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** Direct minimization Hartree-Fock **

** Direct minimization techniques **

Direct Minimization Methods in Quantum Chemistry follows that, to second order, the change in R is [Pg.51]

DM (direct minimization) an algorithm for forcing SCF calculations to converge [Pg.362]

To work in the opposite direction, minimization of the Landau free energy with respect to the order parameter, dip/dV = 0, clearly yields [Pg.510]

In-plant reclamation refers to the sand reclamation process in a foundry facility, which directly minimizes the generation of spent foundry sand. Sand reclamation includes physical, chemical, or thermal treatment of foundry sands so they may be safely substituted for new sand in molding and core-making mixes. [Pg.175]

Step 1. For a function to be minimized, determine its ideal solution and anti-ideal solutions by directly minimizing and maximizing the objective function. [Pg.95]

Going back to Eq. (8), the problem now is that one must minimize Ev with respect to the y/i, instead of directly minimizing it with respect to p. This can, however, be achieved by solving Eq. (9), called the Kohn-Sham equation [Pg.45]

In Section 2 we outlined briefly how the ordinary closed-shell SCF problem could be recast as a problem in direct minimization. In this section we consider the problem in a little more detail and also consider its generalization, particularly in respect of incorporating constraints and finding the relevant gradient expressions. [Pg.50]

In a recent paper Shapiro Shapley [4] have considered the problem of the uniqueness of equilibrium of systems of reactions in several phases in great detail. The computation of equilibrium compositions by direct minimization of the Gibbs free energy function has proved a valuable tool in the discussion of very complex systems and it is important to show that this minimum is unique and achieved under the same conditions that satisfy the mass action laws. This is what Shapiro Shapley have done Sellers has suggested some improvements [5]. [Pg.171]

A finite difference formula is used to estimate the second derivatives of the coordinate vector with respect to time and S is now a function of all the intermediate coordinate sets. An optimal value of S can be found by a direct minimization, by multi-grid techniques, or by an annealing protocol [7]. We employed in the optimization analytical derivatives of S with respect to all the Xj-s. [Pg.270]

See also in sourсe #XX -- [ Pg.362 ]

** Direct minimization Hartree-Fock **

** Direct minimization techniques **

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