Fitting a round peg into a round hole: Asymptotically correcting the generalized gradient approximation for correlation.

We consider the implications of the Lieb-Simon limit for correlation in density functional theory. In this limit, exemplified by the scaling of neutral atoms to large atomic number, local density approximation (LDA) becomes relatively exact, and the leading correction to this limit for correlation has recently been determined for neutral atoms. We use the leading correction to the LDA and the properties of the real-space cutoff of the exchange-correlation hole to design, based upon Perdew-Burke-Ernzerhof (PBE) correlation, an asymptotically corrected generalized gradient approximation (acGGA) correlation which becomes more accurate per electron for atoms with increasing atomic number. When paired with a similar correction for exchange, this acGGA satisfies more exact conditions than PBE. Combined with the known rs -dependence of the gradient expansion for correlation, this correction accurately reproduces correlation energies of closed-shell atoms down to Be. We test this acGGA for atoms and molecules, finding consistent improvement over PBE but also showing that optimal global hybrids of acGGA do not improve upon PBE0 and are similar to meta-GGA values. We discuss the relevance of these results to Jacob's ladder of non-empirical density functional construction.

Brominated Luciferins Are Versatile Bioluminescent Probes.

We report a set of brominated luciferins for bioluminescence imaging. These regioisomeric scaffolds were accessed by using a common synthetic route. All analogues produced light with firefly luciferase, although varying levels of emission were observed. Differences in photon output were analyzed by computation and photophysical measurements. The brightest brominated luciferin was further evaluated in cell and animal models. At low doses, the analogue outperformed the native substrate in cells. The remaining luciferins, although weak emitters with firefly luciferase, were inherently capable of light production and thus potential substrates for orthogonal mutant enzymes.

Accelerating molecular property calculations with nonorthonormal Krylov space methods.

We formulate Krylov space methods for large eigenvalue problems and linear equation systems that take advantage of decreasing residual norms to reduce the cost of matrix-vector multiplication. The residuals are used as subspace basis without prior orthonormalization, which leads to generalized eigenvalue problems or linear equation systems on the Krylov space. These nonorthonormal Krylov space (nKs) algorithms are favorable for large matrices with irregular sparsity patterns whose elements are computed on the fly, because fewer operations are necessary as the residual norm decreases as compared to the conventional method, while errors in the desired eigenpairs and solution vectors remain small. We consider real symmetric and symplectic eigenvalue problems as well as linear equation systems and Sylvester equations as they appear in configuration interaction and response theory. The nKs method can be implemented in existing electronic structure codes with minor modifications and yields speed-ups of 1.2-1.8 in typical time-dependent Hartree-Fock and density functional applications without accuracy loss. The algorithm can compute entire linear subspaces simultaneously which benefits electronic spectra and force constant calculations requiring many eigenpairs or solution vectors. The nKs approach is related to difference density methods in electronic ground state calculations and particularly efficient for integral direct computations of exchange-type contractions. By combination with resolution-of-the-identity methods for Coulomb contractions, three- to fivefold speed-ups of hybrid time-dependent density functional excited state and response calculations are achieved.

Structural, spectroscopic, and theoretical comparison of traditional vs recently discovered Ln(2+) ions in the [K(2.2.2-cryptand)][(C5H4SiMe3)3Ln] complexes: the variable nature of Dy(2+) and Nd(2+).

The Ln(3+) and Ln(2+) complexes, Cp'3Ln, 1, (Cp' = C5H4SiMe3) and [K(2.2.2-cryptand)][Cp'3Ln], 2, respectively, have been synthesized for the six lanthanides traditionally known in +2 oxidation states, i.e., Ln = Eu, Yb, Sm, Tm, Dy, and Nd, to allow direct structural and spectroscopic comparison with the recently discovered Ln(2+) ions of Ln = Pr, Gd, Tb, Ho, Y, Er, and Lu in 2. 2-La and 2-Ce were also prepared to allow the first comparison of all the lanthanides in the same coordination environment in both +2 and +3 oxidation states. 2-La and 2-Ce show the same unusual structural feature of the recently discovered +2 complexes, that the Ln-(Cp' ring centroid) distances are only about 0.03 Å longer than in the +3 analogs, 1. The Eu, Yb, Sm, Tm, Dy, and Nd complexes were expected to show much larger differences, but this was observed for only four of these traditional six lanthanides. 2-Dy and 2-Nd are like the new nine ions in this tris(cyclopentadienyl) coordination geometry. A DFT-based model explains the results and shows that a 4f (n)5d(1) electron configuration is appropriate not only for the nine recently discovered Ln(2+) ions in 2 but also for Dy(2+) and Nd(2+), which traditionally have 4f (n+1) electron configurations like Eu(2+), Yb(2+), Sm(2+), and Tm(2+). These results indicate that the ground state of a lanthanide ion in a molecule can be changed by the ligand set, a previously unknown option with these metals due to the limited radial extension of the 4f orbitals.

Metal effects on ligand non-innocence in Group 5 complexes of the redox-active [ONO] pincer ligand.

Isostructural vanadium, niobium and tantalum complexes of bis(3,5-di-tert-butyl-2-phenol)amine ([ONO]H3), were prepared and characterized to evaluate the impact of the metal ion on redox-activity of the ligand platform. New vanadium and niobium complexes with the general formula, [ONO]MCl2L (M = V, L = THF, 1-V; M = Nb, L = Et2O, 1-Nb) were prepared and structurally analysed by X-ray crystallography. The solid-state structures indicate that the niobium derivative is electronically analogous to the tantalum analog 1-Ta, containing a reduced (ONO) ligand and a niobium(V) metal ion, [ONO(cat)]Nb(V)Cl2(OEt2); whereas, the vanadium derivative is best described as a vanadium(IV) complex, [ONO(sq)]V(IV)Cl2(THF). One-electron oxidation was carried out on all three metal complexes to afford [ONO]MCl3 derivatives (3-V, 3-Nb, 3-Ta). For all three derivatives, oxidation occurs at the (ONO) ligand. In the cases of niobium and tantalum, electronically similar complexes characterized as [ONO(sq)]M(V)Cl3 were obtained and for vanadium, ligand-based oxidation led to the formation of a complex best described as [ONO(q)]V(IV)Cl3. All complexes were characterized by spectroscopic and electrochemical methods. DFT and TD-DFT calculations were used to probe the electronic structure of the complexes and help verify the different electronic structures stemming from changes to the coordinated metal ion.