Ackerman's base salary was $348,140 annually.
Neither Nutter nor School District officials would identify the donors of the $405,000, which is to be channeled through a district-affiliated charity, Philadelphia's Children First Fund.
The nonprofit was established in 2003 to support the district. Board members include Ackerman, SRC Chairman Robert L. Archie Jr., and Ackerman's deputy and now interim superintendent, Leroy Nunery II.
They sit on the board with some of the city's leading philanthropists, including Sheldon M. Bonovitz, chairman emeritus of Duane Morris - where Archie is a partner - and Harold Honickman, the soda magnate.
Nutter insisted that the district spend no more than $500,000 to satisfy Ackerman's buyout, sources said. The mayor said he supported the private fund-raising effort and personally solicited donations "because my interest was minimizing the number of public dollars."
Archie did not return calls seeking comment.
Rep. Mike McGeehan (D., Phila.), an Ackerman critic, asked state Attorney General Linda Kelly to determine the buyout's legality.
"That we have private-interest money mixing with public interest flies in the face of 40 years of progress on transparency," McGeehan said. "The dome of the Capitol should be blowing off and if it isn't, shame on them."
Federal tax law prohibits someone from taking a deduction for a donation earmarked for a specific person, said attorney Laura Solomon, whose Laura Solomon & Associates in Wynnewood works exclusively on nonprofit law.
It is possible, she said, to have one or more donors designate funds for a school district's use, adding, "There is absolutely a legal way to do this."
As long as the organization receiving the contribution is a public charity, as Philadelphia's Children First is, the donations can remain anonymous, she said.
Laura Otten, executive director of the Nonprofit Center at La Salle University, questioned how the money would be funneled to Ackerman: Is the nonprofit accepting the donations or just serving as a pass-through? Is it taking a percentage?
"It smells to me," Otten said, since the district's $629 million budget shortfall led to mass layoffs this year.
"Philosophically, should private citizens be bailing out the government? I don't think so," she said. "To me, that's abhorrent."
The Committee of Seventy, the nonprofit government watchdog organization, called on the SRC to release the donors' names.
"The public has the same right to know the details of Ackerman's departure as it had to know the costs of bringing and keeping her here," said Zack Stalberg, the committee's president and CEO.
Although Gov. Corbett and Nutter may view the private funding as a favor to taxpayers, Stalberg said, the public may never know how that favor might be repaid.
"There is no compelling reason for the lack of transparency. If the donors are insisting upon it, find other donors," Stalberg said.
Paul Vallas, former School District CEO who was paid $180,000 when he left in 2007, blasted the deal.
"In this climate of fiscal distress, with huge layoffs of teachers and administrators, to offer anyone $900,000 not to work is unconscionable," Vallas said. "I think the people who agreed to this deal ought to have their heads examined."
Of the private donations, he said, "That's about as outrageous as it gets. If you are going to raise $400,000 in private money, give it to a school, for crying out loud."
Contact staff writer Susan Snyder at 215-854-4693 or firstname.lastname@example.org.
Inquirer staff writers Troy Graham, Bob Warner, and Amy Worden contributed to this article.