Abstract The simulation of molecular electronic structure on quantum processors is constrained by a spatial mismatch between long-range Coulomb interactions and finite processor connectivity. In this work, we present bounds on the computational resource overhead imposed by the geometric constraint. We show that for molecular systems in the constant-density regime, achieving chemical accuracy requires Hamiltonian nonlocality that scales polynomially with system size and inversely with spatial dimensionality. Due to the finite bisection bandwidths and Lieb–Robinson velocity limits of local processors, this nonlocality imposes a resource cost. Furthermore, we show that in a first-order Trotter–Suzuki-based formulation, the finite duration required to implement non-local Pauli strings amplifies the coherent error accumulation. The geometric constraint requires the non-Clifford gate count to scale quadratically with both the simulation time and the Hamiltonian nonlocality.
Abstract We assess the suitability of the Thomas–Fermi– λ von Weizsäcker (TF λ vW, λ = 0.2 ) functional in orbital-free density functional theory (DFT) for describing itinerant magnetism. We evaluate the magnetic stability through the susceptibility obtained from the second derivative of the total energy with respect to the net magnetization. We perform calculations for the non-ferromagnetic metals Al, Pd, V, Pt, Mo, Ir, and Cr and the canonical ferromagnets Fe, Co, and Ni, benchmarking the results against Kohn–Sham DFT. The TF λ vW results show poor agreement with the Kohn–Sham predictions, failing to correctly identify which systems are ferromagnetic. Using the TF λ vW ground-state density with generalized gradient approximation-level kinetic energy density functionals in a non-self-consistent calculation similarly fails to distinguish ferromagnetic from non-ferromagnetic metals, and yields better agreement with Kohn–Sham benchmarks in some cases and worse in others. Using the TF λ vW ground-state density with the Kohn–Sham functional in a non-self-consistent calculation correctly distinguishes ferromagnetic from non-ferromagnetic metals, although quantitative accuracy remains limited. These results highlight fundamental limitations of the TF λ vW functional for describing itinerant magnetism.
Abstract A solvation model with atom-dependent dielectric constants is developed based on the fragment molecular orbital method interfaced with the polarizable continuum model. Using this method, it is possible to describe heterogeneous solvation, with an interface of media with different dielectric constants. The accuracy of the model is demonstrated for a polypeptide and the method is applied to the hen egg lysozyme protein (1IEE).
Abstract Density functional theory (DFT) is widely used for electronic structure calculations, primarily utilizing the Kohn–Sham scheme. However, this approach reintroduces orbitals, resulting in a high computational cost. In contrast, the original orbital-free Hohenberg–Kohn DFT (OF-DFT) offers the potential for linear-scaling computations suitable for large systems. The advancement of OF-DFT relies on the development of an accurate and universal kinetic energy density functional (KEDF). This review surveys the progress, challenges, and prospects in KEDF development. It presents the essential physical and mathematical constraints that any KEDF must comply with, tracing the evolution from early models like Thomas–Fermi and von Weizsäcker to contemporary semi-local, nonlocal, and machine-learned approaches. While the developed KEDFs have improved the treatment of metals and some semiconductors, achieving transferable accuracy for molecules and systems with considerable density inhomogeneities remains a critical challenge. We highlight two emerging paradigms; the use of physics-guided machine learning to identify accurate KEDFs and information-theoretic approaches that provide deep insights. The path forward requires a renewed focus on fundamental physical constraints, steering the field away from purely empirical fitting toward a universal, computationally efficient KEDF that maximizes the advantages of OF-DFT. The main KEDFs are listed, including gradient expansions, enhancement-factor strategies, density-decomposition methods, and nonlocal KEDFs guided by linear-response theory.
There is hardly anyone doing electronic structure calculations on molecules who has not used the famous B3LYP functional. Many will even know that the "B" in B3LYP stands for Becke, but how many know the history of the B3LYP functional? Behind this functional, Axel Becke has two of the most highly cited papers in both chemistry and physics—both with several tens of thousands of citations—and many less cited, but arguably equally important accomplishments, that led to B3LYP, as well as continued developments in building ever better density-functional approximatons after the appearance of B3LYP. Axel has received much recognition and many honors for his work. In particular, in 2015, Axel was awarded Canada's highest honor for science and engineering—namely the Gerhard Herzberg Gold Medal. Achievements like this require more than "just" brilliance; they require being the right person in the right place at the right time. I will argue that Axel did indeed fulfill these requirements. At the same time, I will try to give some flavor of the field of electronic structure as seen through my own eyes and those of a few others during the period from the beginning of Axel's career up until very recent times.
