TDDFT in Chemistry and Biochemistry III - TDDFT.org
TDDFT in Chemistry and Biochemistry III - TDDFT.org
TDDFT in Chemistry and Biochemistry III - TDDFT.org
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Strategies for Solv<strong>in</strong>g Matrix EquationsIterative methodsSolution of l<strong>in</strong>ear equation on iteratively exp<strong>and</strong>ed subspace S ⊂ L;Matrix elements (A + B) iajb , (A − B) iajb need not to be stored;Time-determ<strong>in</strong><strong>in</strong>g step is computation of matrix-vector products∑jb (A ± B) iajb(X ± Y ) jb ,very similar to ground-state DFT calculations;n iter = 20 − 50 iterations are sufficient for most systems;Integral pre-screen<strong>in</strong>g reduces computational cost to N 2 · n iter ;Resolution-of-the-identity (RI-J) techniques reduce computationalcost by factor 10–100 for non-hybrid functionals.Dmitrij Rappoport (Harvard U.) <strong>TDDFT</strong> <strong>in</strong> <strong>Chemistry</strong> <strong>III</strong> <strong>TDDFT</strong> W<strong>in</strong>ter School 2010 18 / 22
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