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The almost linear curve of the "expected" enthalpy changes is shown by blue dashed lines in the figure for hydration reactions of M<sup>2+</sup> and M<sup>3+</sup> ions. The differences between this curve and the double-humped experimental values are approximately equal to the LFSE values in Table 10.7 for high-spin ... | {
"Header 1": "10.3.3 Ligand Field Stabilization Energy",
"Header 3": "**EXERCISE 10.7**",
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The square-planar complex [Ni(CN)4] <sup>2</sup>-, with *D*4*h* symmetry, provides an instructive example of how this approach can be extended to other geometries. The axes for the ligand atoms are chosen for convenience. The *y* axis of each ligand is directed toward the central atom, the *x* axis is in the plane of t... | {
"Header 1": "10.3.4 **[Square-Planar Complexes](#page-7-0)**",
"Header 3": "**Sigma Bonding**",
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The $\pi$ -bonding orbitals are also shown in Table 10.8. The $d_{xy}(b_{2g})$ orbital interacts with the $p_x(\pi_{\parallel})$ ligand orbitals, and the $d_{xz}$ and $d_{yz}(e_g)$ orbitals interact with the $p_z(\pi_{\perp})$ ligand orbitals, as shown in **Figure 10.15**. The $b_{2g}$ orbital is in the pl... | {
"Header 1": "10.3.4 **[Square-Planar Complexes](#page-7-0)**",
"Header 3": "Pi Bonding",
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The $\pi$ orbitals are challenging to visualize, but if the y axis of the ligand orbitals is chosen along the bond axis, and the x and z axes are arranged to allow the $C_2$ operation to work properly, the results in Table 10.9 are obtained. The reducible representation includes the E, $T_1$ , and $T_2$ irreduci... | {
"Header 1": "10.3.5 Tetrahedral Complexes",
"Header 3": "Pi Bonding",
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The **angular overlap** model is a useful approach for making estimates of orbital energies in coordination complexes, while having the flexibility to deal with a variety of geometries and ligands, including heteroleptic complexes, with different ligands. <sup>19,20</sup> This approach estimates the strength of interac... | {
"Header 1": "10.4 Angular Overlap",
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In the angular overlap model the strongest sigma interaction is defined as between a metal $d_{z^2}$ orbital and a ligand p orbital (or a hybrid ligand orbital of the same symmetry), as shown in Figure 10.20. The strength of all other sigma interactions is determined relative to the strength of this reference interac... | {
"Header 1": "10.4.1 Sigma-Donor Interactions",
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These are octahedral ions with only sigma interactions. The ammonia ligands have no $\pi$ orbitals available for significant bonding with the metal ion. The donor orbital of NH<sub>3</sub> is mostly nitrogen $p_z$ orbital in composition, and the other p orbitals are used in bonding to the hydrogens.
In calculatin... | {
"Header 1": "10.4.1 Sigma-Donor Interactions",
"Header 3": "$[M(NH_3)_6]^{n+}$",
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The energy changes for the ligand orbitals are the same as those above for each interaction. The totals, however, are taken across a row of Table 10.10, including each of the *d* orbitals.
Ligands in positions 1 and 6 interact strongly with $d_{z^2}$ and are lowered by $e_{\sigma}$ . Ligands in these positions do ... | {
"Header 1": "10.4.1 Sigma-Donor Interactions",
"Header 3": "**Ligand Orbitals**",
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Ligands such as CO, CN-, and phosphines (PR3) are p acceptors, with empty orbitals that can interact with metal *d* orbitals in a pi fashion. In the angular overlap model, the strongest pi interaction is defined as between a metal *dxz* orbital and a ligand p\* orbital, as shown in **Figure 10.22** . The antibonding mo... | {
"Header 1": "10.4.2 **[Pi-Acceptor Interactions](#page-7-0)**",
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The interactions between occupied ligand p, d, or $\pi$ orbitals and metal d orbitals are similar to those in the $\pi$ -acceptor case. In other words, the angular overlap model treats $\pi$ -donor ligands similarly to $\pi$ -acceptor ligands except that for $\pi$ -donor ligands, the signs of the changes in energ... | {
"Header 1": "10.4.2 **[Pi-Acceptor Interactions](#page-7-0)**",
"Header 3": "10.4.3 Pi-Donor Interactions",
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Halide ions donate electron density to a metal via $p_y$ orbitals, a sigma interaction; the ions also have $p_x$ and $p_z$ orbitals that can interact with metal orbitals and donate additional electron density by pi interactions. We will use $[MX_6]^{n-}$ , where X is a halide ion or other ligand that is simultan... | {
"Header 1": "10.4.2 **[Pi-Acceptor Interactions](#page-7-0)**",
"Header 3": "$[MX_6]^{n-}$",
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Using the angular overlap model, determine the splitting pattern of d orbitals for a tetrahedral complex of formula MX<sub>4</sub>, where X is a ligand that can act as $\sigma$ donor and $\pi$ donor.
