Liem (Elo 2,744) lost to the U.S.’s Levon Aronian, drew with Poland's Jan-Krzysztof Duda and China's Ding Liren and lost again to the Netherlands’s Anish Giri.
In his fifth match the 29-year-old played with white pieces and beat Russia's Sergey Karjakin.
At the end of the first day on Monday morning Hanoi time, he was in 11th place in the 16-player Swiss league.
Giri currently leads with four points after beating Liem, Karjakin and India's Vidit Gujrathi and drawing with Frenchman Maxime Vachier-Lagrave and American Hikaru Nakamura.
Norway's Magnus Carlsen, the world champion, was in second place with 3.5 points by winning four.
Liem plays Nakamura, Vachier-Lagrave, Gujrathi, the U.S’s Wesley So and Russia’s Peter Svidler on the second day which begins on Tuesday morning.
According to the tournament format, the time control is 15 minutes per player for the whole game. The players get 10 seconds added to the clock for every move they make. Eight will qualify for the knock-out round.
The event, which ends December 1, is part of a series of 10 online tournaments in the Champions Chess Tour featuring the world’s elite players and has prize money of $1.5 million.