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It is now well established that the spin-adapted time-dependent density functional theory [X-TD-DFT; Li and Liu, J. Chem. Phys. 135, 194106 (2011)] for low-lying excited states of open-shell systems has very much the same accuracy as the conventional TD-DFT for low-lying excited states of closed-shell systems. In particular, this has been achieved without computational overhead over the unrestricted TD-DFT (U-TD-DFT) that usually produces heavily spin-contaminated excited states. It is shown here that the analytic energy gradients of X
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