Martin Karplus, a Nobel Prize-winning theoretical chemist who used computers to model how complex systems change during chemical reactions, a process that has led to advances in the understanding of biological processes, died on Dec. 28 at his home in Cambridge, Mass. He was 94.

His wife, Marci Karplus, said he died while recovering from a fall in which he broke a femur.

Over his long career, Dr. Karplus had crossed paths with some of the most important scientists of the 20th century, including Linus Pauling and J. Robert Oppenheimer.

Scientists can control the chemicals in a reaction, and they can measure and evaluate the results, but what happens in between is a mystery.

As Sven Lidin, chairman of the Nobel selection committee explained when announcing the 2013 winners in chemistry: “It’s like seeing all the actors before Hamlet and all the dead bodies after, and then you wonder what happened in the middle. And actually, there is some interesting action there, and this is what theoretical chemistry provides us with — the whole drama.”

Beginning in the 1960s, when computers were only a fraction as powerful as today’s smartphones, Dr. Karplus and his fellow Nobel laureates — Michael Levitt, originally from South Africa, and Arieh Warshel, who was born in Israel — began to build virtual models of molecules to understand what happens to them during complex reactions like photosynthesis and combustion.

The models used classical Newtonian physics to predict how multitudes of atoms and molecules move during reactions, and they used quantum physics to describe how chemical bonds are broken and formed during those reactions. This type of analysis proved particularly useful in understanding biological reactions involving enzymes, the proteins that govern chemical responses in living organisms.

There was initial resistance to the scientists’ work because it was difficult for others to accept that computer models could be accurate enough or could sufficiently account for the many variables in some reactions. But by the time the Nobel Prize was awarded in 2013, that skepticism was gone.

“Today, the computer is just as important a tool for chemists as the test tube,” the academy wrote in its announcement. “Simulations are so realistic that they predict the outcome of traditional experiments.”

At Harvard University, where Dr. Karplus spent most of his career, he and his research team in 1983 created a program for simulating molecular interaction, calling it Chemistry at Harvard Macromolecular Mechanics (CHARMM). The program is available to researchers worldwide.

In the late 1950s, Dr. Karplus made another important contribution to chemistry: He developed what is known as the Karplus equation. It makes it possible to calculate the magnitude and orientation of protons in organic compounds involved in nuclear magnetic resonance spectroscopy, allowing chemists to study the arrangements of atoms in molecules. It is now a basic part of chemistry education.

Martin Karplus was born on March 15, 1930, in Vienna into a well-off and intellectually accomplished Jewish family. He was the second son of Johann Karplus, a banker, and Isabella (Goldstern) Karplus, a hospital dietitian.

His paternal grandfather, Johann Paul Karplus, was a neurologist who discovered the functions of the hypothalamus, the crucial brain region that controls body temperature, hunger, heart rate and other vital activities. An uncle, Eduard Karplus, was an engineer and inventor. And Martin’s older brother, Robert, became a theoretical physicist at the University of California at Berkeley.

In the face of rising antisemitism in the 1930s and a few days after Nazi Germany annexed Austria in the Anschluss of March 1938, Martin, his brother, and his mother fled to Zurich and then to France, eventually arriving in Le Havre.

Martin’s father was initially imprisoned in Vienna, but he was able to join the family before they set sail for New York. They arrived on Oct. 8, 1938, and soon after moved to Newton, Mass.

At Newton High School, Martin discovered that his older brother had made such a mark there that many teachers doubted Martin’s ability to do as well, he recalled in a Nobel biography. One teacher, who was in charge of the Westinghouse Science competition, the nation’s top talent search in the sciences, told Martin that it would be a waste of his time to enter.

But he found another teacher who was willing to proctor his test for the competition. He went on to qualify as one of the country’s 40 finalists. Martin’s project on alcids, an aquatic bird, was chosen as the co-winner of the competition, after which he met President Harry S. Truman in Washington.

Accepted to Harvard University, he concentrated on chemistry and physics. As he was finishing his undergraduate degree in 1950, both the University of California at Berkeley and the California Institute of Technology, known as Caltech, accepted him for graduate studies.

