Why did Napoleon march on Moscow instead of St. Petersburg which was the capital at the time?

Please correct me if I am wrong, but wasn't Moscow not even Napoleon's original objective? If I remember correctly, Napoleon's main goal/hope was to catch the Russian army, fight a battle, win, destroy the Russian army and force Alexander to negotiate/surrender.

Napoleon's first objective was taking Vilnius. When he took Vilnius without having caught the Russian army, he decided to move straight into Russian territory in the direction of Moscow, hoping that this would cause Alexander to lose his nerves. By the time he took Vitebsk, however, nothing had changed. I think Napoleon's subordinates were urging him to stop at Vitebsk (they were well aware that the land would only get more desolate at this point, and it was getting late in the season, and they also knew full well it would be a disaster if they were caught by the winter), but Napoleon saw this as admitting defeat and by this point in time he had begun to show some....delusional (for lack of better word) tendencies, believing in his own glory a bit too much. So he marched on.

He then reached Smolensk and again his subordinates urged strongly to halt the campaign and dig in for the winter, but Napoleon, perhaps realizing, too late, that he had overstretched himself and put his army in a very dangerous situation, only became more and more desperate to catch the Russian army and/or force Alexander to negotiate in a reckless attempt to salvage what was quickly becoming an extraordinarily costly campaign (basically an all-or-nothing maneuvre). So, he made the decision to continue towards Moscow.

In the end, Napoleon's last, desperate gamble almost paid off. The Russian commander responsible for the strategy of constant retreat, Barclay, had refused to change his tactics despite the ever increasing pressure on him from Russian patriots who felt it was a cowardly tactic. This pressure finally caused Alexander to replace Barclay with the old legend Kutuzov when Napoleon marched on Moscow. And just as Napoleon had hoped for the entire duration of the campaign, Kutuzov offered battle at Borodino.

But at Borodino, Napoleon...basically fell apart. It is difficult to say what happened to him. It is known that he was suffering from physical ailments as well as possible depression at the time, but we can only guess at how much influence such things had on the course of events at Borodino. Napoleon and his generals arguably made mistakes at Borodino, and while at the end of the day the French emerged victorious, it was a hollow victory, as the vast majority of the Russian army had been able to extricate itself from the battlefield intact. In other words, the decisive victory that Napoleon needed at that time - the only thing that could have saved his campaign at that point - failed to emerge at Borodino.

As for why Napoleon did not go to St. Petersburg, I have no literary knowledge on this question, but I would assume that since St. Petersburg itself was, despite it being the administrative capital of Russia, located at the periphery of the Empire, marching on it would not have gained Napoleon that much when compared to marching right into the heart of Russia from where he could theoretically do more damage. Furthermore, Napoleon marched from city to city - from Vilnius to Vitebsk to Smolensk. Once at Smolensk, Moscow had become a much more logical next objective compared to St. Petersburg.

Edit: my source is: Russia Against Napoleon: The Battle for Europe, 1807 to 1814, by Dominic Lieven(2009).

2nd Edit: I just remember that the part about Napoleon at Borodino is from Robert Harvey's The War of Wars.