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Jan Brandejs

Publications and source records attributed to Jan Brandejs.

13 recordsLinked to original sources
arXiv2026

Report on the second Toulouse Tensor Workshop

This report documents the program of the second Toulouse Tensor Workshop which took place at the University of Toulouse on September 17-19, 2025, and summarizes the main points of discussion. This workshop follows the first Workshop (CECAM workshop on Tensor Contraction Library Standardization), which took place in Toulouse one year earlier, on May 24-25, 2024 and led to the formation of a tensor standardization working group, which has since specified a low-level standard interface for tensor operations available freely on GitHub. The 2025 workshop brought together developers of applications which rely extensively on tensor computations such as quantum many-body simulations in chemistry and physics (material science and electronic structure calculations), as well as developers and experts of tensor software who have the know-how to provide the technical support for such applications. The workshop enabled the community to provide feedback on the specified low-level interface and how it can be further refined. It also initiated a discussion on how the standardization efforts should be oriented in the near feature, in particular on what should be higher-level interfaces and how to tackle other requirements of the community such as tensor decompositions, symmetric tensors and structured sparsity support.

cs.MS↗
arXiv2026

The nuclear electric quadrupole moment of $^{87}$Sr from highly accurate molecular relativistic calculations

The nuclear electric quadrupole moment (NQM) of $^{87}$Sr has recently been revisited using high-precision relativistic atomic calculations [B. Lu et al., Phys. Rev. A 100, 012504 (2019)], indicating that the currently accepted value should be revised and that their result may serve as a new reference. In the present work, we determine the NQM of $^{87}$Sr from the molecular method, by combining the experimentally measured nuclear quadrupole coupling constants (NQCCs) of SrO and SrS with highly accurate relativistic calculations of the electric field gradient (EFG) at the Sr nucleus. Electronic correlation is treated at the CCSD(T), CCSD-T and CCSD$\tilde{\text{T}}$ levels. The iterative T contribution of the latter, composite scheme was obtained using a newly implemented parallel scheme where the distributed memory tensor library Cyclops Tensor Framework (CTF) was made available to the DIRAC code for relativistic molecular calculations through TAPP, the new community standard for tensor operations. All correlated calculations are performed using the exact two-component molecular mean-field Hamiltonian (X2C$\mathrm{mmf}$). The Gaunt two-electron interaction is incorporated, an even-tempered optimized quadruple-$\zeta$ quality basis set is employed, and vibrational corrections are accounted for. Our best result is $Q($$^{87}$Sr$) = 0.33666 \pm 0.00258$ b, which is about 10% larger than currently accepted standard value, while it is in excellent agreement with recent determinations [Y.-B. Tang, arXiv:2512.07603 [physics.atom-ph] (2025)].

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↗
arXiv2025

The Software Landscape for the Density Matrix Renormalization Group

The density matrix renormalization group (DMRG) algorithm is a cornerstone computational method for studying quantum many-body systems, renowned for its accuracy and adaptability. Despite DMRG's broad applicability across fields such as materials science, quantum chemistry, and quantum computing, numerous independent implementations have been developed. This survey maps the rapidly expanding DMRG software landscape, providing a comprehensive comparison of features among 35 existing packages. We found significant overlap in features among the packages when comparing key aspects, such as parallelism strategies for high-performance computing and symmetry-adapted formulations that enhance efficiency. This overlap suggests opportunities for modularization of common operations, including tensor operations, symmetry representations, and eigensolvers, as the packages are mostly independent and share few third-party library dependencies where functionality is factored out. More widespread modularization and standardization would result in reduced duplication of efforts and improved interoperability. We believe that the proliferation of packages and the current lack of standard interfaces and modularity are more social than technical. We aim to raise awareness of existing packages, guide researchers in finding a suitable package for their needs, and help developers identify opportunities for collaboration, modularity standardization, and optimization. Ultimately, this work emphasizes the value of greater cohesion and modularity, which would benefit DMRG software, allowing these powerful algorithms to tackle more complex and ambitious problems.

