arXiv subjects

Tucker Allen

Publications and source records attributed to Tucker Allen.

13 recordsLinked to original sources

arXiv2026

Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space

We present an efficient mixed deterministic-stochastic approach for constructing the Coulomb operator in real space that preserves accuracy across the full spectral range. The dominant long-range components of the interaction are captured deterministically via a compact, low-rank approximation, constructed using Chebyshev-filtered subspace iteration, while the remaining spectral tail is treated using unbiased probing with a small number of stochastic vectors. The resulting operator is benchmarked within self-consistent field calculations for the extended Hubbard Hamiltonian on periodic, perturbed, and non-periodic three-dimensional lattices. We account for stochastic bias in observables by implementing a jackknife correction. The method systematically improves with deterministic rank and stochastic sample count, while substantially reducing the computational cost of constructing the Coulomb matrix.

physics.chem-ph↗

arXiv2026

Real-Time Approach to the Dynamical Bethe-Salpeter Equation for Finite Systems

We present a real-time linear-response approach to solving the dynamical Bethe-Salpeter equation (BSE). The polarization part of the screened interaction is obtained from time-dependent Hartree propagation of the one-particle density matrix within an orbital basis-set representation. The frequency convolution defining the dynamical kernel is evaluated as a product in time, avoiding numerical integration and storage of the full screened Coulomb operator. The resulting nonlinear eigenvalue problem is then solved directly, going beyond the static screening approximation with full-frequency dependence in the screened interaction. While the deterministic scaling remains $\mathcal{O}(N^6)$, the time propagation formulation is readily compatible with grid-based stochastic sampling methods, which will open the possibility for dynamical BSE calculations of very large systems.

physics.chem-ph↗

arXiv2026

Stochastic GW with the Orthogonalized Projector Augmented Wave Method

We introduce stochastic GW with the orthogonalized projector augmented-wave method (OPAW-sGW). This implementation enables accurate quasiparticle band gaps on significantly coarser real-space grids than norm-conserving pseudopotential sGW (NCPP-sGW). The orthogonalized PAW representation preserves the formal all-electron character and enables stochastic sampling of the Green's function and screened Coulomb interaction.

physics.chem-ph↗

arXiv2026

Environment-Induced Exciton Renormalization in the Photosystem II Reaction Center

Protein electrostatics tune excitation energies in the Photosystem II reaction center (PSII-RC), yet a fully quantum-mechanical many-body description of how the surrounding protein environment renormalizes excitons has remained computationally inaccessible. The Bethe-Salpeter equation (BSE) within many-body perturbation theory accurately describes excitonic physics through an explicit electron-hole interaction, but is prohibitively expensive for systems containing thousands of valence electrons. Here, we show that for sufficiently large systems the BSE becomes simpler to solve when treated with modern stochastic sampling techniques, as atomistic interactions self-average. In this regime, the effective electron-hole interaction mediated by the environment is governed by collective $k$-dependent polarization. These insights enable an ab initio study of the PSII-RC in which all six chlorins forming the hexameric dye core are treated explicitly together with a roughly seven Angstrom local protein environment. We directly compare the low-lying optical excitations of the isolated chromophore hexamer (1276 valence electrons) and the protein-dye cluster (3238 valence electrons). For $Q_y$ excitations near 680 nm, inclusion of the protein environment induces polarization-dependent energy shifts, redistributes spectral weight, and alters exciton delocalization and pigment character. Lateral and transverse asymmetries in the low-lying excited states are captured at the BSE level of theory. These results establish that we now have the tools for many-body calculations of biological nanostructures.

physics.chem-ph↗

arXiv2026

StochasticGW-GPU: rapid quasi-particle energies for molecules beyond 10000 atoms

$\mathtt{StochasticGW}$ is a code for computing accurate Quasi-Particle (QP) energies of molecules and material systems in the GW approximation. $\mathtt{StochasticGW}$ utilizes the stochastic Resolution of the Identity (sROI) technique to enable a massively-parallel implementation with computational costs that scale semi-linearly with system size, allowing the method to access systems with tens of thousands of electrons. We introduce a new implementation, $\mathtt{StochasticGW-GPU}$, for which the main bottleneck steps have been ported to GPUs and which gives substantial performance improvements over previous versions of the code. We showcase the new code by computing band gaps of hydrogenated silicon clusters ($\textrm{S}\textrm{i}_{\textrm{x}}\textrm{H}_{\textrm{y}}$) containing up to 10001 atoms and 35144 electrons, and we obtain individual QP energies with a statistical precision of better than $\pm0.03$ eV with times-to-solution on the order of minutes.

physics.chem-ph↗

arXiv2025

Mixed Planewave and Localized Orbital Basis for Sparse-Stochastic Hybrid TDDFT

We present a mixed basis-set approach to obtain optical absorption spectra within a generalized Kohn-Sham time-dependent density functional theory framework. All occupied valence molecular orbitals (MOs) are expanded in a plane-wave (PW) basis, while unoccupied MOs are derived primarily from localized atomic basis functions. The method accelerates spectral convergence when compared to fully PW-based simulations, with a $2-3$ fold reduction in the number of unoccupied MOs entering the Casida equation. The mixed-basis is placed on a common real-space grid, enabling our previously developed deterministic/sparse-stochastic evaluation of the exact exchange operator (J. Chem. Theory Comput. 2023, 19, 9239-9247). This chemically intuitive and computationally efficient approach is validated across various molecular systems, including $\pi$-conjugated polymethine dyes, aromatic hydrocarbons, and a chlorophyll monomer.

