Dealing with the exponential wall in electronic structure calculations

Peter Fulde; Hermann Stoll

doi:10.1063/1.4983207

Home/Archive/arXiv

arXiv · 1703.02572

Dealing with the exponential wall in electronic structure calculations

Peter Fulde·Hermann Stoll

View original source ↗Read source document ↗Export metadata ↓

Abstract

An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated at a much lower level than the former. This is the case in Density Matrix Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a $H_{10}$ ring these differences are analyzed with the help of the method of increments.

Explore related subjects

physics.chem-ph cond-mat.mtrl-sci

Keep this discovery

BibTeX RIS

Peter Fulde, Hermann Stoll. 2017-03-03. Dealing with the exponential wall in electronic structure calculations. https://doi.org/10.1063/1.4983207

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

KEEP EXPLORING

Related papers

arXiv2026

Breaking Water at Graphene Defects

Water dissociation at solid surfaces underpins processes ranging from corrosion and catalysis to electrochemistry and photovoltaics. Defects often serve as reactive sites for dissociation, yet how solvation influences water dissociation at such sites remains poorly understood. Here, we use state-of-the-art machine-learned interatomic potentials to explore water dissociation at defective graphene-water interfaces. We show that solvation qualitatively changes the reaction mechanism at a graphene single vacancy (SV), opening pathways that are absent for an isolated water molecule. Whereas the gas-phase process proceeds via a single concerted channel, the solvated SV splits water through two competing pathways: a basic route forming SV-H and OH-(aq), and an acidic route forming SV-OH and H3O+(aq). These lower-barrier pathways produce distinct chemisorbed intermediates that enhance graphene-water adsorption. Accordingly, even a simple carbon vacancy gives rise to unexpectedly rich interfacial chemistry, coupling surface chemistry to interfacial charge and wettability, with implications for carbon functionalization and nanofluidic transport.

physics.chem-ph↗

arXiv2026

Comprehensive Study of L-Menthol and Octanoic Acid as a Hydrophobic Eutectic Solvent

Hydrophobic eutectic solvents (HES) based on natural compounds represent promising green alternatives to conventional solvents. In this work, we investigate the physicochemical, structural, and dynamical properties of an ES formed by L-menthol and octanoic acid using a combined experimental and molecular dynamics simulation approach. Five compositions with molar ratios from 1:3 to 3:1 were studied with molecular dynamics simulation in the temperature range 15 degrees C to 35 degrees C. Experimental measurements of density and viscosity in the temperature range from 5 degrees C to 35 degrees C were complemented with results obtained from MD simulations employing the OPLS force field. Structural analyses based on radial distribution functions and Kirkwood-Buff integrals reveal that the dominant interactions in the mixture are hydrogen bonds between L-menthol and octanoic acid molecules. Dynamic properties, including self-diffusion coefficients and hydrogen-bond lifetimes, indicate that intermolecular hydrogen bonds between the two components are stronger and longer-lived than bonds between identical species. These findings provide molecular-level insight into the structure and transport properties of menthol-based ESs relevant for green solvent applications.

physics.chem-ph↗

arXiv2026

More is not always better: Dissociative photoionization limits the EUV absorbing photacid generator pentafluorophenyl triflate in photolithography

Pentafluorophenyl triflate has been explored as a highly absorbing neutral photoacid generator (PAG) candidate for next generation chemically amplified resists used in extreme ultraviolet (EUV) lithography. Although increased fluorination enhances EUV absorption, this study demonstrates that such an approach does not necessarily improve photoacid generation efficiency. Using photoelectron-photoion coincidence (PEPICO) spectroscopy at the 92 eV photon energy of the EUV scanners in combination with quantum chemical calculations, the dissociative photoionization of pentafluorophenyl triflate was systematically investigated. The photoionization mass spectrum reveals extensive fragmentation, with the parent ion contributing only 3.1 % of the total signal and CF$_3^+$ representing the dominant product ion. Computed appearance energies align well with experimental trends and support a sequential fragmentation pathway involving loss of SO$_2$, CF$_3$, and CO. Crucially, none of the major dissociation channels yield precursors capable of forming triflic acid, the strong photoacid required for efficient deprotection reactions in chemically amplified resists. Combined with previous dissociative electron attachment studies indicating similarly unfavorable fragmentation, the results demonstrate that despite its high EUV absorption cross section, pentafluorophenyl triflate is unsuitable as a PAG for EUV lithography. The findings highlight the importance of understanding fundamental photoionization and electron interaction mechanisms to guide the rational design of next generation high performance EUV photoresists.

physics.chem-ph↗