arXiv subjects

Daniel Kats

Publications and source records attributed to Daniel Kats.

At least 19 recordsLinked to original sources

arXiv2026

ElemCo.jl: A Julia package for electron-correlation methods

We present ElemCo.jl, an open-source Julia package for molecular electronic structure and properties calculations with a particular emphasis on Coupled Cluster and Distinguishable Cluster methods. The package provides a high-level, macro-based user interface which makes routine calculations accessible to users with no prior Julia experience. A newly developed visualizer, JLmol, assists in the graphical preparation of ElemCo.jl input files and displays results such as molecular orbitals. ElemCo.jl offers restricted closed-shell and unrestricted variants of state-of-the-art electron-correlation methods such as FCI, MP2, CCSD(T) as well as EOM-CCSD and the DC methods DCSD and DC-CCSDT. In addition to traditional approaches, ElemCo.jl provides recently developed methods that are currently unique to the package. These include tensor-decomposed implementations of DCSD and DC-CCSDT (SVD-DCSD and SVD-DC-CCSDT) as well as two-determinant and fixed-reference CC and DC methods. For excited-state calculations, ElemCo.jl also offers EOM-DCSD, which is benchmarked in this work against CC3 on the QUEST3 benchmark set, alongside EOM-CCSD. Furthermore, both ground and excited states, including those of multireference character, can be treated using CIPHI - an efficient selected Configuration Interaction (CI) approach employing a CIPSI/Heat-Bath-CI-based algorithm. Users can directly invoke internal functions from the input file, enabling them to test and compose new methods without the need to modify ElemCo.jl's source code. Also, ElemCo.jl can be readily interfaced with external quantum chemistry codes through the Fcidump format, for example as the high-level solver for transcorrelated Hamiltonians, periodic embedded fragments, etc. We provide a detailed overview of ElemCo.jl's methodological repertoire and discuss its technical details and implementation, performance, interfaces, and usage.

physics.chem-ph↗

arXiv2026

Orbital-Optimized Quasi-Variational Distinguishable Cluster Doubles Method

We present the orbital-optimized quasi-variational distinguishable cluster doubles (OQVDCD) method, obtained by applying the distinguishable cluster (DC) approximation to orbital-optimized quasi-variational coupled cluster doubles (OQVCCD). The resulting method retains a Hermitian-like energy functional, is size-extensive, obeys the generalized Hellmann-Feynman theorem at a stationary point, is exact in the isolated two-electron and two-hole limits, and scales as O(o2v4), like coupled cluster singles and doubles (CCSD). For the tested closed-shell reaction energies, it is shown that OQVDCD reduces the mean absolute deviation relative to OQVCCD from 1.20 to 0.81 kcal/mol, bringing the errors close to distinguishable cluster singles and doubles (DCSD). In the strongly correlated examples considered here, OQVDCD shifts the OQVCCD energies toward the benchmark, although the convergence remains somewhat less robust than for DCSD.

physics.chem-ph↗

arXiv2026

Compression of virtual spaces in transcorrelated methods via singular value decomposition: application to the G2 set

We introduce a new singular-value-decomposition-based scheme for constructing small virtual spaces out of large basis sets for transcorrelated (TC) calculations, termed SVD-TC. This work builds on the recent finding that the residual basis error in the TC reference energy converges more slowly than that of the correlation energy. Within the new workflow, the post Hartree-Fock TC calculation is performed in a compressed virtual orbital subspace, obtained by projecting the canonical virtual orbitals from a large basis set onto a smaller basis set through singular value decomposition (SVD). This allows us to achieve the high accuracy allowed by the large basis, whilst the bottleneck steps - TC integral calculation and post-HF correlation method such as CCSD(T) - incur the cost of only a small virtual space calculation. The method therefore is highly efficient, whilst avoiding the composite nature of the reference correction method. Using the new scheme, we widen the scope of benchmark-quality TC results into more complex molecules than previously considered: using the G2-1 set of 55 molecules with first- and second-row atoms, we apply SVD-xTC-CCSD(T) to compute atomization energies. We compare our results against the near-exact semistochastic heat-bath configuration interaction (SHCI) reference values and experiment. We find that SVD-xTC-CCSD(T) delivers chemical accuracy already with triple-$\zeta$ basis sets. Finally, we use the quadruple-$\zeta$ results to analyze the accuracy of pseudopotentials within the TC method, and show that pseudopotential TC workflow provides faster basis-set convergence than all-electron TC. We also present timings for computing the atomization energies on G2-1 set, demonstrating the efficiency of our TC workflows.

