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Electron affinities: Basis and correlation effects
Volume 119, number 2.3
ELECTRON
AFFINITIES:
30 August 1985
CHEMICAL PHYSICS LFITERS
BASIS AND CORRELATION
EFFECTS
Received II March 1985: in final form 13 May 1985
The effect or basis qualily and the inclusmn of corrcla~mn on the compuwd (adinb+ttic) cleclron an?nily of sane molecules is stud& The re.4~ show ihal when diNuse runctions are added LOa splil-valence baw XI. and clec~ron ccrrelntion is mcluded at the MP/2 level. the compukd se1 of mokules considered.
elecwon Ainicks
present a rne~n de\iAon
1.Introduction The direct computation of electron affkdties (EAs) is a difficult problem in theoretical chemistry. Simple based on Koopmans’ theorem [I] or on the ASCF procedure 121~give EAs which are systematically too negative, that is, they overstabilize the neutral compound A compared to the associated anion A-. The use of coR~~uratioR interaction (Cl) methods. on the other hand, requires a large expenditure of computational resources and becomes unpractical for large molecules The latter type of methods available for the theoretical computation of EAs include those based on many-body perturbation theory, such as the equation-of-motion method [3], the propagator method [4], or the Green’s function method [5], whrch reproduce highly converged CI results usmg less computer time, but are very complex to use and, therefore, still not very popular. Recently, there has been a renewed effort in the study of anionic systems due, principaUy to the efmethods
forts of Schleyer et al. [6] in extending previous res&s [7J and developing an optknized basis set suitable for the general study of anions. This basis, 63 1+ G, is an extension of the well known 4-3 1G basis to which a set of diffuse sp functions with a single optunized exponent [6] has been added. The computation of proton affinities of a set of anions wrth this new basis give results at the SCF level, with 0 Ok-2614/85/S (North-Holland
03.30 0 Elsevier Science Publishers B-V. Physics Pubhshmg Division)
from experimrnl
or lrss than 10 Iwl/mol
kw the
an average deviation of only 10 kcalfmol compared to the availabie experimental data, a very valuable improvement over the 4-3 IG results. However, the same conclusion does not apply to the computation of EAs. On the other hand, the MNDO semi-empirical method is able to reproduce experimental EAs with minor deviations [8] _Therefore, there is no problem at the semi-empirical level, while at the “ab initio” level some authors [6] suggest the use of thermochemical cycles in order to obtain good “ab initio” EAs The aim of the present work is to show that, with an adequate basis of moderate size and the indusion of electron correlation using M&ler-Plesset [9] perturbation theory taken to the second order (MP2) [IO], it is possible to obtain fairly good ab initio EAs
2. Computational
details
Following the usual conventions, the (adizbatic) electron affinity is computed as the difference in energy between the Iowest rotations-~brational state of a negative ion A- and the lowest rotational-vibrational state of the neutral molecule A_ In general, however, instead of the energy of the lowest rotatronalvibratronal state, it is usual to take the energy at the mmimum of the potential energy curve. The difference between this and the energy of the lowest state is the zero-pomt energy (ZPE)_ its value can be com13.5
Volume
119, number 2,3
CHEMICAL
puted from the force constants at the mmimum, but this 1s a time-consuming step and one which is normalIy omitted because the ZPE of the amon and the neutral molecule are similar and therefore tend to cancel in the EA. Errors of no more than S-10 kcal/ mol are produced by this approximation. AU the computations were done using a version of the GAUSSIAN-80 program [l 1] _The basis sets employed were the standard STO-3G, 4-3 lG, 4-3 lG* and 4-3 lG** sets. Some computations used 4-3 l+ G [6], and 4-31 + G* sets. The latter were constructed by adding the extra diffuse functions of 4-3 1 + G to the standard 4-3 lG*. Three general bases were constructed from a triple-zeta (TZ) set, to which two po-
PHYSICS
30 August 1985
LJXTERS
larization d fun&Ions and two p diffuse functions were added on the heavy atoms to Five TZ + 2P and TZ + 2P + 2D sets, respectively. The exponents and coefficients were taken from van Duljneveldt [12] for the TZ basis set, while the exponents for the extra polarization and diffuse functions were computed as indicated by Dunnmg and Hay [7] _
3. Results and discussion In order to find a good level of approximation in the size of basis and level of correlation, the EA of the neutral systems 0H(211), CH#A,), CH2(3B,),
Table 1 Electron affinity (EA). in kcaI/mol. for the OH(711) molecule. The total energy, in atomic units. for the neutral moleculeE(A) and its anionE(A-) is also given, together with the method, basis and geometry Method
Bads
Geometry
UHF
STOJG 4-31G
opt. opt.
