We have developed and presented two quasi-`black box' schemes for high-accuracy calculation of molecular atomization energies or, equivalently, molecular heats of formation, of first-and second-row compounds.
The less expensive scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires no larger-scale calculations than CCSD/AVQZ+2d1f and CCSD(T)/AVTZ+2d1f (or, for nonpolar first-row compounds, CCSD/VQZ and CCSD(T)/VTZ). On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods.
The more expensive scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.22 kcal/mol, which is lowered to 0.17 kcal/mol for molecules dominated by dynamical correlation. On workstation computers, molecules with up to three heavy atoms can be treated using conventional coupled cluster algorithms, while larger systems can still be treated using a direct CCSD code.
The inclusion of scalar relativistic (Darwin and mass-velocity) corrections is essential for good results in second-row compounds, particularly highly polar ones. Inclusion of inner-shell correlation contributions is absolutely essential: the basis set denoted as MTsmall (for Martin-Taylor small) appears to represent the best compromise between quality and computational expense. We do not recommend the use of lower-level electron correlation methods than CCSD(T) for the evaluation of the inner-shell contribution.
Among the several infinite-basis set extrapolation formulas for the
correlation energy examined, the three-parameter
expression proposed by Martin[13]
and the A+B/l3 expression proposed
by Helgaker and coworkers[56] yield the best results for sufficiently
large basis sets, with the latter formula to be preferred on
grounds of stability of the extrapolated results with the basis sets used.
Geometric and mixed geometric-Gaussian extrapolation formulas[55,63]
are unsatisfactory when applied to the correlation energy,
although they appear to be appropriate
for the SCF component.
The main limiting factor for the quality of our calculations at this stage appears to be imperfections in the CCSD(T) method. This assertion is supported by the fact that the mean absolute error in the computed electron affinities of the atoms H, B-F and Al-Cl drops from 0.009 eV to 0.0009 eV if CCSDT and full CI corrections are included.
Extrapolation of the (T) contribution to the correlation energy can, at no loss in accuracy, be carried out using smaller basis sets than the CCSD contribution.
JM is a Yigal Allon Fellow, the incumbent of the Helen and Milton A. Kimmelman Career Development Chair (Weizmann Institute), and an Honorary Research Associate (``Onderzoeksleider in eremandaat'') of the National Science Foundation of Belgium (NFWO/FNRS). GdO acknowledges the Feinberg Graduate School (Weizmann Institute) for a Postdoctoral Fellowship. This research was supported by the Minerva Foundation, Munich, Germany. The authors acknowledge enlightening discussions with (in alphabetical order) Drs. C. W. Bauschlicher Jr. (NASA Ames Research Center), Dr. Thom H. Dunning (PNNL), Prof. Trygve Helgaker (U. of Oslo, Norway), Dr. Frank Jensen (Odense U., Denmark), Dr. Timothy J. Lee (NASA Ames Research Center), and Prof. Peter R. Taylor (UCSD and National Partnership for Advanced Computing Infrastructure), and thank Dr. Peter Stern for technical assistance with various computer systems.