By Ranganath Muniyappa, Ritu Madan, Ron T. Varghese.

Online text: www.endotext.org/wp-content/uploads/pdfs/assessing-insulin-sensitivity-and-resistance-in-humans.pdf

Cited passages: Assessing Insulin Sensitivity and Resistance in Humans, Hyperinsulinemic Euglycemic Glucose Clamp, PDF pp. 4–6; Hyperinsulinemic Euglycemic Glucose Clamp; Advantages and Limitations, PDF pp. 4–6.

By Michael A. Weiss, Donald F. Steiner, Louis H. Philipson.

Online text: www.endotext.org/wp-content/uploads/pdfs/insulin-biosynthesis-secretion-structure-and-structure-activity.pdf

Cited passages: Weiss, Steiner and Philipson, Introduction; Insulin Biogenesis and Mechanism of Release; Biochemistry and Electrophysiology of Insulin Secretion, PDF pp. 1, 4–8, 10–11.

By Iben Rix, Christina Nexøe-Larsen, Natasha C. Bergmann, Asger Lund, Filip K. Knop.

Online text: www.ncbi.nlm.nih.gov/books/NBK279127/

Cited passages: Glucagon Physiology, Glucagon Receptor Signalling and Glucagon Stimulates Lipolysis and Ketogenesis: controversy over direct human adipose effects; Glucagon Physiology, Glucagon Receptor Signalling; Glucagon Increases Hepatic Glucose Production; Glucagon Physiology, Structure and Synthesis of Glucagon; Regulation of Glucagon Secretion, Figure 2; Glucagon Physiology, The Role of Glucagon in Diabetes.

Endosymbiotic theory explains the bacterial origins of mitochondria and plastids through enduring internal associations and subsequent integration. Survival inside a biological cell is only part of the problem: exchange through membrane transport, inherited division, gene expression and delivery of required proteins must work together. The elegance is evolutionary reuse of an existing cellular capability, followed by changes that make the partners operate as one system. ^[ref]

The historical On the origin of mitosing cells by Lynn Sagan (1967, abstract and Introduction, pp. 225–226) synthesized a symbiotic account of eukaryotic origins and proposed tests using molecular evidence. Its Introduction explicitly acknowledged earlier proposals. It also hypothesized origins for other structures; the modern evidence for mitochondria and plastids should be assessed separately from the rest of that historical scheme.

An endosymbiont is the internal partner in an endosymbiosis. Calling an organism an endosymbiont does not by itself classify it as an organelle or imply an irreversible evolutionary transition.

By Wissam Raji.

Online text: math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_%28Raji%29/07%3A_Introduction_to_Analytic_Number_Theory/7.02%3A_Chebyshev%27s_Functions

Cited passages: Wissam Raji, Elementary Number Theory, Section 7.2, definitions of theta and psi; Wissam Raji, Elementary Number Theory, Section 7.2, finite theta decomposition and Exercise 1.

Bond polarization is unequal sharing of electron density across a chemical bond. An electronegativity difference is a heuristic for its direction and tendency, not a unique partial atomic charge.

A simple two-site model makes the notation explicit. Represent each site by effective positive electric charge $+e$, and allocate expected electron populations $1-s$ to $A$ and $1+s$ to $B$, with $0\le s<1$. Here $e$ is the elementary charge; these effective sites omit the internal structure of real chemical atoms. Subtraction givesFor the stipulated illustration $s=0.35$, the populations are $0.65$ and $1.35$, and the effective partial atomic charges are $+0.35e$ and $-0.35e$. Fractional expected populations do not split an individual electron into pieces. The total population remains two, and the pair remains neutral. No formula connecting $s$ to $\Delta \chi$ has been assumed; many electron density distributions and partitioning conventions can share one qualitative electronegativity ordering.

