Tomasz Adam Wesolowski

Kohn-Sham equations with constrained electron density: an iterative evaluation of the ground-state electron density of interacting molecules

A new method for calculating the ground state electron density of interacting molecules is presented. The supermolecule electron density is obtained using an iterative procedure. At each step the electron density of one molecule is calculated using previously introduced Kohn-Sham equations with constrained electron density. These equations contain terms representing the coupling between constrained and non-constrained electron densities. The coupling terms also involve a new functional, namely the non-additive kinetic energy functional that is not present in the original Kohn-Sham method. Its first-principles analytical form in not yet known. We examine the analytical form of this functional derived from Thomas-Fermi theory. The electron density obtained is compared with that calculated using the original Kohn-Sham method applied to the supermolecule. Good agreement has been found for a broad range of electron density overlaps.

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.

LiSc(BH4)4: A Novel Salt of Li + and Discrete Sc(BH4)4 - Complex Anions

LiSc(BH4)4 has been prepared by ball milling of LiBH4 and ScCl3. Vibrational spectroscopy indicates the presence of discrete Sc(BH4)4(-) ions. DFT calculations of this isolated complex ion confirm that it is a stable complex, and the calculated vibrational spectra agree well with the experimental ones. The four BH4(-) groups are oriented with a tilted plane of three hydrogen atoms directed to the central Sc ion, resulting in a global 8 + 4 coordination. The crystal structure obtained by high-resolution synchrotron powder diffraction reveals a tetragonal unit cell with a = 6.076 A and c = 12.034 A (space group P-42c). The local structure of the Sc(BH4)4(-) complex is refined as a distorted form of the theoretical structure. The Li ions are found to be disordered along the z axis.

Density functional theory with approximate kinetic energy functionals applied to hydrogen bonds

Applicability of the approximate kinetic energy functionals to study hydrogen-bonded systems by means of the formalism of Kohn–Sham equations with constrained electron density (KSCED) [Cortona, Phys. Rev. B 44, 8454 (1991); Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993); Wesolowski and Weber, Chem. Phys. Lett. 248, 71 (1996)] is analyzed. In the KSCED formalism, the ground-state energy of a molecular complex is obtained using a “divide-and-conquer” strategy, which is applied to the Kohn–Sham-like equations to obtain the electron density of a fragment embedded in a larger system. The approximate kinetic energy functional enters into the KSCED formalism in two ways. First, the effective potential in which the electrons of each fragment move contains a component which is expressed by means of a functional derivative of an approximate kinetic energy functional (functional derivative of the non-additive kinetic energy). Second, the KSCED energy functional contains a component (non-additive kinetic ener...

Accuracy of approximate kinetic energy functionals in the model of Kohn-Sham equations with constrained electron density: the FH...NCH complex as a test case

Ground‐state properties of a linear hydrogen‐bonded FH...NCH complex are studied by means of the ‘‘freeze‐and‐thaw’’ cycle of Kohn–Sham Equations with constrained electron density (KSCED) [T. A. Wesolowski and J. Weber, Chem. Phys. Lett. 248, 71, (1996)]. For several geometries of the complex, the electron density and the total energy are compared to the ones obtained by means of the standard Kohn–Sham calculations. The comparisons are made to assess the accuracy of several gradient dependent approximate kinetic energy functionals applied in the KSCED equations. It was found that the closest results to the Kohn–Sham ones were obtained with the functional whose analytical form was proposed by Perdew and Wang for exchange energy [J. P. Perdew and Y. Wang in Electronic Structure of Solids ’91, edited by P. Ziesche and H. Eschrig (Academie Verlag, Berlin, 1991), p. 11] and parametrized by Lembarki and Chermette for kinetic energy [A. Lembarki and H. Chermette, Phys. Rev. A 50, 5328 (1994)]. Around the interac...

A Highly Configurationally Stable [4]Heterohelicenium Cation

Ein konfigurationsstabiles Heterohelicen: Uber die diastereomeren Salze mit dem phosphorhaltigen Anion binphat gelang die Trennung der Enantiomere eines [4](Hetero)heliceniumkations (siehe Bild: N=violett, O=rot). Die absoluten Konfigurationen wurde durch Messung des Schwingungscirculardichroismus bestimmt. Die Energiebarriere fur die Enantiomerisierung der Verbindung ist deutlich groser als beim [6]Helicen.