With ligands that behave as both $\pi$ acceptors and $\pi$ donors (such as CO and CN<sup>-</sup>), the $\pi$ ... | {
"Header 1": "10.4.2 **[Pi-Acceptor Interactions](#page-7-0)**",
"Header 3": "EXERCISE 10.10",
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Ligands are classified by their donor and acceptor capabilities. There is a long tradition in inorganic chemistry of ranking ligands on the basis of how these collective ligand abilities result in d orbital splitting. Because $\sigma$ donation, $\pi$ donation, and $\pi$ acceptance have unique impacts on d orbital... | {
"Header 1": "10.4.4 The Spectrochemical Series",
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Because changing the ligand or the metal affects the magnitudes of $e_{\sigma}$ and $e_{\pi}$ , the value of $\Delta$ also changes. One consequence may be a change in the number of unpaired electrons. For example, water is a relatively weak-field ligand. When combined with Co<sup>2+</sup> in an octahedral geometry... | {
"Header 1": "10.4.5 Magnitudes of $e_{\\sigma}$ , $e_{\\pi}$ , and $\\Delta$",
"Header 3": "**Charge on Metal**",
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The introduction of different ligands clearly can have a dramatic impact on the spin state of the complex. For example, $[\text{Fe}(\text{H}_2\text{O})_6]^{3^+}$ is a high-spin species, and $[\text{Fe}(\text{CN})_6]^{3^-}$ is low spin. Replacing $\text{H}_2\text{O}$ with $\text{CN}^-$ is enough to favor low spi... | {
"Header 1": "10.4.5 Magnitudes of $e_{\\sigma}$ , $e_{\\pi}$ , and $\\Delta$",
"Header 3": "**Different Ligands**",
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**TABLE 10.13 Angular Overlap Parameters for MA4B2 Complexes**
| | | | Equatorial Ligands ( A ) | | Axial Ligands ( B ) | | |
|-------------------|----------|----------|--------------------------|------|---------------------|----------|-----------|
| ... | {
"Header 1": "10.4.5 Magnitudes of $e_{\\sigma}$ , $e_{\\pi}$ , and $\\Delta$",
"Header 3": "**Different Ligands**",
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The angular overlap model describes the electronic energy of complexes with a wide variety of shapes or with combinations of different ligands. The magnitudes of $e_{\sigma}$ and $e_{\pi}$ with different ligands can be estimated to predict the electronic structure of complexes such as $[Co(NH_3)_4Cl_2]^+$ . This c... | {
"Header 1": "10.4.5 Magnitudes of $e_{\\sigma}$ , $e_{\\pi}$ , and $\\Delta$",
"Header 3": "**Special Cases**",
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The spectrochemical series has been used for decades, but is it reliable for all metals and ligand environments? Is it most useful for octahedral complexes with $d^6$ metal ions, such as the Co<sup>3+</sup> complexes examined by Tsuchida? Reed has exploited the magnetic properties of iron(III) porphyrin complexes to ... | {
"Header 1": "10.4.6 A Magnetochemical Series",
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The Jahn–Teller theorem<sup>29</sup> states that degenerate orbitals (those with identical energies) cannot be unequally occupied. To avoid these unfavorable electronic configurations, molecules distort (lowering their symmetry) to render these orbitals no longer degenerate. For example, an octahedral Cu(II) complex, c... | {
"Header 1": "10.5 The Jahn-Teller Effect",
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Using the d-orbital splitting diagram in Table 10.5, show that the Jahn–Teller effects in the table match the guidelines in the preceding paragraph.
Significant Jahn-Teller effects are observed in complexes of high-spin Cr(II) ( $d^4$ ), high-spin Mn(III) $(d^4)$ , Cu(II) $(d^9)$ , Ni(III) $(d^7)$ , and low-spin C... | {
"Header 1": "10.5 The Jahn-Teller Effect",
"Header 3": "**EXERCISE 10.12**",
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Can one predict whether a given metal ion and set of ligands will form an octahedral, square-planar, or tetrahedral coordination complex? This is a challenging fundamental question,<sup>34</sup> and a foolproof strategy does not exist. As a starting point, angular overlap calculations of the energies expected for diffe... | {
"Header 1": "10.6 Four- and Six-Coordinate Preferences",
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Group theory and angular overlap can also be used to determine which d orbitals interact with ligand $\sigma$ orbitals and to approximate the relative energies of the resulting molecular orbitals for a wide variety of geometries. As usual, the reducible representation for the ligand $\sigma$ orbitals is reduced to ... | {
"Header 1": "10.7 Other Shapes",
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- **1.** J. J. R. Fausto da Silva, *J. Chem. Educ.* , **1983** , *60* , 390; R. D. Hancock, *J. Chem. Educ.* , **1992** , *69* , 615.
- **2.** D. P. Shoemaker, C. W. Garland, and J. W. Nibler, *Experiments in Physical Chemistry* , 5th ed., McGraw-Hill, New York, 1989, pp. 418–439.
- **3.** B. Figgis and J. Lewis, in H.... | {
"Header 1": "10.7 Other Shapes",
"Header 3": "**References**",
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One of the best sources is G. Wilkinson, R. D. Gillard, and J. A. McCleverty, editors, *Comprehensive Coordination Chemistry* , Pergamon Press, Elmsford, NY, 1987; Vol. 1, *Theory and Background* , and Vol. 2, *Ligands* , are particularly useful. Others include the books cited in Chapter 4 , which include chapters on c... | {
"Header 1": "10.7 Other Shapes",
"Header 3": "**[General References](#page-7-0)**",
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- 10.1 Predict the number of unpaired electrons for each of the following:
- **a.** a tetrahedral $d^6$ ion
- **b.** $[Co(H_2O)_6]^{2+}$
- c. $[Cr(H_2O)_6]^{3+}$
- **d.** a square-planar $d^7$ ion
- e. a coordination compound with a magnetic moment of 5.1 Bohr magnetons
- **10.2** Identify the *first-row* transit... | {
"Header 1": "10.7 Other Shapes",
"Header 3": "**Problems**",
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based on the preceding answers, would you expect $\pi$ -acceptor ligands to preferentially occupy axial or equatorial positions in five-coordinate complexes? What other factors should be considered in addition to angular overlap?
