J. Phys. Chem. 1987, 91, 155-162
155
Theoretical Thermochemistry. 2. Ionization Energies and Proton Affinities of AH, Species (A = C to F and Si to CI); Heats of Formation of Their Cations John A. Pople Chemistry Department, Carnegie- Mellon University, Pittsburgh, Pennsylvania I5213
and Larry A. Curtiss* Chemical Technology Division/Materials Science and Technology Program, Argonne National Laboratory, Argonne, Illinois 60439 (Received: July 7, 1986)
Ab initio molecular orbital theory (Maller-Plesset theory to fourth order and a series of extended basis sets) is used to compute energies of AH,' monocations, A = C to F and Si to C1. In combination with previously published results on the neutral species, these data are used to obtain ionization potentials and proton affinities. Evidence is presented that the theoretical results are accurate to about A2 kcal/mol or 0.1 eV. Recent experimental data are critically reviewed in the light of these results. For a number of the ions, theory suggests that certain spectroscopic assignments are incorrect and, in some cases, these predictions have been validated by concurrent or later experiments. Finally, the theory is used to prepare a complete set of heats of formation for these ions.
Introduction In a previous paper,' we presented a systematic a b initio molecular orbital study of the total atomization energies of neutral hydrides AH,,, where A is an atom in the first or second row of the periodic table (Li to Cl). Comparison with high-quality experimental data indicated that an accuracy of about f 2 kcal/mol was achieved for first-row compounds and f 3 kcal/mol for the second-row compounds. Uniform application of the method to the whole set of compounds, together with use of generally accepted data for monatomic species and elemental standard states, then permitted estimation of a full set of heats of formation which should have similar reliability. In this paper we extend this work to the monocations AH,', using the same theoretical methods. We limit ourselves to the subset A = C to F in the first row and Si to C1 in the second row. Accurate heats of formation, ionization potentials, and proton affinities are still absent for many of these seemingly simple species. Most experimental data on the energies of these ions are derived from ionization potentials and appearance potentials of appropriate neutral species. Given a complete set of energies at a uniform level, we can compute energy changes for the processes AH,+ + e and AH, + H+ AH,+1+ and then make a AH, careful comparison with experimental observations. The expected level of accuracy of the theory is about 0.1 eV, which is good enough to provide evidence relating to alternative assignments for some spectroscopic observations, where experiment is not fully conclusive. The total energies can then be used to predict a complete set of theoretical heats of formation for these ions. Two previous theoretical studies of subsets of these ions should be mentioned. Rosmus and Meyer2 used CEPA theory in a comprehensive study of the diatomic hydride ions. They were able to achieve agreement with experimental ionization potentials approaching 0.1 eV if the theoretical data were combined with experimental dissociation energies of the neutral species. Pope, Hillier, and Guest3 have published a study of ionization potentials of N, 0, P, and S hydrides, using CASSCF and multireference configuration interaction method^.^ Detailed comparison with their work is hindered by the lack of total energies in their publication, but their results do fall short of the targeted accuracy of 0.1 eV.
-
-
(1) Pople, J. A,; Luke, B. T.; Frisch, M. J.; Binkley, J. S. J . Phys. Chem. 1985,89, 2198. The vibrational frequency of SiH is given incorrectly in this paper. The unscaled frequency in Table I should be 2189 cm-I. As a result, the EDo, AHfoo, and AHfoZg8 (theory) for SiH in Table IV should be 69.9, 89.2, and 89.5 kcal/mol, respectively. Also, the Do(Si-H) and Do(HSi-H) in the discussion on SiH4 should be 69.9, and 76.1 kcal/mol, respectively. (2) Rosmus, P.; Meyer, W. J . Chem. Phys. 1977, 66, 13. (3) Pope, S . A.; Hillier, I. H.; Guest, M. F. Faraday Symp. Chem. SOC. 1984, 19, 109.
0022-3654/87/2091-0155$01.50/0
Theoretical Methods and Results The theoretical methods used for the monocations are very close to those described in part 1 for the neutral AH, species.' Initial studies are made at the Hartree-Fock level (RHF for singlets and U H F for higher multiplicities) using the 6-3 1G(d) basis (usually described as 6-31G*)." This HF/6-31G(d) model is used to locate the global minima, leading to the theoretical structures (bond lengths and angles). The structural data (some of which have been published previously5) are listed in Table I, together with the corresponding total energies. The same HF/6-31G(d) model is next used to compute the complete set of harmonic force constants. These are then used, together with masses of principal isotopes, to obtain the harmonic vibrational frequencies, also listed in Table I. Previous experience at this level of theory6 indicates that such frequencies are systematically too high and that better predictions are obtained by multiplying with a correction factor of 0.89. This has been done to obtain the estimates of zero-point vibrational energy listed in the final column of Table I. A set of more accurate total energies at these geometries is obtained by using fourth-order Mdler-Plesset theory (MP4)' and a series of larger basis sets given in part 1. The final total energies (for first-row compounds) are obtained by assuming additivity of incremental effects beyond the 6-3 1lG(d,p) level, leading to values listed in the last column of Table IIA. Fuller details are given in part 1. For second-row compounds, similar calculations based on increments beyond 6-31G(d,p) are used, the results being listed in Table IIB. The corresponding energies for the neutral AH, molecules are all listed in part 1. The total energies from these single-point calculations are used to determine adiabatic ionization potentials, the energies of the reaction AH,
-
AH,'
+e
(1)
all species being in their vibrational ground states. The simplest way of calculating the ionization energy IP, (without zero-point corrections) is directly from reaction 1, using the total energies listed in Table I1 and part 1. This direct procedure is reasonable for isogyric ionization which does not change the number of unpaired electron spins. An example of such a process is removal of the unpaired electron in the methyl radical to give the closed-shell methyl cation. (4) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acra 1973, 28, 213. (5) Hariharan, P. C.; Pople, J. A. Mol. Phys. 1974, 27, 209. (6) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S . ; Frisch, M. J.; Whitcsides, R. A.; Hout, R. J.; Hehre, W. J. Int. J . Quantum Chem. Symp. 1981, S15, 269. (7) Krishnan, R.; Frisch, M. J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244.