3-21 + G
UHF/4 -3 1G UHF/4-31G
E (A-)
EA
uHI;/4-31G UHF/4-31G UHF/4-3lG UHF/4JlG UHF/4-31G UHF/4-31G
-74.364886 -75.287165 -74.996572 -75.292698 -75.292698 -75 311065 -75.386665 -75.317304 -75 389369 -75.413648 -75.415217
-74.065017 -75.229789 -74.995710 -75.280960 -75.281216 -75248646 -75.375482 -75.254683 -75.355705 -75.375141 -75.403075
-188.17 -36.00 -0.54 -7.37 -7.21 -39.17 -7.02 -39.30 -21.12 -24.17 -7.62
4-31+ G 4-31G* 6-31 + G* 4-31G** TZ TZ+2P TZ+ZP+2D
u-w/4-31G UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 IG UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 1G
-75.376129 -75.091703 -75.384778 -75 450040 -75.529473 -75-461451 -75.491767 -75592606 -75.595667
-75.354304 -75.150819 -75.436978 -75.434248 -75.588325 -75-447391 -75504544 -75.614633 -75.66W62
-13.70 37.10 32.76 -9.91 36.93 -8-82 8.02 13.82 40.4 1
4-31G 3-21-t- G 4-31+ G 4-31 + G 431G* 6-31 + G* 4-31G** TZ TZ+2P TZ+2P+ZD
UHF/4-31G W/4-3 1G UW/4-3 1G opt. UHFf4-31G UHF/4-31G UHFf4-31G UHFf4-31G UHFj4-31G UT-lFf4-31G
-75.382410 -75 096574 -75.390530 -75.391045 -75.461972 -75540840 -75.473527 -75.495454 -75.603733 -75.606471
-75.354569
-75.138788 -75.422366 -75422388 -75.438599 -75.581652 -75.451932 -75.495706 -75.613947 -75.649444
17.46 26 49 19.97 19.66 -14.67 25.61 -1355 0.16 6.41 26.97 (42.20)
4-31 + G 4-31 i-G 4-31G* 6-31 +G* 4-31G** TZ TZ+2P TZ+ZP+2D UhIF.2
uhlP3
4-31G
3-21 + G
opt.
exp.
136
Volume 119, number 2,3
CHEMICX1, PHYSlCS LE-ITERS
02(3 Z;), and CH30(2A’) was computed using the various basis sets using UHF theory with and without correlation. The results for the total energy of both the anion and neutral systems, together with the computed EA, is shown in tables l-5 indicating in each case the basis and the theoretrcal method used (UHF stands for an unrestricted Hartree-Fock computation)- The experimental value of the EA [13] is included between brackets at the end of each table. The fust computed EA is for OH in its ground state, for which results obtained with CI and equation-of-motion methods [ 131 give a useful comparison. The CI result obtained with a (6s, 5p, ld/3s, Ip) basis, very near to a TZ + 1P basis in our conventron, is 30 98 kcal/mol if a conjuration space constructed with the fundamental and the most nnportant single, double and triple excited configurations is used. Using the same basis, the equation-of-motion result is 4.23 kcal/mol worse than the Cl one, and this only if second-order effects are included, otherwise the result is even poorer. Thus for OH the deviation from the experimentai value IS between 12 and 16 kcal/mol. Our approach to the experimental EA of OH started with the computation of a good equilibrium geometry. In this way, we optimized the geometry at the HF level with STO-3G and 4-3 1G bases. It has been found {63 that further optimrzation with 4-31 +- G or 4-3 lG* bases would lead to si~i~cant changes in geometry or, as can be seen in table I, the computed EA. We have therefore used 431G geometries when computing the EAs with larger basis sets. In each case, the geometry used in the computation is shown in the respective table. Once the geometry has been computed, we have used larger basis sets at the UHF level in order to obtain results nearer to the HF limit, e g., the TZ -I- 2P + 2D basis. Those results show, in accordance with Cade’s work [2], that the HF level does not give even the sign of the experimental EA of OH correctly. There is a deviatron of 35 kcalimol. From the UHF results we can, however, draw some useful conclusions. The first is the importance of the diffuse functions. With only one set of extra diffuse functions we obtain the same accuracy as with the TZ + 2P + 2D basis Furthermore, with only the addition of polarization functions we have a result which rs, in the best case, 20 kcal/mol worse, and of the same order as those computed with the Same basis without the use of polari2ation functions.
30 August 1985
The inclusion of correlation in our computations gives a lowermg in the computed EAs by an amount of the order of 20-30 kcalfmol- As consequence, we have now values which are near to the experimental result However, as in the HF case, there is a wide range of results dcpendmg on Ihe basis used_ Again, the basis with diffuse functions gives better results, but now the inclusion of polarrzation functions has a small effect because they improve the correlation ener,T. It is interesting to note that 4-31G with correlation gives almost the same value as the 4-3 1 + G at the HF level, extending to the computation of EAs Kollmar’s resJts [7] on proton affinities. There are two more points to note in relation to table I_ One is the fact that MP? EAs are, for the same basis, always better than MP3 ones. This comes from the fact that the third-order energy correction for the anions is positive and, therefore, raises the total energy. The other point is that the optimization of geometry at the MP3 level does not change significantly the value computed with the HF 4-31G geomtry- Finally, we can compare our resuhs with those already reported for the Cl and equation-of-motion methods_ We see that, at tic