797 publications from this institution
Staircase and ladder methods are proposed for atomic and molecular total and dissociation energies. In both methods, the energies are generated by employing indirect paths via information obtained from effective potentials. In the staircase method, the energies are determined in steps by successive alternations of electron and proton removals. Within the Hartree-Fock (HF) staircase formulation, the energy for electron removal is taken as the negative of the highest-occupied orbital energy, and the energy for proton removal is obtained as the difference of conventional HF total-energy expectation values. The HF staircase total and dissociation energies are significantly superior to the traditional HF values. In the ladder method, total energies are obtained by summing successive highest-occupied orbital energies for fixed nuclei. Both methods are useful within more advanced many-body theories and are exact within exact Kohn-Sham density-functional theory where the magnitude of the highest-occupied orbital energy equals the experimental ionization energy. Self-interaction-corrected density-functional results are presented. We assert two new Koopmans theorems: (1) the energy $\mathcal{E}$ of the highest-occupied HF orbital would give the experimental ionization energy $I$ if the exact ground-state wave function were free of single excitations out of this orbital, and (2) $\mathcal{E}=\ensuremath{-}I$ when the exact correlation potential, ${v}_{c}([n];\mathrm{r})$, is added to the Fock potential and self-consistency is achieved in both the HF orbitals and in the density $n$.
Semilocal density functionals such as the local-spin-density and generalized-gradient approximations are known to overestimate the polarizabilities and especially the hyperpolarizabilities of long-chain molecules, the latter by as much as a factor of 10 or more in model hydrogen chains. These quantities are much better predicted by exact-exchange methods such as Hartree-Fock or optimized effective potential. We show here that the semilocal functionals, after full or scaled-down Perdew-Zunger self-interaction correction (SIC), are about as good as the exact-exchange methods for these quantities. As is the case for the exact-exchange methods, SIC is fully nonlocal and exact for all one-electron densities, and (more relevantly to the electrical response) tends to maintain an integer number of electrons on each ${\mathrm{H}}_{2}$ chain unit to a greater extent than the semilocal functionals do. In this study, the SIC energy is minimized directly, without an optimized effective potential.
For the molecules Be 2 , F 2 , and P 2 of Table For these broken-symmetry solutions, the UHF atomization energies become 17, 220, and 141 kcalmol, respectively, and the mean absolute error of all the UHF atomization energies becomes 69.8 kcalmol.
Langreth and Mehl (LM) and co-workers have developed a useful spin-density functional for the correlation energy of an electronic system. Here the LM functional is improved in two ways: (1) The natural separation between exchange and correlation is made, so that the density-gradient expansion of each is recovered in the slowly varying limit. (2) Uniform-gas and inhomogeneity effects beyond the randomphase approximation are built in. Numerical results for atoms, positive ions, and surfaces are close to the exact correlation energies, with major improvements over the original LM approximation for the ions and surfaces.
Talman and co-workers have presented a realization of the exact Kohn-Sham density-functional theory, neglecting correlation. From their numerical results we conclude that the occupied orbital energy eigenvalues of the local-spin-density (LSD) approximation for exchange and correlation are close to the exact Kohn-Sham orbital energies (apart from a constant shift), but that the latter do not accurately predict the removal energies of tightly-bound electrons in atoms, molecules, and solids. For the calculation of these removal energies, we propose an add-on, single-shot self-interaction correction (SIC) to the LSD orbital energies, based on a simplification and representation-invariant transformation of the original SIC method. This correction's relationship to the Dyson mass operator is briefly discussed.
Using the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) metageneralized gradient approximation, a computationally efficient semilocal functional, we studied the desorption energies of the molecule CO on the (111) surfaces of transition metals as well as the surface energies and lattice constants of the underlying transition metals. Due to its ability to distinguish single-orbital regions from regions of high orbital overlap, revTPSS improves all three properties over the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation. No generalized gradient approximation matches this performance, which has been regarded as unreachable by semilocal approximations.
Semi-local functionals are often more accurate for energies when evaluated on the Hartree-Fock (HF) density than on their own self-consistent densities. HF densities are known to greatly reduce or overcorrect the charge-delocalization error associated with semi-local functionals. Over the last decade, this Hartree-Fock density functional theory (HF-DFT) has been systematized as density corrected DFT (DC-DFT), demonstrating remarkable success: improved chemical barrier heights, near chemical accuracy in water cluster binding energies, highly accurate interaction energies for halogenand chalcogen bonded systems, and more. For reaction barriers and water clusters, some of us found earlier that HFDFT works, not because the HF density is accurate but because of cancellation of negative functional-driven error (FE) by positive density-driven error (DE). In this work, we present evidence that interaction energy errors in halogen and chalcogen bonded molecular complexes in the B30 data set are not primarily driven by density errors, and that the success of HF-DFT for these weakly bonded molecular complexes results from a similar cancellation of FE by DE. Our benchmark Kohn-Sham inversion of the coupled cluster densities for NH3 · · ·ClF, Cl− · · ·SF2 and Cl− · · ·SCF2 presents strong evidence for this error cancellation. For most of the complexes, we employ proxies for the electron transfer in the exact density: the LCωPBE long-range-corrected hybrid and the r2SCAN50 global hybrid. We further investigate several self-interaction correction (SIC) methods for these weakly bonded systems, finding significant improvement from FLOSIC. In the conclusions section, we point out the common feature in our present and previous work: Long bonds can lead to non-negligible functional-driven self-interaction error of the energy from otherwise-accurate semi-local functionals in transition states, water clusters, and halogen or chalcogen bonds.
Complex functional materials are characterized by intricate and competing bond orders, making them an excellent platform for evaluating the newly developed strongly constrained and appropriately normed (SCAN) density functional. In this study, we explore the effectiveness of SCAN in simulating the electronic properties of displacive ferroelectrics (BaTiO3 and PbTiO3) and magnetoelectric multiferroics (BiFeO3 and YMnO3), which encompass a broad spectrum of bonding characteristics. Due to a significant reduction in self-interaction error, SCAN manifests its improvements over the Perdew-Burke-Ernzerhof (PBE) method in three aspects: SCAN predicts more accurate ionicity, produces more compact orbitals, and better captures d-orbital anisotropy. Particularly, these synergistic enhancements lead to notable phenomena in calculating the bandgap of YMnO3: while the PBE+U simulation may suggest a strong correlation appearance attributed to high Hubbard-like U values (∼5 eV), the value is dramatically lower (∼1 eV) in the SCAN+U method. Furthermore, we provide an intuitive analysis of SCAN's operational principles by examining the complex electron densities involved. These insights are theoretically intriguing and have practical implications, potentially encouraging wider adoption of SCAN in the computational modeling of complex functional materials.
The asymptotic behavior of an N-electron ground-state wave function is analyzed, as one electron wanders far from the system. Implications for the one-matrix and pair density are described. The asymptotic behavior currently discussed in the literature, in which the remaining (N−1) electrons relax to their ground state, is generalized to the case where the (N−1)-electron ground state is degenerate. Infinitely long-ranged correlations are reported, in which the selected (N−1)-electron ground state depends upon the direction along which one electron wandered off. We correct a standard limit for the one matrix. Numerical and analytic studies of accurate correlated wave functions illustrate and support the standard asymptotic behavior for the nondegenerate case and its generalization derived here. We extract the (N−1)-electron density from the correlated N-electron wave function. We also discuss the question how large the separation of one electron must be to realize the limiting behavior.
