We present an efficient implementation of the perfect pairing and imperfect pairing coupled-cluster methods,as well as their nuclear gradients,using the resolution of the identity approximation to calculate two-electron integrals.The perfect pairing and imperfect pairing equations may be solved rapidly,making integral evaluation the bottleneck step.The method's efficiency is demonstrated for a series of linear alkanes,for which we show significant speed-ups (of approximately a factor of 10)with negligible error.We also apply the imperfect pairing method to a model of a recently synthesized stable singlet biradicaloid based on a planar Ge-N-Ge-N ring,confirming its biradical character,which appears to be remarkably high.
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