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General build up of K + basis and K + 2 matrix in the diagonalization approach. Determination of Kramers configuration state functions
Author(s) -
Gall Marián,
Bučinský Lukáš,
Komorovsky Stanislav
Publication year - 2018
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25638
Subject(s) - basis (linear algebra) , matrix representation , matrix (chemical analysis) , spinor , gramian matrix , representation (politics) , computer science , basis function , theoretical computer science , algorithm , algebra over a field , mathematics , pure mathematics , eigenvalues and eigenvectors , physics , quantum mechanics , mathematical analysis , group (periodic table) , geometry , materials science , politics , political science , law , composite material , mathematical physics
Algorithms to build theK ̂ +basis andK ̂ + 2matrix representation to obtain theK ̂ + 2Kramers configuration space functions (KCSFs) via diagonalization will be formally generalized to an arbitrary number of unpaired (open shell) fermions. Effective build up of theK ̂ + 2matrix representation will be outlined (including threading and graphical processing unit parallelism) to subsequently obtain the KCSFs via calling external/numerical library routines for diagonalization. The effective build up of theK ̂ + 2matrix representation relays on a binary tree search algorithm to allow evaluation theK ̂ iK ̂ jaction on a givenK ̂ +basis vector. The binary tree search avoids the treatment of zeroK ̂ + 2matrix elements which leads to an exponential acceleration. The implementation (K ̂ +basis creation,K ̂ + 2matrix representation, andK ̂ + 2matrix diagonalization) will be done in an all in core and all at once manner, hence the available core memory sets the physical limits in practical applications. Memory limitations, sparsity of theK ̂ + 2matrix, general case of n fermions in m spinors, and the application of KCSFs will be put into further perspective.