Chengteh Lee

Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

Abstract: Fukui functions (softnesses) are calculated for three species - formaldehyde, the thiocyanate ion and carbon monoxide. The fukui function for a molecule has been defined as the derivative of electron density with respect to the change of number of electrons, keeping the positions of nuclei unchanged; this differentiation is performed by finite difference. Local softness and fukui function are proportional. The calculated results, expressed in terms of contour maps and condensed values of fukui functions, substantiate the previous argument that fukui functions serve as reactivity indices for chemical reactions. Particularly, it is confirmed that: (1) a nucleophilic reagent approaches the carbon atom in formaldehyde from the direction perpendicular to the molecular plane, while an electrophilic reagent approaches the oxygen atom in the molecular plane; (2) the sulphur end is softer than the nitrogen end in the thiocyanate ion; and (3) carbon monoxide behaves like a Lewis acid in bonding with transition metals.

Abstract: Becke [J. Chem. Phys. 84, 4524 (1986); Phys. Rev. A 38, 3098 (1988)] has shown that the Hartree-Fock exchange energy for atoms (and molecules) can be excellently represented by a formula K=${2}^{1/3}$${\mathit{C}}_{\mathit{x}}$F${\mathcal{J}}_{\mathrm{\ensuremath{\sigma}}}$ ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\sigma}}}^{4/3}$(r)[1+\ensuremath{\beta}G(${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$)]dr, where ${\mathit{C}}_{\mathit{x}}$ is the Dirac constant, \ensuremath{\beta} is a constant, G(x) is a function of the gradient-measuring variable ${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$=\ensuremath{\Vert}\ensuremath{ abla}${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\sigma}}}$\ensuremath{\Vert}/${\mathrm{\ensuremath{\rho}}}^{4/3}$, and the summation is over spin densities ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\sigma}}}$. Becke recommends G(${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$)=${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}^{2}$/[1+0.0253${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$${\mathrm{sinh}}^{\mathrm{\ensuremath{-}}1}$(${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$)]. It is demonstrated that the kinetic energy can be represented with comparable accuracy by the formula T=${2}^{2/3}$${\mathit{C}}_{\mathit{F}}$F ${\mathcal{J}}_{\mathrm{\ensuremath{\sigma}}}$ ${\mathrm{\ensuremath{\rho}}}_{\mathrm{\ensuremath{\sigma}}}^{5/3}$(r)[1+\ensuremath{\alpha}G(${\mathit{x}}_{\mathrm{\ensuremath{\sigma}}}$)]dr, where ${\mathit{C}}_{\mathit{F}}$ is the Thomas-Fermi constant, \ensuremath{\alpha} is a constant, and G(x) is just the same function that appears in the formula for K. Recommended values, obtained by fitting data on rare-gas atoms, are \ensuremath{\alpha}=4.4188\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$, \ensuremath{\beta}=4.5135\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$. The best \ensuremath{\alpha}-to-\ensuremath{\beta} ratio, 0.979, is close to unity, and calculations with \ensuremath{\alpha}=\ensuremath{\beta}=4.3952\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ are shown to give remarkably accurate values for both T and K. It is briefly discussed how the above-noted equations for K and T can both result from scaling arguments and a simple assumption about the first-order density matrix.

Abstract: Different sizes of water clusters from a dimer to twenty water molecules are studied using density functional theory. The binding energies of water clusters are calculated, and a relationship in terms of a simple function has been found between binding energy and the size of the water clusters. The interpolation of this correlation function reproduces the binding energies for the other water clusters to an accuracy within 1 kcal/mol. The extrapolation of the function gives the binding energy, −11.38 kcal/mol, which agrees very well with the experimental binding energy of ice, −11.35 kcal/mol. We also find small water clusters composed of mainly planar four membered rings to be more stable, implying the existence of magic numbers for water clusters with sizes of 4, 8, and 12.

Abstract: The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

Abstract: It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.

Abstract: 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.