- 10.15 On the basis of your answers to Problems 10.13 and 10.14, which geometry, squar... | {
"Header 1": "10.7 Other Shapes",
"Header 3": "**Problems**",
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Ozarowski, S. A. Zvyagin, J. Tesler, *Inorg. Chem.*, **2012**, *51*, 4954). Using the angular overlap parameters for molecule 1 in Table 3 of this reference, generate an energy-level diagram for CoCl(PPh<sub>3</sub>)<sub>3</sub>. Does the electronic structure predicted by this method surprise you? Explain. On the basis... | {
"Header 1": "10.7 Other Shapes",
"Header 3": "**Problems**",
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- **10.38** The ion $[\text{TiH}_6]^{2^-}$ has been found to have $O_h$ symmetry. (See I. B. Bersuker, N. B. Balabanov, D. Pekker, J. E. Boggs, *J. Chem. Phys.* **2002**, *117*, 10478.)
- **a.** Using the H orbitals of the ligands as a basis, construct a reducible representation (the symmetry equivalent of a collec... | {
"Header 1": "The following problems require the use of molecular modeling software.",
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Perhaps the most striking aspect of many coordination compounds of transition metals is their vivid colors. The dye Prussian blue, for example, has been used as a pigment for more than two centuries and is still used in blueprints; it is a complicated coordination compound involving iron(II) and iron(III) coordinated o... | {
"Header 1": "[Coordination Chemistry III:](#page-8-0) Electronic Spectra",
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In explaining the colors of coordination compounds, we are dealing with the phenomenon of *complementary colors*: if a compound absorbs light of one color, we see the complement of that color. For example, when white light (containing a broad spectrum of all visible wavelengths) passes through a substance that absorbs ... | {
"Header 1": "11.1 **[Absorption of Light](#page-8-0)**",
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If light of intensity *Io* at a given wavelength passes through a solution containing a species that absorbs light, the light emerges with intensity *I* , which may be measured by a suitable detector ( **Figure 11.2** ).
The Beer–Lambert law may be used to describe the absorption of light (ignoring scattering and ref... | {
"Header 1": "11.1.1 **[Beer–Lambert Absorption Law](#page-8-0)**",
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Absorption of light results in the excitation of electrons from lower to higher energy states; because such states are quantized, we observe absorption in "bands" (as in Figure 11.1), with the energy of each band corresponding to the difference in energy between the initial and final states. To gain insight into these ... | {
"Header 1": "11.2 Quantum Numbers of Multielectron Atoms",
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Determine the possible microstates for an $s^1p^1$ configuration, and use them to prepare a microstate table.
The s electron can have $m_l = 0$ and $m_s = \pm \frac{1}{2}$ .
The p electron can have $m_l = \pm 1$ , 0, -1 and $m_s = \pm \frac{1}{2}$ .
The resulting microstate table is then
| | | ... | {
"Header 1": "11.2 Quantum Numbers of Multielectron Atoms",
"Header 3": "**EXAMPLE 11.1**",
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A P term has L = 1; therefore, $M_L$ can have three values: +1, 0, and -1. The spin multiplicity is 2 = 2S + 1. Therefore, $S = \frac{1}{2}$ , and $M_S$ can have two values: $+\frac{1}{2}$ and $-\frac{1}{2}$ . There are six microstates in a ${}^{2}P$ term (3 rows $\times$ 2 columns). For the minimum case of... | {
"Header 1": "11.2 Quantum Numbers of Multielectron Atoms",
"Header 3": "<sup>2</sup>P (doublet P)",
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Reduce the microstate table for the $s^1 p^1$ configuration to its component free-ion terms, and identify the ground-state term.
The microstate table (prepared in Example 11.1) is the sum of the microstate tables for the ${}^{3}P$ and ${}^{1}P$ terms:
| | | $M_S$ | | |
|-------|----... | {
"Header 1": "11.2 Quantum Numbers of Multielectron Atoms",
"Header 3": "**EXAMPLE 11.3**",
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Determine the possible values of *J* for the carbon terms.
For the term symbols just described for carbon, the <sup>1</sup>D and <sup>1</sup>S terms each have only one J value, whereas the ${}^{3}P$ term has three slightly different energies, each described by a different J. J can have only the value 0 for the ${}... | {
"Header 1": "11.2.1 Spin-Orbit Coupling",
"Header 3": "**EXAMPLE 11.4**",
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We can now make the connection between electron-electron interactions and the absorption spectra of coordination compounds. In Section 11.2, we considered a method for determining the microstates and free-ion terms for electron configurations. For example, a $d^2$ configuration gives rise to five free-ion ${}^3F$ , ... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
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What is the ground term for $d^4$ (low spin)?
