arXiv subjects

Ankit Mahajan

Publications and source records attributed to Ankit Mahajan.

At least 19 recordsLinked to original sources

arXiv2026

Size Extensive Auxiliary-Field Quantum Monte Carlo with Perturbative Coupled Cluster Trial Wavefunction

In this work, we develop a size extensive Auxiliary-Field Quantum Monte Carlo (AFQMC) approach that scales as $O(N^5)$ for local energy evaluation by treating the Coupled Cluster Singles and Doubles (CCSD) trial wavefunctions perturbatively. Comprehensive numerical examinations, spanning from main-group molecules to $3d$ transition metal complexes, demonstrate that this perturbative treatment introduces negligible bias. For small systems, our method achieves an accuracy and level of noise comparable to AFQMC with configuration interaction singles and doubles (CISD) trial wavefunctions while outperforming CCSD(T). This size extensivity offers a decisive advantage for large systems, as suggested by the ground state energies of non-interacting monomers and one-dimensional atomic chains. Finally, the numerical simulations of the uniform electron gas (UEG) provide evidence that, unlike the CCSD(T) method, our new approach does not suffer from infrared divergence in the thermodynamic limit (TDL).

physics.chem-ph↗

arXiv2026

Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo

We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and $U$ values and show that symmetry-adapted trial wave functions substantially improve quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations $\lesssim 1\%$ from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large $U$ regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.

cond-mat.str-el↗

arXiv2026

The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

physics.chem-ph↗

arXiv2026

Nuclear gradients from auxiliary-field quantum Monte Carlo and their application in geometry optimization and transition state search

In this article, we present a method for computing accurate and scalable nuclear forces within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) framework. Our approach leverages automatic differentiation of the energy functional to obtain nuclear gradients at a computational cost comparable to that of energy evaluation. The accuracy of the method is validated against finite difference calculations, showing excellent agreement. We then explore several machine learning (ML) strategies for learning noisy AFQMC data. These ML potentials are subsequently used to perform geometry optimizations and nudged elastic band (NEB) calculations, successfully identifying the transition state of the formamide-formimidic acid tautomerization. The resulting transition state geometry and barrier heights are in close agreement with coupled-cluster reference values. This work paves the way for highly accurate geometry optimization, molecular dynamics, or reaction path calculations.

physics.chem-ph↗

arXiv2025

Fokker-Planck equation governing the distribution of walkers in AFQMC

Auxiliary-field quantum Monte Carlo (AFQMC) is typically formulated as an open-ended random walk in an overcomplete space of Slater determinants, implemented through a Langevin equation. However, the explicit form of the underlying Fokker-Planck equation governing the walker population distribution has remained unknown. In this paper, we derive the Fokker-Planck equation for AFQMC and propose a novel numerical scheme to solve it. The solution of the Fokker-Planck equation reveals the wavefunction actually sampled by the AFQMC algorithm. Interestingly, we find that even when the exact ground state is used as a guiding wavefunction in constrained path AFQMC, contrary to the common assumption, the wavefunction sampled by AFQMC is not exact. Beyond clarifying several fundamental aspects of AFQMC, the availability of a Fokker-Planck equation formulation opens new avenues for systematically improving its accuracy, which we outline in this paper.

physics.chem-ph↗

arXiv2025

Evaluating Multiconfigurational Trials for Accurate Phaseless Auxiliary-Field Quantum Monte Carlo on 3d Transition Metal Complexes

