Relativistic effects, potential energy surfaces

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. 

Because atomic titanium has low-lying electronic excited states, potential energy surfaces of Ti compounds, especially unsaturated compounds, often cross. When such crossings occur, nonradiative transitions can occur via spin-orbit coupling. In such cases, spin-orbit coupling probabilities must be evaluated. Such calculations usually are performed with MCSCF-based wavefunctions. In addition, relativistic effects can have a significant effect on chemical properties, even for compounds containing elements in the first transition series. Fortunately, new models have been developed to treat relativistic effects for all-electron basis sets... 

High accuracy of quantum chemical calculations not only requires a satisfactory treatment of electron correlation, but also relativistic and beyond-Born-Oppenheimer effects need to be considered [16, 17, 18]. These are not in the scope of the present review. We further concentrate on correlation effects on the energy (and on quantities directly derivable from potential energy surfaces) and we ignore correlation effects on properties, which is in important subject at present [19]. We further shall report more on the calculation than on the interpretation of correlation effects. 

Balasubramanian (2002) calculated potential energy surfaces of lawrencium and nobehum dihydrides (LrH2 and N0H2) by the relativistic effective core potentials with the ALCHEMY II code (Balasubramanian 2000). He predicts that Lr and No exhibit unusual non-actinide properties. 7s and 7p orbitals have major contribution to the bonding compared with 5f and 6d shells and they behave unlike other actinides. 

In order to obtain the potential energy surface U (R) one has to solve the electronic Schrbdinger equation for a number of nuclear positions and add the nuclear repulsion term VanfR)- In case further effects, such as spin-orbit, kinematic relativistic effects, etc, are considered, the corresponding operators are added, and the electronic Schrddinger equation is modified. The spin-orbit contribution is often evaluated by perturbation... 

The CPF approach gives quantitative reement with the experimental spectroscopic constants (24-25) for the ground state of Cu2 when large one-particle basis sets are used, provided that relativistic effects are included and the 3d electrons are correlated. In addition, CPF calculations have given (26) a potential surface for Cus that confirms the Jahn-Teller stabilization energy and pseudorotational barrier deduced (27-28) from the Cus fluorescence spectra (29). The CPF method has been used (9) to study clusters of up to six aluminum atoms. 

Assuming that substituted Sb at the surface may work as catalytic active site as well as W, First-principles density functional theory (DFT) calculations were performed with Becke-Perdew [7, 9] functional to evaluate the binding energy between p-xylene and catalyst. Scalar relativistic effects were treated with the energy-consistent pseudo-potentials for W and Sb. However, the binding strength with p-xylene is much weaker for Sb (0.6 eV) than for W (2.4 eV), as shown in Fig. 4. 

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