- 1. $\uparrow$ $\downarrow$ $\uparrow$ $\uparrow$
- 2. Spin multiplicity = 2 + 1 = 3
- **3.** Highest possible value of $M_L = 2 + 2 + 1 + 0 = 5$ ; therefore, H term. Note that here, $m_l = 2$ for the first two electrons does not violate the exclusion princip... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "**EXAMPLE 11.5**",
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The relative intensities of absorption bands are governed by a series of selection rules. On the basis of the symmetry and spin multiplicity of ground and excited electronic states, two of these rules are as follows:1,2
- 1. Transitions between states of the same parity (symmetry with respect to a center of inversion... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "11.3.1 Selection Rules",
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Figure 11.3 is an example of a correlation diagram for the configuration $d^2$ . These diagrams illustrate how the energies of electronic states change between two extremes:
- 1. Free ions (no ligand field). In Exercise 11.4, the terms ${}^{3}F$ , ${}^{3}P$ , ${}^{1}G$ , ${}^{1}D$ , and ${}^{1}S$ were obtained... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "11.3.2 Correlation Diagrams",
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Tanabe-Sugano diagrams are modified correlation diagrams that are useful in the interpretation of electronic spectra of coordination compounds.<sup>5</sup> In Tanabe–Sugano diagrams, the lowest-energy state is plotted along the horizontal axis; consequently, the vertical distance above this axis is a measure of the ene... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "11.3.3 Tanabe-Sugano Diagrams",
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The utility of Tanabe-Sugano diagrams in explaining electronic spectra is provided by the $d^2$ complex $[V(H_2O)_6]^{3+}$ . The ground state is ${}^3T_{1g}(F)$ ; this is the only electronic state that is appreciably occupied under normal conditions. Absorption of light should occur primarily to excited states also... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "$[V(H_2O)_6]^{3+}(d^2)$",
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Tanabe-Sugano diagrams for $d^2$ through $d^8$ are shown in Figure 11.7. The cases of $d^1$ and $d^9$ configurations will be discussed in Section 11.3.4 and illustrated in Figure 11.11. The diagrams for $d^4$ , $d^5$ , $d^6$ , and $d^7$ have apparent discontinuities, marked by vertical lines near the center... | {
"Header 1": "11.3 Electronic Spectra of Coordination Compounds",
"Header 3": "**Other Electron Configurations**",
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We have not yet discussed the spectra of $d^1$ and $d^9$ complexes. By virtue of the simple d-electron configurations for these cases, we might expect each to exhibit one absorption band corresponding to excitation of an electron from the $t_{2g}$ to the $e_g$ levels:
However, ... | {
"Header 1": "11.3.4 Jahn-Teller Distortions and Spectra",
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Identify the following configurations as T, A, or E states in octahedral complexes:
When a ${}^{2}D$ term for $d^{9}$ is split by an octahedral ligand field, two configurations result:
$$\begin{array}{cccccccccccccccccccccccccccccccccccc$$
The lower energy configuration is doubly degenerate in the $e_g$ orb... | {
"Header 1": "11.3.4 Jahn-Teller Distortions and Spectra",
"Header 3": "**EXERCISE 11.6**",
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Absorption spectra of coordination compounds can be used to determine the magnitude of the ligand field splitting, which is $\Delta_o$ for octahedral complexes. The accuracy with which $\Delta_o$ can be determined is limited by the mathematical approaches used to analyze the spectral data. Absorption spectra often ... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
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From a simple perspective each of these cases in Figure 11.11 corresponds to excitation of an electron from a $t_{2g}$ to an $e_g$ orbital, with the final (excited) electron configuration having the same spin multiplicity as the initial configuration. Our discussion in this chapter indicates that when electron-elec... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
"Header 3": "$d^1$ , $d^4$ (High Spin), $d^6$ (High Spin), $d^9$",
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These electron configurations have a ground-state F term. In an octahedral ligand field, an F term splits into three terms: $A_{2g}$ , $T_{2g}$ , and $T_{1g}$ . As shown in Figure 11.12, the $A_{2g}$ is of lowest energy for $d^3$ or $d^8$ . For these configurations, the difference in energy between the two lowe... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
"Header 3": "$d^3$ , $d^8$",
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As in the case of $d^3$ and $d^8$ , the ground free-ion terms for these two configurations are F terms. However, the determination of $\Delta_o$ is not as simple for $d^2$ and $d^7$ . It is necessary to compare the $d^3$ and $d^2$ Tanabe-Sugano diagrams to explain this complication; the $d^8$ and $d^{7}$... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
"Header 3": "$d^2$ , $d^7$ (High Spin)",
"token_count": 1342,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
$[V(H_2O)_6]^{3+}$ has absorption bands at 17,800 and 25,700 cm<sup>-1</sup>. Using the Tanabe–Sugano diagram for $d^2$ , estimate values of $\Delta_a$ and B for this complex.
