6031
J. Phys. Chem. 1992,96,6031-6038
Electron Affinities and Thermodynamic Properties of Some Triatomic Species Dake Yu, A n i R a d , * and David A. Armstrong* Department of Chemistry, The University of Calgary. Calgary. Alberta, Canada T2N 1 N4 (Received: February 18, 1992)
The electron affinities of HCO; and the XYZ triatomic species: N3*,OCN', SCN', NO;, 03, SO2,CIO;, C02, and N 2 0 were calculated by ab initio methods at the G2 level of theory. Comparison of the calculated values for N3', NO2*,03, and SO2with accurate measurements indicates that the G2 procedure is capable of reproducing the experimental results with an average error of 0.06 eV. The present ab initio calculations of structures and electron affinities are compared with earlier ones. Calculations for the other species, where the experimental results are less extensive or less accurate, provide evidence for preferred values. Thermodynamic properties, 9,@ - @, and AG$'(T) for the above species and the corresponding negative ions were calculated as functions of temperature by means of standard statistical thermodynamic methods and using the most accurate molecular properties available from experiment or the G2 results.
e,,
1. Introduction Several different experimental methods' have been developed for determining electron affinities and an extensive number of molecular species have been examined. In many cases there has been satisfactory agreement between the different methods, but unfortunately there are some species for which the experimental values of the electron affinity span a range of 0.5 eV or more. This is often the case for polyatomic systems where the geometries of the ion and neutral are different, and measurements by the highly accurate photodetachmentmethods cannot readily be made. Ab initio molecular orbital methods have also been extensively applied to the calculation of electron affinities and for monoatomic and diatomic species. The rcsults of recent high level calculations2 agree well with experimental data. Similar calculations with polyatomic species are therefore of interest. The adiabatic electron affinity at 0 K is just the difference in computed energies of the Born-Oppenheimer potential energy surfaces of the neutral and anionic species with a correction for the difference in zero-point vibrational energies. The difference in electron count implies that post-Hartree-Fock procedures have to be used. The requirements which must be met by the computational procedure and the expected accuracy of the derived EA values have been examined.'~~The computational requirements for accurate EA values are severe. For example, for a range of molecules, it was shown that very large polarized basis sets with added diffuse functions and inclusion of electron correlation up to fourth order in Merller-Plesset perturbation theory (MP4) were required to achieve accuracies of f0.2 eV3. Where spin contamination of the UHF wave function is severe, errors are substantially larger and methods based on configuration interaction (CI) are preferred. A systematic procedure for the minimization of correlation errors, which is applicable to small molecules, has been proposed by Pople and co-workers2 under the cognomen, GAUSSIAN-2 (G2). Errors in absolute energies are reduced to 0.1-0.2 eV in most cases? Because of cancellation effects, errors in the calculated electron affinities should be even smaller and well within the error bounds of many current experimental determinations. Spbcific objectives of the present investigation were to determine how clapely the electron affinities of triatomic species, which have been observed by accurate experimental methods, could be reproduced by calculations at the G2 level and to provide confirmatory data or best estimates for molecules where experimental data are either lacking or in serious disagreement. Also, since several of the negative ion A- species formed by electron attachment to the neutral A species and some of the neutrals themselves are transitory free radicals with unknown thermodynamic properties, it appeared useful to evaluate thermodynamic functions with the highest possible accuracy by combining the results of ab initio calculations with accepted experimental data. The molecular systems chosen for this study included N3*, OCN', SCN', NO;, 03,SO2,ClO;, C02,N20,and HCO;. The
m(T),
nitrogen oxides, sulfur dioxide, and ozone are key species in atmospheric chemistry? while the others are of primary interest in studies of solution-phase redox reactions of organic and inorganic solutesa6The reason for including HCO; will be explained later. The triatomic species fall into three different classes, depending on whether the geometries of the neutral and ion are both linear (L-L: N;, OCN', and SCN'), the geometries are both bent (B-B NO2', 03, SO2,and ClO2*),or the geometry of the neutral is linear and that of the ion bent (L-B: C 0 2 and N20). In accord with normal convention,' the adiabatic electron affinity has been defined here as the enthalpy of reaction 1 at 0 K,
A
+ e-
-
A-
(1)
@,.'