0 1987 American Chemical Society
156 The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987
Pople and Curtiss
TABLE I: HF/6-31GS Equilibrium Geometries," Energies, and Harmonic Vibrational Frequencies
bond length
sYm
cation CH' CH2+ CH3+ CH4+ CHSf N H+ NH2+
bond angle 138.7 C
c
150.9 110.0
NH3+ NH4+ OH+ OH2+
111.7
OH3+ FH' FH2+ SiH' SiH2+ SiH3' SiH,' SiHS' PH' PH2+
113.1 113.9 119.8 C
e 94.4 121.4 112.8
PH3+ PH,' SH+ SH2+
125.6 95.6 96.9
SH3' ClH' CIH2+
97.4
energy, hartrees -37.895 54 -38.566 19 -39.230 64 -39.754 62 -40.388 50 -54.48706 -55.208 52 -55.12729 -55.873 24 -56,530 77 -74.968 75 -75.61531 -75.578 76 -76.289 34 -99.489 60 -100.197 82 -289.13646 -289.709 83 -290.328 91 -290.843 01 -291.463 85 -340.909 01 -341.50655 -341.506 42 -342.131 56 -342.761 58 -397.727 88 -398.237 36 -398.326 99 -398.941 84 -459.633 97 -460.266 88
frequencies, cm-I 3201 (2,) 1066 (AI), 3259 (AI), 3503 (B2) 1517 ( A T ) , 1539 (E'), 3262 (A'), 3472 (E') c c 3404 (Z,) 814 (AI), 3463 (AI), 3717 (B2) 1562 (AI), 3490 (AI), 3594 (B2) 899 (A;), 1674 (E'), 3573 (Ai'), 3772 (E') 1642 (T2), 1874 (E), 3571 (AI), 3714 (T2) 3353 (2,) 1573 (AI), 3596 (AI), 3658 (BJ 1452i (II), 391 (II), 3461 (2,), 3716 ( 2 , ) 926 (AI), 1825 (E), 3774 (Ai), 3885 (E) 3158 (i,) 1522 (Al), 3612 (B2), 3657 (A,) 2369 (2) 984 (Al), 2410 (Al), 2483 (B2) 91 1 ( A T ) . 1022 (E'), 2492 (A,'), 2565 (E') C
e 2655 (2) 1274 (Al), 2668 (A,), 2682 (B2) 1071 (AI), 2680 (A,), 2755 (B2) 873 (Ai), 1160 (E), 2731 (AI), 2798 (E) 1114 (T&, 1251 (E), 2758 (Ai), 2811 (TI) 2859 (2) 1103 (AI), 2744 (AI), 2795 (B2) 1350 (AI), 2881 (AI), 2892 (B2) 1202 (AI), 1398 (E), 2902 (AI), 2908 (E) 2941 (2) 1395 (Al), 2994 (B2), 2998 (A,)
ZPE,b kcal/mol 4.08 9.96 18.83 22.36 31.01 4.33 10.17 1 1.oo
19.54 29.75 4.26 11.23 9.63d 20.51 4.01 11.19 3.00 7.48 13.46 16.85 22.71d 3.38 8.43 8.30 14.66 21.67 3.64 8.46 9.08 16.18 3.74 9.40
Bond lengths in angstroms, angles in degrees. bZero-point vibrational energies (in kcal/mol) scaled by 0.89; the frequencies are not scaled. CSee Figure 1. dImaginary frequency not included. 'Three structures, two of C, symmetry and one of C, symmetry, are identical in energy to the fifth decimal place. The two C, structures have a very small negative frequency while the Ci structure has all positive frequencies. The structures of the C, forms have been given previously in ref 41. The frequencies corresponding to the Csstructure (three hydrogens in a plane) are 41i (A"), 573 (A'), 672 (A"), 675 (A'), 949 (A'), 955 (A'), 1008 (A"), 1010 (A'), 2502 (A'), 2562 (A'), 2566 (A"), 4379 (A').
For nonisogyric ionization processes, in which an electron pair is broken, this procedure is not expected to give the best prediction of the adiabatic ionization potential. This is because the number of electron pairs is greater in AH,, than in AH,', so that the electron correlation energy will be greater on the left of (1). The ionization of water to give the water radical cation is an example. For systems such as these, a better procedure is to use the theory to predict the energy of an isogyric process closely related to the ionization. We shall use the reaction AH,,
+ H + H+
-
AH,'
+ H2
(2) for this purpose. This reaction combines with the ionic dissociation of H, H, H H+ e (3)
-
+
+
to give the ionization reaction 1. Our procedure for nonisogyric ionization, therefore, is to use the present study to obtain the energy of (2) and add the exact energy of the hydrogen reaction 3. The exact energy of (3), AEe, is 0.67447 hartrees either from experiment* or from best available theory? The ionization potentials IP, obtained by this indirect procedure are higher than those obtained directly by 0.18 eV for first-row and 0.22 eV for second-row compounds, respectively. The full set of theoretical IP,, using the nonisogyric procedure where appropriate, is listed in Table 111. These values are then corrected for zero-point energies, using IPo(AH,) = IP,(AH,) + ZPE(AH,+) - ZPE(AH,) (4)
adiabatic ionization potentials, IPo, are listed in Table 111, along with experimental values for comparison. The theory is also used to evaluate proton affinities of the neutral molecules with maximum valence (CH4, NH,, OH,, FH, SiH4, PH3, SH2, and ClH). Protonation of all these species is isogyric, so proton affinities PA, are evaluated directly as energies of the reactions
-
AH,,''
AH,
+ H'
(5)
These are then corrected for zero-point energies and temperature effects to obtain proton affinities PA, and PA298. These are listed in Table IV, together with experimental values. Finally, a complete set of theoretical heats of formation Mfoo for all of the ions is obtained by considering the reactions AH,,
-
AH,'
+e
(6)
for molecules with ionization potentials listed in Table 111 and AH,
+ H+
-
(7)
for those molecules with proton affinities in Table IV. The theoretical neutral heats of formation obtained in part 1, together with AHFo(H') = 365.236 kcal/mol,I0 lead to the values of Mfoo listed in Table V. Corresponding values of AHf0298 are obtained by corrections described previously,' the free electron being treated as a classical particle (as in the J A N A F Tableslo).
the vibrational energies being obtained from scaled HF/6-3 1G(d) frequencies as described above. The final set of theoretical
Discussion A review of the literature shows a considerable range for many ionization potentials and proton affinities; nevertheless, we have
(8) Huber, K.; Herbzerg, G.Molecular Spectra and Molecular Structure 4. Constants of Diatomic Molecules; Van Nostrand: Princeton, 1979. (9) Kolos, W.: Wolniewicz, L. J . Chem. Phys. 1968, 49, 404.
( I O ) Chase, M. W.; Curnutt, J. L.; Downey, J. R.; McDonald, R. A,; Syverud, A. N.; Valenzuela, E. A. J . Phys. Chem. R e j Data 1982, 1 1 , 695 and references therein.
