Self-consistent charge-field perturbation

If the species is charged then an appropriate Born term must also be added. The react field model can be incorporated into quantum mechanics, where it is commonly refer to as the self-consistent reaction field (SCRF) method, by considering the reaction field to a perturbation of the Hamiltonian for an isolated molecule. The modified Hamiltoniar the system is then given by ... 

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. 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

A particularly convenient improved approximation to this end can be obtained by use of self-consistent, first order, time-dependent perturbation theory. The essential physics to be included is that the external field distorts the atomic charge cloud (by admixture of excited orbitals) which in turn creates an electrostatic potential acting on the system, The self-consistent response of the electrons produces a mean field which reflects the atomic dielectric properties and alters the photoionization amplitudes. If this linear response approach is applied to the HFA one obtains precisely the RPAE, In what follows we consider the same approximation applied to the LDA. Given this parallelism, emphasis will be placed on direct comparisons with the RPAE,... 

With respect to standard molecular-cluster techniques, this approach has some attractive features explicit reference is made to the HF LCAO periodic solution for the unperturbed (or perfect) host crystal. In particular, the self-embedding-consistent condition is satisfied, that is, in the absence of defects, the electronic structure in the cluster region coincides with that of the perfect host crystal there is no need to saturate dangling bonds the geometric constraints and the Madelung field of the environment are automatically included. With respect to the supercell technique, this approach does not present the problem of interaction between defects in different supercells, allows a more flexible definition of the cluster subspace, and permits the study of charged defects. The perturbed-cluster approach is implemented in the computer code EMBEDOl [703] and applied in the calculations of the point defects both in the bulk crystal, [704] and on the surface [705]. The difficulties of this approach are connected with the lattice-relaxation calculations. 

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