Richards, hunting his first Olympic Games medal, finished second in semi-final one in 44.33s, behind American Quincy Hall, who won in 43.95s.
James, a three-time Olympic medallist in the event, seems poised to add to his tally as he rekindled his form of old with a blistering season’s best 43.78s clocking in winning semi-final two. It was just outside his personal best of 43.74s.
Meanwhile, Jamaica’s lone semi-finalist, Jevaughn Powell (44.91s), produced a gallant performance for fourth in semi-final three, but it was not enough to progress.
The other finalists are Great Britain’s Matthew Hudson-Smith (44.07s), American Michael Norman (44.26s), and Christopher Bailey (44.31s), as well as Zambia’s Muzala Samukonga (43.81) and Samuel Ogazi (44.71s) of Nigeria.
The final is scheduled for Wednesday August 7.
Parchment sped to a season’s best mark 13.15 for victory in the Men’s 110m hurdles ahead of the USA's current world leader Devon Allen (13.20) and Jamal Britt (13.30).
The Women’s 100m hurdles was won by the USA’s Alaysha Johnson in 12.50 ahead of Puerto Rican Olympic champion Jasmine Camacho-Quinn (12.52) and Jamaican 2015 World champion Danielle Williams (12.67).
Double Olympic sprint champion Thompson-Herah cruised to victory in the Women’s 100m in 10.93 ahead of Trinidad & Tobago’s Michelle Lee-Ahye (11.06) and the USA’s Shania Collins (11.08).
Bahamian reigning Olympic and World 400m champion Steven Gardiner won the Men’s 300m in 31.52 ahead of the USA’s Vernon Norwood (31.81) and Jamaica’s Nathon Allen (32.04).
2011 World and 2012 Olympic 400m champion Kirani James of Grenada was victorious in the Men’s one-lap event in a season’s best 44.70 ahead of Jamaica’s Sean Bailey (45.42) and the USA’s Trevor Stewart (45.50).
Jamaica’s Junelle Bromfield was third in the Women’s equivalent in 51.82 behind Americans Gabby Scott (51.42) and Olympic 800m champion Athing Mu (50.42).
Moving to the 400m hurdles, Jamaica’s Janieve Russell ran a season’s best 54.09 to win ahead of teammates Shiann Salmon (54.43) and Rushell Clayton (54.90).
In the field, Jamal Wilson of the Bahamas was victorious in the Men’s high jump with 2.22m ahead of the USA’s Jeron Robinson (2.17m) and Puerto Rico’s Luis Castro Rivera (2.17m).
Women’s 4x400 Metres
Cuba and Jamaica both advanced to the final.
The Cuban team of Zurian Hechevarria, Rose Mary Almanza, Sahily Diago and Lisneidy Veitia ran 3:24.04 to finish second in heat 1.
Junelle Bromfield, Roniesha McGregor, Janieve Russell and Stacey Ann Williams formed the Jamaican quartet that finished second in heat 2 to advance with 3:21.95.
The Bahamas quartet of Doneisha Anderson
Megan Moss, Brianne Bethel and Anthonique Strachan also competed in heat 1 but did not finish the race.
Men’s 400 Metres
The Caribbean secured two more medals in the men’s 400 metres.
Bahamian Steven Gardiner won gold in a time of 43.85 and Grenada’s Kirani James secured bronze in 44.19.
This is Gardiner’s second straight global gold medal after winning at the 2019 Doha World Championships.
James has now won 400 metres medals at the last three Olympics after winning gold in London in 2012 and silver in Rio 2016.
Jamaica’s Christopher Taylor was also in the final and finished sixth in a new personal best 44.79.
Antonio Watson was first up and set the track ablaze with a massive personal best 44.13 to take semi-final one over the likes of South African world record holder Wayde Van Niekerk and American Vernon Norwood.
Norwood ran a personal best of his own with 44.26 for second while Van Niekerk ran 44.65 in third and Jereem Richards ran 44.76 in fourth.
Van Niekerk made it through to the final as one of the fastest losers while Richards was just beaten out Norway’s Havard Bentdal Ingvaldsen who ran 44.70 in heat two.
Great Britain’s Matthew Hudson Smith won the second semi-final in a personal best, British and European record 44.26 ahead of 2011 World Champion Kirani James who ran 44.58.
Unfortunately, reigning Olympic Champion Steven Gardiner looked set to book his spot in the final before pulling up injured while leading with about 100m to go in the third semi-final.
The race was eventually won by American Quincy Hall in 44.43 while Jamaica’s Sean Bailey also made it through to the final with 44.94.