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Chapter 1 An Introduction to the State of the Art in Quantum Chemistry

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While computer hardware continues to closely follow Moore's law (doubling the performance-price ratio every 18 months), the introduction of new algorithms over the years has given at least the same amount of improvements. For HF and DFT methods, the scaling with system size appears to have been solved, and these methods are well suited for running in parallel on inexpensive cluster-type computers. There is little doubt that systems containing up to thousands of atoms will be attempted in the near future. Unfortunately, there is at present no clear picture of how the current exchange-correlation functionals can be improved for achieving a better accuracy of DFT methods. Semi-empirical methods have been resurrected after lying dormant for almost a decade, and are being parameterized for more elements, and attempts are being made at developing DFT analogues of semi-empirical methods. Already with the current technology, systems with 10,000 atoms are possible on single CPU machines. Semi-empirical methods currently hold the best promise for performing direct dynamics for systems with thousands of atoms, but the fundamental accuracy is still somewhat lower than desired. The two major problems in wave function based electron correlation methods are the agonizing slow convergence with respect to basis set size and the high scaling of computer time with system size. Methods using the interelectronic distance as a variable hold promises for improving the basis set convergence, but have so far primarily been used for calibration purposes. The few attempts of designing methods with reduced scaling with system size have so far had very little influence, presumably because the break-even point in terms of computer time is well beyond the current feasibilities. The high scaling of these methods is at variance with the fundamental physical interaction being pair-wise, and achieving even a N scaling would be a major breakthrough. Algorithmic improvements are also required before these methods can be used efficiently on massively parallel computers.
Original languageEnglish
JournalAnnual Reports in Computational Chemistry
Pages (from-to)3-17
Number of pages15
Publication statusPublished - 2005
Externally publishedYes

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