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Nuclear quantum effects are important in a variety of chemical and biological processes. The constrained nuclear-electronic orbital density functional theory (cNEO-DFT) has been developed to include nuclear quantum effects in energy surfaces. Herein, we develop the analytic Hessian for cNEO-DFT energy with respect to the change in nuclear (expectation) positions, which can be used to characterize stationary points on energy surfaces and compute molecular vibrational frequencies. This is achieved by constructing and solving the multicom
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