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arXiv:2411.07565 · Journal of Chemical Theory and Computation

Parallel Multicoordinate Descent Methods for Full Configuration Interaction

Yuejia Zhang, Weiguo Gao, Yingzhou Li

Published Feb 28, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1021/acs.jctc.4c01530

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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.
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.
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.
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
The full configuration interaction quantum Monte Carlo (FCIQMC) method, as well as its "initiator" extension (i-FCIQMC), is used to tackle the complex electronic structure of the carbon dimer across the entire dissociation reaction coordinate, as a prototypical example of a strongly correlated molecular system. Various basis sets of increasing size up to the large cc-pVQZ are used, spanning a fully accessible N-electron basis of over 10(12) Slater determinants, and the accuracy of the method is demonstrated in each basis set. Convergence to the FCI limit is achieved in the largest basis with only O[10(7)] walkers within random errorbars of a few tenths of a millihartree across the binding curve, and extensive comparisons to FCI, CCSD(T), MRCI, and CEEIS results are made where possible. A detailed exposition of the convergence properties of the FCIQMC methods is provided, considering convergence with elapsed imaginary time, number of walkers and size of the basis. Various symmetries which can be incorporated into the stochastic dynamic, beyond the standard abelian point group symmetry and spin polarisation are also described. These can have significant benefit to the computational effort of the calculations, as well as the ability to converge to various excited states. The results presented demonstrate a new benchmark accuracy in basis-set energies for systems of this size, significantly improving on previous state of the art estimates.
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 study the effect of compression in Coordinate Descent Full Configuration Interaction (CDFCI) within an unconstrained optimization formulation of the full configuration interaction ground-state problem. Under suitable local assumptions, we prove that the compressed iteration converges linearly to the solution of an associated restricted problem. We also characterize the convergence point of the compressed algorithm. Under an additional exponential decay assumption on the target eigenvector, we show that the resulting eigenvalue error is of order τ2τ^2τ2, where τττ denotes the compression threshold. Numerical results support the analysis.