Peter R. Surjan

The development of “transition metal‐like” reactivity using earth‐abundant p‐block elements is one of the most prominent and challenging goals of contemporary main group chemistry. This difficulty is exemplified by the key, catalytically relevant bond‐forming step of reductive elimination which, while often facile for transition metals, is very difficult to achieve for most main group elements. Efforts to bridge this gap have typically focused on delicate tailoring of electronic structure, supporting ligands, and coordination geometry, a task that is conceptually difficult and synthetically demanding. In this study, we demonstrate an alternative approach. We show that photocatalytic reductive elimination from an already well‐known P(V) complex can be achieved rapidly and under mild conditions, via a transient oxidation strategy analogous to “oxidatively induced reductive elimination”. This concept has previously been applied only to transition metal complexes but is now extended to the field of main group chemistry. These results demonstrate a simple, easily accessible, but potentially very powerful new strategy for ‘turbocharging’ transition metal‐like reactivity at a main group center. Thus, they provide a valuable new tool for the ongoing pursuit of transition metal‐like catalysis using main group elements.

The development of “transition metal‐like” reactivity using earth‐abundant p‐block elements is one of the most prominent and challenging goals of contemporary main group chemistry. This difficulty is exemplified by the key, catalytically relevant bond‐forming step of reductive elimination which, while often facile for transition metals, is very difficult to achieve for most main group elements. Efforts to bridge this gap have typically focused on delicate tailoring of electronic structure, supporting ligands, and coordination geometry, a task that is conceptually difficult and synthetically demanding. In this study, we demonstrate an alternative approach. We show that photocatalytic reductive elimination from an already well‐known P(V) complex can be achieved rapidly and under mild conditions, via a transient oxidation strategy analogous to “oxidatively induced reductive elimination”. This concept has previously been applied only to transition metal complexes but is now extended to the field of main group chemistry. These results demonstrate a simple, easily accessible, but potentially very powerful new strategy for ‘turbocharging’ transition metal‐like reactivity at a main group center. Thus, they provide a valuable new tool for the ongoing pursuit of transition metal‐like catalysis using main group elements.

The accurate modeling of (bio)molecular systems remains a major challenge in computational chemistry. In recent years, machine learning potentials (MLPs) have emerged as a promising approach, combining the efficiency of classical force fields with near quantum-mechanical accuracy. Among these, the physics-informed MLP FFLUX employs the Interacting Quantum Atoms (IQA) energy partitioning scheme to decompose molecular energies into atomic contributions derived from quantum mechanics for machine learning. However, incorporating two-electron correlation energies into IQA, and consequently into FFLUX, is currently unfeasible for larger systems en masse, due to the steep computational scaling associated with the necessary storage and evaluation of the two-particle density matrix (2PDM). In this work, we introduce a proof-of-concept workflow that employs density fitting (DF) to compress the 2PDM into a two-index representation, thereby accelerating the IQA partitioning of two-electron correlation energies. By expressing traditionally four-center electron repulsion integrals in terms of auxiliary basis functions, the DF approximation enables a size reduction of the 2PDM from O(N4) to O(NDF2), where N is the number of basis functions and NDF is the size of the auxiliary basis set. The method proposed here is demonstrated using coupled cluster singles and doubles densities. The resulting reduction in computational cost and memory requirements enables correlated IQA analyses for significantly larger systems than previously accessible. Thus, this development provides an important step toward incorporating explicit electron correlation and hence dispersion directly into FFLUX atomic ML models, thereby improving both their physical robustness and transferability. This advance will eliminate the need to artificially add empirical potentials, or a posteriori dispersion correction.

