Density Functional Theory Exchange-correlation Functionals Research Articles

Hydrogen Bonds and van der Waals Forces in Ice at Ambient and High Pressures

The first principles methods, density-functional theory and quantum Monte Carlo, have been used to examine the balance between van der Waals (vdW) forces and hydrogen bonding in ambient and high-pressure phases of ice. At higher pressure, the contribution to the lattice energy from vdW increases and that from hydrogen bonding decreases, leading vdW to have a substantial effect on the transition pressures between the crystalline ice phases. An important consequence, likely to be of relevance to molecular crystals in general, is that transition pressures obtained from density-functional theory exchange-correlation functionals which neglect vdW forces are greatly overestimated.

Accurate Thermochemistry for Transition Metal Oxide Clusters

Total atomization energies (TAEs) and normalized clustering energies (NCEs) of group IVB (MO(2))(n) (M = Ti, Zr, Hf) and VIB (MO(3))(n) (M = Cr, Mo, W) transition metal oxide clusters up to n = 4 were calculated at the coupled cluster [CCSD(T)] and density functional theory (DFT) levels. For all the clusters studied, the TAEs calculated at the CCSD(T) level were found to be strongly basis set dependent, whereas the NCEs were significantly less basis set dependent. Here we further develop an efficient strategy for calculating accurate thermodynamic properties of large clusters based on those of the cluster unit and the NCEs. The calculated TAEs, NCEs, and heats of formations for these clusters were compared with available experimental data. We also benchmarked the performance of popular DFT exchange-correlation functionals for the calculations of the TAEs and NCEs. The performance of many DFT functionals for the calculation of the TAEs strongly depends on the choice of the electronic state for the transition metal atom. Hybrid functionals were found to generally outperform pure functionals in the calculation of NCEs, and the PBE1PBE functional has the best performance with average deviations of approximately 1 kcal/mol for the dimers and approximately 2 kcal/mol for the trimers and tetramers. The benchmarked functionals all display gradual degradation in performance with increasing cluster size.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters. II. The water hexamer and van der Waals interactions

Second order Møller-Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches predict the so-called prism to be the lowest energy isomer, followed by cage, book, and cyclic isomers. The energies of the four isomers are very similar, all being within 10-15 meV/H(2)O. These reference data are then used to evaluate the performance of several density-functional theory exchange-correlation (xc) functionals. A subset of the xc functionals tested for smaller water clusters [I. Santra et al., J. Chem. Phys. 127, 184104 (2007)] has been considered. While certain functionals do a reasonable job at predicting the absolute dissociation energies of the various isomers (coming within 10-20 meV/H(2)O), none predict the correct energetic ordering of the four isomers nor does any predict the correct low total energy isomer. All xc functionals tested either predict the book or cyclic isomers to have the largest dissociation energies. A many-body decomposition of the total interaction energies within the hexamers leads to the conclusion that the failure lies in the poor description of van der Waals (dispersion) forces in the xc functionals considered. It is shown that the addition of an empirical pairwise (attractive) C(6)R(-6) correction to certain functionals allows for an improved energetic ordering of the hexamers. The relevance of these results to density-functional simulations of liquid water is also briefly discussed.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

Low-Lying Electronic States of M3O9- and M3O92- (M = Mo, W)

