Well... it's complicated. To put it shortly, nobody can really agree on this. It depends on whether you're asking a revisionist historian or one with a more traditional interpretation, what aspect of the state you're talking about, and so on.

The traditional historiographical view goes thusly: the initial invasions killed millions of people and devasted the country. Hulegu's invasions only worsened this, killing millions more and annhilating Baghdad, ending the Golden Age of Islam. The following thirty or forty years was marked by rapacious tax-gathering which took everything the inhabitants of Persia did not physically need to survive, the neglecting of all the agricultural networks and facilities and generally a rule of misery, theft and neglect. Then, in 1295, the Il-khan Ghazan took the throne and, with the help of his vizier Rashid al-Din, enacted sweeping reforms which ushered in a sort of golden age, with the country recovering to a degree until the state's collapse in 1335.

The trouble is that this historiographical position is rather dubious and suspect. It's effectively a mix of Islamic historiography from Rashid al-Din's perspective and the traditional view of the barbaric, destructive Mongols, which I doubt will ever be totally shaken off. Revisionist historians- perhaps most notably George Lane- have attempted to change this view, but have only met with partial success- Lane's most notable book on the matter, "Early Mongol Rule in 13th Century Iran: A Persian Renaissance" has a good core theory (that the early Ilkhans were actually rather better and less destructive leaders than are supposed) but betrays itself by taking its point too far, with some dodgy source interpretations used to fit every fact into his core thesis.

The truth is probably a mixture of positions. Rashid al-Din's assertion that Ghazan's reforms and conversion ushered in a new golden age when compared to the pagan and Buddhist rulers before him has been taken for granted too much, as have wildly inflationary accounts of Mongol destruction, but at the same time it was undeniably a harsh time for some.

Baghdad's sack was violent and destructive, but it was not the total calamity it is described as. The city regained prosperity in a few years, non-Muslims were all spared the sword, and it certainly wasn't the end of the Golden Age of Islam- politically that had ended long ago, and intellectually it had either also ended long before or wouldn't end for another three centuries or so, depending on who you ask. Though an important library, there were many other repositories of knowledge throughout the Middle East, and not so much was really lost. And the Mongols did much to revive learning and culture too- they were active patrons of the arts and sciences, as Tusi's great observatory, the architectural innovations and the artistic exchange aptly demonstrate. It has been argued, indeed, that their destruction of the caliph helped the entire Islamic world politically too- cut off from the old, degenerate Caliphal systems of legitimacy, imperial and Mongol forms of governance came in to replace them, resulting in the glorious era of the great Islamic empires of the Ottomans, Mughals, Uzbeks and Safavids. Greater heterodoxy was introduced into Islam as well, cut off from a beacon of controlling orthodoxy; this resulted in an upsurge of Sufism and theological debate.

The Ilkhans, like all Mongols, encouraged tolerance and favoured many different religions, even to an extent after their conversion to native faiths of the sedentary peoples; their administration was meritocratic, and great literary and historical works were produced under their auspices (the Compendium of Chronicles and Rumi's poetry both spring to mind). Merchants were protected and encouraged, which along with the Pax Mongolica and the links between the two Toluid courts, led to the final resurgence of the Silk Road and the further enhancement of the sea route. Cultural exchange between China and Iran therefore existed on an unparalled level, in the field of art, architecture, cuisine, medicine, astronomy and so on- Thomas Allsen wrote an excellent (and rather important) book on the matter called "Culture and Conquest in Mongol Eurasia", which details the many kinds exchange which took place between east and west under the Mongols.

When put like this, the Ilkhanate seems almost like a golden age; but this is not the whole story either. While the above is true, the neglect of the qamat agricultural systems would cause lasting damage, and it is still true that (at least before Ghazan) the primary purpose the Mongols had for Persia was as a source of money. And while the initial destruction was not anywhere near as bad as is often supposed (in my view, anyway), it was still destructive, with some cities being abandoned and others never quite reaching their former glory again.

So, to sum up, the Ilkhanate would not have been a wonderful time to live in for the average Persian, but it would not quite have been the squalid dark age it is commonly supposed to be. And the cultural, ideological and intellectual developments of the period set the stage for the great empires which would arise in the centuries to follow.

can you elaborate a bit more ? how does one define "the darkest" period ?