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Life and Science of Clemens C. J. Roothaan∗

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Life and Science of Clemens C. J. Roothaan∗ GENERAL ARTICLE Life and Science of Clemens C. J. Roothaan∗ Shridhar R. Gadre, Subhas J. Chakravorty Clemens Roothaan, a Nazi concentration camp survivor and Professor Emeritus of the University of Chicago, passed away on 17 June 2019, 10 months after celebrating his 100th an- niversary. For his doctoral thesis, Roothaan developed the matrix version of the Hartree–Fockequations. These Hartree– Fock–Roothaanequations form the cornerstoneof atomic and Shridhar Gadre served for 30 molecular structure theory. In addition, Roothaan devised years as a Professor of Chemistry at the Savitribai computing methods for quantum chemistry, physics, and other Phule Pune University scientific fields from the early years. After 1988, he actively (SSPU), and later 6 years at helped Hewlett Packard develop the Intel Itanium processor. IIT Kanpur. In 2016, he This article presents the highlights of the life and science of joined as a Distinguished Professor at SPPU. His Roothaan. research interests are Clemens Roothaan, Louis Block Professor Emeritus of Physics theoretical and computational chemistry and Chemistry at the University of Chicago, died 17 June 2019 in Chicago. He was born on 29 August 1918 and celebrated his 100th birthday, about ten months before his death. Roothaan de- veloped a foundational model for computing electronic orbitals in Subhas Chakarvoty did his atoms and molecules, particularly known as the ‘Hartree–Fock– PhD under the supervision of Roothaan equations’ [1, 2]. These equations and several compu- Shridhar Gadre. His postdoctoral training was tational methodologies devised by him with his associates are the with Enrico Clementi at foundation of scientific exploration of the electronic structure of IBM-Kingston (1987–1990), atoms and molecules. He led the University of Chicago Compu- and Ernest Davidson at tation Centre in its early years and devised new digital comput- Indiana University (1990–1996). Thereafter, he ing methods for quantum chemistry, physics and other scientific has been involved in research fields [3, 4]. In his later retired years, he actively helped Hewlett in the field of Packard develop the Intel Itanium processor and served as the cheminformatics and drug company’s liaison with the Large Hadron Collider. discovery and is currently employed at a major Clemens Roothaan was a native of Nijmegen, Netherlands. He pharmaceutical company. had enrolled in the University of Delft in 1935 to study electrical ∗Vol.26, No.6, DOI: https://doi.org/10.1007/s12045-021-1178-0 RESONANCE | June 2021 737 GENERAL ARTICLE Figure 1. Professor Roothaan, at his home in Hyde Park, Chicago, receiving congratulations on his 100th birthday on 27 August 2018, from the Pres- ident, Society of Catholic Scientists. Photo cour- tesy, Society of Catholic Scientists. Keywords engineering. However, he became dissatisfied with the course in LCAO-MO theory, Roothaan 1938–39 and spent the spring semester auditing courses on elec- equations, MCSCF theory, H 2 tronics and acoustics at the Technical University of Karlsruhe in molecule, floating-point arithmetic unit, vector transcendental math Germany. In the fall of 1940, Clemens returned to Delft as a library. graduate student of physics in the laboratory directed by H. van Leeuwen. She is well known for her work in establishing the quantum mechanical nature of magnetism. In late 1942, the allies were gaining strength, and there were ma- jor German defeats in North Africa and Stalingrad. As a con- sequence, the Germans declared martial law in the Netherlands, which was under their occupation since 1940. Roothaan [3] has described how young men were captured and forced to work for German factories. In order to escape from this, Clemens and his As a member of the brothers, Victor and John, were back at their parental home in Ni- Computation Chamber, jmegen. Victor escaped arrest, but SS captured Clemens and John he carried out a despite their non-involvement in the resistance movement. In Au- Kronig-Penney calculation on a gust 1943, they were moved to the Vught concentration camp. In one-dimensional crystal this camp, not far from Eindhoven, the Philips company had the and later calculated the manufacturing operations of electric razors and short wave ra- elastic constants in a dios. The academically inclined prisoners of war (PoW), includ- classical crystal. ing Clemens, were assigned to the ‘Computation Chamber’. As a member of the Chamber, he carried out a Kronig-Penney 738 RESONANCE | June 2021 GENERAL ARTICLE Figure 2. Professor C. C. J. Roothaan Copyright 2020, The Chicago Maroon. Reprinted with permission. calculation on a one-dimensional crystal and later calculated the elastic constants in a classical crystal [2]. The final report of this work was transmitted to the Philips management in Eind- hoven, a few days before the camp was