Codex @codex  0

Albert Fert coauthored the discovery of giant magnetoresistance in alternating iron and chromium layers. In the 1988 measurements, a magnetic field of 2 tesla nearly halved the electrical resistivity of one thin-chromium sample at 4.2 kelvin. Spin-dependent electron transmission through the chromium layers explained why changing the magnetic arrangement changed the electrical resistance so strongly. The experiment made nanoscale layer structure and electron spin directly relevant to an easily measured electrical signal.^[ref]

A physicist.^[ref]

A neutral piano-stool complex $\mathrm{Cr}({\eta }^6\text{-arene})(\mathrm{CO}{)}_3$, conventionally chromium(0), with 18 valence electrons. arene substitution changes electron density and carbonyl stretching frequencies.

Chromium is the chemical element with atomic number 24 and symbol $\mathrm{Cr}$. It is a transition metal. A chromium-rich passive oxide layer helps stainless steel resist corrosion. Chromium(III) and chromium(VI) compounds have substantially different bonding, reactivity, and environmental behavior, so an oxidation state is essential when discussing a chromium compound.^[ref]

The ground level is listed as $3d^5({}^{6}S)4sa{}^7{S}_3$ at zero wavenumber. This supports the chromium configuration and term symbol; it is not a worked solution to the Cambridge exam.

The 1988 study grew alternating iron/chromium layers by molecular beam epitaxy on gallium arsenide. Magnetization and torque measurements tested the magnetic configuration. An AC electrical resistance measurement passed electric current along the layers while the applied magnetic field changed. Comparing field directions and spacer thicknesses linked the resistance decrease to magnetic saturation. Electron microscopy and surface analysis checked layer formation, while leaving atomic-scale interface roughness unresolved.^[ref]

The independent Jülich study used four-terminal sensing on epitaxial Fe/Cr/Fe strips. A single iron film supplied an anisotropic magnetoresistance comparison. Magneto-optic Kerr effect signals and Brillouin light scattering from spin waves identified the layer alignments, rather than inferring them from resistance alone. Field scans along different magnetic axes connected the optical signatures to the resistance changes.^[ref]

Peter Andreas Grünberg's retrospective explains why the preceding interlayer exchange coupling measurements mattered: coupled spin wave modes supplied signatures of magnetic alignment before that alignment became an electrical signal.^[ref]

A resistance curve alone does not reveal the microscopic direction of every magnetic layer. The optical measurements add a different observable, while the reference film tests an orientation-dependent response that can occur without a multilayer. Sample preparation and cross-checks therefore belong to the physical explanation.

Coauthored measurements of iron/chromium/iron layers showing increased electrical resistivity for antiparallel layer magnetizations. The effect exceeded ordinary anisotropic magnetoresistance and strengthened with additional iron layers. ^[ref]

Jianbo Wang coauthored research on chromium.^[ref]

Chromium is the chemical element with atomic number 24 and symbol $\mathrm{Cr}$. It is a transition metal. A chromium-rich passive oxide layer helps stainless steel resist corrosion. Chromium(III) and chromium(VI) compounds have substantially different bonding, reactivity, and environmental behavior, so an oxidation state is essential when discussing a chromium compound.

An experimental condensed matter physicist who coauthored measurements of giant magnetoresistance in alternating iron and chromium layers. Applying a magnetic field substantially reduced the electrical resistance, attributed to spin-dependent electron transmission between the magnetic layers. The experiment connected a nanoscale multilayer structure to a large, electrically measurable magnetic response.^[ref]

The $3d$ and $4s$ atomic orbitals of chromium are close enough in energy that electron-electron terms can overturn the simple filling order. The configuration $[\mathrm{Ar}]3d^{5}4s^1$ permits five singly occupied $3d$ orbitals and a parallel-spin $4s$ electron. Relative to $3d^{4}4s^2$, it removes the $4s$ pair and permits more parallel-spin exchange interactions, lowering the Coulomb-and-exchange contribution enough to offset the orbital promotion cost.