MP2 level with a 4-3 1+ G, we have a result slightly better than that reported in ref. [ 143 for a better basis With the best basis here reported the error is only 1.79 kcal/molIn order to test the general validity of the conclusions discussed above, we have repeated the computation with the same types or basis for CHz in the singlet and triplet states. Tables 2 and 3 show that the same trends already noticed for the OH molecule hold for those molecules. The best available computed value for the EA has a deviation from the experunental value of 5.61 kcal/moI for the singlet, and 3.63 kcal/mol for the triplet. One difference from OH appears for tnplet CH,, where the MP3 and MP2 results are very simrlar. Tables 4 and 5 include the results for 0, and CH30. With minor differences, the general trends are the same. In CH30 the 4-31 + G basis within the MP2 Ievel gives an abnormally high deviation from the experimental result of 19.03 kcal/mol which is lowered to 12.15 kcal/mol when the 4-3 1 + G* is used. This implies that there may be cases in which a further improvement in the basis is needed to give adequate agreement with experiment- In all cases, the direct method discussed here in which correlation is included by the M&ler-Plesset 137
Table 2 Electron affinity (EA). io kcal/ mol, for the CH2 (I Al) molecule. The total energy, in atomic units, for the neutral molecule E(A) and its anion E(A-f is also @en, together with ihe method, basis and geometry Mathod
Basis
Geometry
E (A)
E
EA
UHF
STO-3G 4-31G 3-21 + G 4-31+ G 4-31G+ 631 f-G* 4-31c** TZt2Pt2D
out. UHFiQl-3 1G UHF/4-31G UHF/4-3 1G UHF/4-316 UHF/4-31G UHF,‘431G
-38 372305 -38.610347 -38.316053 -38.816715 -38.833192 -38 876456 -38.835561 -38.888952
-38.193243 -38.781456 -38.312925 -38.824597 -38.800016 -38.881244 -38.804383 -38.892877
-112.37 -18.13 -1.96 4.05 -1956 3.00 --19 56 2.46
wMP2
4-336 3-23 + G 4-31 +c 4-31Gf 6-31 + G’ 4-3iG** TZ+2P+2D
UHF/4-3 1G UHF/4-3 1G uHF/4-3 1G UHF/43 1G UHF/431G UHF/4-31G UHF/431G
-38.875392 -38 411146 -38.884193 -38.928702 -3 8.975569 -38-94625 7 -39.013365
-38.853788 -38 439458 -38.913053 -38.907985 -39.002670 -38.927344 -39.043372
--13.56 17.77 18.11 -13.00 17.01 -11.87 18 33
UhlP3
4-31G 3-214 G 4-31+ G 4-31G* 6-31 + G* 4-31G** TZ+2P+2D
UHFj4-3 i G UHFi4-31G UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHFf4-31G UHF/4-31G
-38_889355 -38.437992 -38.898161 -38.9464468 -38.993286 -38.965239 -39.032373
-38 865190 -38_422415 -38-923269 -38-923161 -39.016281 -38.943719 -39.058052
-15,16 9.77 15 -75 -14.63 14*43 -13.51 16.12
OPi
exp.
(24-44)
Table 3 Electron affinity (EN, m kcWmo1, for the CM, f”BiI molecule. The total energy. VI atomic units, for the neutral molecule E(A) and its anion E(A3 is also &wt. together with the method, basis and geometm Method
Basis
Geometry
.E (A)
E (A->
EA
UHF
STO-3G 4-31G 3-21 + G 4-31 + G 4-31G* 6-31 + G+ 43 lG** TZ-i-2Pc2x.l
opt. opt_ UHFf4-3lG UHF/4-3 1G UHF/4-31G UHF/4-3 IG UHF/4-3 1G UHF/4-31G
-38-436234 -38 869630 -38.352363 -38.872985 -38.88i536 -38.923710 -38.885845 -38.935484
-38.193243 -38 781456 -38.312925 -38.824597 -38.800016 -38.881244 -38.804383 -38.892877
-152.48 -55.33 -24.75 -30.36 -51.15 -26 65 -51.12 -26.74
UMP2
4-31G 3-21+ G 4-31 + G 4-31G” 6-31 + G* 4-31G-* TZ+2P-t-2D
UHF/4-3 1G UHF[4-3 1G UHF/4-31G UHF/43 1G UHFf431G UHF/4-31G UHF/4-31G
-38.922265 -38.426005 -38.927233 -38.963323 -39.006818 -38.979670 -39.041452
-38.853708 -38-439458 -38.913053 -38.907985 -39 002670 -38.927344 -39.043372
97 8.4C -8.90 -34.72 -2.60 -32.84 1.21
wrvY.P3
4-31G 3-21 +G 4-31 + G 4-31G” 6-31+ G’ 4-3 1G** TZ+2Pc21)
UHF/4-31G UHF/4dlG UHF/4-3 1G UHF/4-3 1G UHF/4-31G UHF/4-31G UHF/4-3 1G
-30.932746 -38.434462 -38.937828 -38.977143
-38.865190 -30.437992 -38.923269 -38.923161 -39.016281 -38.943719 -39.058052
-42.39 2.22 -9.14 -33 87 -2.83 -3190 0.86
-39.020787
-38.994547 -39.056684
42
CHEMICAL
Volume 119, number 2.3
PHYSICS LEITERS
30 August 1985
Table 4 Electron affiity (EM, in kcal/mol, for the 02 (‘Ei> molecule. The total energy, in atomic units, for the neutral molecule E(A) and its enion E(A_) is also given, together wrtb the method, basis and geometry Method
Bash
Geometry
E (A)
E (A-1
EA
STO-3G 4-31G 3-21+ G 4-31 -i.G 4-3IG* 631+ G*
opt. opt. UHF/4-3 1G UHFf4dlG UHF/4-3 1G UHF/4-31G
-147.634171 -149.392965 -148.80~90 -149.399600 -149.475514 -149.620617
-147.384062 -149.368558 -148.824765 -149 400299 -149.415287 -149.591159
--156.95 -15.31 15.23 044 -37.79 -18-45
4-31G 3-21 +G 4-31 + G 4-31c* 631+ G*
UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF/4-31G UHF/4-3 1G
-149.630920 -149.04465 I -149.639511 -149.807422 -149.954330
-149.6 13086 --149.086003 -149 658257 -149.769703 --149.960772
-11.19 25.95 11.77 -23.67 4.04
4-3 IG 3-21-i. G 4-3l+ G 4-31G* 6-31 -t-G*
UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-31G
-149 615559 -149.02a272 -149.623739 --149X93369 --149.950087
-149.602335 -149.070421 -149 642858 -149-767516 -149 953388
-829 2645 12.00 -22so 2.07 (10-14)
exp-
Tablc 5 Electron tifinit!! (EA), in kgllmol, for the CHSO(~A’) molecule. The total energy, in atomic units, for tbc neutral molccu!c E(A) and its amon E(A-1 IS also .givcn, togcthcr wrth the method, basis end geometry M&WJd