The Journal of Physical Chemistry, Vol. 91, No, I , 1987 157
Ionization Energies of AH, Species TABLE II: MP4 Total Energies (hartrees) at HF/6-31G* Geometries A
cation C+(2P) CHt('Zt) CHZ'(~AI) CH3*(IAI') CH4+('B2) CH~+(~A') Nt(3P) NH+(~II) NH2+('BI) (]AI) NH3+('A,') NH4+("4,) 0+(4s) OH+(~Z-) OH2+(2Bl)
(2m
OH3'(IAl) F+(3P) FH+(~II) FH2+("4,)
6-311G(d,p) -37.358 02 -38.003 65 -38.678 40 -39.379 24 -39.940 57 -40.6 15 08 -53.965 27 -54.621 71 -55.359 55 -55.303 93 -56.069 87 -56.775 30 -74.457 56 -75.132 40 -75.831 91 -75.79466 -76.562 05 -98.946 59 -99.704 05 -100.477 73
6-31 l+G(d,p) -37.358 89 -37.003 97 -37.618 56 -39.379 38 -39.940 86 -40.615 38 -53.966 52 -54.622 09 -55.35978 -55.30425 -56.070 20 -56.775 80 -74.459 59 -75.133 12 -75.832 52 -75.795 56 -76.563 40 -98.949 04 -99.705 47 -100.47998
6-3 lG(d,p) -288.601 23 -289.21423 -289.789 24 -290.434 67 -290.969 35 -291.616 76 -340.39079 -341.00220 -341.629 52 -341.607 83 -342.262 26 -342.92099 -397.223 23 -397.837 46 -398.469 28 -398.380 58 -399.1 17 84 -459.119 5 1 -459.774 95 -460.447 58
6-31+G(d,p) -288.601 99 -288.215 13 -289.790 19 -290.435 70 -290.970 70 -291.618 15 -340.391 53 -341.003 03 -341.630 45 -341.608 76 -342.263 27 -342.922 06 -397.224 46 -397.838 92 -398.470 86 -398.382 10 -399.1 19 41 -459.12095 -459.776 82 -460.449 62
6-31 1G(2d,p) -37.360 24 -37.007 02 -37.682 24 -39.38400 -39.946 52 -40.622 05 -53.97058 -54.628 35 -55.365 89 -55.312 12 -56.077 34 -56.783 68 -74.466 51 -75.14325 -75.844 35 -75.807 20 -76.574 47 -98.96061 -99.721 40 -100.496 50
6-31 lG(df,p) -37.360 19 -37.009 16 -37.686 29 -39.38943 -39.952 18 -40.627 88 -53.970 34 -54.631 76 -55.371 72 -55.3 17 62 -56.085 50 -56.79260 -56.466 46 -75.146 91 -75.85069 -75.814 77 -76.584 12 -98.964 34 -99.725 63 -100.50208
combined -37.363 28 -38.01285 -38.690 29 -39.394 33 -39.958 42 -40.635 15 -53.976 90 -54.638 78 -55.378 29 -55.326 13 -56.093 30 -56.801 48 -74.477 44 -75.15848 -75.863 74 -75.82821 -76.597 89 -98.98081 -99.744 40 -100.523 10
6-3 1G(2d,p) -288.606 17 -289.220 17 -289.795 05 -290.441 27 -290.977 47 -291.625 54 -340.398 40 -341.011 49 -341.641 13 -341.61631 -342.271 88 -342.93205 -397.232 24 -397.849 42 -397.484 40 -398.395 78 -399.135 43 -459.1 30 87 -459.791 12 -460.467 68
6-31G(df,p) -288.603 57 -289.220 32 -289.798 75 -290.447 76 -290.982 35 -291.633 22 -340.397 18 -341.01 3 96 -341.644 87 -341.622 20 -342.280 38 -342.941 87 -397.235 24 -397.855 62 -398.491 95 -398.406 32 -399.143 58 -459.145 57 -459.805 38 -460.480 89
combined -288.609 27 -289.227 16 -289.805 51 -290.455 39 -290.991 82 -291.643 39 -340.405 53 -341.02408 -341.657 42 -341.631 61 -342.291 02 -342.95400 -397.245 48 -397.869 04 -398.508 65 -398.423 04 -399.162 74 -459.15837 -459.823 42 -460.503 03
B cation
attempted to obtain the best recent values and associated heats of formation to compare with the theoretical numbers. We now consider the full set of data for each cation individually. As with most atomic species, the commonly used experimental reference is Moore," who gives 11.26 eV for the ionization potential of atomic carbon. The theoretical value is 11.23 eV, in excellent agreement. It should be noted that this high level of agreement is only achieved if the basis set extensions are included. At the MP4/6-31 lG(d,p) level, the theoretical value is only 11.05 eV. The biggest effect is the fd-extension which lowers the energy of C by 6.0 mhartrees but that of Cf by only 2.2 mhartrees. CH+.Ionization of the CH radical involves removal of a single a-electron. The best experimental value for the ionization potential is 10.64 eV from a spectroscopic Rydberg series.8 The theoretical value of 10.62 eV is again in excellent agreement. As with the carbon atom, the 2d basis extension increases the theoretical number substantially (lowering the CH energy by 7.4 mhartrees and CH+ by only 3.4 mhartrees). CH,+.Neutral methylene is well-known to have a triplet (3Bl) ground state. Ionization involves removal of a single a-electron (b, symmetry) to give a 2Al ground state of CH2+. Herzbergl* originally measured the ionization potential to be 10.396 eV, at
c.
(1 1) Moore, C. Atomic Energy Leuels; NBS Circular 467; National Bureau of Standards: Washington, DC, 1949; Vol. 1. (1 2) Herzberg, G. Polyatomic Molecules; Van Nostrand: Princeton, NJ, 1966.
a time when the structure of CH, was believed to be linear. The theoretical value is 10.32 eV. CH,'. The methyl radical and cation are both believed to be planar trigonal by theory and experiment. Ionization corresponds to removal of a single unpaired a-electron. The measured potential, obtained by Herzberg,', is relatively low (9.84 eV). The theoretical value of 9.79 eV is in good agreement. CH4'. The highest occupied molecular orbitals in methane are a triply degenerate t2 set. Removal of a single electron leads to a degenerate 2Tzstate of tetrahedral CH4+which must then distort to lower symmetry according to the Jahn-Teller theorem.13 In fact, the equilibrium configuration of CH4' has C,, symmetry, as first found theoretically by MeyerI4 and now confirmed experimentally.ls The ionization potential has been measured by Chupka and BerkowitzI6and by Rabalais" giving values of 12.615 f 0.01 eV and 12.6 eV, respectively. Since ionization of CH4 involves breaking an electron pair bond, the theoretical value with isogyric correction is most appropriate for comparison. This is 12.74 eV or 0.12 eV greater than the experimental value. This (13) Jahn, H. A,; Teller, E. Phys. Reo. 1936.49, 874: Jahn, H. A,; Teller, E. Proc. R . SOC.London 1937, 161, 220. (14) Meyer, W. J. Chem. Phys. 1973, 58, 1017. (15) Knight, Jr., L. B.; Steadman, J.; Feller, D.; Davidson, E. R. J. Am. Chem. SOC.1984, 106, 3700. (16) Chupka, W. A,; Berkowitz, J. J. Chem. Phys. 1971, 54, 4256. (17) Rabalais, J. W.; Debies, T. P.; Berkesky, J. L.; Huang, J. T.; Ellison, F. 0 .J . Chem. Phys. 1974, 61, 516.
158 The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
TABLE III: Adiabatic Ionization Potentials (in eV) theory ionizn Process IP. IPn expt
------------s----
c c+
CH CH' CH2 CH,' CH, CH,' CH4 CH4' N-N' NH NH' NH, NH2'(,BI) NH2 NH2'('Al) NH3 NH3' 0 0' OH OH' OH2 OH2'(,B1) OH, OH2'(211) F F' FH FH' Si Si' SiH SiH+ SiHz SiH2' SiH, SiH,' SiH4 SiH4' P P+ PH PH' PH2 PH2*(IAI) PH2 PH2;('BI) PH3 PH3 +
'S
SH SH' SH, SH2'(2B1) SH, SH2'(2AI) CI Cl+ CIH CIH'
11.23 10.62 10.34 9.72 12.93 14.53 13.49 11.26 12.50 10.28 13.55 13.04 12.72 13.69 17.41 16.17 8.08 7.80 9.16 7.96 11.20 10.45 10.08 9.71 10.63 9.89 10.23 10.36 10.47 12.80 12.90 12.76
11.23 10.62 10.32 9.79 12.74 14.53 13.48 11.20 12.48 10.23 13.55 13.00 12.65 13.55 17.41 16.10 8.08 7.81 9.18 7.99 11.12 10.45 10.09 9.72 10.64 9.89 10.23 10.36 10.46 12.77 12.90 12.75
11.26' 10.64b 1O.4Oc 9.84c 12.62,d 12.6c 14.54" 13.49' 11.46/11.14~ 12.49.8 10.lSh 13.61" 13.01' 12.62' 13.78'J 17.42" 16.04' 8.15' 17.9gk 9.48 f 0.07' 8.14m 11.6," 11.7O 10.49P 10.18 f O.I,q 10.17-10.18' 9.82 O.OO2* 210.539 9.87 f 0.002,q 9.87s 10.36'3' 10.37,"3" 10.43' 10.47'*" 12.78'*" 12.97'*" 12.74 f 0.01: 12.72 f 0.03,' 12.75'
*
'
Reference 1 1. Reference 8. Reference 12. Reference 16. 'Reference 17. 'Reference 21. %Reference 22. "Reference 23. 'Reference 26. 'Reference 28. "Derived from Doo(SiH+) ref 33; Doo(SiH) ref 12; and IP(Si) ref 11. 'Derived in ref 35 by using the heats of formation of SiH2' and SiH,. mReference 35. "Reference 37a. "Reference 37b. PReference 42. 9Reference 43. 'Reference 44. "Reference 45. 'Reference 46. "Reference 47. "Gibson, S. T.; Greene, J. P.; Ruscic, B.; Berkowitz, J., private communication. "Reference 48. "Reference 50. YReference 5 1 'Reference 52.
