A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the standard error function with parameter 0.33.

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We recently presented a new method for developing generalized gradient approximation (GGA) exchange-correlation energy functionals, using a least-squares procedure involving numerical exchange-correlation potentials and experimental energetics and nuclear gradients. In this paper we use the same method to develop a new GGA functional, denoted HCTH, based on an expansion recently suggested by Becke [J. Chem. Phys. 107, 8554 (1997)]. For our extensive training set, the new functional yields improved energetics compared to both the BLYP and B3LYP functionals [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 37, 785 (1988); J. Chem. Phys. 98, 5648 (1993); J. Phys. Chem. 98, 11623 (1994)]. The geometries of these systems, together with those of a set of transition metal compounds, are shown to be an improvement over the BLYP functional, while the reaction barriers for six hydrogen abstraction reactions are comparable to those of B3LYP. These improvements are achieved without introducing any fraction of exact orbital exchange into the new functional. We have also re-optimized the functional of Becke—which does involve exact exchange—for use in self-consistent calculations.

The reaction path on the potential energy surface of a polyatomic molecule is the steepest descent path (if mass-weighted cartesian coordinates are used) connecting saddle points and minima. For an N-atom system in 3-d space it is shown how the 3N-6 internal coordinates can be chosen to be the reaction coordinate s, the arc length along the reaction path, plus (3N-7) normal coordinates that describe vibrations orthogonal to the reaction path.

Conventional continuum exchange-correlation functionals (e.g., local density approximation, generalized gradient approximation) offer a poor description of many response properties, such as static polarizabilities and single photon vertical excitation energies to Rydberg states. These deficiencies are related to errors in the virtual Kohn–Sham orbitals and eigenvalues, which arise due to a fundamental deficiency in the potentials of conventional continuum functionals. Namely, although these potentials approximately average over the exact integer discontinuity in energetically important regions, they fail to do so asymptotically, because they vanish. Our recent functional HCTH [J. Chem. Phys. 109, 6264 (1998)] was designed with this deficiency in mind, although its potential still fails to exhibit the appropriate asymptotic form. In this paper, we present a new procedure that explicitly corrects this asymptotic deficiency for any continuum functional. Self-consistent Kohn–Sham calculations are performed using a corrected potential, which equals the conventional potential δEXC[ρα,ρβ]/δρσ(r) in energetically important regions, but which asymptotically behaves in the required average manner −(1/r)+Iσ+εHOMO,σ. The quantity −(1/r) is determined using a nonlocal expression; Iσ is an approximate σ spin ionization potential; and εHOMO,σ is the highest occupied σ spin eigenvalue. By applying this correction to the HCTH potential, we accurately reproduce the hydrogen atom eigenvalue spectrum, without significantly changing the total energy. We determine corrected orbitals and eigenvalues for a variety of molecules, and use them to compute excitation energies and static polarizabilities. We compare the results with those from a variety of other exchange-correlation functionals. Excitations to Rydberg states are determined as accurately as those to valence states; for CO, N2, H2CO, and C2H4, mean absolute errors are less than 0.35 eV. The static isotropic polarizabilities of 14 small molecules are of MP2 quality.