and the abbreviation EA has been used for Also the ion convention or the "stationary" electron convention' has been used for describing the state of the electron. Details of computational methods are described in section 2. The results of the structure calculations and the electron affinities, determined from the a p propriate energy differences between A- and A, are presented in section 3. Finally in section 4 the results are discussed and compared with previous studies. 2. Computational Details Ab Initio calculrtiolra All ab initio calculations presented here were performed with the GAUSSIAN 90 molecular orbital packages? The energies of the ions and neutrals were calculated at G2 level of theory2. The G2 procedure includes a geometry optimization with the standard HartretFock method and the 6-31G* splitvalence basis set (HF/6-31G*), a vibrational frequency calculation at the H F optimized geometry, MP2/6-31GS geometry optimization and a series of singlepoint post-HF calculations on the MP2 optimized geometry in order to obtain an accurate estimate of the correlation energy. Harmonic frequency analysis is required by the G2 procedure for an estimate of the zero-point vibrational energy. This quantity is not particularly sensitive to the accuracy of the frequencies themselves, and so the HF/6-31G* level with an appropriate empirical correction is adequate for the purpose. The vibrational frequencies calculated at HF/6-31GS level were scaled by a factor of 0.89 to take into account known inadequacies in frequencies calculated at this levels in considering the zerepoint energy, in the calculation of thermodynamic properties, and for comparison with experimental IR frequencies. For some neutrals it was possible to make use of calculations already made by Pople and co-workers.2 In some cases pertaining to the free-radical species, the UHF/6-31GS level is not adequate to obtain reasonable values for the frequencies. In the case of 03*-, the UHF/6-31G5 o g timization yields a structure with C, symmetry and unequal 0-0 distances. The unexpected symmetry breaking was investigated by further geometry optimizations at higher levels of theory. In the cases of N;, OCN', and SCN', the UHF/6-31G* calculation
0022-3654/92/2096-603 1%03.00/0 0 1992 American Chemical Society
Yu et al.
6032 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 TABLE I: HF/6-31G* and MP2/6-31G* Optimized Geometries of the Triatomic Species and Formyl XY 2 X-Y, A Y-Z,A X-Y-Z,deg X-Y,A HF MP2 expa HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP HF MP2 exP
NNN'
1.159 1.184 1.181b 1.165 1.216 1.197 1.204 1.299 1.278 1.414 1.477 1.43 1 1.462 1.514 1.473 1.160 1.166
1.231 1.253
SCN'
1.648 1.671
1.160 1.152
180.0 180.0
SCN-
OCO
1.143 1.179 1.16 1.197 1.170
c0;-
1.194 1.233
180.0 180.0 180.0 106.3 106.9
1.092 1.171 1.126
1.179 1.192 1.186
180.0
N2O'-
ONO'
000
os0 OCIO' OCN'
HC02' NNO
180.0
N 7-
180.0 180.0 136.1 133.7 134 119.0 116.3 116.8 118.8 119.8 119 116.8 120.0 117.6 180.0
N02-
Y-Z,A
X-Y-Z,deg
1.156 1.218 1.18C 1.229 1.28 1 1.25 f 0.02"
180.0 180.0 18O.Oc 116.7 115.4 117.5 & 2.od
1.337 1.19 1.495 1.541 1S 2 3 ' 1.592 1.586 1.56 1.215 1.241 1.18 1.687 1.664 1.65 1.225 1.256 1.258 1.127 1.142
114.8 100 1 15.6 117.1 115.6 115.2 118.1 108 180.0 180.0 180.0 180.0 180.0 180.0 135.0 134.2 1348 114.5 114.5 11 6 S h 122.2 140.8
0,'-
so2*c102OCN'
180.0
HCOc
180.0
1.209 1.174
1.167 1.210 1.20 1.149 1.197 1.17
1.23 1 1.260 1.25h 1.293 1.308
180.0
'Unless otherwise indicated, these are taken from ref 37. *Reference 38. CReference 39. "Reference 12. ' H F optimization with symmetry constraint leads to a saddle point, see text. /Reference 15. #Reference 20. *Reference 40.
