scholarly journals An efficient implementation of the NEVPT2 and CASPT2 methods avoiding higher-order density matrices

2021 ◽  
Author(s):  
Christian Kollmar ◽  
Kantharuban Sivalingam ◽  
Yang Guo ◽  
Frank Neese
Keyword(s):  
Higher Order ◽  
Efficient Implementation ◽  
Density Matrices

scholarly journals Quadratic canonical transformation theory and higher order density matrices

2009 ◽  
Vol 130 (12) ◽  
pp. 124102 ◽  
Author(s):  
Eric Neuscamman ◽  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Higher Order ◽  
Transformation Theory ◽  
Density Matrices

scholarly journals Provably correct, asymptotically efficient, higher-order reverse-mode automatic differentiation

2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-30
Author(s):  
Faustyna Krawiec ◽  
Simon Peyton Jones ◽  
Neel Krishnaswami ◽  
Tom Ellis ◽  
Richard A. Eisenberg ◽  
...  
Keyword(s):  
Automatic Differentiation ◽  
Higher Order ◽  
Efficient Implementation ◽  
Formal Description ◽  
Memory Consumption ◽  
Reverse Mode ◽  
Original Program ◽  
Run Time ◽  
Asymptotically Efficient ◽  
Higher Order Functions

In this paper, we give a simple and efficient implementation of reverse-mode automatic differentiation, which both extends easily to higher-order functions, and has run time and memory consumption linear in the run time of the original program. In addition to a formal description of the translation, we also describe an implementation of this algorithm, and prove its correctness by means of a logical relations argument.

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