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We present OPITeR, a FORM program for the reduction of multi-loop tensor Feynman integrals. The program can handle tensors, including spinor indices, with rank of up to 20 and can deal with up to 8 independent external momenta. The reduction occurs in $D$ dimensions compatible with conventional dimensional regularization. The program is able to manifest symmetries of the integrand in the tensor reduced form., Comment: 11 pages, 1 figure

Self-interaction error (SIE), arising from the imperfect cancellation of the spurious classical Coulomb interaction between an electron and itself, is a persistent challenge in modern density functional approximations. This issue is illustrated using the prototypical one-electron system $H_2^+$. While significant efforts have been made to eliminate SIE through the development of computationally expensive nonlocal density functionals, it is equally important to explore whether SIE can be mitigated within the framework of more efficient semilocal density functionals. In this study, we present a non-empirical meta-generalized gradient approximation (meta-GGA) that incorporates the Laplacian of the electron density. Our results demonstrate that the meta-GGA significantly reduces SIE, yielding a binding energy curve for $H_2^+$ that matches the exact solution at equilibrium and improves across a broad range of bond lengths over those of the Perdew-Burke-Ernzerhof (PBE) and strongly-constrained and appropriately-normed (SCAN) semilocal density functionals. This advancement paves the way for further development within the realm of semilocal approximations.

We present an efficient graphical approach to construct projectors for the tensor reduction of multi-loop Feynman integrals with both Lorentz and spinor indices in $D$ dimensions. An ansatz for the projectors is constructed making use of its symmetry properties via an orbit partition formula. The graphical approach allows to identify and enumerate the orbits in each case. For the case without spinor indices we find a 1 to 1 correspondence between orbits and integer partitions describing the cycle structure of certain bi-chord graphs. This leads to compact combinatorial formulae for the projector ansatz. With spinor indices the graph-structure becomes more involved, but the method is equally applicable. Our spinor reduction formulae are based on the antisymmetric basis of $\gamma$ matrices, and make use of their orthogonality property. We also provide a new compact formula to pass into the antisymmetric basis. We compute projectors for vacuum tensor Feynman integrals with up to 32 Lorentz indices and up to 4 spinor indices. We discuss how to employ the projectors in problems with external momenta., Comment: 58 pages, 32 tables, 3 figures

[Abridged] The extension of conceptual DFT to include external fields in chemical systems is utilised to investigate the effects of strong magnetic fields on the electronic charge distribution and its consequences on the reactivity of $\pi$-systems. Formaldehyde, H$_2$CO, is considered as a prototypical example and current-DFT calculations are used to evaluate the electric dipole moment together with the electron density and the Fukui functions, which provide insight into how H$_2$CO behaves chemically in a magnetic field. In particular, the symmetries of these quantities are analysed based on group, representation, and corepresentation theories using QSym$^2$. This allows us to leverage the simple symmetry constraints on the macroscopic electric dipole moments to make profound predictions on the more nuanced symmetry transformation properties of the microscopic frontier MOs, electron densities, and Fukui functions. This is especially useful for complex-valued MOs in magnetic fields whose detailed symmetry analyses lead us to define the new concepts of modular and phasal symmetry breaking. Through these, the connection between the vanishing constraints on the electric dipole moments and the symmetry of electron densities and Fukui functions can be formalised, and the inability of the magnetic field in all three orientations considered to induce asymmetry with respect to the molecular plane can be understood from a molecular perspective. Furthermore, the detailed forms of the Fukui functions reveal remarkable reversals in the direction of the C=O dipole moment in the presence of a parallel or perpendicular magnetic field, which can be attributed to the mixing between frontier MOs due to their subduced symmetries in magnetic fields. The findings in this work are also discussed in the wider context of a long-standing debate on the possibility to create enantioselectivity by external fields., Comment: Main text: 26 pages (two-column), 7 figures, 9 tables; Supplementary information: 7 pages (one-column), 4 figures, 2 tables