From the Tanabe-Sugano diagram there are three possible spin-allowed transitions (Figure 11.13):
$${}^3T_{1g}(F) \longrightarrow {}^3T_{... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
"Header 3": "**EXAMPLE 11.8**",
"token_count": 1038,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
High-spin $d^5$ complexes have no excited states of the same spin multiplicity (6) as the ground state. The bands that are observed are therefore the consequence of spin-forbidden transitions and are typically very weak as, for example, in [Mn(H<sub>2</sub>O)<sub>6</sub>]<sup>2+</sup>. The interested reader is referr... | {
"Header 1": "11.3.5 Applications of Tanabe-Sugano Diagrams: Determining $\\Delta_o$ from Spectra",
"Header 3": "Other Configurations: $d^5$ (High Spin), $d^4$ to $d^7$ (Low Spin)",
"token_count": 479,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Tetrahedral complexes generally have more intense absorptions than octahedral complexes. This is a consequence of the first (Laporte) selection rule (Section 11.3.1): transitions between d orbitals in a complex having a center of symmetry are forbidden. As a result, absorption bands for octahedral complexes are weak (s... | {
"Header 1": "11.3.6 Tetrahedral Complexes",
"token_count": 773,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Charge-transfer absorptions in solutions of halogens are described in Chapter 6. In these cases, a strong interaction between a donor solvent and a halogen molecule, X2, leads to the formation of a complex in which an excited state (primarily of X<sub>2</sub> character) can accept electrons from a HOMO (primarily of so... | {
"Header 1": "11.3.7 Charge-Transfer Spectra",
"token_count": 1219,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
The pursuit of artificial photosynthesis via capture of solar radiation in solar cells<sup>15</sup> has prompted extensive examination of metal complexes that are photostable, feature broad absorption in the visible region, and possess significantly long-lived excited states to permit photo-promoted electron and energy... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"token_count": 1492,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
- **1.** B. N. Figgis and M. A. Hitchman, *Ligand Field Theory* and its Applications, Wiley-VCH, New York, 2000, pp. 181-183.
- 2. B. N. Figgis, "Ligand Field Theory," in G. Wilkinson, R. D. Gillard, and J. A. McCleverty, eds., Comprehensive Coordination Chemistry, Vol. 1, Pergamon Press, Elmsford, NY, 1987, pp. 243-24... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"Header 3": "References",
"token_count": 1348,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
B. N. Figgis and M. A. Hitchman, *Ligand Field Theory and Its Applications*, Wiley-VCH, New York, 2000; and B. N. Figgis, "Ligand Field Theory," in G. Wilkinson, R. D. Gillard, and J. A. McCleverty, eds., *Comprehensive Coordination Chemistry*, Vol. 1, Pergamon Press, Elmsford, NY, 1987, pp. 213–280, provide extensive ... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"Header 3": "**General References**",
"token_count": 254,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
- **11.1** For each of the following configurations, construct a microstate table and reduce the table to its constituent free-ion terms. Identify the lowest-energy term for each.
- **a.** $p^{3}$
- **b.** $p^1d^1$ (as in a $4p^13d^1$ configuration)
- **11.2** For each of the lowest-energy (ground state) terms in ... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"Header 3": "**Problems**",
"token_count": 1992,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Are the relative positions of the charge-transfer absorptions consistent with the oxidizing abilities of these ions? Explain.
- **11.19** The complexes $[Co(NH_3)_5X]^{2+}(X = Cl, Br, I)$ have charge transfer to metal bands. Which of these complexes would you expect to have the lowest-energy charge-transfer band? Why... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"Header 3": "**Problems**",
"token_count": 1930,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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| Species | Absorp | tion Band | s (cm <sup>-1</sup> ) |
|----------------------------------------------------------------------|--------|-----------|-----------------------|
| $[Ni(H_2O)_6]^{2+}$ | 8,500 | ... | {
"Header 1": "11.3.8 Charge-Transfer and Energy Applications",
"Header 3": "**Problems**",
"token_count": 1005,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
Although early chemists did not know the structures of the coordination compounds they worked with, they did learn how to synthesize complexes containing metals. Werner and Jørgensen prepared specic complexes to test their hypotheses about coordination geometries. These chemists initiated the contemporary strategy of d... | {
"Header 1": "12.1 **[Background](#page-8-0)**",
"token_count": 1206,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Many reactions require substitution, replacing one ligand by another. A well-studied class of substitution reactions involves aqueous metal ions $([M(H_2O)_m]^{n+})$ as reactants. These reactions can produce colored products used to identify metal ions:
$$\begin{split} [\text{Ni}(\text{H}_2\text{O})_6]^{2^+} + 6\,\... | {
"Header 1": "12.2.1 Inert and Labile Compounds",
"token_count": 1946,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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On the other hand, hexaaminecobalt (3+) is thermodynamically unstable in acid:
$$[\text{Co(NH_3)}_6]^{3+} + 6 \text{ H}_3\text{O}^+ \longrightarrow [\text{Co(H_2O)}_6]^{3+} + 6 \text{ NH}_4^+ \quad (\Delta G^{\circ} < 0)$$
But [Co(NH3)6] <sup>3</sup><sup>+</sup> reacts very slowly and is therefore *inert* (the acti... | {
"Header 1": "12.2.1 Inert and Labile Compounds",
"token_count": 957,
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Langford and Gray<sup>2</sup> described a range of possibilities for substitution reactions (**Table 12.2**). At one extreme, the departing ligand leaves, and an intermediate with a lower coordination number is formed, a mechanism labeled **D** for **dissociation**. At the other extreme, the incoming ligand adds to the... | {
"Header 1": "12.2.1 Inert and Labile Compounds",
"Header 3": "12.2.2 Mechanisms of Substitution",
"token_count": 311,
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This chapter describes examples in which the rate law is used to propose reaction mechanisms. We provide two types of information: (1) the information used to propose mechanisms and (2) specific reactions for which mechanisms are known with fairly high levels of confidence. The first is necessary to critically examine ... | {
"Header 1": "12.3 Kinetic Consequences of Reaction Pathways",
"token_count": 276,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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In a dissociative (D) reaction, the first step is loss of a ligand to form an intermediate with a lower coordination number. Subsequent additions of either a new ligand (Y) or the leaving group (X) are two possible reaction pathways for this intermediate:
$$\begin{array}{c} ML_5X \xrightarrow[k_{-1}]{k_1} ML_5 \, + \... | {
"Header 1": "12.3 Kinetic Consequences of Reaction Pathways",
"Header 3": "12.3.1 Dissociation (D)",
"token_count": 789,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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An interchange (I) reaction in its simplest form is a direct replacement of the leaving group with the incoming group that does not proceed via an intermediate, but rather a single transition state leading to the conversion of reactants to products.
