F. Matthias Bickelhaupt

Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis

We present the Voronoi Deformation Density (VDD) method for computing atomic charges. The VDD method does not explicitly use the basis functions but calculates the amount of electronic density that flows to or from a certain atom due to bond formation by spatial integration of the deformation density over the atomic Voronoi cell. We compare our method to the well‐known Mulliken, Hirshfeld, Bader, and Weinhold [Natural Population Analysis (NPA)] charges for a variety of biological, organic, and inorganic molecules. The Mulliken charges are (again) shown to be useless due to heavy basis set dependency, and the Bader charges (and often also the NPA charges) are not realistic, yielding too extreme values that suggest much ionic character even in the case of covalent bonds. The Hirshfeld and VDD charges, which prove to be numerically very similar, are to be recommended because they yield chemically meaningful charges. We stress the need to use spatial integration over an atomic domain to get rid of basis set dependency, and the need to integrate the deformation density in order to obtain a realistic picture of the charge rearrangement upon bonding. An asset of the VDD charges is the transparency of the approach owing to the simple geometric partitioning of space. The deformation density based charges prove to conform to chemical experience.

Understanding reactivity with Kohn–Sham molecular orbital theory: E2–SN2 mechanistic spectrum and other concepts

On the basis of Kohn–Sham density functional (DFT) investigations on elementary organic and organometallic reactions, we show how a detailed understanding of the electronic structure of a reaction system can help recognize certain characteristics of the process, yielding valuable mechanistic concepts. The concept of the base as a selective catalyst in E2 eliminations, for example, leads to a straightforward explanation for the general preference for anti over syn stereochemistry in base‐induced elimination reactions. Furthermore, electronic structure considerations provide the so‐called E2–SN2 mechanistic spectrum, in terms of which one can interpret and understand the competition between elimination and substitution reactions and the shift, on solvation, of the reactivity from E2 to SN2. In addition, mechanistic concepts from organometallic and organic chemistry are linked as we argue that oxidative addition may be conceived, in some respect, as the organometallic analog of the frontside SN2 substitution. Finally, we introduce the ideas of “activation strain” of and “transition state interaction” between the deformed reactants in the activated complex, which together determine the activation energy, ΔE*=ΔE  strain* +ΔE  int* . They prove to be helpful conceptual tools for understanding in detail how activation barriers and relative efficiencies of competing reaction mechanisms arise and how they may be affected (e.g., by changing reactants or by solvation). © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 114–128, 1999

Oxidative addition of Pd to C–H, C–C and C–Cl bonds: Importance of relativistic effects in DFT calculations

To assess the importance of relativistic effects for the quantum chemical description of oxidative addition reactions of palladium to C–H, C–C and C–Cl bonds, we have carried out a systematic study of the corresponding reactions of CH4, C2H6 and CH3Cl with Pd-d10 using nonrelativistic (NR), quasirelativistic (QR), and zeroth-order regularly approximated (ZORA) relativistic density functional theory (DFT) at the BP86/TZ(2)P level. Relativistic effects are important according to both QR and ZORA, the former yielding similar but somewhat more pronounced effects than the latter, more reliable method: activation barriers are reduced by 6–14 kcal/mol and reaction enthalpies become 15–20 kcal/mol more exothermic if one goes from NR to ZORA. This yields, for example, 298 K activation enthalpies ΔH298≠ of −5.0 (C–H), 9.6 (C–C) and −6.0 kcal/mol (C–Cl) relative to the separate reactants at ZORA-BP86/TZ(2)P. In accordance with gas-phase experiments on reactions of Pd with alkanes, we find reaction profiles with pron...

Activation of H-H, C-H, C-C and C-Cl bonds by Pd and PdCl-. Understanding anion assistance in C-X bond activation

