Mn Nitride Bonding Analysis

Unraveling oxidation states

OK, let me see. I'm figuring out the oxidation state of Mn in [PW11O39(Mn-N_3)]^5- by examining the net charge and typical oxidation states of the polyoxotungstate anion and nitrido ligand.

Assessing charges

Examining the lacunary polyoxometalate's charge and azide ligand, the cumulative negative charge is -8, leading to the question of manganese's oxidation state to balance this.

Determining manganese oxidation

Interestingly enough, manganese is at +3 oxidation in the complex. This leaves 4 d-electrons, reduced slightly from its neutral state.

Figuring out oxidation state

I'm concluding that manganese's oxidation state is likely +5 to balance the charges, considering the -10 charge from other components and the usual charge of a terminal nitrido ligand.

Evaluating charges

The Mn oxidation state is +5 after photolysis, and the nitrido species has a d2 electron count. This aligns with the expected changes in oxidation states and electron configurations.

Laying out the options

I'm working through both the azide and nitrido species regarding Mn's oxidation state and d electron count. The exciting aspect might be the final nitrido species.

Mapping manganese's profile

OK, let me see: manganese in a +5 state typically hosts a d2 configuration, matching standard nitrido complexes. The tetragonal metal nitrido complex in C4v features a sigma and two pi bonds.

Labeling molecular orbitals

I'm aligning the molecular orbitals of a tetragonal metal nitrido complex in C4v, categorizing them as sigma, pi, or non-bonding, and matching them with Mulliken symbols.

Charting orbital interactions

I'm mapping out the interactions of orbital pairs in a tetragonal metal nitrido complex. This leads to the sigma bonding between d_z^2 and nitrido p_z orbitals.

Piecing together orbitals

OK, let me see: combining molecular orbitals involves sigma and pi bonding and antibonding interactions, with specific orbitals remaining non-bonding. Also, determining the bond order requires that.

Assessing electron dynamics

I'm thinking through how manganese's d2 empty orbitals can pair with nitrido's 3 p electrons to fill bonding molecular orbitals, forming a stable bond.

Analyzing bonding interactions

OK, let me see: N^3- contributes 3 p electrons, while Mn's d2 orbitals participate in bonding. This setup creates a strong metal-ligand bond in a nitrido complex.

Determining bond order

I'm applying a formal bond order approach to confirm the Mn-N bond order is likely 3, based on electron pairs and their configurations in bonding and non-bonding orbitals.

Deciphering EPR patterns

I'm analyzing the possible EPR signals for [PW11O39(Mn-N3)]^{5-}, considering manganese's oxidation state and electron arrangement to determine any hyperfine splitting that might occur.

Piecing together the EPR signal

Considering if the EPR signal for [PW11O39(Mn-N3)]^{5-} aligns with high spin Mn(III) d4 or low spin configurations, especially in a tetragonal environment with a strong field nitrido ligand.

Mapping potential outcomes

For [PW11O39(Mn-N3)]^{5-}, Mn(III) d4 in a tetragonal field might give zero-field splitting and no clear EPR. We'll see!

Assessing EPR potential

Planning to predict the EPR spectrum of [PW11O39(Mn-N3)]^{5-}, it's worth noting that manganese has a d4 configuration, potentially high spin, and experiences zero-field splitting, which might make it EPR silent at X-band.

Wondering about EPR patterns

I'm curious if the EPR spectrum of [PW11O39(Mn-N3)]^{5-} will show Mn(III) d4 with a broad signal, especially considering zero-field splitting.

Navigating EPR patterns

I'm assessing the EPR spectrum of [PW11O39(Mn-N3)]^{5-}, considering manganese's high spin and zero-field splitting, which might result in a broad spectrum with distinctive characteristic patterns.

Assessing EPR patterns

I'm digging into the EPR spectrum of [PW11O39(Mn-N3)]^{5-}, considering manganese's high spin and zero-field splitting, which might result in a broad spectrum with 10 hyperfine lines.

Wrapping up EPR insights

Taking a closer look at the EPR spectrum for [PW11O39(Mn-N3)]^{5-}, it seems straightforward such that the spectrum includes 6 hyperfine lines from 55Mn and is only observable at low temperatures.