Basis
Geometry
E (AI
E(A-1
EA
UHF
STO-3G 4-31G 3-21+ G 4-31 +G 4-31G* 4-31+ G* 6-31+ G* 4-31G**
opt opt. UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF/4-31G
-113.960886 -114.262848 -113 816368 -114.267371 -114.310204 -114 307516 -114_423704 -114.315641
-112.706368
-159-71 -27.89 -9 26 -13.60 -26.04 -11.21 -8 52 -25.81
uMP2
4-31G 3-21 + G 4-31+ G 4-31G* 4-31+ G” 6-31+ G* 4-31G**
UHF/4-31G UHF/4-3 1G UKF/4-3 1G UHF/4-31G UHF/4-3fC IJHF/4-31G UHF,‘4-3 IG
-114.440615 -114.000538 -114.448669 --114_576180 -114574672 -114.693623 -114_600770
-114 439268 -114.040769 -114_484130 -114586469 -114.623096 -114.744279 -114.613773
-0.85 25.25 22.25 64.5 29-13 31.79 8.16
UhfP3
4-316 3-21 -r-G 4-31 + G 4-31c* 4-31+ G* 6-31 + G+
UHF/4-31G UHF/4-3 IG UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF4-31G
-114.455631 -114.014232 -114.463302 -114598049 -114596418 -114.715179
-114 445251 --114.040460 -114.463622 -114.596977 -114.625541 -114.749515
-6.51 16.46 12.75 -0 67 la.27 21.55 (41.28)
_
-114.218406 -113.801610 -114.265692 -114.268702 -114.289650 -114.410124 -114.274511
exp.
139
Volume
119, number 2.3
CHEMICAL
PHYSICS
formalism is a powerful and economical route for the theoretlcal computation of EAs. To fvd a better standard basis for computation of EAs, we carried out test calculations using the 6-3 1 + G* [15] and the 3-21 + G sets. The results, given in tables 14, show that 3-21 + G gives EAs which are better than those computed with the similar sized 4-3 1 + G basis. One exception to this trend is 02, a case where the 3-21 + G basis overstabilises the anion with respect to the neutral molecule. For 3-21 + G, excluding the O2 result, the mean value of the absolute deviation between the computed and experimental EAs is 7.8 kcal/mol, which is of the same order as that reported [ 161 for the SCF proton affinities with this basis. The results for 6-3 1 + G* are in general better than the 4-3 1 + G and 4-3 1 + G* ones; the computed EA results approach the experimental value as the basis set 1s increased All of these results confirm the conclusions obtained with the 4-3 1 + G bans, namely, that by using diffuse functions an hIP2 calculation can match the experlmental EA to the desired accuracy of a few kcal/mol. The inclusion of the thirdarder perturbation increases the deviation from the experimental value. We have tested what happens when orders higher than three are also mcluded by means of the use of the CIPSI method [ 161 on the computation of the EA of the OH rnolecule The result obtained (30-88 kcal/mol) Y mtermediatc between MP2 and MP3, when the 6-31 + G* basis (but with only five d functions due to program limitations) is used A configuration interaction computation for the same molecule and the standard 6-3 1 + G* basis, including all the double excitations in the wavefunction, gives a result of 26.25 kcal/mol. Both results show that MP2 overstabilises the total energy of the anion with respect to the neutral molecule. However, MPZ gives reasonable accuracy at lower cost than more elaborate methods. Finally, we compare the ab mitio results reported here with the MNDO ones for these molecules, which are G-23, -2.08, -27.44,3.69 and 39.66 kcal/mol for OH, CH, singlet, CH, triplet, 0, and CH,O, respectlvcly. Those values present a deviation from the values measured experimentally of 35.97,26_52,32.28,
140
30 August 1985
LETTERS
6.45, and 1.62 kcal/mol, respectively, that is, the mea1 difference is higher than the one computed in this work and in two cases the MNDO EA has the wrong sign.
Adcnowledgement The authors are Fcratefulfor computer time available through grant CAICYT-657/81: We also thank Dr. F. Illas for the use of his CIPSI program.
Zeferences
111T.
Koopmans.
Physica 1 (1933)
104_
r21 P.E. Cade, J Chem. Phys. 47 (1967)
2390. Simons. Ann. Rev. Phys Chem. 28 (1977) 15, and references therein; D-L. Yeager, Ph.D. tbesls. Cahfornia Institute of Technology, Padena (1975). 141 B.-T. Pickup and 0. Goscinski. Mol. F’hys. 26 (1973) 1013. 151 L.S. Cederbaum and 1%‘.Domcke, Advan. Chem. Phys. 36 (1977) 205. 161 J. Chandrasckhar, J.G. Andrade and P. von R_ Schleyer. J_ Am_ Chem. Sot. 103 (1981) 5609. 171 T.H. Dunning and P.J. Hay, Modern Theoret. Chcm. 3 (1977) 1; H. Kollmar, J. Am. Chem. Sot. 100 (1978) 2665. IEI M J.S Dewar and H.S. Rzepa. J. Am. Chem. Sot. 100 (1978) 784_ 191 C. MQllcr and MS. Plesset, Phys. Rev. 46 (1934) 618_ 1101 J.S Bmkley and JA. Pople, Intern. J. Quantum Chem. 9 (1975) 229. r111 J.S. Binkley, R.A. Whiteside, R. Krishnan, R. Seeger, DJ. DeFrees. H-B. Schlegel, S. Topiol, L.R Kahn and JA. Pople, Program GAUSSIAN-80, Department of Chemistry, Carnegie-Mellon University, Pittsburgh. 1121 F. van Duijneveldt, IBM Technical Report RJ 945 (1971). 1131 B.K. Janousek, Gas Phase Ion Chcm. 2 (1979) 53. r141 M.F. Herman, K.F. Freed, D.L. Yeager and B. Lm, J. Chem. Phys. 72 (1980) 611. 1151 T. Clark. J. chandrasekhar, G-W. Spitznagel and P. von R. Schleycr. J. Comput. Chem. 4 (1983) 294. 1161 B. Huron, J-P. Malrieu and P. Rancurel, J. Chem. Phys. 58 (1973) 5745
