Molecular-energy diagram

Excitation by either process results in the same fluorescence emission spectrum, implying that only the Si state emits, and that anthracene in the S2 state has to reach the Si state before it can emit fluorescence. The molecular-energy diagram in Figure... 

Each process will be discussed below in terms of the molecular-energy diagram in Figure 9.2. It should be stressed that each process involves only Si molecules in the EVo sublevel. 

Draw a molecular-energy diagram showing the transitions involved in the phosphorescence of anthracene, which occurs at 680 nm. 

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

Fig. 2. Simplified molecular orbital diagram for a low spia octahedral complex, such as [Co(NH3 )g, where A = energy difference a, e, and t may be antisymmetric (subscript ungerade) or centrosymmetric (subscript, gerade) symmetry orbitals. See text.

Fig. 1.18. Molecular orbital energy diagram for methane. Energies are in atomic units. ...

Figure 17.2 Schematic molecular orbital energy diagram for diatomic halogen molecules. (For F2 the order of the upper and 7T bonding MOs is inverted.).

Figure 19.17 Schematic molecular energy level diagram for CO. The Is orbitals have been omitted as they contribute nothing to the bonding. A more sophisticated treatment would allow some mixing of the 2s and 2p, orbitals in the bonding direction (z) as implied by the orbital diagram in Fig. 19.18.

Draw an energy diagram for the three molecular orbitals of the cyclopropenyl system (C l I3). How ate these three molecular orbitals occupied in the cyclopropenyl anion, cation, and radical Which of the three substances is aromatic according to Hiickel s rule ... 

Figure 14-11. A polaron in polylliioplicne. Top view is u molecular scheme, llie bottom view is the energy diagram.

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

We now incorporate the bonding and antibonding t2g molecular orbitals of Fig. 6-10 into the energy diagram of Fig. 6-9. So as not to obscure the important issues... 

Figure 3. Molecular-orbital diagrams as obtained by the ROHF method. Dashed lines indicate MOs dominated by the metal d-orbitals, the solid lines stand for doubly occupied or virtual ligand orbitals. Orbitals which are close in energy are presented as degenerate the average deviation from degeneracy is approximately 0.01 a.u. In the case of a septet state (S=3), the singly occupied open-shell orbitals come from a separate Fock operator and their orbital energies do not relate to ionization potentials as do the doubly occupied MOs (i.e. Koopmann s approximation). For these reasons, the open-shell orbitals appear well below the doubly occupied metal orbitals. Doubly occupying these gives rise to excited states, see text.

A schematic molecular orbital diagram for the Fe-Fe interaction in an S = I valence-delocalized Fe Fe pair based on effective C v symmetry at the Fe sites and the observed electronic transitions for the valance-delocalized [Fe2S2l cluster is shown in Fig. 15. The dominant interaction (responsible for the S = ground state) is the a overlap between the pair of orbitals, with progressively smaller tt interactions between pairs of d z and dyz orbitals and S interactions between pairs of d y amd / orbitals. The three highest energy tran-... 

Use molecular orbital diagrams to explain the trend in the following bond energies B2 = 290 kJ / mol, C2 = 600kJ/mol, and N2 =942kJ/mol. 

The data show that bond energies for these three diatomic molecules increase moving across the second row of the periodic table. We must construct molecular orbital diagrams for the three molecules and use the results to interpret the trend. 

C15-0084. Consider the exothermic reaction AC -b B AB -b C. (a) Draw an activation energy diagram for this reaction, (b) Label the energies of reactants and products, (c) Show A reaction by a double-headed arrow, (d) Show a for the forward reaction by a single-headed arrow, (e) Label and draw a molecular picture of the activated complex. 

Figure 6.6 shows the molecular orbital energy diagrams for a few homonudear diatomic molecules. The stability of the molecules can be estimated from the number of electrons occupying bonding orbitals compared with the number of electrons in the antibonding orbitals. (Antibonding orbitals are sometimes denoted with the subscript, as in 2jt. )... 

Figure 7.19. (Left-hand side) Comparison between experimental sticking coefficients of N2 on Fe(l 11) and the prediction on the basis of Eq. (57) with an activation energy of 0.03 eV. (Right-hand side) Potential energy diagram for molecular nitrogen dissociating on Fe(l 11).

The interaction of hydrogen (deuterium) molecules with a transition metal surface c an be conveniently described in terms of a Lennard--Jones potential energy diagram (Pig. 1). It cxxislsts of a shallcw molecular precursor well followed by a deep atomic chemisorption potential. Depending on their relative depths and positions the wells m or may not be separated by an activation energy barrier E as schematically Indicated by the dotted cur e in Fig. 1. 

Fran the one dimensional representation of the potential energy diagram one cannot decide vhether the dissociative adsorption takes place throu intermediate tr plng in the molecular state or throu ... 

Figure 6.1 Schematic potential energy diagram for atomic and molecular nitrogen adsorption on a clean and K-covered Fe(100) surface. Curve (a) is for N2 + Fe(100) curve (b) is for N2 + Fe(100)-K. Note the lowering of the activation energy for dissociation from 3 kcalmol-1 to zero. (Reproduced from Ref. 3).

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