Parallel quantum chemistry algorithms

Typically, parallel quantum chemistry algorithms require that several pairs of processors communicate simultaneously. Potentially, two messages will vie for the same communication path. This will lead to additional efficiency loss not accounted for in our simple model. While difficult to model, some simple rules can be checked to make sure that there are no obvious communication channel contention problems. First, the amount of communication handled by a single processor is limited by each communication channel s bandwidth, /p, and the number of channels possessed by each processor. This is particularly relevant to master-slave schemes where one processor is assigned more communication than the others. Second, the aggregate bandwidth of the network cannot be exceeded. This is particularly pertinent in networks with very limited connectivity, such as a bus network. 

We will illustrate parallel matrix-vector multiplication algorithms using collective communication in section 6.4, and detailed examples and performance analyses of quantum chemistry algorithms employing collective communication operations can be found in sections 8.3,9.3, and 10.3. 

An important consideration in the parallelization of quantum chemistry algorithms for distributed memory computers is the data distribution. The simplest approach is to replicate all the data on all the nodes. Considering, for example, a parallel direct HF computation, this means that each node must store the Fock matrix, the density matrix, the eigenvectors and a variety of other matrices depending on the implementation. Thus, the storage requirement on each node becomes 0 n ), where n is the number of basis functions, and for the large basis sets that can be handled in a reasonable amount of time on a massively parallel computer, this storage requirement may become prohibitive. 

In this section we describe parallel versions of selected quantum chemistry algorithms. Electron repulsion integral evaluation and Fock matrix formation are discussed, and the performance of the computation of the HF energy is examined. We conclude with examples from MP perturbation theory. For each of these methods a variety of parallel algorithms exist. We illustrate a few selected, simplified algorithms, and develop performance models that permit comparison of the algorithms. 

Here we have briefly discussed performance characteristics of parallel computers and presented performance models for a few of the classic quantum chemistry algorithms as implemented on these machines. It is our hope that this will lx)th elucidate the programming of parallel computers and serve as a guide to understanding the performance of new algorithms on parallel machines. 

This line of research has not lost his momentum. One of the reasons is the eontinuing progress in the computer hardware and software. Methods and algorithms are, and will be, continuously updated to exploit new features made available by eomputer seienee, as for example the parallel architectures, or the neuronal networks, to mention things at present of widespread interest, or even conceptually less significant improvements, as the inerease of fast memory in commereial computers. Computer quantum chemistry is not a mere recipient of progresses in eomputer seienee. Many progresses in the software comes from... 

There have also been many theoretical developments that have extended the applicability and functionality of the DMRG method for quantum chemistry. Some have been algorithmic nature, for example, efficient parallel algorithms... 

We now consider the status of parallelized computer codes and algorithms for computation in quantum chemistry, molecular dynamics, and reaction dynamics. Our focus is on the migration to parallel hardware of the major production codes commonly used, both on workstations and on conventional supercomputers, within the chemistry community. 

At present, parallel computing in quantum chemistry continues to be an active field of research new and improved parallel algorithms for well-established quantum chemical methods are steadily appearing in the literature, and reports of new computational methods are often followed by... 

The second part contains detailed discussions and performance analyses of parallel algorithms for a number of important and widely used quantum chemistry procedures and methods. The book presents schemes for the parallel computation of two-electron integrals, details the Hartree-Fock procedure, considers the parallel computation of second-order Moller-Plesset energies, and examines the difficulties of parallelizing local correlation methods. 

Here we provide a brief hisfory of parallel computing in quantum chemistry and discuss trends in hardware as well as trends in the methods and algorithms of quanfum chemisfry. The impacf of fhese frends on future quantum chemistry programs will be considered. 

Enter massively parallel computing and non-standard computation, the topics of this timely volume computation using molecular aggregates and the chemistry of DNA, genetic algorithms, which mimic natural evolution, computation by cellular automata, and last but not least, quantum computation, the ultimate in speed and parallelism. 

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