Closed-shell singlet

IlyperChcm semi-empirical methods usually let you request a calculation on the lowest energy stale of a given multiplicity or the next lowest state of a given spin m ultipliriiy. Sin ce m osl m olecu les with an even num her of electron s are closed-shell singlets without... 

One would normally choose RHF for closed-shell singlets and UHF for open-shell doublets and triplets. 

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... 

The total density is the sum of die a and /3 contributions, p = Pa + Pp, and for a closed-shell singlet these are identical (p, = pp). Functionals for the exchange and correlation energies may be formulated in terms of separate spin-densities however, they are often given instead as functions of the spin polarization C, (normalized difference between p and pp), and the radius of the effective volume containing one electron, rs-... 

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... 

The closed-shell singlet ( A ) has no electrons in the tt orbitals, and the bond lengths indicate only a small amount of delocalization of the six tt electrons into the empty p-TT orbital at the carbenic carbon. In both A", 13A", and 23A" the tt SOMO has the nodal pattern expected for a pentadienyl NBMO mixed... 

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 contrast, the NBO picture describes (aAB)2 in terms of a doubly occupied bond orbital pair function t// ab(NB0) (cf. Eq. (1.31a)), with spatial dependence (in the closed-shell singlet case)... 

Both (3.17) and (3.19) are presumed to be expressed in terms of the same hA and hB bonding hybrids,16 and each function provides only an approximation to the true bond pair wavefunction. In particular, in the closed-shell singlet case V ab(NBO) assumes the same spatial dependence for each electron of the pair, and thus neglects electron-correlation effects that could better be represented as... 

Cyclic voltammetry revealed four reversible one-electron oxidation processes. The ground state structures for HOC and HOC " are aromatic . The structures for HOC" and HOC " are doublets and show Jahn-Teller distortions. The structures for HOC " in the solid is a Jahn-Teller distorted, closed-shell singlet with a canonical structure [37 ], as represented by cyanine/p-phenylenediammonium fragments. The one-to-one complex of HOC" TCNE" was indeed synthesized but found to be antiferromagnetic. 

One important feature of carbenes is the presence of two nonbonding electrons and two available orbitals, which are nominally located on the carbon atom. In bent carbenes, the two orbitals have different energies and are often denoted as a and -ir, with a being the in-plane orbital and -ir the out-of-plane orbital. Within this simple picture, four electronic states can be envisioned, which are depicted in Fig. la. Singlets and S3 have the two electrons in the same orbital (a and -IT, respectively) and are often characterized as closed-shell singlets. On the other hand, singlet S2 has the same open-shell electronic occupation (arr) as the triplet (T) state. 

Number of a and -ir electrons contributed by each diradical center. For example, a /a-ir means that one center has a closed-shell singlet local configuration and the other has cttt occupancy. The latter may correspond to triplet or to open-shell singlet local configuration. 

In the case of carbenonitrenes, the nitrene subunit has an intrinsic preference for a triplet configuration, and, thus, for a A" ground state, a carbene with a very strong preference for a closed-shell singlet ground state is required. Such a case has not been realized yet. On the other hand, if both subunits are carbenes, then. 

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