Orbital nodes
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Understanding Orbital Nodes: Insights from Recent Research
Symmetry and Anomalies in GPS Orbit Ascending Nodes
The configuration of GPS satellite orbits is a critical aspect of the system's functionality. Theoretical models suggest that GPS orbits should be parallel and share six ascending nodes. However, real-world perturbations and system updates prevent this ideal state from occurring. A novel method has been developed to assess the configuration of orbit ascending nodes compared to the nominal constellation state. This method, which uses robust estimation and least-squares methods, has revealed significant anomalies in the symmetry and trends of satellite orbit separations over time1.
Nodal Topology in Superconducting Monolayer FeSe
In the realm of superconductivity, the study of nodal topology in monolayer FeSe on SrTiO3 has provided intriguing insights. The evolution from a nodeless $d$-wave state to a nodal state is influenced by the orbital content of the superconducting degrees of freedom. Two $d$-wave solutions, orbitally trivial and orbitally nontrivial, exhibit different momentum space distributions of positive and negative charges. This difference affects the evolution of nodes as they transition to a nodeless state, with distinct Andreev flat band spectra at the edge for each case2.
Photoelectron Momentum Distributions and Orbital Angular Nodes
Investigations into the imprint of orbital angular nodes in photoelectron momentum distributions have shown that circular polarization provides the clearest signatures of orbital nodes. This conclusion was reached by solving the three-dimensional time-dependent Schrödinger equation and analyzing the photoelectron momentum distributions of an aligned atomic p-type orbital ionized by an intense elliptically polarized laser pulse. The study highlights the role of light ellipticity and the alignment angle of the major polarization axis relative to the probed orbital3.
Nodes in Hartree-Fock Wavefunctions
Hartree-Fock (HF) wavefunctions and orbitals are known to feature nodes and nodal artifacts due to theoretical and computational limitations. Detailed studies on the beryllium atom have shown that these nodal artifacts persist even in high-precision calculations. This has significant implications for Quantum Monte Carlo studies and the numerical investigation of fermion nodes4. Additionally, precise HF calculations for elements from He to Kr have identified nodes in the 1s atomic orbitals, attributed to exchange interactions between different orbitals. These findings confirm that such nodes are not artificial and persist despite increasing the expansion terms of the basis functions5.
Radial Nodes and Chemical Bonding
The role of radial nodes in atomic orbitals is crucial for understanding chemical bonding and periodic trends. The absence of a radial node in valence orbitals, particularly when a shell with angular quantum number l is occupied for the first time, has significant implications. For instance, the compact nature of the 2p shell influences hybridization, multiple bonding, and electronegativity. Similarly, the compact 3d shell in transition metals affects bond strength, color of complexes, and electron-correlation effects in bonding7.
Conclusion
The study of orbital nodes spans various fields, from satellite orbit configurations to superconductivity and atomic structure. Each area provides unique insights into the behavior and implications of nodes, whether in the context of GPS satellite anomalies, superconducting states, photoelectron distributions, or chemical bonding. Understanding these nodes is essential for advancing both theoretical models and practical applications across these diverse domains.
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Most relevant research papers on this topic
The Symmetry of GPS Orbit Ascending Nodes
This study presents a novel method to assess the configuration of GPS orbit ascending nodes compared to the nominal constellation state, detecting anomalies and providing information on satellite orbit separations and deviations from initial hexagonal GPS symmetry.
Nodal topology in d -wave superconducting monolayer FeSe
The evolution from a nodeless state to a nodal state in superconducting monolayer FeSe depends on the orbital content of the superconducting degrees of freedom, with orbitally trivial and orbitally nontrivial solutions exhibiting different topological winding numbers and Andreev flat band
Interrogation of orbital structure by elliptically polarized intense femtosecond laser pulses
Circular polarization provides the clearest imprints of orbital nodes in photoelectron momentum distributions, unaffected by pulse duration.
The nodes of Hartree-Fock wavefunctions and their orbitals
Nodal artefacts in Hartree-Fock wavefunctions and orbitals can occur even in high-precision calculations, impacting Quantum Monte Carlo studies and the numerical investigation of fermion nodes.
Nodes in Hartree-Fock 1s atomic orbitals caused by exchange interactions
The node in the Zn 1s orbital is not artificial and is caused by exchange interactions between 1s and (3s, 2p, 3p, 3d).
SNOD: a fast sampling method of exploring node orbit degrees for large graphs
Our SNOD method is several orders of magnitude faster than existing methods for accurately estimating node orbit degrees in large-scale graphs with millions of edges.
The role of radial nodes of atomic orbitals for chemical bonding and the periodic table
Radial nodes in atomic orbitals play a crucial role in chemical bonding and periodic trends, with their absence affecting bonding and the periodic table.
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Mega-LEO satellite constellations can enable equal access to computing by offloading computing tasks to orbital edge platforms, potentially leading to performance improvements and new challenges in design and setup.
Orbital branching
Orbital branching effectively reduces symmetry in integer programs, outperforming state-of-the-art commercial solvers and isomorphism pruning methods.
Highly CitedOrbital ordering in transition-metal spinels
Recent experimental activity on orbital ordering in transition-metal spinels reveals that geometrical frustration affects the metal's tendency to order in charge, magnetic, and orbital sectors.
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