08 September

Alongside the recent development of the ΔSCF approach for describing excited-state electronic structures using density functional theory (DFT), we extend conceptual density functional theory (CDFT) to evaluate chemical concepts and reactivity descriptors for both ground and excited states. The newly introduced orbital conceptual DFT framework provides a straightforward interpretation of excited-state reactivity analogous to that of the ground state. Within this framework, ground-state CDFT naturally emerges as a special case when the derivative with respect to the number of electrons is evaluated at the frontier-orbital occupation.
Starting from the ground-state system, the spin-polarised analytical linear response function (LRF) is tested by examining the atomic shell structure of alkali atoms and identifying the reactive regions associated with electron-addition and electron-removal processes through the Fukui kernel. The behaviour of the LRF is then illustrated for the ground, singly excited, and doubly excited states of a series of molecular systems, revealing the correct trends and characteristics of bond polarisability and bonding character.
The analytical Fukui function is also presented as a tool for describing local electrophilicity and nucleophilicity. Changes in regioselectivity upon excitation from the ground state to the singlet HOMO–LUMO excited state are compared for a set of widely studied molecules. The dual descriptor, obtained from the analytical Fukui function through a finite-difference approximation, is applied to interpret the Woodward–Hoffmann rules for pericyclic reactions. For thermally driven and photoinduced ring-closure processes in the ground and excited states, respectively, the dual descriptor successfully translates the Woodward–Hoffmann rules from molecular-orbital diagrams into a purely density-based language.

The direct environment of a molecule modifies its ground-state, excited-state, and response properties, including geometry, energy, dynamics, and reactivity. For example, the theoretical description of solvatochromism should involve a realistic representation of the molecules surrounding the solute to faithfully reproduce experimental one- and two-photon absorption spectra (1PA and 2PA). The computational modelling of highly flexible systems, such as molecules in solution, requires the inclusion of dynamic structural effects. However, such treatments can be computationally prohibitive for large molecules or molecular assemblies, particularly at the quantum-mechanical level.
Thanks to recent developments in simplified quantum chemistry (sQC) methods, Löffelsender and co-workers proposed all-atom quantum-mechanics (AQM) workflows to compute the 1PA and 2PA properties of molecules in realistic systems. The term “realistic systems” indicates that the calculations explicitly include large parts of the environment as well as dynamic structural effects, thereby providing model systems that are closer to reality.

A first protocol, termed all-atom single-structure quantum mechanics (ASQM), was proposed for ultra-large systems using a single molecular structure and neglecting dynamic structural effects. An all-atom dynamic-structure quantum-mechanics (ADQM) protocol was subsequently proposed for more structurally dynamic systems, such as chromophores in solution. These workflows originally employed simplified time-dependent density functional theory with a tight-binding xTB ground state (sTD-DFT-xTB). In 2024, I introduced the eXact-integral sTD-DFT (XsTD-DFT) method, which removes the semi-empirical character of the sTD-DFT scheme by explicitly computing atomic-orbital two-electron integrals. It retains similar computational efficiency while improving agreement with conventional TD-DFT.

In this contribution, the ASQM scheme is tested for computing the 1PA and 2PA properties of two proteins: bacteriorhodopsin and iLOV. The results show that the ASQM methodology can describe higher-energy transitions involving π-conjugated amino acids such as tryptophan and tyrosine. The ADQM workflow is then evaluated for reproducing the 1PA and 2PA spectra of flavin mononucleotide (FMN) in aqueous solution using snapshots obtained from GFN2-xTB molecular-dynamics simulations of explicitly solvated systems (ADQM-MD). Spectra computed with the ADQM-MD approach show striking agreement with experiment.

Finally, the AQM methodologies are adapted to employ the XsTD-DFT method for computing excited states and response properties. Comparisons with experiment are presented for the 1PA and circular dichroism spectra of photoactive yellow protein (PYP), the NEXAFS spectra of a collagen model, and the absorption spectra of several dyes in solution.

