Refined Thermochemistry for the Methanol Radical Cation (CH,OH'+)

concerning additivity of basis set increments and/or additivity of ... larger ultimate basis set is employed, leading to results (effectively) ..... M...
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5804

J . Phys. Chem. 1992,96, 5804-5807

Refined Thermochemistry for the Methanol Radical Cation (CH,OH'+) and Its Distonic Isomer (CH,OH;+) Ngai Ling Ma, Brian J. Smith,' and Leo Radom* Research School of Chemistry, Australian National University, Canberra, A.C.T. 2601, Australia (Received: December 3, 1991) Ab initio molecular orbital calculations at levels of theory beyond G2 have been used to obtain the ionization energy (IE,) of methanol and the energy difference (AEZ9*)between CH30H'+ and the methyleneoxonium radical cation, CHzOHz'+. The best estimate of IE, is 1051 kJ mol-', compared with the experimental value of 1047 kJ mol-I. For PEm, the best theoretical estimate is 27 kJ mol-' in favor of CH20H2'+compared with the experimental 30 kJ mol-I. The origins of errors at simpler levels of theory are discussed.

Introduction We have recently reported resultsZof a detailed study of the rearrangement and fragmentation reactions of the methanol radical cation (CH,OH'+) using Gaussian-1 (Gl), and Gaussian-2 (G2)4 theories. In most cases, the agreement between theory and experiment was found to be very good and in particular to be within the G1 and G2 target accuracies of 0.1 eV (about 10 kJ mol-I). However, discrepancies of 0.12 eV (Gl) and 0.11 eV (G2) were found for the ionization energy of methanol. The experimental value of 10.85 eVSappears to be reasonably well established, and so the fault would seem to rest in this case with the theoretical estimates. There are several possible factors within the G1 and G2 approaches that may contribute to the disagreement between theory and experiment. First, G1 and G2 are both based on MP2/631G(d) geometries. It had been noted previouslyZv6that the structure of CH30H'+ changes markedly in going from HF/631G(d) to MP2/6-31G(d), and it is possible that the structure may change further at higher levels of theory. Thus, an error may be introduced due to residual errors in the geometries of the species involved. Secondly, G1 and G2 theories involve assumptions concerning additivity of basis set increments and/or additivity of basis set and correlation effects; either or both of these may not be well satisfied. Finally, the G1 and G2 corrections for zero-point vibrational energies are calculated at the HF/6-31G(d) level, and in the light of the marked changes in geometry in going from HF/6-31G(d) to MP2/6-31G(d), it may be that this introduces a significant error. One of the principal aims of this paper is to examine the extent to which these approximations affect the calculated ionization energy of methanol. A second aim is concerned with the energy difference between CH30H'+ and its isomer, the methyleneoxonium radical cation, CHzOHz'+. This is of interest because CHz0H2'+ represents one of the simplest members of the distonic radical cation family, species that have attracted considerable theoretical and experimental attention in recent years.' In our previous study? we found an energy difference at the G1 and G2 levels (32-33 kJ mol-') that was substantially less than values obtained earlier at very respectable but lower levels of theory (e.g., 46 kJ mol-' at MP4/6-31 lG(df,p)).6 It is of interest to see whether this energy difference is stable with respect to further refinements in the theoretical treatment. The factors used throughout this paper for conversion to SI units are 1 hartree = 2625.5 kJ mol-' and 1 eV = 96.485 kJ mol-'. Method

Standard ab initio molecular orbital calculations*were carried out using the GAUSSIAN as9 and GAUSSIAN golo program packages. Calculations were performed with a variety of basis sets at the Hartree-Fock (HF), Maller-Plesset perturbation theory (MP2, MP4) and quadratic configuration interaction with single, double, and triple excitations (QCISD(T)) levels of theory. Initial calculations were directed toward obtaining results at the G1 and G2 levels of theory. G1 theory3 is a composite pro0022-3654/92/2096-5804!S03.00/0

