Introduction

Thermochemical data such as molecular heats of formation are among the most crucial quantitative chemical data. Thanks to great progress made in recent years in both methodology and computer technology, a broad range of empirical, semiempirical, density functional, and ab initio schemes now exist for this purpose (for a recent collection of reviews, see Ref.[1]).

At present, only ab initio-based methods can claim `chemical accuracy' ($\pm$1 kcal/mol). The most popular such schemes are undoubtedly the G2[2] and G3[3] theories of Pople and coworkers (which are based on a combination of additivity approximations and empirical corrections applied to relatively low-level calculations), followed by the CBS-Q[4,5,6] and CBS/APNO[4] methods which are intricate combinations of extrapolation and empirical correction schemes. With the exception of CBS/APNO (which allows for 0.5 kcal/mol accuracy, on average[7], but is restricted to first-row compounds), all these schemes allow for mean absolute errors of about 1 kcal/mol, although errors for some individual molecules (e.g. SO₂, SiF₄[3]) can be much larger (e.g. about 8-12 kcal/mol for SiF₄ using G2 theory, and 4 kcal/mol using G3 theory[8]).

In fact, many of the experimental data in the "enlarged G2 set"[9] employed in the parametrization of several of these methods (notably G3 theory and several of the more recent density functional methods[10]) themselves carry experimental uncertainties larger than 1 kcal/mol.

The aim pursued in the present work is a more ambitious one than chemical accuracy. In light of the prevalent use of kJ/mol units in the leading thermochemical tables compendia (JANAF[11] and CODATA[12]), we shall arbitrarily define a mean absolute error of one such unit, i.e. 0.24 kcal/mol, as `calibration accuracy' -- with the additional constraint that no individual error be larger than the `chemical accuracy' goal of 1 kcal/mol.

One of us[13,14] has recently shown that this goal is achievable for small polyatomics using present technology. The approach followed employed explicit treatment of inner-shell correlation[15], coupled cluster calculations in augmented basis sets of spdfg and spdfgh quality, and extrapolation of the valence correlation contribution to the atomization energy using formulas[13] based on the known asymptotic convergence behavior[16,17,18] of pair correlation energies. In this manner, total atomization energies (TAE_e) of about 15 first-row diatomics and polyatomics for which experimental data are known to about 0.1 kcal/mol could be determined to within 0.25 kcal/mol on average without any empirical parameters. (Upon introducing an empirical correction for A-N bonds, this could be improved to 0.13 kcal/mol, clearly within the target.) In fact, using this method, an experimental controversy concerning the heat of formation of gaseous boron -- a quantity that enters any ab initio or semiempirical calculation of the heat of formation of any boron compound -- could be resolved[19] by a benchmark calculation of the total atomization energy of BF₃.

Benchmark studies along similar lines by several other groups (e.g. those of Helgaker[20], Bauschlicher[21], Dunning[22]) point in the same direction. Among those, Bauschlicher[21] was the first to suggest that the inclusion of scalar relativistic corrections may in fact be essential for accurate results on second-row molecules.

High-accuracy results on second-row compounds can only be achieved in this manner -- as has been shown repeatedly[23,24,21] -- if high-exponent d and f functions are added to the basis set. As shown by one of us[23], these `inner shell polarization functions' address an SCF-level effect which bears little relationship to inner-shell correlation, and actually dwarfs the latter in importance (contributions as high as 10 kcal/mol having been reported[23,8]).

All these approaches carry a dual disadvantage: their extravagant computational cost and their reliance on the quantum chemical expertise of the operator.

The target of the present study was to develop computational procedures that meet the following requirements:

• they should have mean absolute errors on the order of 0.25 kcal/mol or less, and problem molecules (if any) should be readily identifiable;
• the method should be applicable to at least first-and second-row molecules;
• it should be robust enough to be applicable in a fairly `black-box' fashion by a nonspecialist;
• it should rely as little as possible (preferably not at all) on empirical parameters, empirical additivity corrections, or other `fudges' derived from experimental data;
• relatedly, it should explicitly include all the physical effects that are liable to affect molecular binding energies of first-and second-row compounds, rather than rely upon absorbing them in empirical parametrization;
• last but not least, it should be sufficiently cost-effective that a molecule the size of, e.g., benzene should be treatable on a workstation computer.

In the course of this work, we will present two schemes which we shall denote W1 and W2 (for Weizmann-1 and Weizmann-2) theories. W2 theory yields about 0.2 kcal/mol (or better) accuracy for first-and second-row molecules with up to four heavy atoms, and involves no empirical parameters. W1 theory is applicable to larger systems (we shall present benzene and trans-butadiene as examples), yet still yields a mean absolute error of about 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter which moreover is derived from calculated rather than experimental results.