We introduce an integral-direct, linear-scaling, local explicitly correlated (F12) coupled-cluster (CC) singles, doubles, and perturbative triples [CCSD(T)] approach building on our established local natural orbital (LNO) CCSD(T) [J. Chem. Theory Comput. 2018, 14, 4193] and local second-order Møller–Plesset F12 [J. Chem. Theory Comput. 2026, 22, 2946] techniques. By generating and transforming all the required integrals on-the-fly, the algorithm eliminates integral storage requirements, resulting in asymptotically constant memory usage and negligible disk I/O. A key strength of the implementation is the application of the CCSD(F12*) ansatz alongside our (T+) triples correction—currently the most comprehensive scheme incorporating F12 approximations — which delivers rapid basis set convergence. Benchmark tests show that, under default truncation settings, the method recovers over 99.9% of the canonical explicitly correlated CCSD(T) correlation energy, achieving reaction energy errors under 1 kJ/mol. Compared to the complete basis set limit of CCSD(T), the average deviation of reaction energies remains around 1 kJ/mol. Overall, our results demonstrate that combining LNO-CCSD(T) with explicit correlation provides an efficient strategy for high-accuracy calculations on large molecular systems using modest basis sets.

Generation of numerically converged coupled-cluster reference energies of molecular crystals remains highly non-routine. Yet, such data points are critically needed as computational methodologies strive to reach correlated wave-function accuracy in condensed-phase systems. Localized-orbital coupled-cluster approaches applied within the many-body expansion promise a scalable route to these reference results. Here, we report solutions to a technical challenge when using this methodology─at long intermolecular distances, the numerical noise due to local approximations can accumulate for some molecular crystals into a large-scale drift of the correlation energy, especially in the nonadditive three-body contributions. Within the local natural orbital (LNO) coupled-cluster method, we suggest well-balanced approaches to overcome this issue. At the benchmark level, we propose more accurate LNO-CCSD(T) settings that remove the artifacts at long distances and attain a numerical precision of 0.2 kJ/mol (maximum error) in the lattice energy, with a practical cost that is orders of magnitude lower than that of canonical CCSD(T). As an even more scalable solution, we propose a multi-level strategy that utilizes the established routine LNO-CCSD(T) precision tiers (Tight, vTight) but retains the numerical stability of the benchmark level by treating long-distance three-body systems with the random-phase approximation (RPA).

The accurate modeling of (bio)molecular systems remains a major challenge in computational chemistry. In recent years, machine learning potentials (MLPs) have emerged as a promising approach, combining the efficiency of classical force fields with near quantum-mechanical accuracy. Among these, the physics-informed MLP FFLUX employs the Interacting Quantum Atoms (IQA) energy partitioning scheme to decompose molecular energies into atomic contributions derived from quantum mechanics for machine learning. However, incorporating two-electron correlation energies into IQA, and consequently into FFLUX, is currently unfeasible for larger systems en masse, due to the steep computational scaling associated with the necessary storage and evaluation of the two-particle density matrix (2PDM). In this work, we introduce a proof-of-concept workflow that employs density fitting (DF) to compress the 2PDM into a two-index representation, thereby accelerating the IQA partitioning of two-electron correlation energies. By expressing traditionally four-centre electron repulsion integrals in terms of auxiliary basis functions, the DF approximation enables a size reduction of the 2PDM from O(N^4) to O(NDF^2), where N is the number of basis functions and NDF is the size of the auxiliary basis set. The method proposed here is demonstrated using coupled cluster singles and doubles densities. The resulting reduction in computational cost and memory requirements enables correlated IQA analyses for significantly larger systems than previously accessible. Thus, this development provides an important step towards incorporating explicit electron correlation and hence dispersion directly into FFLUX atomic ML models, thereby improving both their physical robustness and transferability. This advance will eliminate the need to artificially add empirical potentials, or a posteriori dispersion correction.

Electron densities are often subdivided into smaller units, which can then be allocated to atomic centers. The resulting atomic charges usually do not reproduce the total electronic dipole moment of the molecule. We describe a simple optimization procedure for finding atomic populations closest to some input atomic charges, e.g., the Mulliken or Bader ones, but reproduce the molecular dipole when the atomic coordinates are summed up weighted by the new charges. The proposed procedure can be coded by a few lines and is practically cost-less.

