Werner Reckien

System‐Dependent Dispersion Coefficients for the DFT‐D3 Treatment of Adsorption Processes on Ionic Surfaces

Dispersion-corrected density functional theory calculations (DFT-D3) were performed for the adsorption of CO on MgO and C(2) H(2) on NaCl surfaces. An extension of our non-empirical scheme for the computation of atom-in-molecules dispersion coefficients is proposed. It is based on electrostatically embedded M(4)X(4) (M=Na, Mg) clusters that are used in TDDFT calculations of dynamic dipole polarizabilities. We find that the C(MM)(6) dispersion coefficients for bulk NaCl and MgO are reduced by factors of about 100 and 35 for Na and Mg, respectively, compared to the values of the free atoms. These are used in periodic DFT calculations with the revPBE semi-local density functional. As demonstrated by calculations of adsorption potential energy curves, the new C(6) coefficients lead to much more accurate energies (E(ads)) and molecule-surface distances than with previous DFT-D schemes. For NaCl/C(2) H(2) we obtained at the revPBE-D3(BJ) level a value of E(ads) =-7.4 kcal mol(-1) in good agreement with experimental data (-5.7 to -7.1 kcal mol(-1)). Dispersion-uncorrected DFT yields an unbound surface state. For the MgO/CO system, the computed revPBE-D3(BJ) value of E(ads) =-4.1 kcal mol(-1) is also in reasonable agreement with experimental results (-3.0 kcal mol(-1)) when thermal corrections are taken into account. Our new dispersion correction also improves computed lattice constants of the bulk systems significantly compared to plain DFT or previous DFT-D results. The extended DFT-D3 scheme also provides accurate non-covalent interactions for ionic systems without empirical adjustments and is suggested as a general tool in surface science.

Implementation of Empirical Dispersion Corrections to Density Functional Theory for Periodic Systems

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT‐D3) is implemented in the plane‐wave program package VASP. The DFT‐D3 implementation is compared with an implementation of the earlier DFT‐D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT‐D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three‐center terms as implemented in the original molecular DFT‐D3 version is investigated. The empirical parameters are taken from the original DFT‐D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid‐state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT‐D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106).

Theoretical study of the adsorption of benzene on coinage metals

Summary The adsorption of benzene on the M(111), M(100) and M(110) surfaces of the coinage metals copper (M = Cu), silver (M = Ag) and gold (M = Au) is studied on the basis of density functional theory (DFT) calculations with an empirical dispersion correction (D3). Variants of the Perdew–Burke–Ernzerhof functionals (PBE, RPBE and RevPBE) in combination with different versions of the dispersion correction (D3 and D3(BJ)) are compared. PBE-D3, PBE-D3(BJ) and RPBE-D3 give similar results which exhibit a good agreement with experimental data. RevPBE-D3 and RevPBE-D3(BJ) tend to overestimate adsorption energies. The inclusion of three-center terms (PBE-D3(ABC)) leads to a slightly better agreement with the experiment in most cases. Vertical adsorbate–substrate distances are calculated and compared to previous theoretical results. The observed trends for the surfaces and metals are consistent with the calculated adsorption energies.

Car–Parrinello Molecular Dynamics Simulations and Biological Systems

The basic concepts of Car–Parrinello molecular dynamics (CPMD) and its application to biological systems are reviewed. In Car–Parrinello simulations the electronic structure is calculated on the fly, i.e., during the course of simulations the potential is adjusted according to the chemical events occurring in the system. This allows for more unbiased simulations of chemical processes, as opposed to classical molecular dynamics, which utilize predefined potentials. In contrast to Born–Oppenheimer molecular dynamics, where the nuclei are propagated under classical equations of motions and where the wave function is calculated in every time step, CPMD maps this two-component classical/quantum system onto a two-component purely classical system. A short introduction into classical mechanics, which provides the equations of motions, is given. DFT will be briefly outlined because it represents the standard method for obtaining the electronic structure during a CPMD simulation. QM/MM approaches, which combine the CPMD method for a core region with a classical description of its environment, are also reviewed. These schemes provide a more reliable description of biological systems, whose properties are strongly influenced by their surroundings. A brief overview over the application of Car–Parrinello simulations to biological systems is provided. Finally, a case study to illustrate some of the basic possibilities of this method is discussed.

Uncovering Individual Hydrogen Bonds in Rotaxanes by Frequency Shifts

We present a theoretical investigation of amide pseudorotaxane IR spectra in the harmonic approximation. In particular, we focus on the effect of axle substitution on the hydrogen bonds that are formed between axle and wheel. Two types of pseudorotaxanes are studied: one with the substituent affecting mostly the axles carbonyl group and one with the effect influencing primarily the amide NH group. Sizeable red shifts are predicted for the carbonyl stretching frequencies, and large red shifts for the NH stretching frequencies. For the wheel amide groups involved in hydrogen bonding merely with their NH hydrogens, a small shift is observed for the carbonyl stretch mode. A clear relation is observed between the NH stretch shifts and individual hydrogen bond energies. This is confirmed by correlations of the shared electron number with the NH stretch shift showing that this quantity can be taken as an indicator for individual hydrogen bond energies. Axle substitution influences the strengths of the individual hydrogen bonds which is again reflected in the NH stretch frequency shifts. A linear relationship of Hammetts substituent parameters with the NH frequency shifts can be established.

Substitution effect and effect of axle’s flexibility at (pseudo-)rotaxanes

Summary This study investigates the effect of substitution with different functional groups and of molecular flexibility by changing within the axle from a single C–C bond to a double C=C bond. Therefore, we present static quantum chemical calculations at the dispersion-corrected density functional level (DFT-D3) for several Leigh-type rotaxanes. The calculated crystal structure is in close agreement with the experimental X-ray data. Compared to a stiffer axle, a more flexible one results in a stronger binding by 1–3 kcal/mol. Alterations of the binding energy in the range of 5 kcal/mol could be achieved by substitution with different functional groups. The hydrogen bond geometry between the isophtalic unit and the carbonyl oxygen atoms of the axle exhibited distances in the range of 2.1 to 2.4 Å for six contact points, which shows that not solely but to a large amount the circumstances in the investigated rotaxanes are governed by hydrogen bonding. Moreover, the complex with the more flexible axle is usually more unsymmetrical than the one with the stiff axle. The opposite is observed for the experimentally investigated axle with the four phenyl stoppers. Furthermore, we considered an implicit continuum solvation model and found that the complex binding is weakened by approximately 10 kcal/mol, and hydrogen bonds are slightly shortened (by up to 0.2 Å).