cedure in which geometries are optimized at the MP2/6-31G(d) level. Assuming additivity of individual basis set enhancement effects at the MP4 level, and additivity of basis set and correlation effects between MP4 and QCISD(T), relative energies are obtained at effectively the QCISD(T) level with the 6-31l+G(Zdf,p) basis set. The ultimate G1 energy is obtained after correction for isogyric and zero-point vibrational energy effects, the latter obtained from scaled HF/6-3 1G(d) vibrational frequencies. G2 theory4 is a refinement of G1 theory. In G2 theory, the error arising from the assumption of additivity of individual basis set enhancements at the MP4 level is corrected at the MP2 level. A larger ultimate basis set is employed, leading to results (effectively) level, again with isogyric and at the QCISD(T)/6-311+G(3df,2p) zero-point vibrational corrections. Additional calculations were carried out in order to identify possible shortcomings in the G1 and G2 procedures. In the first place, geometry optimizations were performed at the QCISD(T)/ 6-31 1G(d) level to see whether there are significant changes from the MP2/6-3 1G(d) geometries. Secondly, singlepoint QCISD(T) calculations were carried out with the larger 6-311+G(2df,p) and 6-31 1+G(3df,2p) basis sets to eliminate the need for additivity approximations. Finally, vibrational frequencies were obtained at the MP2/6-31G(d) level to examine the effect of the change from HF/6-31G(d) to MP2/6-31G(d) on calculated zero-point vibrational energy corrections.

Results and Discussion Geometry Considerations. Geometries for CH30H (l), CH,OH'+ (2),and CHzOHz'+ (3), as optimized at various levels of theory and defined in Figure 1, are presented in Tables 1-111. The data in Tables I and I11 show that the geometrical parameters for neutral CH30H (I) and for CHzOHz'+ (3) do not show a great sensitivity to the level of theory employed. In addition, for neutral methanol (1) there is a very pleasing agreement between our best results and those from a recent experimental determination (Table I).ll For CH,OH'+ (2),on the other hand, it can be Seen that there are significant changes that accompany an increase in the level of theory (Table 11). Most striking and most important are the calculated C-O lengths which had previously been observedZs6to decrease from 1.577 A at HF/3-21G to 1.477 A at HF/6-31G(d) to 1.382 A at MP2/6-31G(d). If changes of this magnitude were to continue beyond MP2/6-31G(d), they would clearly have a profound effect on the calculated G1 and G2 energies. However, Table I1 shows that the subsequent changes are, in fact, fairly small: the C-O bond length decreases as the basis set is enlarged but increases in going from MP2 to QCISD(T), with the result that there is little overall change in going to our highest level of theory, the value at QCISD(T)/6-311G(d) being 1.386 A. Interestingly, the conformationalpreference also shows a strong dependence on the level of theory used. Previous calculations6 showed that, at HF/3-21G, CH30H'+ has an eclipsed structure of C, symmetry. However, at the HF/6-31G(d) level, the prebut this lies only ferred structure is asymmetric (C, symmetry),2*6 0 1992 American Chemical Society

Refined Thermochemistry for CH30H'+ and CH20H2'+

The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5805

TABLE I: Optimized Geometrical Parameters for CH30H (1) at Various Levels of Thee@ level HF/3-21G HF/6-3 1G(d) MP2/6-3 lG(d) MP2/6-31G(d,p) MP2/6-311G(d) MP2/6-31 lG(d,p) QCISD(T)/6-3 11G(d) expt'

point group CJ

Rco 1.441 1.400 1.423 1.420 1.417 1.416 1.421 1.428 (1)

CS CJ CS CS

CS CS

RCH2 1.079 1.081 1.090 1.085 1.088 1.090 1.094 1.098 (1)

ROH

0.966 0.946 0.970 0.962 0.959 0.957 0.961 0.975 (10)

LCOH 110.3 109.4 107.4 107.3 108.0 106.5 107.9 107.6 (9)

RCH, 1.085 1.087 1.097 1.092 1.096 1.097 1.101 1.098 (1)

LH2CO 106.3 107.2 106.3 106.5 106.6 106.9 106.6 106.4 (3)

LXCO 130.5 130.1 130.7 130.8 130.6 130.9 130.6 129.2 (3)

LHSCH, 108.8 108.7 108.8 108.6 108.8 108.6 108.8 109.1 (2)

"Bond lengths in angstroms, bond angles in degrees. 'The experimental ro structure is taken from ref 11.