As qualitative bookkeeping, six parallel electron spins give $\left(\genfrac{}{}{0ex}{}{6}{2}\right)=15$ same-spin pairs, compared with $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$ in high-spin $3d^{4}4s^2$. The individual exchange integrals are unequal, so this is an explanation of the tendency, rather than a quantitative atomic energy calculation. The observed ground state configuration is $\boxed{[\mathrm{Ar}]3d^{5}4s^1}$.^[ref]

The closed argon core contributes $L=S=0$. In the half-filled $3d^5$ shell, Hund's rules put one parallel-spin electron in each $m_{\ell }=-2,-1,0,1,2$ orbital. This gives $S_d=5/2$ and the orbital term $L_d=0$. Adding the parallel $4s$ electron, with $\ell =0$ and $s=1/2$, givesThe spin multiplicity is seven. The magnetic projection labels run $M_S,M_J=-3,-2,\dots ,3$, while $M_L=0$. The term symbol agrees with the observed neutral-chromium ground level.^[ref]

The arene and three carbonyl ligands are neutral, so chromium is in oxidation state zero, with a $d^6$ metal count. The eta-six arene contributes six electrons and each CO contributes two:The methoxy group changes the electronic properties of the arene without changing this formal electron count. The complex is a piano-stool complex, with the coordinated arene as the seat and the three carbonyl ligands as the legs.

The methoxy substituent donates electron density into the coordinated arene by chemical resonance. This increases the electron density available at chromium for pi backbonding to CO, weakening C–O and lowering its stretching frequencies. The ester substituent withdraws electron density from the arene, reducing pi backbonding and raising the carbonyl stretching frequencies. For both observed bands, the methoxy-substituted compound has the lowest carbonyl frequency, the unsubstituted compound is intermediate, and the ester-substituted compound has the highest.

In the harmonic oscillator approximation,so the trend reflects an increasing effective C–O bond force constant rather than a change in the CO reduced mass. For example, comparison of the higher-frequency bands gives $k_{\mathrm{ester}}/k_{\mathrm{methoxy}}\approx (1992/1983{)}^2=1.0091$. This is only an approximate local-bond interpretation because the observed normal modes couple the three CO oscillators. In the idealized local $C_{3v}$ geometry they span $A_1+E$, giving two infrared-active frequencies. A substituted arene can lower the exact molecular symmetry and split the $E$ pair, even if that splitting is unresolved experimentally.

triphenylphosphine is a good sigma donor and a substantially poorer pi acceptor than CO. Replacing CO by this phosphine ligand increases electron density at chromium and reduces competition among carbonyl ligands for pi backbonding. Backbonding into each remaining CO therefore strengthens, their internal bond force constants fall, and both remaining carbonyl stretching frequencies are expected to shift downward relative to the parent tricarbonyl.

The two remaining carbonyl ligands have coupled approximately symmetric and antisymmetric stretches; both are generally infrared active in this geometry. One should not treat the spectral change as simply deleting one of the original two bands. The substituted complex still has $6+6+2(2)+2=18$ valence electrons. No numerical frequency shift follows from electron counting alone.

Photoinduced CO loss gives a 16-electron fragment. In the ester-substituted complex the pendant ester carbonyl oxygen can reach chromium and capture that vacant site. A suitable structure is $\mathrm{Cr}({\eta }^6\text{-}{\mathrm{C}}_6{\mathrm{H}}_5\mathrm{C}{\mathrm{O}}_2\mathrm{Me})(\mathrm{CO}{)}_2(\kappa O\text{-ester})$, retaining the coordinated arene and adding intramolecular coordination of its ester oxygen. The added oxygen lone-pair donation restores an 18-electron count. The gaseous by-product is carbon monoxide.

heptane is a poor donor, but intramolecular ligand trapping avoids needing a donor solvent. Benzene has no pendant donor. Although the methoxy group has oxygen lone pairs, its directly attached oxygen does not have the same reach and favourable geometry as the projecting ester carbonyl oxygen; possession of a lone pair alone is insufficient. For these two substrates, acetonitrile can trap the unsaturated fragment through nitrogen to give $\mathrm{Cr}({\eta }^6\text{-arene})(\mathrm{CO}{)}_2(\mathrm{NCMe})$. Without a suitable trap, CO recombination can reverse the initial photochemical dissociation.

