arXiv subjects

Rasmus Vikhamar-Sandberg

Publications and source records attributed to Rasmus Vikhamar-Sandberg.

3 recordsLinked to original sources

arXiv2026

Newton optimization for the Multiconfiguration Self Consistent Field method at the basis set limit: closed-shell two-electron systems

The multiconfiguration self-consistent field (MCSCF) method is revisited with a specific focus on two-electron systems for simplicity. The wave function is represented as a linear combination of Slater determinants. Both the orbitals and the coefficients of this configuration interaction expansion are optimized according to the variational principle within the Lagrangian formalism, using a Newton optimization scheme. This reduces the MCSCF problem to solving a particular differential Newton system, which can be discretized with multiwavelets and solved iteratively.

physics.chem-ph↗

arXiv2025

Efficient Boys function evaluation using minimax approximation

We present an algorithm for efficient evaluation of Boys functions $F_0,\dots,F_{k_\mathrm{max}}$ tailored to modern computing architectures, in particular graphical processing units (GPUs), where maximum throughput is high and data movement is costly. The method combines rational minimax approximations with upward and downward recurrence relations. The non-negative real axis is partitioned into three regions, $[0,\infty\rangle = A\cup B\cup C$, where regions $A$ and $B$ are treated using rational minimax approximations and region $C$ by an asymptotic approximation. This formulation avoids lookup tables and irregular memory access, making it well suited hardware with high maximum throughput and low latency. The rational minimax coefficients are generated using the rational Remez algorithm. For a target maximum absolute error of $\varepsilon_\mathrm{tol} = 5\cdot10^{-14}$, the corresponding approximation regions and coefficients for Boys functions $F_0,\dots,F_{32}$ are provided in the appendix.

math.NA↗

arXiv2025

X2C Hamiltonian Models in ReSpect: Bridging Accuracy and Efficiency

Since its inception, the ReSpect program has been evolving to provide powerful tools for simulating spectroscopic processes and exploring emerging research areas, all while incorporating relativistic effects, particularly spin-orbit interactions, in a fully variational manner. Recent developments have focused on exact two-component (X2C) Hamiltonian models that go beyond the standard one-electron X2C approach by incorporating two-electron picture-change corrections. This paper presents the theoretical foundations of two distinct atomic mean-field X2C models, amfX2C and extended eamfX2C, which offer computationally efficient and accurate alternatives to fully relativistic four-component methods. These models enable simulations of complex phenomena, such as time-resolved pump-probe spectroscopies and cavity-modified molecular properties, which would otherwise be computationally prohibitive. ReSpect continues to evolve, providing state-of-the-art quantum chemical methods and post-processing tools, all available free of charge through our website, www.respectprogram.org, to support researchers exploring relativistic effects across various scientific disciplines.

physics.chem-ph↗