Gaussian-2 theory for molecular energies of first- and second-row compounds Larry A. Curtiss Chemical Technology Division/Materials Science Division, Argonne National Laboratory, Argonne, Illinois 6043 9 Krishnan Raghavachari and Gary W. Trucksa) AT&T Bell Laboratories, Murray Hill, New Jersey 07974 John A. Pople Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (Received 5 November 1990; accepted 15 February 1991) The Gaussian-2 theoretical procedure (G2 theory), based on ab initio molecular orbital theory, for calculation of molecular energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compounds containing first- (Li-F) and second- row atoms (Na-Cl) is presented. This new theoretical procedure adds three features to G 1 theory [J. Chem. Phys. 90, 5622 ( 1989) ] including a correction for nonadditivity of diffuse-sp and 2df basis set extensions, a basis set extension containing a third d function on nonhydrogen atoms and a second p function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G 1 theory because it eliminates a number of deficiencies present in Gl theory. Of particular importance is the improvement in atomization energies of ionic molecules such as LiF and hydrides such as C2 H, , NH,, N, H, , H, 0, , and CH, SH. The average absolute deviation from experiment of atomization energies of 39 first-row compounds is reduced from 1.42 to 0.92 kcal/mol. In addition, G2 theory gives improved performance for hypervalent species and electron affinities of second-row species (the average deviation from experiment of electron affinities of second- row species is reduced from 1.94 to 1.08 kcal/mol) . Finally, G2 atomization energies for another 43 molecules, not previously studied with Cl theory, many of which have uncertain experimental data, are presented and differences with experiment are assessed. I. INTRODUCTION In previous papersip we have presented a general theo- retical procedure, based on ab initio molecular orbital theo- ry, for the computation of total energies of molecules at their equilibrium geometries. The objective was to develop a gen- eral predictive procedure, applicable to any molecular sys- tem in an unambiguous manner, which can reproduce known experimental data to a prescribed accuracy of about f 2 kcal/mol and can be applied with similar accuracy to species having larger experimental uncertainty. The theo- retical procedure, referred to as “Gaussian- 1 theory” (“Gl theory’* for short), was a composite one, based on the 6- 3 11 G ( d,p ) basis set and two basis set extensions ( diffuse-sp and 2dfi. Treatment of correlation is by MBller-Plesset (MP) perturbation theory and quadratic configuration in- teraction. The procedure was used to calculate atomization energies, ionization energies, proton affinities, and electron affinities of a large number of molecules for which these quantities have been well established experimentally. For compounds containing first-row elements agreement with experiment was found to be within + 2 kcal/mol ( f 0.1 eV) in most cases and for those containing second-row ele- ments’ agreement was found to be within k 3 kcal/mol ‘) New address: Lorentzian, Inc., 127 Washington Ave., Northhaven, Con- necticut 06473. ( + 0.15 eV) . G 1 theory has also been applied to numerous molecules3-9 where the experimental energies have not been as well established and in these cases it has provided valuable information. Gl theory was conceived as the first in a series of well- defined methods that could be routinely applied to the calcu- lation of molecular energies in a systematic manner. A num- ber of deficiencies in Gl theory were noted and future developments to alleviate these deficiencies were indicated as being desirable. In particular Gl theory does poorly on dissociation energies of ionic molecules such as LiF (3.7 kcal/mol too high), on triplet state molecules such as O2 (2.6 kcal/mol too low) and S, (2.3 kcal/mol too low), on singlet-triplet energy separations such as those of CH, (2.8 kcal/mol too small) and SiH, (2.7 kcal/mol too large), and on some hydrides such as NH, (2.5 kcal/mol too low) and N, H, (4.1 kcal/mol too low). Also, Gl theory does poorly on the hypervalent species SO, and ClO, where the atomiza- tion energies are low by 6-8 kcal/mol. It was found that an additional d function may reduce this discrepancy.2 In this paper we set forth the Gaussian-2 theoretical procedure (referred to as “G2 theory”), which makes a sig- nificant improvement over G 1 theory by eliminating some of the above deficiencies. It has the following new features: ( 1) It eliminates the assumption of additivity of the diffuse-sp ( + ) and 2dfbasis set extensions used in Gl theory. This J. Chem. Phys. 94 (1 I), 1 June 1991 0021-9606/91/l 17221-10$03.00 @ 1991 American Institute of Physics 7221 Downloaded 14 Feb 2004 to 146.186.189.34. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp7222 Curtiss eta/: Gaussian-2 theory for molecular energies change gives significant improvement for ionic species and some anions. (2) It adds a third d function on the nonhydro- gen atoms and a second p function on the hydrogens. The third d function is especially important for some hypervalent molecules containing second-row atoms such as ClO, and SO,, while the second p function significantly improves the atomization energies of some of the hydrogen containing molecules. (3) Finally, the higher level correction (HLC), which was determined in Gl theory by the error in the calcu- lated energy of the H, molecule and the H atom, is deter- mined from the best fit to the experimental atomization ener- gies of 55 molecules for which the experimental value is well established. This also contributes to an improvement in cal- culated energies. In Sec. II the