Model Potential Method

L. Seijo, Z. Barandiaran. The Ab Initio model potential method a common strat-... 

Bonifacic,V. and Huzinaga,S. (1974), J.Chem.Phys., Atomic and molecular calculations with the model potential method , J.Chem.Phys.60, 2779... 

Model potential methods and their utilization in atomic structure calculations are reviewed in [139], main attention being paid to analytic effective model potentials in the Coulomb and non-Coulomb approximations, to effective model potentials based on the Thomas-Fermi statistical model of the atom, as well as employing a self-consistent field core potential. Relativistic effects in model potential calculations are discussed there, too. Paper [140] has examples of numerous model potential calculations of various atomic spectroscopic properties. 

The main advantage of the effective potential method consists in the relative simplicity of the calculations, conditioned by the comparatively small number of semi-empirical parameters, as well as the analytical form of the potential and wave functions such methods usually ensure fairly high accuracy of the calculated values of the energy levels and oscillator strengths. However, these methods, as a rule, can be successfully applied only for one- and two-valent atoms and ions. Therefore, the semi-empirical approach of least squares fitting is much more universal and powerful than model potential methods it combines naturally and easily the accounting for relativistic and correlation effects. 

J. Migdalek. Model-Potential Methods in Atomic Structure Calculations, Zeszyty Naukove Universytetu Jagiellonskiego, MXV, Prace Fizyczne, Zeszyt 32, Krakow, 1990. 

Huzinaga was the recipient of the 1994 John C. Polanyi Award of the Canadian Society for Chemistry. In his award lecture he described his model potential method, which deals only with the active electrons in molecular and solid state calculations. An invited review article,59 based on his 1994 Polanyi Award lecture, chronicles his efforts to develop a sound theoretical framework for the core-valence separation of electrons, a problem Van Vleck and Sherman60 once referred to as the nightmare of the inner core. ... 

L. Seijo and Z. Barandiaran. The ab initio model potential method A common strategy for effective core potential and embedded cluster calculations. In J. Leszczynski, (ed), Computational chemistry Reviews of Current Trends, 4, pp. 55-152, World Scientific, Singapore, 1999. 

Leszcynski, Ed., World Scientific, Singapore, Vol. 4,1999, pp. 55-152. The Ab Initio Model Potential Method A Common Strategy for Effective Core Potential and Embedded Cluster... 

Similar conclusions are reached with a 1-particle model potential method [50] and a model relating Zeg and the scattering length [51]. 

Miyoshi, E., and Y. Sakai (1988). Applications of the model potential method to transition metal compounds. J. Comp. Chem. 9, 719-27. 

In two previous papers [8,9] we have calculated the static polarizabilities and hyperpolarizabilities for ls3p Pj (J = 0, 2)-states of helium. The method was based on degenerate perturbation-theory expressions for these quantities. The necessary dipole matrix elements were found by using the high-precision wave function on framework of the configuration-interaction (Cl) method [10]. The perturbed wave functions are also expanded in a basis of accurate variational eigenstates [11]. These basis sets of the wave functions explicitly take account of electron correlation. To control the result we have also carried out similar calculations with Fues model potential method. 

We have calculated the second- and fourth-order dipole susceptibilities of an excited helium atom. Numerical results have been obtained for the ls2p Pq-and ls2p f2-states of helium. For the accurate calculations of these quantities we have used the model potential method. The interaction of the helium atoms with the external electric held F is treated as a perturbation to the second- and to the fourth orders. The simple analytical expressions have been derived which can be used to estimate of the second- and higher-order matrix elements. The present set of numerical data, which is based on the Green function method, has smaller estimated uncertainties in ones than previous works. This method is developed to high-order of the perturbation theory and it is shown specihcally that the continuum contribution is surprisingly large and corresponds about 23% for the scalar part of polarizability. 

Huzinaga, S., "Atomic and Molecular Calculations with Model Potential Method," Presented at the Quantum Chemistry Symposium, first North American Chemical Congress, Mexico City, December 1975 ... 

Effective Core Potential methods are classified in two families, according to their basic grounds. On the one hand, the Pseudopotential methods (PP) rely on an orbital transformation called the pseudoorbital transformation and they are ultimately related to the Phillips-Kleinman equation [2]. On the other hand, the Model Potential methods (MP) do not rely on any pseudoorbital transformation and they are ultimately related to the Huzinaga-Cantu equation [3,4]. The Ab Initio Model Potential method (AIMP) belongs to the latter family and it has as a... 

The main idea behind the ab initio model potential method is taking a well defined Hamiltonian, identifying cumbersome operators in it, and, if possible. 

Seijo L, Barandiarin Z (1999) The ab initio model potential method a common strategy... 

Schwarz and coworkers have developed a relativistic model potential method. In this method the relativistic effective potential is expressed as... 

In the model potential method, one of the simplest and most useful models is the Lennard-Jones 6-12 p>otential ... 

They used the relativistic model potential method to identify the strongest lines representing 3d-4p transitions in the cobalt, nickel, copper, and zinc sequences, all falling in about the same wavelength range. The groups are very narrow, e.g., the 16 identified features of the 3d -3d 4p transition in Hf 45 lie between 7.56 and 7.08 A. 

Z. Barandi ran, L. Seqo. The Ab Initio Model Potential method. Cowan-Griffin relativistic core potentials and valence basis sets from Li (Z=3) to La (Z=57). Can. ]. Chem., 70 (1992) 409-115. 

M. Casarrubios, L. Seijo. The ab initio model potential method. Relativistic Wood-Boring valence spin-orbit potentials and spin-orbit-corrected basis sets from B(Z= 5) to Ba(Z=56). /. Mol. Struc. (THEOCHEM), 426 (1998) 59-74. 

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