131 J.
ELECTRON
AFFINITIES:
30 August 1985
CHEMICAL PHYSICS LFITERS
BASIS AND CORRELATION
EFFECTS
Received II March 1985: in final form 13 May 1985
The effect or basis qualily and the inclusmn of corrcla~mn on the compuwd (adinb+ttic) cleclron an?nily of sane molecules is stud& The re.4~ show ihal when diNuse runctions are added LOa splil-valence baw XI. and clec~ron ccrrelntion is mcluded at the MP/2 level. the compukd se1 of mokules considered.
elecwon Ainicks
present a rne~n de\iAon
1.Introduction The direct computation of electron affkdties (EAs) is a difficult problem in theoretical chemistry. Simple based on Koopmans’ theorem [I] or on the ASCF procedure 121~give EAs which are systematically too negative, that is, they overstabilize the neutral compound A compared to the associated anion A-. The use of coR~~uratioR interaction (Cl) methods. on the other hand, requires a large expenditure of computational resources and becomes unpractical for large molecules The latter type of methods available for the theoretical computation of EAs include those based on many-body perturbation theory, such as the equation-of-motion method [3], the propagator method [4], or the Green’s function method [5], whrch reproduce highly converged CI results usmg less computer time, but are very complex to use and, therefore, still not very popular. Recently, there has been a renewed effort in the study of anionic systems due, principaUy to the efmethods
forts of Schleyer et al. [6] in extending previous res&s [7J and developing an optknized basis set suitable for the general study of anions. This basis, 63 1+ G, is an extension of the well known 4-3 1G basis to which a set of diffuse sp functions with a single optunized exponent [6] has been added. The computation of proton affinities of a set of anions wrth this new basis give results at the SCF level, with 0 Ok-2614/85/S (North-Holland
03.30 0 Elsevier Science Publishers B-V. Physics Pubhshmg Division)
from experimrnl
or lrss than 10 Iwl/mol
kw the
an average deviation of only 10 kcalfmol compared to the availabie experimental data, a very valuable improvement over the 4-3 IG results. However, the same conclusion does not apply to the computation of EAs. On the other hand, the MNDO semi-empirical method is able to reproduce experimental EAs with minor deviations [8] _Therefore, there is no problem at the semi-empirical level, while at the “ab initio” level some authors [6] suggest the use of thermochemical cycles in order to obtain good “ab initio” EAs The aim of the present work is to show that, with an adequate basis of moderate size and the indusion of electron correlation using M&ler-Plesset [9] perturbation theory taken to the second order (MP2) [IO], it is possible to obtain fairly good ab initio EAs
2. Computational
details
Following the usual conventions, the (adizbatic) electron affinity is computed as the difference in energy between the Iowest rotations-~brational state of a negative ion A- and the lowest rotational-vibrational state of the neutral molecule A_ In general, however, instead of the energy of the lowest rotatronalvibratronal state, it is usual to take the energy at the mmimum of the potential energy curve. The difference between this and the energy of the lowest state is the zero-pomt energy (ZPE)_ its value can be com13.5
Volume
119, number 2,3
CHEMICAL
puted from the force constants at the mmimum, but this 1s a time-consuming step and one which is normalIy omitted because the ZPE of the amon and the neutral molecule are similar and therefore tend to cancel in the EA. Errors of no more than S-10 kcal/ mol are produced by this approximation. AU the computations were done using a version of the GAUSSIAN-80 program [l 1] _The basis sets employed were the standard STO-3G, 4-3 lG, 4-3 lG* and 4-3 lG** sets. Some computations used 4-3 l+ G [6], and 4-31 + G* sets. The latter were constructed by adding the extra diffuse functions of 4-3 1 + G to the standard 4-3 lG*. Three general bases were constructed from a triple-zeta (TZ) set, to which two po-
PHYSICS
30 August 1985
LJXTERS
larization d fun&Ions and two p diffuse functions were added on the heavy atoms to Five TZ + 2P and TZ + 2P + 2D sets, respectively. The exponents and coefficients were taken from van Duljneveldt [12] for the TZ basis set, while the exponents for the extra polarization and diffuse functions were computed as indicated by Dunnmg and Hay [7] _
3. Results and discussion In order to find a good level of approximation in the size of basis and level of correlation, the EA of the neutral systems 0H(211), CH#A,), CH2(3B,),
Table 1 Electron affinity (EA). in kcaI/mol. for the OH(711) molecule. The total energy, in atomic units. for the neutral moleculeE(A) and its anionE(A-) is also given, together with the method, basis and geometry Method
Bads
Geometry
UHF
STOJG 4-31G
opt. opt.
