Mutually consistent field method

In this work we have used this version of the mutually consistent field method (MCF) (48) which has been developed to treat the interactions between polymer chains (69). Each subsystem is computed in the potential field of the partner system. The Coulomb potentials of the elementary cell of one chain, represented by a point charge distribution which are fitted to the Hartree-Fock Coulomb potential are included in the one-electron part of the Fock matrix of the other chain and vice versa (for more details see Section 2.4). The procedure of taking into account the effect of the mutually polarization is repeated until consistent solutions are obtained for the charge distributions. Computing finally the interaction between these point charge representations, one obtains the electrostatic and the polarization energy contribution together. 

In the case of intermolecular interactions between polar molecules Otto and Ladik proposed the so-called mutually consistent field (MCF) method [135-136]. They discussed various aspects of the MCF approach in a series of papers [137-139], and compared it with the conventional SCF supermolecule and perturbational calculations. 

Theoretical methods for the investigation of interactions between polymer chains are described in Chapter 6. Besides the theoretically clear-cut but, in the case of polymers with larger unit cells, numerically unfeasible, superchain approach, theoretical perturbation methods and the mutually consistent field (MCF) procedure recently developed at Erlangen are reviewed. The first application of the MCF method, which takes into account both the electrostatic part and polarization forces, to polynucleotide-polypeptide interactions (modeling DNA-protein interactions) is presented. 

From Czech HRAs perspective, widely known and used second generation HRA method (Hollnagel, 1998), particularly devoted to failures of (highly) cognitive control room crew actions, i.e. such a field, which is not well covered with somewhat static schemes of other well known HRA methods. In fact, the method strucmre is similar to HEART to some extent, where the failure potential is specified by definition of activity type and by evaluation of a set of factors positively or negatively influencing the potential for action success. The spectrum of influencing factors seems to be more complete and mutually consistent than in HEART case. 

The forerunner of Cl is the self-consistent field (SCF) method [1, 2]. A version that properly accounts for the antisymmetry of the electronic wave function was developed independently by Fock [3] and Slater [4] shortly after Schrodinger s papers. It is characterized by an approximate wave function that is a single determinant whose elements are one-electron functions (spin orbitals). The latter orbitals are optimized under two conditions minimization of the energy expectation value and mutual orthonormality. The method produces both the occupied orbitals appearing in the determinant but also a potentially infinite number of unoccupied functions that prove to be the basis for the Cl method. One can look upon a Slater determinant formed by substituting unoccupied for occupied one-electron functions as a representation of an excited state of the molecular system. The possible applications to spectroscopy were obvious. 

The primary solvation number may be determined by means of various mutually independent methods. However, it must be noted that the different methods do not yield identical values in every case. Padova [Pa 63b, Pa 64a] calculated the solvation numbers (n) of certain electrolytes from the molar volumes. He used the assumption that the solute ion gives rise to such a strong electrostatic field that the solvate sheath consisting of solvent molecules bound in the first coordination sphere becomes incompressible. Thus, the molar volume (cm /mole), of the solvated electrolyte can be described by the equation... 

A more affordable alternative is to treat the solvent as a continuous medium with the commonly named continuum methods. Among this type of methods, probably the most widely used is the Self-Consistent Reaction Field (SCRF) [78], which considers the solvent as a uniform polarizable medium with a dielectric constant s, and with the solute placed in a suitable shaped hole in the medium. In this method, the electric charge distribution of the solute polarizes the medium, which in turn acts back on the solute, thereby producing an electrostatic stabilization. This process is iteratively repeated until the mutual polarization between the solute and solvent achieves the self-consistency. ... 

These methods combine a QM representation of solute with a classical continuum description of the solvent [18-23]. The methodology is equivalent to that of classical continuum methods, except that a) the solute charge distribution is allowed to relax by the solvent reaction field, and b) the solute-solvent interaction is computed at the QM level. Most QM continuum methods work within the multipole or apparent surface charge approaches, even though other formalisms are also available [18-23]. The solvent reaction field is introduced into the solute Hamiltonian by means of a perturbation operator (R in equation 22) that couples the solvent reaction field to the solute charge distribution. At this point, it is worth noting that equation 22 is not lineal, since T and R are mutually dependent. This means that a self-consistent process in which both the wavefunction and the reaction field are treated simultaneously is required to solve equation 22. This is the reason why these methods are typically known as self-consistent reaction field (SCRF) methods. 

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