TABLE II: O~timizedGeometrical Parameters for CH,OH+ (2) at Various Levels of Theory" level HF/3-21G HF/6-3 1G(d) HF/6-3 lG(d)' MP2/6-3 lG(d) MP2/6-3 lG(d,p) MP2/6-311G(d) MP2/6-31 lG(d)' MP2/6-31 lG(d,p) MP2/6-31 lG(d,p)' QCISD(T)/6-311G(d)

point group Cs

CI Cs CI CI CI Cs

CI Cs

Cs

RCO 1.577 1.477 1.476 1.382 1.383 1.359 1.355 1.363 1.351 1.386

ROH 0.999 0.978 0.978 0.998 0.989 0.982 0.982 0.984 0.983 0.985

Rcnl 1.078 1.074 1.082 1.097 1.091 1.099 1.118 1.097 1.121 1.119

Rcn, 1.074 1.080 1.076 1.088 1.083 1.086 1.085 1.088 1.085 1.090

Rcn, 1.078 1.084 1.082 1.127 1.121 1.134 1.118 1.137 1.121 1.119

LCOH LHXO LHXO L H L O LH2COHl LH3COHl LH&OHl 121.2 101.8 107.5 101.8 -121.7 0.0 121.7 -49.1 115.0 105.0 106.7 104.3 -171.1 69.5 116.5 103.2 109.6 0.0 103.2 -122.3 122.3 114.2 107.2 114.3 101.5 -148.0 -16.1 103.4 114.2 107.3 114.0 101.2 -149.4 -17.4 101.5 115.0 107.7 115.3 102.1 -147.2 -13.3 107.0 115.3 105.1 115.8 0.0 105.1 -128.4 128.4 113.3 108.4 115.0 101.2 -151.6 -16.9 101.3 0.0 113.7 105.3 116.3 105.3 -129.2 129.2 114.4 105.0 114.8 105.0 -127.5 0.0 127.5

'

Bond lengths in angstroms, bond angles in degrees. First-order saddle point on the potential energy surface.

TABLE III: Optimized Geometrical Parameters for CH20Hi+ (3) at Various Levels of Theory" level HF/3-21G HF/6-31G(d) MP2/6-31G(d) MP2/6-3 lG(d,p) MP2/6-311G(d) MP2/6-31 lG(d,p) QCISD(T)/6-311G(d)

point group CJ CS

cs CS CS CS CS

Rl-0 1.487 1.459 1.466 1.460 1.454 1.457 1.462

Rnn 0.976 0.965 0.989 0.978 0.973 0.975 0.973

Rcn 1.069 1.070 1.079 1.075 1.079 1.079 1.084

LXOC 170.3 141.6 135.2 137.2 141.3 137.1 139.9

LXCO 142.5 138.8 139.5 139.5 139.8 139.8 140.2

LHOH 116.7 111.3 109.9 110.8 112.5 110.5 112.2

LHCH 127.0 125.1 125.4 125.4 125.2 125.6 125.6

" Bond lengths in angstroms, bond angles in degrees. TABLE I V Commrison of Calculated G1 and C2 Total Energies ( E , Hm, hartrees) and Relative Energies ( A E , AHz1, kJ mol-') for MP2/631G(d) and-@ISD(T)/631 IC(d) Optimized Geometries species geometry Eo(G1) fh(G1) @o(G~) U29dG1) Eo(G2) H29dG2) Mo(G2) m ~ s ( G 2 ) expt" CH,OH MP2/6-31G(d) -115.53059 -115.52630 0.0 0.0 -1 15.534 88 -1 15.53059 0.0 0.0 0.0 QCISD(T)/6-311G(d) -1 15.53065 -115.52636 0.0 -115.53497 -115.53068 0.0 0.0 0.0 0.0 CHIOH'* MP2/6-31G(d) -115.12743 -115.12258 1058.5 1060.0 -115.13221 -115.12736 1057.2 1058.7 1046.9 QCISD(T)/6-311G(d) -115.12763 -115.12278 1058.1 1059.6 -115.13236 -115.12751 1057.1 1058.5 1046.9 CHZOHZ'' MP2/6-3 1G(d) -1 15.13976 -1 15.13509 1026.1 1027.1 -115.14437 -115.13970 1025.3 1026.3 1016.6 QCISD(T)/6-311G(d) -1 15.13989 -115.135 22 1025.9 1026.9 -115.14462 -115.13995 1024.9 1025.9 1016.6

Experimental values at 298 K taken from ref 5.

