetrahedral neutral and cation are also performed with the same methods that were used for the anion. The neutral has a bond length of 1.040 8, and frequencies of 1337, 1606, 3089, and 3136 cm-I. The cation has a bond length of 1.024 8, and frequencies of 1497, 1735, 3417, and 3552 cm-I. As electrons are removed, the bond lengths decrease slightly and the frequencies increase. The totally symmetric orbital that receives the additional electrons is nonbonding with slight antibonding character. Calculations in which the VSEPR prediction of a C, structure is employed as an initial guess result in rearrangements to the tetrahedral form. PH4-. The initial guess bond length from the cation optimization is 1.379 A. In the tetrahedral anion, the bond length is 1.444 A. This minimum has frequencies of 455 (T2), 1041 (E), 1853 (Al), and 1975 (T,) cm-I. Electron propagator calculations show a good convergence of results with respect to the order of the self-energy. Koopmans's theorem13 predicts an ionization energy of 0.236 eV. Second, third, and partial f o ~ r t h l ~order !'~ propagator results are 0.495,0.386, and 0.383 eV, respectively. Another geometry optimization was performed from an initial structure inspired by VSEPR theory19 in which one of the equatorial sites of a trigonal bipyramid is occupied by a lone pair instead of a P-H bond. In the optimized, C,, structure, the Haxial-P-Haxial angle is 166.4', the Hcguato ial-P-Hquatorialangle is 103.3', the P-Hafi I bond length is 1.671 and the P-Hquato"al bond length is 1.402 This structure is quite similar to a previous result in which the frequencies were not calculated.2o The present values are 639 (B2), 768 (Al), 1001 (B]), 1004 (Al), 1214 (B2), 1231 (A2), 1402 (Al), 2489 (Al), and 2535 (B,) cm-I. After including zero-point energy corrections, this structure is 1.453 eV more stable than the double-Rydberg isomer. Ionization energies corresponding to the least bound a, level are larger than for the tetrahedral structure; 1.242 eV is the uncorrelated prediction. Second, third, and partial fourth order propagator results are 0.798, 1.037, and 0.949 eV, respectively.
1.
A,
Conclusions Several possibilities for double-Rydberg anions have been found: pyramidal, C3"OH3-, tetrahedral NH4-, and tetrahedral PH,. All three double-Rydberg anions have vertical ionization energies near 0.4 eV. The other double-Rydberg candidates rearrange to transition states with additional elements of symmetry. Structures based on VSEPR concepts either rearrange to double-Rydberg structures or are transition states, with the exception of PH4-, where the lone pair occupies an equatorial position in a stable minimum. This structure is more stable than the double-Rydberg isomer and has a larger ionization energy, 0.95 eV. Acknowledgment. This material is based on work supported by the National Science Foundation under Grant CHE-8723 185. (19) Sheldrick, W. S.;Schmidpeter, A.; Zwaschka, F.; Dillon, K. B.; Platt, A. W. G.:Waddineton. T. C. J . Chem. Soc.. Dalton Trans. 1981. 413. Dillon.
K. B.; Platt, A. Wy G., Schmidpeter, A,; Zwaschka, F.; Sheldrick, W. S. Z . Anorg. Allg. Chem. 1982, 488, I. (20) Trinquier, G., Daudey, J. P ; Caruana, G.; Madaule, Y. J . Am. Chem. SOC.1984,106, 4794.
