Because of the apparent flexibility of the chain attached at C-9, several minima were obtained for 3 by DFT calculations at B3LYP/6 31+G d,p /PCM level.
At present, the energy function is based on the Landau Hamiltonian, the minima of which are stable conformations of protein fragments; these minima are obtained as kink solutions of the Discrete Nonlinear Schrödinger Equation.
This is why, the approximate positions of the minima are obtained from the relation: q_{i} simeq frac{pi}{2 u_{i}},~~~~i=1, cdots, m (26).
α i coefficients, determining the depth of minima, are obtained by [39] alpha_{i}=1-left(frac{gamma_{i}}{gamma_{langle 001rangle}}right)left 1-alpha_{langle 001 rangleft 1-alpha_{langle
The estimates for the global energy minima were obtained from simulated annealing followed by an optimization with analytical gradients using a subspace trust-region method [53].
Absolute valence band maxima and conduction band minima were obtained by calculating the difference between the highest occupied and lowest unoccupied one-electron eigenvalues and a reference vacuum potential.
The maximum IWUE was obtained with the SSD (2.12 kg m−3) and the minimum was obtained with the FI method (1.43 kg m−3).
The maximum total phenol content in locally grown lemon was found in methanol extract and the minimum was obtained in butanol extract.
Thus, according with M06-2X/6-311++G d,p) only one potential energy hypersurface minimum was obtained (See Figure 2).
Imputations were repeated using different initial missing value estimates to provide assurance that a global minimum was obtained.
