Singlet molecules

The UIIF wnive fimction can also apply to singlet molecules. F sn-ally, the results are the same as for the faster RHF method. That is, electron s prefer to pair, with an alpha electron sh arin g a m olecu lar space orbital with a beta electron. L se the L lIF method for singlet states only to avoid potential energy discontinuities when a covalent bond Is broken and electron s can impair (see Bond Breaking on page 46). 

For singlet spin molecules at the equilibrium geometry, RHF and UHF wave functions are almost always identical. RHF wave functions are used for singlets because the calculation takes less CPU time. In a few rare cases, a singlet molecule has biradical resonance structures and UHF will give a better description of the molecule (i.e., ozone). 

To calculate AG = Gts - Greactant, we need and AS AHf is directly the difference in elecfi onic energy between the TS and the reactant. Except for complicated reactions involving several electronic states of different degeneracy (e.g. singlet molecules reacting via a triplet T, A5 g, is zero. 

All of these reactions are exothermic but some of them violate the law of spin conservation since S2 is a triplet molecule while all species on the right side of the above equations are singlet molecules in the ground state. Therefore, a radical-chain reaction has been assumed. S3 may also be formed from S2 by picking a sulfur atom up from a di- or polysulfide in the a-layer. 

An external magnetic field was observed to have practically no effect on the intensity of the thianthrene (430 nm) emission, indicating that no triplet states are involved. The shorter-wavelength emission of the oxadiazole 102, however, is probably due to a triplet-triplet annihilation reaction of diphenyloxadiazole triplets. These are produced in the radical-ion reaction between 101 and 102, yielding thianthrene excited-singlet molecules and diphenyl-oxadiazole excited-triplet molecules ... 

It was obvious, that the parent carbene 21 should be isolable in an argon matrix at 10 K. The barrier for the isomerization of 21 to imidazole 22 is calculated (B3LYP/6-311G(d,p)) to be rather high (41.5 kcal mol-1).45 Because of the interaction of the nitrogen lone pairs with the empty p-orbital of the car-benic center, carbene 21 should be a singlet molecule (S/T-gap = 81.6 kcal mol-1). 

Neutral singlets. This class of systems comprises singlet molecules with transitions to doublet cations or anions. Most applications of the P3 method will pertain to such systems. 

The spin of the radical is characterized by two spin quantum numbers, the total spin S and the component of the total spin along the z-axis M. The simplest type of radical has one unpaired electron, and hence S = and M = , where the sign of M indicates the orientation of the electron spin in the z-direction. The dissociated singlet molecule, described by the N + l)-electron wavefunction, consists of the radical and a hydrogen atom in orbital (j) at infinity, ... 

Table 7.2 Valence correlation energies (—Econ, hiEa) from standard and R12 CCSD calculations and from extrapolation using Eq. (7.57) for seven closed-sheU singlet molecules...

The normal violet fluorescence band of pyrene solutions shows concentration-quenching which is accompanied by the appearance of a blue structureless emission band. Forster and Kasper40 showed that the blue band is due to emission from an excited dimer formed by the combination of an excited singlet molecule with a molecule in the ground state. Most of the light in both spectral bands has a relatively short lifetime but Stevens and Hutton87 observed a long-lived component of the dimer... 

The mechanic. u proposed for this biphotonic delayed emission is that encounter between two triplet molecules gives rise to an intermediate species X. which subsequently dissociates into an excited and a ground state singlet molecule. The excited singlet molecule finally relaxes by emission of radiation. The rate constant of emission is not that of fluorescence but is governed by the rate of formation of triplet molecules. The various steps leading to emission process are ... 

It was not possible to observe radiation at 7620 A. However, the rapid removal of 02(1S9+) by ozone (Sect. V-B-l) would reduce its concentration below the limits of detectability even if it were produced in the primary step. Thus, if a singlet molecule is, indeed, produced in the primary step (14), then for A = 2537 A it is probably in the 12g+ state. This matter will be discussed further in connection with atmospheric chemistry (Sect. VI). 

No difference in the absorption spectrum is observed. The lifetimes of the two fluorescence emissions are both of the order of 10-8 sec. Another effect has been observed with hydrocarbons both as vapor and in solution, namely, a "delayed fluorescence emission with a life of a few milliseconds (56,63). This was at first interpreted as process 9, and the term excimer applied to the hypothetical excited dimer. However, C. A. Parker and C. G. Hatchard have shown that the intensity of the delayed fluorescence, which has the same spectrum as that from the excited singlet molecule, depends upon the square of the intensity of the exciting light (49). The mean life of the delayed fluorescence of anthracene solutions is (about) one-half that of the triplet state, and the effect is not observed in rigid media. These facts show that the delayed emission must be caused by an interaction between two triplet-state molecules ... 

Initially excess vibrational energy is rapidly lost by radiationless processes, such as collision with solvent molecules, to give the thermally equilibrated excited singlet molecules S t. This has a short lifetime ( 10 8 s) and may then lose its energy by any of the processes 2-5 below. 

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