Orbitals in hydrogen atoms

Electronic and nuclear energy in H2. a. Values for non-interacling electrons. 6, Coulomb energy of nuclear repulsion, c, Approximate electronic energy curve for interacting electrons. Units ordinates, 1 = Rydberg constant, abscissas, 1 = radius of first Bohr orbit in hydrogen atom. 

In an alkali metal atom such as sodium, the 3s electron penetrates the neon core, i.e., it moves into the field of attraction of the nucleus, being only partially screened by the K and L shells. In an excited sodium atom the electron in a 3p orbital penetrates the electron cloud to a lesser extent, and the electron raised to a 3d orbital is practically non-penetrating. Thus the 3s, 3p, and 3d orbital in a many-electron atom have different energies whereas these orbitals in hydrogen atom have the same energy. 

Split-Valence Basis Sets. In split-valence basis sets, inner or core atomic orbitals ar e represented by one basis function and valence atomic orbitals are represented by two. The carbon atom in methane is represented by one Is inner orbital and 2(2s, 2pj., 2py, 2pj) = 8 valence orbitals. Each hydrogen atom is represented by 2 valence orbitals hence, the number of orbitals is... 

The most direct evidence that stereoelectronic effects are also important in these reactions follows from the specificity observed in hydrogen atom abstraction from conformationally constrained compounds,18 60 C-H bonds adjacent to oxygen113"118 or nitrogen110 and which subtend a small dihedral angle with a lone pair orbital (<30°) are considerably activated in relation to those where the dihedral angle is or approaches 90°. Thus, the equatorial H in 20 is reported to be 12 times more reactive towards /-butoxy radicals than the axial 11 in 21.115... 

In this expression, the term hydrogen atoms A and B. The term interaction with the electrons interchanged. However, the term A2 represents both electrons 1 and 2 interacting with nucleus A. That means the structure described by the wave function is ionic, HA HB+. In an analogous way, the term B1 Bj2 represents both electrons interacting with nucleus B, which corresponds to the structure HA+ Hb . Therefore, what we have devised for a molecular wave function actually describes the hydrogen molecule as a "hybrid" (a valence bond term that is applied incorrectly) of... 

As is to be expected, all valence electrons and valence orbitals of the boron (4 orbitals) and hydrogen atoms (1 orbital) in the polyboranes and their derivatives are involved in bonding. (H atoms with 1 electron, H- ions with two electrons, B atoms with 3 electrons, NR3 molecules with two electrons, etc.). Then the following equations have to be satisfied ... 

A minimal basis set consists of just enough functions required to accommodate all the filled orbitals in an atom. Thus, for hydrogen and helium, there is only one s-type function for elements lithium to neon, this basis set has Is, 2s, and... 

The first term in the product is associated with the spatial part and the second with the spin labels. The letters ua and b stand for atomic orbitals centered in hydrogen atoms Ha and H respectively. To account for the indistinguishability of the electrons, spatial and spin factors appear in two products (configurations). Consequently, the VB approach is multideterminantal from the outset. This superposition of determinants causes the VB wave function, even in its most simple form, to maintain the indistinguishability of the electrons within the chemical bond. This effect is called exclusion correlation , a non-dynamical correlation effect. 

The combination of 1 s orbitals of hydrogen atoms to form molecular orbitals has been shown in figure below. 

Relative energies of atomic and molecular orbitals in hydrogen molecule are shown in figure below. 

In hydrogen atom there is only one electron which is present in 1 s orbital in ground state. However, in excited state the electron may jump to any of the orbitals belonging to higher energy levels. 

The combination of the atomic Is orbitals to give the two new molecular orbitals is simply shown on an energy level diagram. With one electron in each Is orbital, two hydrogen atoms combine to give a hydrogen molecule. 

Spiro[2.5]octadienyl radical (146), the radical analog of the phenonium ion (105), is a very short-lived species but was detected by its visible absorption and fluorescence on generation by radical abstraction from 147 prior to facile ring-opening to 148 (equation 29). There appeared to be a modest (two-fold) acceleration compared to 1,3- or 1,4-cyclohexadiene in the rate of abstraction from 147, and this was attributed to stabilization by a favorable interaction between cyclopropyl and the adjacent semioccupied orbital in 146. Kinetic acceleration was also proposed to occur in hydrogen atom abstraction from spiro[2.n]alkanes (149). ... 

In Fig. 11.4, the log-and 1ct -orbitals are plotted as functions of z, along the internuclear axis. Both functions have cusps, discontinuities in slope, at the positions of the two nuclei A and B. The I5 orbitals of hydrogen atoms have these same cusps. The shape of the Icrg and 1[Pg.86]

In hydrogen atom abstraction by a ketone the following orbitals are important for the reactant R CO + RH, the orbitals Och and a H of he R—H bond to be broken and the orbitals no, Jico> and jr of the ketone chromophore. For the product RiCOH + -R, the orbitals a and aHn of the newly formed OH bond, plus the orbitals ji(, and of the protonated ketyl radical and the orbital pc of the odd electron on the residue R. Their relative energies can be easily estimated qualitatively. Since both no and Ooh are essentially localized... 

Fig. 39. Atomic orbitals in hydrogen fluoride. The fluorine 2p and 2p atomic orbitals, normal to the axis, are omitted for clarity.

We must now look at the coefficients, c, of equation 2-1. When there are electrons in the orbital, the squares of the c-values are a measure of the electron population in the neighbourhood of the atom in question. Thus in each orbital the sum of the squares of all the c-values must equal one, since only one electron in each spin state can be in the orbital. Now the orbitals in hydrogen are symmetric about the mid-point of the H—H bond in other words c2 must equal c2. Thus we have defined what the values of c, and c2 in the bonding orbital must be, namely 1/ /2 = 0-707. If all molecular orbitals were filled, then there would have to be one electron in each spin state on each atom, and this gives rise to a second criterion for c-values, namely that the sum of the squares of all the c-values on any one atom in all the molecular orbitals must also equal one. Thus the antibonding orbital of hydrogen, [Pg.7]

E1.2 (a) The ground state of hydrogen atom is Is. The wavefunction describing Is orbital in H atom is given with... 

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