To understand the mechanism of anion assistance in palladium-catalyzed H-H, C-H, C-C and C-Cl bond activation, several mechanistic pathways for oxidative addition of Pd and PdCl(-) to H2 (H-H), CH4 (C-H), C2H6 (C-C and C-H) and CH3Cl (C-Cl) were studied uniformly at the ZORA-BP86/TZ(2)P level of relativistic nonlocal density functional theory (DFT). Oxidative addition of the neutral, uncoordinated Pd atom proceeds, as reported earlier, via direct oxidative insertion (ΔH(⧧)298 is -22 to 10 kcal/mol), whereas straight SN2 substitution (yielding, e.g., PdCH3(+) + X(-)) is highly endothermic (144-237 kcal/mol) and thus not competitive. Anion assistance (i.e., going from Pd to PdCl(-)) lowers all activation barriers and increases the exothermicity of all model reactions studied. The effect is however selective:  it favors the highly endothermic SN2 mechanism over direct oxidative insertion (OxIn). Activation enthalpies ΔH(⧧)298 for oxidative insertion of PdCl(-) increase along C-H (-14.0 and -13.5 kcal/mol for CH4 and C2H6) ≈ C-Cl (-11.2 kcal/mol) < C-C (6.4 kcal/mol), i.e., essentially in the same order as for neutral Pd. Interestingly, in case of PdCl(-) + CH3Cl, the two-step mechanism of SN2 substitution followed by leaving-group rearrangement becomes the preferred mechanism for oxidative addition. The highest overall barrier of this pathway (-20.2 kcal/mol) drops below the barrier for direct oxidative insertion (-11.2 kcal/mol). The effect of anion assistance is analyzed using the Activation Strain model in which activation energies ΔE(⧧) are decomposed into the activation strain ΔE(⧧)strain of and the stabilizing transition state (TS) interaction ΔE(⧧)int between the reactants in the activated complex:  ΔE(⧧) = ΔE(⧧)strain + ΔE(⧧)int. For each type of activated bond and reaction mechanism, the activation strain ΔE(⧧)strain adopts characteristic values which differ only moderately, within a relatively narrow range, between corresponding reactions of Pd and PdCl(-). The lowering of activation barriers through anion assistance is caused by the TS interaction ΔE(⧧)int becoming more stabilizing.

Charge Transfer and Environment Effects Responsible for Characteristics of DNA Base Pairing.

A hitherto unresolved discrepancy between theory and experiment is unraveled. Charge transfer and the influence of the environment in the crystal are vital for understanding the nature and for reproducing the structure of hydrogen bonds in DNA base pairs. The introduction of water molecules and a sodium counterion into the theoretical model (see picture) deforms the geometry of AT and GC in such a way that excellent agreement with the experimental structures is obtained.

The activation strain model and molecular orbital theory

The activation strain model is a powerful tool for understanding reactivity, or inertness, of molecular species. This is done by relating the relative energy of a molecular complex along the reaction energy profile to the structural rigidity of the reactants and the strength of their mutual interactions: ΔE(ζ) = ΔEstrain(ζ) + ΔEint(ζ). We provide a detailed discussion of the model, and elaborate on its strong connection with molecular orbital theory. Using these approaches, a causal relationship is revealed between the properties of the reactants and their reactivity, e.g., reaction barriers and plausible reaction mechanisms. This methodology may reveal intriguing parallels between completely different types of chemical transformations. Thus, the activation strain model constitutes a unifying framework that furthers the development of cross‐disciplinary concepts throughout various fields of chemistry. We illustrate the activation strain model in action with selected examples from literature. These examples demonstrate how the methodology is applied to different research questions, how results are interpreted, and how insights into one chemical phenomenon can lead to an improved understanding of another, seemingly completely different chemical process. WIREs Comput Mol Sci 2015, 5:324–343. doi: 10.1002/wcms.1221

Telomere Structure and Stability: Covalency in Hydrogen Bonds, Not Resonance Assistance, Causes Cooperativity in Guanine Quartets

We show that the cooperative reinforcement between hydrogen bonds in guanine quartets is not caused by resonance-assisted hydrogen bonding (RAHB). This follows from extensive computational analyses of guanine quartets (G(4)) and xanthine quartets (X(4)) based on dispersion-corrected density functional theory (DFT-D). Our investigations cover the situation of quartets in the gas phase, in aqueous solution as well as in telomere-like stacks. A new mechanism for cooperativity between hydrogen bonds in guanine quartets emerges from our quantitative Kohn-Sham molecular orbital (MO) and corresponding energy decomposition analyses (EDA). Our analyses reveal that the intriguing cooperativity originates from the charge separation that goes with donor-acceptor orbital interactions in the σ-electron system, and not from the strengthening caused by resonance in the π-electron system. The cooperativity mechanism proposed here is argued to apply, beyond the present model systems, also to other hydrogen bonds that show cooperativity effects.

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).

Analyzing reaction rates with the distortion/interaction-activation strain model

Abstract The activation strain or distortion/interaction model is a tool to analyze activation barriers that determine reaction rates. For bimolecular reactions, the activation energies are the sum of the energies to distort the reactants into geometries they have in transition states plus the interaction energies between the two distorted molecules. The energy required to distort the molecules is called the activation strain or distortion energy. This energy is the principal contributor to the activation barrier. The transition state occurs when this activation strain is overcome by the stabilizing interaction energy. Following the changes in these energies along the reaction coordinate gives insights into the factors controlling reactivity. This model has been applied to reactions of all types in both organic and inorganic chemistry, including substitutions and eliminations, cycloadditions, and several types of organometallic reactions.

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.