0.6 U mol-' below the eclipsed structure; Le., the bamer to rotation in the vicinity of the eclipsed structure is very small. At the MP2/6-3 1G(d) level, the preferred structure of CH30H'+ is still CI,2,6Indeed, introducing electron correlation at the MP2 level increases the asymmetry and the effect is further enhanced when the basis set is changed to 6-311G(d,p). The C-O bond is shortened dramatically, the LH&O angle is narrowed, and the C-H4 bond is lengthened, all indicative of strong hyperconjugation interaction.2 A comparison of the C, and C, structures at MP2/6-3 1lG(d,p) shows that there are significant geometrical changes associated with changes in conformation, which may be rationalized in terms of different CH bonds undergoing hyperconjugative interaction. However, in energy terms the conformational dependence of the hyperconjugative interaction is very small: the rotational barrier at the eclipsed structure a t MP2/ 6-31 lG(d,p) is just 0.3 kJ mol-'. At our highest level of theory, QCISD(T)/6-31 lG(d), the preferred geometry of CH30H'+ again becomes eclipsed with C, symmetry. The strong hyperconjugative interactions are nevertheless maintained, as reflected, for example, in the long C-H2 and C-H, bonds. Because the rotational potential function is very flat, the possibility that calculations at a still higher level of theory might predict an asymmetric structure cannot be discounted. However, the energetic consequences of any such conformational

1

.,

1 .+ /H

0 "

2

3

Figure 1. Definition of geometries of CH30H ( l ) , CH30H'+ (2), and CH20H2'+ (3). change a r e likely to be very small. One of our main objectives in carrying out the detailed geometric study was to see whether the use of MP2/6-31G(d) ge-

5806 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 TABLE V Calculated Total Energies ( E , hartrees) and Relative Energies (AE,, kJ mol-') involving CH,OH (11, CHIOH+ (2), and CH&H ji (3) at Various Levels i f level of theorv EICHtOH) AE,' AE,d Mic -1 15.43629 1046.6 98 1.6 65.0 MP2/6-31 lG(d,p) MP2/6-31 l+G(d,p) -1 15.44492 1064.8 998.0 66.8 -115.46908 1074.2 1011.8 62.4 MP2/6-31 l+G(Zd,p) -1 15.48032 1071.2 1002.3 68.9 MP2/6-31 l+G(df,p) -1 15.49276 1063.4 999.1 64.2 MP2/6-31 1G(2df,p) -1 15.50062 1080.1 1014.7 65.4 MP2/6-31 l+G(2df,p) -115.501 39 1081.6 1015.5 66.I MP2/6-311+G( 2dJp)' -115.50083 1080.0 1014.6 65.5 MP2/6-31 l++G(Zdf,p) -1 15.513 69 1083.5 1017.4 66.1 MP2/6-31 l+G(3df,2p) -115.52086 1085.6 1018.0 67.6 MP2/6-31 l++G(3df,2pd) -1 15.521 75 1086.1 1018.1 68.0 MP2/6-31 l++G(3df,3pd) -1 15.468 58 1030.6 984.2 46.4 MP4/6-31 lG(d,p) -115.47742 1048.7 1000.6 48.1 MP4/6-31 l+G(d,p) -1 15.502 15 1057.2 1014.6 42.6 MP4/6-31 l+G(2d,p) -115.515 19 1054.6 1005.0 49.6 MP4/6-3 1 1+G(df,p) -1 15.52793 1046.7 1002.3 44.3 MP4/6-31 lG(Zdf,p) -1 15.53578 1062.9 1017.5 45.4 MP4/6-31 l+G(Zdf,p) -I 15.536 77 1064.7 1018.7 46.0 MP4/6-311 +G(2dJpy -1 15.532 91 1064.1 101 7.3 46.8 MP4/6-311 +G(2dJp)g -1 15.54902 1066.9 1020.5 46.4 MP4/6-31 l+G(3df,2p) -1 15.468 89 1016.5 981.4 35.2 QCISD(T)/6-3 1 lG(d,p) -1 15.477 38 1033.1 997.1 36.0 QCISD(T)/6-3 1l+G(d,p) -1 15.527 52 1030.4 998.7 31.7 QCISD(T)/6-31 lG(Zdf,p) -1 15.53502 1045.2 1013.2 32.0 QCISD(T)/6-3 1 1+G( 2df,p) -I 15.536 01 1047.0 1014.4 32.6 QCISD( T)/6-311+G(ZdJp)' -I 15.537 08 1050.7 1015.9 34.8 QClSD( T)/6-311+G( 2dJp) QCISD(T)/6-311+G(3df,2p)-1 15.548 10 1048.9 1016.0 33.0 QCISD( T)/6-311+G(3df,2p)' -I 15.549 38 1052.6 IO1 7.8 34.8 'QCISD(T)/C311G(d) optimized geometries used throughout. bValues in italics obtained using additivity relationships. ' h E , is the electronic energy difference (IE,) between CHIOH" and CH,OH. AE2 is the electronic energy difference between CH20H2'+ and CH,OH. e AE, is the electronic energy difference between CH,OH'+ and CH20H2'+. /Obtained by assuming the basis set enhancement additivity relationship: E(6-31 l+G(Zdf,p)) = E(6-31 lG(d,p)) + [E(6-31 l+G(d,p)) - E(6-31 lG(d,p))] + [E(6-31 lG(Zdf,p)) - E(631 lG(d,p))]. 8Obtained by assuming the basis set and correlation additivity relationship: E[MP4(6-31 l+G(Zdf,p))] = E[MP4(6-311G(d,p))] + E[MP2(6-31 l+G(Sdf,p))] - E[MP2(6-31 lG(d,p))]. hThis estimate is based on the G1 additivity scheme, without the isogyric and zero-point energy corrections. 'This estimate is based on the G2 additivity scheme, without the isogyric and zero-point energy corrections.

