Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/9711020

The hydrogen molecule in magnetic fields: The ground states of the Sigma manifold of the parallel configuration

T. Detmer·P. Schmelcher·F. K. Diakonos·L. S. Cederbaum
View original source ↗Read source document ↗Export metadata ↓

Abstract

The electronic structure of the hydrogen molecule is investigated for the parallel configuration. The ground states of the Sigma manifold are studied for ungerade and gerade parity as well as singlet and triplet states covering a broad regime of field strengths from B = 0 up to B = 100a.u. A variety of interesting phenomena can be observed. For the ^1Sigma_g state we found a monotonous decrease of the equilibrium distance and a simultaneously increase of the dissociation energy with growing magnetic field strength. The ^3Σ_g state is shown to develop an additional minimum which has no counterpart in field-free space. The ^1Σ_u state shows a monotonous increase in the dissociation energy with first increasing and than decreasing internuclear distance of the minimum. For this state the dissociation channel is H_2 to H^- + H^+ for magnetic-field strengths B greater than 20a.u. due to the existence of strongly bound H^- states in strong magnetic fields. The repulsive ^3Σ_u state possesses a very shallow van der Waals minimum for magnetic-field strengths smaller than 1.0a.u. within the numerical accuracy of our calculations. The ^1Σ_g and ^3Σ_u states cross as a function of B and the ^3Σ_u state, which is an unbound state, becomes the ground state of the hydrogen molecule in magnetic fields B greater than 0.2a.u. This is of particular interest for the existence of molecular hydrogen in the vicinity of white dwarfs. In superstrong fields the ground state is again a strongly bound state, the ^3Π_u state.

Explore related subjects

physics.chem-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. Detmer, P. Schmelcher, F. K. Diakonos, L. S. Cederbaum. 1997-11-20. The hydrogen molecule in magnetic fields: The ground states of the Sigma manifold of the parallel configuration. https://doi.org/10.1103/physreva.56.1825

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Global approximations to the error function of real argument for vectorized computation

The error function of real argument can be approximated to a given uniform relative accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or also using the exponential function. The coefficients have been tabulated for up to 128-bit precision. Tests of a computer code implementation using the standard single- and double-precision floating-point arithmetic show good performance and vectorizability. Approximations to the complementary error function have also been found, including those where only additions, multiplications, and one division are needed to reach a uniform absolute accuracy.

physics.chem-ph↗
arXiv2026

From Heuristics to Machine Learning: The Performance Ceiling for Single-Ion Magnets and Its Electronic Origin

Machine learning (ML) is expected to speed up the discovery of single-ion magnets (SIMs), but does the structural information available before synthesis allow such predictions? For 1215 lanthanide complexes from the SIMDAVIS 1.2.1 database we compared three increasing levels of structural description: tabular features of the coordination site, continuous symmetry measures of the coordination polyhedron, and the complete 3D arrangement of atoms. All three converge to an accuracy near 76%, only slightly above the 71% of the single rule "predict SIM for Dy3+". To explain the failures, we combined multireference ab initio calculations with an inspection of the structures behind the high-confidence errors. The SIMs missed by the geometric models are field-induced relaxers whose ground Kramers doublets are prone to tunnelling, a property invisible to geometric descriptors. Many false positives contain several lanthanide centers or radicals, so their relaxation is collective and outside the single-ion picture. The electronic-structure and connectivity information needed to identify SIMs is therefore not accessible to geometric methods alone. Geometric models remain useful: restricting the screening to compounds with high prediction confidence raises the accuracy to 88% while retaining 48% of the dataset. Building on the analysis of the failures, we propose a strategy that combines simple filters for nuclearity and for radicals with ligand-field descriptors from ab initio calculations.

physics.chem-ph↗
arXiv2026

Composition-Dependent Self-Diffusion Coefficients in Liquid Mixtures from Hybrid Machine Learning

Self-diffusion coefficients are key descriptors of molecular mobility, yet experimental data remain scarce, highlighting the need for reliable prediction methods. In previous work, we introduced the hybrid Enhanced Stokes-Einstein (ESE) model, which advanced the state of the art in the physically consistent prediction of self-diffusion coefficients of solutes at infinite dilution in pure solvents by integrating the Stokes-Einstein equation with machine learning (ML). Here, we extend this approach to concentration-dependent self-diffusion coefficients and multicomponent solvents with HADES. This hybrid architecture leverages a deep-set neural network to connect pure-component and mixture prediction within a single framework. HADES predicts self-diffusion coefficients in liquid mixtures with any number of components at any composition and temperature. The only required inputs are SMILES-encoded molecular structures of the components and the pure-component viscosities, making the method broadly applicable. Trained and evaluated on a comprehensive dataset of 2526 data points for 600 systems, HADES significantly outperforms benchmark prediction methods. The trained model and its source code are fully disclosed, and the application is available via an interactive website https://ml-prop.mv.rptu.de/.

physics.chem-ph↗