Zero point energy ZPE

Step 1. Produce an initial equilibrium structure at the Hartree-Fock level using the 6-31G(d) basis set. Verify that it is a minimum with a frequency calculation and predict the zero-point energy (ZPE). This quantity is scaled by 0.8929. 

Table 3. Enthalpies, free enthalpies, zero point energies (ZPE) (all in kJ mol-1) and entropies (J K 1 mol-1) of the activation and reaction steps for Eqs. (3)-(5)...

The allyl anion ground-state conformation is Czv at 6-31G HF and C2 at MP2. The energy difference, however, is only 0.2 kcalmol-1 and when the zero-point energy (ZPE)... 

The MP2/TZDP optimized structures were then used to calculate the stationary state geometry force constants and harmonic vibrational frequencies, also at the MP2 level. These results serve several purposes. Firstly, they test that the calculated geometry is really an energy minimum by showing all real frequencies in the normal coordinate analysis. Secondly, they provide values of the zero-point energy (ZPE) that can be used... 

TABLE 24. MP2 level zero point energies (ZPE, in kcal mol ) for RYa ... 

The secondary a-deuterium KIEs calculated for the uncatalysed reaction were in the range found experimentally for other SN2 methyl transfers. The calculated KIE was also analysed in terms of the zero-point energy (ZPE), the molecular mass-moment of inertia (MMI) and the excitation (EXC) contributions to the total isotope effect. The inverse KIE was found to arise from an... 

As for graphite, its zero-point energy, ZPE = R6 + jR0 , is most conveniently deduced from Debye s theory [197,198] by separating the lattice vibrations into two approximately independent parts, with Debye temperatures (in plane) and 6j (perpendicular). A balanced evaluation gives ZPE 3.68 kcal/mol [199]. 

Including zero-point energy (ZPE) corrections, which range from -0.3 to 0.1 kcal/mol for transition structures and from 0.9 to 1.4 kcal/mol for products. 

Direct dynamics calculations using the PM3 method were carried out for reaction l.4 The trajectories starting from the TS between the biradical intermediate and norbornene (2, 3) with 2kcalmol 1 kinetic energy on the imaginary frequency mode together with zero-point energy (ZPE) on other real... 

As microscopic systems, these oscillators have a zero-point energy (ZPE) equal to hvc aii and the difference in zero-point energies for a particular vibration in isotopomers depends upon vibrational frequencies. These, in turn, depend on the force constant (the same for... 

The other approach to calibration, by comparison with experimental data, also presents difficulties. Here, the problem is in ensuring that the calculations relate correctly to the experiment, which, in this field, most frequently refers to finite-temperature free energy differences in the condensed phase. As well as obtaining accurate electronic energy differences, therefore, zero-point energy (zpe), thermal or enthalpic (H), entropic (S), and medium ef-... 

The chiral self-discrimination of twelve molecules showing axial chirality (Scheme 3.13), has been studied by means of DFT (B3LYP/6-31+G ) and ab initio (MP2/6-31+G and MP2/6-311++G ) methods [25]. The interaction energy of the complexes was corrected with the inherent basis set superposition error (BSSE) and the zero point energy (ZPE). The results show similar qualitative tendencies for the three methods considered. 

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