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Communications on quantum similarity (2): A geometric discussion on holographic electron density theorem and confined quantum similarity measures
ArticleAbstract: The so-called holographic electron density theorem (HEDT) is analyzed from an algebraic perspective,Palabras claves:Atomic shell approximation (ASA), Confined QSM, Electronic density functions (DF), General Taylor series expansion (TSE) of DF, Holographic electron density theorem (HEDT), Quantum similarity measures (QSM)Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusCommunications on quantum similarity, part 3: A geometric-quantum similarity molecular superposition algorithm
ArticleAbstract: This work describes a new procedure to obtain optimal molecular superposition based on quantum similPalabras claves:Carbó QS index, geometric QS MS algorithm, inward functions of QS matrices, Kruskal trees, molecular superposition (MS), QS Aufbau principle, QS integrals, QS matrices, quantum similarity (QS), restricted elementary Jacobi rotationsAutores:Besalu E., Mercado L., Ramón Carbö-D̈orcaFuentes:scopusA postulate involving quantum mechanical momentum in position space, density function expression of the kinetic energy and Heisenberg's uncertainty relation
ArticleAbstract: A postulate is enunciated involving the construction of the quantum mechanical linear momentum vectoPalabras claves:Atomic shell approximation density functions, Gaussian model density functions, Heisenberg's uncertainty, Kinetic energy, LCAO MO density functions, Momentum operator in position spaceAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusExtended Sobolev and Hilbert spaces and approximate stationary solutions for electronic systems within the non-linear Schrödinger equation
ArticleAbstract: The definition of Sobolev spaces, which has already been shown to be a convenient way to set up thePalabras claves:Extended Hilbert spaces, Kinetic energy distribution, N-electron wavefunctions, Nested sums formalism, Non-linear Schrödinger equation, Quantum self-similarity measures, Sobolev spacesAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusNested summation symbols and perturbation theory
ArticleAbstract: A new mathematical concept, the nested summation symbol (NSS) has been developed. This concept is atPalabras claves:Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusMathematical aspects of the LCAO MO first order density function (4): A discussion on the connection of Taylor series expansion of electronic density (TSED) function with the holographic electron density theorem (HEDT) and the Hohenberg-Kohn theorem (HKT)
ArticleAbstract: Taylor series expansion of electronic density (TSED) functions are set up in order to propose them aPalabras claves:Hohenberg-Kohn theorem (HKT), Holographic electron density theorem (HEDT), Taylor series of electronic density (TSED)Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusShells, point cloud huts, generalized scalar products, cosines and similarity tensor representations in vector semispaces
ArticleAbstract: This study provides an as complete as possible set of precise definitions, within the mathematics dePalabras claves:Generalized cosine of a point cloud, Generalized scalar products, Point cloud huts, Point clouds, Quantum Similarity, Shells in vector semispaces, Tensorial representation of molecules, vector semispacesAutores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusRayleigh-Schrödinger perturbation theory in matrix form
ArticleAbstract:Palabras claves:Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopusRayleigh-schrödinger perturbation theory: Practical implementation of matrix and vector formalisms and description of an heuristic sufficiency convergence criterion
ArticleAbstract: Starting from previous work, where Rayleigh-Schrödinger perturbation theory has been reformulated inPalabras claves:Autores:Besalu E., Ramón Carbö-D̈orcaFuentes:scopus