arXiv subjects

Edward F. Valeev

Publications and source records attributed to Edward F. Valeev.

At least 19 recordsLinked to original sources

arXiv2026

Comment on "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets"

In J. Chem. Phys. 152, 144105 (2020) Lehtola et al introduced the efficient Gaussian-basis representation of Superposition of Atomic Potentials (SAP) which "can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals". Here we demonstrate that it is possible to evaluate Gaussian AO representation of SAP by nearly trivial modification of one-electron nuclear attraction integrals.

physics.chem-ph↗

arXiv2026

Tensor Algebra Processing Primitives (TAPP): Towards a Standard for Tensor Operations

To address the absence of a universal standard interface for tensor operations, we introduce the Tensor Algebra Processing Primitives (TAPP), a C-based interface designed to decouple the application layer from hardware-specific implementations. We provide a mathematical formulation of tensor contractions and a reference implementation to ensure correctness and facilitate the validation of optimized kernels. Developed through community consensus involving academic and industrial stakeholders, TAPP aims to enable performance portability and resolving dependency challenges. The viability of the standard is demonstrated through successful integrations with the TBLIS and cuTENSOR libraries, as well as the DIRAC quantum chemistry package.

cs.MS↗

arXiv2026

SAP-X2C: Optimally-Simple Two-Component Relativistic Hamiltonian With Size-Intensive Picture Change

We present a simple relativistic exact 2-component (X2C) Hamiltonian that models two-electron picture-change effects using Lehtola's superposition of atomic potentials (SAP) [S. Lehtola, J. Chem. Theory Comput. 15, 1593-1604 (2019)]. The SAP-X2C approach keeps the low-cost and technical simplicity of the popular 1-electron X2C (1eX2C) predecessor, but is significantly more accurate and has a well-defined thermodynamic limit, making it applicable to extended systems (such as large molecules and periodic crystals). The assessment of the SAP-X2C-based Hartree-Fock total and spinor energies, spin-orbit splittings, equilibrium bond distances, and harmonic vibrational frequencies suggests that SAP-X2C is similar to the more complex atomic mean-field (AMF) X2C counterparts in its ability to approximate the 4-component Dirac-Hartree-Fock reference.

physics.chem-ph↗

arXiv2025

Why are diffuse atomic orbitals needed for accurate electronic wave functions of even neutral molecules?

An accurate description of electron correlation energies in molecules requires either basis set extrapolation or the use of explicitly-correlated wave functions that address the deficiencies of standard determinantal expansions at short interelectronic distances. Practical and robust explicitly-correlated F12 methods require the use of standard or specialized atomic orbital (AO) basis sets that include diffuse AOs, even for neutral species. Although modern reduced-scaling formulations of explicitly-correlated many-body methods have become routinely applicable to molecules with hundreds of atoms, application of F12 methods to large molecular systems can be severely hampered due to the onset of ill-conditioning spurred by the presence of diffuse AOs in the F12-appropriate orbital basis sets. Here we re-examine why diffuse AOs are necessary for application of F12 methods. To help such an investigation, we developed a dual-basis formulation of traditional and F12 coupled-cluster singles and doubles (CCSD) methods in which the reference (occupied) and correlating (virtual) orbitals are expanded in separate AO basis sets. Our conclusion is that diffuse AOs are fundamentally important for the traditional (non-F12) description of dynamical correlation; the necessity of diffuse AOs in F12 calculations arises indirectly due to the dramatic reduction of the basis set error by the F12 terms such that the error due to the lack of diffuse AOs becomes comparable to the residual basis set incompleteness. The dual-basis CC methods are suggested as an important candidate formalism for accurate (in particular, F12) reduced-scaling many-body methods in extended systems.

physics.chem-ph↗

arXiv2025

Pauli propagation enables fast classical simulation of strongly correlated quantum systems

Ground state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here we present a variational double bracket flow (vDBF) algorithm that leverages Pauli Propagation, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient-based fluctuation truncation and energy-variance extrapolation, we obtain results with sub-1% relative accuracy compared to DMRG benchmarks for the Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 1 minute on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For the 8x8 half-filled Hubbard model, corresponding to 128 qubits, vDBF reaches the 1% error regime in less than one hour, while our DMRG calculations required more than 10 hours on 64 threads. We further test vDBF on the 84-qubit {\pi}-valence active space of hexabenzocoronene, where the tighter-threshold calculations achieve sub-1% agreement with DMRG. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

quant-ph↗

arXiv2025

SeQuant Framework for Symbolic and Numerical Tensor Algebra. I. Core Capabilities

