Model core potential calculation

Systematic analysis of the data with respect to different schemes of density functional calculations given in Table 1 shows clearly that the model core potential (MCP) describing inner electrons in molybdenum gives rise to the results of the same quality as the all-electron calculations. Not only is the use of MCP for heavy atom calculations justified by numerical efficiency but also it may incorporate part of relativistic effects, which may be crucial in describing properties of such atoms. This tendency has been checked and found to be valid also for other states of MoO thus from now on only the frozen core approximation for molybdenum will be presented. 

Keywords Model core potential Pseudopotential Scalar-relativistic effects ECP spin-orbit calculation Fragment molecular orbital... 

Fig. 8.2 The radial functions and orbital energies of the Au 5d oibital from the all-electron (AE), effective core potential (ECP) and model core potential (MCP) calculations. The AE calculation was at the DK3 relativistic level with uncontracted well-tempered basis fimctions [22], The ECP calculation was performed using the ECP60MDF [23] potential and basis set. The MCP calculation was performed using our recently developed potentials (at the DK3 relativistic level) and basis set [24]. The orbital energies in the unit of eV are listed for comparison...

An important development related to the MCPs was the introduction of the model core potentials to the fragment molecular orbital (FMO) calculations [115]. The FMO/MCP method allows to carry out quantum mechanical calculations for large scale systems containing heavy metal atoms. 

C3. Linear combination of Gaussian-type orbitals (LCGTO) — either all-electron or model core potentials [229] (deMon-KS code, introduced in Ref. [265]). Auxiliary Gaussians are used as in C2. Calculations are based on either LDA or GGA. 

Model core potential (MCP) methods replace core orbitals by a potential just as in ECP. On the other hand, MCP valence orbitals preserve the nodal structure of valence orbitals, unlike ECP valence orbitals. The expectation values of (r ) for the valence orbitals show that the results of MCP are closer to those calculated with all-electron orbitals when comparing MCP, ECP, and the all electron case. Comparisons between MCP and an all electron basis utilizing the full Breit-Pauli spin-orbit Hamiltonian based on multiconfigura-tional quasidegenerate perturbation theory (MCQDPT) calculations show good agreement between the two methods for hydrides of P, As, and Sb. The MCP based spin-orbit calculation appears to be a promising technique, but systematic studies of many different molecular systems are still needed to assess its characteristics and accuracy. 

Rykova, E.A., Zeitsevskii, A., Mosyagin, N.S., Isaev, T.A., Titov, A.V. Relativistic effective core potential calculations of Hg and eka-Hg (El 12) interactions with gold spin-orbit density functional theory modelling of Hg-Au and El 12-Au systems. J. Chem. Phys. 125, 241102(3) (2006)... 

Some scalar relativistic effects are included implicitly in calculations if pseudopotentials for heavy atoms are used to mimic the presence of core electrons there are several families of pseudopotentials available the effective core potentials (ECP) (Cundari and Stevens 1993 Hay and Wadt 1985 Kahn et al. 1976 Stevens et al. 1984), energy-adjusted pseudopotentials (Cao and Dolg 2006 Dolg 2000 Peterson 2003 Peterson et al. 2003), averaged relativistic effective potentials (AREP) (Hurley et al. 1986 Lajohn et al. 1987 Ross et al. 1990), model core potentials (MCP) (Klobukowski et al. 1999), and ab initio model potentials (AIMP) (Huzinaga et al. 1987). 

The alkali metals tend to ionize thus, their modeling is dominated by electrostatic interactions. They can be described well by ah initio calculations, provided that diffuse, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ah initio calculations on the heavier elements. 

Although the pseudopotential is, from its definition, a nonlocal operator, it is often represented approximately as a multiplicative potential. Parameters in some chosen functional form for this potential are chosen so that calculations of some physical properties, using this potential, give results agreeing with experiment. It is often the case that many properties can be calculated correctly with the same potential.43 One of the simplest forms for an atomic model effective potential is that of Ashcroft44 r l0(r — Rc), where the parameter is the core radius Rc and 6 is a step-function. 

To date, the only applications of these methods to the solution/metal interface have been reported by Price and Halley, who presented a simplified treatment of the water/metal interface. Briefly, their model involves the calculation of the metal s valence electrons wave function, assuming that the water molecules electronic density and the metal core electrons are fixed. The calculation is based on a one-electron effective potential, which is determined from the electronic density in the metal and the atomic distribution of the liquid. After solving the Schrddinger equation for the wave function and the electronic density for one configuration of the liquid atoms, the force on each atom is ciculated and the new positions are determined using standard molecular dynamics techniques. For more details about the specific implementation of these general ideas, the reader is referred to the original article. ... 

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]. 

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. 

All of the measurements employed the technique described above that involves the analysis of the isotope composition of 02 released from the carrier complexes in preequilibrated solutions. In addition, an established DFT method (mPWPW91)34 with the atomic orbital basis functions, Co, Fe, and Cl (the compact relativistic effective core potential basis CEP-31G),35 N and O (6-311G ), P (6-311G ), C(6-31G), and H (STO-3G),36 were used to calculate the 180 EIE in terms of actual and model structures. The latter approach has also been employed for hypothetical intermediates in enzymes as described below. 

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 core model potential calculations (SCF level) the (n - l)d subshell is included in the valence space (i.e. 14-valence electrons). The reaction energies do not include ZPE from Reference 103. 

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