Experimental Ionization Potentials

We can compare this result with the experimental first and second ionization potentials (IPs) for helium... 

If we compare the calculated total ionization potential, IP = 4.00 hartiees, with the experimental value, IP = 2.904 hartiees, the result is quite poor. The magnitude of the disaster is even more obvious if we subtract the known second ionization potential, IP2 = 2.00, from the total IP to find t c first ionization potential, IPi. The calculated value of IP2, the second step in reaction (8-21) is IP2 = Z /2 = 2.00, which is an exact result because the second ionization is a one-election problem. For the first step in reaction (8-21), IPi (calculated) = 2.00 and IPi(experimental) = 2.904 — 2.000 =. 904 hartiees, so the calculation is more than 100% in error. Clearly, we cannot ignore interelectronic repulsion. 

Continue the calculation in Exeivise 8-3 substituting 1.6 as the initial value of P, minimizing to find a new value of a. How much in error is the calculated value of the first ionization potential of He relative to the experimental value of 0.904 hartrees ... 

Look up the experimental values of the first ionization potential for these atoms and calculate the average difference between experiment and the computed values. Depending on the source of your experimental data, the arithmetic mean difference should be within 0.010 hartrees. Serious departrues from this level of agreement may indicate that you have one or more of your spin multiplicities wrong. 

How many iterations does it take to achieve self-consistency for the helium problem treated (partially) in Exercises 8-3 and 8-4 What is the % discrepancy between the calculated value of the first ionization potential and the experimental value of 0.904 hartiees when the solution has been brought to self-consistency ... 

Here P°g,v is a eonstant (having energy units) eharaeteristie of the bonding interaetion between X i and Xv its value is usually determined by foreing the moleeular orbital energies obtained from sueh a qualitative orbital treatment to yield experimentally eorreet ionization potentials, bond dissoeiation energies, or eleetronie transition energies. 

An extended Huckel calculation is a simple means for modeling the valence orbitals based on the orbital overlaps and experimental electron affinities and ionization potentials. In some of the physics literature, this is referred to as a tight binding calculation. Orbital overlaps can be obtained from a simplified single STO representation based on the atomic radius. The advantage of extended Huckel calculations over Huckel calculations is that they model all the valence orbitals. 

The electron alfinity (FA) and ionization potential (IP) can be computed as the difference between the total energies for the ground state of a molecule and for the ground state of the appropriate ion. The difference between two calculations such as this is often much more accurate than either of the calculations since systematic errors will cancel. Differences of energies from correlated quantum mechanical techniques give very accurate results, often more accurate than might be obtained by experimental methods. 

The correspondence between calculated and experimental values for the of the monomethine dyes. 404 nm for 410 nm, 404 nm for 412 nm, are satisfactory but this does not imply that 43 and 44 possess the same first ionization potential and the same electronic affinity simultaneously. 

Ultraviolet photoelectron spectroscopy allows the determination of ionization potentials. For thiazole the first experimental measurement using this technique was preformed by Salmona et al. (189) who later studied various alkyl and functional derivatives in the 2-position (190,191). Substitution of an hydrogen atom by an alkyl group destabilizes the first ionization potential, the perturbation being constant for tso-propyl and heavier substituents. Introduction in the 2-position of an amino group strongly destabilizes the first band and only slightly the second. 

The original paper defining the Gaussian-2 method by Curtiss, Raghavachari, Trucks and Pople tested the method s effectiveness by comparing its results to experimental thermochemical data for a set of 125 calculations 55 atomization energies, 38 ionization potentials, 25 electron affinities and 7 proton affinities. All compounds included only first and second-row heavy atoms. The specific calculations chosen were selected because of the availability of high accuracy experimental values for these thermochemical quantities. 

The total energy in ab initio theory is given relative to the separated particles, i.e. bare nuclei and electrons. The experimental value for an atom is the sum of all the ionization potentials for a molecule there are additional contributions from the molecular bonds and associated zero-point energies. The experimental value for the total energy of H2O is —76.480 a.u., and the estimated contribution from relativistic effects is —0.045 a.u. Including a mass correction of 0.0028 a.u. (a non-Bom-Oppenheimer effect which accounts for the difference between finite and infinite nuclear masses) allows the experimental non-relativistic energy to be estimated at —76.438 0.003 a.u. ... 

Experimental. The mass spectra in Figures 1-8 are positive-ion spectra produced by electron impact and were obtained from a single-focusing, magnetic deflection Atlas CH4 Mass Spectrometer. The ionizing potential was 70 e.v. and the ionizing current 18/a a. An enamel reservoir heated to 120°C. was used from which the sample was leaked into the ion source. 

Whether or not 0+(2D) ions undergo fast reaction with N2 at low energies is of great interest since they satisfy both rules. Unfortunately, the experimental evidence is not decisive. The resonance potential (8) in this case would be repulsive but weak since the ionization potential of O to this state, 16.94 e.v., is considerably greater than that of N2, 15.56 e.v. The resonance potential may be strong enough to inhibit reaction of 0+(2Z)) ions at low energies. 

The properties of the hydrogen molecule and molecule-ion which are the most accurately determined and which have also been the subject of theoretical investigation are ionization potentials, heats of dissociation, frequencies of nuclear oscillation, and moments of inertia. The experimental values of all of these quantities are usually obtained from spectroscopic data substantiation is in some cases provided by other experiments, such as thermochemical measurements, specific heats, etc. A review of the experimental values and comparison with some theoretical... 

Fig. 4. Experimental (T0 values. The circles are obtained from X-ray term values corrected for the spin-relativity effect and external screening, the squares from optical ionization potentials.

The competing pathways to radical or carbenium ion derived products are determined, apart from experimental factors (see chap. 2), by the ionization potential of the radical. From product ratios and ionization potentials of the intermediate radicals, the conclusion could be drawn that such radicals with ionization potentials above 8 eV lead preferentially to coupling products, whilst those with ionization potentials below 8 eV are further oxidized to carbenium ions [8 c]. 

Until now, applications of semiempirical all-valence-electron methods have been rare, although the experimental data for a series of alkyl radicals are available (108,109). In Figure 9, we present the theoretical values of ionization potentials calculated (68) for formyl radical by the CNDO version of Del Bene and Jaffe (110), which is superior to the standard CNDO/2 method in estimation of ionization potentials of closed-shell systems (111). The first ionization potential is seen, in Figure 9, to agree fairly well with the experimental value. Similarly, good results were also obtained (113) with some other radicals (Table VII). 

Figure 9. Determination of the first electron affinity, and the first and higher ionization potentials of formyl radical from the SCF orbital energies and electronic repulsion integrals, and K,j (cf. eqs. (90), (92), and (93)). The experimental value (112), 9.88 eV, for the first ionization potential corresponds to the theoretical value I . All entries are given in eV. With A and I a lower index stands for MO the upper one indicates the state multiplicity after ionization.

Calculated and Experimental First Ionization Potentials of Small Radicals (113)... 

The ionization potential (7.9 eV) falls right outside the bracket of experimental IP s reported for carbon clusters with 40 to 100 atoms (6.42 eV IP 7.87 eV, Ref. 11). Inclusion of correlation effects will lower the calculated ASCF IP by 0.25 to 0.50 eV, so that the corrected IP will be at the upper end of the experimental IP>bracket. Due to the diffuseness of the n orbital from which an electron is removed, the correlation error in the ASCF value will be smaller than in cases where an electron is removed from a well localized bond. In these cases a correction of 1 eV is usually applied. 

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