Bonds and lone pairs in molecules

As a simple diatomic example, let us first consider the hydrogen fluoride molecule of Section 3.2. Following the NPA and natural electron configuration summaries (1/0-3.2), the NBO search summary appears as shown below (I/0-4.1). 

As shown in the output, this particular NBO search terminated successfully after only a single cycle, which satisfied the default search criteria. The search yielded a Lewis structure with one core (CR), one bond (BD), and three lone pair (LP) Lewis-type (L) NBOs, which described about 99.95% of the total electron density (i.e., 9.995 of the 10 electrons). These five L-type NBOs easily satisfied the default threshold (1.90e) for pair occupancy [the 0 under Low occ (L) ] and the remaining 17 non-Lewis (NL) NBOs were all well below the O.le occupancy threshold [ High occ (NL) ] to be considered a satisfactory Lewis structure. [The Dev entry refers to deviations from the initial guess that steers multiple cycles of the search algorithm (if required), beyond the scope of this book consult the NBO 

SLiucture a cepi ed Hb low o eupaoey Lewis OEbit-aljf 

Bibliography website link (www.chem.wisc.edu/ nbo5) for further details.] The final lines quantify the overall accuracy of this NLS description ( 99.95%), including the NMB (valence) versus Rydberg-type contributions to the NL remnant, confirming the high accuracy of the expected freshman-level dot diagram 

Following the details of NBO composition, which are described in Section 4.2, the occupancies and energies of NBOs appear in the NBO summary table, as shown in I/0-4.2. 

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The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

Two-electron/two-orbital h5q>erconjugative interactions of the t3q>e responsible for the anomeric effect depend on the relative orientation of bonds and lone pairs in a molecule and are also inversely proportional to the energy difference between the interacting orbitals. Spectroscopic manifestations of stereoelectronic interactions are particularly useful experimental signatures of these effects, which can be utilized for testing molecular models. Empirical observations together with theoretical interpretations in cyclohexane and six-membered heterocycles confirm the relevance of ffc uax Hax/ nx Hax (X = O or N), [Pg.210]

VSEPR theory (7.8) Valenee-sheU eleetron-pair repulsion theory. A simple method for predieting the shapes of molecules it states that molecules assume a shape that allows them to niinunize the repulsions between bonds and lone pairs in the valence shell of the central atom. 

The following model is a representation of citric acid, the key substance in the so-called citric acid cycle by which food molecules are metabolized in the body. Only the connections between atoms are shown multiple bonds are not indicated. Complete the structure by indicating the positions of multiple bonds and lone-pair electrons (gray = C, red = O, ivory = H). 

Trimethylboron is an example of one type of Lewis acid. This molecule has trigonal planar geometry in which the boron atom is s hybridized with a vacant 2 p orbital perpendicular to the plane of the molecule (Figure 21-11. Recall from Chapter 9 that atoms tend to use all their valence s and p orbitals to form covalent bonds. Second-row elements such as boron and nitrogen are most stable when surrounded by eight valence electrons divided among covalent bonds and lone pairs. The boron atom in B (CH ) can use its vacant 2 p orbital to form a fourth covalent bond to a new partner, provided that the new partner supplies both electrons. Trimethyl boron is a Lewis acid because it forms an additional bond by accepting a pair of electrons from some other chemical species. 

Epoi also relies on a local picture as it uses polarizabilities distributed at the Boys LMOs centroids [44] on bonds and lone pairs using a method due to Garmer et al. [35], In this framework, polarizabilities are distributed within a molecular fragment an therefore, the induced dipoles do not need to interact together (like in the Appleq-uist model) within a molecule as their value is only influenced by the electric fields from the others interacting molecules. 

Since rigorous theoretical treatments of molecular structure have become more and more common in recent years, there exists a definite need for simple connections between such treatments and traditional chemical concepts. One approach to this problem which has proved useful is the method of localized orbitals. It yields a clear picture of a molecule in terms of bonds and lone pairs and is particularly well suited for comparing the electronic structures of different molecules. So far, it has been applied mainly within the closed-shell Hartree-Fock approximation, but it is our feeling that, in the future, localized representations will find more and more widespread use, including applications to wavefunctions other than the closed-shell Hartree-Fock functions. 

