AUTOMOTIVE

The calculation requires solving an approximation of the Schrödinger equation, one of the central equations of quantum mechanics. It can be approximated as the sum of an infinite number of terms, each additional term contributing a bit more to the accuracy of the result. For all but the simplest systems or a relative handful of terms, however, the calculation rapidly becomes impossibly complex. While very precise calculations have been done for systems of just three components such as helium (a nucleus and two electrons), Sims and Hagstrom are the first to reach this level of precision for H2 with two nuclei and two electrons. Their calculations were carried out to 7,034 terms. To make the problem computationally practical, Sims and Hagstrom merged two earlier algorithms for these calculations—one which has advantages in ease of calculation, and one which more rapidly achieves accurate results—into a hybrid with some of the advantages of both. They also developed improved computer code for a key computational bottleneck (high-precision solution of the large-scale generalized matrix eigenvalue problem) using parallel processing. The final calculations were run on a 147-processor parallel cluster at NIST over the course of a weekend—on a single processor it would have taken close to six months.