A permanent electric dipole moment gives evidence of separated positive and negative electric charge in an overall neutral molecule. This is a more direct probe of chemical polarity than an electronegativity table. For hydrogen chloride, NIST lists about $1.109$ debye for the lowest vibrational state and $1.093$ debye for the equilibrium value. They describe different averaging conventions, not two contradictory measurements. The NIST WebBook traces the vibrational value $1.1085$ debye to molecular-beam electric-resonance measurements in 1970.^[ref][ref]

How does molecular beam electric resonance reveal an electric dipole moment? A source and apertures form a beam of molecules in vacuum. A first nonuniform electric field, A, selects quantum states through their different Stark effects. In a central region, C, electrodes supply a nearly uniform electric field and applied radiation drives transitions at selected frequencies. A second nonuniform electric field, B, analyzes the outgoing quantum states; a detector measures the rate of arriving molecules. In a transmission-loss arrangement, resonant radiation transfers some molecules to a quantum state rejected by B, so the measured arrival rate dips. The observable is a change in detected molecules as the radiation frequency is scanned, rather than light absorption itself. This general apparatus description is documented in a later experimental thesis; it is not a reconstruction of the exact 1970 HCl instrument.^[ref]

The inference comes from how transition frequencies change with the known electric field. The interaction $-\mathbf{\mu }\cdot \mathbf{E}$ couples the electric dipole moment to the electric field; fitting the quantum mechanics of the relevant rotational states extracts its magnitude. A free rotating molecule need not show a first-order shift proportional to $|\mathbf{E}|$: the weak-field Stark effect can be quadratic. The diagram uses a simplified rigid rotor, with $B$ an energy constant, to illustrate this behavior. It omits the fine details of actual spectra.

Useful controls include scans with the radiation off to measure the baseline arrival rate, repeated scans at several calibrated electric fields, and agreement between independently assigned transitions. These are methodological checks, not claims about undocumented steps of the 1970 experiment. Field calibration and state assignment limit the inferred electric dipole moment. The published 1970 abstract confirms analysis of HCl and DCl beam-resonance spectra and combination with infrared spectroscopy intensities to obtain a distance-dependent electric dipole moment; its full apparatus and calibration record were unavailable here.^[ref]

Even an accurately measured electric dipole moment is not an absolute partial atomic charge. Replacing a hydrogen chloride molecule by two point electric charges $\pm q$ separated by bond length $r$ gives $|\mu |=|q|r$. Using $1.109$ debye and $r=1.27455\times 10^{-10}\mathrm{m}$ gives $|q|\approx 0.181$ times the elementary electric charge. This is an effective two-point model, combining a vibrationally averaged electric dipole moment with an equilibrium bond length, not a unique partition of the actual electron density or a measured “18.1 percent ionic bond”.^[ref]

For a molecule with several chemical bonds, molecular geometry can cancel opposing contributions to the total electric dipole moment. Carbon dioxide illustrates why an overall nonpolar molecule need not have unpolarized individual chemical bonds. An electronegativity comparison helps anticipate local bond polarization; the measured molecular electric dipole moment tests the entire electric charge distribution.

A tabulated electronegativity is useful because it compresses many comparisons, but one number per chemical element suppresses chemical context. Changing the bonded partners, bond length or electron configuration changes the conditions under which a chemical atom attracts electron density. The bond-dissociation energy can change for reasons beyond bond polarization, so attributing every extra unit of energy solely to an electronegativity difference is an approximation.^[ref]

An oxidation state labels a formal allocation of electrons; it is not a measured partial atomic charge. State-sensitive electronegativity models may give different values for different oxidation states or electron configurations, while a simple chemical element table intentionally provides a common comparison convention. Likewise, replacing an isolated chemical atom by a site in an ionic crystal introduces a surrounding electric field and many neighbours. Applying the same tabulated electronegativity without adjustment becomes an additional assumption.^[ref]

For the ground-state Mulliken scale, the state dependence is visible directly in the formula. Replacing $X$ by $X^{+}$ replaces $E(X^{+})-E(X)$ with $E(X^{2+})-E(X^{+})$ as the removal cost, and replaces $E(X)-E(X^{-})$ with $E(X^{+})-E(X)$ as the attachment release. These are different ionization energies and electron affinities. This isolated-ion arithmetic does not claim that a bonded chemical atom with the same formal oxidation state is an isolated ion. In a molecule, the actual electron density and dipole evidence for bond polarization supply complementary information about that environment.

