Relativistic effective core potentials basis sets

Unlike semiempirical methods that are formulated to completely neglect the core electrons, ah initio methods must represent all the electrons in some manner. However, for heavy atoms it is desirable to reduce the amount of computation necessary. This is done by replacing the core electrons and their basis functions in the wave function by a potential term in the Hamiltonian. These are called core potentials, elfective core potentials (ECP), or relativistic effective core potentials (RECP). Core potentials must be used along with a valence basis set that was created to accompany them. As well as reducing the computation time, core potentials can include the effects of the relativistic mass defect and spin coupling terms that are significant near the nuclei of heavy atoms. This is often the method of choice for heavy atoms, Rb and up. 

Correlation Consistent Basis Sets with Relativistic Effective Core Potentials The Transition Metal Elements Y and Hg... 

The present work represents a preliminary attempt to incorporate many of these strategies in conjunction with the use of small-core relativistic effective core potentials for obtaining compact series of correlation consistent basis sets... 

At B3LYP/6-311G(2d,p), pseudo-relativistic effective core potential and a (31/31/1) valence basis set were used for Si, Ge, Sn, Pb, from Ref 40. 

Slovenia), using the DFT implementation in the Gaussian03 code. Revision C.02 (8). The orbitals were described by a mixed basis set. A fully uncontracted basis set from LANL2DZ was used for the valence electrons of Re (9), augmented by two / functions Q =1.14 and 0.40) in the full optimization. Re core electrons were treated by the Hay-Wadt relativistic effective core potential (ECP) given by the standard LANL2 parameter set (electron-electron and nucleus-electron). The 6-3IG basis set was used to describe the rest of the system. The B3PW91 density functional was used in all calculations. 

ECPS relativistic effective core potential of Stevens et TZ triple-zeta basis set... 

The basis sets used in the reactions including F and Cl are the augmented correlation consistent polarized valence double zeta (aug-cc-pVDZ) sets [16]. In the reactions including Br and I, the relativistic effective core potential (ECP) due to Stevens et al. [17,18] and their associated basis sets were used for Br and I, and the cc-pVDZ set for H. The basis sets of Br and I were augmented by adding a d polarization function with an exponent of 0.389 (Br) / 0.266 (I) and sp diffuse functions with an exponent 0.03574 (Br) / 0.03007 (I). The diffuse p polarization function of the aug-cc-pVDZ set of H was omitted for consis-... 

If several electronically excited states are relevant for describing the photodissociation then one or more of the Rydberg orbitals of the molecule must be included in the (CAS) [13], As the number of orbitals and electrons increases in the CAS, the computational time increases dramatically. In order to obtain accurate potential energy surfaces for the excited electronic states, one must include diffuse functions in the basis set [4], For heavier atoms, a relativistic effective core potential (ECP) can be used to treat the scalar relativistic effects. The ECP basis sets have been developed by several research groups [15,16] and have been implemented in most of the standard electronic structure programs. 

Effective core potentials address the aforementioned problems that arise when using theoretical methods to study heavy-element systems. First, ECPs decrease the number of electrons involved in the calculation, reducing the computational effort, while also facilitating the use of larger basis sets for an improved description of the valence electrons. In addition, ECPs indirectly address electron correlation because ECPs may be used within DFT, or because fewer valence electrons may allow implementation of post-HF, electron correlation methods. Finally, ECPs account for relativistic effects by first replacing the electrons that are most affected by relativity, with ECPs derived from atomic calculations that explicitly include relativistic effects via Dirac-Fock calculations. Because ECPs incorporate relativistic effects, they may also be termed relativistic effective core potentials (RECPs). 

For the heavier elements, relativistic effects due to the core may become important. To account for this in the simplest way, the electrons in the core can be replaced by a potential that produces the same valence electron distribution as an all-electron relativistic computation. This also reduces the computer time needed as well, since the number of functions is reduced. Another hazard of doing all-electron calculations with small basis sets on lower-row elements is that the bond lengths have large error. The relativistic effective core potential (RECP) that we employed was CEP-121G (12). For this RECP, the geometry was optimized at the MP2 level of theory, and a single-point energy was computed at the CCSD(T) level of theory (13). 

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. 

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. 

In 1992 Dmitriev, Khait, Kozlov, Labzowsky, Mitrushenkov, Shtoff and Titov [151] used shape consistent relativistic effective core potentials (RECP) to compute the spin-dependent parity violating contribution to the effective spin-rotation Hamiltonian of the diatomic molecules PbF and HgF. Their procedure involved five steps (see also [32]) i) an atomic Dirac-Hartree-Fock calculation for the metal cation in order to obtain the valence orbitals of Pb and Hg, ii) a construction of the shape consistent RECP, which is divided in a electron spin-independent part (ARECP) and an effective spin-orbit potential (ESOP), iii) a molecular SCF calculation with the ARECP in the minimal basis set consisting of the valence pseudoorbitals of the metal atom as well as the core and valence orbitals of the fluorine atom in order to obtain the lowest and the lowest H molecular state, iv) a diagonalisation of the total molecular Hamiltonian, which... 

Martin, J.M.L., Sundermann, A. Correlation consistent valence basis sets for use with the Stuttgart-Dresden-Bonn relativistic effective core potentials The atoms Ga-Kr and In-Xe, J. Chem. Phys. 2001,114,3408. 

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