Marcel Swart

Performance of the OPBE exchange-correlation functional

In a recent evaluation of density functional theory (DFT) functionals OPBE, which combines Handys optimized exchange (OPTX) with the PBE correlation, was shown to correctly predict the spin states (singlet through sextet) of seven different iron complexes (2004, J. Phys. Chem. A, 108, 5479). The present study provides a further test of OPBE as well as that of the OPerdew and OLYP functionals, in which OPTX is combined with the Perdew and LYP correlations, respectively. These three are compared to other pure DFT functionals for their performance in calculating the atomization energies for the G2-set of up to 148 molecules, six reaction barriers of SN2 reactions, geometry optimizations of 19 small molecules and four metallocenes, and zero-point vibrational energies for 13 small molecules. OPBE performs exceptional well in all cases.

Accurate Spin-State Energies for Iron Complexes

A critical assessment of the OPBE functional is made for its performance for the geometries and spin-states of iron complexes. In particular, we have examined its performance for the geometry of first-row transition-metal (di)halides (MnX2, FeX2, CoX2, NiX2, CuX, X=[F, Cl]), whose results were previously [J. Chem. Theory Comput. 2006, 2, 1282] found to be representative for a much larger and more diverse set of 32 metal complexes. For investigating the performance for spin ground-states of iron complexes, we examined a number of small iron complexes (Fe(II)Cl4(2-), Fe(III)Cl4(1-), Fe(II)Cl6(4-), Fe(III)Cl6(3-), Fe(II)CN6(4-), Fe(III)CN6(3-), Fe(VI)O4(2-), Fe(III)(NH3)6(3+)), benchmark systems (Fe(II)(H2O)6(2+), Fe(II)(NH3)6(2+), Fe(II)(bpy)3(2+)), and several challenging iron complexes such as the Fe(II)(phen)2(NCS)2 spin-crossover compound, the monopyridylmethylamine Fe(II)(amp)2Cl2 and dipyridylmethylamine Fe(II)(dpa)2(2+), and the bis complex of Fe(III)-1,4,7-triazacyclononane (Fe(III)((9)aneN3)2(3+). In all these cases OPBE gives excellent results.

A charge analysis derived from an atomic multipole expansion

A new charge analysis is presented that gives an accurate description of the electrostatic potential from the charge distribution in molecules. This is achieved in three steps: first, the total density is written as a sum of atomic densities; next, from these atomic densities a set of atomic multipoles is defined; finally, these atomic multipoles are reconstructed exactly by distributing charges over all atoms. The method is generally applicable to any method able to provide atomic multipole moments, but in this article we take advantage of the way the electrostatic potential is calculated within the Density Functional Theory framework. We investigated a set of 31 molecules as well as all amino acid residues to test the quality of the method, and found accurate results for the molecular multipole moments directly from the DFT calculations. The deviations from experimental values for the dipole/quadrupole moments are also small. Finally, our Multipole Derived Charges reproduce both the atomic and molecular multipole moments exactly.

A new all-round density functional based on spin states and S N 2 barriers

We report here a new empirical density functional that is constructed based on the performance of OPBE and PBE for spin states and S(N)2 reaction barriers and how these are affected by different regions of the reduced gradient expansion. In a previous study [Swart, Sola, and Bickelhaupt, J. Comput. Methods Sci. Eng. 9, 69 (2009)] we already reported how, by switching between OPBE and PBE, one could obtain both the good performance of OPBE for spin states and reaction barriers and that of PBE for weak interactions within one and the same (SSB-sw) functional. Here we fine tuned this functional and include a portion of the KT functional and Grimmes dispersion correction to account for pi-pi stacking. Our new SSB-D functional is found to be a clear improvement and functions very well for biological applications (hydrogen bonding, pi-pi stacking, spin-state splittings, accuracy of geometries, reaction barriers).

QUILD: QUantum-regions interconnected by local descriptions

A new program for multilevel (QM/QM and/or QM/MM) approaches is presented that is able to combine different computational descriptions for different regions in a transparent and flexible manner. This program, designated QUILD (for QUantum‐regions Interconnected by Local Descriptions), uses adapted delocalized coordinates (Int J Quantum Chem 2006, 106, 2536) for efficient geometry optimizations of equilibrium and transition‐state structures, where both weak and strong coordinates may be present. The Amsterdam Density Functional (ADF) program is used for providing density functional theory and MM energies and gradients, while an interface to the ORCA program is available for including RHF, MP2, or semiempirical descriptions. The QUILD optimization setup reduces the number of geometry steps needed for the Baker test‐set of 30 organic molecules by ∼30% and for a weakly‐bound test‐set of 18 molecules by ∼75% compared with the old‐style optimizer in ADF, i.e., a speedup of roughly a factor four. We report two examples of using geometry optimizations with numerical gradients, for spin‐orbit relativistic ZORA and for excited‐state geometries. Finally, we show examples of its multilevel capabilities for a number of systems, including the multilevel boundary region of amino acid residues, an SN2 reaction in the gas‐phase and in solvent, and a DNA duplex.

