Excited Ground State

As described at the end of section Al.6.1. in nonlinear spectroscopy a polarization is created in the material which depends in a nonlinear way on the strength of the electric field. As we shall now see, the microscopic description of this nonlinear polarization involves multiple interactions of the material with the electric field. The multiple interactions in principle contain infomiation on both the ground electronic state and excited electronic state dynamics, and for a molecule in the presence of solvent, infomiation on the molecule-solvent interactions. Excellent general introductions to nonlinear spectroscopy may be found in [35, 36 and 37]. Raman spectroscopy, described at the end of the previous section, is also a nonlinear spectroscopy, in the sense that it involves more than one interaction of light with the material, but it is a pathological example since the second interaction is tlirough spontaneous emission and therefore not proportional to a driving field... 

At this stage we may distinguish between excitation involving different electronic states and excitation occurring within the same electronic (ground) state. Wlien the spectroscopic states are located in different electronic states, say the ground (g) and excited (e) states, one frequently assumes the Franck-Condon approximation to be applicable ... 

Plenary 11. W Kiefer et al, e-mail address wolfgang.kiefer mail.imi-wue.de (TR CARS). Ultrafast impulsive preparation of ground state and excited state wavepackets by impulsive CARS with REMPI detection in potassium and iodine duners. 

The simplest approach to simulating non-adiabatic dynamics is by surface hopping [175. 176]. In its simplest fomi, the approach is as follows. One carries out classical simulations of the nuclear motion on a specific adiabatic electronic state (ground or excited) and at any given instant checks whether the diabatic potential associated with that electronic state is mtersectmg the diabatic potential on another electronic state. If it is, then a decision is made as to whedier a jump to the other adiabatic electronic state should be perfomied. 

C3.4.13)). The dimer has a common ground state and excitation may temrinate in eitlier tire or excited state (see tire solid arrows in figure C3.4.3). The transition dipole moments of tliese transitions are defined as ... 

Absorption of electromagnetic radiation causes a molecule to be excited from Its most stable state (the ground state) to a higher energy state (an excited state)... 

You can use Cl to predict electronic spectra. Since the Cl wave function provides ground state and excited state energies, you can obtain electronic absorption frequencies from the differences between the energy of the ground state and the excited states. 

The calculation mixes all single determinant wavefunctions that can be obtained from the ground state by exciting electrons from a subset of the occupied orbitals (of the ground state) to a subset of the unoccupied orbitals. The subsets are specified as a fixed number (highest occupied or lowest unoccupied) or by an energy criterion associated with the energy difference between the occupied orbital and the unoccupied orbital. 

The vibrational term values for any electronic state, ground or excited, can be expressed, as in Equation (6.16), by... 

In a molecule with electrons in n orbitals, such as formaldehyde, ethylene, buta-1,3-diene and benzene, if we are concerned only with the ground state, or excited states obtained by electron promotion within 7i-type MOs, an approximate MO method due to Hiickel may be useM. 

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Energy Transfer. In addition to either emitting a photon or decaying nonradiatively to the ground state, an excited sensitizer ion may also transfer energy to another center either radiatively or nonradiatively, as illustrated in Figure 4. 

Fig. 1. Schematic energy-level diagram for a dye molecule. Electronic states Sq = ground singlet state = first excited singlet state S2 = second excited singlet state Tj = first excited triplet state T2 = second excited triplet state EVS = excited vibrational states. Transitions A = absorption excited states ...

Many other measures of solvent polarity have been developed. One of the most useful is based on shifts in the absorption spectrum of a reference dye. The positions of absorption bands are, in general, sensitive to solvent polarity because the electronic distribution, and therefore the polarity, of the excited state is different from that of the ground state. The shift in the absorption maximum reflects the effect of solvent on the energy gap between the ground-state and excited-state molecules. An empirical solvent polarity measure called y(30) is based on this concept. Some values of this measure for common solvents are given in Table 4.12 along with the dielectric constants for the solvents. It can be seen that there is a rather different order of polarity given by these two quantities. 

Fig. 5 Schematic representation of the electronic transitions during luminescence phenomena [5]. — A absorbed energy, F fluorescence emission, P phosphorescence, S ground state. S excited singlet state, T forbidden triplet transition.

Figure 8-7. Model of the alkylpyridinium iodide complex (4) ground state. (B) Excited state [after Kosower ]...

The photochemical behavior of butadienes has been closely studied. When these compounds are exposed to light, they move from the ground state to an excited state. This excited state eventually returns to one of the ground state conformations via a process that includes a radiationless decay (i.e., without emitting a photon) from the excited state potential energy surface back to the ground state potential energy surface. 

The blue colour of oxygen in the liquid and solid phases is due to electronic transitions by which molecules in the triplet ground state are excited to the singlet states. These transitions are normally forbidden in pure gaseous oxygen and, in any case, they occur in the infrared region of the spectrum at 7918 cm" ( Ag) and 13 195 cm" ( ]+). However, in the condensed phases a... 

Electronic absorption spectra are produced when electromagnetic radiation promotes the ions from their ground state to excited states. For the lanthanides the most common of such transitions involve excited states which are either components of the ground term or else belong to excited terms which arise from the same 4f" configuration as the ground term. In either case the transitions therefore involve only a redistribution of electrons within the 4f orbitals (i.e. f—>f transitions) and so are orbitally forbidden just like d—>d transitions. In the case of the latter the rule is partially relaxed by a mechanism which depends on the effect of the crystal field in distorting the symmetry of the metal ion. However, it has already been pointed out that crystal field effects are very much smaller in the case of ions and they... 

Greater reactivity gamma to an azine-nitrogen would be expected on the basis of the greater ara-quinoid than orf/io-quinoid interactions between various substituents and azine-nitrogens in ground states and excited states. Such a difference in interaction is supported by several kinds of data spectral,basicity, dipole moment, and chlorine quadrupole resonance of halo, methoxy,... 

The irradiation is usually carried out with light of the near UV region, in order to activate only ihc n n transition of the carbonyl function," thus generating excited carbonyl species. Depending on the substrate, it can be a singlet or triplet excited state. With aromatic carbonyl compounds, the reactive species are usually in a Ti-state, while with aliphatic carbonyl compounds the reactive species are in a Si-state. An excited carbonyl species reacts with a ground state alkene molecule to form an exciplex, from which in turn diradical species can be formed—e.g. 4 and 5 in the following example ... 

In this section, you will learn how to predict the electron configurations of atoms of elements. There are a couple of different ways of doing this, which we consider in turn. It should be emphasized that, throughout this discussion, we refer to isolated gaseous atoms in the ground state. (In excited states, one or more electrons are promoted to a higher energy level)... 

The relationship between the ground-state and excited-state populations is given by the Boltzmann equation... 

N = number of electrons, G = ground state, E = excited state. 

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