Beryllium atoms

The magnitude and shape of such a mean-field potential is shown below [21] in figure B3.1.4 for the two 1 s electrons of a beryllium atom. The Be nucleus is at the origin, and one electron is held fixed 0.13 A from the nucleus, the maximum of the Is orbital s radial probability density. The Coulomb potential experienced by the second electron is then a function of the second electron s position along the v-axis (coimecting the Be nucleus and the first electron) and its distance perpendicular to the v-axis. For simplicity, this second electron... 

Boys S F 1950 Eleetronie wave funetions II. A ealeulation for the ground state of the beryllium atom Proc. R. See. A 201 125-37 Shavitt I 1977 The method of eonfiguration interaetion Modern Theoretical Chemistry vo 3, ed H F III Sehaefer (New York Plenum) pp 189-275... 

The normalisation factor is assumed. It is often convenient to indicate the spin of each electron in the determinant this is done by writing a bar when the spin part is P (spin down) a function without a bar indicates an a spin (spin up). Thus, the following are all commonly used ways to write the Slater determinantal wavefunction for the beryllium atom (which has the electronic configuration ls 2s ) ... 

The magnitude and "shape" of sueh a mean-field potential is shown below for the Beryllium atom. In this figure, the nueleus is at the origin, and one eleetron is plaeed at a distanee from the nueleus equal to the maximum of the Is orbital s radial probability density (near 0.13 A). The radial eoordinate of the seeond is plotted as the abseissa this seeond eleetron is arbitrarily eonstrained to lie on the line eonneeting the nueleus and the first eleetron (along this direetion, the inter-eleetronie interaetions are largest). On the ordinate, there are two quantities plotted (i) the Self-Consistent Field (SCF) mean-field... 

Neutron radiation is emitted in fission and generally not spontaneously, although a few heavy radionueleides, e.g. plutonium, undergo spontaneous fission. More often it results from bombarding beryllium atoms with an a-emitter. Neutron radiation deeays into protons and eleetrons with a half-life of about 12 min and is extremely penetrating. 

The mass of a beryllium atom is 1.4965 X 10-23 g. Using that fact and other information in this chapter, find the mass of a Be24 ion. 

Notice that the beryllium atom has no unpaired electrons, the boron atom has one, and the carbon atom two. Simple valence bond theory would predict that Be, like He, should not form covalent bonds. A boron atom should form one bond, carbon two. Experience tells us that these predictions are wrong. Beryllium forms two bonds in BeF2 boron forms three bonds in BF3. Carbon ordinarily forms four bonds, not two. 

The formation of the BeF2 molecule can be explained by assuming that, as two fluorine atoms approach Be, the atomic orbitals of the beryllium atom undergo a significant change. Specifically, the 2s orbital is mixed or hybridized with a 2p orbital to form two new sp hybrid orbitals. (Figure 7.12). 

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... 

The beryllium atom, like boron and carbon, can promote an electron in order to form more chemical bonds ... 

Beryl. 385 Beryllium atomic size, 379 boiling point, 374 bonding capacity, 285 chemistry of, 382 electron configuration. 378 heat of vaporization, 374 ionization energies, 379 occurrence, 384 preparation, 385 properties, 381 structure, 381... 

Alternative methods are based on the pioneering work of Hylleraas ([1928], [1964]). In these cases orbitals do not form the starting point, not even in zero order. Instead, the troublesome inter-electronic terms appear explicitly in the expression for the atomic wavefunction. However the Hylleraas methods become mathematically very cumbersome as the number of electrons in the atom increases, and they have not been very successfully applied in atoms beyond beryllium, which has only four electrons. Interestingly, one recent survey of ab initio calculations on the beryllium atom showed that the Hylleraas method in fact produced the closest agreement with the experimentally determined ground state atomic energy (Froese-Fischer [1977]). 

Boys, S. F., Proc. Roy. Soc Londno) A201, 125, Electronic wave functions. II. A calculation for the ground state of the beryllium atom." a. 

McWeeny, R., Proc. Roy. Soc. [London) A235, 496, (i) The density matrix in self-consistent field theory. I. Iterative construction of the density matrix." Beryllium atom is studied. Steepest descent method is described. 

How many beryllium atoms are present in a beryllium film of mass 0.210 g used as a window on an x-ray tube ... 

E.4 In your new nanotechnology lab you have the capability to manipulate individual atoms. The atoms on the left are aluminum atoms (molar mass 27 g-mol 1), those on the right are atoms of beryllium (molar mass 9 g-mol ). How many beryllium atoms would have to be added to the pan on the right for the masses on the two pans to be equal ... 

