Mercury(I) nitrite

Only a few Hg(I) mercurous compound is known. They contain the mercurous ion (Hg-Hg)2+, not Hg+. The two Hg atoms are bonded together using the 6s orbitals. Mercury is unique in forming stable dinuclear metal ions. At Hg(+I) state, it consists of two directly linked metal atoms. The mercurous ion thus has the structure [Hg-Hg]2+. Evidence for this comes from several sources:
1. X-ray diffraction
The crystal structures of several mercurous compounds have been determined by X-ray diffraction. For example, consider Hg(I)Cl. If the compounds comprised Hg+ and Cl- the structure should contain alternate Hg+ and Cl- ions, in fact it isn't, it have a linear arrangement of Cl-Hg-Hg-Cl. Other Hg(I) compounds also have similar structure. The Hg-Hg bond length varies in different compounds: Hg2F2 2.51A, Hg2Cl2 2.53A, Hg2Br2 2.49A, Hg2I2 2.69A, Hg2(NO3)2.2H2O 2.54A, Hg2SO4 2.50A. These are all much shorter than the Hg-Hg distance of 3.0A in solid mercury.

2. Equilibrium constant
Equilibrium constants can be measured and provide evident about thespecies present. Mercurous compounds can often be made from the corresponding mercuric compound by treatment with mercury. If the reaction is
Hg(NO3)2 + Hg --> 2HgNO3
Hg2+ + Hg --> 2Hg+
then by the law of mass action
[Hg+]^2/[Hg2+] = constant.
Experiments have shown this to be untrue. If, however:
Hg2+ + Hg --> [Hg2]2+ then [Hg2]2+/[Hg2+] = constant.
This has been verified experimentally, thus proving that mercurous ions are [Hg2]2+, that is (Hg-Hg)2+.

3. Concentration cell
Measurement of the e.m.f. of a concentration cell of mercurois nitrate shows that the mercurous ion carries two positive charges.
For the cell below, the potential Eo was measured and found to be 0.029C at 25 deg C.
Hg | A | B | Hg
where A is 0.005M mercurous nitrate in M/10 HNO3 and B is 0.05M mercurous nitrate in M/10 HNO3
E = [2.303RT/(nF)] * lg (cb / ca)
0.029=(0.059/n) * log (0.05/0.005)
n = 2
Thus confirming [Hg2]2+.

4. Magnetic properties
All mercurous compounds are diamagnetic both in the solid state and in solution. Hg+ (if exist) would have an unpaired electron and would be paramagnetic, but in [Hg2]2+ the electrons are all paired and it should therefore be diamagnetic.

5. Raman spectra
The Raman spectrum for mercurcous nitrate contains the lines characteristic of the [NO3]- group. Similar lines appear in the spectra of many other nitrates. Mercurcous nitrate has an extra line in the spectrum at 171.7cm-1 which is attributed to the Hg-Hg bond. Homonuclear stretching of a diatomic species is Raman active but not infra-red active. This was the first example of Raman spectra identifying a new species.

6. Cryosopic measurements
The depression of freezing point produced depends on the number of particles dissolved in the liquid. The observed depression fits for mercurous nitrate ionizing into [Hg2]2+ and two [NO3]- ions, not into Hg+ and [NO3]-.

In simple quantitative analysis, you can take HgR instead of Hg2R2 for simplicity (in calculation), but you have to be cautious that Hg+ is not likely to exist (at least in normal condition for observation).
I hope this can help your understanding. :)