WASHINGTON — On July 28, Diana Toebbe posted a Fb message on the lookout for a babysitter to care for her youngsters early on the approaching Saturday morning for 5 to 6 hours.

Later the put up, seen solely to mates, was up to date with the phrase “*FOUND*.” And on that Saturday, Ms. Toebbe accompanied her husband, Jonathan, to south-central Pennsylvania.

Unbeknown to Ms. Toebbe, she and her husband have been being watched by the F.B.I. as they left their residence in Annapolis, Md. And the bureau’s brokers continued to observe in Pennsylvania as Jonathan Toebbe faraway from his shorts pocket a 32-gigabyte reminiscence card hidden in a sealed Band-Support wrapper, which he then, in line with court papers, positioned in a container arrange by an undercover F.B.I. operative.

The Toebbes, accused by the U.S. authorities of trying to sell some of America’s most closely guarded submarine propulsion secrets to a overseas authorities, are scheduled to look in federal court docket in West Virginia on Tuesday. They are going to face costs associated to violating the Atomic Power Act’s prohibition on sharing nuclear know-how.

For now, the large questions surrounding the couple — what nation they’re accused of attempting to promote the nuclear secrets and techniques to, and what motivated them to take the chance — stay unanswered.

Mr. Toebbe was described by acquaintances as a diligent and arranged grad pupil in nuclear physics who was commissioned within the Navy as an officer and skilled in submarine propulsion. He continued as a civilian within the Navy after ending his army service, thought-about by some a plum project for essentially the most gifted nuclear physicists.

Ms. Toebbe was a 10-year veteran of the Key College, a progressive personal faculty in Annapolis, the place she taught historical past and English. There, in line with mother and father, she was susceptible to speaking about her Ph.D. in anthropology from Emory College and her love of knitting. She was a revered adviser, each formally and informally, on the faculty.

“You might simply inform she was insanely good,” mentioned Craig Martien, 20, a 2019 graduate of Key College who labored intently with Ms. Toebbe on the yearbook and an after-school anthropology membership. “She was very pleasant and down-to-earth, and I bought alongside along with her very nicely.”

When Mr. Martien went off to Williams School, he introduced alongside a toy squid that Ms. Toebbe had knitted. Like different Key graduates, Mr. Martien described her as a powerful feminist and really liberal.

She was greatly surprised by President Donald J. Trump’s 2016 election, he mentioned, and talked about a number of occasions that she was contemplating transferring to Australia.

“She mentioned she couldn’t stand the present state of politics and really had discovered some job alternatives over there,” he mentioned.

On social media platforms, Ms. Toebbe shared pictures of her canine, her youngsters, meals cooking on the range, a household trip and selfies — strange scenes of an strange life, one far completely different than the novice cloak-and-dagger act portrayed within the F.B.I. affidavit.

Having made contact with the as-yet undisclosed different nation about offering submarine secrets and techniques, the Toebbes have been reluctant to reveal themselves in an in-person assembly, in line with the narrative specified by court docket paperwork by the F.B.I. However their obvious need for cryptocurrency funds led them to comply with the undercover operative’s demand they deposit data in a useless drop location — a choice that in the end uncovered their identification to the F.B.I.

Proof within the court docket paperwork suggests the overseas nation the Toebbes allegedly tried to promote the data to was an ally, or not less than one thing of a accomplice, because it cooperated with the F.B.I. because the sting operation unfolded. Whereas some specialists speculated France may have been the goal, French officers mentioned they weren’t concerned within the incident.

The listening to on Tuesday might be brief. As far as the federal government is aware of, neither Jonathan nor Diana Toebbe has a lawyer. Prosecutors requested the court docket on Monday to carry Mr. Toebbe quite than granting him bail, saying he may face life in jail and was a flight risk. The Justice of the Peace choose may additionally set a listening to date for the couple’s continued detention.

Public data searches turned up no indicators of economic misery that would present a motivation for them to attempt to promote American secrets and techniques.

But the F.B.I. affidavit portrayed the couple as keen to take dangers for the promise of funds in a cryptocurrency known as Monero.

In February, F.B.I. brokers, posing as a consultant of the overseas nation, proposed an in-person assembly. The response, which was signed “Alice,” a standard placeholder title in army cryptography, wrote that “nose to nose conferences are very dangerous for me, as I’m positive you perceive,” in line with the affidavit. The author then proposed passing data electronically in alternate for $100,000 within the cryptocurrency.

“Please bear in mind I’m risking my life in your profit and I’ve taken step one. Please assist me belief you totally,” the word to the undercover F.B.I. brokers learn.

The F.B.I. brokers then pressed for a impartial drop location. The response got here just a few days later: “I’m involved that utilizing a useless drop location your buddy prepares makes me very susceptible,” the word from “Alice” mentioned, in line with the affidavit. “If different events are observing the placement, I might be unable to detect them. I’m not an expert, and don’t have a staff supporting me.”

The word went on to suggest that the author would select a drop location for the encrypted recordsdata. The F.B.I. brokers responded that they might give first $10,000 then $20,000 in cryptocurrency at a drop location of their selecting.

“I’m sorry to be so cussed and untrusting, however I can not comply with go to a location of your selecting,” the response from “Alice” mentioned. “I need to take into account the likelihood that I’m speaking with an adversary who has intercepted my first message and is trying to reveal me.”

The author subsequent proposed that the nation present reassurance by sending a sign from its complicated in Washington over Memorial Day weekend.

Writing from an encrypted Proton mail account, “Alice” mentioned the sign had been acquired, and agreed to drop the fabric on the location chosen by the undercover operative — a mistake in tradecraft, some specialists mentioned.

“It was considerably stunning that somebody who has studied submarine warfare follows the F.B.I.’s route to floor for these supposedly clandestine drop offs,” mentioned Michael Atkinson, a former inspector common for the intelligence neighborhood.

The willingness on the a part of the nation to convey the unspecified sign suggests its cooperation with the USA all through the investigation. Mr. Atkinson mentioned it was very uncommon for a overseas nation to permit its embassy or different facility for use to ship a sign to a suspect being pursued by the F.B.I.

Mr. Atkinson, now a accomplice on the regulation agency Crowell & Moring, mentioned the same false flag operation by the F.B.I. involving a authorities scientist attempting to promote secrets and techniques to an ally resulted in a jail sentence of 13 years after a plea discount.

On the Key College, the place Ms. Toebbe taught, and of their Annapolis neighborhood, colleagues, college students and neighbors tried to course of the arrest of the couple and the accusations in opposition to them.

Luke Koerschner, 20, a 2019 Key College graduate now at Michigan State College, was in Ms. Toebbe’s advisory group for 4 years. He described her as “very pleasant and welcoming,” an outgoing instructor who cherished to cheer on her college students within the faculty’s cornhole tournaments.

Matthew Nespole, the top of the Key College, mentioned he was “shocked and appalled” to study of the costs in opposition to the Toebbes and that the college “helps the administration of justice by the F.B.I. and NCIS, and can cooperate with the investigation.” The Key College positioned Ms. Toebbe on depart indefinitely.

Julian E. Barnes reported from Washington, and Brenda Wintrode and JoAnna Daemmrich from Annapolis, Md. Kitty Bennett contributed analysis. David E. Sanger contributed reporting from Washington.