Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Journal of Chemical Physics

A sparse matrix based full-configuration interaction algorithm

Zoltán Rolik, Ágnes Szabados, Péter R. Śurján

Published Apr 8, 2008• 29 citations
Publisher

Abstract

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers.

DOI
10.1063/1.2839304

Related papers

Sparse Full Configuration Interaction

Wang, Lijun

We propose an efficient deterministic method to calculate the full configuration interaction (FCI) ground state energy. This method leverages the sparseness of the Lanczos basis vectors that span the Krylov subspace associated with the Hamiltonian to rapidly calculate the lowest eigenvalue of the effective Hamiltonian formed in this basis. By iteratively performing the spanning and diagonalization steps, this method is capable of rapidly reaching chemical accuracy for a variety of strongly correlated molecules, including stretched N$_2$ and C$_2$, in merely several tens of iterations. To accelerate our algorithm, we implement parallelized sparse matrix-sparse vector multiplication, which features a novel hashing method that establishes a one-to-one correspondence between the set of full configuration Slater determinants and a set of consecutive integers. A near-linear acceleration was observed.

arXiv:2312.01846•Dec 4, 2023•0 citations

A vector and parallel full configuration interaction algorithm

Gian Luigi Bendazzoli, Stefano Evangelisti

A full configuration interaction (FCI) algorithm is presented and discussed. It is an integral driven formalism based on the explicit construction of tables which realize the correspondence between the FCI vector x and the vector Hx, H being the Hamiltonian matrix of the system. In this way no decomposition of the identity is needed, and in the simplest implementation only the two vectors x and Hx need to be kept on disk. The main test has been done on the cyclic polyene C18H18 in the Pariser–Parr–Pople approximation, where the size of the FCI vector can be reduced to about 73 million components. Running on a CRAY Y-MP with 4 CPU and 32 MW of core memory, we obtained an elapsed CPU time per iteration of about 300 s and a total elapsed time of 1000 s, which correspond to about 4 and 14 s per million determinants, respectively. The parallel CPU speed-up obtained by running with the 4 CPU is greater than 3, without any substantial increasing of the memory or disk requirements.

The Journal of Chemical Physics•Feb 15, 1993•111 citations

Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format

Karl-Heinz Böhm, Alexander A. Auer, Mike Espig

In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.

The Journal of Chemical Physics•Jun 22, 2016•19 citations

Perturbative Coordinate Descent Full Configuration Interaction

Z D Zhang, Mingyu Qiu, Yingzhou Li +1 more

The coordinate descent full configuration interaction (CDFCI) is an accurate and efficient method for calculating ground-state energies of molecular systems. In this work we introduce two perturbative extensions of original CDFCI. We first propose a direct CDFCI + PT to further correct variational energy by perturbation theory. We also propose an iterative perturbative CDFCI (IP-CDFCI) to avoid evaluating the overlarge perturbative space and catch the information encoded in variational stage. In IP-CDFCI, we store three sparse vectors in a Hash table: c, b and d, where c is the variational wave function, b is the compressed approximation of H c and d is the perturbative wave function, respectively. By utilizing the redundant memory in the storage of c, we can calculate perturbation without any extra memory compared to original CDFCI. We also use a strategy to eliminate the expensive repetitive evaluation of diagonal elements of Hamiltonian by creating a vector h which stores the diagonal entries of Hamiltonian. This strategy trades memory usage for computational time and reduces the computing time significantly. Furthermore, we use quadruple-precision floating-point numbers to improve the numerical stability of perturbative energy. We demonstrate the effectiveness of the single-threaded IP-CDFCI and the multithreaded CDFCI + PT, respectively, by performing calculations on several small molecular benchmarks as well as challenging correlated system: the chromium dimer.

Journal of Chemical Theory and Computation•May 7, 2026•0 citations

NECI: N -Electron Configuration Interaction with an emphasis on state-of-the-art stochastic methods

Kai Guther, Robert J. Anderson, Nick S. Blunt +22 more

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.

arXiv:2006.14956•The Journal of Chemical Physics•Jul 16, 2020•96 citations

Distributed Implementation of Full Configuration Interaction for One Trillion Determinants

Hong Ming Gao, Satoshi Imamura, Akihiko Kasagi +1 more

High Resolution Image Download MS PowerPoint Slide Full configuration interaction (FCI) can provide an exact molecular ground-state energy within a given basis set and serve as a benchmark for approximate methods in quantum chemical calculations, including the emerging variational quantum eigensolver. However, its exponential computational and memory requirements easily exceed the capability of a single server and limit its applicability to large molecules. In this paper, we present a distributed FCI implementation employing a hybrid parallelization scheme with multithreading and multiprocessing to expand FCI’s applicability. We optimize this scheme to minimize the bottlenecks arising from interprocess communications and interthread data management. Our implementation achieves higher scalability than the naive combination of prior works and successfully calculates the exact energy of C 3 H 8 /STO-3G with 1.31 trillion determinants, which is the largest FCI calculation to the best of our knowledge. Furthermore, we provide a comprehensive list of FCI results with 136 combinations of molecules and basis sets for future evaluation and development of approximate methods.

