Molinari, who has finished in the top ten in each of the past three years at Wentworth Club, followed his flawless opening round of 65 by dropping two shots in the first three holes of his second round, but hit back strongly with five birdies to move to ten under par for the tournament.
"I'm really happy," said the Italian. "The start is really tricky, with the first three holes. I think I played them okay. My chipping wasn't good enough on the first and on the third to save par. I managed to steady the ship and made a few birdies coming in at the end, so it is a good day.
"I enjoy playing here. I've played well the last few years. There's a bit of good Italian karma here with (Costantino) Rocca winning and Matteo (Manassero) winning a few years ago."
The round of the day belonged to Korean rookie An, who opened with five birdies in his first seven holes, before picking up three more shots on the back nine to surge through the field and into second place on nine under par.
An, a former US Amateur Champion who graduated via the Challenge Tour in 2014, has already recorded three top tens in his rookie season and further conformed his promise with such a great round over the West Course at Wentworth.
Argentine Emiliano Grillo posted two eagles on the back nine - on the 12th and 18th holes "“ in a seven under par round of 65 to sit two shots back in a share of third place with Thongchai Jaidee at the halfway mark.
Thai Jaidee carded six birdies in his bogey-free round of 66, while a shot further back is Englishman James Morrison, winner of last week's Open de EspaÃƒÂ±a, who continued his good form with a round of 66 to lie three shots off the pace in fifth position.
The biggest story of the day was the missed cut by pre tournament favourite, world number one and defending champion, Rory McIlroy, who missed the cut by four shots after a second round of 78 which included a closing nine of 42.
"I'm not angry," said McIlroy. "A little disappointed I'm not going to be here for the weekend, but if there was any weekend to miss, coming off the back of three good weeks in the States, I'm probably in need of a little bit of a rest. As I said, I'd still rather be here but it's not all bad getting to go home for the weekend."
The leading Australians through 36 holes are Marcus Fraser and Richard Green, both at 1 under and in a share of 36th position and nine shots from the lead.
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