Faraday Symp. Chem. SOC.,1984 19 109-123 Structure Stability and Energetics of the Neutral and Singly and Doubly Ionized First- and Second-row Hydrides BY SUSAN A. POPEAND IAN H. HILLIER* Chemistry Department University of Manchester. Manchester M 13 9PL AND MARTYN F. GUEST S.E.R.C. Daresbury Laboratory Warrington WA4 4AD Received 13th August 1984 Geometry-optimization studies have been carried out on the neutral and singly and doubly ionized states of the first- and second-row hydrides AH?+ (A = nitrogen oxygen phosphorus sulphur; m = 0 1,2; n = 1,2,3; except H,O and H,S) and AHF+ (A = nitrogen phosphorus; m = 0,1,2). Calculations have been performed at both the SCF and CASSCF levels. Comparison with experimental geometries show that for the first-row hydrides the underesti- mation of the bond lengths and overestimation of the bond angles found at the SCF level are successfully corrected at this MCSCF level.For the second-row hydrides the errors in the SCF values are smaller whilst the subsequent MCSCF corrections are close to those for the first- row hydrides yielding poorer agreement with experimental geometries. Barriers to deprotonation of the dications have been calculated to interpret mass-spectrometric charge-stripping data. All the dications studied except OH2+,NH2+,H202+and NH:+ have relatively large barriers in qualitative agreement with experiment. The calculated adiabatic ionization energies for the monocations of nitrogen and oxygen are except for NH significantly larger than the experimental values.This discrepancy is unlikely to reflect inadequacies in the calculations and points to excited vibrational states of the monocations being involved experimentally. One of the most successful examples of electronic structure theory complementing experiment is in the interpretation and understanding of molecular ionization phen0mena.l The use of ab initio molecular-orbital (MO) calculations with or without the inclusion of correlation effects to calculate the vertical molecular ionization energies obtained from photoelectron spectroscopy is well In such work the calculation of the differential correlation energy between parent molecule and ion may present a severe problem since quantitative estimates demand that a large percentage of the correlation energy is recovered for both species.The more demanding computation of adiabatic ionization energies usually requires the theoretical determination of the equilibrium geometry of at least the molecular ion and has benefitted from the comparatively recent development of analytic gradient techniques.* Such methods allow the determination of not only energy minima but also transition-state structures so that the stability as well as the equilibrium structures of the ionic species may be studied.j Although single ionization energies can be measured by a number of techniques double ionization energies or appearance energies of doubly charged ions are more difficult to obtain experimentally. Recent developments in mass spectrometry by Beynon and c~workers~-~ have yielded new information on both the adiabatic 109 STRUCTURE OF HYDRIDES ionization energy of the cation and the stability of the resulting dication for a series of simple hydrides.It is the purpose of the present paper to provide a theoretical interpretation of these data and to present such results in the context of a more general study of the structure stability and energetics of the neutral and singly and doubly ionized first- and second-row hydrides. EXPERIMENTAL BACKGROUND The charge-stripping method6 is now an established technique for measuring the difference between single- and double-ionization energies. When ions (M+) having high translational energy collide with neutral gas molecules (N) in a mass-spectrometer drift region the charge-stripping process M++N -+ M2++N+e (1) can occur.The minimum loss of translational energy (Qmin)of M+ necessary to allow observation of M2+ may be equated to the first adiabatic ionization energy of M+. Such experimental studies* on the hydrides derived from NH, H20 and H2S imply that all species except H202+,OH2+ NH2+ and NHg+ have lifetimes of several microseconds suggesting a significant barrier to the strongly exothermic process AH:+ +AH:- +H+. (2) In this paper we report calculations of the equilibrium structures of the species AHF+ (A = nitrogen oxygen phosphorus sulphur; nz = 0 1,2; n = 1,2,3; except H30 and H3S) and AHF+ (A = nitrogen phosphorus; m = 0,1,2) thus