Pople and Curtiss TABLE V Heats of Formation (kcal/mol) of AH.' Cations AHf00
theory CH+ CH2' CH,' CH4+ CH5' NH' NH2+ NH,' NH4+ OH+ OH2' OH,' FH' FH2'
386.5 332.6 26 1.O 275.9 220.9 397.7 304.8 226.8 153.6 309.6 235.2 144.8 306.0 185.5 SiH' 269.3 SiH2+ 275.5 SiH,' 232.8 SiH4+ 265.0 SiH5+ 222.0 PH' 292.1 PH2' 259.8 PH3' 234.0 PH4' 184.9 SH' 274.4 SH2' 238.4 SH,' 195.3 CIH' 272.7 CIH,' 212.1
H o 298.15 -Hen" 387' 2.1 -334' 2.4 262' 2.4 5275b 2.6 2.9 396.3 f O.Se 2.1 -302' 2.4 225' 2.4 2.4 308' 2.1 234' 2.4 2.4 304' 2.1 2.4 271.5' 2.1 2.4 2.5 279b 2.6 2.9 2.1 262b 2.4 -233' 2.5 2.5 -274' 2.1 237' 2.4 2.4 272b 2.1 2.4
exvt
AHf0298
theory 388.8 334.2 261.6 275.7 223.0 399.2 305.6 226.6 152.4 311.1 236.0 144.6 307.5 186.3 271.1 276.6 233.0 264.3 220.5 293.5 260.7 233.7 183.5 275.8 239.2 195.1 274.1 212.8
exvt 388.SC
217.5d 224.5d 152.5d 314.8,'3O9.Od 234.62 f 0.1' 142.9 f 4.c 142.5d >304.Sd 185.5d 274.3; 273.y 277.7 0.78 234.2 f 8h
*
220.5d 292.7 f 0.4' 261.5 f 0.6' 179.5d 275.5d 191.5d 273.2d 210.5d
'
Calculated by using scaled vibrational frequencies. Reference 5 1. 'Reference 10. dReference 19; note that values from this reference were increased by 1.5 kcal/mol because of the electron heat convention. eReference 22. 'Calculated from DoO(SiHt)in ref 33; AHoo(H) in ref 10; AHo&) from CODATA Tables (see ref l), and IP of Si in ref 11; correction to 298 K was done with the theoretical correction. %Reference36. *Reference 35. 'Reference 43.
I
TABLE IV: Proton Affinities of AH. Molecules AH, PA," AE,ibb PA0 PA298' PA298(exptl) CH4 130.63 4.21 126.4 128.4 132,d 128% NH3 211.55 9.05 202.5 204.0 204.0: 203.6 f 1 . q OH2 171.48 7.61 163.9 165.3 166.7,h 166.5: 167.2 f 1.8% FH 119.96 5.59 114.4 115.5 117d SiH4 155.77 4.02 151.8 152.9 155d PH, 193.15 6.90 186.2 187.7 188.6d SH2 174.05 6.98 167.1 168.5 170.2: 168.6' CIH 137.17 5.35 131.8 133.0 134.8: 135 & 1'
3296 (A' I
l:3,@2,$e
3337 ( A ' I
34 I 2 ( A")
H
'From combined energies in Table 11. 'Difference in zero point energies (scaled) from Table I and ref 1. CCorrectionto 298 K is made + A(PV). Scaled vibraby using (AEZ: - Aeib) + AE;:' + tional frequencies are used and RT 2 is assigned to each rotational and translational degree of freedom. /Reference 19. eReference 16; PAo value corrected by theory to PA298. fReference 24. %Reference29. Reference 30. 'Reference 49. 'Reference 52. deviation is somewhat greater than the target of 0.1 eV for accuracy. There does not seem to be any reason to doubt the correctness of the experimental value (Chupka and Berkowitz carried out studies at low temperatures to eliminate any spurious results due to hot bands). A possible source for the slight discrepancy is the calculation of zero-point energies. The zero-point correction to the ionization potential is quite large, since ZPE(CH,) = 26.8 kcal and ZPE(CH4+) = 22.4 kcal, giving a correction of 0.19 eV. It may be that this correction should be even larger, since the potential surface of CH4' is very anharmonic, with low-energy paths connecting equivalent minima.'*
Figure 1. HF/6-3 1G* structures and vibrational frequencies of CH4', CH,', and SiH4+. Bond lengths in Angstroms.
CH,'. The structure of protonated methane is predicted theoretically to be the C, form shown in Figure 1, with three C H bonds of normal length and two long bonds with a small angle between them. Experimental evidence about the energy of CH5+ comes from proton affinity studies. Chupka and BerkowitzI6 (18) Paddon-Row, M. N.; Fox, D.J.; Pople, J. A,; Houk, K. N.; Pratt, D. W. J . Am. Chem. SOC.1985, 107, 7696.