3-21 + G
UHF/4 -3 1G UHF/4-31G
E (A-)
EA
uHI;/4-31G UHF/4-31G UHF/4-3lG UHF/4JlG UHF/4-31G UHF/4-31G
-74.364886 -75.287165 -74.996572 -75.292698 -75.292698 -75 311065 -75.386665 -75.317304 -75 389369 -75.413648 -75.415217
-74.065017 -75.229789 -74.995710 -75.280960 -75.281216 -75248646 -75.375482 -75.254683 -75.355705 -75.375141 -75.403075
-188.17 -36.00 -0.54 -7.37 -7.21 -39.17 -7.02 -39.30 -21.12 -24.17 -7.62
4-31+ G 4-31G* 6-31 + G* 4-31G** TZ TZ+2P TZ+ZP+2D
u-w/4-31G UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 IG UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 1G
-75.376129 -75.091703 -75.384778 -75 450040 -75.529473 -75-461451 -75.491767 -75592606 -75.595667
-75.354304 -75.150819 -75.436978 -75.434248 -75.588325 -75-447391 -75504544 -75.614633 -75.66W62
-13.70 37.10 32.76 -9.91 36.93 -8-82 8.02 13.82 40.4 1
4-31G 3-21-t- G 4-31+ G 4-31 + G 431G* 6-31 + G* 4-31G** TZ TZ+2P TZ+2P+ZD
UHF/4-31G W/4-3 1G UW/4-3 1G opt. UHFf4-31G UHF/4-31G UHFf4-31G UHFf4-31G UHFj4-31G UT-lFf4-31G
-75.382410 -75 096574 -75.390530 -75.391045 -75.461972 -75540840 -75.473527 -75.495454 -75.603733 -75.606471
-75.354569
-75.138788 -75.422366 -75422388 -75.438599 -75.581652 -75.451932 -75.495706 -75.613947 -75.649444
17.46 26 49 19.97 19.66 -14.67 25.61 -1355 0.16 6.41 26.97 (42.20)
4-31 + G 4-31 i-G 4-31G* 6-31 +G* 4-31G** TZ TZ+2P TZ+ZP+2D UhIF.2
uhlP3
4-31G
3-21 + G
opt.
exp.
136
Volume 119, number 2,3
CHEMICX1, PHYSlCS LE-ITERS
02(3 Z;), and CH30(2A’) was computed using the various basis sets using UHF theory with and without correlation. The results for the total energy of both the anion and neutral systems, together with the computed EA, is shown in tables l-5 indicating in each case the basis and the theoretrcal method used (UHF stands for an unrestricted Hartree-Fock computation)- The experimental value of the EA [13] is included between brackets at the end of each table. The fust computed EA is for OH in its ground state, for which results obtained with CI and equation-of-motion methods [ 131 give a useful comparison. The CI result obtained with a (6s, 5p, ld/3s, Ip) basis, very near to a TZ + 1P basis in our conventron, is 30 98 kcal/mol if a conjuration space constructed with the fundamental and the most nnportant single, double and triple excited configurations is used. Using the same basis, the equation-of-motion result is 4.23 kcal/mol worse than the Cl one, and this only if second-order effects are included, otherwise the result is even poorer. Thus for OH the deviation from the experimentai value IS between 12 and 16 kcal/mol. Our approach to the experimental EA of OH started with the computation of a good equilibrium geometry. In this way, we optimized the geometry at the HF level with STO-3G and 4-3 1G bases. It has been found {63 that further optimrzation with 4-31 +- G or 4-3 lG* bases would lead to si~i~cant changes in geometry or, as can be seen in table I, the computed EA. We have therefore used 431G geometries when computing the EAs with larger basis sets. In each case, the geometry used in the computation is shown in the respective table. Once the geometry has been computed, we have used larger basis sets at the UHF level in order to obtain results nearer to the HF limit, e g., the TZ -I- 2P + 2D basis. Those results show, in accordance with Cade’s work [2], that the HF level does not give even the sign of the experimental EA of OH correctly. There is a deviatron of 35 kcalimol. From the UHF results we can, however, draw some useful conclusions. The first is the importance of the diffuse functions. With only one set of extra diffuse functions we obtain the same accuracy as with the TZ + 2P + 2D basis Furthermore, with only the addition of polarization functions we have a result which rs, in the best case, 20 kcal/mol worse, and of the same order as those computed with the Same basis without the use of polari2ation functions.