Journal of Chemical Theory and Computation•Feb 5, 2024•62 citations
We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers.
We propose an efficient deterministic method to calculate the full configuration interaction (FCI) ground state energy. This method leverages the sparseness of the Lanczos basis vectors that span the Krylov subspace associated with the Hamiltonian to rapidly calculate the lowest eigenvalue of the effective Hamiltonian formed in this basis. By iteratively performing the spanning and diagonalization steps, this method is capable of rapidly reaching chemical accuracy for a variety of strongly correlated molecules, including stretched N2_22​ and C2_22​, in merely several tens of iterations. To accelerate our algorithm, we implement parallelized sparse matrix-sparse vector multiplication, which features a novel hashing method that establishes a one-to-one correspondence between the set of full configuration Slater determinants and a set of consecutive integers. A near-linear acceleration was observed.
A full configuration interaction (FCI) algorithm is presented and discussed. It is an integral driven formalism based on the explicit construction of tables which realize the correspondence between the FCI vector x and the vector Hx, H being the Hamiltonian matrix of the system. In this way no decomposition of the identity is needed, and in the simplest implementation only the two vectors x and Hx need to be kept on disk. The main test has been done on the cyclic polyene C18H18 in the Pariser–Parr–Pople approximation, where the size of the FCI vector can be reduced to about 73 million components. Running on a CRAY Y-MP with 4 CPU and 32 MW of core memory, we obtained an elapsed CPU time per iteration of about 300 s and a total elapsed time of 1000 s, which correspond to about 4 and 14 s per million determinants, respectively. The parallel CPU speed-up obtained by running with the 4 CPU is greater than 3, without any substantial increasing of the memory or disk requirements.
In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.
The coordinate descent full configuration interaction (CDFCI) is an accurate and efficient method for calculating ground-state energies of molecular systems. In this work we introduce two perturbative extensions of original CDFCI. We first propose a direct CDFCI + PT to further correct variational energy by perturbation theory. We also propose an iterative perturbative CDFCI (IP-CDFCI) to avoid evaluating the overlarge perturbative space and catch the information encoded in variational stage. In IP-CDFCI, we store three sparse vectors in a Hash table: c, b and d, where c is the variational wave function, b is the compressed approximation of H c and d is the perturbative wave function, respectively. By utilizing the redundant memory in the storage of c, we can calculate perturbation without any extra memory compared to original CDFCI. We also use a strategy to eliminate the expensive repetitive evaluation of diagonal elements of Hamiltonian by creating a vector h which stores the diagonal entries of Hamiltonian. This strategy trades memory usage for computational time and reduces the computing time significantly. Furthermore, we use quadruple-precision floating-point numbers to improve the numerical stability of perturbative energy. We demonstrate the effectiveness of the single-threaded IP-CDFCI and the multithreaded CDFCI + PT, respectively, by performing calculations on several small molecular benchmarks as well as challenging correlated system: the chromium dimer.
We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24 000 central processing unit cores. In this paper, we describe the core functionalities of NECI and its recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing us to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs, and it is licensed under GPL-3.0.
High Resolution Image Download MS PowerPoint Slide Full configuration interaction (FCI) can provide an exact molecular ground-state energy within a given basis set and serve as a benchmark for approximate methods in quantum chemical calculations, including the emerging variational quantum eigensolver. However, its exponential computational and memory requirements easily exceed the capability of a single server and limit its applicability to large molecules. In this paper, we present a distributed FCI implementation employing a hybrid parallelization scheme with multithreading and multiprocessing to expand FCI’s applicability. We optimize this scheme to minimize the bottlenecks arising from interprocess communications and interthread data management. Our implementation achieves higher scalability than the naive combination of prior works and successfully calculates the exact energy of C 3 H 8 /STO-3G with 1.31 trillion determinants, which is the largest FCI calculation to the best of our knowledge. Furthermore, we provide a comprehensive list of FCI results with 136 combinations of molecules and basis sets for future evaluation and development of approximate methods.