2016/03/17 by Bastien Mussard, Dario Rocca, Georg Jansen +2 · 34 citations
Chemical Engineering · Mathematics · Physics and Astronomy · #Adiabatic process #Advanced Chemical Physics Studies #Ammonia Synthesis and Nitrogen Reduction #Applied mathematics #Cholesky decomposition #Dissipation #Kernel (algebra) #Logarithm #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Random phase approximation #Spectroscopy and Quantum Chemical Studies #Statistical physics #physics.chem-ph
paper · pdf · doi:10.1021/acs.jctc.5b01129
published in Journal of Chemical Theory and Computation 12(5), 2191-2202 (American Chemical Society)
openalex publication_date 2016/03/17 · arxiv created 2016/04/22 · arxiv updated 2016/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case, the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed, and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental for improvement over direct RPA results.