Molecular orbitals and electron

The one-electron functions, J/h in the separation of variables schemes are called molecular orbitals. These molecular orbitals form the basis for the conceptual treatment of bonding in molecules (see Luther, Chapter 6, this volume). If the approximate solution (Eq. 6) is inserted into equation 3, one obtains a set of differential equations for the one-electron molecular orbitals and for the electronic energy eigenvalue, e often termed the molecular-orbital energy. The e are, in fact, closely related to the ionization potentials of the molecule. In principle, we could solve these equations numerically for molecular orbitals as a sum over some set of prescribed atomic orbitals,... 

The one-electron molecular orbitals and the corresponding orbital energies can be calculated with the aid of various approximation methods, e.g., that of Hiickel 62, 63) or that of Pariser and Parr (64, 65). The most convenient starting point for the discussion of the ir-electronic spectra of the anions are the Hiickel one-electron molecular orbitals. These have the advantage that the same set of MO s can be used for both the molecule and its mono- and dinegative ion. 

In order to further describe the molecular wavefunctions or the molecular orbitals. Linear Combinations of Atomic Orbitals (LCAO) are normally used (LCAO method). Such a method of solution is possible since the directional dependence of the spherical-harmonic functions for the atomic orbitals can be used. The Pauli principle can be applied to the single-electron molecular orbitals and by filling the states with the available electrons the molecular electron configurations are attained. Coupling of the angular momenta of the open shell then gives rise to molecular terms. 

Jameson and Gutowsky used the independent electron molecular orbital and the valence bond approaches, including d orbitals explicitly. Their equations were applied extensively to shielding by Letcher and Van Wazer. ... 

IlyperCl hem can display molecular orbitals and the electron density ol each molecular orbital as contour plots, showing the nodal structure and electron distribution in the molecular orbitals. 

The treatment of electronic motion is treated in detail in Sections 2, 3, and 6 where molecular orbitals and configurations and their computer evaluation is covered. The vibration/rotation motion of molecules on BO surfaces is introduced above, but should be treated in more detail in a subsequent course in molecular spectroscopy. 

The macmolplt graphics package is designed for displaying the output of GAMESS calculations. It can display molecular structures, including an animation of reaction-path trajectories. It also may be used to visualize properties, such as the electron density, orbitals, and electrostatic potential in two or three dimensions. 

Multiple solutions /j and 8j are possible for this last equation. The wave functions for individual electrons, /j, are called molecular orbitals, and the energy, 8j, of an electron in orbital /j is called the orbital energy. 

Free Electron Molecular Orbital method colour and constitution, 1, 342 Freelingyne occurrence, 4, 706 Free radical processes in photography, 1, 387-389 Friedlander synthesis quinolines, 2, 443 thioindigo dyes, 4, 910 Fries rearrangement chroman-4-one synthesis from, 3, 850 Fructose, 1-deoxy- C NMR, 4, 575 Frusemide as diuretic, 1, 174 metabolism, 1, 245 FS-32 — see 1/f-Indazole, l-[3-... 

Multiplying a molecular orbital function by a or P will include electron spin as part of the overall electronic wavefunction i /. The product of the molecular orbital and a spin function is defined as a spin orbital, a function of both the electron s location and its spin. Note that these spin orbitals are also orthonormal when the component molecular orbitals are. 

Frontier Orbitals and Chemical Reactivity. Chemical reactions typically involve movement of electrons from an electron donor (base, nucleophile, reducing agent) to an electron acceptor (acid, electrophile, oxidizing agent). This electron movement between molecules can also be thought of as electron movement between molecular orbitals, and the properties of these electron donor and electron acceptor orbitals provide considerable insight into chemical reactivity. 

There are m doubly occupied molecular orbitals, and the number of electrons is 2m because we have allocated an a and a spin electron to each. In the original Hartree model, the many-electron wavefunction was written as a straightforward product of one-electron orbitals i/p, i/ and so on... 

The concept of natural orbitals may be used for distributing electrons into atomic and molecular orbitals, and thereby for deriving atomic charges and molecular bonds. The idea in the Natural Atomic Orbital (NAO) and Natural Bond Orbital (NBO) analysis developed by F. Weinholt and co-workers " is to use the one-electron density matrix for defining the shape of the atomic orbitals in the molecular environment, and derive molecular bonds from electron density between atoms. 

Octet rule The principle that bonded atoms (except H) tend to have a share in eight valence electrons, 166-171 exceptions to, 172-176 molecular geometry and, 181t molecular orbitals and, 650 Octyl acetate, 596t Open-pit copper mine, 540 Oppenheimer, J. Robert, 523 Optical isomer Isomer which rotates the... 

Figure 6.14. CO chemisorption on a transition metal. Molecular orbitals and density of states before (a,b) and after (c and d) adsorption. Effect of varying 0 and EF on electron backdonation (c) and donation (d). Based on Fig. 4 of ref. 98. See text for discussion. Reprinted with permission from Elsevier Science.

FIGURE 3.28 The two electrons in an H2 molecule occupy the lower-energy (bonding) molecular orbital and result in a stable molecule. 

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

The raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

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