*for their outstanding achievements in the development of* *direct methods for the determination of crystal structures*

**Jerome Karle**

*Born New York City, 18 June 1918, died 6 June 2013*

Karle entered the City College of New York in 1933 where he studied some additional mathematics, some physics, and much chemistry and biology in addition to the broad course requirements for all students of mathematics, the physical sciences, the social sciences and literature. The year after graduation from City College was spent studying biology at Harvard University for which he was awarded an MA in 1938.

After a brief hiatus, he went to work with the New York State Health Department in Albany where he developed a procedure for determining the amount of fluorine in water supplies that became a standard method. In 1940 he entered the Chemistry Department of the University of Michigan where he worked with Professor Lawrence O. Brockway whose speciality was the investigation of gas-phase molecular structure by means of electron diffraction. Although his PhD was awarded in 1944, he had completed all the work for it during the summer of 1943 and went off to work on the Manhattan Project at the University of Chicago.

In 1944, he returned to the University of Michigan and went to work on a project of the Naval Research Laboratory. While at the University of Michigan, he performed some experiments on the structure of monolayers of long-chain hydrocarbon films involved in the boundary lubrication of metallic surfaces and derived a theory that explained the electron diffraction patterns obtained from the oriented monolayers. In 1946 he went to work permanently for the Naval Research Laboratory in Washington. His interest continued in developing the quantitative aspects of gas electron diffraction analysis. At about that time, Herbert Hauptman joined him at the Naval Research Laboratory and they decided to pursue the implications for crystal structures. This eventually led to the development of the direct methods for crystal structure analysis with the major part of the mathematical foundations and procedural insights established in the early 1950s.

The initial applications of the procedure for structure determination for centrosymmetric crystals involving probability measures and formulas derived from the joint probability distribution were performed in the middle 1950s in collaboration with colleagues at the US Geological Survey.

During the 1960s, there was an intensive program in his laboratory to develop a procedure for crystal structure determination of broad applicability that would encompass noncentrosymmetric as well as centrosymmetric crystals. Largely through the efforts of Isabella Karle, such a procedure was developed and called the symbolic addition procedure. The first application of the symbolic addition procedure was published in 1963 and the first essentially equal atom noncentrosymmetric crystal structure to be solved by direct phase determination was published in 1964. This was followed by a number of exciting applications and toward the end of the 1960s many laboratories started to become interested in the potential of the direct method for structure determination.

During the 1960s, he collaborated with Isabella in some of her investigations and derived with her a variance formula that was the basis for applying probability measures to procedures for analyzing noncentrosymmetric crystals. During the 1950s and 1960s, he maintained an interest in gas electron diffraction and made some experimental and theoretical studies of internal rotation and coherent diffraction associated with excitation processes.

In the 1970s, he continued theoretical work in crystal structure analysis that included the derivation of a "tangent formula" for phase determination that was based on the more restrictive higher and higher order determinants from the determinantal inequalities. He participated with Wayne Hendrickson in some refinements of macromolecular structure with the use of the tangent formula and also had some early participation with John Konnert and Wayne Hendrickson in the constrained refinement technique for macromolecules. In collaboration with John Konnert and Peter D'Antonio, procedures were developed for determining atomic arrangements in amorphous materials based on criteria similar to those applied to molecular vapors. Collaborations on structural problems also included Judith Flippen-Anderson, Clifford George, Richard Gilardi and Alfred Lowrey.

At the end of the 1970s Wayne Hendrickson made some valuable advances in the application of anomalous dispersion to the determination of macromolecular structure. Karle developed an exact, linear algebraic theory that includes any number and type of anomalous scatterer and any number of wavelengths. It can also incorporate information from isomorphous replacement measurements.

In 1980 Karle published a linear algebraic theory for the multiwavelength anomalous dispersion technique. More recently, he was concerned with additional developments in the anomalous dispersion technique and became interested in some aspects of the solution of nonlinear simultaneous equations, the determination of electron densities in crystals and some new approaches to phase determination in crystal structure problems. His research program changed very much over the years, the main objective becoming to develop a broad and detailed understanding of how nature operates in carrying out the processes that are known to occur in the human body*.*

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