allowing predictions of the adiabatic ionization energies of the neutral and cationic species to be made.A number of geometry-optimization studies particularly of the neutral and singly charged species involving first-row atoms have been reported by other workers. We include our results on these species to allow for a consistent comparison between all 40 species studied herein. We also report calculations of the structure and energetics of the transition state associated with the deprotonation reaction (2) involving all 14 dications mentioned above. COMPUTATIONAL DETAILS The following gaussian basis sets were employed throughout this work (i) The split-valence 3-21G and 4-31G basis sets due to Pople et aZ.l0(ii) A triple-zeta (TZ) valence basis for hydrogen (5s/3s);11 for first-row atoms (10~6p/Ss3p);~l for second- row atoms (12S9p/6s5p).12 The TZ basis was augmented with a Rydberg s gaussian on the heavy atom ([ = 0.02) to permit a description of those radical species deemed to exhibit a ground electronic state of Rydberg character such as NH4.13 (iii) Polarization was introduced by augmenting the TZ basis by appropriate functions on each atom.In this basis (denoted TZP) a hydrogen p function with exponent 1.O was used while for the heavy atoms sets of six d functions having the following exponents were employed nitrogen 0.98; phosphorous 0.465; oxygen 1.28 ;sulphur 0.542.14 (iv) A more extensive polarization basis denoted TZ +2dlp comprising the TZ basis augmented by two sets of d-polarization functions on each heavy atom15* l6and a single set of 2p functions on hydrogen.14 Two levels of theory have been employed in obtainingminima on the potential-energy surfaces and in locating any barrier associated with the deprotonation reaction (2).(a) Spin-restricted Hartree-Fock SCF-gradient calculations. Singlet states of the various diradical species involved (e.g. H2S2+ PH; NH; H202+) were represented S. A. POPE I. H. HILLIER AND M. F. GUEST by two-configuration SCF wavefunctions to ensure consistency with the use of RHF methods for the corresponding triplet states.17 These calculations were performed within the GVB- 1/PP formalism.lS (b) MCSCF-gradient calculations using the complete active space SCF (CASSCF) method.lg? 2o In the present calculations the 1s orbital of the first-row atoms and Is 2s and 2p orbitals of the second-row species were chosen to be inactive i.e.doubly occupied in all configurations. The active space was generally taken to be a full-valence-orbital space with the CASSCF geometric structures thus obtained subsequently investigated by extending this space. The CASSCF calculations were performed using the TZP and TZ+2dlp basis sets. Subsequent to optimization of the HF/TZP CASSCF/TZP and CASSCF/TZ + 2dlp structures single calculations were conducted at these points with highly correlated wavefunctions. Single-reference state and multi-reference state CI cal- culations (hereafter referred to as SDCI and MRDCI respectively) were performed including all single and double excitations of the valence electrons using the direct-CI method,21 utilizing in general the appropriate set of molecular orbitals derived in obtaining the optimized geometry.Two series of MRDCI calculations were under- taken. (i) All configurations having coefficients > 0.05 were included in the reference set. (ii) More extensive calculations on the triatomic hydrides were performed in which the reference set was taken to comprise all configurations which could be generated by single and double excitations of the valence electrons amongst the active orbitals of the CASSCF zeroth-order wavefunction with respect to the leading term of that wavefunction (usually the HF configuration). Generating all single and double excitations from such a reference set which typically comprised some 100 terms led to CI expansions of up to 150000 configurations.It is hoped that the major part of the dynamic correlation effects would be recovered from such a treatment,, hereafter referred to as MRDCI2. We adopt the notation MRDCI2/TZ +2dlp//CASSCF/TZP for example to indicate a multi-reference CI calculation with the TZ +2dlp basis set at a geometry optimized at the CASSCF level with the TZP basis. Finally harmonic vibrational frequencies were obtained for stationary points on the HF/3-2 1G surface allowing for the determination of zero-point vibrational energies (ZPVE). These energies were scaled by 0.9 when used in the evaluation of reaction