Degenerate orbitals calculation

Be careful when you use the Orbital Criterion for symmetrical system s. To get correct resnlis, you in u st include all or none of any set of degenerate orbitals in the Cl, n ot jn si some of them. Carrying out an RIIF calculation first and studying the Orbitals dialog box will help you to spot degenerate orbitals and avoid this pitfall. 

Degenerate orbitals, 522 Degree of unsaturation. 174 calculation of, 174-176 Dehydration, 214... 

The structure of the parametric UA for the 4-RDM satisfies the fourth-order fermion relation (the expectation value of the commutator of four annihilator and four creator operators [26]) for any value of the parameter which is a basic and necessary A-representability condition. Also, the 4-RDM constructed in this way is symmetric for any value of On the other hand, the other A-representability conditions will be affected by this value. Hence it seems reasonable to optimize this parameter in such a way that at least one of these conditions is satisfied. Alcoba s working hypothesis [48] was the determination of the parameter value by imposing the trace condition to the 4-RDM. In order to test this working hypothesis, he constructed the 4-RDM for two states of the BeHa molecule in its linear form Dqo/,. The calculations were carried out with a minimal basis set formed by 14 Hartree-Fock spin orbitals belonging to three different symmetries. Thus orbitals 1, 2, and 3 are cr orbitals 4 and 5 are cr and orbitals 6 and 7 are degenerate % orbitals. The two states considered are the ground state, where... 

In many instances it is helpful to plot the calculated energies of MOs as in Figure 7.1. The energy scale is vertical, and each orbital is represented as a short horizontal line placed at the position corresponding to the energy of the orbital. For doubly degenerate orbitals a pair of closely spaced lines is used. The occupation of the orbitals by electrons is indicated by placing small circles on the lines. 

The GMS wave function [1,2] combines the advantages of the MO and VB models, preserving the classical chemical structures, but dealing with self-consistently optimized orbitals. From a formal point of view, it is able to reproduce all VB or MO based variational electronic wave functions in its framework. Besides that, it can deal in a straightforward way with the nonadiabatic effects of degenerate or quasi-degenerate states, calculating their interaction and properties. 

In many ways, the order of one-electron energies in Table 3 is much more similar in different calculations than for UOj2 in Table 1. General agreement exists that the lowest I among the filled orbitals belongs to the y8 component (two degenerate orbitals in the... 

The labels show the total spin (Si), the orbital representation (Ai), the 2-component of spin (m 1) and the degenerate orbital component ( i). The final state /) in Eq. (1) represents the ionised state of the molecule, together with the resulting photoelectron, and we shall assume that the matrix element in this equation can be calculated by taking an antisymmetrized product of these two parts ... 

The ground electronic state of C5H5 in Dsh symmetry is E", with three electrons occupying the doubly degenerate orbital (one hole). Using group theory it is easy to show, see Sect. 2 that the distortion coordinate is e. The descent in symmetry goes to C2V. The electronic state E ( splits into 2 and and the JT active distortion splits into ai and b2. The results of the DFT calculation are summarised in the Table 4. 

In the cyclopropenyl radical with three Ti-electrons, the third electron has to be accommodated in one of the two degenerate molecular orbitals causing the Jahn-Teller distortion, which results in a change in symmetry from Dj, to C2,.. The ab initio (STO-3G 4-31G), as well as semi-empirical (CNDO/2), molecular orbital calculations demonstrate that the odd electron is incorporated in the pyramidalized rr-type orbital giving rise to loss of resonance stabilization in the three-membered ring. Thus, the cyclopropenyl radical is considered to be a highly unstable, short-lived species. 

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