There you go,
Docrock got the spirit.
Now afcourse youre capital might be a good food city and/or start next to a mountain, and then you should build NC there. But as i said, there is a good probabilety that youre capital isn't so optimal for it, and there is a good probabilety that you will find better land nearby like jungle with a mountain if youre on liberty. In fact more likely there is a higher likelyhood that youll find a better spot outside youre capital if youre capitol didn't start near mountains to begin with, and very often indeed this comes to large patches of jungleland with a mountain, some hills and some bonusses around. I do have to note i play medium sized maps, but as i said before various settings can affect the game but this strategy is meant to be made for when the situation asks for it.
While it's true that the capitol will be older than the 2nd city and thus had more growth and production time, it's also so that the capitol will need to spend quite some growth and production on building settlers in liberty. The 2nd city will grow and typicly produce buildings while the capitol will be busy with such things like settlers and maybe also workers or units, in fact it might be possible for the 2nd city to overtake the capitol in size by the time it had finished building settlers, if planted in a good enough spot for that and focussed on growth early on and constructing granery and maybe even wattermill, stables, stonemassonry or lighthouse depending whats around, such might not be too hard to do.
Indeed, it has quite often happened for me in liberty to see my second city overtake my capitol, and it's easily understood by the size i aimed my capitol to grow for production vs time constraints to build the amount of settlers i need. The more settlers i need, the more time my 2nd city has to overtake my capitol.
And then, interrestingly enough it seems to me that this shouldn't even be so much an issue to see this 2nd NC city overtake youre capitol. If it's going to be the best city for NC, all the better that it has more pops than other city's in regards to the happyness you have. So this would allow one to focus somewhat more on production in his capitol than wanting it to grow so much early on, thus easier to use it for building workers, settlers, units, caravans and wonders. Even not needing to build NC in youre capitol allows it to use the production it would have needed for it on a wonder, although its fair to say that because of slower growth that in a longer terms the capitol would have less of a productional advantage versus youre NC city, but it could be valuable for a liberty player to have his capitol "more free" for production early on.
Right, and then you could make trading posts on the jungles for more science when you have the university and the observatory for being next to a mountain.
Indeed the optimal spot for an NC city would seem like jungle with bonusses and a mountain and maybe a bit of other land around, and hey maybe even a river to top it off. I have tried restarting civ for 10x and then scounting the land around, and in most cases i can find a far better NC spot outside the capitol atleast on pangea. Let alone for those damn Tundra or dessert starts lol.
You would then run youre caravans to that city instead and make it maximize growth compared to other city's who might get get a production focus if hapyness is short, and when the appropiate tech would come around you would improve all those sweet jungle tiles and make the city balloon to a science heaven.