energies and barrier COMPUTATIONAL RESULTS PREDICTED GEOMETRIES AND ELECTRONIC STRUCTURES AH MOLECULES AND IONS We consider here the neutral and mono- and di-cation structures for AH molecules where A is nitrogen oxygen phosphorus or sulphur.Omitting the inner-shell molecular orbitals the electronic structures of these species may be specified in terms of the occupancy of the (lal lh, 2a1 lb,) MO for C, symmetry and the corresponding (1 ag 1a, 1nu)MO in Dmh.The states considered here involve double occupancy of the lal(lag) and lb (la,) MO. It is well known that the equilibrium bond angle of these molecules may be discussed by the use of Walsh’s rules,24 focusing on the 2a1 MO which favours a bent rather than a linear structure and leading to the configurations and approximate geometries shown in table 1. The 8-valence-electron systems H,O and H,S. The optimum geometries from SCF and CASSCF calculations employing the 4-3 I G TZ TZP and TZ +2dlp basis sets on H,O and H,S are given in table 2 along with the results of previous studies STRUCTURE OF HYDRIDES Table 1.Low-lying states of AH, AH and AH:+ ~~ valence-electron configuration approximate molecule Dmil c2 bond angle/" HZO H2S 10; 10;1.yq laf lbi2a lb?(lA,) 90 H,O+ H2S+ PH, NH 10; 10; l.",("rI,) laf lb2,2af lb;(2Bl) 90 la? lbi 24 lb?(2A1) 120 'qlAg 1.; 10;10; ("c,, H202+,H2S2+ NH PH; 1a; I b; 24 1b;(3~,) 120 la 16 2a lbY(lAl) 90 laf lb 24 1b?(lAl) 180 NHi+,PHi+ 1.; 10; 1.',(2nn,) la lbi 24 lbyA,) 120 la? lb 2ay lbi(2Bl) 180 Table 2. Optimized geometrical parametersa of H,O and H,S treatment basis r(H-0) LHOH r(H-S) LHSH HF 4-3 1G 0.950 111.2 1.354 95.5 HF DZ25 0.951 112.5 HF TZ 0.950 112.6 1.362 96.0 HF DZdp25 0.944 106.7 HF TZP 0.941 107.1 1.333 94.4 SDCI DZdpZ5 0.960 105.0 CASSCF/32 10 TZP 0.964 103.7 1.359 93.2 CASSCF/3210 TZ2d2~~~ 0.965 103.0 CASSCF/4220 TZP 0.961 105.9 1.348 93.0 CASSCF/4220 TZ +2dlp 0.962 105.1 1.333 92.2 CASSCF /4220 TZ2d2pZ6 0.964 104.8 UMP4(SDQ) 6-3 1G**27 0.957 102.7 UMP2 6-3 lG*28 0.968 103.9 ex tended29 0.955 105.4 experiment3O,31 -0.957 104.5 1.328 92.2 a In all tables distances are in ingstroms (A) and angles in degrees (").including the CASSCF study on H,O by Roos.,~The general trends in predicted geometries with improved basis are well illustrated by these molecules. Considering the water molecule the bond lengths are predicted quite well at the HF/4-31G level although the bond angle is too large by some 7".No improvement in the geometry is found upon extending the s,p basis while the inclusion of polarization functions reduces the bond angle by 4.1" which is accompanied by a marked shortening of the bond length. The CI/DZdp calc~lation~~ gives good agreement with experiment by increasing the bond length and decreasing the angle. The dominant valence-electron configuration for the 8-valence-electron systems (table 1) is in C, symmetry (1~1,)~(2a,)~( 1bJ2(lb,), the unoccupied valence orbitals being 3a and 2b,. Geometry optimization using the CASSCF method26 suggests that employing this full-valence orbital space (with an associated very short CI expansion of 37 configurations) leads to rather disappointing results the bond angle of 103.0" S.A. POPE I. H. HILLIER AND M. F. GUEST underestimating the experimental value by 1.5". The relative 'failure' of this calculation denoted CASSCF/3210 (the notation describing the number of orbitals in the four symmetry species a, b, b and a, respectively) has been rationalized26 in the uneven way the four electron pairs are correlated by the two orbitals 3a and 2b,. These orbitals are used to correlate two of the strongly occupied orbitals one lone-pair orbital (2a,) and one OH bonding orbital (1 b,). Clearly a balanced treatment requires all four electron pairs to be correlated to the same extent. In a CASSCF/4220 treatment (492 configurations) the 4a orbital is used to correlate the la (OH bonding) and the 2b1 correlates the 7c lone-pair orbital lb, such a treatment leads to much better agreement with experiment.26 The present results suggest that the CASSCF optimum geometries are sensitive to basis-set variations thus at the CASSCF/4220 level use of the TZP and TZ+2dlp basis set leads to a small overestimation of the bond angle compared to the (6s4p2d/5s2p) basis of Roos with values of 105.9 and 105.lo respectively compared to the estimate of 104.8' from ref. (26). The general pattern in predicted geometries of the FA ground state of H,S as a function of theoretical treatment is similar to