We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new MCPT(2) framework uses coupled-cluster perturbation theory and an expansion in terms of molecular dimer interactions to obtain molecular wavefunctions that are infinite-order in both the electronic fluctuation operator and all possible dimer (and products of dimers) interactions. The MCPT(2) framework has been implemented in the new SIA/Aces4 parallel architecture, making use of the advanced dynamic memory control and fine grained parallelism to perform very large explicit molecular cluster calculations. To illustrate the power of this method, we have computed energy shifts, lattice site dipole moments, and harmonic vibrational frequencies via explicit calculation of the bulk system for the polar and non-polar polymorphs of solid hydrogen fluoride. The explicit lattice size (without using any periodic boundary conditions) was expanded up to 1,000 HF molecules, with 32,000 basis functions and 10,000 electrons. Our obtained HF lattice site dipole moments and harmonic vibrational frequencies agree well with the existing literature.
The Super Instruction Architecture (SIA) is a parallel programming environment designed for problems in computational chemistry involving complicated expressions defined in terms of tensors. Tensors are represented by multidimensional arrays which are typically very large. The SIA consists of a domain specific programming language, Super Instruction Assembly Language (SIAL), and its runtime system, Super Instruction Processor. An important feature of SIAL is that algorithms are expressed in terms of blocks (or tiles) of multidimensional arrays rather than individual floating point numbers. In this paper, we describe how the SIA was enhanced to exploit GPUs, obtaining speedups ranging from two to nearly four for computational chemistry calculations, thus saving hours of elapsed time on large-scale computations. The results provide evidence that the "programming-with-blocks" approach embodied in the SIA will remain successful in modern, heterogeneous computing environments.
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