Lithium atom sets

Each of a lithium atom s three electrons also has its own unique set of quantum numbers, as you can see helow. (Assume these quantum numbers represent a ground state lithium atom.)... 

Refer to the sets of quantum numbers for hydrogen and helium that you saw earlier. Then use the quantum numbers for lithium to infer why a lithium atom has the ground state electron configuration that it does. 

Duncanson and Coulson [242,243] carried out early work on atoms. Since then, the momentum densities of aU the atoms in the periodic table have been studied within the framework of the Hartree-Fock model, and for some smaller atoms with electron-correlated wavefunctions. There have been several tabulations of Jo q), and asymptotic expansion coefficients for atoms [187,244—251] with Hartree-Fock-Roothaan wavefunctions. These tables have been superseded by purely numerical Hartree-Fock calculations that do not depend on basis sets [232,235,252,253]. There have also been several reports of electron-correlated calculations of momentum densities, Compton profiles, and momentum moments for He [236,240,254-257], Li [197,237,240,258], Be [238,240,258, 259], B through F [240,258,260], Ne [239,240,258,261], and Na through Ar [258]. Schmider et al. [262] studied the spin momentum density in the lithium atom. A review of Mendelsohn and Smith [12] remains a good source of information on comparison of the Compton profiles of the rare-gas atoms with experiment, and on relativistic effects. 

Tables 6 and 7 display the corresponding values of a and (3 for the lithium atom Table 6 giving the optimized values (scheme (b)) and Table 7 giving the values obtained by using the recursions (40) and (41) after optimizing the values for the smallest basis set (scheme (c)).

The same pseudo-spectral expansion has also been applied to the case of two lithium atoms.70 In this, owing to the more complicated nature of Ho, difficulties arise from the finite size of the basis set. The authors use an extrapolation procedure to surmount this difficulty. Because the summation in the second-order energy is dominated by the first term, whose magnitude can be obtained experimentally from the excitation energy and oscillator strength of the corresponding electronic transition, the authors plot the calculated value of Co against the calculated first term for various sizes of basis set, and choose for Co that value which corresponds to the experimental value of the first term. In this way they obtain... 

In this paper, we propose an experiment to test neutrality of isolated lithium atoms. Atom interferometry has been shown to be the ideal technique to measure weak interactions of an atom with its environment [1,2]. In particular, in 1991, Kasevich and Chu have mentionned the test of neutrality of atoms as a possible utilisation of their atomic interferometer [2], As far as we know, no further details have been published. The experimental set-up we propose is based on a Mach-Zehnder atom interferometer like the ones developped by the research groups of D. Pritchard [3], Siu Au Lee [4], A. Zeilinger [5] and the one under construction in our group [6]. If the same uniform electric field E is applied on both arms of the interferometer, a phase shift of the interferometric signal will appear. This phase shift will be proportional to the residual charge of lithium atom and to the electric field E. 

Fig. 1. The experimental set-up proposed to test neutrality of lithium atom is based on a Mach-Zehnder atom interferometer working in the Bragg configuration. Gi, G2, G3 are the three diffraction gratings and the detector is placed in front of one of the two complementary exits. The capacitor of length Lc extends from 2 = zm to z = zout-Some plates defining the zero potential in a symmetrical way are not represented...

A lithium atom has three electrons. The hrst two of these can have the same sets of quantum numbers as the two electrons of hehum. What should the set of quantum numbers for the third electron be We cannot choose the lowest permitted value for n, which is 1, because C and m would then both be 0. If we choose -j as the value of m, the third electron would have a set of quantum numbers exactly the same as that of one of the hrst two electrons, and if we choose the value = +5, the third electron would have the same set of quantum numbers as the other. Because neither of these situations is permitted by the Pauli principle, n cannot be 1 for the third electron. We must choose the next higher value, = 2. With = 2, the permitted values of are 0 and 1. Because = 0 wUl give a lower value for the sum + , we choose that value for . With = 0, must be 0, and we can choose either 5 or +5 for m. The quantum numbers for the three electrons of the Uthium atom can thus be as follows ... 

The benzophenonedilithium compound 50, formed by reduction of benzophenone with lithium metal, crystallizes as a dimer (69). The four lithium atoms in the structure are divided into two different sets. The two benzophenone moieties are bridged, through the carbonyl oxygen atoms, by two symmetry-equivalent lithium atoms. Each of the two other lithiums is bonded to one phenyl ring and the ketone functionality reminiscent of that observed in benzyllithium (29), dilithiodibenzyl ketone (42), and dilithiodibenzylacetylene (49). The two different types of lithium atoms are complexed further to THE and TMEDA. 

Schleyer, Pople and coworkers have shown calculationally that polylithiated methanes with one or two additional lithium atoms should form very stable hypervalent species of high symmetry. Thus both trigonal-bipyramidal CLij 44 (Dj symmetry) and octahedral CLig 45 (O, symmetry) deduced from CLi 5 are indicated by ab initio calculations (3-21G basis set) to be highly stable toward loss of a lithium atom from 44 or loss of Li from 45 ... 

