Model potential ab initio

Role of electron correlation in nonadditive forces and ab initio model potentials for small metal clusters... 

Abstract. The physical nature of nonadditivity in many-particle systems and the methods of calculations of many-body forces are discussed. The special attention is devoted to the electron correlation contributions to many-body forces and their role in the Be r and Li r cluster formation. The procedure is described for founding a model potential for metal clusters with parameters fitted to ab initio energetic surfaces. The proposed potential comprises two-body, three-body, and four body interation energies each one consisting of exchange and dispersion terms. Such kind of ab initio model potentials can be used in the molecular dynamics simulation studies and in the cinalysis of binding in small metal clusters. 

In this section we discuss model potentials for small metal clusters with parameters fitted to ab initio calculated potential surfaces. We named such potentials as ab initio model potentials This approach was first elaborated by Clementi and coworkers and used for the Monte-Carlo simulation of biological systems in liquid water... 

The ab initio model potential for Age was used in molecular dynamics (MD) simulation of the thermal behavior of different isomers of Age in our studies The advantages of using such kind of potential in MD simulation studies are related to the reliability of the quantitative predictions obtained, due to the use of an accurate model potential at the electron correlation level and to the extended length of the simulation time (comparing with other ab initio MD approaches) during which a good statistics is collected. 

The ab initio model potentials is useful not only for a MD simulation. When the model potential is found, we obtain the explicit expressions for the... 

The dependence of distance of the m-body interaction energies and their physical contributions into the ab initio model potential (50) for an equilateral triangle geometry of the Bea cluster are presented in Table III. For intermediate and equilibrium distances IV2I is less or much less than IV3I, however the main contribution to the total exchange, and dispersion, energies... 

The shape-consistent (or norm-conserving ) RECP approaches are most widely employed in calculations of heavy-atom molecules though ener-gy-adjusted/consistent pseudopotentials [58] by Stuttgart team are also actively used as well as the Huzinaga-type ab initio model potentials [66]. In plane wave calculations of many-atom systems and in molecular dynamics, the separable pseudopotentials [61, 62, 63] are more popular now because they provide linear scaling of computational effort with the basis set size in contrast to the radially-local RECPs. The nonrelativistic shape-consistent effective core potential was first proposed by Durand Barthelat [71] and then a modified scheme of the pseudoorbital construction was suggested by Christiansen et al. [72] and by Hamann et al. [73]. 

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

Since in current molecular modeling tasks the Gaussian orbitals or their linear combinations are used, one can guess that they provide the explicit form of the core states. Inserting the Gaussians in the expressions for the Coulomb and exchange superoperators yields numerous approximate forms of the pseudopotentials, which can be exemplified by the formulae employed in the ab initio model potential (AIMP) [36] ... 

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. 

Quasi-relativistic ab initio model potential calculations, Reference 60. 

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... 

L. SeijoChem. Phys., 102, 8078 (1995). Relativistic Ab Initio Model Potential Calculations... 

Ab Initio Model Potential Calculations on the Electronic Spectrum of Ni2+-Doped MgO Including Correlation, Spin-Orbit and Embedding Effects. 

Relativistic correction included by perturbation theory, Reference 61. Quasi-relativistic ab initio model potential calculations. Reference 60. 

Seijo [120] has performed relativistic ab initio model potential calculations including spin-orbit interaction using the Wood-Boring Hamiltonian. Calculations ere performed for several atoms up to Rn, and several dimer... 

The most common quantum chemical programs—Gaussian (8), GAMESS (9), Turbomole (10), CADPAC (11), ACES II (12), MOLPRO (13), MOLCAS (14), and the newly developed TITAN (15)—are able to run pseudopotential calculations. Please note that CADPAC and MOLCAS can only use so-called ab initio model potentials (AIMPs) in pseudopotential calculations. Such AIMP differ from ECPs in the way that the valence orbitals of the former retain the correct nodal structure, while the lowest-lying valence orbital of an ECP is a nodeless function. Experience has shown that AIMPs do not give better results than ECPs, although the latter do not have the correct nodal behavior of the valence orbitals... 

In the calculations based on effective potentials the core electrons are replaced by an effective potential that is fitted to the solution of atomic relativistic calculations and only valence electrons are explicitly handled in the quantum chemical calculation. This approach is in line with the chemist s view that mainly valence electrons of an element determine its chemical behaviour. Several libraries of relativistic Effective Core Potentials (ECP) using the frozen-core approximation with associated optimised valence basis sets are available nowadays to perform efficient electronic structure calculations on large molecular systems. Among them the pseudo-potential methods [13-20] handling valence node less pseudo-orbitals and the model potentials such as AIMP (ab initio Model Potential) [21-24] dealing with node-showing valence orbitals are very popular for transition metal calculations. This economical method is very efficient for the study of electronic spectroscopy in transition metal complexes [25, 26], especially in third-row transition metal complexes. 

Since the model potential approach yields valence orbitals which have the same nodal structure as the all-electron orbitals, it is possible to combine the approach with an explicit treatment of relativistic effects in the valence shell, e.g., in the framework of the DKH no-pair Hamiltonian [118,119]. Corresponding ab initio model potential parameters are available on the internet under http //www.thch.uni-bonn.de/tc/TCB.download.html. 

Atomization energies (in a.u.), bond lengths (in A), and force constants k of the breathing mode (in a.u.), from one-component SCF calculations using energy-consistent scalar-relativistic pseudopotentials (EC-PP), ab initio model potentials (AIMP) and valence basis sets of double zeta (DZ) and polarized double-zeta (DZP) quality, in comparison to all-electron (AE) relativistic SCF calculations. Numbers in parentheses are differences to corresponding non-relativistic results. 

All structures were optimized at the CASSCF(8,8) level with the cc-pVDZ basis set. For multireference calcidations involving bromine and iodine, the Cowan-Griffin ab initio model potential with a relativistic effective core potential was used.222 CASPT2 calculations were performed on all optimized CASSCF(8,8)/cc-pVDZ geometries, using the CASSCF wave functions as the reference wave functions. SOCs were computed by using the Pauli-Breit Hamiltonian. 

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