# ABBA molecules

Aufbau principle In building up the electronic configuration of an atom or a molecule in its ground state, the electrons are placed in the orbitals in order of increasing energy. [c.46]

For NDO calculations (see NDO Methods on page 126), the Aufbau also produces the lowest energy wave function. However, in some cases, a calculation may converge to a result that is not the ground state (lowest energy), even though the Aufbau is satisfied (for example, RHF calculations on singlet biradicals or molecules with highly distorted bonds). [c.42]

We shall continue basing our discussion on the step-growth polymerization of the hypothetical monomer AB. In Sec. 5.7 we shall take a second look at this problem for the case of unequal concentrations of A and B groups. For now, however, we assure this equality by considering a monomer which contains one group of each type. In a previous discussion of the polymer formed from this monomer, we noted that remnants of the original functional groups are still recognizable, although modified, along the backbone of the polymer chain. This state of affairs is emphasized by the notation Ababab. . . abaB in which the a s and b s of the ab linkages are groups of atoms carried over from the initial A and B reactive groups. In this type of polymer molecule, then, there are n - 1 a s and 1 A if the degree of polymerization of the polymer is n. The a s differ from the A s precisely in that the former have undergone reaction while the latter have not. At any point during the polymerization reaction the fraction of the initial number of A groups which have reacted to become a s is given by p, and the fraction which remains as A s is given by 1 - p. In these expressions p is the same extent of reaction defined by Eq. (5.3). [c.292]

MOs around them - rather as we construct atomic orbitals (AOs) around a single bare nucleus. Electrons are then fed into the MOs in pairs (with the electron spin quantum number = 5) in order of increasing energy using the aufbau principle, just as for atoms (Section 7.1.1), to give the ground configuration of the molecule. [c.226]

The only way to solve the boundary problem is to make an arbitrary decision abou which part of the electron cloud to pay attention to and which part to ignore. For example we see that when two electron clouds overlap there is a point where both clouds havi the same electron density. This is a logical place to mark each molecule s boundary [c.24]

In general, the adsorption frequency i uv is not equal to the ionization frequency for isolated molecules they are related through the Clausius-Mossotti-Lorentz-Lorentz equation as vv / = voV3/(n + 2) [1]. The difference between the frequencies is often not significant to the result for Aeff [3]. The values of j/uv have been tabulated for various materials and are generally in the range of 3 x 10 sec" [1,3]. Often, the second term in Eq. VI-30 dominates over the first, and in an electrolyte, the ions screen the interaction, causing the first term to be negligible [3]. [c.236]

In a general case, we assume the potential energy part of the Hamiltonian in the form of an expansion involving the terms p pp cos [k(cj)p — < ) ()] (a and P stand for 1 and 2 in the case of ABCD molecules, and for T and C if we consider symmetric ABBA species), subject to certain symmetry constraints (see [144]). [c.522]

In this section, we consider H electronic state (A = 1) of ABBA type molecules. The additional Hamiltonian H is of the form [c.523]

We restrict ourselves again to symmetric tetraatomic molecules (ABBA) with linear eqnilibrium geometi7. After integrating over electronic spatial and spin coordinates we obtain for A elecbonic states in the lowest order (quartic) approximation the effective model Hamiltonian H — Hq+ H, which zeroth-order part is given by Eq. (A.4) and the perturbative part of it of the form [c.539]

The conformations of a molecule are traditionally defined as those arrangements of its atom in space that can be interconverted purely by rotation about single bonds. This definition i usually relaxed in recognition of the fact that small distortions in bond angles and bon lengths often accompcmy conformational changes, 2md that rotations can occur aboi bonds in conjugated systems that have an order between one and two. [c.473]

Otlier groups have applied the linear response method to problems other than prot( ligand binding. A good problem for any new free energy approach is to predict the energies of hydration of small organic molecules. Accurate hydration data are avaih for a wide variety of systems, and the calculations can usually be run relatively quic One immediate problem with the two-parameter linear response method is that, as a d are both positive, it is not possible for any solute to have a positive hydration I energy (both the electrostatic and van der Waals interactions between solutes and wa give negative solute-solvent energies). To deal with this problem, Carlson and Jorgen introduced an additional term which was related to the penalty for forming a sol cavity [Carlsen and Jorgensen 1995]. This third term was proportional to the solv< accessible surface area [c.607]

Only the last factor is a little tricky it is also different with and without additives. With no additive, polycaprolactam can be represented A BABAB. . . ABAB, where the A and B are acid and base groups, respectively, and those marked with the asterisk are those analyzed. Thus every molecule has one of each. In this case, then, we use the average of 12.0 and 11.6 as the end group concentration, and unity as the number of ends of each kind to obtain [c.32]