$$ML_5X + Y \xrightarrow{k_1} ML_5Y + X$$
If the substitution reac... | {
"Header 1": "12.3.2 Interchange (1)",
"token_count": 428,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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As mentioned above, an aspect that complicates mechanistic studies is when multiple pathways result in similar reaction kinetics, rendering pathways difficult to distinguish from each other. One such complication is when a rapid equilibrium occurs between the incoming ligand and the 6-coordinate reactant to form an ion... | {
"Header 1": "12.3.4 Preassociation Complexes",
"token_count": 1008,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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In the event of a dissociative mechanism, an octahedral complex loses one ligand (X) to yield a 5-coordinate transition state, and the incoming ligand ultimately fills the vacant site to form the octahedral product. The inert and labile classifications (Section 12.2.1) were rationalized partially from ligand field theo... | {
"Header 1": "12.4 Experimental Evidence in Octahedral Substitution",
"Header 3": "12.4.1 Dissociation",
"token_count": 2042,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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The rate of reaction changes only slightly with changes in the incoming ligand. In many cases, aquation (substitution by water) and anation (substitution by an anion) rates are comparable. If ligand dissociation is the rate-determining step, the entering group should have no effect on the reaction rate. How much can a ... | {
"Header 1": "12.4 Experimental Evidence in Octahedral Substitution",
"Header 3": "12.4.1 Dissociation",
"token_count": 406,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Kinetic effects are related to thermodynamic effects by linear free-energy relationships (LFER). A LFER can be observed when the bond strength of a metal-ligand bond (correlated to a thermodynamic parameter) plays a major role in determining the dissociation rate of a ligand (correlated to a kinetic parameter). When th... | {
"Header 1": "12.4.2 Linear Free-Energy Relationships",
"token_count": 1895,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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| TABLE 12.5 Rate Constants for [Ni(H <sub>2</sub> O) <sub>c</sub> ] <sup>2+</sup> Substitution Reaction | <b>TABLE 12.5</b> | Rate Constants for | or [Ni(H <sub>-</sub> O) <sub>-</sub> ] <sup>2+</sup> | <sup>+</sup> Substitution Reaction |
|----------------------------------------------------------------------------... | {
"Header 1": "12.4.2 Linear Free-Energy Relationships",
"token_count": 659,
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Associative reactions are less common with octahedral complexes. 11 Table 12.6 gives data for both dissociative and associative interchanges for similar reactants. In the case of water substitution by several different anions in $[Cr(NH_3)_5(H_2O)]^{3+}$ , the rate constants are similar (within a factor of 6), indicat... | {
"Header 1": "12.4.2 Linear Free-Energy Relationships",
"Header 3": "12.4.3 Associative Mechanisms",
"token_count": 934,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Some cases in which second-order kinetics suggest an associative mechanism are believed to proceed via a conjugate base mechanism, <sup>12</sup> called S<sub>N</sub>1CB for substitution, nucleophilic, unimolecular, conjugate base. 13 These reactions depend on amine, ammine (NH<sub>3</sub>), or aqua ligands that can be ... | {
"Header 1": "12.4.2 Linear Free-Energy Relationships",
"Header 3": "12.4.4 The Conjugate Base Mechanism",
"token_count": 2036,
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The chelate effect (Section 10.1.1) causes polydentate complexes to be thermodynamically more stable than their monodentate counterparts.<sup>17</sup> Substitution for a chelated ligand is generally a slower reaction than that for a similar monodentate ligand. Explanations for this effect center on two factors. First, ... | {
"Header 1": "12.4.2 Linear Free-Energy Relationships",
"Header 3": "12.4.5 The Kinetic Chelate Effect",
"token_count": 326,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Dissociative mechanisms lead to products where the stereochemistry may be the same or different than the starting complex. Table 12.9 shows that cis- $[Co(en)_2L(H_2O)]^{(1+n)+}$ is a hydrolysis product of both cis- $[Co(en)_2LX]^{n+}$ and trans- $[Co(en)_2LX]^{n+}$ in acid solution. While these aquation reactions w... | {
"Header 1": "12.5 Stereochemistry of Reactions",
"token_count": 1703,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Beyond the possibility of the conjugate base mechanism, substitution of Y for X in $trans-[M(LL)_2BX]$ (LL = a bidentate ligand) can proceed by three dissociative pathways. If dissociation of X from the reactant leaves a square-pyramidal intermediate that adds the new ligand to the vacant site, the result is retentio... | {
"Header 1": "12.5.1 Substitution in trans Complexes",
"token_count": 650,
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Follow the example of Figure 12.9b with the structure at the right and show that the first two products could be $\Delta$ rather than $\Lambda$ .
