Experimental energies

The term resonance energy has been used in several w ays in the literature, but it is generally used to mean the difference between an experimentally determined energy of some relatively complicated molecule and the experimental energy... 

There was less agreement between calculated and experimental energy values. The use of 6-3IG, the best procedure in energy calculations of three-membered rings, yielded a value too low by more than 40 kJ moF in the case of diazirine bond separation energy was calculated as -45 kJ moF the experimental value is +0.4 kJ moF . Vibrational correction and extrapolation to 0 K would reduce this difference by several kJ moF . 

Even more recent calculations using STO-3G and 6-31G basis sets could not safely predict diazomethane as the more stable compound in comparison with diazirine, although there is an experimental energy difference of 125 kJ moP 79JST(52)275). 

There is a nice point as to what we mean by the experimental energy. All the calculations so far have been based on non-relativistic quantum mechanics. A measure of the importance of relativistic effects for a given atom is afforded by its spin-orbit coupling parameter. This parameter can be easily determined from spectroscopic studies, and it is certainly not zero for first-row atoms. We should strictly compare the HF limit to an experimental energy that refers to a non-relativistic molecule. This is a moot point we can neither calculate molecular energies at the HF limit, nor can we easily make measurements that allow for these relativistic effects. 

Experimental measurements by calorimetry usually involve amounts different from one mole. The molar energy change can be found from an experimental energy change by dividing by the number of moles that reacted, as ... 

There exists a fair agreement between the calculated and the experimental energy levels. The sequence of the 3d MQ s 17—21 is the same as that expected on the basis of EPR measurements 64). The high energy of the 3 d MO accounts for the spinpairing of the fifth 3 d electron. In table 5 the coefficients of the 3 d and 4 p orbitals are Usted for the MO s of interest. It can be seen that the covalency is strongly anisotropic. 

Fig. 17. The angle-dependent integrated opacity function dan(00 —> v = 0,1, f = 0 6, Eq, Jmax) versus Jmax computed for the experimental energy Eq = 1.200eV. This quantity is computed by restricting the partial wave sum in the DCS to the terms J < Jmax- The result is shown for forward and backward scattering to illustrate the J-contributions to scattering at different 0.

Here m is electron mass, N is the number density of gas molecules, B is the rotational constant, and q = (8/15)jta02Q2, ag and Q being respectively the Bohr radius and the quadrupole moment of the molecule. The experimental energy loss rate for nitrogen agreed well with Eq. (8.1) over the ambient temperature range 300-735 K. Typical values are -0.5 ts at 300 K and 6 torr, and -1 p.s at 735 K and 4 torr. The variation of relaxation time with gas temperature and pressure are also well predicted. For oxygen, Mentzoni and Rao (1965) measure relaxation times -160-350 ns for T = 300-900 K and at 3 torr. 

Fig. 10.11. Maximal experimental energies and number of particles for protons (a) and (c) and carbon ions (b) and (d) as a function of foil thickness. Open and closed black circles and squares are experimental data. The solid lines are the estimates from the analytical model. Closed diamonds are 2D PIC code results...

Figure 7. Low lying nucleon (left plot) and delta (right plot) states with total spin and parity JT The left and right bars are the theoretical energies predicted from the GBE and OGE models as described in the text, respectively. The shaded boxes represent the experimental energies with their uncertainties (Eidelman et al, 2004). 

Pearson and Edwards98 report that the thermal conversion of tetraborane without diborane being present is also first order, but is about one order of magnitude slower. The experimental energies of activation for both reactions, however, have been found to be almost the same. 

Table 1.7 CCSD(T) total energies calculated with the cc-pCVXZ basis sets and compared with the corresponding experimental total energies (Eh). The last row contains the mean absolute deviations from the experimental energies. All calculations have been carried out at the optimized all-electron CCSD(T)/cc-pCVQZ geometries [25].

As expected from our previous discussion of the CCSD valence correlation energies, the convergence towards the experimental energies is slow, with mean absolute errors of 511, 163, 61, 28, and 17 kJ/mol as... 

Comparison is made to experimental energies that have been averaged over the J quantum number. This works well for the first row atoms where the spin-orbit coupling is small and there is little interaction between different electronic states but becomes more questionable for the second and third row atoms. We shall return to this problem later. 

The relativistic version (RQDO) of the quantum defect orbital formalism has been employed to obtain the wavefunctions required to calculate the radial transition integral. The relativistic quantum defect orbitals corresponding to a state characterized by its experimental energy are the analytical solutions of the quasirelativistic second-order Dirac-like equation [8]... 

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