Bonding in Extended Systems

Whereas classical and early modern science often represented chemical bonds as springs, barbs, or wires, our understanding has since evolved towards immaterial forces and quantum-chemically defined electron distributions.

Modern quantum chemistry provides a practical toolbox for probing chemical bonds and investigating their properties, formation, and breaking. Density functional theory (DFT), in particular, has played a central role because it enables realistic and chemically relevant systems to be described at the quantum-mechanical level, ranging from hydrogen bonding to temperature-dependent reaction coefficients at surfaces.

In this work, we follow the dimerisation of lignin units as a non-trivial case study to illustrate the range of DFT-based approaches available for tracing the formation of a chemical bond. We show that bond formation is a continuous process that begins at large intermolecular separations. The climbing-image nudged elastic band pathway provides the activation energy, while temperature-dependent reaction coefficients are obtained from the evolution of the vibrational spectrum.

Projection of the Hessian identifies the atoms involved and reveals the earliest signatures of long-range interactions. These observations are further supported by long-range charge transfer analysed using the Hirshfeld-I method, linking physical and chemical perspectives on bonding. The electrostatic potential, V(r), and its evolution along the reaction pathway show how it guides the approach of the lignin units. The complementary role of the local ionisation energy, I(r), is also highlighted, as it identifies the atomic sites most prone to electron donation and therefore the potential sites of bond formation in these extended systems.

Through this example, we aim to demonstrate that chemical bonding is far richer than simply replacing a mechanical spring with an electron cloud. By combining multiple complementary perspectives, a more complete and fundamental understanding of bond formation and breaking can be achieved.

Silicates are a family of materials based on the SiO₄/₂ unit and constitute a large proportion of the Earth’s crust. They are widely used in numerous industries, including glass and cement production, detergent manufacturing, adhesive formulation, and wastewater treatment. Their versatility arises from substantial topological diversity, which gives rise to a broad range of properties. However, this structural complexity also makes it challenging to understand how silicate materials form and behave. A deeper insight into their structures and formation mechanisms could therefore enable new discoveries and practical applications.
Experimental Raman spectroscopy has previously been used to study silicates, as it allows in situ measurements. To support the interpretation of these measurements, theoretical prediction of Raman spectra is essential for elucidating the structure and bonding of the system. As an alternative to computational methods based on an explicit description of the electronic structure, such as density functional theory and ab initio molecular dynamics, and to overcome their limited sampling capabilities in time and space, we have attempted to simulate Raman spectra directly from molecular-dynamics trajectories using the polarisable AMOEBA force field.
This force field provides a detailed description of electrostatic interactions, which are essential for vibrational spectroscopy, through permanent atomic multipoles and induced atomic dipoles.
Building on previous work, this presentation will describe the extension of the Raman-spectroscopy implementation in the Tinker software package to hydrated systems and silicic acids. New force-field parameters have also been introduced to provide a specific description of these species.

Understanding surface–adsorbate bonding in chemically intuitive terms remains a central challenge in computational surface science. In this talk, I will present a molecular-orbital-based analysis of H₂ adsorption and dissociation on Cu(111) and the Pd/Cu(111) single-atom alloy using density functional theory in combination with LOBSTER-based bonding tools. Projected densities of states, crystal orbital Hamilton populations, crystal orbital bond indexes, and Löwdin population analyses are used to connect familiar molecular concepts—forward donation, back-donation, and bond order—to periodic metal surfaces. Application of these tools shows how adsorption progressively weakens the H–H bond while strengthening H₂–surface interactions along the dissociation pathway. Compared with Cu(111), Pd/Cu(111) lowers the calculated H₂ dissociation barrier by stabilizing the transition state through localized charge redistribution at the Pd site and stronger H₂–metal bonding interactions. This work demonstrates how modern orbital-projection methods can translate plane-wave DFT results into bonding descriptions that are accessible to molecular chemists and useful for interpreting reactivity at catalytic surfaces.

We present the adaptation of Neese’s “corresponding orbital” formalism1 to our recently developed periodic frozen-density embedding technique in LOBSTER2, making the “cor-responding orbital” analysis available to the solid-state community for the first time3. The analysis is showcased on Ba2N, a representative of the layered Ae2N alkaline-earth sub-nitride structures. While the overall crystal structure is stabilized by covalent Ba-6s–N-2p bonds including a few antibonding levels below F, the “corresponding orbital” analysis identifies unpaired electrons populating bonding Ba–Ba orbitals within the layers as well as antibonding orbitals between layers, alluding to the electride character of this structure and giving insight into the whereabouts of the unpaired electron.

