Tensor-factorization for higher excitation order Coupled-Cluster amplitudes for calculating ground-state energy. Automatic code generation

• Applicant: Dr. Daniel Kats
• Subject Area: Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
• Term: from 2010 to 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 189789310

• Final Report Year: 2013

Final Report Abstract

We have developed a new sparse general tensor framework that allows fast implementation of linear-scaling methods for calculation of ground-state energies and properties. The efficiency of resulting implementations is comparable to the best native linear-scaling programs. This tool allows explorations of new approaches as well as implementations of already established methods with local approximations, which will result in a broader selection of computational methods with significantly reduced computational cost available. This framework was used by us to explore the applicability of a recently proposed tensor-factorization scheme (that utilizes orbital-specific virtuals to span the virtual space) to a variety of coupled-cluster based approaches. It also allows to try out novel algorithms for already well-known methods, which was demonstrated by implementing new algorithms for local perturbative iterative methods (like local MP2 or (T) correction to CCSD) that do not require to hold amplitudes or residuals in memory. This program also enabled fast implementations of two new very promising methods, the linearized coupled-cluster doubles (LCCD) with an imaginary correction and the distinguishable cluster approximation. The former has all of the computational advantages of LCCD with a significantly increased stability and can be used as a ground-state reference for hermitian linear-response approaches for excited states. The latter works surprisingly well in all potential surface regions of even extremely difficult cases like the nitrogen molecule and outperforms CCSD in accuracy and computational cost. This method has a potential to become a widely used tool, which can be applied to molecular systems that were unattainable before.

Publications

• Sparse tensor framework for implementation of general local correlation methods, J. Chem. Phys., 138, 144101 (2013)
  D. Kats and F. R. Manby
  
• The distinguishable cluster approximation, J. Chem. Phys., 139, 021102 (2013)
  D. Kats and F. R. Manby