SeQuant is an open-source library for symbolic algebra of tensors over commutative (scalar) and non-commutative (operator) rings. The key innovation supporting most of its functionality is a graph-theoretic tensor network (TN) canonicalizer that can handle tensor networks with symmetries faster than their standard group-theoretic counterparts. The TN canonicalizer is used for routine simplification of conventional tensor expressions, for optimizing application of Wick's theorem (used to canonicalize products of tensors over operator fields), and for manipulation of the intermediate representation leading to the numerical evaluation. Notable features of SeQuant include support for noncovariant tensor networks (which often arise from tensor decompositions) and for tensors with modes that depend parametrically on indices of other tensor modes (such dependencies between degrees of freedom are naturally viewed as nesting of tensors, "tensors of tensors" arising in block-wise data compressions in data science and modern quantum simulation). SeQuant blurs the line between pure symbolic manipulation/code generation and numerical evaluation by including compiler-like components to optimize and directly interpret tensor expressions using external numerical tensor algebra frameworks. The SeQuant source code is available at https://github.com/ValeevGroup/SeQuant.

cs.MS↗

arXiv2025

Towards Balanced Description of Ground and Excited States with Transcorrelated F12 Methods

By correlating only the 1-particle states occupied in the reference determinant the conventional design for the single-reference R12/F12 explicitly-correlated methods biases them towards the ground state description thereby making treatment of response properties of the ground state, and energies and other properties of excited states less robust. While the use of multireference methods and/or extensions of the standard SP projected geminals can achieve a more balanced description of ground and excited states, here we show that the same goals can be achieved by extending the action of F12 correlators to the occupied and valence unoccupied 1-particle states only. This design choice reflects the strong dependence of the optimal correlation lengthscale of the F12 ansatz on the orbital energies/structure, and helps to avoid the unphysical raising of the ground state energy if the F12 geminals are used to correlate pairs of all 1-particle states. The improved F12 geminal design is incorporated into the unitary transcorrelation framework to produce a unitary 2-body Hamiltonian that incorporates the short-range dynamical correlation physics for ground and low-energy excited states in a balanced manner. This explicitly-correlated effective Hamiltonian reduces the basis set requirement on the correlation-consistent basis cardinal number by 1 or more over the uncorrelated counterpart for the description of the ground state coupled-cluster singles and doubles (CCSD) energies, the vertical excitation energies and harmonic vibrational frequencies of equation-of-motion CCSD low-energy excited states.

physics.chem-ph↗

arXiv2025

Physics-Driven Construction of Compact Primitive Gaussian Density Fitting Basis Sets

We present model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm produces DFBSs suitable for accurate robust DF approximation of 2-particle interactions in mean-field and correlated electronic structure. The algorithm is designed to (a) saturate the OBS product space by a large regularized set of primitive solid-harmonic Gaussian shells with nonuniform distribution of exponents followed by (b) pruning of the shells according to their contributions to the 2-body energy of a correlated atomic ensemble. Building the DFBS generator model almost exclusively on mathematical and physical principles allows one to limit the number of parameters that control the density fitting error to three, with a single set of parameters sufficient for computations with all basis cardinal numbers, with and without correlation of core electrons, with and without scalar and spin-dependent relativistic effects, spanning almost all of the Periodic Table. Performance assessment included basis sets up to quadruple-zeta quality from several major basis set families, using molecules composed of main-group, d-block, and f-block elements. The resulting DF errors in Hartree-Fock and second-order MP2 energies (with relativistic all-electron treatments, when appropriate) were on the order of 20 and 10 microhartree per electron, respectively.

physics.chem-ph↗

arXiv2025

Implementation of McMurchie-Davidson algorithm for Gaussian AO integrals suited for SIMD processors

We report an implementation of the McMurchie-Davidson evaluation scheme for 1- and 2-particle Gaussian AO integrals designed for processors with Single Instruction Multiple Data (SIMD) instruction sets. Like in our recent MD implementation for graphical processing units (GPUs) [J. Chem. Phys. 160, 244109 (2024)], variable-sized batches of shellsets of integrals are evaluated at a time. By optimizing for the floating point instruction throughput rather than minimizing the number of operations, this approach achieves up to 50% of the theoretical hardware peak FP64 performance for many common SIMD-equipped platforms (AVX2, AVX512, NEON), which translates to speedups of up to 30 over the state-of-the-art one-shellset-at-a-time implementation of Obara-Saika-type schemes in Libint for a variety of primitive and contracted integrals. As with our previous work, we rely on the standard C++ programming language -- such as the std::simd standard library feature to be included in the 2026 ISO C++ standard -- without any explicit code generation to keep the code base small and portable. The implementation is part of the open source LibintX library freely available at https://github.com/ValeevGroup/libintx.

