Interactive quantum chemistry: A divide-and-conquer ASED-MO method

We present interactive quantum chemistry simulation at the atom superposition and electron delocalization molecular orbital (ASED-MO) level of theory. Our method is based on the divide-and-conquer (D&C) approach, which we show is accurate and efficient for this non-self-consistent semiempirical theory. The method has a linear complexity in the number of atoms, scales well with the number of cores, and has a small prefactor. The time cost is completely controllable, as all steps are performed with direct algorithms, i.e., no iterative schemes are used. We discuss the errors induced by the D&C approach, first empirically on a few examples, and then via a theoretical study of two toy models that can be analytically solved for any number of atoms. Thanks to the precision and speed of the D&C approach, we are able to demonstrate interactive quantum chemistry simulations for systems up to a few hundred atoms on a current multicore desktop computer. When drawing and editing molecular systems, interactive simulations provide immediate, intuitive feedback on chemical structures. As the number of cores on personal computers increases, and larger and larger systems can be dealt with, we believe such interactive simulations-even at lower levels of theory-should thus prove most useful to effectively understand, design and prototype molecules, devices and materials.