Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations

Journal of Chemical Physics

Volumn 118, Issue 14, 2003, Pages 6144-6151

  Shao, Yihan ^a   Saravanan, Chandra ^a   Head Gordon, Martin ^a   White, Christopher A ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NOKIA RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ATOMS; CALCULATIONS; HAMILTONIANS; HYDROGEN BONDS; MATRIX ALGEBRA; ONE DIMENSIONAL; OPTIMIZATION; PARAFFINS; PURIFICATION; TWO DIMENSIONAL; WATER;

CANONICAL PURIFICATION METHOD; CURVY STEP; DENSITY MATRIX BASED ENERGY MINIMIZATION; LARGE SCALE SELF CONSISTENT FIELD CALCULATIONS; LINEAR SCALING ALGORITHMS; MOLECULAR SIZE; MULTIATOM BLOCKED MATRIX; ONE-DIMENSIONAL ALKANE CHAINS; TWO-DIMENSIONAL WATER CLUSTERS;

PROBABILITY DENSITY FUNCTION;

EID: 0037961619     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1558476     Document Type: Article

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53. We believe the explanation for why Ref. 41 required projection of redundant variables and our approach does not is not because of our use of an orthogonal basis, vs the nonorthogonal basis of Ref. 41. In an orthogonal basis, there is no distinction between covariant and contravariant vectors, and thus a covariant gradient can automatically be converted into a contravariant step which has no component in the occupied-occupied or virtual-virtual spaces. This applies either to steepest descent or to a full Newton step. It is no longer exactly true when cutoffs are applied or when a level shift is added to the Hessian. However, the latter is only done far from convergence. By contrast, in a nonorthogonal basis, when the inverse metric is not used to convert covariant vectors to contravariant, even a steepest descent step will have artificial components in the occupied-occupied and virtual-virtual spaces, because such a step is not tensorially correct.