The concept of “bond strength” is of essence for modeling every kind of reactive chemistry. Particularly within the field of catalysis and surface science, the interaction strength of adsorbates to surfaces affects the activity, selectivity, and stability of intermediates and transition states. Here, we introduce a simple approach to chemical reactions through an analogy with business. We regard rehybridization as the investment a molecule makes to prepare its electronic and geometrical structure to form new bonds. The resulting bond strength is the total proceeds from bond formation, and the difference (exothermicity) is the profit. The predictive power lies in the fact that any change in the electronic structure to prepare for bond formation requires the involvement of specific excited states. Thus, with knowledge of the energy needed for this excitation (investment) and the strength of the resulting interaction one can predict whether a specific reaction or bonding mode will be favored. We apply this concept to rationalize observed binding modes at surfaces and the often observed large structural changes even for “weakly” chemisorbed systems and finally to justify using small metal clusters to correct chemisorption energies from periodic DFT calculations.

The water molecule’s electronic Cartesian multipole moment and polarizability tensors have been fitted with Gaussian process regression to the internal coordinates and are used to evaluate accurate electrostatic, induction, and dispersion energy components between flexible molecules. The model yields a handful of damping and scaling parameters that were adjusted for the energy components to agree with 2-body symmetry-adapted perturbation theory decomposition and then fine-tuned in order for the total energy to agree with CCSD(T) for small clusters. We present a simple algorithm for rotating symmetric Cartesian tensors and employ a dispersion potential based on multipole polarizabilities. At short range, the 2- and 3-body potential energy was corrected to CCSD(T) accuracy using Gaussian approximation potentials. The radial distribution function and self-diffusion coefficient obtained with molecular dynamics simulations agree well with experiments.

This article was originally published online on 2 September 2025 with an error in Sec. IV C 3. The last two sentences in the section, near the top of the left column of p. 094103-13, beginning with “After completing 500 ps, . . .” should have appeared as a note added in proof. The text has been moved to the end of the Conclusions section and reads as follows: “Note added in proof. After another 250 ps (i.e., a total of 500 ps), the densities in Fig. 8 at 260, 280, and 290 K had decreased by around 0.005 g/cm3 while the others changed less, leaving a less smooth curve (than the one presently in Fig. 8) with a sharp maximum at 270 K. The true (ensemble average) densities likely form a smooth curve, but have yet to be adequately estimated.” All online versions of this article were corrected on 15 September 2025. AIP Publishing apologizes for these errors.

In this work, we present a non-orthogonal configuration interaction (NOCI) approach to address the rotational corrections in multicomponent quantum chemistry calculations where hydrogen nuclei and electrons are described with orbitals under Hartree-Fock (HF) and density functional theory (DFT) frameworks. The rotational corrections are required in systems such as diatomic (HX) and nonlinear triatomic molecules (HXY), where localized broken-symmetry nuclear orbitals have a lower energy than delocalized orbitals with the correct symmetry. By restoring rotational symmetry with the proposed NOCI approach, we demonstrate significant improvements in proton binding energy predictions at the HF level, with average rotational corrections of 0.46 eV for HX and 0.23 eV for HXY molecules. For computing rotational excitation energies, our results indicate that HF kinetic energy corrections are consistently accurate, while discrepancies arise in total energy predictions, primarily from an incomplete treatment of dynamical correlation effects. Rotational energy corrections in multicomponent DFT calculations, using the epc17-2 proton-electron correlation functional, lead to an overestimation of proton binding energies. This is as a result of double-counting of proton-electron correlation effects in the off-diagonal NOCI terms. As a correction, we propose a scaling scheme that effectively adjusts the proton-electron correlation contributions, bringing our results into close agreement with reference CCSD(T) data. The scaled rotational corrections, on average, increase the epc17-2 proton binding energy predictions by 0.055 eV for HX and 0.025 eV for HXY and yield average deviations of 1.0 cm−1 for rotational transitions.

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two ³He atoms encapsulated in C₆₀. At the Hartree–Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree–Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-³He₂@C₆₀) and triplet (ortho-³He₂@C₆₀) nuclear spin configurations, respectively. The ortho-³He₂@C₆₀ ground state is 5.69 cm⁻¹ higher in energy than the para-³He₂@C₆₀ ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C₆₀ embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of ³He₂@C₆₀. 