30 August 1985
The inclusion of correlation in our computations gives a lowermg in the computed EAs by an amount of the order of 20-30 kcalfmol- As consequence, we have now values which are near to the experimental result However, as in the HF case, there is a wide range of results dcpendmg on Ihe basis used_ Again, the basis with diffuse functions gives better results, but now the inclusion of polarrzation functions has a small effect because they improve the correlation ener,T. It is interesting to note that 4-31G with correlation gives almost the same value as the 4-3 1 + G at the HF level, extending to the computation of EAs Kollmar’s resJts [7] on proton affinities. There are two more points to note in relation to table I_ One is the fact that MP? EAs are, for the same basis, always better than MP3 ones. This comes from the fact that the third-order energy correction for the anions is positive and, therefore, raises the total energy. The other point is that the optimization of geometry at the MP3 level does not change significantly the value computed with the HF 4-31G geomtry- Finally, we can compare our resuhs with those already reported for the Cl and equation-of-motion methods_ We see that, at tic MP2 level with a 4-3 1+ G, we have a result slightly better than that reported in ref. [ 143 for a better basis With the best basis here reported the error is only 1.79 kcal/molIn order to test the general validity of the conclusions discussed above, we have repeated the computation with the same types or basis for CHz in the singlet and triplet states. Tables 2 and 3 show that the same trends already noticed for the OH molecule hold for those molecules. The best available computed value for the EA has a deviation from the experunental value of 5.61 kcal/moI for the singlet, and 3.63 kcal/mol for the triplet. One difference from OH appears for tnplet CH,, where the MP3 and MP2 results are very simrlar. Tables 4 and 5 include the results for 0, and CH30. With minor differences, the general trends are the same. In CH30 the 4-31 + G basis within the MP2 Ievel gives an abnormally high deviation from the experimental result of 19.03 kcal/mol which is lowered to 12.15 kcal/mol when the 4-3 1 + G* is used. This implies that there may be cases in which a further improvement in the basis is needed to give adequate agreement with experiment- In all cases, the direct method discussed here in which correlation is included by the M&ler-Plesset 137
Table 2 Electron affinity (EA). io kcal/ mol, for the CH2 (I Al) molecule. The total energy, in atomic units, for the neutral molecule E(A) and its anion E(A-f is also @en, together with ihe method, basis and geometry Mathod
Basis
Geometry
E (A)
E
EA
UHF
STO-3G 4-31G 3-21 + G 4-31+ G 4-31G+ 631 f-G* 4-31c** TZt2Pt2D
out. UHFiQl-3 1G UHF/4-31G UHF/4-3 1G UHF/4-316 UHF/4-31G UHF,‘431G
-38 372305 -38.610347 -38.316053 -38.816715 -38.833192 -38 876456 -38.835561 -38.888952
-38.193243 -38.781456 -38.312925 -38.824597 -38.800016 -38.881244 -38.804383 -38.892877
-112.37 -18.13 -1.96 4.05 -1956 3.00 --19 56 2.46
wMP2
4-336 3-23 + G 4-31 +c 4-31Gf 6-31 + G’ 4-3iG** TZ+2P+2D
UHF/4-3 1G UHF/4-3 1G uHF/4-3 1G UHF/43 1G UHF/431G UHF/4-31G UHF/431G
-38.875392 -38 411146 -38.884193 -38.928702 -3 8.975569 -38-94625 7 -39.013365
-38.853788 -38 439458 -38.913053 -38.907985 -39.002670 -38.927344 -39.043372
--13.56 17.77 18.11 -13.00 17.01 -11.87 18 33
UhlP3
4-31G 3-214 G 4-31+ G 4-31G* 6-31 + G* 4-31G** TZ+2P+2D
UHFj4-3 i G UHFi4-31G UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHFf4-31G UHF/4-31G
-38_889355 -38.437992 -38.898161 -38.9464468 -38.993286 -38.965239 -39.032373
-38 865190 -38_422415 -38-923269 -38-923161 -39.016281 -38.943719 -39.058052
-15,16 9.77 15 -75 -14.63 14*43 -13.51 16.12
OPi
exp.
(24-44)
Table 3 Electron affinity (EN, m kcWmo1, for the CM, f”BiI molecule. The total energy. VI atomic units, for the neutral molecule E(A) and its anion E(A3 is also &wt. together with the method, basis and geometm Method
Basis
Geometry
.E (A)
E (A->
EA
UHF
STO-3G 4-31G 3-21 + G 4-31 + G 4-31G* 6-31 + G+ 43 lG** TZ-i-2Pc2x.l
opt. opt_ UHFf4-3lG UHF/4-3 1G UHF/4-31G UHF/4-3 IG UHF/4-3 1G UHF/4-31G
-38-436234 -38 869630 -38.352363 -38.872985 -38.88i536 -38.923710 -38.885845 -38.935484
-38.193243 -38 781456 -38.312925 -38.824597 -38.800016 -38.881244 -38.804383 -38.892877
-152.48 -55.33 -24.75 -30.36 -51.15 -26 65 -51.12 -26.74
UMP2
4-31G 3-21+ G 4-31 + G 4-31G” 6-31 + G* 4-31G-* TZ+2P-t-2D
UHF/4-3 1G UHF[4-3 1G UHF/4-31G UHF/43 1G UHFf431G UHF/4-31G UHF/4-31G
-38.922265 -38.426005 -38.927233 -38.963323 -39.006818 -38.979670 -39.041452
-38.853708 -38-439458 -38.913053 -38.907985 -39 002670 -38.927344 -39.043372
97 8.4C -8.90 -34.72 -2.60 -32.84 1.21
wrvY.P3
4-31G 3-21 +G 4-31 + G 4-31G” 6-31+ G’ 4-3 1G** TZ+2Pc21)
UHF/4-31G UHF/4dlG UHF/4-3 1G UHF/4-3 1G UHF/4-31G UHF/4-31G UHF/4-3 1G
-30.932746 -38.434462 -38.937828 -38.977143
-38.865190 -30.437992 -38.923269 -38.923161 -39.016281 -38.943719 -39.058052
-42.39 2.22 -9.14 -33 87 -2.83 -3190 0.86
-39.020787
-38.994547 -39.056684
42
CHEMICAL
Volume 119, number 2.3
PHYSICS LEITERS
30 August 1985