physics.comp-ph↗
arXiv2025

Highly Accurate Expectation Values Using High-Order Relativistic Coupled Cluster Theory

This work presents the automatic generation of analytic first derivatives of the energy for general coupled-cluster models using the \text{tenpi} toolchain. We report the first implementation of expectation values for CCSDT and CCSDTQ methods within the DIRAC program package for relativistic molecular calculations. As pivotal calculations, we focus on the electric field gradient (EFG) evaluated at the lithium nucleus in LiX (X = H, F, Cl) compounds, enabling the extraction of the nuclear electric quadrupole moment $Q({}^{7}Li)$, and at the aluminum nucleus in AlY (Y =H, F, Cl, Br) compounds, for the determination of $Q({}^{27}Al)$. These high-order methods are applied to compute corrections for triple and quadruple excitations for the EFG, a crucial quantity for determining nuclear quadrupole moments. We obtain $Q({}^{27}Al)$ = 0.1466 b, in excellent agreement with the recommended value, and $Q({}^{7}Li)$ = -0.0386 b, which is smaller than the currently recommended value, that indicates the need for further investigation.

physics.chem-ph↗
arXiv2024

Generating coupled cluster code for modern distributed memory tensor software

Using GPU-based HPC platforms efficiently for coupled cluster computations is a challenge due to heterogeneous hardware structures. The constant need to adapt software to these structures and the required man-hours makes a systematization of high-performance code development desirable, even more so for higher-order coupled cluster. This is generally achieved by introducing a high-level representation of the problem, which is then translated to low-level instructions for the hardware using a compiler/translator component. Designing such software comes with another challenge: Allowing efficient implementation by capturing key symmetries of tensors, while retaining the abstraction from the hardware. We review ways to address these two challenges while presenting design decisions which led us to the development of a general-order coupled cluster code generator. The systematically produced code shows excellent weak scaling behavior running on up to 1200 GPUs using the distributed memory tensor library ExaTENSOR. We present an open-source modular tensor framework "tenpi" for coupled cluster code development with diagrammatic derivation, visualization module, symbolic algebra, intermediate optimization and support for multiple tensor backends. Tenpi brings higher-order CC functionality to the massively parallel ExaCorr module of the DIRAC code for relativistic molecular calculations.

physics.chem-ph↗
arXiv2024

DMRG-tailored coupled cluster method in the 4c-relativistic domain: General implementation and application to the NUHFI and NUF$_3$ molecules

Heavy atom compounds represent a challenge for computational chemistry, due to the need for simultaneous treatment of relativistic and correlation effects. Often such systems exhibit also strong correlation which hampers the application of perturbation theory or single-reference coupled cluster (CC) methods. As a viable alternative, we have proposed to externally correct the CC method using the density matrix renormalization group (DMRG) wave functions, yielding the DMRG-tailored CC method. In a previous paper [J. Chem. Phys. {\bf 152}, 174107 (2020)] we have reported a first implementation of this method in the relativistic context, which was restricted to molecules with real double group symmetry. In this work we present a fully general implementation of the method, covering complex and quaternion double groups as well. The 4c-TCC method thus becomes applicable to polyatomic molecules including heavy atoms. For assessment of the method, we performed calculations of the chiral uranium compound NUHFI, which was previously studied in the context of the enhancement of parity violation effects. In particular, we performed calculations of a cut of the potential energy surface of this molecule along the dissociation of the N-U bond, where the system exhibits a strong multireference character. Since there are no experimental data for NUHFI, we have performed also an analogous study of the (more symmetric) NUF$_3$ molecule, where the vibrational frequency of the N-U bond can be compared with spectroscopic data.

