Molecular-orbital calculations 1.3- dipolar

On the other hand, electric dipolar moments of the solute molecules can be obtained with standard methods in ab initio molecular orbital calculations, whereas the induced dipole moments in solution are determined from differences between the values obtained in solution and in the gas phase. 

We saw correlation earlier on p. 5, when we learned that two electrons can be placed into one orbital, provided, of course, that their spins are opposed. The correlated movement of the electrons within that orbital keeps them, on average, far apart but there is an energetic penalty from putting a second electron into an orbital already singly occupied. The electron correlation reduces the severity of the penalty, and is often needed in calculations to get the right answers. In the same way, van der Waals interactions often have to be invoked when calculations based on molecular orbitals and dipolar effects do not explain all the attractions or repulsions found in practice. 

The limited number of molecular orbital calculations, which deal with the regioselectivities of isomunchnone 1,3-dipolar cycloaddition reactions, are covered in Section 4.4.3.2. 

The question of which resonance structure is the principal contributor has been a point of considerable discussion. Since the nonpolar ylene resonance structures have 10 electrons at the phosphorus of sulfur atom, these structures imply participation of d orbitals on the heteroatoms. Structural studies indicate that the dipolar ylide structure is probably the main contributor. Molecular orbital calculations confirm the stabilizing effect that the second-row elements phosphorus and sulfur have in ylides, relative to the corresponding first-row elements nitrogen and oxygen. ... 

STO-3G and 3-21G molecular orbital calculations indicate a rotational barrier that is substantially reduced relative to the corresponding barrier in ethylene. The transition state for the rotation is calculated to have a charge separation of the type suggested by the dipolar resonance structure. ... 

The structures shown above the dotted line illustrate the implications of these criteria and suggest more stable structures. In addition although the stmcture shown for N2O2 is consistent with the Lewis formalism, the weak N-N single bond means that the structure is only observed at low temperatures. The dissociation energy of the NO dimer is only 8.3 kJ moP and it represents an example of a molecule which is not adequately represented by Hartree-Fock molecular orbital calculations [76]. The structures below the dotted line are disfavoured because of they are dipolar or have identical charges on adjacent atoms. 

Ab Initio molecular orbital calculations on methanedithiol and thiolmethanol have been used as models for the anomeric effect in S-C-S and 0-C-S carbohydrate systems. The lower anomeric effect in sulphur systems was attributed to lower dipolar contributions to the total energy compared to the oxygen systems. 

This chapter will try to cover some developments in the theoretical understanding of metal-catalyzed cycloaddition reactions. The reactions to be discussed below are related to the other chapters in this book in an attempt to obtain a coherent picture of the metal-catalyzed reactions discussed. The intention with this chapter is not to go into details of the theoretical methods used for the calculations - the reader must go to the original literature to obtain this information. The examples chosen are related to the different chapters, i.e. this chapter will cover carbo-Diels-Alder, hetero-Diels-Alder and 1,3-dipolar cycloaddition reactions. Each section will start with a description of the reactions considered, based on the frontier molecular orbital approach, in an attempt for the reader to understand the basis molecular orbital concepts for the reaction. 

The molecular geometries and the frontier orbital energies of heterophospholes 28-31 were obtained from density functional theory (DFT) calculations at the B3LYP/6-311- -G, level. The 1,3-dipolar cycloaddition reactivity of these heterophospholes in reactions with diazo compounds was evaluated from frontier molecular orbital (FMO) theory. Among the different types of heterophospholes considered, the 2-acyl-l,2,3-diazaphosphole 28, 377-1,2,3,4-triazaphosphole 30, and 1,3,4-thiazaphosphole 31 were predicted to have the highest dipolarophilic reactivities. These conclusions are in qualitative agreement with available experimental results <2003JP0504>. 

If the activities of the laboratory in this field are said to be at the borders of quantum chemistry and statistical thermodynamics, these two disciplines are declared to be techniques." The problems raised by molecular liquids and solvent effects can be solved, or at least simplified by these techniques. This is firmly stated everywhere the method of calculation of molecular orbitals for the o-bonds was developed in the laboratory (Rinaldi, 1969), for instance, by giving some indications about the configuration of a molecule. The value and direction of a dipolar moment constitutes a properly quantum chemistry method to be applied to the advancing of the essential problems in the laboratory. In the same way, statistical mechanics or statistical thermodynamics constitute methods that were elaborated to render an account of the systems studied by chemists and physicists. In Elements de Mecanique Statistique, these methods are well said to constitute the second step, the first step being taken by quantum chemistry that studies the stuctures and properties of the constitutive particles. [53]... 

Density functional theory (DFT) calculations at the B3LYP/6-31H-G"" level were carried out on the 1,3-dipolar cycloadditions of various heterophospholes, including 1,3-azaphosphole, with diazo compounds across the P=N bond <2003JP0504>. In most cases, the dominant frontier orbital interaction is between HOMO(diazo) with LUMO(heterophosphole) however, 1,3-azaphosphole has a HOMO of high energy and for it, HOMO(heterophosphole)-LUMO(diazo) is also important (HOMO = highest occupied molecular orbital LUMO = lowest unoccupied molecular orbital). 

There is a somewhat similar phenomenon in which the presence of a dipole within a molecule induces a temporary dipole, either elsewhere in the molecule or in another molecule. The induced dipole is then attracted to the inducing charge or dipole, and another small attractive force comes into play that is not included in the molecular orbital picture at the most simple level of calculation, but is included when larger basis sets are used. Weak dipolar attractions like these, both the static and the induced, are not strong, and so nonpolar molecules are not well solvated by polar molecules the polar solvent molecules would rather solvate each other and the nonpolar molecules are left to their own devices. As it happens they do not repel each other as much as one might expect. 

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