Regium Bonding Characterized by the Molecular Surface Property Approach

Speaker: Joakim Halldin Stenlid
Institute: Stockholm University
Country: Sweden
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Joakim Halldin Stenlid

Department of Physics, Stockholm University, Stockholm, Sweden

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When interacting with electron-donors, neutral compounds of copper, silver and gold form bonds that are similar to hydrogen and halogen bonds. This type of bonding is referred to as regium bonding and it have been used to rationalize e.g. noble metal catalysis. Compounds donating regium, halogen and hydrogen bonds have in common local regions deficient in electron density, known as σ-holes. The chemistry of such regions can be characterized by local maxima in the electrostatic potential evaluated on contour surfaces of constant electron density (VS,max); the position of the VS,max identify sites susceptible to interactions with nucleophiles, e.g. H2O, H2S, NH3 and CO, while the magnitude of a VS,max scales with the strength of the corresponding interaction. By this approach, information on the reaction and interaction tendencies of a compound can be readily accessed by standard DFT calculations. Regium bonds contains contributions from electrostatics, but also from polarization and charge-transfer. The latter are not directly captured by VS,max, but can be well-described by a newly introduced property called the local surface electron attachment energy. Minima in this property (ES,min) provide a measure of the local electron affinity. ES,min is used complementary to VS,max to identity and rank interaction sites.
The use of molecular properties, such as the electrostatic potential and the electron attachment energies, is generally referred to as the Molecular Surface Property Approach (MSPA). These properties can be computed by e.g. DFT and provides estimate of reaction and/or interaction propensities of multiple sites of a compound from a single calculation. Historically MSPA has primarily been employed within the molecular science. The current presentation will exemplify how the MSPA can also be used as a guide to understand and predict the chemistry of materials and nanoparticles, opening up for a new realm of applications..

Joakim Halldin - image

Figure. Left, the electrostatic potential plotted on an 0.001 au isodensity surface of an icosahedral Au nanoparticle. Red > yellow > green sites mark VS,max (σ-holes) susceptible to interactions with nucleophiles (i.e. to the formation of regium bonds). In agreement with the experimental knowledge, corner sites are more activated followed by edge and (111) terrace atop sites. Right, comparison of the regium, halogen and hydrogen bonds with Nu being a nucleophile. e.g. H2O or NH3.


Introduction to regium bonding:
J. H. Stenlid, A. J. Johansson and T. Brinck, σ-Holes and σ-Lumps Direct the Lewis Basic and Acidic Interactions of Noble Metal Nanoparticles: Introducing Regium Bonds, Phys. Chem. Chem. Phys., 2018, 20, 2676–2692

σ-holes in catalysis and transition metal nanoparticle interactions (note that the term regium bonding is not explicitly used in the references):
J. H. Stenlid and T. Brinck, Extending the σ-Hole Concept to Metals: An Electrostatic Interpretation of the Effects of Nanostructure in Gold and Platinum Catalysis, J. Am. Chem. Soc., 2017, 139, 11012–11015; J. H. Stenlid, A. J. Johansson and T. Brinck, σ-Holes on Transition Metal Nanoclusters and Their Influence on the Local Lewis Acidity, Crystals, 2017, 7, 222.

The molecular surface property approach including regium bonding of surfaces:
T. Brinck and J. H. Stenlid, The Molecular Surface Property Approach: A Guide to Chemical Interactions in Chemistry, Medicine and Material Science, Adv. Theory Sim., 2018, DOI: 10.1002/adts.201800149

The surface electrostatic potential:
J. S. Murray and P. Politzer, The Electrostatic Potential: an Overview, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2011, 1, 153–163.

The local electron attachment energy:
T. Brinck, P. Carlqvist and J. H. Stenlid, Local Electron Attachment Energy and Its Use for Predicting Nucleophilic Reactions and Halogen Bonding, J. Phys. Chem. A, 2016, 120, 10023–10032.


The electrostatic potential can be obtained as a postprocessing step in most quantum chemical codes, e.g. Gaussian (, Orca (, and VASP (

The local electron attachment energy has not yet been implemented in any standard program. The HS95ver18 code of T. Brinck can be used in combination with Gaussian. This program can also be used to compute the electrostatic potential, and to identify local minima/maxima on isodensity surfaces. In addition, the program can compute an analogous property to the local electron attachment energy that may be used for interactions with electrophiles (i.e. the local average ionization energy). Contact for information.

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