Doubly excited electron configuration calculation

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

In this paper we examined quantum aspects of special classical configurations of two-electron atoms. In the doubly excited regime, we found quantum states of helium that are localized along ID periodic orbits of the classical system. A comparison of the decay rates of such states obtained in one, two and three dimensional ab initio calculations allows us to conclude that the dimension of the accessible configuration space does matter for the quantitative description of the autoionization process of doubly excited Rydberg states of helium. Whilst ID models can lead to dramatically false predictions for the decay rates, the planar model allows for a quantitatively reliable reproduction of the exact life times. 

Steer et al. [8, 48] have proposed that the dark state is a new state, C, that is formed when two electrons are lifted from the n orbital and placed into the 7t orbital in a doubly excited configuration, infill )1. Multireference CASSCF calculations of Strickler and Gruebele [6] indicate, however, that this phantom state is very likely the C 1 B2( ,ct ) electronic state, formed from the one electron n —> a excitation. Their calculations show that the C state is planar and intersects the nonplanar B 1 1(71,71 ) state at increasing C—S bond distances ( 2.5 A). The barrier separating the B from the C state ranges from 300 cm-1 (0 = 0) to about 1650 cm-1 (0=45°). Calculations of the transition dipole moments along the C—S bond shows that the (C p X), element is about three orders of magnitude smaller than (B p X) and provides the rationalization of C state darkness. 

Since spin-orbit coupling is very important in heavy element compounds and the structure of the full microscopic Hamiltonians is rather complicated, several attempts have been made to develop approximate one-electron spin-orbit Hamiltonians. The application of an (effective) one-electron spin-orbit Hamiltonian has several computational advantages in spin-orbit Cl or perturbation calculations (1) all integrals may be kept in central memory, (2) there is no need for a summation over common indices in singly excited Slater determinants, and (3) matrix elements coupling doubly excited configurations do not occur. In many approximate schemes, even the tedious four-index transformation of two-electron integrals ceases to apply. The central question that comes up in this context deals with the accuracy of such an approximation, of course. 

In the vast majority of calculations of the electron correlation energy of atoms and small molecules it is usually only possible to include configurations which are singly- and doubly-excited... 

There are only two states to be considered in the calculation of jS the ground state, g), where the MO tj/i is doubly occupied (configuration i/ ), and an excited state, a), where one electron is promoted from i]/i (HOMO) to i/>2 (LUMO) (configuration tf) i/4)- The doubly excited configuration ij4 does not... 

Note that 1/ is independent of c. For a two-electron system, three states have to be considered in the calculation of p. The configuration of the ground state g) is and there are two excited states, a) and b), with configurations ijj 1/ and ij/l tpi. Again, no doubly excited configurations contribute to (3 since the transition dipole to the ground state is zero. The transition a) <— g) is polarized perpendicularly to the C2 axis (z axis), while the transition b) g)... 

In the case of calculations of electronic contributions to y the problem of inclusion of double excitations is much more pronounced than in the case of computations of 3. This can be illustrated as follows. Let the electronic states appearing in Eqs. (5) and (9) be classified as pure singly or doubly excited states. This is plausible under assumption that no mixing of singly and doubly excited configurations with the ground states occurs without the perturbation. According to the rules of evaluation... 

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