Assessment of a semi integral-direct local multi-reference configuration interaction implementation employing shared-memory parallelization
Graphical abstract
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.
References (37)
- et al.
Shared-memory parallelization of a local correlation multi-reference ci program
Comp. Phys. Comm.
(2014) Localizability of dynamic electron correlation
Chem. Phys. Lett.
(1983)- et al.
Local configuration interaction: an efficient approach for larger molecules
Chem. Phys. Lett.
(1985) - et al.
Multi-reference weak pairs local configuration interaction: efficient calculations of bond breaking
Chem. Phys. Lett.
(2001) - et al.
Advances in electronic structure theory: GAMESS a decade later
- et al.
Symmetric group approach to configuration interaction methods
Comput. Phys. Rep.
(1985) - et al.
Integral-direct electron correlation methods
Mol. Phys.
(2011) - et al.
Numerical challenges in a cholesky-decomposed local correlation quantum chemistry framework
- et al.
Low-order scaling local electron correlation methods. I. Linear scaling local MP2
J. Chem. Phys.
(1999) - et al.
Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD)
J. Chem. Phys.
(2001)
Rigorous integral screening for electron correlation methods
J. Chem. Phys.
Cholesky decomposition within local multireference singles and doubles configuration interaction
J. Chem. Phys.
Approximately size extensive local multireference singles and doubles configuration interaction
Phys. Chem. Chem. Phys. PCCP
Local treatment of electron correlation
Annu. Rev. Phys. Chem.
Local weak-pairs pseudospectral multireference configuration interaction
J. Chem. Phys.
Local correlation in the virtual space in multireference singles and doubles configuration interaction
J. Chem. Phys.
Cited by (9)
Eliminating Systematic Errors in DFT via Connectivity-Based Hierarchy: Accurate Bond Dissociation Energies of Biodiesel Methyl Esters
2019, Journal of Physical Chemistry AAb Initio Reaction Kinetics of CH<inf>3</inf>OC(=O) and CH<inf>2</inf>OC(=O)H Radicals
2016, Journal of Physical Chemistry BAb initio kinetics studies of hydrogen atom abstraction from methyl propanoate
2016, Physical Chemistry Chemical PhysicsDensity fitting and Cholesky decomposition of the two-electron integrals in local multireference configuration interaction theory
2015, Journal of Chemical Theory and ComputationAb Initio Unimolecular Reaction Kinetics of CH<inf>2</inf>C(=O)OCH<inf>3</inf> and CH<inf>3</inf>C(=O)OCH<inf>2</inf> Radicals
2015, Journal of Physical Chemistry A