The impact of the Tamm–Dancoff approximation (TDA) for time-dependent density functional theory (TDDFT) calculations of X-ray absorption and X-ray emission spectra (XAS and XES) is investigated, showing small discrepancies in the excitation energies and intensities. Through explicit diagonalization of the TDDFT Hessian, XES was considered by using full TDDFT with a core-hole reference state. This has previously not been possible with most TDDFT implementations as a result of the presence of negative eigenvalues. Furthermore, a core–valence separation (CVS) scheme for XES is presented, in which only elements including the core-hole are considered, resulting in a small Hessian with the dimension of the number of remaining occupied orbitals of the same spin as the core-hole (CH). The resulting spectra are in surprisingly good agreement with the full-space counterpart, illustrating the weak coupling between the valence–valence and valence–CH transitions. Complications resulting from contributions from the discretized continuum are discussed, which can occur for TDDFT calculations of XAS and XES and for TDA calculations of XAS. In conclusion, we recommend that TDA be used when calculating X-ray emission spectra, and either CVS-TDA or CVS-TDDFT can be used for X-ray absorption spectra.

Electrochemical conversion of glycerol offers a promising route to synthesize value-added glycerol oxidation products (GOPs) from an abundant biomass-based resource. While noble metals provide a low overpotential for the glycerol electrooxidation reaction (GEOR) and high selectivity toward three-carbon (C3) GOPs, their efficiency and cost can be improved by incorporating non-noble metals. Here, we introduce an effective strategy to enhance the performance of Pd nanoparticles for the GEOR by alloying them with Ni. The resulting PdNi nanoparticles show a significant increase in both specific activity (by almost 60%) and mass activity (by almost 35%) during the GEOR at 40 °C. Additionally, they exhibit higher resistance to deactivation compared to pure Pd. Analysis of the GOPs reveals that the addition of Ni into Pd does not compromise the selectivity, with glycerate remaining at around 60% of the product fraction and the other major product being lactate at around 30%. Density functional theory calculations confirm the reaction pathways and the basis for the higher activity of PdNi. This study demonstrates a significant increase in the GEOR catalytic performance while maintaining the selectivity for C3 GOPs, using a more cost-effective nanocatalyst.

We investigate the performance of time-dependent density functional theory (TDDFT) for reproducing high-level reference x-ray absorption spectra of liquid water and water clusters. For this, we apply the integrated absolute difference (IAD) metric, previously used for x-ray emission spectra of liquid water [T. Fransson and L. G. M. Pettersson, J. Chem. Theory Comput. 19, 7333-7342 (2023)], in order to investigate which exchange-correlation (xc) functionals yield TDDFT spectra in best agreement to reference, as well as to investigate the suitability of IAD for x-ray absorption spectroscopy spectrum calculations. Considering highly asymmetric and symmetric six-molecule clusters, it is seen that long-range corrected xc-functionals are required to yield good agreement with the reference coupled cluster (CC) and algebraic-diagrammatic construction spectra, with 100% asymptotic Hartree-Fock exchange resulting in the lowest IADs. The xc-functionals with best agreement to reference have been adopted for larger water clusters, yielding results in line with recently published CC theory, but which still show some discrepancies in the relative intensity of the features compared to experiment.

We discuss a simple intuitive chemical interpretation of XPS shifts in terms of the Z+1 approximation and the chemical bonding in the final core-ionized state. We show how this applies to vibrational excitations and discuss the effects of metallic screening as well as when the Z+1 approximation can be expected to break down. Approaches to compute XPS shifts are discussed and exemplified with a focus on the case of CO/Ni(100). We discuss new experimental advances to study heterogeneous catalytic reactions - CO oxidation and CO hydrogenation - using XPS at high pressure (~1 bar) where reactants, intermediates, and products all contribute to the XPS signal. To disentangle the spectra, we perform microkinetic modeling of the reactions combined with a genetic algorithm to determine which initial data need to be re-examined due to DFT inaccuracy, adsorbate-adsorbate interaction, side reactions that are not included, or uncontrolled experimental features. Combined with computed XPS positions, the resulting coverages of various species can then be used to build theoretical XPS spectra to be directly compared with the experiment. Here, we describe the first steps towards this goal.

The structure and dynamics of liquid water continue to be debated, with insight provided by, among others, X-ray emission spectroscopy (XES), which shows a split in the high-energy 1b1 feature. This split is yet to be reproduced by theory, and it remains unclear if these difficulties are related to inaccuracies in dynamics simulations, spectrum calculations, or both. We investigate the performance of different methods for calculating XES of liquid water, focusing on the ability of time-dependent density functional theory (TDDFT) to reproduce reference spectra obtained by high-level coupled cluster and algebraic-diagrammatic construction scheme calculations. A metric for evaluating the agreement between theoretical spectra termed the integrated absolute difference (IAD), which considers the integral of shifted difference spectra, is introduced and used to investigate the performance of different exchange-correlation functionals. We find that computed spectra of symmetric and asymmetric model water structures are strongly and differently influenced by the amount of Hartree-Fock exchange, with best agreement to reference spectra for similar to 40-50%. Lower percentages tend to yield high density of contributing states, resulting in too broad features. The method introduced here is useful also for other spectrum calculations, in particular where the performance for ensembles of structures are evaluated.