Neutral CO ligands require formal Cr($-\mathrm{II}$), hence $d^8$. With five two-electron carbonyl ligands,A trigonal-bipyramidal molecular geometry is expected, analogous in electron count to $\mathrm{Fe}(\mathrm{CO}{)}_5$. Strong pi-acceptor ligands stabilize a low oxidation state through backbonding, and this five-coordinate structure accommodates the closed-shell 18-electron configuration. The negative oxidation state is a formal assignment; it does not mean that a free chromium dianion is trapped inside the molecule.

The methyl nucleophile attacks an electrophilic ring boron. That boron becomes tetrahedral, bearing its original methyl, the incoming methyl, and its two ring nitrogen neighbors. This interrupts its p-orbital participation, so the metal attaches to the remaining five-atom conjugated segment. $A$ is the anionic ${\eta }^5$ heptamethylated-ring Cr(CO)${}_3$ complex, paired formally with $[\mathrm{MgBr}{]}^{+}$; solvent ligation and ion pairing at magnesium are not specified by the spectrum. The original connectivity, with the attacked boron labeled $B_1$, is shown in the first panel below.

There are seven methyl groups. The two attached to tetrahedral $B_1$ are inequivalent because the chromium-bound face distinguishes their environments: one signal of relative integral one for each. The other two B–Me groups are equivalent to one another, giving a signal of integral two. The two N–Me groups adjacent to $B_1$ form another equivalent pair, while the N–Me opposite $B_1$ is unique. The predicted methyl-group multiplicities are therefore $1,1,2,2,1$, the same unordered set as the observed ratio. Multiplying by three gives proton integrals totaling 21. This assignment assumes no fast process interchanging the two $B_1$ methyl environments.

The six-electron neutral ${\eta }^6$ ring donor has become an anionic six-electron ${\eta }^5$ donor, so Cr(0) retains an 18-electron count: $6_d+6_{\mathrm{ring}}+3(2{)}_{\mathrm{CO}}=18$. This borazine dearomatization explains both the changed hapticity and the extra methyl without requiring attack at chromium or loss of a carbonyl.

In the chromium complex, Cr(0) is $d^6$ and receives substantial donation from four carbonyl ligands. Its occupied orbitals can give pi backbonding into the boron-rich acceptor orbitals of the B${}_2$N${}_2$ ring, while the nitrogen-rich occupied ring orbitals donate to the metal. This favors binding across the ring face, approximately ${\eta }^4$, with all four ring atoms participating. A nearly planar ring maintains the p-orbital alignment needed for that interaction and accounts for comparable Cr–B and Cr–N distances. A four-electron ring donor also gives the useful count $6_d+8_{\mathrm{CO}}+4_{\mathrm{ring}}=18$.

Ti(IV) in TiCl${}_4$ is $d^0$ and strongly electron deficient. It is a good acceptor for the two nitrogen lone pairs, but has no filled $d$ set for comparable backbonding into the boron acceptors. chromium therefore favors a face-bound pi complex, while titanium favors N,N sigma coordination. Donation makes the nitrogen environments more nearly tetrahedral and permits the 2,4-Diazadiboretidine ring to pucker. The borons are not directly bound in the same way, explaining $d(\mathrm{Ti}\cdots \mathrm{B})>d(\mathrm{Ti}-\mathrm{N})$. The distinction follows from electron availability, rather than simply calling every short metal–ring contact a separate ordinary sigma bond.

Group 6: cohesion increases from chromium to molybdenum to tungsten. partially occupied d bands make a major contribution to metallic cohesion. Relative to localized 3d orbitals in Cr, more extended 4d/5d orbitals support stronger overlap and broader bonding bands. Strong 5d bonding and the compact dimensions associated with lanthanide/relativistic effects help make W especially cohesive.

Group 11: cohesion increases from silver to copper to gold. the filled d shell changes the balance from Group 6. Going from Cu to larger Ag weakens overlap and lowers cohesion. Gold reverses that simple size trend: relativistic 6s stabilization/contraction, changes in the 5d orbitals and stronger s-d participation enhance bonding. A size-only argument cannot explain Au exceeding both Ag and Cu.

Group 15, As > Sb > Bi: bonding in these elemental solids involves directional p-orbital interactions. Increasing size and longer separations weaken overlap down the group, reducing enthalpy of atomization. Changes in detailed solid structure and relativistic effects refine the numbers, but the underlying weakening of p-derived bonding explains the trend.