physics.chem-ph↗

arXiv2025

Parameterized Attenuated Exchange for Generalized TDHF@$v_W$ Applications

Building upon our previously developed time-dependent Hartree-Fock (TDHF)@$v_W$ method, based on many-body perturbation theory and specifically the Bethe-Salpeter Equation (BSE), we introduce a parameterization scheme for the attenuated exchange kernel, $v_W(|r - r'|)$. In the original method, $v_W$ was determined individually for each system via an efficient stochastic short-time TD Hartree propagation for the screened Coulomb interaction, $W(r,r')$. The new parameterization leverages photochemical similarities in exciton binding energies (or exchange interaction attenuation) among molecules with comparable static dielectric responses. We parameterize the inverse dielectric function using a low-order polynomial with error function apodization, calibrated on a few representative molecules, each with its own $v_W$. Using only 7 parameters, the parameterized $v_W$ is fully grid-independent and broadly applicable within a family of molecules. This enables TDHF@$v_W$ that retains BSE-level accuracy, achieving a mean absolute error of $\sim0.1$ eV compared to experimental optical gaps and representing a five- to ten-fold improvement over conventional TD density functional theory or TDHF while reducing the cost to that of standard TDHF.

physics.chem-ph↗

arXiv2025

Efficient plane-wave approach to generalized Kohn-Sham density-functional theory of solids with mixed deterministic/stochastic exchange

An efficient mixed deterministic/sparse-stochastic plane-wave approach is developed for bandstructure calculations of large supercell periodic generalized-Kohn-Sham density functional theory, for any hybrid-exchange density functional. The method works for very large elementary cells and supercells, and we benchmark it on covalently bonded solids and molecular crystals with nonbonded interactions, for supercells of up to 33,000 atoms. Memory and CPU requirements scale with supercell size quasi-linearly.

cond-mat.mtrl-sci↗

arXiv2024

No more gap-shifting: Stochastic many-body-theory based TDHF for accurate theory of polymethine cyanine dyes

We introduce an individually fitted screened-exchange interaction for the time-dependent Hartree-Fock (TDHF) method and show that it resolves the missing binding energies in polymethine organic dye molecules compared to time-dependent density functional theory (TDDFT). The interaction kernel, which can be thought as a dielectric function, is generated by stochastic fitting to the screened-Coulomb interaction of many-body perturbation theory (MBPT), specific to each system. We test our method on the flavylium (Flav) and indocyanine green (ICG) dye families with a modifiable length of the polymethine bridge, leading to excitations ranging from the visible to short-wave infrared (SWIR). Our approach validates earlier observations on the importance of inclusion of medium range exchange for the exciton binding energy. Our resulting method, TDHF@$v_W$, also achieves a mean absolute error on par with MBPT at a computational cost on par with local-functional TDDFT.

physics.chem-ph↗

arXiv2024

GW with hybrid functionals for large molecular systems

A low-cost approach for stochastically sampling static exchange during TDHF-type propagation is presented. This enables the use of an excellent hybrid DFT starting point for stochastic GW quasiparticle energy calculations. Generalized Kohn-Sham molecular orbitals and energies, rather than those of a local-DFT calculation, are used for building the Green's function and effective Coulomb interaction. The use of an optimally tuned hybrid diminishes the starting point dependency in one-shot stochastic GW, effectively avoiding the need for self-consistent GW iterations.

physics.chem-ph↗

arXiv2024

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid TDDFT Calculations

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state hybrid DFT (ngH-DFT) to calculate absorption spectra within linear-response time-dependent Generalized Kohn-Sham DFT (LR-GKS-TDDFT), for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

physics.chem-ph↗

arXiv2023

Deterministic/Fragmented-Stochastic Exchange for Large Scale Hybrid DFT Calculations

We develop an efficient approach to evaluate range-separated exact exchange for grid or plane-wave based representations within the Generalized Kohn-Sham DFT (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long wavelength (low-$k$) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-$k$ part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1,320 electrons.

physics.chem-ph↗

arXiv2023

Optimized Attenuated Interaction: Enabling Stochastic Bethe-Salpeter Spectra for Large Systems

We develop an improved stochastic formalism for the Bethe-Salpeter equation, based on an exact separation of the effective-interaction $W$ to two parts, $W=(W-v_W)+v_W$ where the latter is formally any translationally-invariant interaction $v_W(r-r')$. When optimizing the fit of $v_W$ exchange kernel to $W$, by using a stochastic sampling of $W$, the difference $W-v_W$ becomes quite small. Then, in the main BSE routine, this small difference is stochastically sampled. The number of stochastic samples needed for an accurate spectrum is then largely independent of system size. While the method is formally cubic in scaling, the scaling prefactor is small due to the constant number of stochastic orbitals needed for sampling $W$.

physics.chem-ph↗