Energies, calculated by ab initio methods

The rearrangements 67 —> 70, 71 —> 72 and 74 —> 75 include the transformation of conjugated dienes to cumulenes. Nevertheless, these reactions take place with very high yields in some cases, because either an irreversible step of hydrolysis such as 69 —> 70 is involved or the very exothermic transformation from cyanates to isocyanates is used. Comparison of the energies, calculated by ab initio methods [121], shows that, for example, the energy of methyl isocyanate is lower than that of methyl cyanate by 26.8 kcal mol-1 and that of vinyl isocyanate is lower than that of vinyl cyanate by 28.1 kcal mol-1. 

Various intramolecular transformations are conceivable for dicarbene 127, which would result from twofold elimination of molecular nitrogen from bis(diazomethyl)silane 126. HF energies, calculated by ab initio methods, for the possible rearrangement products 128-134 are given in Scheme 665. 

Experimental values from reference133 unless otherwise stated. This table is taken from reference81. Reproduced with permission from ref. 81. Copyright 1998. American Chemical Society. dValues based on distortion energies calculated by AMI values in parentheses based on distortion energies calculated by ab initio methods at the 3-21 + G level. 

Core binding energies calculated by ab initio methods including electronic relaxation were 01s 4.52 eV relative to HOCH3, FIs 0.89 eV relative to FCH3 [7]. 

Ab initio calculations on the equilibrium between (14a) and (14b) are carried out with the 3-21G basis set. Figure 4 shows a plot of the calculated activation energy E vs. the reaction energy AE for the cyclization reactions. The plot is linear and provides a striking confirmation of Hammond s postulate. The cyclic structures (14b) are found to be planar, while the terminal =NH group in (14a) is ca. 50° out of the plane formed by the other atoms in (14a) <90CC882>. The gas phase basicity and acidity of 1,2,3-triazole have been calculated by ab initio methods (6-31G //6-31G) and compared with experimental values <89MI 401-01 >... 

Illas et al. compared in detail the MEP maps calculated by ab initio method using a variety of Gaussian basis sets [36] with those obtained by the MNDO method [37], Since the MNDO method is based on the ZDO approximation, in accordance with the previously published results [22, 27], the ZDO molecular electron density function was used for generating the MEP maps after inverse Lowdin s transformation (deorthogonalization). It was found that, whereas the MNDO MEP maps could reproduce the main characteristics of the HF/6-31G MEP maps, the position of the MNDO minima were too close to the molecules and they were deeper than the corresponding ab initio ones. Fortunately, the ratios of the HF/6-31G and MNDO MEP minima energies are constant, and therefore the MNDO MEP minima energies can be scaled to reproduce the... 

As is already clear, a reliable functional representation of the potential-energy surface is of extreme importance. Such a functional form must be as simple as possible in order to facilitate solving the dynamical problem, but must contain sufficient complexity that the reliability of the representation will not be jeopardized.105 In this spirit we have suggested models which have physical motivation and allow a simple, yet reliable, representation of the EHF and corr two-body17 136 140 and three-body17,21141 energy terms. Since the EHF terms are, in principle, calculable by ab initio methods (and subsequently represented in analytic form) whereas the corr terms are calculated semi-... 

More recently, the gas-phase structures of lithiated A. S.S-trimethylsulfoximine have been calculated by ab initio methods.44 It was found that a Li-Ca-S-N four-membered chelate 21 was the most stable isomer and the complex involving a Li-N-S-O four-membered chelate (22) was only 1.4 kcal/mol higher in energy. The alternative complex involving a Li-Ca-S-0 four-membered chelate was 6.1 kcal/mol higher in energy. 

Kinetics of isomerization of glyceraldehyde to dihydroxyacetone—and the formation of pyruvaldehyde from both— have been studied in sub- and super-critical water. Formaldehyde reacts with isoeugenol [l-(3-methoxy-4-hydroxyphenyl)propene] in alkaline medium to give a 1,3-dioxane derivative via an unusual Prins-type reaction. The potential-energy surface for the equihbriimi, HCO - - HCN H2CO - - CN, has been calculated by ab initio methods. 

Quantum mechanical calculations (by ab initio method) "" performed on diprotonated methane showed that the symmetrical structure (18) with two stabilizing orthogonal 3c-2e interactions is the only minimum on the potential energy surface. The other structures (19-22), in turn, were calculated to be saddle points on the potential energy surface. These were found to be... 

The calculation by ab initio methods is of the total molecular energy as a function of the dihedral angles. The potential has three maxima coinciding with the eclipsed configurations, and three minima at the staggered configurations. The... 

The energies of molecules can be calculated by MM, SE, ab initio or DFT. The method chosen depends very much on the particular problem. Reactivity, which depends largely on electron distribution, must usually be studied with a quantum-mechanical method (SE, ab initio or DFT). Spectra are most reliably calculated by ab initio methods, but useful results can be obtained with SE methods, and some MM programs will calculate fairly good IR spectra (balls attached to springs vibrate ). 

All the properties that can be calculated by ab initio methods can in principle also be calculated semiempirically, bearing in mind that the more the molecule of interest differs from the training set used to parameterize the SE program, the less reliable the results will be. Eor example, a program parameterized to predict the UV spectra of aromatic hydrocarbons may not give good predictions for the UV spectra of heterocyclic compounds. NMR spectra are usually calculated with ab initio (section 5.5.5) or density functional (chapter ) methods. UV spectra, and ionization energies (ionization potentials) and electron affinities will be discussed here. 

The parameters used in Eqs. 64 - 68 have to be adjusted either to experimental data or ab initio data from highly correlated calculations for the one valence electron atoms or ions. Similarly, the core dipole polarizability may be taken from experiment or could be calculated by ab initio methods. Although the experimental ionization potentials (and excitation energies) for not too small cores... 

Figure 8.12 Energy level diagram for the alkylation of benzene with propylene, over the acid form of mordenite, as calculated by ab initio methods, and illustrating that the transition state is carbenium-ion-like .

The application of refractions to the study of structures is based on comparing the experimental values with those calculated on various structural assumptions, of which the most important is additivity (Landolt, 1862) in the first approximation (within ca 10 %), the refraction of a compound is the sum of constant increments of different atoms, ions and bonds. Refractions of some isolated atoms can be measured by the deviation of an atomic beam in an inhomogeneous electric field or by spectroscopic methods. In other cases electronic polarizabilities of free atoms were calculated by ab initio methods. All available experimental and the best of the computed refractions of free atoms are presented in Table 11.5. These values can be used to calculate the energy of van der Waals interactions, magnetic susceptibility, or to establish correlations with atomic and molecular-physical properties. The formation of covalent bonds changes the refractions of isolated atoms and their values transform into the covalent refractions, which are different for isolated molecules and for crystals. Direct measurements of RI of A2 molecules or elemental solids give the most accurate information on the covalent refractions, in other cases the latter have to be calculated from molecular refractions by the additive method. 

---