that in H,O with configuration interaction shifting the optimum geometry to longer bond lengths and smaller bond angles.The agreement between the experimental S-H bond length and the HF/TZP estimate is perhaps surprising [see also ref. (33)] while the marked decrease in this quantity on improving the CASSCF treatment is worthy of note. Thus the CASSCF/3210 estimate of 1.359 A decreases by 0.01 1 A on extending the active space and by a further 0.015 A on improving the basis set. Thus the final CASSCF/4220 estimate of 1.333 A and a bond angle of 92.2" is in surprisingly good agreement with the experimental geometry of 1.328 A and 92.2°.30 This agreement should be viewed with some caution the natural orbital occupation numbers reveal that no effective correlation of the la orbital is achieved even at the CASSCF/4220 level. In the latter calculation the 4a orbital appears to act as a second correlator for the 2a valence orbital rather than correlating the 1a orbital.The 7-valence-electron systems NH, OH PH and SH:. The ground state (X2Bl)of these species corresponds to a half-filled 1 b MO and a doubly occupied 2a1 MO lead-ing to an expected bond angle far from linearity whilst the first excited state (A,A,) has this occupancy reversed and an expected larger bond angle. Our optimized geometries (table 3) are in accord with these predictions and with previous calc~lations.~~~ 399 We note that at the HF/TZP level bond lengths in the X2B,states of NH and H,O+ are underestimated by 0.015 and 0.019 A respectively whilst the bond angles are overestimated by 1.9 and 2.2' res ectively. Both effects are compensated for at the CASSCF level increases of 0.025 x(H,O+) and 0.029 A (NH,) in bond lengths and decreases of 3.9" (H,O+) and 3.1" (NH,) in bond angles are found relative to the SCF estimates in the CASSCF/3210 calculations.A more extensive MCSCF treatment at the CASSCF/4220 level with a TZ +2dlp basis yields bond lengths within 0.01 A and bond angles within 1" of the experimental data. The situation is less satisfactory for the second-row hydrides. Although the bond lengths are again given to within 0.01 A by this CASSCF treatment the overestimation of the bond angle given in the HF/TZP calculation is not sufficiently compensated being too large by 1.8" and 1.5" for H,S+ and PH, respectively. Similar effects are evident in our treatment of the *A,excited states (table 3); the good agreement found between the CASSCF geometry and experiment in NH (and for H,S+) is not evident for PH,.The 6-valence-electron systems NH PH H,02+ and H,S2+.By analogy with the well known situation in the isoelectronic CH molecule,41 candidates for the ground states of these molecules are 3B,or ,A (in C2J and 31=; or ,As (in Dmh)(table 1). STRUCTURE OF HYDRIDES Table 3. Optimized geometrical parametersa for AH molecule HF/TZP CASSCF/TZPb experiment 0.980 112.7 1.005 108.8 0.999 1 10.534 1.009 105.2 1.348 95.4 1.038 102.1 1.373 94.1 1.024 103.331p 35 1.358 92.536 1.414 93.7 1.442 92.9 1.428 91.531737 0.976 180.0 0.987 180.0 - 0.985 142.9 1.351 126.7 1.000 143.1 1.370 126.3 1.004 lU3l I .369 1 2736338 1.387 122.0 1.413 121.5 1.403 123.131337 1.019 143.1 1.037 149.7 1.173 180.0 1.182 180.0 1.397 121.0 1.421 122.0 1.428 128.6 1.447 131.8 1.031 110.0 1.058 106.2 1.412 94.4 1.439 94.1 1.402 97.7 1.428 96.6 1.145 180.0 1.169 180.0 1.464 180.0 1.496 180.0 1.449 125.2 1,483 124.8 a The A-H bond length is given first followed by the HAH bond angle.CASSCF/3210. we In agreement with previous MRDCI cal~dations~~ find the ground state of NH; to be the quasi-linear 3B1. The 1A,-3B splitting at the (MRDCI2/TZ + 2dlp//CASSCF/TZ + 2dlp) level 3 1.2 kcal mol-l,* is close to the MRDCI value 42 (29.9 kcal mol-l). In contrast the stabilization of the 2a1 MO in PHZ results in a lA1 ground state for this molecule predicted at the CI/TZP//HF/TZP level to lie some 15 kcal mo1-1 below the 3B state.A similar situation is evident in the dications of H20 and H2S.The vertical 2Bl-2Alenergy separation is ca. 1 eV larger in H2S+ than in H20+ so that ionization to the ground state of H2S2+is from the lb MO leading to a strongly bent lA1 ground-state dication with an estimated (at the zero point corrected CI/TZP//HF/TZP level) 1A1-3B1separation of 2.5 kcal mol-l. In contrast ionization of H20+(2B,) is from the 2a1 MO leading to a linear 3E; ground state of H202+(table 3). The 5-ualence-electron systems NHi+ and PHi+. Ionization from the quasilinear 3B1 ground state of NHZ leads