The element with Z = 4 is beryllium (Be), with four electrons. The first three electrons form the configuration ls22s1, like lithium. The fourth electron pairs with the 2s-electron, giving the configuration ls22s2, or more simply [He 2s2 (41. A beryllium atom therefore has a heliumlike core surrounded by a valence shell of two paired electrons. Like lithium—and for the same reason—a Be atom can lose only its valence electrons in chemical reactions. Thus, it loses both 2s-electrons to form a Be2+ ion. 

The arrangement of atoms in the molecule of Be40(CH3C00)6. Small circles represent carbon atoms, large circles oxygen atoms. The beryllium atoms occupy the centers of the four tetrahedra. One of the six acetate groups is not shown. 

The arrangement of the centers of the molecules in the crystal is that corresponding to the diamond structure. Each molecule is surrounded tetrahedrally by four molecules. If we consider a molecule as roughly tetrahedral in shape with similar orientation to the tetrahedron formed by the four beryllium atoms, then the adjacent molecules are so oriented as to present tetrahedral faces to one another. 

C08-0054. The following are hypothetical configurations for a beryllium atom. Which use nonexistent orbitals, which are forbidden by the Pauli principle, which are excited states, and which is the... 

This approximation was denoted initially by the acronym IQG [34] and later on by IP (Independent Pairs) [35]. It gave satisfactory results in the study of the Beryllium atom and of its isoelectronic series as well as in the BeH system. The drawback of this approximation is that when the eigen-vectors are diffuse, i.e. there is more than one dominant two electron configuration per eigen-vector, the determination of the corresponding nj is ambiguous. In order to avoid this problem the MPS approximation, which does not have this drawback, was proposed. 

While from the energy point of view, the correlation effects seem to be overestimated, the RDAf s are particularly satisfactory. Thus, when comparing the 2-RDAf s obtained with these approximations for the ground state of the Beryllium atom with the corresponding FCI one, the standard deviations are 0.00208236 and 0.00208338 for the MPS and IP respectivelyFor this state, which has a dominant four electron configuration of the type, 1122 >, the more important errors, which nevertheless can be considered small, are given in table 2. 

In my opinion this partitioning is particularly suitable for analysing electronic correlation effects. To illustrate this point a set of calculations for the three lowest singlet states of the Beryllium atom are reported in table 3 (in all cases —tr v) = —19.72037 Hartrees). 

Under these conditions, the 3-RDM of the three lower states of the Beryllium atom and the two lower ones of the Water molecule were determined [48] by taking as initial data the 2-RDM obtained in a Full Configuration Interaction. In Table 4 some of these results are given and as can be seen they are very satisfactory. 

Conroy and Perlow [235] have measured the Debye-Waller factor for W in the sodium tungsten bronze Nao.gWOs. They derived a value of/= 0.18 0.01 which corresponds to a zero-point vibrational amplitude of R = 0.044 A. This amplitude is small as compared to that of beryllium atoms in metallic beryllium (0.098 A) or to that of carbon atoms in diamond (0.064 A). The authors conclude that atoms substituting tungsten in bronze may well be expected to have a high recoilless fraction. 

Although dimethylberyllium is a coordination polymer in the solid state,27 it has long been known to be monomeric in the gas phase.28 It has also been found to be monomeric when synthesized from the co-condensation of laser-ablated beryllium atoms and a methane/argon mixture at 10 K.11 Formed in conjunction with several other species, including hydrides (see Section 2.02.2.4), (CH3)2Be was identified from its infrared absorption bands, which were compared to DFT-calculated frequencies (DFT = density functional theory). 

Beryllium atoms generated under similar conditions react in an acetylene/argon matrix at 10 K to produce HBeCCH (//,Be-Hi = 2,119cm-1).10 The observation of BeH, BeH2, -CCH, and HCC-CCH as co-products indicates that some fraction of the beryllium atoms abstracts hydrogen from HCCH (Equation (2)) ... 

The structure of dimethylberyllium is similar to that of trimethylaluminum except for the fact that the beryllium compound forms chains, whereas the aluminum compound forms dimers. Dimethylberyllium has the structure shown in Figure 12.3. The bridges involve an orbital on the methyl groups overlapping an orbital (probably best regarded as sp3) on the beryllium atoms to give two-electron three-center bonds. Note, however, that the bond angle Be-C-Be is unusually small. Because beryllium is a Lewis acid, the polymeric [Be(CH3)2] is separated when a Lewis base is added and adducts form. For example, with phosphine the reaction is... 

---