In this section, you have used Lewis structures to represent bonding in ionic and covalent compounds, and have applied the quantum mechanical theory of the atom to enhance your understanding of bonding. All chemical bonds—whether their predominant character is ionic, covalent, or between the two—result from the atomic structure and properties of the bonding atoms. In the next section, you will learn how the positions of atoms in a compound, and the arrangement of the bonding and lone pairs of electrons, produce molecules with characteristic shapes. These shapes, and the forces that arise from them, are intimately linked to the physical properties of substances, as you will see in the final section of the chapter. 

A Lewis structure shows the approximate locations of bonding electrons and lone pairs in a molecule. However, because it is only a two-dimensional diagram of the links between atoms, except in the simplest cases it does not depict the arrangement of atoms in space. 

As might be expected, NMR calculations that ignore electron correlation often give poor results, especially for molecules which typically require a correlated treatment in order to predict other properties accurately. For example, a good description of multiple bonds and lone pairs generally requires a correlated method. Thus, RHF NMR predictions for molecules such as CO and acetonitrile are poor (20). Furthermore, it has recently been shown that isotropic chemical shift calculations at the RHF level are unreliable for benzenium (21) and related carbenium ions which we often encounter in catalysis. 

Carbon dioxide is a linear molecule with equivalent C O distances of 1.16 A (Vol pin and Kolomnikov, 1973). The bond strength in C02 is measured to be D= 127.1 kcal mol 1, relatively weak compared with the CO bond in carbon monoxide (D = 258.2 kcal mol ) (Bard et al., 1985 Latimer, 1952 Weast, 1978). Resonance structures of the C02 molecule as illustrated in Figure 3.2 show that its chemical reactivity is associated either with the presence of carbon oxygen double bonds and lone-paired electrons on the oxygen atoms or with the electrophilic carbon atom. The quantitative mole-... 

The determinant (= total molecular wavefunction T) just described will lead to (remainder of Section 5.2) n occupied, and a number of unoccupied, component spatial molecular orbitals i//. These orbitals i// from the straightforward Slater determinant are called canonical (in mathematics the word means in simplest or standard form ) molecular orbitals. Since each occupied spatial ip can be thought of as a region of space which accommodates a pair of electrons, we might expect that when the shapes of these orbitals are displayed ( visualized Section 5.5.6) each one would look like a bond or a lone pair. However, this is often not the case for example, we do not find that one of the canonical MOs of water connects the O with one H, and another canonical MO connects the O with another H. Instead most of these MOs are spread over much of a molecule, i.e. delocalized (lone pairs, unlike conventional bonds, do tend to stand out). However, it is possible to combine the canonical MOs to get localized MOs which look like our conventional bonds and lone pairs. This is done by using the columns (or rows) of the Slater T to create a T with modified columns (or rows) if a column/row of a determinant is multiplied by k and added to another column/row, the determinant remains kD (Section 4.3.3). We see that if this is applied to the Slater determinant with k = 1, we will get a new determinant corresponding to exactly the same total wavefunction, i.e. to the same molecule, but built up from different component occupied MOs i//. The new T and the new i// s are no less or more correct than the previous ones, but by appropriate manipulation of the columns/rows the i// s can be made to correspond to our ideas of bonds and lone pairs. These localized MOs are sometimes useful. 

The HF method tends to overestimate the barriers, making unstable molecules seem stabler than they really are. Geometries are discussed further in Section 5.5.1. Approximate versions of the MP2 method that speed up the process with little loss of accuracy are available in some program suites LMP2, localized MP2, and RI-MP2, resolution of identity MP2. LMP2 starts with a Slater determinant which has been altered so that its MOs are localized, corresponding to our ideas of bonds and lone pairs (Section 5.2.3.1), and permits only excitations into spatially nearby virtual orbitals [93]. RI-MP2 approximates four-center integrals (Section 5.3.2) by three-center ones [94]. 

Each geminal function is a singlet-coupled GVB pair (

associated with a particular bond or lone pair in the molecule. For example, CH4 will have the familiar Lewis structure and its wave function will involve a product of four geminal functions, each corresponding to a C-H bond. 

We have shown the BOVB description of n and a bonds in the previous examples. We conclude this section with the BOVB description of the water molecule in which we allow both the bonding and lone-pair electrons to be described in nonorthogonal orbitals. This leads to an eight electron problem which we describe with a BOVB(S, 1+S+RC1)/cc-pVDZ wavefunction. Again the geometry is HF/cc-pVDZ. The BOVB(8,1+S+RCT) energy lies approximately 0.008 au above the BOVB(S, V) energy. 

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