Professor Masao Kotani, Japanese theoretical physicist and a member of the editorial board of IJQC, passed away of stomach cancer on June 6, 1993, at the age of 87. He is survived by his wife, Yaeko, and a daughter and son.

Professor Kotani was born on January 14, 1906, in Kyoto and spent his primary and middle school days in Osaka. He moved to Tokyo to enter the First High School and then The Tokyo Imperial University. In 1929, he received his BSc degree in physics and was appointed as a lecturer at the Faculty of Engineering in the same university. Three years later, he became an associate professor in the Physics Department. In 1943, he received the degree of DSc and was promoted to a full professor in the same department. Twenty- two years later, in 1965, Professor Kotani moved from The University of Tokyo to Osaka University as a professor in the Faculty of Engineering Science. He retired from the chair in 1969. One year later, Professor Kotani was elected president of The Tokyo Science University, which is a highly renowned private university. He served as president for three terms, a total of 12 years, and retired in 1982. He was associated with The Tokyo Science University until his death, as an expert advisor to its two institutes, General and Life Sciences.

Professor Kotani received many awards. He was a recipient of the Japan Academy Prize in 1948. This was for his joint work with the late Professor Sin-Itiro Tomonaga on the theory of magnetrons and microwave circuits. He received the 1969 Tohyoh Rayon Prize for the work in quantum mechanical study of molecular electronic structure, the 1974 Fujiwara Award for his contribution to the basic studies of molecular physics and biophysics, and the 1977 International Society of Quantum Biology Award. In 1977, the Japanese government commended him in recognition of his cultural services. In 1980, he received an Order of Culture in the presence of the late Emperor Hirohito.

Professor Kotani attended high school from 1922 to 1926 and liked both mathematics and physics but was not good at memorizing unrelated items. He had dreamed how wonderful it would be if properties of molecules could be theoretically calculated. After he entered The Tokyo Imperial University, he and his close friend, the late Professor Tetsuro Inui, studied the emerging new mechanics together in the form of a two-man seminar, using journals reaching the library from Europe via Siberia. Upon graduation from the university, he and Inui were appointed, respectively, as a lecturer and an assistant in the same laboratory. The late Professor Takahiko Yamanouchi had been there as an associate professor and the Yamanouchi—Kotani—Inui triplet {set bold by this website} joined forces and enjoyed studying the bases and applications of quantum mechanics. This triplet was probably one of the strongest units on quantum theory in the Far East in those days. Heitler-London's famous paper of the hydrogen molecule appeared in 1927. Professor Kotani was deeply impressed by this paper and realized that the mystery of the covalent chemical bond was solved in principle and that chemistry and physics were united on a common foundation. The possibility he had dreamed of, when he was still in high school, had thus been realized. In the early 1930s, he was asked to join a newly established Committee for the Investigation of Catalytic Action under the Japan Society for Promotion of Sciences. He was the only member from the physics field, while others were from chemistry.

This gave him enough motivation to embark on a systematic calculation of diatomic molecular integrals. Before the Second World War, electronic computers did not exist, so they had to use mechanical hand calculators. With a few but ardent collaborators, he had managed to report his results in four separate papers published in 1938, 1940, 1953, and 1954 and in a book in 1955, a revised edition of which was published in 1963. In this book, he included a very lucid paper about his method of treating many-electron systms, with an explanation of constructing representation matrices of a symmetric group of permutations. {all items set bold by this website}

These tables were welcomed by researchers in the field. The late Professor C. A. Coulson had asked him to send a second copy of the off-print, since the first copy had become worn out through heavy use. Professor Kotani‘s way of treating the many-electron systems was later revitalized as "spin-free quantum chemistry," advocated by Professor F. A. Matsen and others.

In Japan before the 1930s, theoretical physics had been understood almost as a synonym of mathematical physics, that is, mostly as an application of mathematics for solving differential equations in physics, with certain initial and boundary conditions. This tradition was particularly strong in The Tokyo Imperial University. Professor Kotani was one of the main members of new theoretical physicists, who tried to obtain numerical values that could be directly compared with experimental results. One example of this direction is his paper entitled "On the Magnetic Moment of Complex Ions," published in 1949. In this paper, he started from the strong-field coupling scheme, now known as the ligand-field theory. He then proceeded to derive formulas for the temperature dependence of effective magnetic moments of the transition metal ions under a cubic field. These formulas have been cited as Kotani's formulas in many papers. In order to compare the theoretical results with experimental results, he had examined Chemical Abstracts year by year. To his pleasant surprise, he found that the magnetic moment of hemoglobin derivatives measured at Pauling's laboratory in the early 1930s fitted his theory quite nicely. This was his first encounter with biological molecules {set in italic-bold by this website}.

