A systematic comparison of molecular properties obtained using Hartree–Fock, a hybrid Hartree–Fock density-functional-theory, and coupled-cluster methods

Abstract

We present results of a systematic study of the theoretical determination of equilibrium geometries, harmonic frequencies, total atomization energies, and dipole moments using Hartree–Fock, a hybrid Hartree–Fock density-functional-theory, and coupled-cluster methods in conjunction with a triple zeta basis set for a large set of molecules. This allows a direct comparison of the three theoretical methods applied to a range of chemical systems. The average errors (‖experimental value-theoretical value‖) for the Hartree–Fock, hybrid Hartree–Fock density-functional-theory, and coupled-cluster methods, respectively, are bond length (Å) 0.022, 0.005, 0.005; bond angle (degrees) 2.7, 1.7, 1.9; harmonic frequencies (cm−1) 144, 40, 30; atomization energies (kcal/mol) 81.9, 3.6, 11.5; and dipole moments (debye) 0.29, 0.14, 0.10. This clearly demonstrates that the relatively inexpensive hybrid Hartree–Fock density-functional-theory method yields results which represent a reliable, significant improvement over those obtained with the Hartree–Fock method. The results obtained using the hybrid Hartree–Fock density-functional-theory method are, in fact, quite comparable with the corresponding results obtained using the high level, ab initio coupled-cluster method. For certain difficult open shell examples, the hybrid Hartree–Fock density-functional theory using a spin restricted open shell Hartree–Fock density is much improved over the corresponding hybrid Hartree–Fock density-functional-theory results obtained using a spin unrestricted Hartree–Fock density.

Perspective: Fifty years of density-functional theory in chemical physics

“…Post-Hartree-Fock DFT is not new. The 1992 implementation of BLYP by Gill et al 66 was post-HF, followed by Oliphant and Bartlett 209 and others. Numerous DFT researchers had used HF orbitals long before then.…”

Theoretical constraints on the effects of pH, salinity, and temperature on clumped isotope signatures of dissolved inorganic carbon species and precipitating carbonate minerals

“…Results from hybrid DFT methods on aqueous clusters may perform as well as the MP2 method (Xantheas, 1995). The RHF method can be a good first order approximation, but is typically outperformed by other methods at higher levels of theory (e.g., Lee and Scuseria, 1995;Johnson et al, 1993;Thomas et al, 1993a,b;Oliphant and Bartlett, 1994;Bartlett, 1995;Scott and Radom, 1996 and references therein; Wong, 1996;Halls and Schlegel, 1998;Crawford and Schaefer, (2000).…”

“…The CCSD and QCISD ab initio methods are the most accurate approaches considered here, but the computational cost becomes prohibitive for studies of large molecules (e.g., Johnson et al, 1993;Thomas et al, 1993a,b;Oliphant and Bartlett, 1994;Bartlett, 1995;Bartlett and Musial (2007); Scott and Radom, 1996 and references therein). Results from hybrid DFT methods on aqueous clusters may perform as well as the MP2 method (Xantheas, 1995).…”

Molecular Geometries at Sixth Order Møller−Plesset Perturbation Theory. At What Order Does MP Theory Give Exact Geometries?

“…However, one often finds that most correlation corrected ab initio methods, even though they do not provide high-accuracy equilibrium geometries, describe trends in molecular geometries reasonably well and that deviations from exact geometries are systematic. [1][2][3][4][5][6][7][8][9][10] In structural chemistry, one often needs calculated molecular geometries with the highest precision possible to verify experimentally based equilibrium geometries or to use the calculated data together with spectroscopic data to derive a more precise equilibrium geometry. (See, e.g., refs 11-13.…”