If the Figure 12.9b mechanism is operative, the statistical probability of a change from trans to cis with a trans-[M(LL)<sub>2</sub>BX] reactant is expected to be two t... | {
"Header 1": "12.5.1 Substitution in trans Complexes",
"Header 3": "**EXERCISE 12.2**",
"token_count": 1554,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Isomerization mechanisms involving compounds containing chelating ligands can also involve twists. The trigonal, or Bailar, twist, requires twisting the two opposite trigonal faces through a trigonal prismatic transition state to the new structure (Figure 12.11a). In tetragonal twists (Figures 12.11b and 12.11c), one c... | {
"Header 1": "12.5.3 Isomerization of Chelate Rings",
"Header 3": "**Pseudorotation**",
"token_count": 312,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Because many reactions of platinum compounds have been studied, we will use as our initial example the generic reaction
$$T-Pt-X+Y \longrightarrow T-Pt-Y+X$$
where T is the ligand trans to the departing ligand X, and Y is the incoming ligand. We will designate the plane of the molecule the xy plane and the Pt axis ... | {
"Header 1": "12.6.1 Kinetics and Stereochemistry of Square-Planar Substitutions",
"token_count": 719,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Evidence for a 5-coordinate intermediate is strong, and the transition state sometimes may even be 6-coordinate, with assistance from solvent.<sup>23</sup> The highest energy transition state may be either during the formation of the intermediate or as the exiting ligand dissociates from the intermediate.
This mechan... | {
"Header 1": "12.6.1 Kinetics and Stereochemistry of Square-Planar Substitutions",
"Header 3": "12.6.2 Evidence for Associative Reactions",
"token_count": 1920,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Values of $\eta_{\rm Pt}$ are subsequently found with kinetic data from these reactions via
$$\eta_{\text{Pt}} = \log\left(\frac{k_{\text{Y}}}{k_{\text{CH}_3\text{OH}}}\right)$$
The s factors for the hard $[Pt(dien)H_2O]^{2+}$ and the soft trans- $[Pt(PEt_3)_2Cl_2]$ , found by plotting $\log k_{\rm Y}$ versus... | {
"Header 1": "12.6.1 Kinetics and Stereochemistry of Square-Planar Substitutions",
"Header 3": "12.6.2 Evidence for Associative Reactions",
"token_count": 488,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Chernyaev<sup>26</sup> introduced the *trans* effect in platinum chemistry. In reactions of squareplanar Pt(II) compounds, ligands trans to chloride are more easily replaced than those trans to ammonia; chloride has a stronger trans effect than ammonia. The trans effect allows the formation of isomeric Pt compounds (Fi... | {
"Header 1": "12.7 The trans Effect",
"token_count": 330,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Predict the products of these reactions (there may be more than one product when there are conflicting preferences).
$$[PtCl_4]^{2^-} + NO_2^- \longrightarrow (a) \qquad (a) + NH_3 \longrightarrow (b)$$
$$[PtCl_3NH_3]^- + NO_2^- \longrightarrow (c) \qquad (c) + NO_2^- \longrightarrow (d)$$
$$[PtCl(NH_3)_3]^+ + NO... | {
"Header 1": "12.7 The trans Effect",
"Header 3": "**EXERCISE 12.3**",
"token_count": 444,
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The *trans* effect is rationalized by two factors, weakening of the Pt—X bond and stabilization of the presumed 5-coordinate transition state. Pertinent energy coordinate diagrams are shown in **Figure 12.14**.
**FIGURE 12.14** Activation Energy and the *trans* Effect. The depth of the ... | {
"Header 1": "12.7.1 Explanations of the trans Effect<sup>27</sup>",
"Header 3": "**Sigma-Bonding Effects**",
"token_count": 476,
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The additional factor needed is Pt—T $\pi$ bonding. When the T ligand engages in a strong $\pi$ -acceptor (backbonding) interaction with Pt, charge is removed from Pt, rendering the metal center more electrophilic and more susceptible to nucleophilic attack. This is the prerequisite for formation of the 5-coordinate... | {
"Header 1": "12.7.1 Explanations of the trans Effect<sup>27</sup>",
"Header 3": "**Pi-Bonding Effects**",
"token_count": 1620,
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When the ligands of both reactants are tightly held, reaction proceeds by outer-sphere electron transfer with no change in the coordination spheres. Classic examples are in Table 12.14.
