Electrons singlet state

S j where denotes an electronic singlet state) of a coloured molecule [6]. Vibronic relaxation may be... 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

Merchan M, Serrano-Andres L (2003) Ultrafast internal conversion of excited cytosine via the lowest it it electronic singlet state. J Am Chem Soc 125 8108... 

Thus, we have the / -electron wave function with separated spatial and spin parts only in the cases of two-electron singlet states and N-electron (N- - l)-plet states. The Hartree-Fock orbitals are defined as those functions t which make the wave functions (1.5), (1.6), and (1.7) best. The usual variation technique leads to the N(case A) or v(case B) simultaneous differential equations which have to be satisfied by... 

Pople refers to a specific set of approximations as defining a theoretical model. Hence the ab initio or Hartree-Fock models employ the Born-Oppenheimer, LCAO and SCF approximations. If the system under study is a closed-shell system (even number of electrons, singlet state), the constraint that each spatial orbital should contain two electrons, one with a and one with P spin, is normally made. Such wavefunctions are known as restricted Hartree-Fock (RHF). Open-shell systems are better described by unrestricted Hartree-Fock (UHF) wavefunctions, where a and P electrons occupy different spatial orbitals. We have seen that Hartree-Fock (HF) models give rather unreliable energies. 

Figure 20. An energy-level diagram for the low-lying electronic singlet states of...

Fig. 1. Schematic energy level diagram for fluorescence and dissociation of some polyatomic molecules. A0 to X are vibration levels of the normal electronic state. Y to Y are the vibration levels of the electronic (singlet) state formed by absorption. Zo to Zm are vibration levels of the long lived (triplet) electronic state. Fluorescence occurs by transition to X levels from F0 to Za. Dissociation is possible at higher energies than D (Noyes98).

Figure 16.3 Modified Jablonski diagram ows the energy absorption effects of near metal surface enhanced fluorescence. The process involves o eating an excited electronic singlet state by optical absorption and subsequent emission of fluorescence with different decay paths.

The sequence of steps involved in fluorescence is described in Fig. 2. The initial absorption takes the molecule or ion pair from the ground electronic singlet state (So) to the electronically excited singlet state (5i), and the resulting absorption (excitation) spectrum should resemble that showm in Fig. 3a. 

TABLE 3. Fundamental vibrational frequencies (cm-1) and associated potential energy distributions of aniline in its ground electronic (singlet) state. Calculated values were obtained from scaled B3LYP/6-311++G(3df,2p) harmonic frequencies... 

The origins of the enhanced acidity of hydroxyarenes and other photoacids are clearly due to the differences between the quantum-mechanical properties of the first electronic singlet state (the fluorescence emitting state) and the ground electronic state of the photoacid. Aside from the question whether acid or base is more important in determining the Kl of the excited photoacid, one faces a more fundamental question as to why photoacidity occurs at all. To answer this question one should deal with the electronic structure of... 

At first look, such an approximation seems to be very crude. However, there are molecular systems for which such an approximation works quite well. An example of such a molecule is p-nitroaniline. The results presented in Fig. 1 show that the inclusion of the third electronic singlet state (with excitation energy near 4 eV) gives the value of /3 close to the converged value for 100 electronic states in SOS method. This is partially due to fortuitous cancellation of contributions from higher-lying excited electronic states with excitation energies near 10 eV. 

In their first electronic singlet state, hydroxy aromatic compounds are much stronger acids than in their ground state (Weller, 1961 Gutman et al., 1981 Schullman, 1977). The pK shift ApK = pK — pKo can be... 

Abbreviations (0-0) - transition between zero-point vibrational levels of two electronic states (= electronic origin) HOMO -highest occupied molecular orbital LUMO - lowest unoccupied molecular orbital PPP-CI - PPP-MO Theory which includes configuration interaction PPP-MO- Pariser Parr Pople Molecular Orbital Theory So, S, Sj - ground (S ) and excited (S, Sj) electronic singlet states T, Tj - excited electronic triplet states ... 

Gaier K, Angerhofer A and Wolf HC (1991) The lowest excited electronic singlet states ofa//-/rans-/J-carotene single crystals. Chem Phys Lett 187 103-109... 

We shall describe the various steps in the evolution of the methods and knowledge of proton diffusion on the membrane surface. The methods used for our studies all emanate from one basic technique—the laser-induced proton pulse (I). The common step of the various forms of this method is a pulse excitation of aromatic alcohols (OH), such as naphthols, sulfono naphthols, or pyranine (8-hydroxypyrene- 1,3,6-trisulfonate), to their first excited electronic singlet state (OH ). In this state the compound is very acidic and the hydroxyl proton dissociates in subnanosecond dynamics. 

Schematic potential energy diagraim for ground and excited electronic singlet states of a diatomic molecule, A-B and A-B, respectively. The horizontal lines represent vibrational energy levels. The wavy lines represent the arrival or departure of light quanta. It is important to recognize that the curves shown here are schematic and, for actual systems, the positions and shapes of the curves may be quite different from those shown.

A classic example is formaldehyde (I) which in its ground state is a planar molecule with no unpaired electrons (singlet state), a double CO bond, and a dipole moment of 2.3 D. In its lowest excited state, this molecule has 76 kcal/mole more energy than the ground state, it is not planar but pyramidal, and it has two unpaired electrons (triplet state), an essentially single CO bond, and a dipole moment of 1.3 D. Obviously, the two states exhibit completely diflFerent reactivity. 

UV/VIS absorption and luminescence spectra are related to electronic and vibrational transitions. The term luminescence summarizes a combination of basic processes like fluorescence or phosphorescence, which are described below. Transitions occur between energy levels described like S t, where S indicates an electronic singlet state and n v the corresponding electronic (n) and vibrational (v) excitation levels. The intensity of a transition from an electronic and vibrational ground state Sq o to a corresponding excited state S is proportional to the square of the transition dipole moment M, which itself can be separated into an electronic part Mq and the vibrational contribution Fo q. ... 

Fig. 1 The Jablonski diagram the energies of the ground electronic singlet state So, excited singlet. Si, and triplet T are depicted by bold horizontal lines-, vibrational states by narrow lines-, the most important transitions are depicted by arrows and wavy lines-, the typical values (in orders of magnitudes) of rate constants of the processes have been also included...

The further prediction that the dipositive ion (2tt electrons) corresponding to cyclobutadiene should have paired electrons (singlet state) and a resonance energy comparable. to benzene has not as yet been confirmed. 

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