Adding the atomic probability distributions along these displacement vectors also defines the ADPs as symmetric tensors corresponding to 3D trivariate Gaussian probability densities (Figure 2 d), which are similar to those obtained from the simpler local approach. Vibrational and librational analysis then yields 3 N−6 fundamental modes for non-linear molecules, along with the corresponding IR vibrational frequencies, the force-constants, reduced masses, and atomic displacement vectors (Figure 2 c).
Micromate allowable vibrations from structure full#
In real molecules, vibrational (stretch) and librational (angular bending) motions occur in correlated modes, and therefore models that are more accurate can be obtained diagonalizing the full Hessian. c) Superposition of normalized Cartesian displacement vectors (scaled by a factor of 2.5 for visualization) computed for all 81 vibration modes of IPC using the full Hessian matrix, and d) the 2 σ ADPs computed therefrom (DFT B3LYP/6–311+G(2d,p)). b) Displacement ellipsoids set at the 2 σ level (95.4 % probability) computed for IPC using the local approach. Though thermal motions are vastly faster than the NMR time-scale and only time-averaged expectation values are measured, any quantitative estimate on the probability with which two or more models can be distinguished by a given method has to consider structure fluctuations and thermal motions as well (Figure 1).Ī) Harmonic potentials (black) and Gaussian-type atomic displacement probability densities (orange) derived from the local harmonic oscillator approximation for H-3 of IPC ( 1 a), whereĭenote the major axes (eigenvectors) of the ADP ellipsoid, and the squared standard deviations σ 2 of displacement derived from the force-constants are the corresponding eigenvalues (Ġ.082 Å). Instead, we discuss a much more fundamental and quantum chemical source of “ structural noise” that has not yet been evaluated with respect to RDC-based configurational analysis, namely thermal vibrations. 4 Unlike in our previous report 5 where structure uncertainties were estimated purely based on geometric considerations, we here would like to abandon this traditional classical approach entirely. 5 For this, we have been criticized as to introducing “ spurious structural noise” which “ has to largely undermine discrimination capabilities of the AIC procedure”. In a recent report we have demonstrated that even for simple molecules such as Isopinocampheol (IPC, 1), the inclusion of error estimates on the structure models themselves substantially lowers the certainties of RDC-based configurational assignments from ≈1:10 −11 to 95 %:5 %.
1c, 1d, 4, 5 Though this method is used frequently in the literature, we have observed that the back-calculation of anisotropic NMR data subtly depends on the method from which the structure models were obtained (e.g. Standard Monte-Carlo (MC) based analysis of experimental errors yields distributions of AIC scores for alternate models, which can be used to compute quantitative estimates on diastereomeric differentiabilities.
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