physics.chem-ph↗

arXiv2025

Slimmer Geminals For Accurate F12 Electronic Structure Models

The Slater-type F12 geminal lengthscales originally tuned for the second-order M{\o}ller-Plesset F12 method are too large for higher-order F12 methods formulated using the SP (diagonal fixed-coefficient spin-adapted) F12 ansatz. The new geminal parameters reported herein reduce the basis set incompleteness errors (BSIE) of absolute coupled-cluster singles and doubles F12 correlation energies by a significant - and increasing with the cardinal number of the basis - margin. The effect of geminal reoptimization is especially pronounced for the cc-pVXZ-F12 basis sets (specifically designed for use with F12 methods) relative to their conventional aug-cc-pVXZ counterparts. The BSIEs of relative energies are less affected but substantial reductions can be obtained, especially for atomization energies and ionization potentials with the cc-pVXZ-F12 basis sets. The new geminal parameters are therefore recommended for all applications of high-order F12 methods, such as the coupled-cluster F12 methods and the transcorrelated F12 methods.

physics.chem-ph↗

arXiv2025

Relativistic Core-Valence-Separated Molecular Mean-Field Exact-Two-Component Equation-of-Motion Coupled Cluster Theory: Applications to L-edge X-ray Absorption Spectroscopy

L-edge X-ray absorption spectra for first-row transition metal complexes are obtained from relativistic equation-of-motion singles and doubles coupled-cluster (EOM-CCSD) calculations that make use of the core-valence separation (CVS) scheme, with scalar and spin--orbit relativistic effects modeled within the molecular mean-field exact two-component (X2C) framework. By incorporating relativistic effects variationally at the Dirac--Coulomb--Breit (DCB) reference level, this method delivers accurate predictions of L-edge features, including energy shifts, intensity ratios, and fine-structure splittings, across a range of molecular systems. Benchmarking against perturbative spin--orbit treatments and relativistic TDDFT highlights the superior performance and robustness of the CVS-DCB-X2C-EOM-CCSD approach, including the reliability of basis set recontraction schemes. While limitations remain in describing high-density spectral regions, our results establish CVS-DCB-X2C-EOM-CCSD as a powerful and broadly applicable tool for relativistic core-excitation spectroscopy.

physics.chem-ph↗

arXiv2024

Orbital Anatomy of Self-Interaction in Kohn-Sham Density Functional Theory

Self-interaction is a fundamental flaw of practical Kohn-Sham Density Functional Theory (KS DFT) approximations responsible for numerous qualitative and even catastrophic shortcomings. Whereas self-interaction is easy to characterize in one-electron systems, its orbital-dependent nature makes it difficult to uniquely define and decompose it and other components of the KS energy into orbital components. By starting from the orthogonal Hartree ansatz as the exchange-free self-interaction-free model, it is possible to uniquely define self-interaction and genuine exchange total energies as well as their decomposition into orbital contributions. Using Edmiston-Ruedenberg orbitals as a close numerical surrogate of the Hartree orbitals we investigate the accuracy of genuine exchange energies predicted by several levels of Jacob's ladder of functionals and their Perdew-Zunger (PZ) self-interaction corrected counterparts. Among several notable insights provided by the per-orbital breakdown of the KS energies the key is the delicate cancellation of errors between core and valence orbitals that belies the remarkable accuracy of many functionals (particularly, GGAs). Disruption of the cancellation by the PZ correction accounts for its relatively modest impact on GGAs and other semilocal functionals.

physics.chem-ph↗

arXiv2024

Revisiting Artifacts of Kohn-Sham Density Functionals for Biosimulation

We revisit the problem of unphysical charge density delocalization/fractionalization induced by the self-interaction error of common approximate Kohn-Sham Density Functional Theory functionals on simulation of small to medium-size proteins in vacuum. Aside from producing unphysical electron densities and total energies, the vanishing of the HOMO-LUMO gap associated with the unphysical charge delocalization leads to an unphysical low-energy spectrum and catastrophic failure of most popular solvers for the Kohn-Sham (KS) self-consistent field (SCF) problem. We apply a robust quasi-Newton SCF solver [Phys. Chem. Chem. Phys. 26, 6557 (2024)] to obtain solutions for some of these difficult cases. The anatomy of the charge delocalization is revealed by the natural deformation orbitals obtained from the density matrix difference between the Hartree-Fock and KS solutions; the charge delocalization can occur not only between charged fragments (such as in zwitterionic polypeptides) but also may involve neutral fragments. The vanishing-gap phenomenon and troublesome SCF convergence are both attributed to the unphysical KS Fock operator eigenspectra of molecular fragments (e.g., amino acids or their side chains). Analysis of amino acid pairs suggests that the unphysical charge delocalization can be partially ameliorated by the use of {\em some} range-separated hybrid functionals, but not by semilocal or standard hybrid functionals. Last, we demonstrate that solutions without the unphysical charge delocalization can be located even for semilocal KS functionals highly prone to such defects, but such solutions have non-Aufbau character and are unstable with respect to mixing of the non-overlapping "frontier" orbitals.