to a linear dication (X2n,) with the valence configuration 10; la In,. In contrast stabilization of the 2a1 MO of PH; leads to a bent 2Al ground state of PHi+ arising from ionization from this MO.The strongly P-H bonding character of the 2a1 MO leads to an increase in the bond angle from 94.1 to 124.8' upon ionization. The first excited state of PHi+ which is found to be linear (",) is predicted to lie 19.4 kcal mol-l above the ground state at the CASSCF/TZP//CASSCF/TZP level. AH MOLECULES AND IONS The possible low-lying states of the AH molecules and ions considered here are given in table 4 and the results of bond-length optimization calculations are shown in table 5. These species have been studied extensively by Meyer and Ros~us.~~~~~ The * 1 cal = 4.184 J. S. A. POPE I. H. HILLIER AND M. F. GUEST Table 4. Low-lying states of AH AH+ and AH2+ electronic molecule configuration state OH SH 1 a22a2 1n3 2II OH+,SH+ PH NH 1 a22a2 1 712 3x-OH2+,SH2+,PH+,NH+ la228 1711 2n 4.2x-2A 2z+ 1022a’ 1 n2 9 PH2+,NH2+ la22a2 lx+ 3,1n 10220171 Table 5.Equilibrium bond lengths of the ground states of AHm+ ~~ molecule ~~ HF/TZP CASSCF/TZP experiment43,44 1.020 1.049 1.037 1.049 1.078 1.070 - - - 0.952 0.976 0.971 1.005 1.029 1.029 - - - 1.419 1.443 1.422 1.417 1.448 1.425 1.452 1.474 - 1.337 1.363 1.341 1.354 1.374 1.364 1.425 1.451 a Repulsive potential curve. CASSCF results utilized the full valence space la,2a,3aand ln MO. The ground-state symmetries of the six- and seven-valence-electron systems present no problems being 3E-and 211 respectively. However for the five-valence-electron systems 211 and 4Z-are the contenders for the ground state.For NH+ and PH+a 211ground state is found the X 211-A 4C-separation being greater for PH+ (1.6 eV45)than for NH+ (0.07 eV49. We find a similar pattern in the isovalent OH2+ and SH2+ radicals. Thus SH2+ exhibits a 211ground state whilst calculations on OH2+ at the geometry of OH+ suggests that the 4Ec-state lies some 1.6 eV lower in energy than the 211state. However no minimum is found in the Hartree-Fock potential curve of either state with any of the basis sets. Clearly the ground-state potential curve is repulsive suggesting that dissociation to O+(4S)and H+ will be instantaneous. The ground state of PH2+ is calculated to be lZ+(la22a2). However for NH2+ calculations at the NH+ bond length suggest a 311ground state.As for OH2+ this Hartree-Fock state is found to be repulsive for all basis sets used so that we again conclude that dissociation of NH2+ to N+ and H+ would be spontaneous. Comparison with the experimental bond lengths shows that for the first-row species the CASSCF calculation corrects the inadequacies of the HF/TZP calculations. However for the second-row species the CASSCF bond lengths are uniformly too long. For SH we find that increasing the CASSCF space from (30 In) to (40 2n) whilst increasing the correlation energy recovered from 0.019 to 0.059 a.u. changes STRUCTURE OF HYDRIDES Table 6. Ground states of AH, AH and AH$+ D:m c,tj ____~___ molecule configuration state configuration state Table 7.Optimized geometrical parameters for the AH speciesa molecule HF/TZP CASSCF/TZP experiment 0.998 108.9 1.010 120.0 1.022 106.0 1.030 120.0 1.013 1O7.Og7 - 1.084 120.0 1.110 120.0 I 0.957 119.9 -. - 1.055 120.0 1.078 120.0 - 1.410 95.6 1.392 1 12.4 I .424. 120.0 1.439 94.3 1.416 113.0 1.451 120.0 1.412 93.448 - 1.344 96.8 1.389 116.0 1.410 118.2 - - The A-H bond length is given first followed by the HAH bond angle. the bond length by only 0.001 A. Both the (30 171) and (40 271) CASSCF bond lengths decrease by 0.007 A on utilizing the TZ +2dlp basis However the calculated bond length is still 0.014 A larger than experiment. AH MOLECULES AND IONS In table 6 we show the ground-state configuration of these species for D,,and C, symmetry.Table 7 lists the optimized geometries at the HF/TZP and CASSCF/TZP levels the full valence space of seven MO being used in the CASSCF calculations. The geometry of these species is in general determined by the occupancy of the 2a1 lone-pair MO (1 a; in D3h).49For those species with more than six valence electrons this MO is occupied and its increased stability away from a planar structure implies a strong trend towards a pyramidal equilibrium geometry for such species. It is well known that the eight-valence-electron molecules (NH, PH, H,O+) are pyramidal and many calculations have been carried out to predict their inversion Ionization from the 2a1 MO is less likely to lead to a planar structure for the second row than for the first row species. Thus NH$ is planar,52 whilst PH$ has been shown both e~perirnentally~~7 j6 to be non-planar.Large basis SCF-CI 54 and the~retically,~~? calculations on SiH, PH,+ and SH:+ predict all three to be n~n-planar.