Orbitals of electrons

We do not know the orbitals of the electrons either. (An orbital, by the way, is not a ball of fuzz, it is a mathematical function.) We can reasonably assume that the ground-state orbitals of electrons I and 2 are similar but not identical to the Is orbital of hydrogen. The Slater-type orbitals... 

C. their outermost orbital of electrons is nearly complete, and they attract electrons from other atoms... 

The ab initio method begins by solving the Schrodinger equation for the orbitals of electrons around a molecule, using as little simplification and approximation as is practical. This exact method is available only for small molecules with few atoms. The Schrodinger equation for a system with only one nucleus and a single electron... 

Fig. 22. Electron density contour maps of the three frontier orbitals of electron-deficient M(it-C5Hs)2 fragments. The plots represent a section through the yz plane. [Reproduced from Lauher and Hoffmann (134), by permission of the American Chemical Society.]...

Jj( 1) is the potential energy of interaction between the point charge of electron 1 and electron 2 considered to be smeared out into a hypothetical charge cloud of charge density (charge per unit volume) - e)Hartree-Fock method considers average interelectronic interactions, rather than instantaneous inter-... 

Electrons in exterior orbitals of electron-donor atoms A small number of such electrons they are excited with difficulty Some such electrons they are excited easily Vacant orbitals of electron-donor atoms Practically inaccessible Accessible... 

A specific wave function solution is called an orbital. The different orbitals define different energies and distributions for the different electrons. The name orbital goes back to earlier theories where the electron was thought to orbit the nucleus in the way that planets orbit the sun. It seems to apply more to an electron seen as a particle, and orbitals of electrons thought of as particles and wave functions of electrons thought of as waves are really two different ways of looking at the same thing. Each different orbital has its own individual quantum numbers, , , and mg. 

Niels Bohr s planetary model of the hydrogen atom—in which a nucleus is surrounded by orbits of electrons—resembles the solar system. Electrons could be excited by quanta of energy and move to an outer orbit (excited level). They could also emit radiation when falling to their original orbit (ground state). Basic components of the Bohr model include the following ... 

Should it surprise us that the model these fellows concocted worked so remarkably well to explain so many chemical phenomena In fact, it worked to such an extent that it is still being taught to high school students today, a hundred years later. It had only a few parameters to adjust, namely number and capacity of orbits of electrons and rules for losing, gaining and sharing of outside electrons. Yet it explained, in the end, a virtual infinity of chemical reactions of wide ranging variety. No wonder that the picture Bohr... 

Start with canonical SCF orbitals of electronic ground state. Active space (in Cj, symmetry) 2a,-6ai, lb -2b, Ib2-2b2, la, orbital frozen. 

Solutions of Schrodinger s wave equation give the allowed energy levels and the corresponding wavefunctions. By analogy with the orbits of electrons in the classical planetary model (see Topic AT), wavefunctions for atoms are known as atomic orbitals. Exact solutions of Schrodinger s equation can be obtained only for one-electron atoms and ions, but the atomic orbitals that result from these solutions provide pictures of the behavior of electrons that can be extended to many-electron atoms and molecules (see Topics A3 and C4-C7). 

Here Xi(0 X<( >) > (>0 represents the spin-orbital of electron i. The type of wavefunction represented by Eq. [5] is not complete because it does not (1) account for the indistinguishability of electrons and (2) satisfy the Pauli principle, which requires that if the coordinates of electrons i and / are interchanged in the above wavefunction, the wavefunction must change sign. To account for indistinguishability and ensure antisymmetry, the spin-orbitals for a closed-shell atom are arranged as a Slater determinant. 

Bohr first proposed an electron motion model to solve the problems of the Rutherford model. For the electron in a hydrogen atom, Bohr presented an atomistic model, in which the periodic orbits of electrons are quantized, and proposed the following hypothesis, known as the Bohr hypothesis (Bohr 1913) ... 

Because the orbitals of electrons in atoms and molecules overlap, it is impossible to know at any given time which electron is in which orbital, that is, the electrons are indistinguishable. Because of this, the probability density (that is, the wavefunction squared) must remain the same when the identities of the electrons are switched. 

Bohr, Niels Hendrik David (1885-1962) Danish physicist. Niels Bohr was responsible for a key development in our understanding of atomic structure when he showed (1913) how the structure of the atom could be explained by imposing quantum conditions on the orbits of electrons, thus allowing only certain orbits. This theory accounted for details of the hydrogen spectrum. Bohr also contributed to nuclear physics, particularly the theory of nuclear fission. He was awarded the 1922 Nobel Prize for physics for his work on atomic theory. 

Minor orbit A smaller helical orbit of electron beam in a double-coil electron beam gyrotron. 

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