Coupled cluster theory tackles a protein

Numerically solving the Schrödinger equation for all N electrons in an atom or molecule is impractical: The computational effort required scales exponentially with N. So computational chemists must develop approximations. (See the article by Martin Head-Gordon and Emilio Artacho, Physics Today, April 2008, page 58 .) The sticking point is in accurately treating the electron correlations: the difference between the true N-electron wavefunction and the antisymmetrized product of N single-electron wavefunctions. The most widely used form of one favorite approximation, called coupled cluster theory, treats two-electron correlations exactly and genuine three-electron correlations perturbatively. Such a calculation is accurate enough for most purposes, but its computational cost scales as N⁷, making it prohibitively slow for molecules with more than a few dozen atoms. It’s long been recognized that electron correlations are mostly local—two widely separated electrons are unlikely to be significantly correlated—and several groups have been working to exploit that locality to develop a faster version of coupled cluster theory. Now Frank Neese and colleagues at the Max Planck Institute for Chemical Energy Conversion have done it. Using a so-called domain-based local pair natural orbital (DLPNO) approach, they’ve implemented a coupled cluster method that scales nearly linearly with N. On a test set of medium-sized organic molecules, the DLPNO-based method captured more than 99.8% of the electron-correlation energy found by standard coupled cluster calculations. Neese and colleagues then used their new method to calculate the electronic energies of the linear hydrocarbon C₁₅₀H₃₀₂ and the 644-atom protein crambin (shown in the figure ). The crambin calculation took 30 days; a standard coupled cluster calculation on the same molecule would have taken many thousands of years. (C. Riplinger et al., J. Chem. Phys., in press.)—Johanna L. Miller