~~ The geometries shown in table 7 reveal the behaviour previously noted between first- and second-row species. Thus the underestimation of the experimental bond length at the HF/TZP level is far greater in the first-row species (NH, 0.015 A) than in the second-row species (PH, 0.002 A). The constant increase in redicted bond length at the CASSCF level ranging from 0.020 A (NH;) to 0.029 1(PH,) relative to the S. A. POPE I. H. HILLIER AND M. F. GUEST Table 8. Optimized geometrical parameters of AH, AH and AH:+ value molecule symmetry state parameter HF/TZP CASSCF/TZP r(N-H) r(N-H) 1.018 1.011 1.031 r(N-H) 1.125 r(N-H) r(N-H) 1.104 1.102 1.125 1.126 LHNH 147.2 146.2 r(P-H) r(P-H) r(P-H) r(P-H) 1.414 1.389 1.495 1.481 1.415 LHPH 135.1 r(P-H) 1.882 1.877 r(P-H) 1.416 1.438 LHPH 95.6 95.5 HF/TZP estimates results in poorer agreement with experiment for PH at the MCSCF than at the SCF level.The decrease in bond angle found in both NH and PH at the correlated level of treatment leads however to improved agreement with experiment. AH MOLECULES AND IONS The optimized geometrical parameters for the AH species are summarized in table 8 the CASSCF studies utilizing the full valence space of eight MO. In agreement with previous work,13. 57 NH (G)corresponds to a minimum on the potential-energy surface lying 3.3 kcal mol-1 below H +NH at the CI/TZP//TZP level.Zero-point corrections decrease this value to -5.2 kcal mol-l again suggesting that the stability of this species is controlled by zero-point effects. Calculations on PH suggest that the tetrahedral structure is similarly a minimum on the ground-state potential-energy surface but in contrast to NH the dissociation of PH to PH +H is predicted to be exothermic at all levels of treatment being 28.5 kcal mol-l when zero-point corrections are applied to the CI/TZP//TZP estimate. Both NH and PH have tetrahedral structures our values of the N-H bond lengths of 1.01 1 A (HF/TZP) and 1.031 A (CASSCF/TZP) being close to previous SCF and CI values of 1.0107 and 1.0185 A re~pectively.~~ We find a similar increase in the P-H bond length of PH being 1.389 A at the HF/TZP level and 1.41 5 A at the CASSCF/TZP level.The dications NHi+ and PHi+ have seven valence electrons and as in the isovalent CH,f cation distortion from G is expected.5s Investigations of both tetrahedral and lower-symmetry structures of NHi+ reveal at least three stationary points of G,D2d and D,,symmetry (table 8). Preliminary studies suggest that C, structures converge to a Dadconfiguration whilst C, structures dissociate to NH; +H+. Lower-symmetry structures are unlikely since dissociation would probably occur owing to charge localization. Both SCF and CI calculations place the 2T state significantly higher in energy than the distorted Dzd and Ddhstructures.We find the 2A (D2J state to be a minimum on the potential-energy surface whilst 2A2u(D4J corresponds to a STRUCTURE OF HYDRIDES Table 9. Calculated and experimental adiabatic ionization potentials (eV) of the neutral hydrides ~~ HF CASSCF CI molecule state TZ TZP TZP TZ+2dlp TZP MRDCI2 experiment 2A 4.0 4.0 -4.4 -4.760,61 'A 8.5 8.7 8.7 -9.6 -10.262 2Bl 9.3 9.6 9.6 10.9 10.5 10.9 1 1.563 3Z-12.8 12.8 12.3 -13.1 -13.564 2Al -3.5 -3.8 IA1 8.7 8.6 8.7 -9.3 -10.054 2Bl 9.1 8.6 8.6 -9.4 -3C-9.8 9.6 9.3 -9.5 -9.865 2A' 4.6 4.6 -5.1 lA1 11.0 11.0 11.0 12.3 12.0 12.3 12.666 217 11.4 11.4 11.3 -12.3 -1 3.06' 'A 9.5 9.4 9.2 9.3 9.8 10.0 10.566 2l-I 9.3 9.2 9.1 -9.7 -10.46s transition structure with one imaginary frequency.Similarly for PH:+ we find the 2& (q)state to be significantly higher in energy than the CS2, and Dzd structures. The C3vstructure (,A,)corresponds to an energy minimum with one very long P-H bond. The Dzd (2A,) structure is not a minimum at the HF/3-21G level but a hill-top characterized by a doubly degenerate imaginary frequency. At the HF/TZP level this Dzd structure lies 23.8 kcal mol-l above the C, structure. ADIABATIC IONIZATION POTENTIALS THE NEUTRAL HYDRIDES In table 9 we show the calculated first adiabatic ionization potential of the neutral hydrides. As expected the SCF values are too small compared with experiment an increase towards the