ometries in G1 and G2 theories is likely to lead to si&icant errors. Table IV presents a comparison of relative energies of 1-3 at the G1 and G2 levels using both MP2/6-31G(d) and QCISD(T)/ 6-31 1G(d) optimized geometries. The differences are uniformly small. We conclude that the use of MP2/6-31G(d) geometries in the evalulation of G1 and G2 energies for these systems is not a source of significant error. Additivity of Basis Set Enhancement Effects. The difference in electronic energies ( U ,between ) CH30Hand CH30H.+,Le.,

Ma et al. the electronic ionization energy (IE,) of CH30H, is strongly dependent on the basis set employed (Table V). With geometries optimized at QCISD(T)/6-3 1lG(d), addition of diffuse functions 6-311+G(d,p) and 6on the heavy atoms (6-311G(d,p) 31 1G(2df,p) 6-31 l+G(Zdf,p)) increases the MP2 IE, value by 18.2 and 16.7 kJ mol-', respectively. Adding additional and higher polarization functions to the heavy atoms (6-3 1lG(d,p) 6-31lG(Zdf,p)) also has a large effect, in combination leading to an increase in IE, by 16.8 kJ mol-'. On the other hand, adding diffuse functions on hydrogen (6-3 11+G(2df,p) 6-3 11++G(2df,p)) has virtually no effect on IE,. The changes at the MP4 level of theory are very similar to those at MP2. Thus, addition of diffuse functions on the heavy atoms to the 6-311G(d,p) and 6-31 1G(2df,p) basis sets increases the energy difference by 18.1 and 16.2 kJ mol-', respectively, while addition of extra polarization functions to the 6-31 lG(d,p) basis (giving rise to 6-31 lG(Zdf,p)) leads to an increase in IE, of 16.1 kJ mol-'. As noted above, the G1 procedure assumes additivity of basis set enhancement effects in the course of estimating the ultimate G1 energies. The approximation used is: E(6-311+G(Zdf,p)) E(6-311G(d,p)) + [E(6-311+G(d,p)) - E(6-311G(d,p))] [E(6-31 lG(Zdf,p)) - E(6-31 lG(d,p))] (1) Our directly calculated MP2/6-311 +G(2df,p) results suggest that such a scheme overestimates the MP2 energy difference by 1.5 kJ mol-'. At the MP4 level, used within the G1 procedure, the corresponding error is 1.8 kJ mol-'. Additivity of Basis Set Enhancemeot and Correlation Effects. Another approximation in G1 theory is the assumption that the effect of basis set enhancement at MP4 and QCISD(T) levels is the same, i.e. E[QCISD(T)/6-3 11+G(2df,p)] = E[QCISD(T)/6-31 lG(d,p)] + E[MP4/6-31 l+G(Zdf,p)] E[MP4/6-31 lG(d,p)] (2) Our direct calculations show, in fact, that for the calculation of IE, the effect of basis set enhancement decreases from 32.3 kJ mol-' at MP4 to 28.7 kJ mol-' at the QCISD(T) level of theory; Le., an error of 3.6 kJ mol-' is introduced by assuming that these are equal. This error, together with the error associated with the assumption of basis set additivity in obtaining the MP4/6311+G(2df,p) energy, contributes a total of 5.4 kJ mol-' to the overestimation of the IE, calculated by the G1 procedure. In G2 theory, the possible nonadditivity of basis set enhancements is corrected at the MP2 level. As a consequence, the residual difference of 3.7 kJ mol-' (Table V) between the directly energy and that obtained calculated QCISD(T)/6-311+G(3df,2p) using the G2-type procedure largely reflects the nonadditivity of basis set and correlation effects. Zero-Point Vibrational Energy Corrections. The theoretical relative energies can be further improved by employing zerepoint vibrational energy corrections at the MP2/6-3 1G(d) level instead