physics.chem-ph↗

arXiv2026

An Additive Reference Correction Scheme for the Transcorrelated Method

We introduce an additive reference correction for the transcorrelated (TC) method and its three-body mean-field approximation (xTC), to improve energy differences computed in small orbital basis sets. The correction is motivated by the observation that, for xTC atomization energies, the dominant error in double-{\zeta} bases originates from the reference contribution rather than from the correlation energy. In the proposed reference-corrected scheme (RC-xTC), the small-basis correlation energy is retained, while the corresponding TC reference energy is replaced by its value from a larger basis. Benchmark calculations for the non-relativistic HEAT set with the Dunning basis-set family show that RC-xTC substantially improves both total and atomization energies relative to standard xTC in double-{\zeta} bases. At the CCSD(T) level, RC-xTC yields better atomization energies than CCSD(T)-F12a in the double-{\zeta} regime, while preserving the favorable total-energy accuracy of xTC. At the CCSD level, RC-xTC improves atomization energies relative to F12a throughout the full basis-set sequence. As the basis set is enlarged, xTC and RC-xTC become progressively identical, as expected from the construction of the correction.

physics.chem-ph↗

arXiv2026

Application of the aperiodic defect model to a negatively charged monovacancy in phosphorene

We apply the recently introduced aperiodic defect model (ADM) to a negatively charged monovacancy in a phosphorene monolayer. In contrast to conventional supercell approaches, the ADM treats a single defect embedded in the true non-defective crystalline mean field thereby avoiding spurious defect-defect interactions and the need for charge corrections. At the same time, it effectively reduces the calculation to a fragment, enabling the use of high-level molecular electronic-structure methods. Converging the Hartree-Fock and correlation contributions to the thermodynamic limit yields a benchmark CCSD(T)/POB-TZVP-rev2 formation energy of 0.81 eV for the negatively charged monovacancy in the (5|9) configuration. The excitation energy to the lowest singlet excited state of this defect at the EOM-CCSD/POB-TZVP-rev2 level is found to be 1.95 eV. Overall, the ADM provides a highly promising route towards quantitatively accurate and systematically improvable descriptions of defects in solids and on surfaces, bridging the gap between solid-state physics and molecular quantum chemistry.

physics.chem-ph↗

arXiv2025

A Transcorrelated Wave-Function Framework for Solids: An Application to Bulk and Defected Silicon

Accurate wave-function descriptions of pristine and defected solids remain challenging due to the simultaneous presence of finite-size, basis-set, and correlation errors. While embedding techniques alleviate finite-size effects and correlated wave-function approaches systematically improve correlation, basis-set incompleteness continues to limit practical accuracy. Here we present a study of transcorrelated (TC) many-body wave-function methods on properties of solid state systems. We augment the existing xTC theory to periodic systems, and establish an unified transcorrelated embedding framework that integrates periodic TC theory with fragment-based correlated solvers. Using silicon as a test case, we validate the method against coupled-cluster, FCIQMC, and diffusion Monte Carlo benchmarks for bulk. Then we apply TC embedding to calculation of formation energies of two silicon self-interstitials. The TC Hamiltonian yields rapid basis convergence and quantitatively reliable defect formation energies at the triple-$\zeta$ level, substantially reducing the basis-set bottleneck for wave-function treatments of crystalline defects.

cond-mat.mtrl-sci↗

arXiv2025

Deterministic Optimisation of Jastrow Factors

Highly flexible Jastrow factors have found significant use in stochastic electronic structure methods such as variational Monte Carlo (VMC) and diffusion Monte Carlo, as well as in quantum chemical transcorrelated (TC) approaches, which have recently seen great success in generating highly accurate electronic energies using moderately sized basis sets. In particular for the latter, the intrinsic noise in the Jastrow factor due to its optimisation by VMC can pose a problem, especially when targeting weak (non-covalent) interactions. In this paper, we propose a deterministic alternative to VMC Jastrow optimisation, based on minimising the "variance of the TC reference energy" in a standard basis set. Analytic expressions for the derivatives of the TC Hamiltonian matrix elements are derived and implemented. This approach can be used to optimise the parameters in the Jastrow functions, either from scratch or to refine an initial VMC-based guess, to produce noise-free Jastrows in a reproducible manner. Applied to the first row atoms and molecules, the results show that the method yields Slater-Jastrow wavefunctions whose variances are almost as low as those obtained from standard VMC variance optimisation, but whose energies are lower, and comparable to those obtained from energy-minimisation VMC. We propose that the method can be used both in the context of the transcorrelated method or in standard VMC as a new way to optimise Jastrow functions.

