Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2211.00173

Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in \emph{ab initio} Systems

Ke Liao·Huanchen Zhai·Evelin Martine Christlmaier·Thomas Schraivogel·Pablo López Ríos·Daniel Kats·Ali Alavi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians, and show applications in \emph{ab initio} molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron-electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by some recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem; but this is currently limited to treating the ground state, and has lower efficiency than the time-independent DMRG (TI-DMRG), due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. Accelerated basis set convergence rate is also observed, as expected, within the TC framework.

Explore related subjects

physics.chem-phcond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ke Liao, Huanchen Zhai, Evelin Martine Christlmaier, Thomas Schraivogel, Pablo López Ríos, Daniel Kats, Ali Alavi. 2022-11-03. Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in \emph{ab initio} Systems. https://arxiv.org/abs/2211.00173

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↗