physics.chem-ph↗
arXiv2023

Hilbert space multireference coupled clusters tailored by matrix product states

The DMRG method, despite its favorable scaling, it is in practice not suitable for computations of dynamic correlation. Several approaches to include that in post-DMRG methods exist; in our group we focused on the tailored-CC (TCC) approach. This method works well in many situations, however, in exactly degenerate cases (with two or more determinants of equal weight), it exhibits a bias towards the reference determinant representing the Fermi vacuum. Although in some cases it is possible to use a compensation scheme to avoid this bias for energy differences, as we did in a previous work on the singlet-triplet gap in the tetramethylenethane (TME) molecule, it is certainly a drawback. In order to overcome the single-reference bias of the TCC method, we have developed a Hilbert-space multireference version of tailored CC, which can treat several determinants on an equal footing. We have employed a multireference analysis of the DMRG wave function in the matrix product state form to get the active amplitudes for each reference determinant and their constant contribution to the effective Hamiltonian. We have implemented and compared the performance of three Hilbert-space MRCC variants - the state universal one, and the Brillouin-Wigner and Mukherjee's state specific ones. We have assessed these approaches on the cyclobutadiene and tetramethylenethane (TME) molecules, which are both diradicals with exactly degenerate determinants at a certain geometry. Two DMRG active spaces have been selected based on orbital entropies, while the MRCC active space comprised the HOMO and LUMO orbitals needed for description of the diradical. We have also investigated the sensitivity of the results on orbital rotation of the HOMO-LUMO pair, as it is well known that Hilbert-space MRCC methods are not invariant to such transformations.

physics.chem-ph↗
arXiv2020

Towards DMRG-tailored coupled cluster method in the 4c-relativistic domain

There are three essential problems in computational relativistic chemistry: electrons moving at relativistic speeds, close lying states and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems with one or two of these issues. However, there is a significant class of molecules, in which all the three effects are present. These are the heavier transition metal compounds, lanthanides and actinides with open d or f shells. For such systems, sufficiently accurate numerical methods are not available, which hinders the application of theoretical chemistry in this field. In this paper, we combine two numerical methods in order to address this challenging class of molecules. These are the relativistic versions of coupled cluster methods and density matrix renormalization group (DMRG) method. To the best of our knowledge, this is the first relativistic implementation of the coupled cluster method externally corrected by DMRG. The method brings a significant reduction of computational costs, as we demonstrate on the system of TlH, AsH and SbH.

physics.chem-ph↗
arXiv2020

Massively parallel quantum chemical density matrix renormalization group method

We present, to the best of our knowlegde, the first attempt to exploit the supercomputer platform for quantum chemical density matrix renormalization group (QC-DMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.

physics.chem-ph↗
arXiv2019

Near-linear Scaling in DMRG-based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T)

We present a new implementation of DMRG-based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO-TCCSD). Compared to the previous LPNO version of the method, the new implementation is more accurate, offers more favorable scaling and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen) and Iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8-99.9% of the total canonical correlation energy which is the improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for Iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

physics.chem-ph↗
arXiv2019

Quantum information-based analysis of electron-deficient bonds

Recently, the correlation theory of the chemical bond was developed, which applies concepts of quantum information theory for the characterization of chemical bonds, based on the multiorbital correlations within the molecule. Here for the first time, we extend the use of this mathematical toolbox for the description of electron-deficient bonds. We start by verifying the theory on the textbook example of a molecule with three-center two-electron bonds, namely the diborane(6). We then show that the correlation theory of the chemical bond is able to properly describe bonding situation in more exotic molecules which have been synthetized and characterized only recently, in particular the diborane molecule with four hydrogen atoms [diborane(4)] and neutral zerovalent s-block beryllium complex, whose surprising stability was attributed to a strong three-center two-electron $\pi$ bond stretching across the C-Be-C core. Our approach is of a high importance especially in the light of a constant chase after novel compounds with extraordinary properties where the bonding is expected to be unusual.

physics.chem-ph↗