experimental value being evident as the basis size and level of correlation are increased.A balanced treatment of correlation in both molecule and ion must be capable of recovering 90-95% of the valence-shell correlation in order to yield ionization energies accurate to 0.1 eV. This percentage is clearly not obtained using the present TZP and limited MRDCI calculations so that the CI/TZP calcu- lations in table 9 underestimate the ionization energies by ca. 0.7 eV. Extensive calcu- lations which we have carried out of the adiabatic ionization energy of H,S illustrate the slow convergence of the calculated value. Thus using a (12~9p2dlf/7~5p2dlf) sulphur basis and a (5s2p/3s2p) hydrogen basis at the SDCI level with estimates of the importance of higher excitations being obtained using the modification of Davidson's c~rrection~~ due to Pople et aZ.,'O leads to a value of 10.22 eV compared with the experimental value of 10.48 eV.THE CATIONIC HYDRIDES The calculated and experimental8 ionization energies of the cationic hydrides are compared in table 10. We find the same trends with successive improvements in the theoretical treatment as was found for the neutral hydrides. Thus the HF/TZP estimates increase as more account is taken of the differential correlation between the S. A. POPE I. H. HILLIER AND M. F. GUEST 119 Table 10. Calculated and experimental adiabatic ionization potentials (eV) of the cationic hydrides HF/TZP CASSCF/TZP CI/TZP CI + cation state //TZP //CASSCF/TZP //HF/TZP ZPVE experimental*.a NH ,A 23.3 23.7 24.0 23.6 24.5 NH; 2Ai 22.5 22.3 23.2 23.0 22.2 NH; 3B 24.0 23.8 24.5 24.4 23.3 NH+b 25.6 -26.9 -25.0 PH lA 20.0 20.7 20.3 PH,f 2Al 17.6 17.4 18.0 18.0 PH; ,A 18.9 18.7 19.2 19.2 -PH+ 18.4 17.7 18.7 18.7 OH 'A 22.3 -23.2 22.9 22.5 OH 2Bl 23.5 23.6 24.5 24.3 23.5 OHtb 3C-28.4 28.5 29.6 -29.0 SHT 'A 19.2 -19.8 19.6 21.4 SH; 2BB 20.0 20.1 20.9 20.8 21.0 SH+ 3C-21.7 21.4 21.9 21.9 21.2 a Accuracy is k0.3 eV except for NH; NH+ OH and OH+ for which the accuracy is estimated to be f1.0 eV.Values derived at the monocation equilibrium geometries. mono- and di-cation. Little improvement at the CASSCF level is found for the ionization energies of both the neutral and cationic hydrides since this treatment favours the species with the fewer number of electrons. The most extensive calculation carried out that of the ionization energy of H2S+ which parallels that of H2S previously described yields a value of 2 1.12 eV 0.3 eV larger than the best calculated value in table 10.We note that differences in zero-point energy between the mono- and di-cation which act to decrease the calculated ionization energy are more important than for the neutral hydrides since the bonding in the parent monocation is significantly stronger than in the corresponding metastable dication. This effect is found to be greatest for NHZ and PHZ decreasing the ionization energy of both species by 0.4 eV. Comparison of the calculated adiabatic ionization energies of the monocations with the experimental charge stripping values (table 10) shows that for all the species NH; and OH; except NHZ the calculated values are 0.5 to 1.9 eV greater than the experimental values.A similar effect has been noted for the CHL 72 For the monocations SHL we find no systematic deviation between theory and experiment and for the PHL species no experimental data are available. The origin of these discrepancies is unclear. It is possible that transitions from vibrationally excited monocations to ground-state dications provide an explanation where the theoretical ionization energy is larger than the charge-stripping value. STABILITY OF THE DICATIONS The calculations previously described have shown that of the fourteen dications studied all except OH2+ and NH2+are characterized by a local minimum on the potential-energy surface. The stability of these cations will clearly depend upon the magnitude of the barrier for the deprotonation reaction (2).We estimate that the lowest asymptote is in each case AH:- +H+ while the lowest attractive channel generally corresponds to AH2,$_ +H. The most probable mechanism for reaction (2) is thus an initial motion along this attractive channel followed by an electron jump STRUCTURE OF HYDRIDES -396.85--397.001 -397.05 1 --397.10 I11III 12 3 4 5 6 7 8 9 10 r(S-H)/ A Fig. 1. Potential curve for SH2+at various levels of treatment. corresponding to dissociation on the former repulsive curve. This is clearly illustrated in the potential