Thus the three-electron lithium atom cannot have the electron configuration (Is) the ground state is (1s)2(2s)1. Whenp, d,... orbitals are occupied it is important to remember that 3, 5,.. m values are possible. A set of p orbitals with any n can be occupied by a maximum of six electrons, and a set of d... 

The bonding of the empty p orbital of the lithium atom to the dianion molecule is not determined solely by the symmetry of the HOMO of the dianon instead, it seems to be the result of a number of MO s of the complex. For example, at least four particular eigenfunctions involving lithium pa- -carbon pz overlap appear to be important in the naphthalene complex. These are shown at the left in Figure 34 in order of increasing stability. The top two correspond to the two HOMOs of the isolated anion and suggest that the lithium atoms should be positioned to the outside edges of the naphthalene molecule as observed. From our experience with the monoanion systems we expect that if the empty p orbital of the lithium atom were to interact with the carbon pz orbitals, it would do so in a 1-3 or 2-4 fashion—that is, across a set of three atoms. The B2g, Au, and... 

The examples shown in the table list the primitive Gaussians and the splitting schemes for the case of the lithium atom with added p character in the form of an ip-hybrid and then rfip-hybrid character. Note the symbolism used in the labelling 6-31g), which identifies the core linear combination to be comprised of six primitive Gaussians, while the valence orbital representation, 6-3 Ig ), is a contraction to two linear combinations of three and one primitives. Then, the 6-31g ) basis includes the extra polarization effect of one added d Gaussian. In basis set theory, to provide for the individual symmetry characters of the radial functions being modelled it is customary to define six d functions, the normal set of five in atomic orbital theory and then an additional s-function as + z -... 

Construction of the 2s-A1s) numerical radial function for the lithium atom, using the miniinal Pople el al sto-3g> sets. 

Incidentally, the same kind of technique is applicable to separate core electronic energies from valence electronic energies, and this can be used as numerical test of the relevance of our o—jt separation. Consider a ring of six lithium atoms and a distortion that keeps nn constant, as in 6a 6b. The valence electronic system is a set of six electrons moving over the field created by six positive charges of just one unit. 

Not a superbase, but closely related, is the adduct of w-butyllithiiun with lithium t-butoxide, 206 [179]. Evidence for adduct formation between the two components came initially from NMR studies [180], and it was shown that in benzene solution tetrameric associates are present [181, 182]. Crystallization from hexane gave a well-defined self-assembled tetramer containing two types of differently coordinated Li atom. One set of lithium atoms is bonded to two a-C atoms of n-butyl groups and one oxygen, with additional close contact with a / -carbon atom the other lithium atoms are connected to two oxygens and only one a-carbon [183]. 

As another example, consider the lithium atom (Z = 3) which has three electrons. The third electron cannot go into the Is orbital because it would inevitably have the same set of four quantum numbers as one of the first two electrons. Therefore, this electron enters the next (energetically) higher orbital, which is the 2s orbital (see Figure 7.23). The electron configuration of lithium is ls 2s and its orbital diagram is... 

Another computational study at the Hartree-Fock level, using the 3-21G and 6-31G basis sets, probed the decomposition of di- i-Li2B2H4 into diborane(4) products containing 0,1, or 2 lithium atoms. The three reactions and the energies (relative to Li2B2H4 = 0.0 kcal/mol) are [6] ... 

The heteronuclear variant of NOESY is HOESY (Heteronuclear Overhauser Effect SpectroscopY). Figure 4.60 shows a HOESY spectmm for the tetramethylethylenediamine (tmeda) adduct of 2-lithio-l-phenylpyrrole, whose dimeric structure is also shown in the figure. The normal H and Li NMR spectra are shown along the axes of the 2D contour plot, which contains just three peaks. The lithium atom is therefore close (i.e. less than about 3.5 A) to three different sets of three protons, which can be readily identified as H(7) and H(ll), equivalent by virtue of fast rotation about the N(l)-C(6) bond in solution, H(3), and the methyl protons of the tmeda ligand. Note that the hydrogen atoms are numbered according to the numbers of the carbon atoms to which they are attached. The close contact between Li and H(11) seen in the crystal structure is thus maintained in solution, and it is of chemical significance, as it leads to... 

In a number of nonempirical calculations, starting from Ref. [10], this molecule appeared to prefer (65kcal/mol, STO-3G basis set) non-classical structure IV to the classical form in which the lithium atoms are linked with carbon by normal two-center two-electron bonds. However, a recent calculation on IV (STO-3G, 4-3IG basis sets) supplemented with a calculation of its vibration spectrum has shown that this structure does not correspond to the true minimum on the PES of The vibration spectrum of IV contains... 

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