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987 159
Ionization Energies of AH,, Species
-
established that P&(CH4) 1 5.46 eV by noting that the reaction CH4+ CH4 CH5+ CH3 goes without activation. After considering other data, these authors recommend a value of 5.50 eV or 126.8 kcal/mol. This is in excellent agreement with the theory, which gives PA, = 130.6 kcal/mol and PAo = 126.4 kcal/mol after correction for zero-point vibrations. This correction is quite large because of additional vibrational degrees of freedom after protonation. Lias, Liebman, and LevinI9 recommend a value of 132 kcal/mol for PAZ9,based on proton-transfer reactions in considerable disagreement with the theoretical value at 298 K of 128.4 kcal/mol. It is noted that there are few direct measurements of proton affinities and that in some cases such as CH4 it is hard to reconcile the differences between theory and experiment. W . The ionization potential of the nitrogen atom is given by Moore" as 14.54 eV, which is in excellent agreement with the theoretical value of 14.53 eV. Again, it may be noted that lower values are obtained with smaller basis sets; at MP4/6-31 lG(d,p), the ionization potential is only 14.30 eV. NH+. The N H radical is known to have a 32-ground state. Its ionization to a 211radical, however, is not well documented experimentally. An early electron impact study impact study by Foner and HudsonZoindicated a value of 13.1 f 0.2 eV. More recently, Dunlavey, Dyke, Jonathan, and Morrisz1have made a tentative assignment in a photoelectron spectrum of a reaction mixture of ammonia and fluorine atoms. They suggested that a band at 13.49 eV corresponds to this process. The theory gives 13.48 eV in excellent agreement, providing some support for the assignment. It should also be noted that the CEPA calculations of Rosmus and Meyer2 gave a similar result of 13.5 eV. NH2+. The amino cation is of considerable interest because it is isoelectronic with methylene, for which there has been a long controversy about the singlet-triplet separation. Photoelectron spectroscopy of N H 2 should give a direct measurement of the ionization potential difference for the ion states 'Al and 3B1. An experimental study of this was first reported by Dunlavey, Dyke, Jonathan, and Morris?I They identified two bands corresponding to these states at ionization potentials of 12.45 and 11.46 eV, 2B1is dominated respectively. The spectrum assigned to 'Al by the 0 0 vibrational line, consistent with the small predicted geometry change in ionization. The theory for this transition gives 12.48 eV in excellent agreement. The lines assigned to the ionization 3B1 ZB, give a long vibrational series, consistent with the large predicted angle opening. However, there is a large discrepancy of 0.26 eV between the theoretical value and the origin as determined by Dunlavey et al. They did find the series to be overlapped by the ammonia photoelectron spectrum, so it is reasonable to propose that they did not detect the true 0 0 origin. The spacing they found for the vibrational series was 660 cm-' which compares well with the theoretical value of 810 cm-I (Table I). Theory and experiment are brought into good agreement if the vibrational numbering in this series is changed by three quanta. Since these computations were carried out, a further experimental study of N H z ionization has been performed by Gibson, Greene, and Berkowitz,22 who find an origin for the lowest ionization at 11.14 eV; this is now in satisfactory agreement with our theoretical value of 11.20 eV. NH3+. The ionization of ammonia leads to a planar cation, and the photoelectron spectrum is known to show a long Franck-Condon series. The most recent experimental study is due to Rabalais, Karlsson, Werme, Bergmark, and SiegbahnZ3 These authors found a long progression starting with a weak line at 10.073 eV. However, they were unable to determine whether this line was the true origin or a hot band enhanced in intensity
+
+
-
-
-
+-
(19) Lias, S . G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. Rex Data 1984, 13, 695. (20) Foner, S. N.; Hudson, R. L. J . Chem. Phys. 1966, 45, 40. (21) Dunlavev. S. J.: Dyke. J. M.: Jonathan, N.: Morris, A. Mol. Phys. 1980, 39, 1121. (22) Gibson, S. T.; Greene, J. P.; Berkowitz, J. J . Chem., Phys. 1985, 83, 4319. (23) Rabalais, J. W.; Karlsson, L.; Werme, L. 0.;Bergmark, T.; Siegbahn, 0. K. J . Chem. Phys. 1973, 58, 3370.
by a large Franck-Condon factor. Our theoretical value is 10.23 eV which is in better agreement with the next experimental band at 10.18 eV. Thus, theory favors the hot-band interpretation of the 10.073 eV absorption. The theoretical frequency for the out-of-plane bending vibration of the NH3+ion is 899 cm-I (0.1 1 eV) which is in reasonable agreement with the spacing observed in the experimental progression. NH4+. The proton affinity of ammonia has played an important role as a possible "standard" in a scale of proton affinities, as measured by ion cyclotron resonance spectroscopy. The experimental data in this field has recently been reviewed by Lias, Liebman, and Levin,Igwho note that proton affinities varying from 202 to 210 kcal/mol have been cited for ammonia. These authors select a final value of 204 kcal/mol for PA298. The most direct determination of the proton affinity is due to Ceyer, Tiedeman, Mahan, and Lee,24 who measured the appearance potential of NH4+in the process (NH3)2
-
NH4+ + NH2
+e
Assuming an ammonia dimerization energy of 3.5 kcal/mol, they deduce PA, = 202.3 f 1.3 kcal/mol (corresponding to about 203.6 kcal/mol for PA298). Our theoretical treatment gives 202.5 kcal/mol for PAo and is in excellent agreement with the experimental value of Ceyer et al.24 It should be noted that an earlier theoretical value due to Eades et al.?5gave a somewhat higher value (PA, = 213.2 kcal/mol; PAo = 204.1 kcal/mol). O+.The ionization potential of the oxygen atom is 13.61 eV as given by Moore." The theoretical value is 13.55 eV, in satisfactory agreement. However, it should be noted that ionization of 0 is a nonisogyric process, since an electron pair is broken. Agreement is only achieved if the corrected value is used. This is, perhaps, a somewhat artificial procedure for the oxygen atom when no hydrogen atoms are involved, but we have chosen to use the same technique in a systematic manner for all of the data. OH+. The hydroxyl radical has a 211ground state with three a-electrons and ionization leads to an open-shell 3 X state for the OH+ cation. This process is nonisogyric and the indirect procedure is preferred. The experimental value8 of 13.01 eV is well established and is in excellent agreement with the 13.00 eV result from theory. OH2+. Ionization of the water molecule has received a great deal of experimental attention. The first ionization potential corresponds to removal of one of the pure p (1 b, in C, symmetry) a-type lone-pair electrons on the oxygen atom. This leads to a relatively small change in molecular geometry, so that the photoelectron spectrum is dominated by the 0 0 transition. The experimental value of IPo is known with high accuracy at 12.62 eV.26 The theoretical value is 12.65 eV, in excellent agreement. The relation between theory and experiment is less clear for the second ionization potential of water, which corresponds to removal of one of the (3al) u-type lone-pair electrons on oxygen, to give a 'A, state. The equilibrium bond angle for this state opens out a long way from the value (- 104') for neutral water. This is indicated by a long Franck-Condon series in the photoelectron spectrum. Theory predicts that the equilibrium angle for this state is 180°, so that the molecule becomes linear, with an electronic wave function corresponding to one component of a 211state. The other component becomes the 'B1 ground state of OH2+ on bending, so we have an example of the Renner-Teller effect.27 The origin of the second ionization band in OH2 has been placed at 13.78 eV by Potts and PriceZ6in their photoelectron experiments. The theoretical value is 13.55 eV, unacceptably far away from the experimental number. It seems likely that the very large geometry change on ionization has led to such a low intensity for the 0 0 transition that it has not been located. The mean value
-
-
(24) Ceyer, S.T.; Tiedemann, P. W.; Mahan, B. H.; Lee, Y . T. J . Chem. Phys. 1979, 70, 14. (25) Eades, R. A,; Scanlon, K.; Ellenberger, M. R.; Dixon, D. A.; Marynick, D. S. J . Phys. Chem. 1980, 84, 2840. (26) Potts, A. W.; Price, W. C. Proc. R . SOC.London 1972, A326, 181. (27) Herzberg, G.; Teller, E. Z . Phys. 1933, B21, 410. Renner, R. Z. Phys. 1934, 92, 172