Chemical bonding at metal surfaces is central to reactivity, but how does this concept evolve under realistic operating conditions? Surface reactivity is often rationalized using chemisorption models and electronic-structure descriptors, such as d-band theory, which implicitly assume well-defined interactions between adsorbates and electronically homogeneous surfaces. In this talk, I argue that such a picture is inherently incomplete and examine surface bonding from a spatially resolved perspective using the electrostatic potential, V(r), as a descriptor. The subatomic resolution of V(r) reveals that even ideal metal sites exhibit pronounced directionality, confinement, and local Lewis acidity and basicity, giving rise to weak interactions that blur the distinction between chemisorption and noncovalent bonding. Alloying, adsorbate-dependent interactions, and local coordination further challenge universal scaling relations, revealing surface bonding as intrinsically context-dependent. At the same time, these effects do not preclude the identification of useful descriptors but rather indicate that capturing reactivity requires sampling a broader configurational and environmental space and incorporating additional physical contributions into extended, yet still interpretable, descriptors. These effects are illustrated for reactions such as CO2 electroreduction, where interfacial structure and adsorbate environment critically influence reactivity. At electrified interfaces, this complexity becomes unavoidable: solvation, interfacial electric fields, and potential-controlled charge redistribution render bonding dynamic and environment-defined. Rather than replacing existing models, these observations invite us to reconsider how bonding concepts are applied across catalysis, electrochemistry, and functional materials under realistic conditions.

Conceptual Density Functional Theory (cDFT) provides a rigorous framework to rationalize chemical reactivity through density-based response functions. Its extension to solids, however, is hindered by formal and computational challenges associated with periodic boundary conditions and charged systems. Here, we further develop cDFT descriptors for extended systems, focusing on the Fukui function and its associated electrostatic potential.
We analyze different strategies to compute these quantities in solids, highlighting the impact of compensating background charges and electronic relaxation. By introducing practical correction schemes, we obtain physically meaningful Fukui functions and Fukui potentials for metallic and semiconducting surfaces. These descriptors consistently identify reactive regions and capture trends in surface reactivity.

Crucially, we show that these quantities can be embedded within a cDFT perturbation theory framework to predict interaction energies between atomic species and surfaces. The resulting model separates electrostatic and charge-transfer contributions, enabling the estimation of adsorption trends without explicit total-energy calculations. Applications to prototypical surfaces reproduce the ordering of interaction energies for reducing and oxidizing species, demonstrating predictive capability.

These results establish cDFT as a predictive framework for surface chemistry, bridging chemical bonding concepts and materials modeling.

Hydrostatic pressure challenges our chemical intuition in many ways. It introduces structural rearrangements of molecules, alters reactivity, and, more fundamentally, modifies the electronic structure of molecules, thereby affecting chemical bonding and aromaticity. In this talk, computational approaches for the simulation of chemical systems under hydrostatic pressure are presented, with particular emphasis on the (eXtended) Hydrostatic Compression Force Field (HCFF/X-HCFF) and the Gaussians on Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) approaches. The application of these methods to molecular systems demonstrates how pressure influences geometries, molecular volumes, and the nature of non-covalent interactions as well as chemical bonding. The results provide insight into the evolution of bonding descriptors under compression and highlight how fundamental concepts of chemical bonding must be reconsidered under extreme conditions.

The 229Th isotope has a laser-accessible nuclear transition, not only in the gas phase, but also in 229Th doped large-band gap solids. This feature should allow a number of exciting applications: the construction of a robust and portable optical nuclear clocs; exploration of nuclear superradiance; tests of fundamental physics; and, perhaps, a new temperature standard. Solid-state 229Th nuclear clocks require a host material whose band gap is larger than the 8.4 eV nuclear transition energy. Other requirements include maximally uniform environment for every 229Th atom to avoid broadening of the transition due to dipole-dipole interactions, minimal covalency of Th with the environment to prevent the formation of intragap electronic states that can interfere with the nuclear excitation or provide undesirable decay channels via hyperfine coupling, and preferably the lack of nuclear spins in the material host. Hence, this material design task is essentially a chemical bonding task. I will present several material hosts for 229Th nuclear clocks that have been designed and tested experimentally.