By using wavefunction overlaps you can run nonadiabatic dynamics without computing coupling vectors. This little trick gives you lots of freedom and allows you to run dynamics for any method as long as it gives you gradients. Different people have done that for TDDFT, we have added interfaces for coupled cluster and ADC, and for multireference methods with spin-orbit coupling. However, the one big problem about wavefunction overlaps is that computing them can get really expensive very quickly. Since the orbitals change between the two geometries, the Slater Condon rules do not apply anymore meaning that you have to compute one overlap determinant for every pair of Slater determinants in the expansion.
Fortunately, the situation is not quite as bad, as there are many repetitive terms. If you precompute those and reuse them, things get better. The first step was to identify those repetitive terms, the second one was to think of an algorithm that takes advantage of them, the third one was actually implementing it in a code that works. The result was quite nice: Typical calculations run a thousand times as fast as our previous code and produce exactly the same result. At the same time our formalism is completely general and allows you to do also other things than dynamics. More about that later ...
Read more about our algorithm in our new JCTC paper "Efficient and Flexible Computation of Many-Electron Wavefunction Overlaps". If you want to try it out yourself, wait for the new SHARC release or contact me.
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