-

-

-

-

+

TABLE VI: Zero-Point Vibrational Energies (ZPE, hnrtrees), Relative Zero-Point Vibrational Ihergies (AZPE, kJ mot'), and Enthalpy Temperature Corrections (Hm- H m millihartrees) for CH30H (l), CH30H+ (2), and CH20H2'+ (3) species ZPE (HF)' ZPE (MP2)b AZPE (HF)" AZPE (MP2)' H298 - Ho (MP2)b 0.048 94 0.0 0.0 4.28 0.049 41 CHBOH CHIOH'+ 0.046 30 0.044 92 -8.2 -10.6 4.59 0.047 03 -5.6 -5.0 4.58 0.047 29 CH20H2'+ "Calculated using HF/6-31G(d) frequencies, scaled by 0.8929. bCalculated using MP2/6-31G(d) frequencies, scaled by 0.93. TABLE VII: Comparison of Best Calculated Relative Energies" with Experimental Valuesb (kJ mol-', eV in Parentbeaes) O 298. K - _K_ -. _. theory expt' theory expt reaction 1051.8 (10.90) 1046.9 (10.85) 1046.9 (10.85) CHIOH CHIOH'+ + e 1051.0 (10.89) 1024.4 (10.62) 1016.6 (10.54) 1023.6 (10.61) 1015.8 (10.53) CHIOH CH20H2'+ + e 27.4 (0.28) 30.3 (0.31) 30.3 (0.31) CH20H2'" CHIIOH" 27.4 (0.28)

--

-.

Obtained at the QCISD(T)/6-3 1 1+G(3df,2p) level of theory with isogyric corrections and with zero-point vibrational energy corrections calculated at MP2/6-31G(d) (Table VI). bObtained using data in ref 5, unless otherwise noted. 'Temperature corrections obtained, where necessary, using (scaled) MP2/6-3 1G(d) vibrational frequencies (Table VI).

Refined Thermochemistry for CH30H'+ and CH20H2'+ of at the HF/6-31G(d) level that is standard for the G1 and G2 procedures. Such a refinement is important in this case because of the substantial geometry change for CH30H'+ in going from HF/6-31G(d) to MP2/6-31G(d). This results in a decrease in the zero-point vibrational energy of CH30H'+ by 3.6 kJ mol-' (Table VI). At the same time, the zero-pint vibrational energy of CH30H is only decreased by 1.2 kJ mol-'. Therefore, the ionization energy is decreased by 2.4 kJ mo1-I if MP2/6-31G(d) rather than HF/6-31G(d) zero-point vibrational energies are used. Similar significant differences between HF/6-3 1G(d) and MP2/6-3 1G(d) zero-point vibrational energies might be found in other cases (e.g., FOOF) for which the geometries at these levels differ substantially. In evaluating zero-point vibrational energies, we have used standard scale factors of 0.8929 (HF)3and 0.93 (MP2).12 It has recently been suggestedI3that somewhat higher values (e.g., 0.91 for HF/6-31G(d)) might be more appropriate. For the energy differences examined in this paper, the effect of using such higher scale factors is found to be less than 0.2 kJ mol-'. Calculated Ionizptioa Energy of Methand. In summarizing our analysis, we begin by noting that the adiabatic ionization energy of methanol calculated at the standard G2 level (1057.2 kJ mol-') differs from the experimental value (1046.9 kJ mol-') by 10.3 kJ mol-'. We have seen that the effect of using QCISD(T) geometries contributes a marginal 0.1 kJ mol-' improvement, avoidance of additivity approximations contributes a more significant 3.7 kJ mol-', and the MP2/6-31G(d) zero-point vibrational energy correction contributes a further 2.4 kJ mol-'. The combined improvement is 6.2 kJ mol-', leading to an acceptable remaining discrepancy of 4 kJ mol-' in our best estimate (1051 kJ mol-') for IE, of methanol. Very recent calculation^'^ have indicated that the higher level correction in standard G2 theory should be modified slightly if the additivity approximations are not used. We have estimated that the effect of such a modification in the present study would be to increase the calculated IE, of methanol by 1 kJ mol-'. Methylewoxonium Radical Cation. We have used our higher level energies to examine two energy comparisons involving the methyleneoxonium radical cation, CH20H;+ (3), included in Table V. The energy difference (A&) between CH20H2*+(3) and CH30H (1) does not change significantly in going beyond G2. Thus, the improved geometry contributes -0.4 kJ mol-', the removal of additivity approximations contributes -1.8 kJ mol-', and the improved zero-point vibrational energy contributes f0.6 kJ mol-'. The overall effect takes the standard G2 value of 1025.3 kJ mol-' to our best calculated value of 1023.6 kJ mol-'. There is a somewhat greater change in the energy difference (M3) between CH30H'+ (2) and CH20H;+ (1). Here, improved geometry contributes +0.3 kJ mol-', the avoidance of the additivity approximation contributes -1.8 kJ mol-', and the improved zero-point vibrational energy contributes -3.0 kJ mol-'. Our best estimate of 27.4 kJ mol-' for the energy difference between CH30H'+ (2) and its distonic isomer 3 may be compared with

