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2542463671
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Strictly speaking, these are partial functional derivatives.
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24
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0003893794
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27
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2542443122
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note
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PP · δP includes the contraction of the perturbed density matrix δP with the ERIs. The perturbed density matrices for the ground and excited states can all be contracted simultaneously using only a single evaluation of the costly ERIs, and hence the cost of evaluating seven roots is only 50% greater than for a single root.
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29
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2542497462
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note
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3Natom/SO(3). Our implementation presently uses Cartesian coordinates, so we have adopted the parallel-transport approach.
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30
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2542481412
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note
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PP-1 is valid.
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31
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2542476691
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note
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For the first step of the geometry optimization, the preconditioner from the previous step is not available, so Lindh's empirical preconditioner is used (see Ref. 28).
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32
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33645226065
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2542484149
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note
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In order to obtain rigorous integral bounds, the screening algorithm should be adapted for derivative ERIs (see Ref. 32). We have not done this; instead, have simply used the Schwartz bound appropriate for undifferentiated ERIs.
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34
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2542438398
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note
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Reference 2 suggests that the RFO Lagrangian can be made size consistent using the metric G= 1/√3 Natom, but this may contain a typographical error because the denominator of the Lagrangian, G δ· δ, then scales as the square root of molecule size, and hence is not size intensive.
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36
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2542464630
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See Eqs. (4b), (16), and (A10)
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See Eqs. (4b), (16), and (A10).
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37
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2542489889
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note
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To determine whether the geometry step should be rescaled, the step vector is transformed to the eigenvector basis of the subspace Hessian. If the maximum component exceeds 1 a.u., then the entire geometry vector is multiplied by a scaling factor.
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38
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0001329184
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2542460839
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note
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For a summary of covariant and contravariant matrix representations in a nonorthogonal basis, see, for example, Ref. 41.
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41
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0031565710
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C. A. White, P. Maslen, M. S. Lee, and M. Head-Gordon, Chem. Phys. Lett. 276, 133 (1997).
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