相关论文: Hilbert-space partitioning of the molecular one-el…

For the Hirshfeld-I atom-in-molecule model, associated single-atom energies and interaction energies at the Hartree-Fock level are determined efficiently in one-electron Hilbert space. In contrast to most other approaches, the energy terms…

A double-index atomic partitioning of the molecular first-order density matrix is proposed. Contributions diagonal in the atomic indices correspond to atomic density matrices, whereas off-diagonal contributions carry information about the…

This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree--Fock…

The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…

The construction of the Extended Hilbert Space (EHS) is presented in the form of a direct sum of the spaces of vectors of finite and infinite norms as the main space in the mathematical formalism of quantum mechanics of a multielectron…

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors,…

We develop a model of molecular binding based on the Bohr-Sommerfeld description of atoms together with a constraint taken from conventional quantum mechanics. The model can describe the binding energy curves of H2, H3 and other molecules…

Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinite-dimensional Hubbard model is developed on the basis of a…

Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…

We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately…

The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric…

The charge density and pair correlation function of three interacting electrons confined within a two-dimensional disc-like hard wall quantum dot are calculated by full numerical diagonalization of the Hamiltonian. The formation of a…

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…

We theoretically study the Hilbert space structure of two neighbouring P donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their…

Donor-based quantum devices in silicon are attractive platforms for universal quantum computing and analog quantum simulations. The nearly-atomic precision in dopant placement promises great control over the quantum properties of these…

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

New ways to treat electron correlation in electronic structure problems are discussed in the context of many-electron theory. The present work focuses primarily on static correlation. In related work, a method for including dynamical…