The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5807 the standard G2 value of 31.9 kJ mol-' and the experimental value of 30 kJ mol-I. Concluding Remarks

Our best values of the various relative energies, calculated at the QCISD(T)/6-311 +G(3df,2p) level on geometries optimized at QCISD(T)/6-31 lG(d) together with MP2/6-3 1G(d) zero-point vibrational energies and isogyric corrections, are summarized in Table VII. Satisfactory agreement between theory and experiment is achieved in all cases. The improved estimates of the ionization energy of methanol and of the energy difference between methanol radical cation and methyleneoxonium radical cation, compared with the standard G2 values, arise largely from the removal of additivity approximations and from better estimates of zero-point vibrational energies. The sensitivity of the calculated zero-point energies, in turn, arises because of the substantial difference between the HF/6-31G(d) and MP2/6-31G(d) geometries for CH30H'+ (2). Acknowledgment. We gratefully acknowledge a generous allocation of time on the Fujitsu FACOM VP-100 and VP 2200 computers of the Australian National University Supercomputing Facility. Registry No. 1, 67-56-1; 2, 12538-91-9.

References and Notes (1). Current address: Biomolecular Research Institute, 343 Royal Parade, Parkville, Victoria 3052, Australia. (2) Ma, N. L.; Smith, B. J.; Pople, J. A,; Radom, L. J . Am. Chem. Soc. 1991. 113. 7903. ( 3 ) Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari,K.; Curtiss, L. A. J . Chem. Phys. 1989, 90, 5622. (4) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys: 1991, 94, 7221. (5) Lias, S.G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J . Phys. Chem. Ref. Data 1988, 17, Suppl. 1 . (6) Yates, B. F.; Bouma, W. J.; Radom, L. J. Am. Chem. Soc. 1987,109, 2250. 171 For leading references.see: (al Radom. L.: Bouma. W. J.: Nobes. R. H.;'Yates, B. F. &re Appl. Chem. la,56, 1831: (b) Hammerum, S. niass Spectrom. Rev. 1988, 7 , 23. (8) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory: Wilev: New York, 1986. (9) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Fluder, E. M.; Topiol, S.;Pople, J. A. GAUSSIAN 88; Gaussian Inc.: Pittsburgh, PA, 1988. (10) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.;Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Pople, J. A. GAUSSIAN 90, Gaussian Inc.: Pittsburgh, PA, 1990. (11) Iijima, T. J . Mol. Struct. 1989, 212, 137. (12) Hout, R. F.; Levi, B. A.; Hehre, W. J. J. Compur. G e m . 1982, 3, 234. (13) Grev, R. S.;Janssen, C. L.; Schaefer, H. F. J. Chem. Phys. 1991,95, 5128. (14) Curtiss, L. A.; Carpenter, J. E.; Raghavachari, K.; Pople, J. A. To be published.