160 The Journal of Physical Chemistry, Vol. 91, No.
for the bending vibration frequency observed in the ion is 975 cm-IeZ6This is much larger than the value of 391 cm-I obtained theoretically from the force constant in the linear (minimum energy) form. This may well be due to the fact that the potential curve is only just a minimum at 180° and that there is a lot of quartic anharmonicity. Another relevant experimental study is that of Lew,28who examined the electronic spectrum connecting the 2B1and 2A, states. He assigned some vibrational quantum numbers based on a treatment of the Renner effect, which permits distinction of odd and even levels. However, the origin of the bands was chosen to fit the photoelectron data. If the vibrational quantum numbers in this study are to be altered, the Lew assignments would have to be increased by an even number (probably 2). A fuller theoretical study of the Renner-Teller surface and associated levels for OH2+would clearly be desirable. OH,+. The proton affinity of water has been studied by a number of experimental techniques. The most direct measurement is that of Ng, Trevor, Tiedemann, Ceyer, Kronebusch, Mahan, and Lee,29 who studied the reaction (H20),
-
H30+
+ OH + e
and, assuming 4 kcal/mol for the dimerization energy of water, obtained a value of 165.8 f l . 8 kcal/mol for PAo, corresponding to about 167.2 kcal/mol for PAzs8. Other experimental estimates are in the same region. Thus, Collyear and McMahon30 list PA298 values of 166.4, 168.2, 167.3, and 165.1 and recommend an average value of 166.7 kcal/mol. Lias et aI.l9 give 166.5 kcal/mol. The theoretical treatment gives slightly smaller values (PAo = 163.9 and PA298= 165.3 kcal/mol) but the agreement with experiment is within the 2 kcal/mol target range. P.The experimental ionization potential" of fluorine atom is 17.42 eV, in excellent agreement with the theoretical value of 17.41 eV. Again, this concurrence is only obtained if the nonisogyric correction is made. FH+. The ionization potential of hydrogen fluoride is well established as 16.04 eV,8 corresponding to removal of x-electron, leaving a 211 state. The theory reproduces this well, giving 16.10 eV, within the target accuracy. FH2+.The experimental proton affinity of hydrogen fluoride has proved somewhat inaccessible. Lias et al.I9 quote a value of 117 kcal/mol for PA298,which is derived from measurements ~ theoretical relative to N2 by Foster and B e a ~ c h a m p . ~The number obtained here is slightly lower (PA298= 115.5 kcal/mol), but within acceptable bounds. It may be noted that a recent direct calculation using extra basis functions on hydrogen (MP4/631 1++G(3df, 3pd) by Frisch et al.32gives PA, = 121.7 kcal/mol, about 1.7 kcal/mol higher than our value. Si+.The experimental ionization potential" of the silicon atom is 8.15 eV, in satisfactory agreement with the theoretical value of 8.08 eV. S i p . The ionization potential of SiH+ has not been directly measured until very recently. Earlier experimental values in the literature are based on combining the energies of the three processes
-
SiH+ Si
SiH
+H Si+ + e Si+
Si
Pople and Curtiss
I, 1987
+H
Using Do= 3.23 eV33for the first of these, 8.15 eV for the silicon ionization, and Do5 3.06 eV for the neutral dissociation,8the SiH potential becomes IPo I7.98 eV. This upper bound is considerably (28) Lew, H. Can. J . Phys. 1976, 54, 2028. (29) Ng, C. Y.; Trevor, D. J.; Tiedemann, P. W.; Ceyer, S. T.; Kronebusch, P. L.; Mahan, B. H.; Lee, Y. T. Chem. Phys. 1977, 67, 4735. (30) Collyear, S.N.; McMahon, T. B. J . Phys. Chem. 1983, 87, 909. (31) Foster, M. S.; Beauchamp, J. L. Inorg. Chem. 1975, 14, 1229. (32) Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.;Schaefer, 111, H. F. J . Chem. Phys. 1986, 84, 2279. ( 3 3 ) Elkind, J. L.; Armentrout, P. B. J . Phys. Chem. 1984, 88, 5454.
larger than the theoretical IPo = 7.81 eV. However, a recent direct measurement by Berkowitz, Greene, and Cho34gives IPo(SiH) = 7.91 eV, now in reasonable agreement. SiH2+. Until recently, there was little direct experimental information on the ionization potential of the singlet ground state of SiH,. Dyke, Jonathan, Morris, Ridha, and Winter35suggest IPo = 9.48 eV using a heat of formation of SiH2+obtained by Corderman and Bea~champ,,~ together with the heat of formation of SiH2. Both quantities are subject to some uncertainty. Our theoretical value is IPo = 9.18 eV, substantially lower than the experimental estimate. A new and direct experimental value of 9.15 eV (possibly as low as 9.02 eV) due to Berkowitz, Greene, and C ~ O ,on) ~the other hand, is in good agreement. It may be noted that part of the discrepancy with the former experimental estimate (9.48 eV) is probably due to the inadequate heat of formation of neutral SiH2. Our earlier theoretical study' of this suggested that AHfozss(SiH2)is 63.4 kcal/mol, 4.1 kcal/mol higher than the value used by Dyke et aL3' SiH,'. The first direct measurement of the ionization potential of the silyl radical is due to Dyke et Since the geometry changes from pyramidal in the neutral species to planar in the ion, a long Franck-Condon series is observed. They obtain IPo = 8.14 f 0.01 eV for the adiabatic potential, although the 0 band is made difficult by other identification of the 0 overlapping systems. Our theoretical value for IP, is 7.99 eV, significantly lower. This suggests that the Franck-Condon series may extend further to lower energies. Dyke et al. find an outof-plane bending frequency (Ai') of 820 f 40 cm-' in the ion. This is in good agreement with the theoretical value of 9 1 1 cm-' (without scaling). Increasing the assigned vibrational quantum numbers by one would bring the observed spectrum into satisfactory agreement with the theory. Indeed, a recent experimental study by Berkowitz, Greene, and Cho34suggests that the true 0 0 band is at about 8.01 eV. SiH4+. Some early measurements of the photoelectron spectrum of silane appear to give ionization potentials in the region of 11.6-1 1.7 eV.37 A more recent experimental study indicates that the ionization threshold may be as low as 10.97 eV.38 However, the parent ions were not detected. Our theoretical procedure finds that the HF/6-31G(d) structure of SiH4+is a donor-acceptor complex of H2with SiH2+(Figure l), the bond length in the H 2 portion being 0.749 A. This is a new result. Two previous Hartree-Fcck studies39of SiH4+with smaller basis sets have found a potential minimum for a C3, pyramidal structure. We also find a local C,, minimum (6-31G(d) energy = -290.831 66 hartrees), but this is 7.1 kcal/mol above the global minimum shown in Figure 1. The C2, structure, analogous to CH4+,was also investigated (6-3 lG(d) energy = -290.822 64 hartrees), but found to lie higher still. The search for the C, structure was simulated by preliminary experimental results of Berkowitz, Greene, and Cho34which indicated that the ionization potential was considerably lower than 11.6-1 1.7 eV. The ionization potential IPo corresponding to the loose complex (C, structure) for the ion is found to be 1 1.12 eV which is in reasonable agreement with the final result of 11.OO eV of Berkowitz, Greene, and C ~ Obut, ~not~ with the earlier measurement^.^^ According to the theory, the energy of dissociation of SiH4+into SiH2+ H2 is 10.2 kcal/mol. SiH5+. There appears to be no direct measurement of the proton affinity of monosilane. In 1973, Cheng and Lampe40 established that the proton affinity of SiH4was greater than that of C3H7,but less than that of C2H2and C2H5. Using thermochemical data tabulated at that time, they set bounds of 150 and +-
-
+
(34) Berkowitz, J.; Greene, J.; Cho, H. J . Chem. Phys., to be published. (35) Dyke, J. M.; Jonathan, N.; Morris, A.; Ridha, A,; Winter, M. J. Chem. Phys. 1983, 81, 481. (36) Corderman, R. R.; Beauchamp, J. L., as quoted in ref 35. (37) (a) Potts, A. W.; Price, W. C. Proc. R. Soc. London 1972, A326 165. (b) Potzinger, P.; Ritter, A.; Krause, J. Z . Nafurforsch 1975, 30a, 347. (38) (a) Heinis, T.; Borlin, K.; Jungen, M. Chem. Phys. L e f f .1984, 110, 429. (b) Borlin, K.; Heinis, T.; Junge, M. Chem. Phys. 1986, 103, 93. (39) (a) Gordon, M. S. Chem. Phys. Left. 1978, 59, 410. (b) Power, D.; Brint, P.; Spalding, T. J . Mol. Sfruct. 1984, 108, 81. (40) Cheng, T.M. H.; Lampe. F. W. Chem. Phys. Lett. 1973, 19, 5 3 2 .
