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- W2569306166 abstract "Excited states are often treated within the context of time-dependent (TD) density-functional theory (DFT), making it important to be able to assign the excited spin-state symmetry. While there is universal agreement on how Δ〈Sˆ2〉, the difference between 〈Sˆ2〉 for ground and excited states, should be calculated in a wave-function-like formalism such as the Tamm–Dancoff approximation (TDA), confusion persists as to how to determine the spin-state symmetry of excited states in TD-DFT. We try to clarify the origins of this confusion by examining various possibilities for the parameters (σ1,σ2) in the formula Δ〈Sˆ2〉=[Δ〈SˆTDA2〉(X→)+Δ〈SˆTDA2〉(Y→∗)+σ1Δ〈Sˆmixed2〉(X→,Y→∗)]/(X→†X→+σ2Y→†Y→), where X→ is the particle–hole part and Y→ is the hole–particle part of the response theory vector. A first principles derivation leads directly to (σ1,σ2)=(+1,−1) which we argue is the best simple formula linking spin with energy, albeit approximately. On the other hand, if the desire is to recover wave-function-like values of Δ〈Sˆ2〉, then we argue that the choice (σ1,σ2)=(+1,+1) should be made. Additional examples are offered to justify that the choice of σ1=0 should also be made when seeking wave-function-like values of Δ〈Sˆ2〉." @default.
- W2569306166 created "2017-01-13" @default.
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- W2569306166 date "2017-04-01" @default.
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- W2569306166 title "On the calculation of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>Δ</mml:mi><mml:mrow><mml:mo>〈</mml:mo><mml:msup><mml:mrow><mml:mover accent=true><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mo>ˆ</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>〉</mml:mo></mml:mrow></mml:math> for electronic excitations in time-dependent density-functional theory" @default.
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- W2569306166 doi "https://doi.org/10.1016/j.cpc.2016.12.011" @default.
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