12. PRONOSTICO DE LA DEMANDA
13.1 Elección del modelo de inventario
The energy at the onset of a PI spectrum is the adiabatic ionization energy (AIE) of a molecule. The shape of a PI spectrum and ionization energy are unique to every molecule. In an experiment this can help identifying an unknown species. When there is an idea of what the unknown species may be, the literature photoionization spectrum may be superimposed onto the experimental PI spectrum of the species. If the two match, the unknown species is determined. If there is an idea of what the unknown species may be, and no literature PI spectrum is available, a Franck-Condon simulation can be performed to provide a photoionization spectrum.20 This Franck-Condon simulation is also applicable to identification of multiple isomers at a certain mass, since each isomer has unique FC factors for ionization transitions. To simulate a photoionization
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spectrum, the CBS-QB323-25 composite model is used within the Gaussian 0926 program. For a possible unknown compound, the neutral and cationic states are optimized to obtain the adiabatic ionization energy and the optimized geometrical parameters to simulate a PI spectrum. The optimization of each structure, done in the Gaussian 0926 program using the CBS-QB323-25 composite model, provides information about bond lengths, bond angles, ionization energies, vibrational frequencies, and force constants. This composite model is chosen due to its high accuracy at a low computational cost, and its mean average deviation (MAD) of 4-5 kJ mol-1.24-25 The zero-point vibrational corrected total electronic energy (E0) is obtained from the optimized
neutral and cationic state. When the two energies are subtracted, the AIE is found:
𝐴𝐼𝐸 = 𝐸SŸ¡− 𝐸UA² (21)
The AIE is applicable in generating Franck-Condon simulations of the photoelectron spectrum (PE). To do this, a second calculation is run, in addition to the AIE, but this calculation does not use a basis set, instead it uses the neutral’s and cation’s Franck-Condon factors to create a photoelectron spectrum.4 Photoelectron spectra are simulated using Franck-Condon (FC)27-29 and
Franck-Condon-Herzberg-Teller (FCHT)29 methods in the Gaussian 0926 program, which approximates the FC factors for vibronic transitions of the neutral to cationic state of a species. In addition, the FCHT method determines the vibrational normal modes using the Duschinsky rotation matrix.30 Afterwards, a set of recursive formulas, created by Ruhoff,31 is used to calculate the FC overlap integrals. Resulting photoelectron spectra are then integrated to give the photoionization spectra, which are compared to experimental PI spectra. The photoionization spectra will be used to determine the species at specific masses. The Franck-Condon factors determine the shape of the photoionization spectra while the adiabatic ionization energy determines the onset of the curve in the photoionization spectra.26
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The ZPE corrected electronic energy can also be used to find other thermodynamic quantities, such as reaction enthalpies24 based on Hess’ law:
∆𝐻8±U = 𝑍𝑃𝐸\8£_²S¡¥‚0}(°0c− 𝑍𝑃𝐸8AŸS¡ŸU¡¥‚0}(°0c (22)
The heat of the reaction is used to show if a proposed reaction mechanism is thermodynamically feasible. Proving a reaction mechanism is also aided using potential energy surface (PES) scans at the B3LYP level (a level used in CBS-QB3 optimizations). Transition states (saddle points) are found from the maximum energy in the scans and must contain one imaginary vibrational frequency. Transition states are optimized using the CBS-QB3 method, with the respect to the imaginary frequency. To further prove the transition state, Intrinsic reaction coordinate (IRC) calculations (forward and reverse) are used to validate the minima on both sides of the transition state. Using all these values determines the enthalpy change (kJ mol-1) of proposed mechanisms, which also determines the exothermicity of a reaction.
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3.11 References
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