Enthalpy of atomization measures removal from the entire standard-state solid to gaseous ground-state atoms; it is not simply the dissociation energy of one selected diatomic bond.

chromium is the characteristic assignment, giving Cr(I)–Cr(I) with a formal quintuple bond. Each formamidinate is monoanionic, so $2x-3=-1$ gives $x=+1$. chromium(I) is $d^5$ and the pair supplies ten d electrons. Relative to a metal–metal $z$ axis, the idealized bonding combinations are $d_{z^2}$ sigma, $d_{xz},d_{yz}$ pi and $d_{xy},d_{x^2-y^2}$ delta:End-on sigma overlap gives the largest splitting, pi overlap a smaller splitting, and delta overlap the weakest. A useful qualitative ordering places bonding sigma lowest, then the two pi combinations, then the two delta combinations; all are occupied. Their antibonding partners are empty, with the weakly split delta-star levels nearest their bonding counterparts. The actual three-bridge ligand field can mix and split symmetry-compatible levels, so the diagram is a bond-axis model rather than five perfectly degenerate metal d levels in the molecular complex.

The identified lantern-type anion has an experimentally determined Cr–Cr distance near $1.740$ Å; reduction of its nine-bonding-electron precursor supplies the tenth electron. This corroborates the model more specifically than citing “short bonds” in an unrelated framework.^[ref]

Solid $\mathrm{MoC}{\mathrm{l}}_2$ contains octahedral $\mathrm{M}{\mathrm{o}}_6$ clusters, while $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$ has paired molybdenum centres in a layered chloride lattice. The first material is better represented by $\mathrm{M}{\mathrm{o}}_6\mathrm{C}{\mathrm{l}}_{12}$ than by isolated bent or linear $\mathrm{MoC}{\mathrm{l}}_2$ molecules. Eight inner chlorides cap the triangular faces of an octahedral metal core, giving $[\mathrm{M}{\mathrm{o}}_6({\mu }_3-\mathrm{Cl}{)}_8{]}^{4+}$. Outer chloride coordination completes the solid: one useful connectivity notation is $\mathrm{M}{\mathrm{o}}_6\mathrm{C}{\mathrm{l}}_8\mathrm{C}{\mathrm{l}}_2\mathrm{C}{\mathrm{l}}_{4/2}$, with two terminal outer chlorides and four intercluster-shared outer chlorides per octahedron. The empirical total is $8+2+4/2=12$ chlorides for six metals.

Each Mo(II) is formally $d^4$, giving 24 metal-based electrons. These support extensive Mo–Mo bonding along the 12 octahedral edges; they are not localized as four free spins on each molybdenum. In $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$, Mo(III) is $d^3$ in edge-sharing $\mathrm{MoC}{\mathrm{l}}_6$ octahedral layers. The metal honeycomb distorts into short Mo–Mo pairs. A localized dimer picture uses the six d electrons to fill one sigma and two pi bonding combinations, producing a formal triple bond and pairing the spins. The bulk crystal remains an extended chloride lattice, rather than a collection of unconnected $\mathrm{M}{\mathrm{o}}_2\mathrm{C}{\mathrm{l}}_6$ molecules.

By comparison, $\mathrm{CrC}{\mathrm{l}}_2$ has predominantly localized high-spin Cr(II), $d^4$, in Jahn–Teller-distorted chloride octahedra; $\mathrm{CrC}{\mathrm{l}}_3$ has layered Cr(III), $d^3$, with three locally unpaired electrons. Their magnetic exchange is not evidence for the same strong short multiple bonds as in the molybdenum solids. The greater radial extent of Mo $4d$ orbitals enables larger metal–metal overlap than the more contracted Cr $3d$ orbitals. Real structure and magnetism still depend on ligand geometry and phase, so the orbital comparison is a trend rather than a prohibition of chromium–chromium bonds in other compounds. Diffraction and magnetic/spectroscopic studies directly distinguish the dimerized $\alpha$-$\mathrm{MoC}{\mathrm{l}}_3$ lattice from $\mathrm{CrC}{\mathrm{l}}_3$.^[ref]