Energy levels, diagrams vibrational

Once you have calculated an ab initio or a semi-empirical wave function via a single point calculation, geometry optimization, molecular dynamics or vibrations, you can plot the electrostatic potential surrounding the molecule, the total electronic density, the spin density, one or more molecular orbitals /i, and the electron densities of individual orbitals You can examine orbital energies and select orbitals for plotting from an orbital energy level diagram. 

We can use the energy level diagram in Figure 10.14 to explain an absorbance spectrum. The thick lines labeled Eq and Ei represent the analyte s ground (lowest) electronic state and its first electronic excited state. Superimposed on each electronic energy level is a series of lines representing vibrational energy levels. 

Energy level diagram for a molecule showing pathways for deactivation of an excited state vr Is vibrational relaxation Ic Is Internal conversion ec Is external conversion, and Isc Is Intersystem crossing. The lowest vibrational energy level for each electronic state Is Indicated by the thicker line. 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

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 ...

Figure 10.1 Schematic energy-level diagram for a molecule. Two electronic levels A and B are present, with their vibrational levels (v) and rotational levels (/). The relative separation of electronic and vibrational levels is generally much greater than we have shown here.

Figure 3.16 Energy level diagram for the CO ro-vibrational spectrum...

Fig. 2 Jablonski energy level diagram illustrating possible transitions, where solid lines represent absorption processes and dotted lines represent scattering processes. Key A, IR absorption B, near-IR absorption of an overtone C, Rayleigh scattering D, Stokes Raman transition and E, anti-Stokes Raman transition. S0 is the singlet ground state, S, the lowest singlet excited state, and v represents vibrational energy levels within each electronic state.

FIGURE 7.10 An energy level diagram for a molecule or complex ion showing the vibrational energy states superimposed on the electronic states. 

Figure 4.4 Energy-level diagram showing how the electronic and vibrational energy levels in the ground-state (S0) and first excited-state (Si) anthracene molecule are related to the absorption and fluorescence emission spectra...

Fig. 7. Vibrational energy level diagram of CH4 and decay paths after excitation by the He-Ne laser line X = 3.39 jLtm...

Figure 1. Energy level diagram depicting vibrational Stokes, Rayleigh, and anti-...

Figure 6.13 Schematic vibrational energy-level diagrams of medium-mass even-even nuclei. [From Eichler (1964).]...

Fig. 6.8. A Principle of frequency-multiplexed CARS microspectroscopy A narrow-bandwidth pump pulse determines the inherent spectral resolution, while a broad-bandwidth Stokes pulse allows simultaneous detection over a wide range of Raman shifts. The multiplex CARS spectra shown originate from a 70 mM solution of cholesterol in CCI4 (solid line) and the nonresonant background of coverglass (dashed line) at a Raman shift centered at 2900 cm-1. B Energy level diagram for a multiplex CARS process. C Schematic of the multiplex CARS microscope (P polarizer HWP/QWP half/quarter-wave plate BC dichroic beam combiner Obj objective lens F filter A analyzer FM flip mirror L lens D detector S sample). D Measured normalized CARS spectrum of the cholesterol solution. E Maximum entropy method (MEM) phase spectrum (solid line) retrieved from (D) and the error background phase (dashed line) determined by a polynomial fit to those spectral regions without vibrational resonances. F Retrieved Raman response (solid line) calculated from the spectra shown in (E), directly reproducing the independently measured spontaneous Raman response (dashed line) of the same cholesterol sample...

Fig. 13. Energy level diagram showing transitions for a molecule with two active vibrational modes.

Fig. 11.2. Energy-level diagram of H20(A) in the lowest vibrational state for total angular momentum quantum number J = 4 E = 0 corresponds to the lowest rotational level 00o. The nomenclature Jk k+ with K+ = J, J — 1,..., 0 and K = 0,1,..., J follows the standard spectroscopic convention (Levine 1975 ch.5 Zare 1988 ch.6).

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