The Lithium Atom

9 Find the possible term symbols for the excited configuration (2p)(3d) of the helium atom. 

11 Pretend that the direction of angular momentum vectors can be specified exactly. If the spin angular momentum vector for one electron with spin up lies in the yz plane, and the spin angular momentum vector for another electron with spin down also lies in the yz plane, find the 

A lithium atom has three electrons and a nucleus with Z = 3. The Hamiltonian operator for a lithium atom with a stationary nucleus is 

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There is evidently a grave problem here. The wavefiinction proposed above for the lithium atom contains all of the particle coordinates, adheres to the boundary conditions (it decays to zero when the particles are removed to infinity) and obeys the restrictions = P23 that govern the behaviour of the... 

As fonnulated above, the FIF equations yield orbitals that do not guarantee that F has proper spin symmetry. To illustrate, consider an open-shell system such as the lithium atom. If Isa, IsP, and 2sa spin orbitals are chosen to appear in F, the Fock operator will be... 

Some excited configurations of the lithium atom, involving promotion of only the valence electron, are given in Table 7.4, which also lists the states arising from these configurations. Similar states can easily be derived for other alkali metals. 

ButyUithium is available as a 15—20 wt % solution in //-pentane or heptane. Noticeable decomposition occurs after alb reflux in heptane (bp 98.4°C) but not after a 15 min reflux in ben2ene (bp 80.1°C) or hexane (bp 68°C). /-ButyUithium in pentane or heptane is more stable than //-butyUithium in hexane (125). Solutions of /-butyUithium in pentane and heptane are flammable Hquids and are considered pyrophoric. The /-butyl compound is more reactive than either the n- and sec-huty. Di-//-butylether is cleaved by /-butyUithium in 4—5 h at 25°C, compared to the 2 d for j iZ-butyUithium and 32 d for //-butyUithium (126). /-ButyUithium can be assayed by aU of the techniques used for //-butyUithium. /-ButyUithium is a useful reagent in syntheses where the high reactivity of the carbon—lithium bond and smaU si2e of the lithium atom promote the synthesis of stericaUy hindered compounds, eg,... 

The heart of the energy-dispersive spectrometer is a diode made from a silicon crystal with lithium atoms diffiised, or drifted, from one end into the matrix. The lithium atoms are used to compensate the relatively low concentration of grown-in impurity atoms by neutralizing them. In the diffusion process, the central core of the silicon will become intrinsic, but the end away from the lithium will remain p-type and the lithium end will be n-type. The result is a p-i-n diode. (Both lithium-... 

A limited number of non-transition-metal derivatives of thiophene will be considered in this subsection. There are no short-range contacts between the lithium atoms originating from the (LiO)6 cores and the sulfur atoms in [Li—O—EMc2 (2-C4H3S)]6 (E = C, Si) (97OM5032), and evidence for Tr-interactions can be found in the X-ray crystal structures of these compounds. Theoretical computations show that a- (S ) Li" " interactions are weak, whereas Tr-Li" contributions are considerable, in accord with the general reasoning on the electronic characteristics of uncomplexed thiophene. 

The beryllium atom has one more electron than does the lithium atom. The fourth electron that enters the beryllium atom can occupy the 2s orbital to give a configuration of Is22s2. The two 2s electrons will be most easily removed, tending... 

Clearly the fluorine atom holds electrons much more strongly than does the lithium atom. As a result, the electron pair in the lithium fluoride bond is more strongly attracted to the fluorine atom than to the lithium. The energy is lower if the electrons spill toward the fluorine atom. 

Cyclization of an organolithium tethered to a suitably positioned carbon-carbon jt-bond is a thermodynamically favorable process that proceeds in a totally regioselective exo-fashion with a high degree of stereocontrol via a transition state in which the lithium atom is intramolecularly coordinated with the remote rc-bond.9 The stereochemical outcome of the cyclization of a substituted 5-hexenyllithium follows from the preference of the substituent to occupy a pseudoequatorial position in the chair-like transition state depicted below.7... 

