Experimental and computational results about the structure, dynamics, and rovibrational spectra of protonated methane have challenged a considerable number of traditional chemical concepts. Hereby theoretical and computational results are provided about the dynamical structure of CH. It is shown that the ground vibrational state investigated thus far by computations, forbidden by nuclear-spin statistics, has a structure similar to the first allowed vibrational state and, in fact, the structures of all vibrational states significantly below 200 cm are highly similar. Spatial delocalization of the nuclei, determined by nuclear densities computed from accurate variational vibrational wave functions, turns out to be limited when viewed in the body-fixed frame, confirming that the effective structure of CH is well described as a CH tripod with a H unit on top of it. The interesting and unusual qualitative aspects of the sophisticated state-dependent variational results receive full explanation via simple quantum-graph models.
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http://dx.doi.org/10.1021/acs.jctc.2c00991 | DOI Listing |
Phys Rev E
March 2024
Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds.
View Article and Find Full Text PDFIEEE Trans Neural Netw Learn Syst
April 2024
This article proposes a quantum spatial graph convolutional neural network (QSGCN) model that is implementable on quantum circuits, providing a novel avenue to processing non-Euclidean type data based on the state-of-the-art parameterized quantum circuit (PQC) computing platforms. Four basic blocks are constructed to formulate the whole QSGCN model, including the quantum encoding, the quantum graph convolutional layer, the quantum graph pooling layer, and the network optimization. In particular, the trainability of the QSGCN model is analyzed through discussions on the barren plateau phenomenon.
View Article and Find Full Text PDFPhys Rev E
August 2023
Department of Physics, Astronomy, and Geology, Berry College, Mount Berry, Georgia 30149-5004, USA.
Statistical properties of the sequence of energy eigenvalues in a quantum system are related to the classical dynamics of the system. Sequences of energy levels for classically regular systems generally exhibit Poisson statistics, while those for classically chaotic systems exhibit random matrix statistics. For many systems the classical dynamics can change from regular to chaotic as the result of changing a system parameter and the quantum system shows a corresponding change in its eigenvalue statistics.
View Article and Find Full Text PDFMaterials (Basel)
June 2023
School of Electrical Engineering & ITRC of Quantum Computing for AI, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.
Inspired by classical graph neural networks, we discuss a novel quantum graph neural network (QGNN) model to predict the chemical and physical properties of molecules and materials. QGNNs were investigated to predict the energy gap between the highest occupied and lowest unoccupied molecular orbitals of small organic molecules. The models utilize the equivariantly diagonalizable unitary quantum graph circuit (EDU-QGC) framework to allow discrete link features and minimize quantum circuit embedding.
View Article and Find Full Text PDFJ Chem Theory Comput
January 2023
Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary.
Experimental and computational results about the structure, dynamics, and rovibrational spectra of protonated methane have challenged a considerable number of traditional chemical concepts. Hereby theoretical and computational results are provided about the dynamical structure of CH. It is shown that the ground vibrational state investigated thus far by computations, forbidden by nuclear-spin statistics, has a structure similar to the first allowed vibrational state and, in fact, the structures of all vibrational states significantly below 200 cm are highly similar.
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