In this study, we evaluate multi-configurational trial wave function protocols for phaseless auxiliary field quantum Monte Carlo (ph-AFQMC) on transition metal containing systems. First, we benchmark vertical ionization potentials for 22 3d transition metal complexes against published high-accuracy ph-AFQMC values in a double zeta basis set. We then compute the vertical ionization potential for a set of six metallocenes using our best-performing protocol, alongside ph-AFQMC using a configuration interaction singles and doubles (CISD) trial state. We also analyze the performance of canonical coupled-cluster theory with singles, doubles and perturbative triples (CCSD(T)), as well as its local approximation using domain-based local pair natural orbitals (DLPNO-CCSD(T1)) using different reference orbitals. To reach the complete-basis-set (CBS) limit, we examine several extrapolation schemes and report CBS-limit ph-AFQMC and CCSD(T) values alongside experimental results. We find that ph-AFQMC with the best-performing trial in a triple zeta basis, followed by CBS correction from DLPNO-CCSD(T1) with unrestricted B3LYP reference orbitals, yields small deviations from experiment at modest cost. Using a CISD trial state in ph-AFQMC gives the closest agreement with experiment (errors < 2 kcal/mol), albeit with lower scalability.

physics.chem-ph↗

arXiv2025

Excited states in auxiliary field quantum Monte Carlo

We systematically investigate the calculation of excited states in quantum chemistry using auxiliary field quantum Monte Carlo (AFQMC). Symmetry allows targeting of the lowest triplet excited states in AFQMC based on restricted open-shell determinants, effectively as a ground-state calculation. For open-shell singlet states, excited state calculations can be stabilized with the appropriate trial states, but their quality can have a larger effect on the accuracy in AFQMC. We find that active space-based configuration interaction trial states are often not sufficient to obtain accurate results. We instead use truncated equation of motion coupled cluster with single and double excitations (EOM-CCSD) as trial states. We benchmark the performance of these calculations on a set of small and medium molecules and polyacenes, focusing on predominantly single excitations. We find that the AFQMC results, obtained at a per-sample cost scaling of $O(N^6)$, are systematically more accurate than those obtained using EOM-CCSD, reducing excitation energy errors by approximately half for open-shell singlets. In regimes where EOM-CC triples are impractical, these results position AFQMC as a scalable, higher-accuracy complement for low-lying excited states.

physics.chem-ph↗

arXiv2025

Mixed Quantum-Classical Methods for Polaron Spectral Functions

In this work, using two distinct semiclassical approaches, namely the mean-field Ehrenfest (MFE) method and the mapping approach to surface hopping (MASH), we investigate the spectral function of a single charge interacting with phonons on a lattice. This quantity is relevant for the description of angle-resolved photoemission experiments. Focusing on the one-dimensional Holstein model, we compare the performance of these approaches across a range of coupling strengths and lattice sizes, exposing the relative strengths and weaknesses of each. We demonstrate that these approaches can be efficiently applied with reasonable accuracy to ab initio polaron models. Our work provides a route to the calculation of spectral properties in realistic electron-phonon-coupled systems in a computationally inexpensive manner with encouraging accuracy.

physics.chem-ph↗

arXiv2024

Beyond CCSD(T) accuracy at lower scaling with auxiliary field quantum Monte Carlo

We introduce a black-box auxiliary field quantum Monte Carlo (AFQMC) approach to perform highly accurate electronic structure calculations using configuration interaction singles and doubles (CISD) trial states. This method consistently provides more accurate energy estimates than coupled cluster singles and doubles with perturbative triples (CCSD(T)), often regarded as the gold standard in quantum chemistry. This level of precision is achieved at a lower asymptotic computational cost, scaling as $O(N^6)$ compared to the $O(N^7)$ scaling of CCSD(T). We provide numerical evidence supporting these findings through results for challenging main group and transition metal-containing molecules.

physics.chem-ph↗

arXiv2024

Improved modularity and new features in ipie: Toward even larger AFQMC calculations on CPUs and GPUs at zero and finite temperatures

ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [J. Chem. Theory Comput., 2023, 19(1): 109-121]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations of large systems that otherwise would not fit on single CPU node or GPU card. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals with multi-GPUs. Using CUDA and cupy for NVIDIA GPUs, ipie supports GPU-accelerated multi-slater determinant trial wavefunctions [arXiv:2406.08314] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu$_2$O$_2$]$^{2+}$ and [Fe$_2$S$_2$(SCH$_3$)$_4$]$^{2-}$. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron--phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications.

