Is it permissible for an accountant to accept a sum of money from a programmer with whom his company has contracted, under the pretext that it is for financial consultations, knowing that the accountant did not stipulate this amount or bargain for it in exchange for signing the contract?

It is not permissible to take this money except with the company's permission, because it is either in exchange for facilitating the contract with the programmer, in which case you are an agent for the company and are not entitled to take it without its permission. Or it is in exchange for financial consultations you provide to the programmer; if these consultations are part of your duties to your employer, or if they occur during official working hours, then you are not entitled to receive compensation except with the company's permission. However, if the consultations are outside official working hours and are not part of your duties, then there is no objection to accepting the money.