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The Journal of Chemical Physics

A vector and parallel full configuration interaction algorithm

Gian Luigi Bendazzoli, Stefano Evangelisti

Published Feb 15, 1993• 111 citations
Publisher

Abstract

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.

DOI
10.1063/1.464087

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The Journal of Chemical Physics•Jun 22, 2016•19 citations
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.
A parallel full configuration interaction (FCI) code, implemented on a distributed memory MPP computer, has been modified in order to use a direct algorithm to compute the lists of mono- and biexcitations each time they are needed. We were able to perform FCI calculations on the ground state of the acetylene molecule with two different basis sets, corresponding to more than 2.5 and 5 billion Slater determinants, respectively. The calculations were performed on a Cray-T3D and a Cray-T3E, both machines having 128 processors. Performance and comparison between the two computers are reported and discussed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 658–672, 1998
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.
Full configuration interaction (FCI) serves as a benchmark tool for evaluating the accuracy of approximate quantum chemical methods. However, its exponential computational cost limits its practical use. The inherently parallel and compute-intensive nature of matrix and vector operations in FCI is well-suited for acceleration on modern GPU architectures. Despite this potential, prior research has only focused on accelerating the matrix and vector multiplication, thus failing to fully exploit the power of GPUs. In this paper, we present a fully GPU-accelerated FCI implementation that uses a CUDA-enabled GPU for the entire computational workflow, achieving end-to-end acceleration. Our implementation incorporates and refines advanced optimization strategies from previous studies, while crucially eliminating redundant computational steps and minimizing CPU-GPU data transfers. To facilitate broad usability and integration, we offer both Python- and C-based implementations. Our C implementation achieves up to a 35.4× speedup over a multithreaded CPU implementation and up to a 15.9× speedup over the current leading GPU-based implementation, respectively. Our Python implementation also delivers substantial acceleration, reaching up to 18.9× and 8.7× speedups over CPU and prior GPU implementations, respectively.
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.
We develop a multithreaded parallel coordinate descent full configuration interaction algorithm (mCDFCI) for the electronic structure ground-state calculation in the configuration interaction framework. The FCI problem is reformulated as an unconstrained minimization problem and tackled by a modified block coordinate descent method with a deterministic compression strategy. mCDFCI is designed to prioritize determinants based on their importance, with block updates enabling efficient parallelization on shared-memory, multicore computing infrastructure. We demonstrate the efficiency of the algorithm by computing an accurate benchmark energy for the chromium dimer in the Ahlrichs SV basis (48e, 42o), which explicitly includes 2.07 × 10 9 variational determinants. We also provide the binding curve of the nitrogen dimer under the cc-pVQZ basis set (14e, 110o). Benchmarks show up to 79.3% parallel efficiency on 128 cores.
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.