physics.chem-ph↗

arXiv2024

Benchmarking the Exponential Ansatz for the Holstein model

Polarons are quasiparticles formed as a result of lattice distortions induced by charge carriers. The single-electron Holstein model captures the fundamentals of single polaron physics. We examine the power of the exponential ansatz for the polaron ground-state wavefunction in its coupled cluster, canonical transformation, and (canonically transformed) perturbative variants across the parameter space of the Holstein model. Our benchmark serves to guide future developments of polaron wavefunctions beyond the single-electron Holstein model.

cond-mat.mtrl-sci↗

arXiv2024

Ab Initio Polaron Wave Functions

In this work we demonstrate that accurate ground state wave functions may be constructed for polarons in a fully ab initio setting across the wide range of couplings associated with both the large and small polaron limits. We present a single general unitary transformation approach which encompasses an ab initio version of the Lee-Low-Pines theory at weak coupling and the coherent state Landau-Pekar framework at strong coupling while interpolating between these limits in general cases. We show that perturbation theory around these limits may be performed in a facile manner to assess the accuracy of the approach, as well as provide an independent route to the ab initio properties of polarons. We test these ideas on the case of LiF, where the electron-polaron is expected to be large and relatively weakly coupled, while the hole-polaron is expected to be a strongly coupled small polaron.

cond-mat.str-el↗

arXiv2024

Structure and dynamics of electron-phonon coupled systems using neural quantum states

In this work, we use neural quantum states (NQS) to describe the high-dimensional wave functions of electron-phonon coupled systems. We demonstrate that NQS can accurately and systematically learn the underlying physics of such problems through a variational Monte Carlo optimization of the energy with minimal incorporation of physical information even in highly challenging cases. We assess the ability of our approach across various lattice model examples featuring different types of couplings. The flexibility of our NQS formulation is demonstrated via application to ab initio models parametrized by density functional perturbation theory consisting of electron or hole bands coupled linearly to dispersive phonons. We compute accurate real-frequency spectral properties of electron-phonon systems via a novel formalism based on NQS. Our work establishes a general framework for exploring diverse ground state and dynamical phenomena arising in electron-phonon systems, including the non-perturbative interplay of correlated electronic and electron-phonon effects in systems ranging from simple lattice models to realistic models of materials parametrized by ab initio calculations.

cond-mat.str-el↗

arXiv2024

Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions

In this work, we report, for the first time, an implementation of fermionic auxiliary-field quantum Monte Carlo (AFQMC) using matrix product state (MPS) trial wavefunctions, dubbed MPS-AFQMC. Calculating overlaps between an MPS trial and arbitrary Slater determinants up to a multiplicative error, a crucial subroutine in MPS-AFQMC, is proven to be #P-hard. Nonetheless, we tested several promising heuristics in successfully improving fermionic phaseless AFQMC energies. We also proposed a way to evaluate local energy and force bias evaluations free of matrix product operators. This allows for larger basis set calculations without significant overhead. We showcase the utility of our approach on one- and two-dimensional hydrogen lattices, even when the MPS trial itself struggles to obtain high accuracy. Our work offers a new set of tools that can solve currently challenging electronic structure problems with future improvements.

physics.chem-ph↗

arXiv2024

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T) and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the last decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule datasets. Firstly, we selected molecules from the G2 and G3 datasets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation (RMSD) of less than 1 kcal/mol across the combined dataset, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

physics.chem-ph↗

arXiv2023

Toward linear scaling auxiliary field quantum Monte Carlo with local natural orbitals

We develop a local correlation variant of auxiliary field quantum Monte Carlo (AFQMC) that is based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with system size for a target accuracy, the method has linear scaling. Applying LNO AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.

physics.chem-ph↗

arXiv2023

Response properties in phaseless auxiliary field quantum Monte Carlo

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo (AFQMC) through the application of automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices (RDMs) with the same computational cost scaling as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations.

physics.chem-ph↗

arXiv2023

Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multi-layered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multi-layered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

cond-mat.mtrl-sci↗