Ionization Energies of AH,, Species
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987 161
156 kcal/mol on the proton affinity of silane. Lias et al.19 list 155 kcal/mol in their review. The theoretical value of 152.9 kcal/mol is clearly consistent with the experimental observation. A previous c a l c ~ l a t i o n without ,~~ the basis set extensions, led to a similar value of 153.1 kcal/mol. P+. For the phosphorus atom, the theoretical ionization potential of 10.45 eV is in satisfactory agreement with the best experimental value of 10.487 eV.42 PH'. There appears to be no report of a direct measurement of the ionization potential of the PH radical. Berkowitz et al.43 report a threshold for the appearance of PH' from PH3, which leads to a heat of formation, AHfo0(PH'). Combining this with other experimental estimates for the dissociation energy of PH (and hence AHf"o(PH)), they arrive at a value of 10.18 f 0.1 eV for the ionization potential of PH. Further support for this value comes from photoelectron studies of products resulting from the reaction F PH3 reported by Dyke et al.44 The lowest peak assigned to PH is estimated43to be in the region 10.17-10.18 eV. The theoretical value for the ionization potential is 10.09 eV, which is within the experimental error range. PH2+. The present theoretical results have been compared with the most recent experimental data on PH2' in a previous publication.43 The most important feature, well confirmed by theory, is that PH2+ has a singlet ground state, like the isoelectronic neutral molecule SiH2. The calculated and experimental ionization potentials are again consistent to within 0.1 eV. PH3+. The ionization of phosphine has been studied, using photoelectron spectroscopy, by Maripuu et al.45 These authors also carried out theoretical calculations. Phosphine, unlike ammonia, remains pyramidal after ionization. However, the bond angle is considerably reduced and the spectrum shows a long progression in the bending vibration. The origin is assigned at 9.868 f 0.005 eV. A similar value of 9.870 f 0.002 eV has been reported by Berkowitz et al.,43 using the threshold potential of PH3' from PH,. The present theoretical method gives 9.89 eV, in excellent agreement with both of these experiments. PH4'. The recommended proton affinity of phosphine of 188.6 kcal/mol given by Lias et al.19 is based on the energies of various proton-transfer reactions. The theoretical value of 187.7 kcal/mol is close to the recommended value. S'. The ionization potential of the sulfur atom is well established as 10.36 eV'1*46and is significantly greater than the theoretical value of 10.23 eV. This is the largest deviation between theory and experiment for all the entries in Table 111. Part of the discrepancy of 0.13 eV can be ascribed to the neglect of spin-orbit interaction in our theory. .The 3Pground state of neutral sulfur has significantly separated spin-orbit components for J = 0, 1 , and 2. The lowest component (J = 2) is about 200 cm-' (-0.03 eV) below the weighted mean. Since there is no corresponding effect for the S+ ion, the theoretical ionization should be low by this amount. SH'. The photoelectron spectrum of the SH radical has been measured by Dunlavey et al.47 There is relatively little change in the bond length on ionization (1.330 to 1;338 A by theory), so the spectrum is dominated by the 0 0 line at 10.37 eV. This is somewhat below the spectroscopic value of 10.43 eV given in Huber and Herzberg8 The theory gives 10.36 eV in excellent agreement with the value of Dunlavey et al. SH,'. The photoelectron spectrum of hydrogen sulfide has been studied several times, most completely by Karlsson et al.48 They
+
-
(41) Schleyer, P. v. R.; Apeloig, Y.; Arad, D.; Luke, B. T.; Pople, J. A . Chem. Phys. Lett. 1983, 95, 477. (42) Martin, W. C. J . Opt. SOC.A m . 1959, 49, 1071. (43) Berkowitz, J.; Curtiss, L. A.; Gibson, S.T.; Greene, J. P.; Hillhouse, G . L.; Pople, J. A . J . Chem. Phys. 1986, 84, 375. (44) Dyke, J. M.; Jonathan, N . ; Morris, A. Int. Rev. Phys. Chem. 1982, 2, 3. (45) Maripuu, R.; Reineck, I.; Agren, H.; Nian-Zu, Wu; Ming Rong, Ji; Veenhuizen, H.; AI-Shamma, S . H.; Karlsson, L.; Siegbahn, K. Mol. Phys. 1983, 48, 1255. (46) Kaufman, V. Phys. Scr. 1982, 26, 439. (47) Dunlavey, S . J.; Dyke, J. M.; Farad, N. K.; Jonathan, N.; Morris, A. Mol. Phys. 1979, 38, 729.
find that the lowest ionization potential shows features similar to that of water. A single nonbonding a-electron (b, symmetry) is removed, so the change in valence angle is small (94.4' in SH2 to 96.0' in SH2+according to the theory). This means that the 0 0 line dominates and the ionization is determined at 10.466 eV with considerable accuracy. Our theoretical value is 10.46 eV, in excellent agreement. The second ionization potential of SH2corresponds to removing an a-type electron giving a 2Al state for the ion. As for water, this causes the bond angle to open out. However, unlike water, it only increases to 125.6O (by theory). The experimental spectrum of Karlsson et a1.@shows a vibration progression, starting at 12.777 eV. Again this is in excellent agreement with the theory. The theoretical bending vibration frequency in this state is 1103 cm-I, or 982 cm-', if the scaling factor is used. This compares reasonably with the experimental value of 896 cm-I found experimentally for early members of the series. SH,'. Early studies of the proton affinity of hydrogen sulfide were based on proton transfer to other ions; Lias et al.I9 obtained a value of 107.2 kcal/mol for PA298from these studies. This is in satisfactory agreement with the theoretical value of 168.5 kcal/mol from Table IV. More recently, a direct measurement of the threshold proton affinity has been made by Prest et al.,49 using a technique similar to that mentioned above for water. Their value is PAo = 167.2 kcal/mol which is in excellent agreement with the theoretical result of 167.1 kcal/mol. C1'. The ionization potential of the chlorine atom is well established at 12.97 eV.11350 The theoretical value (12.90 eV) is slightly less, but within the target accuracy of 0.1 eV. Spin-orbit corrections are significant both for C1 and C1' (-0.02 eV). In this case, their inclusion would slightly worsen the agreement with experiment. C I P . The ionization potential of hydrogen chloride has been studied by many spectroscopic techniques, the recommended literature value being 12.74 f 0.01 eV.51 This involves removal of a nonbonding a-electron, with little change in bond length. Theory reproduces this well, giving IPo = 12.75 eV. CIH2+. The proton affinity of HC1 has been obtained from the photoionization of dimers by Tiedemann et al.52 They obtain PA298 = 135 f 1 kcal/mol. Using this and other relative data, Lias et al.19list a value of 134.8 kcal/mol. The theoretical number is 133.0 kcal/mol, in reasonable agreement. We now turn to the theoretical and experimental heats of formation listed in Table V. The results for AHfooand A H f O 2 9 8 are compared with values from standard compilations and other sources. We comment only on those systems for which the apparent deviation between theory and experiment exceeds our target accuracies of f 2 kcal/mol for first-row compounds and f 3 kcal/mol for second-row compounds. The experimental 0 K heats of formation (mostly from the Rosenstock ~ o m p i l a t i o n ~are ~ ) in satisfactory agreement with theory, except for SiH4'. In this case, the tabulated value is based on old ionization potentials of SiH4, now believed to be in error (see preceding discussion). Several of the 298 K heats of formation show significant deviation between theory and experiment. For CH5' the value given by Lias et al.19 is 5.5 kcal/mol lower than the theoretical value. Their recommended value is based on proton-transfer reactions. The threshold value for the proton affinity16,19gives a heat of formation (221.4 kcal/mol at 0 K) in good agreement with the theoretical value (220.9 kcal/mol at 0 K). For OH', the JANAF value (314.8 kcal/mol) appears to be too high and is, in any case, much larger than the later estimate (309.0 kcal/mol) listed by
-
(48) Karlsson, K.; Mattsson, L.; Jadrny, R.; Bergmark, T.; Siegbahn, K. Phys. Scr. 1979, 13, 229. (49) Prest, H. F.; Tzeng, W. B.; Brom, Jr., J. M.; Ng, C. Y . J . Am. Chem. SOC.1983, 105, 7531. (50) Radzunski, L. J.; Kaufman, V. J . Opt. SOC.A m . 1967, 59, 424. (51) Rosenstock. H. M.; Draxl, K.; Steiner, B. W.; Herron. J. T. J . Phvs. Chem. Ref. Data 1977, 6 , Suppl. 1 . (52) Tiedemann, P. W.; Anderson, S. L.; Ceyer, S . T.; Hiroka, T.; Ng, C. Y . ;Mahan, B. H.; Lee, Y. T. J . Chem. Phys. 1979, 71, 605.
