Assessment of a semi integral-direct local multi-reference configuration interaction implementation employing shared-memory parallelization

https://doi.org/10.1016/j.comptc.2014.10.030Get rights and content

Highlights

  • Avoiding the serial I/O bottleneck: simple, direct integral reassembly on-the-fly.

  • Higher parallel efficiency through integral-direct computations.

  • Local correlation approximations and Cauchy–Schwarz prescreening drastically reduce the number of significant integrals.

Abstract

We present different integral-direct implementations in a local Cholesky-decomposed multi-reference configuration interaction framework. We discuss their performance, parallel efficiency and scaling properties for a range of alkyne test systems. As we are able to introduce accuracy-preserving integral truncations within a direct algorithm, we observe superior performance and, through the drastically reduced I/O operations, better parallel efficiency for the truncated integral-direct kernels compared to their conventional counterparts.

Introduction

Integral-direct schemes are traditionally used to reduce the huge storage requirements that are a property of correlated wavefunction methods [1]. The increased, redundant, floating-point operations required to reduce input/output (I/O) to disk causes these methods to be computationally more expensive than their conventional counterparts. Today, with typical hardware configurations already focusing on parallel processing power more than I/O, reduction of the latter is required for future-proof codes. In future hardware, it may be that standard configurations will be those for which recomputing even complex intermediate quantities concurrently is faster than reading them from storage.

Local correlation methods typically employ integral-direct implementations because keeping track of only the relevant integrals proves cumbersome [2], [3], [4]. Others have shown that a rigorous prescreening of the integrals can be used to reduce the scaling of, e.g., Møller–Plesset perturbation theory [5]. Prescreening naturally exploits the local character of electron correlation.

In this contribution, we discuss our new integral-direct, parallel [6] implementation of Cholesky-decomposed local multi-reference singles and doubles configuration interaction (CD-LMRSDCI [7]) and its size-extensive extension, multi-reference averaged coupled-pair functional (MRACPF) [8] theory within our TigerCI code [2]. Since I/O is intrinsically a process of low parallelism, fewer I/O operations directly translate to reducing bottlenecks in the code. We assess herein the parallel efficiency of this new integral-direct implementation. Additionally, we discuss how augmenting the existing local approximations [9], [10], [11], [12], [13], [14] with a Cauchy–Schwarz (CS) prescreening [15], [16], [17] of integrals on the molecular orbital level is used to reduce the scaling of our MRSDCI implementation.

The overall implementation discussed here is a semi-direct one, meaning that not all integrals are computed on-the-fly. Instead, depending on the number of integrals of a certain type and access character, the integrals are either recomputed or stored on disk with optional buffering provided by our IOBuffer [2]. We will discuss the reasons for integral-direct reformulations of various different types of kernels in what follows.

Section snippets

Algorithms

All algorithms presented in this contribution were implemented in our TigerCI program for Cholesky-decomposed (CD) local multi-reference SDCI/ACPF [2], [7], [8], [13], [14], [18], [19], [20]. TigerCI currently is a plugin to either MOLCAS [21] or GAMESS [22], [23], [24]. As both the algorithms and numerical challenges have been reviewed at length elsewhere [2], [8], we focus here on concise discussions of the properties relevant for our integral-direct implementation.

Starting from a reference

Performance and accuracy analysis

In order to assess the performance and accuracy of the integral-direct local multi-reference SDCI/ACPF implementation, we compute the total ground-state electronic energy of the 1-decyne, 1-pentadecyne, and 1-icosyne molecules (from here on referred to as decyne, pentadecyne, and icosyne, respectively) in their equilibrium geometries, where the latter are taken from predictions by classical force fields [32], [33]. We use as a reference wavefunction a CAS(4e,4o) SCF wavefunction [21] with all

Conclusions and outlook

We have presented and analyzed integral-direct implementations within our multi-reference configuration interaction program, TigerCI. We have one mode targeted at canonical and small local calculations that does not truncate any integrals, and a second mode exploiting both the local approximations and employing the Cauchy–Schwarz (CS) prescreening on the MO level.

For large molecules, we find the latter mode to be vastly superior to the conventional as well as the regular direct mode even

Acknowledgements

We thank the U.S. National Science Foundation (Grant No. 1265700) for support of this work. All calculations presented in the performance assessment section were carried out using Princeton’s TIGRESS High Performance Computing resources.

JMD wishes to thank Dr. Christoph Riplinger and Nari Baughman for critically reading this manuscript. JMD wishes to thank Victor Oyeyemi for providing the methyldecanoate test case.

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