evacuated on 5 Septem- ber 1944. The PoW’s, including the two Roothaan brothers, were transferred to the Sachsenhausen camp in Germany. Near the end of the war, the camp inmates, including Clemens, were sent on a death march. John, his younger brother, was sent in an earlier transport to the infamous camp of Bergen-Belsen, where he suc- cumbed to deprivation and typhoid in March 1945. The death march of tens of thousands of undernourished prisoners was con- ducted by SS troops, chased by the Russian army, which lasted 12 days, covering 160 km. Clemens later estimated that one-third of these prisoners perished. Nijmegen was razed to the ground, killing many residents and wounding almost all others. Clemens survived, and after the war, his work in the ‘Computation Cham- ber’, and his technical report was accepted by TU Delft as his master’s thesis. He was awarded a master’s degree in physics in RESONANCE | June 2021 739 GENERAL ARTICLE 1945. In January 1946, Clemens arrived at the University of Chicago with a postgraduate fellowship. During this period, Chicago was the most exciting place to be for physicists. The first self-sustaining nuclear chain reactor and a physics faculty, with heavyweights like Enrico Fermi, Edward Teller, Maria Goeppert-Mayer, and Robert Mulliken. Nuclear research was, of course, de rigueur! Yet, Roothaan arrived in Chicago and opted for research in molec- ular structure and spectra as a research student of Robert Mul- liken. He spent the period between January 1946 and June 1947 learning quantum mechanics, linear algebra and group theory, passing the PhD candidacy examination in physics. Shortly there- after, Roothaan was offered a faculty position in physics at the Catholic University of America in Washington, DC. He spent the next two years teaching in Washington, while working on his the- Roothaan realized that sis, making frequent trips to Chicago to confer with Mulliken on although the linear the semiempirical molecular orbital (MO) calculations on substi- combination of atomic tuted benzenes as his thesis subject. After publishing a research orbitals (LCAO) approximation of MO’s article on UV spectra of benzene and borazol jointly with Mul- was not new, entering liken in the Journal of Chemical Physics in 1948, he became dis- this approximation satisfied with semiempirical MO theory. formally into the N-electron variation He realized that although the linear combination of atomic or- principle provided a new bitals (LCAO) approximation of MO’s was not new, entering this and much better approximation formally into the N-electron variation principle mathematical point of foundation for electronic provided a new and much better mathematical point of founda- structure calculations on tion for electronic structure calculations on molecules (See Box molecules. 1). When he communicated his insight to Mulliken, who fully understood its significance, he encouraged Roothaan to devote his PhD thesis to this topic [1]. This work was later published as a paper in the Reviews of Modern Physics [2] and is regarded as a seminal contribution of Roothaan to quantum chemistry. Due to space constraint, it is not possible to describe here the full techni- cal details of this paper of Roothaan. Only a brief and simplified account of the important aspects is presented, using the notations in [5]. For this, it is necessary to be familiar with the basics of the Hartree–Fock theory, which are given below. 740 RESONANCE | June 2021 GENERAL ARTICLE The starting point in the non-relativistic treatment of molecules is the Born–Oppenheimer approximation. Since nuclei are much Since nuclei are much heavier than electrons, they move more slowly. Hence, the kinetic heavier than electrons, energy of the nuclei can be neglected and the repulsion between they move more slowly. Hence, the kinetic the nuclei can be considered to be constant for a fixed nuclear energy of the nuclei can configuration. The Schr¨odinger equation for the electronic mo- be neglected and the tion is hence separated out and can be written as repulsion between the nuclei can be considered to be constant for a fixed HˆeΨe({ri}; {RA}) = ǫeΨe({ri}; {RA}). (1) nuclear configuration. Here the electronic wave function Ψe depends explicitly on the electronic co-ordinates, {ri}, but has an implicit, parametric de- pendence on the position of the nuclei, viz. {RA}. In Eqn. (1), Hˆ e is the electronic hamiltonian, with the eigenvalue ǫe. Eqn. (1) is written using the atomic units (viz. me = |e| = ~ = 1 and so on), describing the motion of N electrons in the field of M nuclei, treated as point charges, viz. N 1 N M Z N N 1 Hˆ = − ∇ˆ 2 − A + . (2) e 2 i r r Xi=1 Xi=1 XA=1 iA Xi=1 XJ=i i j In Eq. (2), the subscripts i, j are used for denoting the electron indices and A, B stand for the nuclear ones. The first term is the electronic kinetic energy operator, the second one denotes the nuclear-electron attraction and the third one, the electron-electron repulsion energy.
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