The rate constants show large differences since they depend on the ability of the electrons to tunnel through the ligands. This is a... | {
"Header 1": "12.8 Oxidation–Reduction Reactions",
"Header 3": "12.8.1 Inner-Sphere and Outer-Sphere Reactions",
"token_count": 2033,
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Although [Cr(bipy)<sub>3</sub>]<sup>2+</sup> is formally labile, the chelate effect may predispose this complex to an outer-sphere mechanism. The delocalized $\pi$ systems of the bipy ligands of $[Cr(bipy)_3]^{2+}$ may lower the barrier for outer-sphere electron transfer relative to [Ru(NH<sub>3</sub>)<sub>6</sub>]... | {
"Header 1": "12.8 Oxidation–Reduction Reactions",
"Header 3": "12.8.1 Inner-Sphere and Outer-Sphere Reactions",
"token_count": 861,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Chem., 1965, 4, 756; data for $[Co(NH_3)_6]^{3+}$ reactions with $Cr^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ and $V^{2+}$ a... | {
"Header 1": "12.8 Oxidation–Reduction Reactions",
"Header 3": "12.8.1 Inner-Sphere and Outer-Sphere Reactions",
"token_count": 2015,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Ligands that are easier to reduce can result in complexes that are more quickly reduced.<sup>32</sup> A useful comparison is between the oxidizing agents [(NH<sub>3</sub>)<sub>5</sub>CoL]<sup>2+</sup>, where L is benzoate (difficult to reduce) and 4-carboxy-N-methylpyridine (easier to reduce). The rate constants for ... | {
"Header 1": "12.8 Oxidation–Reduction Reactions",
"Header 3": "12.8.1 Inner-Sphere and Outer-Sphere Reactions",
"token_count": 1794,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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The overall stability of complexes with different charges on the metal ion depends on the LFSE, metal-ligand bonding, and redox properties of the ligands. The hard and soft character of the ligands also has an effect. All the very high oxidation numbers for the transition metals are found in combination with hard ligan... | {
"Header 1": "12.8.2 Conditions for High and Low Oxidation Numbers",
"token_count": 1303,
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Coordination to the metal changes ligand properties sufficiently to make possible reactions at the ligands that either (a) could not happen with the unbound ligand or (b) could occur without the metal but much more slowly. Reactions at coordinated ligands are a vital aspect of organometallic chemistry (Chapter 14). We ... | {
"Header 1": "12.9 Reactions of Coordinated Ligands",
"token_count": 211,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Amino acid esters, amides, and peptides can be hydrolyzed in basic solution, and metal ions (Cu(II), Co(II), Ni(II), Mn(II), Ca(II), and Mg(II), and others) speed these reactions. The uncertain mechanism is either through bidentate coordination of the $\alpha$ -amino group and the carbonyl, or only through the amine. ... | {
"Header 1": "12.9.1 Hydrolysis of Esters, Amides, and Peptides",
"token_count": 439,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Template reactions are those in which formation of a complex places the ligands in the correct geometry for reaction. One of the earliest was for the formation of phthalocyanines (Figure 12.17). The study of this chemistry began in 1928, after discovery of a blue impurity in phthalimide prepared by reaction of phthalic... | {
"Header 1": "12.9.1 Hydrolysis of Esters, Amides, and Peptides",
"Header 3": "12.9.2 Template Reactions",
"token_count": 635,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Acetylacetone complexes are known to undergo a wide variety of reactions that are similar to aromatic electrophilic substitutions. Bromination, nitration, and similar reactions have been studied.<sup>39</sup> In all cases, coordination forces the ligand into an enol form and promotes reaction at the center carbon by pr... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"token_count": 294,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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- 1. H. Taube, Chem. Rev., 1952, 50, 69.
- C. H. Langford and H. B. Gray, *Ligand Substitution Processes*, W. A. Benjamin, New York, 1966.
- R. B. Jordan, Reaction Mechanisms of Inorganic and Organometallic Systems, 3rd ed., Oxford (New York), 2007, p. 86.
- **4.** F. Wilkinson, *Chemical Kinetics and Reactions Mechani... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "References",
"token_count": 2024,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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Price, "Dyes and Pigments," in G. Wilkinson, R. D. Gillard, and J. A. McCleverty, eds., *Comprehensive Coordination Chemistry* , Vol. 6, Pergamon Press, Oxford, 1987, pp. 88–89.
- **37.** D. St. C. Black, "Stoichiometric Reactions of Coordinated Ligands," in Wilkinson, Gillard, and McCleverty, *Comprehensive Coordinati... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "References",
"token_count": 213,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
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The general principles of kinetics and mechanisms have been described by R. B. Jordan, *Reaction Mechanisms of Inorganic and Organometallic Systems* , 3 rd ed., Oxford University Press, New York, 2007, J. W. Moore and R. G. Pearson, *Kinetics and Mechanism* , 3rd ed., Wiley InterScience, New York, 1981, and in F. Wilki... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "**[General References](#page-8-0)**",
"token_count": 340,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
- **12.1** The high-spin $d^4$ complex $[Cr(H_2O)_6]^{2+}$ is *labile*, but the low-spin $d^4$ complex ion $[Cr(CN)_6]^{4-}$ is *inert*. Explain.
- **12.2** Why is the existence of a series of entering groups with different rate constants evidence for an associative mechanism (A or $I_{\alpha}$ )?
- **12.3** P... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "**Problems**",
"token_count": 1865,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
Incoming nucleophilic ligands: (1) P(C<sub>2</sub>H<sub>5</sub>)<sub>3</sub>, (2) $P(n-C_4H_9)_3$ , (3) $P(C_6H_6)(C_2H_5)_2$ , (4) $P(C_6H_5)_2(C_2H_5)$ , (5) $P(C_6H_5)_2(n-C_4H_9)$ , (6) $P(p-CH_3OC_6H_4)_3$ (7) $P(O-n-C_4H_9)_3$ , (8) $P(OCH_3)_3$ , (9) $P(C_6H_5)_3$ , (10) P(OCH<sub>2</sub>)<sub>3</sub>CCH... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "**Problems**",
"token_count": 2046,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
The osmium–nitrogen distances are:
Os-N(1): 210.1(7) pm
Os-N(3): 206.6(8) pm
Os-N(5): 206.9(7) pm
- **a.** Which ligand, Cl or NSe, has the larger *trans* influence? Explain briefly.
- b. The nitrogen-selenium distance in this compound is among the shortest N—Se distances known. Why is this distance so short? (... | {
"Header 1": "12.9.3 Electrophilic Substitution",
"Header 3": "**Problems**",
"token_count": 1657,
"source_pdf": "datasets/websources/biochem/inorganic-chemistry-g-l-miessler-2014.pdf"
} |
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