Closed-shell singlet state

We would have P = 2R] and R2 = 0 for a closed-shell singlet state. The closed-shell electronic energy expression given earlier,... 

So, if we consider a closed-shell singlet state with m electron pairs and electronic configuration... 

Note 0 The CISD energies, which include Davidson correction for unlinked quadruple excitations, where obtained ot the MCSCF/6-31 G(d)optimized geometries and used a TC-SCF reference for closed-shell singlet states and a single configuration reference for triplet and open-shell singlet states. The SCF/6-31G(d) geometry was employed for the A state. See Ref. 55. 

The closed-shell C2v symmetric Ai state is a transition state, similar to the closed-shell singlet state of cyclopentadienylidene discussed above. Note... 

In general, linear 7r-electron systems with Z1r = 2N electrons at the lowest energy levels have closed-shell singlet states while cyclic systems reach closed shell structures only when ZT = 4N + 2. Cyclic 7r-electron systems with Zn 4N + 2 will therefore exhibit multiplet ground states according to Hund s rules, and should be chemically reactive because of the unpaired electrons. Hiickel s rule that predicts pronounced stability for so-called aromatic ring systems with 4jV + 2 7r-electrons is based on this shell structure. The comparison with cyclic systems further predicts that ring closure of linear 7r-electron systems should be exothermic by an amount... 

In certain favorable instances, one can coax the SCF equations to converge to different determinants of the same electronic state symmetry. For instance, phenylnitrenes have two different closed-shell singlet states, as re-illustrated in Figure 14.3 (cf. Section 8.5.3),... 

Of course, with HF wave functions in hand, it is possible to carry out post-HF calculations to partially correct for electron correlation effects. The poor quality of the HF wave functions, however, militate against any treatment much less sophisticated than coupled-cluster. At the CCSD(T)/cc-pVDZ level, the predicted energy of the lowest closed-shell singlet is in fair agreement with experiment (other data in the table suggest that use of a triple- basis set would improve the CCSD(T) estimate). The energy of the second closed-shell singlet state... 

Basch in 1970 carried out one of the first MCSCF calculations on a polyatomic system216 in an investigation of the least-motion, coplanar approach of two methylenes to give C2H4. For two closed shell, singlet state methylenes, the reaction path is purely repulsive, and the reaction occurs for two appropriately oriented bent triplet methylenes. 

As in the case of susceptibilities, there can be in general three contributions to the magnetic shielding a the paramagnetic term again dominates when present, but for a closed-shell singlet-state molecule there are just two contributions... 

CHa + CH2— C2H4.—-The coplanar approach of two methylenes to form ethylene was investigated by Basch268 using the MCSCF method. The states of bent methylene that correlate with the ground state of ethylene are the triplet states. It is found that for two closed-shell singlet-state methylenes, the reaction path is purely repulsive. 

The SAC/SAC-CI method is a correlated electronic-structure theory for the ground and excited states in various spin multiplicities. The SAC method belongs to the coupled-cluster theory [30, 31]. In the case of a closed-shell singlet state, the SAC wave function is written as... 

Several structures may be envisioned for compounds MLx 2( r-C ), which are broadly distinguished by whether or not they describe closed-shell singlet states or open-shell triplet states, and the number and combination of bonds between the metal and carbon as well as adjacent carbon centers. There have been several reports rationalising the valence bond descriptions of complexes containing even387 389 or odd values of / 390,391 and related polymeric materials and Sponsler has offered a comparison of the... 

In the Hartree-Fock method, the wave function for a closed shell singlet state has the antisymmetrized form... 

We further neglect the commutator [fC, ri2 ] > which is justified in the so-called standard approximation A [11]. (For a two-electron closed-shell singlet state a formulation in which K does not arise is always exactly possible [10]). This allows us to rewrite (53) as... 

Molecular fragment SCF geometry optimized in the 6-31G basis (neutral species) or in the 6-31 4- G basis (anions). bUsing the 6-31 + G basis set. c Closed-shell singlet state. 

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