Vibrational energies, chemical accuracy

In addition, simple and efficient CCSD(T)-F12 approximations x = a, b) [57] were proposed and benchmarked [58] by Werner s group. They obtained improvements in basis set convergence for calculations of equilibrium geometries, harmonic vibrational frequencies, atomization energies, electron affinities, ionization potentials, and reaction energies of open- and closed-shell reaction systems, where chemical accuracy of total reaction energies was obtained for the first time using valence double-zeta basis sets. 

Rotational quadrupole alignment parameters as a function of the translational energy represent another example of the role of the SDOFs. In Fig. 2.12 experimental and quantum simulated A for D2 as a function of the translations energy are shown. This figure shows the good agreement between experiments [42] and quantum theory [20]. But, this agreement is not within chemical accuracy as in the case of dissociative adsorption or vibrational deexcitation, despite the fact that the same accurate SRP-PES is used in all the cases. In order to explore the role played by the SDOFs, AIMD calculations [33] have shown themselves to be a very useful tool [68]. AIMD simulations, which include the SDOFs, yielded values... 

Tables C. 1-C.4 provide conversion factors from a.u. to SI units and a variety of practical (thermochemical, crystallographic, spectroscopic) non-SI units in common usage. Numerical values are quoted to six-digit precision (though many are known to higher accuracy) in an abbreviated exponential notation, whereby 6.022 14(23) means 6.022 14 x 1023. In this book we follow a current tendency of the quantum chemical literature by expressing relative energies in thermochemical units (kcal mol-1), structural parameters in crystallographic Angstrom units (A), vibrational frequencies in common spectroscopic units (cm-1), and so forth. These choices, although inconsistent according to SI orthodoxy, seem better able to serve effective communication between theoreticians and experimentalists.

A very important aspect of the results described above for De is that the error obtained at a certain level of approximation is systematic. This fact combined with the fact that the results improve as the method improves are aspects of ab initio methods which are at least as important as the final accuracy of the results. So far the only property discussed is De. It is clear that the most important chemical information, such as reaction pathways and thermochemistry, is obtained from relative energies, but the accuracy of other properties is also of interest. If we look at the equilibrium bond distance Re and the harmonic vibrational frequency we, these properties also display a systematic behaviour depending on the method chosen and this systematic behaviour is easy to understand. Since the RHF method dissociates incorrectly, the potential curves tend to rise too fast as the bond distance is increased. At the RHF level this leads to too short equilibrium bond distances and vibrational frequencies that are too high. When proper dissociation is included at the MCSCF level, the opposite trend appears. Since the dissociation energies are too small at this level the potential curves rise too slowly as the bond distance increases. This leads to too long bond distances and too low frequencies. These systematic trends are nicely illustrated by the results for three of the previously discussed diatomic molecules. For H2 the experimental value for Re is 1.40 ao and for uje it is 4400 cm-1. At the RHF level Re becomes too short, 1.39 ao, and we becomes too high, 4561 cm-1. At the two configuration MCSCF level Re becomes... 

One of the main aims of quantum mechanical methods in chemistry is the calculation of energies of molecules as a function of their geometries. This requires the generation of potential energy hypersurfaces. If these surfaces can be calculated with sufficient accuracy, they may be employed to predict equilibrium geometries of molecules, relative energies of isomers, the rates of their interconversions, NMR chemical shifts, vibrational spectra, and other properties. Carbocations are ideally suited for calculations because relative energies of well-defined structural isomers are frequently not easily determined experimentally. It should, however, be kept in mind that theoretical calculations usually refer to isolated ion structures in the gas phase. 

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