yielded linear structures with unequal bending force constants. " d y n a m i c Properties. As stated in the introduction, A@ for reaction 1, the EA of each A species, was calculated from the difference in G2 energy of A and A-. Values of C$, So, and HO - I$ at several temperatures in the range 0-298.15 K and 1 bar were calculated for each A and A- by standard statistical thermodynamic methods based on the rigid rotor-harmonic oscillator model. As a means of establishing the confidence limits of the absolute values of the present G2 energies, the heats of formation of all species were calculated directly from the G2 values. Previous experience suggests that errors as large as 20 kJ/mol may be incurred by the direct approach.2 More accurate values of AI-$ and also of A@ were obtained following an assessment of the theoretical calculations and reliable literature data. The specific procedures for this are described after consideration of the results. 3. Results Geometries of the triatomic species optimized at HF/6-31G* and MP2/6-31G* levels are reported in Table I. The vibrational frequencies calculated at HF/6-3 IG* or higher level, as appropriate, are presented in Table I1 together with the IR intensities and rotational constants. The available experimental data on geometries and vibrational frequencies have also been given in Tables I and 11. Because crystal-field effects may cause significant perturbations of the anion structures, a preference has been given to results from gas-phase spectroscopic investigations or, in one instance, matrix isolation studies. For the eight neutrals where the experimental geometries are available, the optimized bond lengths at H F level are shorter compared with those of experimental values by 0.03 A in average. On the other hand the MP2 bond lengths are longer in most cases. The average difference is also 0.03 A. Both H F and MP2 predict accurate bond angles for the neutrals, differing from the experimental values by less than 2O and l o , respectively. For the ions, the available comparisons show similar agreement in bond lengths and bond angles except for 0,'and CIOz- where crystal data were used. The geometries obtained by use of the basis sets and level of theory prescTibed by the G2 procedure are expected to be in reasonable
agreement with experimental geometries but are not the primary focus of the calculations. The total energies calculated at G2 level are given in Table 111. Electron affinities calculated by the G2 procedure are listed in Table IV and compared with those of experiments and other calculations. Ideal gas thermodynamic functions C$, So, H" - I$, AI-$, and A@ in the temperature range 0-298.15 K and 1 bar for the neutral and ion systems are listed in Table V. 4. Discussion
Electron Affinities and 6 2 Results. The many experimental methods by which electron affinities can be derived have been previously discussed,' and they need not be reviewed in detail here. However, as already intimated, the laser photodetachment (LPD) and laser photoelectron spectroscopic (LPES) methods provide a very high level of accuracy (f0.002 eV) and usually give very reliable values of the adiabatic EA when the geometries of the ion and neutral are similar enough that there are good overlaps of the ground vibrational states. They also often yield information on vibrational frequencies. We therefore start by considering the results for the four systems, all of the L-L or