Charting new territory

OK, let me see: the Mn oxidation state in the nitrido species is +5, the molecular orbitals are mapped with sigma and pi bonds, and the EPR spectrum is consistent with an S=2 system.

Clarifying the EPR spectrum

I’m thinking through that the EPR signal for the azide complex is likely a 6-line pattern from 55Mn hyperfine splitting, with the potential to see multiple sets of lines depending on zero-field splitting.

Assessing EPR implications

I'm curious about the EPR spectrum of [PW11O39(Mn-N3)]^{5-}. If the zero-field splitting is significant, the Mn(III) system might be EPR silent at X-band due to integer spin.

Examining EPR implications

I'm mapping out the EPR spectrum of [PW11O39(Mn-N3)]^{5-}, considering the stability of the nitrido species, and analyzing the result of the photolysis reaction.

Assessing EPR patterns

I'm examining the EPR spectrum for [PW11O39(Mn-N3)]^{5-} to determine if a broad signal makes sense, especially in light of advanced inorganic chemistry.

Thought about manganese nitride complex，持续 44 秒

Below is a structured outline of how one typically arrives at each of the answers. Note that many of these points hinge on “formal” oxidation‐state assignments and standard MO arguments for a linear (or nearly linear) M≡N multiple bond in $C_{4v}$ symmetry.

(i) Oxidation State and $d$-Electron Count

We are told that the complex $\{PW_{11}O_{39}(MnN)\}^{5-}$ is formed upon loss of $N_2$ from $\{PW_{11}O_{39}(Mn-N_3)\}^{5-}$. The polyanion “framework” $\{PW_{11}O_{39}\}$ is usually assigned a charge of $-7$.

1. Azide complex

   • Overall charge: $-5$.
   • Polyoxometalate (POM) fragment: $-7$.
   • Azide ($\mathrm{N_3^-}$) has a formal charge of $-1$.
   • Let the metal’s oxidation state be $x$. Then $$(-7) + (-1) + x \;=\; -5 \;\;\Longrightarrow\;\; x=+3.$$
   • Hence in the azide species, the manganese is formally Mn(III).
   • Manganese’s ground‐state electron configuration is $[\mathrm{Ar}]\,3d^5\,4s^2$. Removing 3 electrons gives $d^4$.

2. Nitrido complex

   • Overall charge: $-5$.
   • Polyoxometalate: $-7$.
   • A terminal nitrido ($\mathrm{N}^{3-}$) is assigned $-3$.
   • Let the oxidation state of Mn be $y$. Then $$(-7)\;+\;(-3)\;+\;y\;=\;-5 \;\;\Longrightarrow\;\; y=+5.$$
   • Therefore, in the nitrido complex, manganese is formally Mn(V) and thus has $d^2$ configuration.

Most questions about the “bonding” in a high‐valent metal–nitrido generally focus on the final Mn(V), $d^2$ state.

(ii) Partial MO Diagram for a Tetragonal $\mathrm{M}\equiv\mathrm{N}$ Bond

Take the $z$-axis along the M–N bond and use $C_{4v}$ symmetry. The key points:

• The nitrido ($\mathrm{N}^{3-}$) has three 2p orbitals (p$_x$, p$_y$, p$_z$) relevant for bonding.
• In a linear (or nearly linear) arrangement, $\mathrm{p}_z$ will be the $\sigma$-type orbital; $\mathrm{p}_x$ and $\mathrm{p}_y$ can serve as $\pi$-type orbitals.
• The metal $d$-orbitals split in $C_{4v}$ (with the z‐axis as the principal axis) into the following irreps: $$d_{z^2} \;\to\; A_1,\quad d_{x^2-y^2} \;\to\; B_1,\quad d_{xy} \;\to\; B_2,\quad (d_{xz},\,d_{yz}) \;\to\; E.$$
• The nitrido orbital that is along $z$ ($\mathrm{p}_z$) also transforms as $A_1$. Hence it $\sigma$-couples with the metal $d_{z^2}$.
• The pair ($\mathrm{p}_x$, $\mathrm{p}_y$) transforms as $E$. They form $\pi$-type bonds with the metal $d_{xz},\, d_{yz}$ (also $E$).
• The remaining metal orbitals, $d_{x^2-y^2}(B_1)$ and $d_{xy}(B_2)$, have no partner orbitals on the nitrido of the same symmetry and thus end up nonbonding in this simple view.