Frozen-Density Embedding Strategy for Multilevel Simulations of Electronic Structure

Modeling properties of chemical species and chemical reactions requires usually the quantum-mechanical level of description. Methods from the ever-growing toolbox of quantum chemistry1,2 are used for this purpose. Due to unfavorable scaling of quantum chemistry methods, a compromise must be made between the accuracy of the numerical results and the size of the system described at the wave function level. The same strategy can be extended for separating molecular fragments or molecules. Nonlocal embedding operators based on either transferrable pseudopotentials or frozen orbitals obtained from localization procedures have been developed in many groups. The essential feature of all such local potentials is that they comprise a component which takes into account the intermolecular Pauli repulsion.

Density functional theory with an approximate kinetic energy functional applied to study structure and stability of weak van der Waals complexes

In view of further application to the study of molecular and atomic sticking on dust particles, we investigated the capability of the “freeze-and-thaw” cycle of the Kohn–Sham equations with constrained electron density (KSCED) to describe potential energy surfaces of weak van der Waals complexes. We report the results obtained for C6H6⋯X (X=O2, N2, and CO) as test cases. In the KSCED formalism, the exchange-correlation functional is defined as in the Kohn–Sham approach whereas the kinetic energy of the molecular complex is expressed differently, using both the analytic expressions for the kinetic energy of individual fragments and the explicit functional of electron density to approximate nonadditive contributions. As the analytical form of the kinetic energy functional is not known, the approach relies on approximations. Therefore, the applied implementation of KSCED requires the use of an approximate kinetic energy functional in addition to the approximate exchange-correlation functional in calculations...

Gradient-free and gradient-dependent approximations in the total energy bifunctional for weakly overlapping electron densities

We analyze the performance of gradient-free local density approximation (LDA) and gradient-dependent generalized gradient approximation (GGA) functionals in a density functional theory variational calculations based on the total energy bifunctional (E[ρ1,ρ2]). These approximations are applied to the exchange-correlation energy and to the nonadditive component of the kinetic energy of the complex. Benchmark ab initio interaction energies taken from the literature for 25 intermolecular complexes for which the interaction energies fall into the 0.1–3.0 kcal/mol range are used as reference. At the GGA level, the interaction energies derived from E[ρ1,ρ2] are more accurate than the Kohn–Sham ones. LDA leads to very good interaction energies for such complexes where the ρ1,ρ2 overlap is very small (Ne-Ne, Ar-Ar, for instance) but it is not satisfactory for such cases where the overlap is larger. Introduction of gradient-dependent terms into the approximate part of E[ρ1,ρ2] improves significantly the overall acc...

Optimizing sensitization processes in dinuclear luminescent lanthanide oligomers: selection of rigid aromatic spacers.

This work illustrates a simple approach for optimizing the lanthanide luminescence in molecular dinuclear lanthanide complexes and identifies a particular multidentate europium complex as the best candidate for further incorporation into polymeric materials. The central phenyl ring in the bis-tridentate model ligands L3–L5, which are substituted with neutral (X = H, L3), electron-withdrawing (X = F, L4), or electron-donating (X = OCH3, L5) groups, separates the 2,6-bis(benzimidazol-2-yl)pyridine binding units of linear oligomeric multi-tridentate ligand strands that are designed for the complexation of luminescent trivalent lanthanides, Ln(III). Reactions of L3–L5 with [Ln(hfac)3(diglyme)] (hfac– is the hexafluoroacetylacetonate anion) produce saturated single-stranded dumbbell-shaped complexes [Ln2(Lk)(hfac)6] (k = 3–5), in which the lanthanide ions of the two nine-coordinate neutral [N3Ln(hfac)3] units are separated by 12–14 Å. The thermodynamic affinities of [Ln(hfac)3] for the tridentate binding sites in L3–L5 are average (6.6 ≤ log(β(2,1)(Y,Lk)) ≤ 8.4) but still result in 15–30% dissociation at millimolar concentrations in acetonitrile. In addition to the empirical solubility trend found in organic solvents (L4 > L3 >> L5), which suggests that the 1,4-difluorophenyl spacer in L4 is preferable, we have developed a novel tool for deciphering the photophysical sensitization processes operating in [Eu2(Lk)(hfac)6]. A simple interpretation of the complete set of rate constants characterizing the energy migration mechanisms provides straightforward objective criteria for the selection of [Eu2(L4)(hfac)6] as the most promising building block.