The reaction mixture in line 4 of Table 5.1 is characterized by an average degree of polymerization of 10/3 = 3.3, with only 30% of the functional groups remaining. This means that 70% of the possible reactions have already occurred, even though we are still dealing with a very low average degree of polymerization. Note that the average degree of polymerization would be the same if the 70% reaction of functional groups led to the mixture AbababababababaB and two AB s. This is because the initial 10 monomers are present in three molecules in both instances and is a consequence of the fact that we are using number averages to talk about these possibilities. The weight averages would be different in the two cases. This poses still another question How does the molecular weight distribution vary with the extent of reaction [c.276]

We have now completed the first stage of the problem we set out to consider. We have arrived at the probability that chains are capped at both ends by potential branch points. The second stage of the derivation is concerned with the reaction between these chain ends via the remaining f - 1 reactive A groups. By hypothesis, the mixture contains an excess of B groups, so there are still unreacted BB monomers or other polymer chain segments with terminal B groups which can react with the Aj- j groups we have been considering. Table 5.6 shows the connecting of such groups-by BB molecules for simplicity for several values of f. For each of the situations shown in Table 5.6, converting the boxed A BB A groups into a condensed abba sequence amounts to linking into a linear polymer the capped segments which had been separate until now. Since the capped ends have f - 1 remaining functional groups at this point, a linear condensation product results when any one of these groups reacts. Thus l/(f- 1) is the probability of this particular eventuality. [c.318]

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). [c.142]

In terms of molecular stmcture, there are three principal categories of polymers, illustrated schematically in Figure 1. If each monomer is diftmctional, that is, can react with other monomers at two points, a linear polymer is formed. AH the examples given above are linear polymers. Polymers that contain two different repeating units, say A and B, are known as copolymers (qv). A linear polymer with a random (AABBABAAABABB) arrangement of the repeating units is a random or statistical copolymer, or just copolymer. It is termed poly(A—B), with the primary constituent Hsted first. A molecule in which the two repeating units are arranged in long, contiguous blocks ([A] —E ] ) block (b) copolymer, poly(A—B). [c.430]

Copolymers can be further described by specifying the number and distribution of monomer units within the copolymer molecule. Thus a polymer with a statistical placement of monomer units, eg, ABBABABAAB is called a random copolymer. An alternating copolymer consists of an alternating arrangement of the comonomers, ABABABABA. On the other hand, a block copolymer has a long segment of one monomer followed by a long segment of another monomer, AAAABBBB. A graft copolymer is a type of block copolymer in which a polymer chain (main chain or backbone) has chains (branched chains) of another polymer attached at intervals along the backbone. A network copolymer is a cross-linked or three-dimensional copolymer. [c.176]

The character of the organized media, which ai e widely used in analysis, is the appeai ance of the host-guest phenomena. These phenomena are studied for organized media with the molecules of receptors (crowns, calyxarenes, cyclodextrines etc.) in details. Nevertheless such effects for surfactants based organized media (micellar solutions, emulsions, microemulsions etc.), which ai e also referred to organized systems, ai e mostly declared but not yet studied or even described. On the basis of own experimental and literature data some demonstrations of the host-guest phenomena in the surfactant-based organized systems ai e presented. The effects appear for both two- and multicomponent systems in the premicellai and micellar surfactant systems [c.26]

Orbitals are occupied by a maximum of two electrons, beginning with the orbital of lowest energy (the Aufbau principle). The number of electrons is determined by the number of electrons present on the interacting atoms. The orbitals in Fig. 1.14A could be applied to systems such as H2 (one electron), H2 (two electrons), He2 (three electrons), or Hc2 (four electrons). A reasonable conclusion would be that H2 would be the most stable of these diatomic species because it has the largest net number of electrons in the bonding orbital (two). The He2 molecule has no net bonding because the antibonding orbital contains two electrons and cancels the bonding contribution of the occupied bonding orbital. Both H2 and He2 have one more electron in bonding orbitals than in antibonding orbitals. These species have been determined to have bond energies of 61 and 60kcal/mol, respectively. The bond energy of H2, for comparison, is 103kcal/mol. [c.37]

AfiO is obtained by taking the difference of the total energies predicted in single point energy calculations for the reactants and products. We U be running B3LYP energy calculations with a reasonably large basis set—6-311+G(2df,2p)—to produce these values. We ll need to run one calculation for each distinct molecule in the reaction. [c.168]

See pages that mention the term

**ABBA molecules**:

**[c.475] [c.523] [c.527] [c.240] [c.519] [c.533] [c.55] [c.311] [c.192] [c.278] [c.285] [c.250]**

The role of degenerate states in chemistry (0) -- [ c.631 , c.632 ]