Quantum chemical bases are mostly linearly independent, whether orthonormal or not. However, in certain applications, using an overcomplete set of functions, not forming a basis in the strict sense offers distinct advantages. Localized molecular orbitals (LMO) projected from atomic orbitals (PAO) are a primary example. Use of redundant LMOs is facilitated by the mathematical theory of frames. Along with a systematic presentation of the necessary background, it is shown that the trace of one-electron operators can be obtained by a formula analogous to the orthonormal case. For instance, the electronic dipole moment can be expressed as a sum of frame LMO centroids multiplied by their fractional populations as weights. An advantage of frame LMOs is demonstrated when following reaction coordinates. When a system passes through a high-symmetry point between lower-symmetry arrangements, orthogonal LMOs often exhibit abrupt changes. This occurs when a specific set of localized orbitals does not represent the molecular point group of the high-symmetry structure, resulting in equivalent sets of orthogonal LMOs that may induce discontinuities in LMO based quantities. It is shown that PAO related frame LMOs transition smoothly in these scenarios, without any extra algorithmic effort.

Accurately modeling noncovalent interactions (NCIs) involving charged systems remains an outstanding challenge in density functional theory (DFT), with implications across natural and life sciences, engineering, e.g., in biochemistry, catalysis, and materials science. For these interactions, the interplay between electrostatics, polarization, and dispersion leads to systematic errors of up to tens of kilocalories per mole in standard dispersion–enhanced DFT methods. We solve this problem by introducing (r ² SCAN+MBD)@HF, a DFT method without empirically fitted parameters that combines the r ² SCAN functional and many-body dispersion, both evaluated on Hartree-Fock densities. We show that the unique synergy of these three components enables balanced treatment of short- and long-range correlation, which is crucial for accurate description of NCIs involving charged systems. Evaluations on standard benchmarks show that (r ² SCAN+MBD)@HF significantly improves accuracy for NCIs involving charged systems while maintaining robust performance for neutral systems. Further tests on the Metal Ion Protein Clusters dataset introduced here demonstrate its improved accuracy for metal-protein interactions, including cases where the metal ion is surrounded by negatively charged ligands for which standard DFT can completely break down. Given the ubiquity of such interactions, (r ² SCAN+MBD)@HF is broadly applicable from biochemistry and materials science, including for generating high-quality data to train machine-learning force fields.

We present the development of local natural orbital (LNO)-based arbitrary order coupled cluster (CC) methods and a rigorous assessment of the beyond CCSD(T)-level correlation through LNO-CCSDTQ. Both the closed- and open-shell implementations inherit from our LNO family of methods the asymptotically linear-scaling framework, support for point group symmetry, multilevel embedding, as well as greatly reduced memory and disk use. The accuracy of LNO approximations and basis set completeness is benchmarked for thermochemistry and noncovalent interactions through CCSDTQ. Even for complicated atomizations and barrier heights, the CCSDT–CCSD(T), (Q), and especially the CCSDT(Q)–CCSD(T) contributions are obtained reliably within 85–95% relative and 0.05–0.1 kcal/mol absolute accuracy, already with the default LNO threshold set. Tightening LNO settings generally improves this performance, useful when aiming at high relative accuracy in even smaller effects, such as in noncovalent interactions or when pursuing the basis set limit of post-CCSD(T) atomization contributions. Thus, the LNO approximation greatly expands the reach of post-CCSD(T) methods, especially beyond a few atoms and small (double-ζ) basis sets, i.e., above ca. 100 orbitals. For example, via our multilevel approach, we report an unprecedented CCSDT(Q)–CCSD(T) reaction energy correction computation for a real-life enzyme reaction. Thus, LNO-based higher-order CC methods enable thermochemistry protocols aiming at kJ/mol accuracy for practical, 3D molecular systems that are much larger than previously accessible.