In the late 1950s Professor Kotani's scientific interests had moved to biophysics. As he was excited by the unification of physics and chemistry, he was fascinated by the largely unexplored fertile field between biology and physicochemical science. He presided over a laboratory of biophysics at Osaka University for 4 years. In this laboratory, experimental and theoretical studies on hemoproteins were conducted. He and his students prepared single crystals of hemoglobin molecules, measured the magnetic susceptibilities and their anisotropies down to liquid helium temperature, analyzed the coexistence of high-spin and low-spin states of hemoglobin molecules, and examined their electron paramagnetic resonance spectra. From these studies of physical properties of biological molecules, they proceeded to tackle problems related to their biological activities. One problem on which they concentrated their energies was the so-called "oxygenation curve" of hemoglobin. Professor Kotani proposed a nice theory describing the cooperativity of four subunits in a hemoglobin molecule, which is the origin of the "oxygenation curve". From these studies, a total of 19 publications were produced by him and his co-workers between 1963 and 1974, of which 17 were in English. He seemed to have had deep feelings of satisfaction because molecular biology and physics had common ground at the microscopic level.

Professor Kotani had written many monographs, review articles, and textbooks. The fields covered by them are mechanics, group theory, electromagnetism, theory of chemical reactions, interatomic and intermolecular forces, table of molecular integrals, quantum mechanics, quantum mechanics of atoms and molecules, special functions, theory of chemical bonds, radiation material science, "Mathieu functions, spheroidal functions, and their applications", quantum mechanics of electronic structure of simple molecules, electronic theory of haem, structure of matter, "introduction to molecular sci- ence, outline of quantum mechanics", paramagnetic properties and electronic structure of iron in heme proteins, and electronic structure of iron in porphyrin complexes. This is a formidable list.

M. Kotani Shelter Island 1951

Professor Kotani went abroad, for the first time in his life, in 1950. lt was a difficult time to make a foreign trip. One had to submit several kinds of documents well in advance just to obtain a passport. Then, at the end, one had to ask permission from the Bank of Japan to get a small amount of foreign currency. When he met the secretary general of the IUPAP (1), Professor P. Fleury in Paris, Professor Fleury told him that the IUPAP had never disqualified Japan as a member, since science and politics were separate fields. Professor Kotani was delighted to learn that Japan could reopen its activity as a member if only membership dues were paid. A possibility of an international conference of physics in Japan was hinted at by the secretary general on this occasion. This possibility became a reality as the International Conference of Theoretical Physics which was held in Kyoto in September 1953. Professor Kotani played a key role in its organization and displayed indomitable and unremitting energy in leading to its success. Especiahly to young Japanese physicists, the door to the world was opened by this conference.

Professor Kotani‘s brilliance, particularly in mathematics, was legendary among his friends and students. In his final year as a student at the university, he attended lectures on celestial mechanics. He found a proof of a theorem given at the lecture, and he showed it to the professor. The professor found his proof new, simple, and worth publishing. Thus, his first paper was published in the journal Astronomische Nachrichten in 1929! Another example of his mathematical skillfulness was his way of obtaining the exact value of electric polarizability of the hydrogen atom from the first-order Rayleigh-Schrödinger perturbation equation. This method was quoted by Schiff (Quantum Mechanics, 3rd ed., 1968) with the following footnote: "This approach appears to have been first published by M. Kotani, Quantum Mechanics I, p. 127 (Yu [sic] {I} wanami Book Co., Tokyo, 1951)." {note of this website: The [sic]-note is contained in the original!}

Almost 50 years after his first printed paper, he read a paper at the 1977 annual meeting of the Biophysical Society of Japan (This society was established in 1960 by Professor Kotani and others and who elected him as its first president.) This was possibly his last contributed paper. The subject dealt with chemical kinetics of polymerization of single monomers and contained his "small" trick. If one denotes the concentration of monomer by x1, that of dimer by x2, that of trimer x3, and so on, one can describe a model polymerization process by a set of seemingly nonlinear equations:

and so on. Changing a variable from t to s, where ds = kx₁ dt, he could linearize the equations and solve thern easily.

Those who had a chance to meet him would probably agree that he was gentle, sincere, and modest and that the way he worked was always meticulous and careful. He was not a talkative person, but one could feel his warmth and attentiveness in a short time. On the other hand, when he was not satisfied with an explanation, or he thought an argument was not self-consistent, he kept asking questions calmly, politely, and logically until he was convinced. In this sense, he had a strong will and a quiet tenacity. He also had a steady nerve. lt was around 1974 when I visited him at the temporary president's office. The storm of student power was raging through all major universities in Japan and the original president's office was occupied by radical students. While we were chatting, typical student whistles and shouts started and became louder and louder. When they reached the staircase leading to his office and were still approaching, his secretary opened an adjoining door and told him, "They are coming, they are coming". The president looked up, said "Ah, so" quietly, and continued our discussion of an item in a dictionary.

In judging a situation or a person, Professor Kotani did not have any dogma or prejudice. He had an emotionally detached attitude to all problems. He was interested in a phenomenon and its cause. There must be reasons for any phenomenon, he thought, and tried hard to understand them. Other people's words and deeds could be incomprehensible to him, but he was very cautious in judging whether they were right or not. During my 13 years' association with him in his laboratory, I never heard a harsh remark about anybody from him. lt seems that Professor Kotani reached this admirable frame of mind not by mental training: He seems to have been a rare person who was born with these positive attributes and maintained them throughout his whole life.

Professor Kotani was not only an outstanding scientist, but also a man of a warm and remarkable personality. He could be called the father of Japanese quanturn chemistry. Professor Kotani will be missed by the international quantum chemistry community.