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Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our…
In this paper the conformal Dirac operator on the sphere is defined to be operating on the space of square-integrable Clifford algebra-valued functions. The spinorial Laplacian of order d>0 is defined and used to establish Sobolev embedding…
In this paper we discuss the existence and regularity of solutions of strongly indefinite systems involving fractional elliptic operators on a smooth bounded domain $\Omega$ in $\R^n$.
Nonprehensile actions such as pushing are crucial for addressing multi-object rearrangement problems. Many traditional methods generate robot-centric actions, which differ from intuitive human strategies and are typically inefficient. To…
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems,…
The recently developed hypercomplex Kohn-Sham (HCKS) theory shows great potential to overcome the static/strong correlation issue in density functional theory (DFT), which highlights the necessity of further exploration of the HCKS theory…
Reduced density matrix functional theory (RDMFT) calculations are usually implemented in a decoupled manner, where the orbital and occupation optimizations are repeated alternately. Typically, orbital updates are performed using the unitary…
Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…
Despite the success of deep learning methods in quantum chemistry, their representational capacity is most often confined to neutral, closed-shell molecules. However, real-world chemical systems often exhibit complex characteristics,…
The strong boundary normalized condition of wavefunction for fully occupied semicore 3d orbitals leads the linear response DFT+U on such metal oxide to have an insurmountable obstacle in Hubbard U determination. We treated the orbital…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
The time-dependent multiconfiguration self-consistent-field method based on the occupation-restricted multiple active space model is proposed (TD-ORMAS) for multielectron dynamics in intense laser fields. Extending the previously proposed…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
An atom placed inside a cavity of finite dimension offers many interesting features, and thus has been a topic of great current activity. This work proposes a density functional approach to pursue both ground and excited states of a…
Accurate 3D reconstruction of vertebral anatomy from ultrasound is important for guiding minimally invasive spine interventions, but it remains challenging due to acoustic shadowing and view-dependent signal variations. We propose an…
Density Functional Theory's Kohn-Sham (KS) potential emerges as the minimizing effective potential in an unconstrained variational scheme that does not involve fixing the unknown single-electron density. The physical content behind the…
The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
In order to realize supersymmetric quantum mechanics methods on a four dimensional classical phase-space, the complexified Clifford algebra of this space is extended by deforming it with the Moyal star-product in composing the components of…