Bare nuclear potential

A so-called bare nuclear potential descriptors that probably describe interactions involving polar and hydrogen bonding. 

The first term in the definition (4.4) of the molecular electrostatic potential is the potential Vn(r) generated by the nuclei, also called the "bare nuclear potential" ... 

R.G. Parr and A. Berk, "The Bare-Nuclear Potential as Harbinger for the Electron Density in a Molecule", in Chemical Applications of Atomic and Molecular Electrostatic Potentials, P. Politzer and D.G.Truhlar (Eds,), Plenum, New York, 1981, pp. 51-62. 

Vext will arise as a superposition of the potentials associated with each of the nuclei making up the solid. In the most direct of pictures, one can imagine treating the solid by superposing the bare nuclear potentials for each atom, and subsequently solving for the disposition of each and every electron. This approach is the basis of the various all-electron methods. 

The way i>f p is generated from the atomic calculation is not unique. Common pseudopotentials are generated following the prescription of, e.g., Bachelet, Hamann and Schlriter [82], Kleinman and Bylander [83], Vanderbilt [84] or Troullier and Martins [85]. Useful reviews are Refs. [86, 87, 88]. The pseudopotential approach is very convenient because it reduces the number of electrons treated explicitly, making it possible to perform density-functional calculations on systems with tens of thousands of electrons. Moreover, the pseudopotentials upp are much smoother than the bare nuclear potentials vext. The remaining valence electrons are thus well described by plane-wave basis sets. 

This can be used to simplify the expression for E. We note that L4 given by (533) and given by (535) contain a term [L2, U ] and [G2, U ] respectively. In view of (537) these do not contribute to E4. The resulting expression is still rather lengthy. If we choose X2 in the sense of Hartree-Fock theory (rather than for a bare nuclear potential) [17, 18], the contributions (536) cancel with corresponding contributions in G2. If we, moreover, use perturbation-adapted zeroth-order spin-orbitals, the final result is simple ... 

An early advance in the study of the connection between electronic density and nuclear interactions was made by Parr, Gadre, and Bartolotti, followed by Parr and Berk, who pointed out the striking similarities between quantum-chemical electronic densities of molecules and another, simple molecular function that can be easily obtained from an essentially classical model based solely on the nuclear arrangement the composite nuclear potential. (In the original work of Parr and Berk the term bare nuclear potential was used.) In what follows, the basic relations between electronic density and the composite nuclear potential will be reviewed. 

For a given collection of the nuclei of the molecule, the composite nuclear potential Vn(r) (the bare nuclear potential in the terminology of Parr and Berk ) is defined as... 

An important fact has been pointed out by Parr and Berk the bare nuclear potential Vn(r) shows many similarities with the electronic density function p(r). The computed isopotential contours of the composite nuclearpotential VnC lwere remarkably similar to some of the molecular isodensity contours (MIDCOs) of the electronic ground states in several simple molecules. One may regard the composite nuclear potential as the harbinger of electronic density, and isopotential contours of the composite nuclear potential V (r) can serve as surprisingly good approximations of MIDCOs. The nuclear potential contours (NUPCOs) are suitable for an inexpensive, approximate shape representation of molecules. 

R. G. Parr and A. Berk, The bare-nuclear potential as harbinger for the electron density in a molecule,... 

Popelier, P.L.A. and Bremond, E.A.G. (2009) Geometrically faithful homeomorphisms between the electron density and the bare nuclear potential. International Journal of Quantum Chemistry, 109, 2542-2553. 

In the case of the GAPW method we also have the possibility to avoid pseudo potentials and use only the bare nuclear core potential. We can cast this potential into a form similar to the above defined pseudo potentials... 

The total energy in ab initio theory is given relative to the separated particles, i.e. bare nuclei and electrons. The experimental value for an atom is the sum of all the ionization potentials for a molecule there are additional contributions from the molecular bonds and associated zero-point energies. The experimental value for the total energy of H2O is —76.480 a.u., and the estimated contribution from relativistic effects is —0.045 a.u. Including a mass correction of 0.0028 a.u. (a non-Bom-Oppenheimer effect which accounts for the difference between finite and infinite nuclear masses) allows the experimental non-relativistic energy to be estimated at —76.438 0.003 a.u. ... 

Fig. 6 compares the nuclearity effect on the redox potentials [19,31,63] of hydrated Ag+ clusters E°(Ag /Ag )aq together with the effect on ionization potentials IPg (Ag ) of bare silver clusters in the gas phase [67,68]. The asymptotic value of the redox potential is reached at the nuclearity around n = 500 (diameter == 2 nm), which thus represents, for the system, the transition between the mesoscopic and the macroscopic phase of the bulk metal. The density of values available so far is not sufficient to prove the existence of odd-even oscillations as for IPg. However, it is obvious from this figure that the variation of E° and IPg do exhibit opposite trends vs. n, for the solution (Table 5) and the gas phase, respectively. The difference between ionization potentials of bare and solvated clusters decreases with increasing n as which corresponds fairly well to the solvation free energy of the cation deduced from the Born solvation model [45] (for the single atom, the difference of 5 eV represents the solvation energy of the silver cation) [31]. 

This is quite different from the first two. Due to the reflection symmetry of this potential, the instanton path always remains directed along the Q axis. The transverse q vibration changes only the width of the reactive channel according to Eqs. (4.23) and (4.24). When C > 0, the vibrational-ly adiabatic squeezed barrier is greater than the bare one. This case of dynamically induced formation of the barrier was studied by Auerbach and Kivelson [1985] in context of nuclear physics. The opposite case C < 0, corresponding to the vibration-assisted tunneling, will be considered in Section 8.3. 

At this stage, the formalism can be implemented in a computer program. The applications described below [15-21] rely on the expansion of the electronic wavefunctions in terms of a large number of plane waves, as well as on the replacement of nuclear bare potentials by accurate norm-conserving pseudopotentials. The Local Density Approximation was used, with the Ceperley and Alder data for the exchange-correlation energy of the homogeneous electron gas. 

The Hamiltonian is now a pure nuclear operator dictating, in the Born-Oppenheimer approximation, the evolution of the nuclear wavefunction [115]. The electrons enter Hn only through a potential energy term, o(R/), added to the bare nuclei-nuclei interaction Vnn- This potential energy term due to the electrons is the ground state energy of the electronic system at fixed ionic configuration. 

Ej is the orbital energy associated with the target wave function Here Vpg is an effective potential seen hy the active electron, which contains the screening effect produced by other electrons from the medium. For bare incident ions, the active-electron projectile interaction Vpg is just the Coulomb potential. However, in the case where the projectile carries electrons, we use a screened potential made up of the Coulomb part due to the projectile-nuclear charge and the static potential produced by the target electrons that screen the projectile-nuclear charge... 

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