Accurate approximation of the exchange-correlation (XC) energy in density functional theory (DFT) calculations is essential for reliably modelling electronic systems. Many such approximations are developed from models of the XC hole; accurate reference XC holes for real electronic systems are crucial for evaluating the accuracy of these models however the availability of reliable reference data is limited to a few systems. In this study, we employ the Lieb optimization with a coupled cluster singles and doubles (CCSD) reference to construct accurate coupling-constant averaged XC holes, resolved into individual exchange and correlation components, for five spherically symmetric atoms: He, Li, Be, N, and Ne. Alongside providing a new set of reference data for the construction and evaluation of model XC holes, we compare our data against the exchange and correlation hole models of the established LDA and PBE density functional approximations. Our analysis confirms the established rationalization for the limitations of LDA and the improvement observed with PBE in terms of the hole depth and its long-range decay, demonstrated in real-space for the series of spherically-symmetric atoms.

Symmetry provides a powerful machinery to classify, interpret, and understand quantum-mechanical theories and results. However, most contemporary quantum chemistry packages lack the ability to handle degeneracy and symmetry breaking effects, especially in non-Abelian groups, nor are they able to characterize symmetry in the presence of external magnetic or electric fields. In this article, a program written in Rust entitled QSym$^2$ that makes use of group and representation theories to provide symmetry analysis for a wide range of quantum-chemical calculations is introduced. With its ability to generate character tables symbolically on-the-fly, and by making use of a generic symmetry-orbit-based representation analysis method formulated in this work, QSym$^2$ is able to address all of these shortcomings. To illustrate these capabilities of QSym$^2$, four sets of case studies are examined in detail in this article: (i) high-symmetry $\textrm{C}_{84}\textrm{H}_{64}$, $\textrm{C}_{60}$, and $\textrm{B}_9^-$ to demonstrate the analysis of degenerate molecular orbitals (MOs); (ii) octahedral $\textrm{Fe(CN)}_6^{3-}$ to demonstrate the analysis of symmetry-broken determinants and MOs; (iii) linear hydrogen fluoride in a magnetic field to demonstrate the analysis of magnetic symmetry; and (iv) equilateral $\textrm{H}_3^+$ to demonstrate the analysis of density symmetries., Comment: Main text: 36 pages (double column, single spacing), 7 figures, 5 tables; Supporting information: 13 pages (single column, double spacing), 2 figures, 1 table; Revised version accepted on 29th November 2023 for publication in Journal of Chemical Theory and Computation

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic-field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic-field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation.

On any night in Canada, at least 35,000 individuals experience homelessness. These individuals use emergency shelters to transition out of homelessness and into permanent housing. We designed and deployed a technology to support front-line staff at the largest emergency housing shelter in Calgary, Canada. Over a period of five months in 2022, we worked closely with front-line staff to co-design an interface for supporting a holistic understanding of client context and facilitating decision-making. The tool is currently in-use and our collaboration is ongoing. In this paper, we reflect on preliminary findings regarding the second iteration of the tool. We find that supporting shelter staff in understanding the human behind the data was a critical component of design. This work contributes to literature on how data tools may be integrated into homeless shelters in a way that aligns with shelters' values., Comment: 7 pages

In density functional theory the exchange-correlation (XC) energy functional can be defined exactly through the coupling-constant ($\lambda$) averaged XC hole $\bar{n}_\text{xc}(\mathbf{r},\mathbf{r}')$, representing the probability depletion of finding an electron at $\mathbf{r}$ due to an electron at $\mathbf{r}$. Accurate knowledge of $\bar{n}_\text{xc}(\mathbf{r},\mathbf{r}')$ has been crucial for developing various XC energy density functional approximations and understanding their performance for real molecules and materials. However, there are very few systems for which accurate XC holes have been calculated, since this requires evaluating the one- and two-particle reduced density matrices for a reference wave function over a range of $\lambda$ whilst the electron density remains fixed at the physical ($\lambda=1$) density. Although the coupled-cluster singles and doubles (CCSD) method can yield exact results for a two-electron system in the complete basis set limit, it cannot capture the electron-electron cusp with commonly used finite basis sets. In this study, focusing on the Hooke's atom as a two-electron model system for which certain analytic solutions are known, we examine the effect of this cusp error on the XC hole calculated using CCSD. The Lieb functional is calculated at a range of coupling constants to determine the $\lambda$-integrated XC hole. Our results indicate that, for the Hooke's atoms, the error introduced by the description of the electron-electron cusp using Gaussian basis sets at the CCSD level is negligible compared to the basis set incompleteness error. The system-, angle- and coupling-constant-averaged XC hole is calculated using the same approach and provides a benchmark against which the Perdew-Burke-Ernzerhof (PBE) and local density approximation (LDA) XC hole models are assessed., Comment: 16 pages, 7 figures

