Free complement method

Free Complement Method for Solving the Schrodinger Equation How Accurately Can We Solve the Schrodinger Equation... 

Free Complement Method for Solving the Schrodinger Equation... 

Solving the Schrodinger Equation for the Hydrogen Molecular Ion in a Magnetic Field Using the Free-Complement Method... 

Savage DF, Anderson CL, Robles-Cohnenares Y, Newby ZE, Stroud RM. Cell-free complements in vivo expression of the E. coli membrane proteome. Protein Sci. 2007 16 966-976. Wiener MC. A pedestrian guide to membrane protein crystallization. Methods 2004 34 364-372. 

We referred to this wave function as the free ICI wave function. It converges faster to the exact wave function than the original SICI one, because of the increased freedom. In the SICI scheme, the (n -I- l)-th result, tAn+i, depends on all the former results, and Cm(tn = 0...n), but in the free ICI method, all the coefficients d are reoptimized at each n, and therefore, this method is not an iterative method. Then, the naming, the free ICI method may be confusing. So, hereafter we use the new name free complement (EC) method instead of the free ICI method. We refer to n of the FC method as an order, instead of an iteration number. Thus, the EC method gives a general method of solving the SE in an analytical expansion form. 

Recently, we have discovered a general method for solving the SE [41-47]. The free-complement (FC) method [45] is the most popular method. A number of highly accurate results have been obtained for various atoms and molecules [41-58]. This was possible because the FC wave functions converge to the exact wave functions as the accuracy (order) is increased. An important feature is that the complement functions, which are the elements of the FC wave function, are automatically produced by applying the Hamiltonian to a simple initial wave function [45]. Therefore, this method can be applied to any system where the analytical form of the Hamiltonian is known. 

In addition to the fragment condensation of side-chain fuUy protected segments, a number of improved thiol handle-free Ugatimi methods have been developed, which complement NCL and enhance our capability of synthesizing proteins by chemical methods. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

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