curves for the 211state of SH2+computed at three levels of treatment (fig. 1). Whilst the HF/TZP curve is expected to provide a good zero-order description of the reaction the close agreement in both the height and location of the barrier for the three calculations is gratifying.The calculated deprotonation energies and activation barriers are given in table 11. The major trend observed is for an increase in the barrier between the first- and second-row species. Note however that the ground state of the monocations is not obtained in all cases. Thus deprotonation of SH;+(lA,) and NH;+(lA;) leads to the excited states SH+(lA) and NH;(lA,). We see that correlation generally has an effect on the deprotonation energies not exceeding 9 kcal mol-l although no consistent trend is apparent. The zero-point corrections always lead to a larger deprotonation energy owing to the additional degrees of vibrational freedom in the dication.Activation barriers of < 10 kcal mol-1 are found for deprotonation of H202+and NHt+. The detection of these dications together with OH2+ and NH2+ which are predicted to have repulsive potential curves would thus not be expected in the charge-stripping experiments. Deprotonation of the remaining dications is ac-companied by a substantial activation barrier indicating that these species should be observed. These predictions are in complete agreement with experiment.8 The transition-state structures are illustrated by showing in table 12 those for deprotonation of XH;+. For all dications the transition state corresponds to one considerably elongated H-X bond whilst the others remain within ca.0.2 A of their equilibrium values. Deprotonation of the species XHZ+ proceeds through a quasi-planar C S. A. POPE I. H. HILLIER AND M. F. GUEST Table 11. Calculated activation barriers and deprotonation energies (kcal mol-l) deprotonation energy activation barrier HF/TZP CI/TZP CI+ HF/TZP CI/TZP CI+ molecule //TZP //TZP ZPVE //TZP //TZP ZPVE 120.8 117.9 118.4 9.6 8.7 8.1 66.8 57.7 62.0 44.0 42.3 38.6 101.1 105.5 108.6 14.5 13.4 11.4 -202.9 208.6 -0.0 0.0 62.2 66.0 69.0 23.5 19.8 17.0 27.3 20.5 25.9 57.5 65.0 60.9 42.3 48.1 51.6 47.6 42.8 23.1 14.2 16.9 -67.2 64.5 82.7 81.2 84.1 24.7 25.3 23.9 131.6 130.8 131.8 1.6 2.1 1.4 -260.9 262.6 -0.0 0.0 50.7 51.3 53.5 42.3 42.6 40.5 45.0 51.1 61.8 50.9 49.7 39.3 76.6 67.4 69.7 39.3 38.6 36.3 Table 12.Optimized geometrical parameters for the deprotonation transition structures XH;+ -+ XH++ H+ value parametera HF/TZP CASSCF/TZP NH;+(211,)-+ NH+(211)+H+ r(N-H) 1.088 1.114 r(N-H,) 1.824 1.863 WNH 180.0 180.0 0~;+(3zg)-+ OH+(~Z-)+H+ r(0-H) 1.099 1.108 r(O-H,) 1.459 1.553 WOH 180.0 180.0 PH;+(2A,)-+ PH+(211)+ H+ r(P-H) 1.426 -r(P-H,) 2.890 -(HPH 123.7 -SHZ+('A,) -+ SH+(lA)+ H+ r(S-H) 1.370 -r(S-H,) 2.754 -(HSHl 105.8 -~ a H labels the departing proton. 122 STRUCTURE OF HYDRIDES transition state with deviations of < 6" from planarity. Deprotonation of PH:+ which has a C31) ground state proceeds via a C31)transition state the long P-H bond length having increased to 3.437 A.Deprotonation of NH:+(D,,) is predicted to occur through a C structure in which one N-H bond is stretched by 0.3 A. However this transition state is only 8.7 kcal mo1-l above the D2d minimum (reduced to 8.1 kcal molP1 by zero-point corrections). Thus although we have not explained the role of the D, saddle point which lies 7.1 kcal mol-1 above the DBd minimum we conclude that in view of these small barriers NH:+ can have at best a very short lifetime. CONCLUSIONS The principal conclusions resulting from the calculations described herein are as follows. (a) Comparison with experimental geometries reveals a greater underestimation of bond lengths and greater overestimation of bond angles at the HF/TZP level for the first-row than for the second-row hydrides.The subsequent increase and decrease respectively of these quantities at the CASSCF level leads to good agreement with experiment for the first-row species but not for the second-row species indicating an inadequacy in the TZP basis or in the CASSCF space. (b) All the dications studied except OH2+,NH2+,H202+and NHi+ have relatively large activation barriers to deprotonation in qualitative agreement with the results of charge-s tripping experiments. (c) The calculated adiabatic ionization energies for the monocations of nitrogen and oxygen are except for NH significantly larger than experimental values. 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