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Special solutions of the Hartree-Fock (HF) problem for Coulomb interacting electrons, being described by a simple model of the Cu-O planes in La2CuO4, are presented. One of the mean field states obtained, is able to predict some of the…
In this paper, we report on a correctly scaling novel coupled cluster singles and doubles (CCSD) implementation for arbitrary high-spin open-shell states. The chosen cluster operator is completely spin-free, i.e. employs spatial…
We present a configuration interaction method optimized for Fock-Darwin states of two-dimensional quantum dots with an axially symmetric, parabolic confinement potential subject to a perpendicular magnetic field. The optimization explicitly…
In this paper, we present the Reduced Order Hysteretic Flux (ROHF) model to describe the relationship between time-varying transport current and internal magnetic flux for composite superconductors. The ROHF model is parametrized using…
The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). Applying…
Designing robust algorithms for the optimal power flow (OPF) problem is critical for the control of large-scale power systems under uncertainty. The chance-constrained OPF (CCOPF) problem provides a natural formulation of the trade-off…
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…
In order to study light unstable nuclei systematically, we propose a new method ''AMD + Hartree-Fock''. This method introduces the concept of the single particle orbits into the usual AMD. Applying AMD + HF to Be isotopes, it is found that…
This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chance-constrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance…
We introduce the fermionized time-dependent Hartree-Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact…
We propose a new class of random feature methods for linearizing softmax and Gaussian kernels called hybrid random features (HRFs) that automatically adapt the quality of kernel estimation to provide most accurate approximation in the…
We present a thorough analysis of symmetry breaking observed in Hartree-Fock (HF) solutions of fullerenes C$_{60}$, C$_{36}$, and C$_{20}$ in order to characterize the nature of electron correlation in them. Our analysis is based on (1) the…
We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We…
Multiconfiguration Hartree-Fock (MCHF) and multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations are performed for the $2p^{5}~^{2}P^{o}$, $2p^4(^{3}P)3s~^{4}P$, $2p^4(^{3}P)3s~^{2}P$ and $2p^4(^{3}P)3p~^{4}S^o$ states of $^{19}$F~I to…
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies…
We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function $f$ over a convex set $K$ given by a separation oracle. Our method utilizes the Frank--Wolfe algorithm over the cone of valid…
Most {\em ab initio} calculations on fullerene molecules have been carried out based on the paradigm of the H\"uckel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even…
Fractional-spin errors are inherent in all current approximate density functionals, including Hartree-Fock theory, and their origin has been related to strong static correlation effects. The conventional way to encode fractional-spin…
In view of the difficulty in calculating the atomic structure parameters of high-$Z$ elements, the HFR (Hartree-Fock with relativistic corrections) theory in combination with the ridge regression (RR) algorithm rather than the Cowan code's…
The efficiency of the recently proposed iCIPT2 [iterative configuration interaction (iCI) with selection and second-order perturbation theory (PT2); J. Chem. Theory Comput. 16, 2296 (2020)] for strongly correlated electrons is further…