physics.chem-ph↗

arXiv2025

Transcorrelated Methods for Multireference Problems

We apply the transcorrelated method to problems of multireference character. For this, we show that the choice of reference wavefunction during the Jastrow optimisation procedure is vital, and we propose a workflow wherein we use conventional multi-configurational methods to provide a reference wavefunction for Jastrow factor optimisation. This Jastrow function is subsequently used with transcorrelated-full configuration interaction quantum Monte Carlo within the xTC approximation (TC-FCIQMC) to yield highly accurate transcorrelated energies. This is demonstrated for N$_2$ using the aug-cc-pVTZ basis set, achieving chemical accuracy across the entire binding curve compared with experiment. We also apply the method to compute excitation energies of dinitrogen, CO and the ammonia molecule, where accurate results, comparable to the best available theoretical predictions, are obtained with modest basis sets.

physics.chem-ph↗

arXiv2024

Transcorrelated Theory with Pseudopotentials

The transcorrelated (TC) method performs a similarity transformation on the electronic Schr\"odinger equation via Jastrow factorization of the wave function. This has demonstrated significant advancements in computational electronic structure theory by improving basis set convergence and compactifying the description of the wave function. In this work, we introduce a new approach that incorporates pseudopotentials (PPs) into the TC framework, significantly accelerating Jastrow factor optimization and reducing computational costs. Our results for ionization potentials, atomization energies, and dissociation curves of first-row atoms and molecules show that PPs provide chemically accurate descriptions across a range of systems and give guidelines for future theory and applications. The new pseudopotential-based TC method opens possibilities for applying TC to more complex and larger systems, such as transition metals and solid-state systems.

physics.chem-ph↗

arXiv2024

Transcorrelated Methods Applied to Second Row Elements

We explore the applicability of the transcorrelated method to the elements in the second row of the periodic table. We use transcorrelated Hamiltonians in conjunction with full configuration interaction quantum Monte Carlo and coupled cluster techniques to obtain total energies and ionisation potentials, investigating their dependence on the nature and size of the basis sets used. Transcorrelation accelerates convergence to the complete basis set limit relative to conventional approaches, and chemically accurate results can generally be obtained with the cc-pVTZ basis, even with a frozen Ne core in the post-Hartree--Fock treatment.

physics.chem-ph↗

arXiv2024

Tensor Decomposed Distinguishable Cluster. I. Triples Decomposition

We present a cost-reduced approach for the distinguishable cluster approximation to coupled cluster with singles, doubles and iterative triples (DC-CCSDT) based on a tensor decomposition of the triples amplitudes. The triples amplitudes and residuals are processed in the singular-value-decomposition (SVD) basis. Truncation of the SVD basis according to the values of the singular values together with the density fitting (or Cholesky) factorization of the electron repulsion integrals reduces the scaling of the method to $N^6$, and the DC approximation removes the most expensive terms of the SVD triples residuals and at the same time improves the accuracy of the method. The SVD basis vectors for the triples are obtained from the approximate CC3 triples density matrices constructed in an intermediate SVD basis of doubles amplitudes. This allows us to avoid steps that scale higher than $N^6$ altogether. Tests against DC-CCSDT and CCSDT(Q) on a benchmark set of chemical reactions with closed-shell molecules demonstrate that the SVD-error is very small already with moderate truncation thresholds, especially so when using a CCSD(T) energy correction. Tests on alkane chains demonstrated that the SVD-error grows linearly with system size confirming the size extensivity of SVD-DC-CCSDT within a chosen truncation threshold.