Dispersion Corrections Essential for the Study of Chemical Reactivity in Fullerenes

In a previous paper (J. Phys. Chem. A2009, 113, 9721), we analyzed theoretically the Diels-Alder cycloaddition between cyclopentadiene and C(60) for which experimental results on energy barriers and reaction energies are known. One of the main conclusions reached was that the two-layered ONIOM2(B3LYP/6-31G(d):SVWN/STO-3G) method provides results very close to the full B3LYP/6-31G(d) ones. Unfortunately, however, both the exothermicity of the reaction and the energy barrier were clearly overestimated by these two methods. In the present work, we analyze the effect of the inclusion of Grimmes dispersion corrections in the energy profile of this reaction. Our results show that these corrections are essential to get results close to the experimental values. In addition, we have performed calculations both with and without dispersion corrections for the Diels-Alder reaction of C(60) and several dienes and for the Diels-Alder cycloaddition of a (5,5) single-walled carbon nanotube and 1,3-cis-butadiene. The results obtained indicate that inclusion of dispersion corrections is compulsory for the study of the chemical reactivity of fullerenes and nanotubes.

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta‐GGA as well as hybrid DFT to reproduce high‐level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta‐GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta‐GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 Å and 0.6°, even better than the best meta‐GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta‐GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.

The role of aromaticity in determining the molecular structure and reactivity of (endohedral metallo)fullerenes

The encapsulation of metal clusters in endohedral metallofullerenes (EMFs) takes place in cages that in most cases are far from being the most stable isomer in the corresponding hollow fullerenes. There exist several possible explanations for the choice of the hosting cages in EMFs, although the final reasons are actually not totally well understood. Moreover, the reactivity and regioselectivity of (endohedral metallo)fullerenes have in the past decade been shown to be generally dependent on a number of factors, such as the size of the fullerene cage, the type of cluster that is being encapsulated, and the number of electrons that are transferred formally from the cluster to the fullerene cage. Different rationalizations of the observed trends had been proposed, based on bond lengths, pyramidalization angles, shape and energies of (un)occupied orbitals, deformation energies of the cages, or separation distances between the pentagon rings. Recently, in our group we proposed that the quest for the maximum aromaticity (maximum aromaticity criterion) determines the most suitable hosting carbon cage for a given metallic cluster (i.e. EMF stabilization), including those cases where the IPR rule is not fulfilled. Moreover, we suggested that local aromaticity plays a determining role in the reactivity of EMFs, which can be used as a criterion for understanding and predicting the regioselectivity of different reactions such as Diels-Alder cycloadditions or Bingel-Hirsch reactions. This review highlights different aspects of the aromaticity of fullerenes and EMFs, starting from how this can be measured and ending by how it can be used to rationalize and predict their molecular structure and reactivity.

A Ditopic Ion-Pair Receptor Based on Stacked Nucleobase Quartets†

Pass the salt, please! State-of-the-art computations indicate that the stacking complex of a guanine quartet and an adenine quartet (G(4)A(4)) can function as a potent ditopic receptor for NaCl in aqueous solution (see picture; Na(+), Cl(-) yellow, O red, N blue, C black, H white).

DRF90: a polarizable force field

The direct reaction field (DRF) approach has proven to be a useful tool to investigate the influence of solvents on the quantum/classical behaviour of solute molecules. In this paper, we report the latest extension of this DRF approach, which consists of the gradient of the completely classical energy expressions of this otherwise QM/MM method. They can be used in (completely classical) molecular dynamics (MD) simulations and geometry optimizations, that can be followed by a number of single point QM/MM calculations on configurations obtained in these simulations/optimizations. We report all energy and gradient expressions, and results for a number of interesting (model) systems. They include geometry optimization of the benzene dimer as well as MD simulations of some solvents. The most stable configuration for the benzene dimer is shown to be the parallel-displaced form, which is slightly more stable (0.3 kcal/mol) than the T-shaped dimer.