J . Phys. Chem. 1987, 91, 162-170
162
Lias. The theoretical value (31 1.0 kcal/mol) is closer to the latter. For FH+, the value given by Lias et al.I9 is a lower bound from proton-transfer reactions; the theoretical value is consistent with spectroscopic results8 (i.e,, by combining the ionization potential and heat of formation of HF). The 298 K value for SiH+ given in the JANAF tables appears high. A value about 1 kcal/mol lower can be derived (see Table V) from the recently measured dissociation energy of SiH+. The large deviation for PH4+can be attributed mainly to the poor performance of the theory on the atomization energy of phosphine (error 2.3 kcal/mol).’ For SH3+the apparent deviation is 3.6 kcal/mol. However, as in the case of CHS+,the experimental value recommended by Lias et is lower than that derived from the direct measurement of the threshold. The latter would give 193.1 kcal/mol in agreement with the theoretical value of 195.1 kcal/mol.
Conclusions The results documented in this paper clearly indicate that the theory, used previously for neutral AH, molecules, also gives
energies for AH,’ cations to an accuracy close to f 2 kcal/mol. Resulting ionization potentials and proton affinities have considerable value in making a critical assessment of the interpretation of experimental data. For a number of ions (NH,+, PH+, PH2+, SiH+, SiH,’, SiH,’), computations preceded or were concurrent with new experimental data. In all these cases, theory supports the revised values. The theoretical heats of formation listed in Table V constitute a complete set of data. The successful comparison with available experimental heats suggests that the theory could be used to make predictions for other species (involving elements Li-B, Na-AI) where experimental data are sparse.
Acknowledgment. We thank Dr. Joseph Berkowitz for numerous helpful discussions during the course of this work and permission to quote his results for the SiH, series. This work was supported by the National Science Foundation (Grant No. CHE-84-09405) and the Division of Materials Science, Office of Basic Energy Sciences, U S . Department of Energy (Contract W-3 1-109-ENG-38).
Transition-State-Theory Calculations for Reactions of OH with Haloalkanes N. Coben* Aerophysics Laboratory, The Aerospace Corporation, P.O. Box 92957, Los Angeles, California 90009-2957
and S . W. Benson The Loker Hydrocarbon Research Institute, University of Southern California, Los Angeles, California 90089- 1661 (Received: November 18, 1985)
A method previously used for extrapolating rate coefficients for reactions of OH radicals with alkanes and of 0 atoms with alkanes using conventional transition-state theory is applied to reactions of OH radicals with 10 halomethanes and 18 haloethanes. For each halomethane, AS* calculated, which, together with experimental values of k(298), is used to calculate k( r ) at higher temperatures. Because of the greater difficulty in calculating vibrational frequencies for the haloethane-activated complexes, a slightly more approximate scheme was used. For these reactions, the model for the activated complex is the same for all the cases except for two differences between the a-hydrogen and the @-hydrogenatom abstractions: (1) In the former case, there are two new low-frequency bends in the activated complex, while in the latter there is only one. ( 2 ) There is a much larger increase in entropy due to internal rotations in the @-hydrogenabstractions. Calculations for both free and slightly hindered internal rotations were made; the former gave slightly better agreement with experiments. For the free internal rotor model, the calculated values for all the haloalkanes differ from experimental values by no more than 25% in all cases save that of OH + CHC13, for which the possibility of experimental errors is considered.
Introduction It is generally accepted that variational transition-state theory provides a suitable conceptual framework for the theoretical calculation of reaction rate coefficients for bimolecular reactions. Unfortunately, the rigorous application of the theory requires a detailed knowledge qf the potential energy surface over which the reaction is taking place, and except for extremely simple cases, such as H + Hz or F + H,, there is little promise of being able to calculate the required properties of the surface without dozens or even hundreds of hours of machine time even on the largest of the current generation of supercomputers. The desire for a way around this impasse led Benson and co-workers to the development of the thermochemical kinetics variation of conventional transition-state theory as a conceptually simple procedure for obtaining at least activation entropies-and therefore, Arrhenius preexponential A factors-without the need for a fully characterized potential energy surface. To calculate the entropy of activation, AS*,requires knowledge only of the activated complex (its bond lengths and angles, vibrational frequencies, internal rotor parameters, electronic degeneracy, and symmetry properties) and, of course, the same properties of the reagent molecules. The method assumes that properties of the surface away from the saddle point are not required and that the 0022-3654/87/209 1-0162$01 S O / O
location of the saddle point (i.e., the properties of the activated complex) is essentially independent of temperature. Whether this conventional transition-state-theory approach is more justified than the variational transition-state-theory approach is a question that ultimately will require more sophisticated probing to answer than we propose to do now; we prefer to let the case for the simpler approach rest on an empirical justification. Does the method give results in agreement with reliable experiment? And if so, under what constraints? If there is a broad class of reactions or conditions for which the simpler theory gives predictions that are sufficiently accurate, then its utility is vindicated notwithstanding its lack of rigor. “Sufficient accuracy” is a term that needs quantification in itself. We believe that for most purposes to be able to extrapolate the rate of a reaction rate coefficient from 300 K up to 1000 or 2000 K within a factor of 2 or 3 is a sufficient accomplishment for many purposes. In previous studies’**we have applied the method to two classes of reactions: OH radicals with alkanes and 0 atoms with alkanes. In both cases, the theory succeeded within the aforementioned criterion. In those studies we did not claim to have determined the real details of the (1) Cohen, N. In?. J. Chem. Kinet. 1982, 14, 1339; 1983, 15, 503. (2) Cohen, N.; Westberg, K. R. In?. J . Chem. Kine?. 1986, 18, 9 9 .
0 1987 American Chemical Society
