Frank J. Coppola, a 37-year-old convicted murderer on Virginia's Death Row, is scheduled to die in the electric chair in Richmond late Tuesday night, becoming the first man to be executed in the state in 20 years and the fifth in the country since 1967.

Coppola, an ex-policeman and Catholic seminary student convicted in 1978 of the torture murder of a Newport News woman, asked for the execution last spring when, frustrated by a lengthy appeals process, he ordered his lawyers to drop his case. So far, he has also managed to prevent civil rights attorneys from intervening in the case to save his life.

Coppola's decision puts the politically sensitive matter before Gov. Charles S. Robb, who has the power either to stay the execution or to commute Coppola's sentence. So far, Robb, a supporter of the death penalty in the 1981 gubernatorial campaign, has given no indication he will do either.

Coppola was sentenced to death in 1978 after a jury found him guilty of murdering Muriel Hatchell. According to testimony given at the trial, Coppola struck Hatchell in the face and beat her head on the floor to get her to tell where money was hidden in her house. When police arrived, she was tied to a chair and already dead. Five of her front teeth were found scattered through the house, according to evidence presented by the prosecution.

Last March, Coppola, still maintaining his innocence as he has done all along, said he would rather be executed than stay on Death Row in Mecklenburg State Prison. "Further incarceration . . . can only lead to my being stripped of all personal dignity and continue to induce tremendous hardship on my family," he wrote in a letter to his attorneys.

Coppola's one request was that the execution date be set in the summer months, after the school term, to minimize the "traumatic effect my demise in this matter will have on my children who are of school age."

Robb, out of the state on a speaking tour in the West, is scheduled to return to Virginia at 8 p.m. Tuesday, three hours before Coppola's execution is scheduled. The governor's office is making sure Robb is available at a moment's notice, even on his flight home aboard a commercial airline, in case Coppola changes his mind and decides to fight the death sentence, a Robb spokesman said.

On Monday, a group of Virginia religious leaders, representing six major denominations, appealed to Robb on "moral and spiritual grounds" to halt the execution. A letter-writing campaign, initiated by clergy in the Richmond area and by national civil rights groups, is also gaining momentum. Robb's office has received about 125 letters urging him to stay the execution, most of them from members of Amnesty International. The clergy group sent another 640 letters to Richmond area churches and synagogues this week, asking for more letters opposing the death penalty. Former U.S. attorney general Ramsey Clark also wrote to Robb asking him to delay the execution.

Counteracting these lobbying efforts, some said, is the prevailing public opinion in Virginia in support of the death penalty. "It is probably the most no-win situation a politician could be in," said George Ricketts, one of the chief organizers in the interdenominational lobbying effort.

Several attorneys also plan to appeal to Robb on constitutional grounds, arguing that Virginia's death penalty law, adopted in 1977 to conform to Supreme Court standards, has not yet been fully tested in the federal courts. Another case, involving another of the 17 inmates awaiting the death sentence in Virginia, is pending in the Fourth U.S. Circuit Court, which includes Maryland and Virginia.

"Virginia's statute is unique," said Lloyd Snook, a Charlottesville attorney with five clients under sentence of death. "There are some central issues that have not been resolved . . . and ought to be explored in detail . . . . My feeling is that the interests of the Commonwealth are not best served by executing somebody just because he wants to be executed."

The Coppola case marks the second time in recent years that Virginia has come close to using the state penitentiary's massive oak electric chair, in which 236 men died between 1908 and 1962.

But unlike Death Row inmate Michael Girratano, who changed his mind 10 days before his scheduled execution date in 1980, Coppola has remained firm in his decision. "It is the judgment of most folks that the chances of this being stopped are very slim," said Ricketts, director of Chaplain Services, which provides ministers to Virginia prisons. "They say he is very adamant about this." Ricketts said Coppola, a Catholic, has refused to see a priest or to agree to allow one to be present at his execution.

"As recently as yesterday, his wife said he is holding true and fast, that he wants to go ahead and be executed," said Augustus Anninos, a Norfolk attorney who was fired by Coppola last April for failing to heed his wish to drop all legal appeals. Anninos plans to meet today with David McCloud, Robb's chief of staff, to outline some of the outstanding legal problems in Coppola's case.

"These are not delaying tactics," said Anninos, "They are real issues. The governor should be concerned about the state executing somebody where the law has not been properly construed or interpreted."

Despite Coppola's insistence that he die, civil rights lawyers have been frantically searching for some legal avenue to block the execution. The most promising approach is through a member of the prisoner's family who in a "next friend" suit asks the court to stop the execution. The approach has been used with mixed success in other cases.

So far, however, no member of Coppola's family has initiated the case. In fact, some who know Coppola said his family, including his mother, ex-wife and two teen-aged children, aged 13 and 14, have been as resolute as Coppola in sticking by his decision.

Attorneys said Coppola, described as "very smart" and articulate, has shown no overt signs of the mental instability that would warrant intervention against his wishes. "He's set and he's sane," said one American Civil Liberties official.