16-year-old Isobel Narayan found a drug used on death row prisoners in the US while scouting online forums about suicide.
The college student was found dead at her family home in Didsbury, Manchester, in December 2011 after taking the drugs delivered to her by post.
During an inquest hearing at Manchester Crown Court on Wednesday, coroner Nigel Meadows said he will write to the UK government's chief pharmaceutical officer to see if anything could be done to tighten regulations about access to harmful drugs.
He described the fact that she was able to access the drugs so easily as a matter of "public concern" and appealed to the "relevant authorities to try to minimise the risk of it happening again".
The teenager's father, Harry Narayan, a barrister and crown court recorder in Manchester, told the inquest his youngest daughter was top of her year in physics and was hoping to study to be a vet like her older sister Freya.
Her family said there was nothing to suggest she was unhappy.
Detective Inspector Kevin Marriott from Greater Manchester Police, who investigated the death, said searches of her computer found she had made inquiries about obtaining the drug.
It also revealed she suffered "misplaced" and "unfathomable" feelings of low self-esteem and worthlessness, the hearing was told.
The coroner said he had to record a verdict that Isobel killed herself.