The contrast between Pauling electronegativity and Mulliken electronegativity becomes clearer by following the measurements into the formulas. A Pauling bond-energy excess compares three compatible bond-dissociation energies; Mulliken electronegativity takes the arithmetic mean of an ionization energy and an electron affinity. The former asks how much stronger an unlike-atom chemical bond is than a stipulated baseline; the latter combines two different isolated-species energy gaps.

Actual readouts precede those model choices. In the nitrogen dissociation threshold from fragment images, fitted squared image radii versus assigned excitation energies reveal a threshold after accounting for the product quantum states. In the chlorine photodetachment threshold experiment, mass-selected anions overlap a tunable laser, and neutral-atom counts reveal the onset of electron detachment. Opposite laser directions control the Doppler shift. That second threshold supplies an electron affinity, not an electronegativity; the Mulliken scale still needs an independent ionization energy.^[ref][ref]

For an original arithmetic comparison, stipulate isolated-species $I=(8,7,6)\mathrm{eV}$ and positive attachment-release $A_{\mathrm{ea}}=(0.5,3,3)\mathrm{eV}$ for fictitious species $A,B,C$. Their Mulliken electronegativities are $(4.25,5,4.5)\mathrm{eV}$. The largest ionization energy belongs to $A$, while the largest Mulliken electronegativity belongs to $B$: accepting an electron matters as well as retaining one. Using signed attachment energies $(-0.5,-3,-3)\mathrm{eV}$ in $(I-\Delta E_{\mathrm{attach}})/2$ gives exactly the same results.

Independently stipulate $D_{RR}=300$ and $D_{XX}=(200,300,450)\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for $X=A,B,C$, with unlike-atom valuesThus $D_{RX}=(274.12125,396.485,592.09125)\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, and the Pauling scale differences from $R$ are $(0.5,1,1.5)$. If all three fictitious species are placed above $R$ on that scale, their ordering is $A<B<C$, whereas the stipulated Mulliken scale gives $A<C<B$. The bond-dissociation energies and isolated-species energies were invented independently: this demonstrates what the formulas do, not a measured disagreement for actual chemical elements. A unit conversion cannot force these two input models to agree.

Mulliken electronegativity uses both the cost of removing an electron and the energy released by accepting an electron. For specified isolated-atom states, the common ground-state convention isThe free electron's energy is the zero reference. Here $I$ is the ionization energy and $A_{\mathrm{ea}}$ is the electron affinity, positive for exothermic attachment. If attachment is instead tabulated as the signed energy change $\Delta E_{\mathrm{attach}}=E(X^{-})-E(X)$, the same expression is $(I-\Delta E_{\mathrm{attach}})/2$. Stating the sign convention prevents adding the wrong quantities. The 1934 original treated suitable valence states, which are not automatically the ground states used in this example.^[ref]

Mulliken electronegativity has energy units before any additional rescaling. With $I$ and $A_{\mathrm{ea}}$ in electronvolts per chemical atom, ${\chi }_{\mathrm{M}}$ is in electronvolts; with both in $\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, it is a molar energy. For hydrogen, the RSC ground-state inputs are $I=1312.05$ and $A_{\mathrm{ea}}=72.769\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, giving ${\chi }_{\mathrm{M}}=692.4095\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\approx 7.176\mathrm{eV}$ per chemical atom. For chlorine, $I=1251.186$ and $A_{\mathrm{ea}}=348.575\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ give $799.8805\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\approx 8.290\mathrm{eV}$. These are calculated ground-state Mulliken electronegativities, not the RSC's tabulated Pauling electronegativities.^[ref][ref]

Both schemes place chlorine above hydrogen here, but their numerical differences cannot be subtracted from one another or equated. Dividing a molar Mulliken electronegativity by an energy conversion factor changes units; it does not transform it into a Pauling electronegativity. A further empirical mapping would require its own calibration and stated domain.