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(Formula presented) and (Formula presented) are entirely distinct. For instance the equation (Formula presented) does not hold.
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(Formula presented) and (Formula presented) are entirely distinct. For instance the equation (Formula presented) does not hold.
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This is in the spirit of the standard Ewald summation and requires that the diverging term in (Formula presented) cancel against the (Formula presented) terms in the other two terms in Eq. (16). We will not derive this in detail, and the treatment is analogous to J. Ihm, A. Zunger, and L. Cohen, J. Phys. C 12, 4409 (1979).
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In the way we use the force theorem here it is equivalent to the Hellmann-Feynman force theorem because plane waves are independent of the ionic positions.
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In the way we use the force theorem here it is equivalent to the Hellmann-Feynman force theorem because plane waves are independent of the ionic positions.
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It is possible to construct US-PP with unfrozen (Formula presented) electrons, but these US-PP are not more precise than PP without unfrozen (Formula presented) electrons, unless the augmentation charges are exceedingly hard.
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It is possible to construct US-PP with unfrozen (Formula presented) electrons, but these US-PP are not more precise than PP without unfrozen (Formula presented) electrons, unless the augmentation charges are exceedingly hard.
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