Potential-energy surfaces Calculation

HCR and co-workers carried out a number of studies by employing 3D potential energy surfaces calculated by means of highly sophisticated ab initio approaches [88,91-101]. The results of these computations are in impressive agreement with the corresponding experimental findings. The discrepancies in the order of 100 wavenumbers, as in early ab initio studies [16,17], have been reduced in the HCR studies to only a few wavenumbers. In conclusion of their paper on the ( H ) system of NH2, Gabriel et al. state We believe... 

Potential energy surfaces calculated by means of the London equation (5-15) cannot be highly accurate, but the results have been very useful in disclosing the general shape of the surface and the reaction coordinate. The London equation also forms the basis of some semiempirical methods. 

Fig. 2.4. Left potential energy surfaces calculated for the ground state (Te = 1 mRy) and for excited electronic states (Te = 17.6 and 22 mRy) of Bi. Vertical arrows show transitions of the atoms from the ground state to an excited energy surface. From [23], Right crystalline structure of Bi and Sb crystals. The directions of the Aig and Eg modes are indicated in both panels...

The C2 symmetric structure for the 2-propyl cation 6 is the only open-chain minimum on the C3117" potential energy surface calculated at MP2/6-31 lG(d,p) level.25... 

The Born-Oppenheimer isotope independent potential energy surface calculated with the bath atoms frozen in place as outlined in the paragraph above was employed by the authors to compare TST and VTST rate constants and kinetic isotope effects. The results are shown in Table 11.9. 

Figure 6.10 Structures of dimers (NH3BH3)2 located at the energy minima of the potential energy surface calculated at the DFT/B3LYP level. The dark spheres are the nitrogen atoms. (Reproduced with permission from ref. 18.)...

Potential-energy surface calculations and optimization methods A - Pseudo-potential calculation... 

Figure 56 shows a typical potential energy surface calculated for one effective bond length shorter than the other six ... 

There are three important minima on the potential energy surfaces calculated for [M(bidentate)5]. At b x 1.1, isomers I and II correspond to two of the possible ways of arranging bidentate ligands around a bicapped square antiprism, whereas isomer III is a sphenocorona (Figure 102). 

Fig. 2.7 The ozone/isoozone potential energy surface (calculated by the AMI method Chapter 6), a 2D surface in a 3D diagram. The dashed line on the surface is the reaction coordinate (intrinsic reaction coordinate, IRC). A slice through the reaction coordinate gives a ID surface in a 2D diagram. The diagram is not meant to be quantitatively accurate...

Fig. 2.14 The l-propen-2-ol potential energy surface (calculated by the AMI method) (see Fig. 2.13)...

Hartree-Fock Potential Energy Surface Calculations Asymptotic Behaviour of Single Determinantal Wavefunctions.—In general, a single determinantal wavefunction, whether or not it is at the Hartree-Fock limit, does not provide an adequate description of a molecular system over the complete range of intemuclear separations, because of the failure of such a function to describe... 

Kupperman et a/.223-228 compared transition-state, classical, and quantum mechanical thermal rate constants using the SSMK surface.112 In ab initio potential energy surface calculations, the potential energy is known only as a list of values at selected geometries of the system. It becomes necessary, then, if trajectory calculations are to be made, to fit the calculated points to a smooth and continuous map . In their calculations, Kupperman et al. fit the collinear SSMK surface by the rotating Morse function procedure of Wall and Porter.227... 

Figure 4. Potential energy surface calculations for the chemical dynamicist.

A mechanism below 325 nm must definitely invoke the radical process (22) in addition to the mechanism for the 325 to 360-nm region just described above. Here, it is possible that the triplet state (T ) may dissipate directly by the H + HCO channel as justified by the potential-energy-surface calculations of Hayes and Morokuma (104) and Jaffe and Morokuma (123). However, it is not possible to rule out the intermediacy of hydroxycarbene. It is apparent from Table 5 that the ratio of levels off at... 

These results also follow from the cross sections through the potential energy surfaces calculated in the semiempirical all-valence electron approximation by the MNDOC-CI method for acetaldehyde, acrolein, and benzal-dehyde, which are displayed in Figure 7.13. Stabilization of the state... 

This vibration is illustrated in Fig. 3, potential energy surface calculation along it on Fig. 4, and the Mexican-hat-like plot on Fig. 5. 

Fig. 4 VCI4 potential energy surface calculation along the JT active vibration (A) (times) and least square fitting of the data (minus), energies are given in cm relative to the HS point...

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