Multiple low-lying electronic states of M(3)O(9)(-) and M(3)O(9)(2-) (M = Mo, W) arise from the occupation of the near-degenerate low-lying virtual orbitals in the neutral clusters. We used density functional theory (DFT) and coupled cluster theory (CCSD(T)) with correlation consistent basis sets to study the structures and energetics of the electronic states of these anions. The adiabatic and vertical electron detachment energies (ADEs and VDEs) of the anionic clusters were calculated with 27 exchange-correlation functionals including one local spin density approximation functional, 13 generalized gradient approximation (GGA) functionals, and 13 hybrid GGA functionals, as well as the CCSD(T) method. For M(3)O(9)(-), CCSD(T) and nearly all of the DFT exchange-correlation functionals studied predict the (2)A(1) state arising from the Jahn-Teller distortion due to singly occupying the degenerate e' orbital to be lower in energy than the (2)A(1)' state arising from singly occupying the nondegenerate a(1)' orbital. For W(3)O(9)(-), the (2)A(1) state was predicted to have essentially the same energy as the (2)A(1)' state at the CCSD(T) level with core-valence correlation corrections included and to be higher in energy or essentially isoenergetic with most DFT methods. The calculated VDEs from the CCSD(T) method are in reasonable agreement with the experimental values for both electronic states if estimates for the corrections due to basis set incompleteness are included. For M(3)O(9)(2-), the singlet state arising from doubly occupying the nondegenerate a(1)' orbital was predicted to be the most stable state for both M = Mo and W. However, whereas M(3)O(9)(2-) was predicted to be less stable than M(3)O(9)(-), W(3)O(9)(2-) was predicted to be more stable than W(3)O(9)(-).

Evaluation of ⟨Ŝ2⟩ in density functional theory

The evaluation of ⟨Ŝ2⟩ in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for ⟨Ŝ2⟩ and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for ⟨Ŝ2⟩ is then proposed and investigated.

Characterization of the tunneling conductance across DNA bases

Characterization of the electrical properties of the DNA bases (adenine, cytosine, guanine, and thymine), in addition to building the basic knowledge on these fundamental constituents of a DNA, is a crucial step in developing a DNA sequencing technology. We present a first-principles study of the current-voltage characteristics of nucleotidelike molecules of the DNA bases, placed in a 1.5 nm gap formed between gold nanoelectrodes. The quantum transport calculations in the tunneling regime are shown to vary strongly with the electrode-molecule geometry and the choice of the density-functional theory exchange-correlation functionals. Analysis of the results in the zero-bias limit indicates that distinguishable current-voltage characteristics of different DNA bases are dominated by the geometrical conformations of the bases and nanoelectrodes.

Semiempirical hybrid functional with improved performance in an extensive chemical assessment

It is demonstrated that there is still scope for improvement in the quality of conventional, semiempirical hybrid exchange-correlation functionals in density-functional theory. A new functional, denoted B97-3, is determined from a fit to eight chemical properties (316 data points). For a series of 25 chemical assessments (850 data points) including 17 assessments and 10 chemical properties absent from the fitting data, B97-3 provides the lowest or joint-lowest mean absolute error on 15 occasions, compared to 6, 5, and 4 occasions for B3LYP, PBE0, and B97-2, respectively [A. D. Becke, J. Chem. Phys. 98, 5648 (1993); M. Ernzerhof and G. E. Scuseria, J. Chem. Phys. 110, 5029 (1999); C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999); P. J. Wilson, T. J. Bradley, and D. J. Tozer, J. Chem. Phys. 115, 9233 (2001)]. Mean absolute errors from B97-3 are, on average, 21%, 18%, and 12% smaller than from these three functionals. The most notable improvements are obtained for classical reaction barriers, where the error reductions are 60%, 54%, and 27%.

Density functional theory study of bulk platinum monoxide

The ground state electronic structure of platinum monoxide (PtO) has been calculated using density functional theory (DFT) with periodic boundary conditions and Gaussian type orbitals. Several DFT exchange-correlation functionals, including a hybrid functional based on a screened Coulomb potential for exact exchange have been used. Our study reveals that functionals based on the generalized gradient approximation (GGA) or meta-GGA do not give qualitatively different results from those of the local spin density approximation, predicting PtO to be metallic, whereas the hybrid functional predicts a semiconductor with a band gap of $0.86\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. A reduced band gap of $0.56\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ is found in the oxygen deficient $\mathrm{Pt}{\mathrm{O}}_{0.9}$ system.

Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods.

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.

Exploring the limits of gradient corrections in density functional theory

We have recently proposed a simple and systematic approach to the generation of exchange-correlation functionals in density-functional theory by linear least-squares fitting to accurate thermochemical reference data. In a series of four publications, new functionals with gradient corrections of first and also second order have been found in this way. In the present article we review and summarize our approach, highlighting the common threads and the most extensive fits from the heretofore published studies. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 63–69, 1999