Accurate Coupled-Cluster Solutions of the Molecular Schrodinger Equation

This paper derives from the proceedings of an invited talk I presented at the American Conference on Theoretical Chemistry (ACTC) in 1978. Besides being timely scientifically, the paper’s creation offers some amusing insight into how science is done. Quantum chemistry approxim:’ I /so!sc4.? Schrodinger equation. To be predictive “electron correlation” must be included. In the 19505 two developments occurred that would have important ramifications for the problem of correlation. The first was the work of LA. Brueckner and I. Goldstone, who recognized that certain terms in Rayleigh-Schrödin~erperturbation theory that had the wrong behavior on the number of electrons in a system would cancel from the exact energy and wavefunction. Without this cancellation no meaningful answers could be obtained for extended systems, and poorer results woukl be obtained for small molecules. These unphysical terms came to be called “unlinked”diagrams because of the use of field-theory methods in establishing the fad that the correct energy and wavefunction are obtained exclusively from linked diagrams. The approach based upon the linked-diagram theorem was termed (many-body) perturbation theory because it was suitable for many-electron systems. We presented some of the initial molecular applications in 1974. fSee reference 1 for a reviewj Another aspect of the same physics is that the linked-diagram wavefunction could he written in terms of an exponential cluster-type operator. This was recognized by 1-lubband, F. Coester, and H. Kummel and eventually became the basis for coupled-cluster (CC) theory. In applications to correlation this offered an alternative to finite-order manybody perturbation theory (MBPT): choosing instead to evaluate selected cluster contributions to all orders of perturbation theory. Initial equations for the CC doubleexcitation (CCD) approximation were presented by l -Cazek,~ under the term coupfed-pasr many-electron theory. My paper with G.D. Purvis offers three elements: 1) Along with the adjacent paper by J-& Pople et at, 3 it reports the first general a!, inifio applications of the CCD method for a varietyof small molecules. 12) It reports on the often important effects of quadruple excitations in molecular calculations for both CCC) and MBPT. Such information had not been generally obtainable from the configuration interaction (Cl) method because of different computational limitations. (3) It emphasizes the importance ofcorrect scaling with molecular size in quantum chemistry lie., size-extensivity), showing that CCJMBPT methods eliminate the important unlinked-diagram error remaining in Cl methods. The paper’s populanty derives from the crystallization of these three developments in 1978, combined with the later, extensive application of CC/MBPT approaches as an alternative to the older Cl method. I understand this paper is the eighth most-cited paper from the lnternationa! Journal of Quantum Chemistry. To get results prior to the ACTC, we worked feverishly at debugging our code. Asoften happens— vent “e about to get long-sought results, fate inters~r.e~~htningstruck the lattelle laboratory and decommissioned the computer! After another two days recovering, we ran calculations day and night, with Purvis staying behind an extra day to ohtam the final results. Considering the complexity of the CCIMBPTequations and programs, internal checks may not reveal all errors in codes; but, when doing newthings, you seldom have an independent check. In this instance, we knew that Pople’s group was writing programs for the same purpose. Pople was also scheduled to speak at the ACTC. Armedwith results for the same trial molecule, we met with Pople the Sunday before the ACTCbegan and compared numbers. To our mutual relief, the independently computed values agreed, enabling us to present our lectures as plannedt Since 1978 we have extended CC methods to include single excitations (CCSD$ and triple excitations (CCSDT), 5 demonstrating highly accurate results for a variety of molecular properties. Attesting to accuracy versus efficiency, in the last two years CC methods have become the methodof choice for other computational-chemistry groups.’ This should guarantee the long-term impact of CC methods in chemistry.