We developed a generalized model that considers light as energy contributed through the thermalization of excited carriers to generate excitation-intensity- and temperature-dependent phase diagrams. We find that the model replicates the light-induced phase segregation behavior of the MAPb(I,Br)3 system. From there, we sought to study how best to design new, stable, mixed-halide alloys. The resultant first-principles predictions show that the pseudo halide anion BF4- suppresses phase segregation in FA0.83Cs0.17Pb(I0.6Br0.4)3, resulting in enhanced operating stability. The findings reveal that photostability is linked with the structure and electronic properties of materials and may be overcome using informed alloying strategies.

Machine learning techniques have received growing attention as an alternative strategy for developing general-purpose density functional approximations, augmenting the historically successful approach of human designed functionals derived to obey mathematical constraints known for the exact exchange-correlation functional. More recently efforts have been made to reconcile the two techniques, integrating machine learning and exact-constraint satisfaction. We continue this integrated approach, designing a deep neural network that exploits the exact constraint and appropriate norm philosophy to deorbitalize the strongly constrained and appropriately normed SCAN functional. The deep neural network is trained to replicate the SCAN functional from only electron density and local derivative information, avoiding use of the orbital dependent kinetic energy density. The performance and transferability of the machine learned functional are demonstrated for molecular and periodic systems.

Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are discussed, highlighting the dual relationship between the ground-state energy and the universal density functional. Applications of the Lieb variation principle are reviewed, demonstrating how it may be utilized to calculate the Kohn-Sham potential of atoms and molecules, to study the exchange-correlation functional and the adiabatic connection by high-precision many-body methods, and to calculate the exchange-correlation hole and energy densities of atoms and molecules., Comment: Submitted to the book in honour of Elliott Lieb's 90th birthday, edited by Rupert L. Frank, Ari Laptev, Mathieu Lewin and Robert Seiringer, published by EMS Press

We investigate the Stark shift in Rydberg rubidium atoms through electromagnetically induced transparency for the measurement of direct current (dc) and 60~Hz alternating current (ac) voltages. This technique has direct applications to atom-based measurements of dc and ac voltage and the calibration of voltage instrumentation. We present experimental results for different atomic states that allow for dc and ac voltage measurements ranging from 0~V to 12~V. A Rydberg atom-based voltage standard could become an alternative calibration method with more favorable size, weight, power consumption, and cost compared to the more precise Josephson voltage standard. In this study, we also demonstrate how the voltage measurements can be utilized to determine the atomic polarizability for the Rydberg states. The Rydberg atom-based voltage measurement technology would become a complimentary method for dissemination of the voltage scale directly to the end user., Comment: 13 pages, 14 figures, 3 tables

We present a Gaussian-basis implementation of orbital-free density-functional theory (OF-DFT) in which the trust-region image method (TRIM) is used for optimization. This second-order optimization scheme has been constructed to provide benchmark all-electron results with very tight convergence of the particle number constraint, associated chemical potential and electron density. It is demonstrated that, by preserving the saddle-point nature of the optimization and simultaneously optimizing the density and chemical potential, an order of magnitude reduction in the number of iterations required for convergence is obtained. The approach is compared and contrasted with a new implementation of the nested optimization scheme put forward by Chan, Cohen and Handy. Our implementation allows for semi-local kinetic-energy (and exchange-correlation) functionals to be handled self-consistently in all-electron calculations. The all-electron Gaussian-basis setting for these calculations will enable direct comparison with a wide range of standard high-accuracy quantum-chemical methods as well as with Kohn-Sham density-functional theory. We expect that the present implementation will provide a useful tool for analysing the performance of approximate kinetic-energy functionals in finite systems.