It should also be noted that the 5-exo-trig cyclization of achiral olefinic organolithiums has been found to proceed enantioselectively when conducted in the presence of a chiral ligand that serves to render the lithium atom stereogenic. Thus, for example, R) 1 -allyl-3-methylindolinc has been prepared in 86 % ee by cyclization of an achiral aryllithium in the presence of an equivalent of (-)-sparteine.15... 

The energy of the one-electron bond in the lithium molecule ion is calculated with consideration of the s-p separation to be 1.19 e. v and the hybrid bond orbital involved is shown to involve about equal contributions from the 25 and 2p orbitals of the lithium atom. 

Consider a crude approximation to the ground state of the lithium atom in which the electron-electron repulsions are neglected. Construct the ground-state wave function in terms of the hydrogen-like atomic orbitals. 

The crystal structures of many organolithium compounds have been determined.44 Phenyllithium has been crystallized as an ether solvate. The structure is tetrameric with lithium and carbon atoms at alternating corners of a highly distorted cube. The lithium atoms form a tetrahedron and the carbons are associated with the faces of the tetrahedron. Each carbon is 2.33 A from the three neighboring lithium atoms and an ether molecule is coordinated to each lithium atom. Figures 7.2a and b show, respectively, the Li-C cluster and the complete array of atoms, except for hydrogen 45 Section 6.2 of Part A provides additional information on the structure of organolithium compounds. 

These stereochemistry outcomes would be easily predicted based on the assumption that the carbonyl oxygen is coordinated to the lithium atom such as d in 70. The larger aryl function will locate in the less sterically hindered side (left-hand side in 70), providing the desired stereoselectivity. Semiempirical (MENO) computational methods were applied and the results supported our conclusion. 

The antibonding LU MO of lithium hydride localizes more on the lithium atom than on the hydrogen atom, so that hydride anion will attack the lithium to form a linear anion. 

The Li-Ion system was developed to eliminate problems of lithium metal deposition. On charge, lithium metal electrodes deposit moss-like or dendrite-like metallic lithium on the surface of the metal anode. Once such metallic lithium is deposited, the battery is vulnerable to internal shorting, which may cause dangerous thermal run away. The use of carbonaceous material as the anode active material can completely prevent such dangerous phenomenon. Carbon materials can intercalate lithium into their structure (up to LiCe). The intercalation reaction is very reversible and the intercalated carbons have a potential about 50mV from the lithium metal potential. As a result, no lithium metal is found in the Li-Ion cell. The electrochemical reactions at the surface insert the lithium atoms formed at the electrode surface directly into the carbon anode matrix (Li insertion). There is no lithium metal, only lithium ions in the cell (this is the reason why Li-Ion batteries are named). Therefore, carbonaceous material is the key material for Li-Ion batteries. Carbonaceous anode materials are the key to their ever-increasing capacity. No other proposed anode material has proven to perform as well. The carbon materials have demonstrated lower initial irreversible capacities, higher cycle-ability and faster mobility of Li in the solid phase. 

We have just explained that the wave equation for the helium atom cannot be solved exacdy because of the term involving l/r12. If the repulsion between two electrons prevents a wave equation from being solved, it should be clear that when there are more than two electrons the situation is worse. If there are three electrons present (as in the lithium atom) there will be repulsion terms involving l/r12, l/r13, and l/r23. Although there are a number of types of calculations that can be performed (particularly the self-consistent field calculations), they will not be described here. Fortunately, for some situations, it is not necessary to have an exact wave function that is obtained from the exact solution of a wave equation. In many cases, an approximate wave function is sufficient. The most commonly used approximate wave functions for one electron are those given by J. C. Slater, and they are known as Slater wave functions or Slater-type orbitals (usually referred to as STO orbitals). 

Write the complete Hamiltonian operator for the lithium atom. Explain why the wave equation for Li cannot be solved exactly. 

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