physics.chem-ph↗

arXiv2024

Aperiodic defects in periodic solids

To date, computational methods for modeling defects (vacancies, adsorbates, etc.) rely on periodic supercells in which the defect is far enough from its repeated image such that they can be assumed non-interacting. Yet, the relative proximity and periodic repetition of the defect's images may lead to spurious, unphysical artifacts, especially if the defect is charged and/or open-shell, causing a very slow convergence to the thermodynamic limit (TDL). In this Letter, we introduce a "defectless" embedding formalism such that the embedding field is computed in a pristine, primitive-unit-cell calculation. Subsequently, a single (i.e. "aperiodic") defect, which can also be charged, is introduced inside the embedded fragment. By eliminating the need for compensating background charges and periodicity of the defect, we circumvent all associated unphysicalities and numerical issues, achieving a very fast convergence to the TDL. Furthermore, using the toolbox of post-Hartree-Fock methods, this scheme can be straightforwardly applied to study strongly correlated defects, localized excited states and other problems, for which existing periodic protocols do not provide a satisfactory description.

physics.chem-ph↗

arXiv2024

Orbital optimisation in xTC transcorrelated methods

We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Besides, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.

physics.chem-ph↗

arXiv2024

Two Determinant Distinguishable Cluster

A two reference determinant version of the distinguishable cluster with singles and doubles (DCSD) has been developed. We have implemented the two determinant distinguishable cluster (2D-DCSD) and the corresponding traditional 2D-CCSD method in a new open-source package written in Julia called ElemCo.jl. The methods were benchmarked on singlet and triplet excited states of valence and Rydberg character, as well as for singlet-triplet gaps of diradicals. It is demonstrated that the distinguishable cluster approximation improves the accuracy of 2D-CCSD.

physics.chem-ph↗

arXiv2023

xTC: An efficient treatment of three-body interactions in transcorrelated methods

An efficient implementation for approximate inclusion of the three-body operator arising in transcorrelated methods via exclusion of explicit three-body components (xTC) is presented and tested against results in the "HEAT" benchmark set [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)]. Using relatively modest basis sets and computationally simple methods, total, atomization, and formation energies within near-chemical accuracy from HEAT results were obtained. The xTC ansatz reduces the nominal scaling of the three-body part of transcorrelation by two orders of magnitude to O(N^5) and can readily be used with almost any quantum chemical correlation method.

physics.chem-ph↗

arXiv2023

Transcorrelated coupled cluster methods. II. Molecular systems

We demonstrate the accuracy of ground-state energies of the transcorrelated Hamiltonian, employing sophisticated Jastrow factors obtained from variational Monte Carlo, together with the coupled cluster and distinguishable cluster methods at the level of singles and doubles excitations. Our results show that already with the cc-pVTZ basis the transcorrelated distinguishable cluster method gets close to complete basis limit and near full configuration interaction quality values for relative energies of over thirty atoms and molecules. To gauge the performance in different correlation regimes we also investigate the breaking of the nitrogen molecule with transcorrelated coupled cluster methods. Numerical evidence is presented to further justify an efficient way to incorporate the major effects coming from the three-body integrals without explicitly introducing them into the amplitude equations.

physics.chem-ph↗

arXiv2022

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

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.

physics.chem-ph↗

arXiv2021

Combined unitary and symmetric group approach applied to low-dimensional spin systems

A novel combined unitary and symmetric group approach is used to study the spin-$\frac{1}{2}$ Heisenberg model and related Fermionic systems in a spin-adapted representation, using a linearly-parameterised Ansatz for the many-body wave function. We show that a more compact ground state wave function representation is obtained when combining the symmetric group, $\mathcal{S}_n$, in the form of permutations of the underlying lattice site ordering, with the cumulative spin-coupling based on the unitary group, $\mathrm{U}(n)$. In one-dimensional systems the observed compression of the wave function is reminiscent of block-spin renormalization group approaches, and allows us to study larger lattices (here taken up to 80 sites) with the spin-adapted full configuration interaction quantum Monte Carlo method, which benefits from the sparsity of the Hamiltonian matrix and the corresponding sampled eigenstates that emerge from the reordering. We find that in an optimal lattice ordering the configuration state function with highest weight already captures with high accuracy the spin-spin correlation function of the exact ground state wave function. This feature is found for more general lattice models, such as the Hubbard model, and ab initio quantum chemical models, in this work exemplified by a one-dimensional hydrogen chain. We also provide numerical evidence that the optimal lattice ordering for the unitary group approach is not generally equivalent to the optimal ordering obtained for methods based on matrix-product states, such as the density-matrix renormalization group approach.

cond-mat.str-el↗