When American and Soviet scientists met in Washington, D.C., last fall to compare notes at a conference on ''The World After Nuclear War,'' they may not have known that a relatively small foundation in Cleveland gave money to help make their conference possible.
Like Cleveland's Gund Foundation, philanthropic foundations across the United States are responding to the specter of nuclear war with stepped-up support for arms control research and East-West tension reduction.
Foundation officials say heightened interest in the issue stems from the chill gripping US-Soviet relations and increased international tension in the wake of new US missiles in Western Europe, the Soviet destruction of the Korean airliner in September, and conflict in the Middle East. Also playing a role were President Reagan's speech on what has been dubbed ''Star Wars'' weaponry, and the televised movie ''The Day After,'' which attempted to dramatize the aftermath of a nuclear strike.
''To put it simply, much of the concern is a result of US-Soviet relations, which have gotten pretty lousy,'' says Frederic Mosher, a program officer at the Carnegie Corporation.
At the same time, some observers see a new dimension to much of the arms control research being funded. William Martel, a defense analyst in Cambridge, Mass., says there is less emphasis on ''counting warheads and targets'' and more on analyzing the reasons for war and how it might be stopped. Analysts are ''beginning to ask the nonempirical, less strategic questions, and looking more into political and social questions in the process of nuclear war.''
The major new effort in this area comes from the Carnegie Corporation, which recently announced it would award more than $5 million annually to foster a variety of projects - initially in the academic world - aimed at helping to prevent a nuclear holocaust.
A small number of universities with established records in the field are the principal beneficiaries of the larger foundations. The University of California at Berkeley and Stanford University, for example, are among institutions receiving grants from the Rockefeller Foundation to develop a joint program for the study of Soviet behavior in international affairs.
The Ford Foundation, which has awarded $33 million for research and training in arms control and international security over the past quarter-century, this week announced grants amounting to $3.7 million to 16 institutions in the US and abroad for continued work in peace and international security.
But many smaller foundations are also taking part in the new push. Some emphasize support to regional or grass-roots organizations seeking to educate the public on the nuclear threat. Others, like the C.S. Fund in Santa Rosa, Calif., prefer to support experts probing what might be termed ''progressive'' directions in war-prevention studies. (The C.S. Fund is one of several foundations run by heirs of the late Charles Stuart Mott, a longtime major stockholder in General Motors.)
Marty Titel, executive director of the C.S. Fund, says about $1.5 million in annual grants are divided among four areas of interest: war and peace, poison and toxics, genetic diversity, and dissent.
The Gund Foundation gives $200,000 a year to organizations promoting awareness of the nuclear threat. The program began when the governing board decided such work meets its purpose - to improve the quality of life in northeast Ohio. Says Henry Doll, Gund's associate director, ''The board members decided that, if they are concerned about life, then they ought to be concerned about the nuclear arms race.'' After first concentrating on local peace groups, Gund has now opened its coffers to such national organizations as International Physicians for the Prevention of Nuclear War.
The Carnegie Corporation's new grants follow the appointment of David Hamburg as president. Mr. Hamburg had made clear his intention to develop the foundation's participation in efforts to prevent nuclear war. In addition to grants to Stanford and Harvard Universities, awards to Columbia University and the Massachusetts Institute of Technology are being negotiated.
The Stanford grant will be used in part to fund fellowships for mid-career scientists. Largely the idea of Sidney Drell, director of Stanford's linear accelerator and a prominent arms control authority, the fellowships will help train a new generation of nuclear arms experts. Many of the first American experts in the field are now approaching retirement.
The grant will also fund research in crisis prevention - a topic Harvard, too , will study. Scott Sagan, a research fellow at Harvard's Center for International Affairs, says the uniqueness of the ''Avoiding Nuclear War'' project is that it will analyze various paths by which nuclear conflict might begin, and then determine ways each might be cut short. It will be a ''truly interdisciplinary effort,'' Mr. Sagan says, with contributors from such fields as political science, psychology, and history.