I am seeing images of tetrazolate ion where the negative charge is placed at different locations:
or 
Is there any electronic charge distribution calculation done on this anion to confirm where is the negative charge situated? Is resonance playing a part?
(Final update at end - TLDR: I did a Bader aka Atoms in Molecules analysis)
I did a quick run with CRYSTAL23, a local basis set code that concentrates on periodic structures rather than isolated molecules (disclaimer: I am an author of CRYSTAL) on a structure for the tetramethylammonium salt found on the Cambridge Structural Database. I have put CIF file, the input for the run, and the output on bitbucket in a git repository
Firstly note this is about the quickest calculation I can do. Should time, effort and willingness permit I want to check the computational parameters, where I have essentially just used the defaults, the basis set, and especially I would want to do a geometry optimization rather than just an SCF at the experimental geometry. However I would hope the single point SCF will get the essence.
The CIF reports a P-1 structure. In the cell the "left" hand side of the ion is related to the right by an inversion. CRYSTAL pairs the atoms off such that the odd numbered atom N is related by the inversion to the even numbered atom N+1. Due to the symmetry we only need look at the odd numbered atoms. Here is the numbering (but I need to check I have 5<->7 and 9<->11 the right way around, but it doesn't really change the discussion if I haven't)
Atom number 1 is the nitrogen in the tetramethylammonium counter anion.
For the calculation I have used a triple zeta POB basis set, and uses the B3LYP DFT functional. The shrinking factor for the Monkhorst k-point net is 2, resulting in 8 k points - if I come back to this I would want to investigate increasing that to check convergence.
Here are the electronic Mulliken charges as reported by CRYSTAL for the relevant atoms. To get the formal charge on the "atom" you have to subtract that from the nuclear charge:
ALPHA+BETA ELECTRONS
MULLIKEN POPULATION ANALYSIS - NO. OF ELECTRONS 168.000000
ATOM Z CHARGE A.O. POPULATION
3 N 7 7.314 0.819 1.153 0.738 0.748 0.414 0.510 0.586 0.480
0.512 0.669 0.156 0.159 0.232 0.038 0.022 0.035
0.023 0.020
5 N 7 7.436 0.819 1.153 0.734 0.754 0.481 0.555 0.480 0.548
0.595 0.511 0.245 0.268 0.159 0.030 0.031 0.043
0.016 0.015
7 N 7 7.380 0.819 1.153 0.737 0.733 0.471 0.536 0.510 0.540
0.578 0.528 0.212 0.207 0.232 0.035 0.023 0.030
0.022 0.015
9 N 7 7.156 0.819 1.152 0.749 0.708 0.483 0.541 0.455 0.542
0.558 0.474 0.194 0.208 0.139 0.037 0.029 0.034
0.016 0.015
11 N 7 7.193 0.819 1.152 0.750 0.726 0.441 0.437 0.597 0.510
0.470 0.593 0.166 0.150 0.249 0.021 0.024 0.041
0.027 0.021
13 C 6 5.319 0.854 1.119 0.735 0.296 0.404 0.443 0.449 0.101
0.093 0.077 0.339 0.183 0.069 0.048 0.025 0.044
0.020 0.020
It can be seen that using the Mulliken charges the carbon has a charge of about +0.7e, while all the nitrogens are negatively charged, with a small concentration of the charge on atoms 5, 7, and 3. The total charge on this half of the ion is ~-0.8e. Mulliken charges have many drawbacks, so take this with a pinch of a salt, but this suggests that of the descriptions mentioned in the question number 2 is most consistent with these results.
I let the geometry optimization run through the day, also increasing the shrinking factor to 4 for better k point sampling, and changing the DFT function to B3LYP-D3 to include semi-empirical corrections for non-bonded interactions.The GitHub repository has had the new files added to it.
In practice the optimization made only a very small difference to the structure. For instance the initial lattice parameters are
LATTICE PARAMETERS (ANGSTROMS AND DEGREES) - PRIMITIVE CELL
A B C ALPHA BETA GAMMA VOLUME
5.65440 8.19370 9.22620 99.80700 92.70200 99.24400 414.516015
while the final one for the optimized structure are
LATTICE PARAMETERS (ANGSTROMS AND DEGREES) - BOHR = 0.5291772083 ANGSTROM
PRIMITIVE CELL - CENTRING CODE 1/0 VOLUME= 389.474865 - DENSITY 1.331 g/cm^3
A B C ALPHA BETA GAMMA
5.55974580 7.98775603 9.08121415 99.559810 92.668200 100.741178
and this is reflected by only a small change in the Mulliken charges:
3 N 7 7.302 0.819 1.153 0.736 0.749 0.423 0.491 0.593 0.489
0.513 0.667 0.153 0.152 0.227 0.038 0.023 0.033
0.024 0.019
5 N 7 7.437 0.819 1.153 0.736 0.779 0.484 0.541 0.475 0.552
0.590 0.519 0.240 0.254 0.160 0.030 0.032 0.041
0.017 0.015
7 N 7 7.374 0.819 1.153 0.738 0.756 0.473 0.523 0.508 0.546
0.575 0.536 0.205 0.201 0.216 0.036 0.023 0.029
0.023 0.015
9 N 7 7.139 0.820 1.152 0.752 0.749 0.484 0.529 0.446 0.547
0.561 0.471 0.188 0.187 0.123 0.036 0.030 0.035
0.016 0.014
11 N 7 7.186 0.820 1.152 0.753 0.766 0.435 0.429 0.589 0.509
0.475 0.591 0.160 0.143 0.230 0.020 0.026 0.040
0.027 0.020
13 C 6 5.309 0.854 1.119 0.735 0.282 0.405 0.433 0.449 0.099
0.093 0.076 0.332 0.205 0.070 0.049 0.026 0.042
0.018 0.020
These are essentially the same as before.
Due to the use the deficiencies of the Mulliken Population analysis I have now also performed a Bader aka Atoms In Molecules population analysis, this being considered the "gold standard" for this kind of thing, see e.g. Which one, Mulliken charge distribution and NBO, is more reliable?.
Here are the results for the atoms of interest, comparing the Mulliken and Bader results:
It can be seen that the Bader results roughly follow the Mulliken ones, with in general the Bader results showing a greater degree of charge separation than the Mulliken ones. Thus the conclusion above does not change, model 2 with the charge delocalised around the ring and onto the pendant nitrogen is the one most consistent with these results.