physics.chem-ph↗

arXiv2024

"Best" iterative coupled-cluster triples model: More evidence for 3CC

To follow up on the unexpectedly-good performance of several coupled-cluster models with approximate inclusion of 3-body clusters [J. Chem. Phys. 151, 064102 (2019)] we performed a more complete assessment of the 3CC method [J. Chem. Phys. 125, 204105 (2006)] for accurate computational thermochemistry in the standard HEAT framework. New spin-integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-zeta basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean absolute errors in cc-pVDZ {3CC, CCSDT, and CCSD(T)} electronic (per valence electron) and atomization energies relative to the CCSDTQ reference for the HEAT dataset [J. Chem. Phys. 121, 11599 (2004)], were {24, 70, 122} $\mu E_h/e$ and {0.46, 2.00, 2.58} kJ/mol, respectively. The mean absolute errors in the complete-basis-set limit {3CC, CCSDT, and CCSD(T)} atomization energies relative to the HEAT model reference, were {0.52, 2.00, and 1.07} kJ/mol, The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry applications, as well as the preferred alternative to CCSDT in general.

physics.chem-ph↗

arXiv2024

Relativistic coupled cluster with completely renormalized and perturbative triples corrections

We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems changes the dissociation energies by about 0.1--0.2 eV or about 4--7\%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au$_2$ than in Ag$_2$ or Cu$_2$.

physics.chem-ph↗

arXiv2024

3-center and 4-center 2-particle Gaussian AO integrals on modern accelerated processors

We report an implementation of the McMurchie-Davidson (MD) algorithm for 3-center and 4-center 2-particle integrals over Gaussian atomic orbitals (AOs) with low and high angular momenta $l$ and varying degrees of contraction for graphical processing units (GPUs). This work builds upon our recent implementation of a matrix form of the MD algorithm that is efficient for GPU evaluation of 4-center 2-particle integrals over Gaussian AOs of high angular momenta ($l\geq 4$) [$\mathit{J. Phys. Chem. A}\ \mathbf{127}$, 10889 (2023)]. The use of unconventional data layouts and three variants of the MD algorithm allow to evaluate integrals in double precision with sustained performance between 25% and 70% of the theoretical hardware peak. Performance assessment includes integrals over AOs with $l\leq 6$ (higher $l$ is supported). Preliminary implementation of the Hartree-Fock exchange operator is presented and assessed for computations with up to quadruple-zeta basis and more than 20,000 AOs. The corresponding C++ code is a part of the experimental open-source $\mathtt{LibintX}$ library available at $\mathbf{github.com:ValeevGroup/LibintX}$.

physics.comp-ph↗

arXiv2024

CoNST: Code Generator for Sparse Tensor Networks

Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data science. After a transformation into a tree of binary contractions, the network is implemented as a sequence of individual contractions. Several critical aspects must be considered in the generation of efficient code for a contraction tree, including sparse tensor layout mode order, loop fusion to reduce intermediate tensors, and the interdependence of loop order, mode order, and contraction order. We propose CoNST, a novel approach that considers these factors in an integrated manner using a single formulation. Our approach creates a constraint system that encodes these decisions and their interdependence, while aiming to produce reduced-order intermediate tensors via fusion. The constraint system is solved by the Z3 SMT solver and the result is used to create the desired fused loop structure and tensor mode layouts for the entire contraction tree. This structure is lowered to the IR of the TACO compiler, which is then used to generate executable code. Our experimental evaluation demonstrates very significant (sometimes orders of magnitude) performance improvements over current state-of-the-art sparse tensor compiler/library alternatives.

cs.PL↗

arXiv2023

High-performance evaluation of high angular momentum 4-center Gaussian integrals on modern accelerated processors

We present a high-performance evaluation method for 4-center 2-particle integrals over Gaussian atomic orbitals with high angular momenta ($l\geq4$) and arbitrary contraction degrees on graphical processing units (GPUs) and other accelerators. The implementation uses the matrix form of McMurchie-Davidson recurrences. Evaluation of the 4-center integrals over four $l=6$ ($i$) Gaussian AOs in the double precision (FP64) on an NVIDIA V100 GPU outperforms the reference implementation of the Obara-Saika recurrences (${\tt Libint}$) running on a single Intel Xeon core by more than a factor of 1000, easily exceeding the 73:1 ratio of the respective hardware peak FLOP rates while reaching almost 50\% of the V100 peak. The approach can be extended to support AOs with even higher angular momenta; for lower angular momenta ($l\leq3$) additional improvements will be reported elsewhere. The implementation is part of an open-source ${\tt LibintX}$ library feely available at https://github.com/ValeevGroup/LibintX.

physics.comp-ph↗