Conceptual Density Functional Theory (DFT) is a powerful framework for rationalising chemical reactivity at both the molecular and atomic levels. To compress local reactivity information, such as atom-condensed Fukui functions, into a single, chemically meaningful global scalar, we introduce the Gini reactivity descriptor (G), which adapts an economic inequality index to quantify how unevenly atom-condensed reactivity is distributed across molecules. Using the Quantum Theory of Atoms in Molecules (QTAIM) to partition spatial descriptors into atom-resolved scalars and applying a Gini-based socio-economic analysis to the distribution of reactivity descriptors, we quantify the reactivity inequality among individual atoms within their molecular context. Validated on controlled molecular series and applied to large molecular datasets, we demonstrate that the Gini reactivity descriptor provides a compact, physically grounded bridge between local electronic structure and global reactivity. In combination with traditional Conceptual DFT descriptors, these quantities define a multivariate reactivity space for molecular design, with direct implications for chemical feature engineering in machine-learning workflows and high-throughput molecular screening.

The reaction pathway on the potential energy surface (i.e. the minimal energy pathway, MEP) determines the reaction’s reactivity. Most reaction analyses focus only on one dimension of the MEP, namely the relative energies of reactant, transition structure (TS) and product. However, the MEP has also other dimensions, or characteristics, such as slope and width. These are rarely considered, but can nevertheless influence reaction rates directly, especially when tunneling dominates, or indirectly through their effect on barrier heights, for thermal rates. While chemists are used to thinking in terms of manipulating barrier heights by (de)stabilization of the TS or product, ways to manipulate barrier widths or slopes remain ill understood. Using computational tools to analyze MEPs, we explore methods to manipulate barrier widths.
In this presentation, I will show examples of effects that influence barrier widths, with a special emphasis on synchronicity. In many catalytic reactions, multiple bond-forming/breaking events occur during the same elementary step. The degree of reaction synchronicity (i.e. how simultaneously different events occur along the reaction coordinate), is directly related to the shape and width of the reaction barrier. We used DFT methods to investigate the guanidine-catalyzed ring-opening polymerization of γ-butyrolactone. Our results show that by introducing different substituents onto the catalyst, we can systematically control bond strengths and reaction synchronicity, and thus barrier width. Computed thermal and tunneling rates revealed an increase in tunnelling contribution with increasing reaction synchronicity. Our results suggest synchronicity as a new rational design principle for increasing tunneling rates, with the potential to guide the design of catalysts with significant tunneling rate accelerations.

In this contribution, I will present, within the framework of conceptual Density Functional Theory and based on the topological domains of the Electron Localization Function (ELF), a mechanistic methodology designed to identify the most favorable reaction pathway between frozen reactants at low computational cost. In the first part, I will show how a combined approach based on ELF topology and the condensed Dual Descriptor (DD) can be used to drive the optimal orientation between reactants and to mimic the potential energy surfaces of molecular systems at the early stages of the chemical pathway. The DD was chosen for its ability to evaluate the regioselectivity of neutral and soft species, and potentially to mimic the interaction energy arising from mutual interactions between nucleophilic and electrophilic regions. In the second part, this approach will be generalized toward a broader donor–acceptor reactivity model, which can be related to previous studies showing that molecular reactivity results from a balance between electrostatic control and electron-transfer (frontier-orbital) control. Some illustrative examples will be given for non-covalent donor–acceptor systems as well as for reactive systems. Finally, the strengths and limitations of the proposed models for predicting chemical reactivity will be outlined.

We present an efficient implementation of the Interacting Quantum Atoms (IQA) energy‑decomposition scheme in AMS, built within a Kohn–Sham DFT framework and using a QTAIM real‑space partitioning following the original IQA formalism and its DFT extensions. A distance‑adaptive algorithm treats short‑range atomic pairs through explicit 6D numerical integration, while medium‑ and long‑range interactions rely on multipolar and asymptotic approximations to reduce cost without losing chemical accuracy. Intra‑atomic Coulomb and exchange‑correlation self‑terms are reconstructed from total‑energy components, and hybrid functionals are handled through a combination of density‑based XC contributions and a Becke–Roussel‑type approximation of the HF‑like exchange fraction. The implementation supports open‑shell, scalar‑relativistic, and spin‑orbit two‑component calculations. Preliminary results indicate that most IQA energy components, and exchange in particular, can be efficiently learned through machine‑learning models.

The second part of the talk introduces our recent work on exchange‑correlation effects in interatomic energies for pure density functionals. Standard LDA, GGA, and meta‑GGA functionals yield only intra‑atomic XC terms, meaning that “atoms will interact the one with the others only by classical electrostatics.” Using Green’s second identity, the XC energy is rewritten as a Coulomb‑type interaction between the density and an XC charge, restoring interatomic XC contributions and ensuring exact recovery of the self‑consistent DFT energy.