B-B type, where such data are available and for which there is general acceptance of the reliability of the experimental EA values. N3*/Ny:The calculated geometries and the scaled vibrational frequencies (Tables I and 11, respectively) are in reasonable agreement with experimental values. The calculations also confirm, as have ~ t h e r s , ~the * ~ similar * I ~ geometries of the neutral and ion, a case where photodetachment experiments should yield highly reliable values of the adiabatic electron affinity. The LPD experiment of Illenberger et aL9 gave a value of 2.76 f 0.04 eV, a value very similar to a previous LPD experiment, 2.69 f 0.12 eV," within the range of other experimental measurements, 2.5-3.1 eV1,and supported by their theoretical computationswhich yielded a value of 2.73 eV at MP2/6-31G* level. The G2 value is 2.663 eV (Table IV), which is within 0.1 eV of the best experimental value but outside the estimated error limits. Calculations at MP4/6-31 l++G(d,p)//HF/6-31G* level yielded 2.79 eV while RCISD(Q) calculations with the same basis set afforded 2.15 eV., The EA of N,' has also been calculated by density
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 6033
Triatomic Species
TABLE II: Infrared Data and Rotatio~lConstants Calculated at HF/631G* Level: I, Calculated Frequencies; 11, Serled Frequencies (Experiwatal, cm-')P 111, IR Inteusities (km/mol); IV, Rotatio~lConstants (GHz) bend sym Str asym str bend sym str asym str N.' I 530.679 1504 1703 SCN' I 360, 443' 756 2028 ' 11 472; 604' (500 f SOY 1516 (1645)d I1 320. 394' 673 1805 , 339 I11 6.8,'6.06 11.8 0.0 654.0 34.5 I11 17.8, 14.7' IV 6.1042 IV 13.4265 I 517 739 2440 1569 2295 I 781 I1 460 658 2172 1396 (1350y 2043 (2020)L I1 695 (640). I11 16.6 7.2 288.6 0.0 1589.8 I11 38.6 IV 5.9597 IV 13.4989 I 508 1068 1277 1613 1880 I 832 I1 452 (447) 951 (945) 1137 (1109) 1436 (1320)' 1673 (1634)' I1 740 (750)' I11 37.3 16.3 287.7 4.2 757.1 I11 14.8 IV 51.6069 10.1901 13.5458 12.9067 8.5098 IV 273.5342 I 380 698 866 1608 1580 I 893 I1 338 622 77 1 1431 (1284 f 30)' 1406 (1244)' I1 795 (776 30)' I11 26.0 7.6 40.7 34.0 753.1 I11 12.0 IV 41.5154 8.7454 7.2237 12.9410 14.4381 IV 124.8074 I 746 1518 2585 1454 1538 I 849 1351 (1343) I1 664 (667) 2301 (2349) 1294 (1043) 1369 (1110) I1 756 (705) I11 68.9 0.0 988.5 786.2 I11 12.0 0.3 IV 12.0861 14.6722 13.1512 IV 126.8585 I 810 1495 1867 1366 393 I 669 I1 721 (800)' 1331 (1400)' 1662 (1671)' 1300 (982)h 373 (-800)' I1 636 (550)h . . I11 24.8. . 47.2 12706.6' 793.2 6.1 I11 7.9 11.7791 IV 262.9545 12.3315 10.9626 12.4591 IV 91.2683 I 573 920 1188 1363 1899 2248 1569 1359 I 592 I1 510 819 1057 1213 1690 2001 1210 (1151) 1396 (1362) I1 527 (518) I11 34.02 9.8 1.9 37.8 47.9 2511.1 321.9 63.8 I11 61.8 IV 167.3252 12.0162 11.2111 10.6614 9.0760 IV 61.0329 I 837 1218 1515 1559 1922 2779 1129 1247 I 510 I1 745 (762)" 1084 (1069)" 1348 (1351)" 1388 (1383)" 1005 (985)& 1110 (1042)& I1 454 (496)' 1711 (1585)n 2473 (2803)" 83.8 343.0 I11 35.4 I11 47.9 34.1 210.2 28.4 789.4 566.2 9.8779 8.2432 IV 49.8119 IV 112.7160 12.5806 11.3174 1407 1959 I 555,6306 I 689 1393 2633 1252 1744 I1 494, 561' 11 613 (589) 1240 (1277) 2343 (2224) 1.3 20.3 I11 54.8, 33.5' I11 19.6 164.9 490.0 IV 12.0209 IV 13.0838 1372 2432 I 704 I 556 1145 1221 2164 1433 I1 627 I1 495 1019 1275 77.0 756.6 I11 37.1 111 7.0 267.9 69.4 IV 11.9003 IV 145.7 14.0 12.8 .
~~
I
'Unless otherwise stated, taken from ref 37. 'Nondegenerate at UMP2 level.
