Ab initio results

This chapter centers on the mathematical aspects of the non-adiabatic coupling terms as single entities or when grouped in matrices, but were it not for the available ab initio calculation, it would have been almost impossible to proceed thus far in this study. Here, the ab initio results play the same crucial role that experimental results would play in general, and therefore the author feels that it is now appropriate for him to express his appreciation to the groups and individuals who developed the numerical means that led to the necessary numerical outcomes. 

Ab Initio Results for 1H-Indole and 3H-Indole (Energies in Hartrees) (99UP1)... 

Scheme 4. Ab initio results for protonated furans [86JCS(P2)147].

Benzofuroxan 79 can be generated from 2-nitrophenyl azide 80 (Scheme 49). Neighboring-group assistance within the pyrolysis leads to a one-step mechanism with an activation barrier of 24.6 kcal/mol at the CCSD(T)/6-31 lG(2d,p) level [99JPC(A)9086]. This value closely resembles the experimental one of 25.5 kcal/mol. Based on the ab initio results for this reaction, rate constants were computed using variational transition state theory. 

Contrary to the simple ab initio methods, semiempirical procedures favour the bridged structure b. The correction of the ab initio results by inclusion of the electron... 

Table 4 Comparison of various ab initio results and experimental estimates for the dispersion coefficients of the electronic hyperpolarizabilities 7jj and 7 of methane. (All results in atomic units. Results for the dispersion coefficients refer to single point calculations at the equilibrium geometry. Where available, dispersion coefficients for the vibrational average are given in parentheses.)...

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

All of the ab initio results are collected in Tables 2 and 3. The tables differ only in the theoretical method used. Table 2 used the ROHF method and Table 3 used the UHF method using optimised geometries from Table 2. 

The efficiency of the methods outlined above has been tested by calculating the intermolecular Coulomb energies and forces for a series of water boxes (64,128,256, 512 and 1024) under periodic boundary conditions [15, 62], The electron density of each monomer is expanded on five sites (atomic positions and bond mid-points) using two standard ABSs, A2 and PI.These sets were used to fit QM density of a single water molecule obtained at the B3LYP/6-31G level. We have previously shown that the A1 fitted density has an 8% RMS force error with respect to the corresponding ab initio results. In the case of PI, this error is reduced to around 2% [15, 16], Table 6-1 shows the results for the 5 water boxes using both ABSs (Table 6-7). 

Fig. 14. Energy diagram of the ring-opening dissociation C6D6 —> C5D3 + CD3 from ab initio results (Ref. 29). Note that there are many intermediates which can dissociate into C4D3 + C2D3 by a simple C-C bond fission.

Note The harmonic frequencies are MP2/6-31G ab initio results from Tticker, S. C. Truhlar, D. G. J. Phys. Ckem. 1989, 93, 8138. 

The reliability of molecular mechanics calculations hinges entirely on the validity and range of applicability of the force field. The parameterisation of these functions (the force field) represents the chemistry of the species involved. Many force fields have been developed and the one used in any application usually depends on the molecular mechanics package being used. The force field itself can be validated against experimental and ab initio results. Because of the relative speed of molecular mechanics calculations, it is possible to consider routine calculations of a large number of atoms, certainly tens of thousands, which makes the method amenable to calculations on polymers. To remove surface effects, calculations of bulk properties are normally carried out employing 3D periodic boundaries. In this way it is possible to perform calculations on both amorphous and crystalline systems. 

Petrongolo, C., and J. Tomasi. 1975. The Use of the Electrostatic Molecular Potential in Quantum Pharmacology. I. Ab Initio Results. Int. J. Quant. Chem., Quant. Biol. Symp. 2, 181. 

Old semi-empirical (Bach and Henneike, 1970) and recent ab initio (Hamilton and Schaefer, 1990, 1991) calculations are in complete agreement with experimental data as regards the structure of the parent ethylene-bromonium ion. Its most stable structure is definitely symmetrically bridged. Early ab initio results showed that the bridged form [7] is more stable than the 2-bromoethylcation [8] and the 1-bromoethylcation [9] by 1-4 and... 

TABLE 2. Experimental ionization energies and pseudopotential ab initio results for Me2SnCl2a. Reprinted with permission from Reference 40. Copyright (1986) American Chemical Society... 

Typical lone pair ionization potential data have been presented before and AO overlap integral data in support of these ideas are given in Table 8. Ab initio results are shown in Table 9 and support the notions that the pi donating ability of heteroatoms is energy gap controlled in CH2X but matrix element controlled in CH2=CHX. 

Ab initio results are summarized in Table 19f. They seem to suggest the existence of two energy minima, a trans and a gauche, the tram being the more stable. 

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