Unsure where to go, he visited his brother, Robert, who by then was working at the Institute for Advanced Study in Princeton, N.J. Robert showed him around, introducing him to Albert Einstein and J. Robert Oppenheimer, who had led the Manhattan Project that developed the atomic bomb and who had become the institute’s director. Dr. Oppenheimer recommended Caltech, where he had been a professor, calling it “a shining light in a sea of darkness,” according to Dr. Karplus’s biography. Decision made.

At Caltech he focused on biophysics, joining a graduate group led by Max Delbrück, who, along with Salvador E. Luria, had proved that Darwin’s theory of evolution also applied to bacteria. They, along with Alfred D. Hersey, would be awarded the Nobel Prize in Physiology or Medicine in 1969 for their work.

As Dr. Karplus wrote in his Nobel biography, a turning point in his life came two months after he started at Caltech. Dr. Delbrück suggested that Dr. Karplus present a seminar on his intended area of research: how vision works.

He began his presentation, but after 10 minutes Dr. Delbrück interrupted him to say that he did not understand what Dr. Karplus was saying. Dr. Karplus began anew, and Dr. Delbrück interrupted again, saying he still did not understand. Dr. Karplus began again, and Dr. Delbrück interrupted a third time.

At this point, Dr. Richard Feynman, who was awarded the Nobel Prize in Physics in 1965 and who was sitting in the audience, turned around and said to Dr. Delbrück: “I can understand, Max. It is perfectly clear to me.” Dr. Delbrück turned red and stormed out. Later that day, he called Dr. Karplus to his office and told him that he could no longer work with him.

Dr. Karplus switched to chemistry.

In the chemistry department, Dr. Karplus initially worked with Prof. John Kirkwood, but then Dr. Kirkwood left for Yale University. His graduate students were given the chance to switch to working with Linus Pauling. Only Dr. Karplus accepted.

Dr. Pauling was on the short list of the greatest scientists of the 20th century. He was one of only five people to receive two Nobel Prizes: the first in 1954 for chemistry, for determining how atoms are chemically bound in molecules; and the second, the Nobel Peace Prize, in 1962, for promoting nuclear disarmament. His scientific work led to the founding of quantum chemistry and molecular biology.

Dr. Karplus’s time with Dr. Pauling proved fruitful: He finished his doctoral dissertation just before Dr. Pauling departed on a trip in late 1953. Dr. Karplus, who had received a National Science Foundation postdoctoral fellowship, then left to spend two years at Oxford University.

In 1955, he was hired by the University of Illinois, which was doing advanced work on nuclear magnetic resonance (NMR) spectroscopy. It was during his five years in Illinois that he put together his Karplus equation.

In 1960, Dr. Karplus was hired to be a researcher at the IBM Watson Scientific Laboratory and to teach at Columbia University. With access to state-of-the-art computing power, he continued his research on NMR and also began to investigate creating models to explain chemical reactions.

Dr. Karplus changed jobs again in 1966, returning to Harvard. There he started to concentrate on biological reactions, which are the most complex. The work would lead to the creation of CHARMM and to his Nobel Prize.

In the 1990s, Dr. Karplus was appointed a professor at Louis Pasteur University, later renamed the University of Strasbourg, in France. He spent the next 20 years going back and forth between there and Harvard.

Dr. Karplus met Marci Hazard at Harvard, where she has worked for 51 years. They married in 1981. His first wife was Susan Karplus; their marriage ended in divorce.

In addition to his wife, he is survived by two children from the earlier marriage, Reba and Tammy; one child from his second marriage, Mischa; and one grandchild. (Susan Karplus died in 1982. His brother, Robert, died in 1990.)

In 2020, Dr. Karplus published his autobiography, “Spinach on the Ceiling: The Multifaceted Life of a Theoretical Chemist.” The title referred to the landing spot of a launched spoonful of spinach that he had been ordered to eat as a boy.

Over his career, Dr. Karplus supervised close to 250 graduate and doctoral students, most of whom have gone on to successful academic careers. They are collectively known as Karplusians.