In molecular orbitals

The carbon atom has a share in eight electrons (Ne structure) whilst each hydrogen atom has a share in two electrons (He structure). This is a gross simplification of covalent bonding, since the actual electrons are present in molecular orbitals which occupy the whole space around the five atoms of the molecule. 

Flehre W J, Ditchfieid R and Popie J A 1972 Self-consistent molecular-orbital methods XII. Further extension of Gaussian-type basis sets for use in molecular orbital studies of organic molecules J. Chem. Phys. 56 2257-61 Flariharan P C and Popie J A 1973 The influence of polarization functions on molecular orbital hydrogenation energies Theoret. Chim. Acta. 28 213-22... 

The gradient of the PES (force) can in principle be calculated by finite difference methods. This is, however, extremely inefficient, requiring many evaluations of the wave function. Gradient methods in quantum chemistiy are fortunately now very advanced, and analytic gradients are available for a wide variety of ab initio methods [123-127]. Note that if the wave function depends on a set of parameters X], for example, the expansion coefficients of the basis functions used to build the orbitals in molecular orbital (MO) theory. 

Ferrocene Figure 2-47) provides a prime ex.ample of multi-haptic bonds, i.e, a situation where the electrons that coordinate the cyclopentadienyl rings with the iron atom arc contained in molecular orbitals delocalised over the iron atom and the 10 carbon atoms of the cyclopentadienyl rings [82. ... 

Tie hydrogen molecule is such a small problem that all of the integrals can be written out in uU. This is rarely the case in molecular orbital calculations. Nevertheless, the same irinciples are used to determine the energy of a polyelectronic molecular system. For an ([-electron system, the Hamiltonian takes the following general form ... 

In molecular orbital tcnninology. the hybrid might be represented by one structure with delocalized tt electrons spread over the sigrna-bonded framework... 

MOBAS was written by the author (Rogers, 1983) in BASIC to illustrate matrix inversion in molecular orbital calculations. It is modeled after a program in FORTRAN n given by Dickson (Dickson, 1968). 

The electronic theory of organic chemistry, and other developments such as resonance theory, and parallel developments in molecular orbital theory relating to aromatic reactivity have been described frequently. A general discussion here would be superfluous at the appropriate point a brief summary of the ideas used in this book will be given ( 7- )-... 

Section 2 4 In molecular orbital theory the molecular orbitals (MOs) are approxi mated by combining the atomic orbitals (AOs) of all of the atoms m a molecule The number of MOs must equal the number of AOs that are combined... 

The second step determines the LCAO coefficients by standard methods for matrix diagonalization. In an Extended Hiickel calculation, this results in molecular orbital coefficients and orbital energies. Ab initio and NDO calculations repeat these two steps iteratively because, in addition to the integrals over atomic orbitals, the elements of the energy matrix depend upon the coefficients of the occupied orbitals. HyperChem ends the iterations when the coefficients or the computed energy no longer change the solution is then self-consistent. The method is known as Self-Consistent Field (SCF) calculation. 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

In atoms in which electrons in M or A shells take part to some extent in molecular orbital formation some transitions in the L spectmm may be broadened. Similarly, in an M emission spectmm, in which the initial vacancy has been created in the M shell, there is a greater tendency towards broadening due to molecular orbital involvement. 

H. B. Schlegel and M. J. Frisch, Computational Bottlenecks in Molecular Orbital Calculations, in Theoretical and Computational Models for Organic Chemistry, ed. S. J. Formosinho et. al. (Kluwer Academic Pubs., NATO-ASI Series C 339, The Netherlands, 1991), 5-33. 

In molecular orbital terms, the stability of the allyl radical is due to the fact that the unpaired electron is delocalized, or spread out, over an extended 7T orbital network rather than localized at only one site, as shown by the computer-generated MO in Fig 10.3. This delocalization is particularly apparent in the so-called spin density surface in Figure 10.4, which shows the calculated location, of the unpaired electron. The two terminal carbons share the unpaired electron equally. 

Craig, D. P., Proc. Roy. Soc. London) A200, 474, Configurational interaction in molecular orbital theory. A higher approximation in the non-empirical method." (i)... 

There are two complementary lines of approach to examining the part played by 3d orbitals in molecular orbital theory and to appreciating current doubts as to their role. On the one hand, there is the question of 3d orbitals in relation to the basic formulation of molecular orbitals by overlapping atomic orbitals on the other hand, there is the question of the effect of including or excluding 3d functions in molecular orbital calculations, particularly of the ab initio type. We shall consider each of these briefly in turn. 

In molecular orbital theory, electrons occupy orbitals called molecular orbitals that spread throughout the entire molecule. In other words, whereas in the Lewis and valence-bond models of molecular structure the electrons are localized on atoms or between pairs of atoms, in molecular orbital theory all valence electrons are delocalized over the whole molecule, not confined to individual bonds. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

At first sight, the molecular orbital description of N2 looks quite different from the Lewis description ( N=N ). However, it is, in fact, very closely related. We can see their similarity by defining the bond order (b) in molecular orbital theory as the net number of bonds, allowing for the cancellation of bonds by antibonds ... 

The boranes are electron-deficient compounds (Section 3.8) we cannot write valid Lewis structures for them, because too few electrons are available. For instance, there are 8 atoms in diborane, so we need at least 7 bonds however, there are only 12 valence electrons, and so we can form at most 6 electron-pair bonds. In molecular orbital theory, these electron pairs are regarded as delocalized over the entire molecule, and their bonding power is shared by several atoms. In diborane, for instance, a single electron pair is delocalized over a B—H—B unit. It binds all three atoms together with bond order of 4 for each of the B—H bridging bonds. The molecule has two such bridging three-center bonds (9). 

Nakajima, T., in Molecular orbitals in chemistry, physics and biology, p. 457. New York Academic Press 1964. 

Berthier, G., Self-Consistent Field Methods for Open-Shell Molecules, in Molecular Orbitals in Chemistry, Physics, and Biology, P. O. Lbwdin and B. Pullman, Eds., Academic Press, New York, 1964, pp. 57-82. 

A. O. Turner, Methods in Molecular Orbital Theory, Chapter 5, Prentice-Hall, Englewood Cliffs, NJ, 1974. 

Hydroboration is a stereospecific syn addition that occurs through a four-center TS with simultaneous bonding to boron and hydrogen. The new C—B and C—H bonds are thus both formed from the same face of the double bond. In molecular orbital terms, the addition is viewed as taking place by interaction of the filled alkene it orbital with the empty p orbital on boron, accompanied by concerted C—H bond formation.158... 

Hehre, W. J., Ditchfield, R., Pople, J. A., 1972, Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules J. Chem. Phys., 56, 2257. 

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