Absolute energy minimum

The problem associated with the solution of the matrix equations (2.30) is to explore the energy surface for the total Hamiltonian H. to study its local minima and extreme values, and - if possible - to find the absolute energy minimum connected with the Hartree-Fock method. Thanks to Fukutome s work [26], this problem has now been essentially... 

The X point is on the A axis of the BZ with <100> orientation and the absolute energy minimum of the CB of the corresponding cubic crystals of Table 3.4 is sixfold degenerate in k-space. For germanium, it is only fourfold... 

Independently of the method used for conformational analysis, the conformations generated are analysed for conformational similarity and classified according to energy content, and only dissimilar conformers within a defined energy window are retained for further investigation. Depending on the molecular mechanics force field used, the window may extend from 5 to 10 kcal mol above the absolute energy minimum. 

Utilizing Quantum Mechanics to analyze the geometry of the glycine in the absence of solvent, two energy minima are obtained (Figure 2.1.9), differentiated essentially by the rotation of the acid group. One of them is the absolute energy minimum in the gas phase (I), and the other is the conformation directly related with the ionic structure (II) The structure which is furthest from the zwiterionic form, I, is 0.7 Kcal/mol more stable than II, which... 

W. Yang Absolute-energy-minimum principles for linear-scaling electronic-structure calculations, Phys. Rev. B 56, 9294-9297 (1997). 

Absolute energy minimum principle. Kohn developed an absolute energy minimum principle in terms of density matrix also for the case of noninteracting electrons. The method is based on a penalty functional for imposing the idem-potency condition. It does not require a series of calculations with increasing values of the coefficient for the penalty functional. One fixed value of the coefficient suffices. Kohn proved that for a nonself-consistent Hamiltonian h, the ground-state... 

Absolute energy minimum principle. Yang developed two absolute energy minimum principles for first-principle linear-scaling electronic structure calculations. One is with a normalization constraint and the other without any constraint. The density matrix is represented by a set of nonorthogonal localized orbitals [i/] and an auxiliary matrix X which at the minimum becomes the (l)-inverse of the overlap matrix S of the localized orbitals. The number of localized orbitals is allowed to exceed the number of occupied orbitals. 

In the case of iP4MP, the increased bulkiness of the side groups makes the distorted helical conformations (T G )n, corresponding to the 7/2 and 4/1 symmetries, more stable than the 3/1 helix. The absolute energy minimum is at values of torsion angles close to the 7/2 helical conformation, found in the form I of iP4MP [38, 48] and 4/1 helix, found in form II [49-51] and form III... 

According to these calculations, two crystalline forms of sPB have been found [68,70,71] the most stable form I with chains in the s(2/l)2 helical conformation [68,70] and the metastable form II characterized by chains in the helical conformation with s(5/3)2 symmetry [68,71]. For sP4MP, only one crystalline form with chains in the distorted helical conformation with s(12/7)2 symmetry has been found [69,72], which corresponds to the absolute energy minimum [69]. The helical conformations of... 

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