Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1802.01058

Tangent space formulation of the Multi-Configuration Time-Dependent Hartree equations of motion: The projector-splitting algorithm revisited

Matteo Bonfanti·Irene Burghardt
View original source ↗Read source document ↗Export metadata ↓

Abstract

The derivation of the time-dependent variational equations of the Multi-Configuration Time-Dependent Hartree (MCTDH) method for high-dimensional quantum propagation is revisited from the perspective of tangent space projection methods. In this context, we focus on a recently introduced algorithm [C. Lubich, Appl. Math. Res. eXpress 2015, 311 (2015), B. Kloss et al., J. Chem. Phys. 146, 174107 (2017)] for the integration of the MCTDH equations, which relies on a suitable splitting of the tangent space projection. The new integrator circumvents the direct inversion of reduced density matrices that appears in the standard method, by employing an auxiliary set of non-orthogonal single-particle functions. Here, we formulate the new algorithm and the underlying alternative form of the MCTDH equations in conventional chemical physics notation, in a complementary fashion to the tensor formalism used in the original work. Further, key features of the integration scheme are highlighted.

Explore related subjects

physics.chem-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Matteo Bonfanti, Irene Burghardt. 2018-09-25. Tangent space formulation of the Multi-Configuration Time-Dependent Hartree equations of motion: The projector-splitting algorithm revisited. https://doi.org/10.1016/j.chemphys.2018.05.029

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

KEEP EXPLORING

Related papers

arXiv2026

Charge Transfer with a Spin. I: A Variational Constrained-CASSCF Framework for Investigating Charge Transfer in the Presence of Spin-Orbit Coupling

Charge transfer in open-shell molecular systems can involve a delicate interplay between charge localization, orbital relaxation, and spin-orbit coupling (SOC), particularly near ground-excited state crossings. Here, we introduce a very inexpensive variational framework for treating these effects in odd-electron systems by extending the electron/hole-transfer Dynamically-weighted State-Averaged Constrained CASSCF (eDSC/hDSC) method to include SOC. Our method incorporates the SOC Hamiltonian directly into the variational orbital optimization through complex-valued spinor orbitals, allowing orbital and spin degrees of freedom to relax self-consistently while preserving the time-reversal symmetry of doublet states. The method achieves smooth potential energy surfaces and rapid self-consistent field (SCF) convergence; moreover, from physically small to artificially large SOC strengths, the calculation can be converged to very tight thresholds across the whole potential energy surface. While the results presented here are for systems with two charge centers, as shown in the appendix, the theory is quite general and can be adapted to either a system of $N$ charge centers or a metal-molecule surface with a continuum of states, so that charge transport (and not just charge transfer) can also be studied. The approach therefore provides a route towards ab initio studies of spin-dependent charge transfer and charge transport in molecular systems with nontrivial spin degrees of freedom.

physics.chem-ph↗
arXiv2026

Charge Transfer with a Spin. II: A Framework for Diabatization which Localizes Charge and Spin

We investigate a diabatization procedure that localizes charges (in real space) and localizes spins (in spin space) for open-shell systems that exhibit charge transfer in the presence of spin-orbit coupling. The procedure is applied to a two-state crossing between pairs of Kramers-restricted doublet states (which can also be considered effectively a four-state crossing). To generate the relevant diabatic states, we employ a two-step optimization over complex-unitary rotations that sequentially maximizes dipole and spin moments through iterative Jacobi sweeps; the resulting update rules are effectively equivalent to those of approximate joint diagonalization (AJD) applied to charge and spin. The method converges rapidly and yields smooth diabatic potential energy surfaces that preserve dipole and spin properties (e.g., a smoothly varying spin quantization axis) along the reaction coordinate while maintaining time-reversal symmetry.

physics.chem-ph↗
arXiv2026

Fixed-Dimensional Latent Flow for Generating Variable-Size 3D Molecules

Molecular size is coupled to composition, structure, and function, yet most 3D molecular generators require a predefined atom count. We introduce Equivariant-Free Transformer-Autoencoded Latent Flow Matching, a two-stage framework that samples a fixed-dimensional latent vector using flow matching and uses an autoregressive Transformer to determine molecular size, atom types, coordinates, and chemical attributes. Canonical atom ordering and rigid-pose alignment enable Transformers without equivariant layers, while decoded attributes guide bond reconstruction. On PCQM4Mv2, unconditional generation yields 87.9\% unique, novel molecules passing sanitization and PoseBusters checks, exceeding baselines with lower end-to-end training and sampling time and higher end-to-end throughput. Across ten target HOMO-LUMO gaps, internal ranking retains 30\% of screened candidates and increases the density functional theory-verified hit rate within 0.1 eV from 25.0\% to 52.4\%, while largely preserving novelty and diversity. These results demonstrate fixed-dimensional latent generation with autoregressive decoding as a practical approach to molecular design without prespecifying size.

physics.chem-ph↗