Table 4 Electron affiity (EM, in kcal/mol, for the 02 (‘Ei> molecule. The total energy, in atomic units, for the neutral molecule E(A) and its enion E(A_) is also given, together wrtb the method, basis and geometry Method
Bash
Geometry
E (A)
E (A-1
EA
STO-3G 4-31G 3-21+ G 4-31 -i.G 4-3IG* 631+ G*
opt. opt. UHF/4-3 1G UHFf4dlG UHF/4-3 1G UHF/4-31G
-147.634171 -149.392965 -148.80~90 -149.399600 -149.475514 -149.620617
-147.384062 -149.368558 -148.824765 -149 400299 -149.415287 -149.591159
--156.95 -15.31 15.23 044 -37.79 -18-45
4-31G 3-21 +G 4-31 + G 4-31c* 631+ G*
UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF/4-31G UHF/4-3 1G
-149.630920 -149.04465 I -149.639511 -149.807422 -149.954330
-149.6 13086 --149.086003 -149 658257 -149.769703 --149.960772
-11.19 25.95 11.77 -23.67 4.04
4-3 IG 3-21-i. G 4-3l+ G 4-31G* 6-31 -t-G*
UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-31G
-149 615559 -149.02a272 -149.623739 --149X93369 --149.950087
-149.602335 -149.070421 -149 642858 -149-767516 -149 953388
-829 2645 12.00 -22so 2.07 (10-14)
exp-
Tablc 5 Electron tifinit!! (EA), in kgllmol, for the CHSO(~A’) molecule. The total energy, in atomic units, for tbc neutral molccu!c E(A) and its amon E(A-1 IS also .givcn, togcthcr wrth the method, basis end geometry M&WJd
Basis
Geometry
E (AI
E(A-1
EA
UHF
STO-3G 4-31G 3-21+ G 4-31 +G 4-31G* 4-31+ G* 6-31+ G* 4-31G**
opt opt. UHF/4-31G UHF/4-31G UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF/4-31G
-113.960886 -114.262848 -113 816368 -114.267371 -114.310204 -114 307516 -114_423704 -114.315641
-112.706368
-159-71 -27.89 -9 26 -13.60 -26.04 -11.21 -8 52 -25.81
uMP2
4-31G 3-21 + G 4-31+ G 4-31G* 4-31+ G” 6-31+ G* 4-31G**
UHF/4-31G UHF/4-3 1G UKF/4-3 1G UHF/4-31G UHF/4-3fC IJHF/4-31G UHF,‘4-3 IG
-114.440615 -114.000538 -114.448669 --114_576180 -114574672 -114.693623 -114_600770
-114 439268 -114.040769 -114_484130 -114586469 -114.623096 -114.744279 -114.613773
-0.85 25.25 22.25 64.5 29-13 31.79 8.16
UhfP3
4-316 3-21 -r-G 4-31 + G 4-31c* 4-31+ G* 6-31 + G+
UHF/4-31G UHF/4-3 IG UHF/4-31G UHF/4-3 1G UHF/4-3 1G UHF4-31G
-114.455631 -114.014232 -114.463302 -114598049 -114596418 -114.715179
-114 445251 --114.040460 -114.463622 -114.596977 -114.625541 -114.749515
-6.51 16.46 12.75 -0 67 la.27 21.55 (41.28)
_
-114.218406 -113.801610 -114.265692 -114.268702 -114.289650 -114.410124 -114.274511
exp.
139
Volume
119, number 2.3
CHEMICAL
PHYSICS
formalism is a powerful and economical route for the theoretlcal computation of EAs. To fvd a better standard basis for computation of EAs, we carried out test calculations using the 6-3 1 + G* [15] and the 3-21 + G sets. The results, given in tables 14, show that 3-21 + G gives EAs which are better than those computed with the similar sized 4-3 1 + G basis. One exception to this trend is 02, a case where the 3-21 + G basis overstabilises the anion with respect to the neutral molecule. For 3-21 + G, excluding the O2 result, the mean value of the absolute deviation between the computed and experimental EAs is 7.8 kcal/mol, which is of the same order as that reported [ 161 for the SCF proton affinities with this basis. The results for 6-3 1 + G* are in general better than the 4-3 1 + G and 4-3 1 + G* ones; the computed EA results approach the experimental value as the basis set 1s increased All of these results confirm the conclusions obtained with the 4-3 1 + G bans, namely, that by using diffuse functions an hIP2 calculation can match the experlmental EA to the desired accuracy of a few kcal/mol. The inclusion of the thirdarder perturbation increases the deviation from the experimental value. We have tested what happens when orders higher than three are also mcluded by means of the use of the CIPSI method [ 161 on the computation of the EA of the OH rnolecule The result obtained (30-88 kcal/mol) Y mtermediatc between MP2 and MP3, when the 6-31 + G* basis (but with only five d functions due to program limitations) is used A configuration interaction computation for the same molecule and the standard 6-3 1 + G* basis, including all the double excitations in the wavefunction, gives a result of 26.25 kcal/mol. Both results show that MP2 overstabilises the total energy of the anion with respect to the neutral molecule. However, MPZ gives reasonable accuracy at lower cost than more elaborate methods. Finally, we compare the ab mitio results reported here with the MNDO ones for these molecules, which are G-23, -2.08, -27.44,3.69 and 39.66 kcal/mol for OH, CH, singlet, CH, triplet, 0, and CH,O, respectlvcly. Those values present a deviation from the values measured experimentally of 35.97,26_52,32.28,
140
30 August 1985
LETTERS
6.45, and 1.62 kcal/mol, respectively, that is, the mea1 difference is higher than the one computed in this work and in two cases the MNDO EA has the wrong sign.
Adcnowledgement The authors are Fcratefulfor computer time available through grant CAICYT-657/81: We also thank Dr. F. Illas for the use of his CIPSI program.
Zeferences
111T.
Koopmans.
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104_
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131 J.