A common schematic (not to exact scale) is:

         -- (σ*) A1  <-- antibonding combination of d_z^2 & p_z
         -- (π*) E   <-- antibonding of d_xz/d_yz & p_x/p_y
   NB -->    B1      <-- d_x^2 - y^2
   NB -->    B2      <-- d_xy
         -- (π) E    <-- bonding of d_xz/d_yz & p_x/p_y
         -- (σ) A1   <-- bonding of d_z^2 & p_z

Labels “$\sigma$, \pi), or “NB” (non‐bonding) and the corresponding Mulliken symbols $A_1, E, B_1, B_2$ in $C_{4v}$ round out the diagram.

(iii) Mn–N Bond Order

From the simple MO picture above, a terminal metal–nitrido is typically described as having:

• One strong $\sigma$-bond (M $d_{z^2}$ with N $p_z$),
• Two $\pi$-bonds (M $(d_{xz}, d_{yz})$ with N $(p_x, p_y)$).

Hence the metal–nitrido linkage is conventionally considered to be a triple bond; so the formal bond order is 3.

(iv) Prediction of the EPR Spectrum of $\{PW_{11}O_{39}(Mn-N_3)\}^{5-}$

Here we focus on the azide complex, i.e. before photolysis to the nitrido. From part (i), the manganese in the azide complex is Mn(III), $d^4$. The question is the spin state and the resulting EPR behavior:

1. Likely High‐spin $d^4$.

   • In an octahedral or pseudo‐octahedral environment, high‐spin $d^4$ implies $S=2$.
   • Integer‐spin ($S=2$) complexes often exhibit significant zero‐field splitting (ZFS).

2. Zero‐field splitting and EPR

   • Because $S=2$ is an integer spin, it does not have simple Kramers degeneracy like half‐integer systems (e.g., $S=5/2$ in Mn(II)).
   • Large zero‐field splitting often pushes the EPR transitions outside the usual X‐band range or makes them very broad at room temperature.
   • As a result, many high‐spin Mn(III) complexes are “EPR‐silent” (or show only very broad, weak signals) under standard conditions.
   • If one cools the sample sufficiently and/or uses lower/higher microwave frequencies (Q‐band, etc.), sometimes partial signals are observed—but in a typical undergraduate‐level discussion, the simpler statement is that “the high‐spin $d^4$ Mn(III) complex is usually EPR‐silent at X‐band due to large zero‐field splitting.”

Hence the conventional textbook prediction is that $\{PW_{11}O_{39}(Mn-N_3)\}^{5-}$ (with Mn(III), $d^4$, $S=2$):

• Will be paramagnetic,
• But is likely EPR‐silent (or at most shows a very broad or complex signal) in normal X‐band due to the combination of integer spin and large zero‐field splitting.

Summary of Answers

1. Oxidation state and $d$-count (for the nitrido complex):

   $$\text{Mn is }+5,\quad d^2.$$

2. MO Diagram (tetragonal M≡N in $C_{4v}$):

   • $\sigma$-bond = $d_{z^2}(A_1) + p_z(A_1)$.
   • $\pi$-bonds = $(d_{xz}, d_{yz})(E) + (p_x, p_y)(E)$.
   • $d_{x^2 - y^2}(B_1)$ and $d_{xy}(B_2)$ = nonbonding (no match in symmetry with N p‐orbitals).

3. Mn–N bond order:

   $$3 \quad (\text{one }\sigma\text{ plus two }\pi\text{ bonds}).$$

4. EPR spectrum of $\{PW_{11}O_{39}(Mn-N_3)\}^{5-}$:

   • Mn(III), $d^4$, high‐spin ($S=2$).
   • Large zero‐field splitting typically leads to EPR silence (or only a broad signal) at standard X‐band frequencies.