Molecular Modeling as an Inorganic Chemistry Exercise Carmen Canales, Laura Egan, and Marc ~irnrner' Connecticut College, New London, CT 06320 Computational Chemistry has become a n established laboratory tool. One only needs to page through the most recent issue of the Journal of the American Chemical Society, to see that computational modeling is no longer limited to theoretical chemists, it is used extensively in synthetic, inorganic, biochemical, and organic chemistry. Despite its acceptance in the research community, computational chemistry is not taught a t many undergraduate schools, nor is i t featured i n standard undergraduate textbooks. This laboratory is intended to familiarize the undergraduate student with both the concepts and the practice of molecular mechanical analysis. Molecular mechanics is a n empirical method requiring less computer time and resources than ah initio or semiempirical approaches. The method has been reviewed in this Journal (I), books on computational chemistry have been published (2,3), inorganic molecular mechanics have been reviewed (4, 5). and two organic modeling exercises have been published (6, 7). We have run the experiment using however, the MM2 option of the Macromodel program (8); it can just a s easily be carried out with Chem 3D Plus (9) (Mac) or Alchemy (10) (Mac 11, I k , IIcx; IBM PC, XT, AT). The exercise was part of our junior/senior level inorganic analysis and synthesis class; however, i t can be incorporated into inorganic laboratories a t any level or even spectroscopy and chemical methods courses. I n this experiment, molecular mechanics is used to d e t e r m i n e t h e ideal m e t a l size for binding to diaminoethane a n d diaminopropane. I n molecular mechanics, i t i s common practice to drive a certain parameter, for example, a torsion angle, through a series of fixed values to obtain the strain energy as a function of the parameter. Similarly, a curve of the strain energy versus the M-N bond distance can be obtained by systematically increasine the ideal M-N distance in the force field and c;llrulating the strain after carh incrrusc. The minimum of such a eravh occurs :lt the ideal M-N bond leneih. becausr the striin'energy is a t a minimum when th;liiand bite size perfectly matches the metal size (5,111.
for M-N-C-C and N - M G C ; ul = 0; uz = 0; us = 0.267 kcallmol for M-N-C-H. For van der Waals interactions, a radius of 2.300 Aand E = 0.32 kcallmol was used. Once the a~uronriate force field has been established it .. is used in the minimuation ofstruin energy ofthecomplex. The resultinrr strain encrw is recorded. and the M-N bond length increased beforerepeating thk minimization. I n this way the strain energy of the complex can be monitored with a n increasing M-N bond length. From a plot of the M-N bond length versus the strain energy the ideal M-N bond length can be established. The same procedure is followed with diaminopropane a s the ligand. Finally, examination of the individual energy contributions (only possible on Chem 3D plus and Macromodel) a t the different imposed M-N bond lengths pin points the steric interactions responsible for determining the bite size of both ligands.
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Experimental Using the draw function of the program used, enter a metal diaminoethane complex. Caution Be sure to enter the diaminoethane complex with the ethyl hydrogens staggered. Also enter the M-diaminopropane complex in the chair configuration because this configuration will lead to the global minimum. I n order to energy minimize this structure, the program has to have the appropriate metalnitrogen bond length, bond angles, and torsional force constants in its force field. In our experiments wehave used a bond stretching force constant of 2 4 0 m-dyneliland varied the bond length fmm 1.9 A to 2.1 A, stepsize 0.02 A. The following bond angle deformation potentials were used MN-C: 0.4 m-dyne A/rad; M-N-H: 0.2 m-dyne Nrad and NM-N: 0.4 m-dyne Nrad. The M-N-H and M-N-C angles were set at 109" and the N-M-N angle a t 90". The N-M-N force constant is deliberatelv " kent . a t 90" so that sauare planar and octahedrnl geomctrles are rxnmined. ~orsion;ll constants used were ol = 0.2: u = 0.27; c:, = 0.093 kcal mol '~uthorto whom correspondence should be addressed,
M-N ideal distance(A1
Plot of the relative strain energy of diaminoethane and diaminopropane as a function of the imposed M-N distance (A). Volume 69 Number 1 January 1992
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Results Diaminopropane h a s a minimym s t r a i n energy at a metal-nitrogen distance of 1.95 A, while d i q i n o e t h a n e h a s a n ideal metal-nitrogen distance of 2.03 A. (See the figure.) This finding is substantiated by experimentally determined stability constants, which show t h a t i n both macrocyclic a n d nonmacrocyclic ligands a change from five-membered to six-membered chelators destabilizes large metal ions more t h a n small metal ions ( 4 ) (see the table). Analysis of t h e s t r a i n contributing interactions show t h a t t h e six-membered diaminopropane complex maintains its low-strain chair form a s long as the metal is about the same size a s sp3 carbon. Five-membered rings prefer larger metals with a high coordination number (i.e., small N-M-N bond angle). Amore complete analysis of the origin of t h e size-selectivity of five- a n d six-membered rings can be found i n t h e literature (4,5,12). Summary This i s a safe a n d cheap experiment t h a t does not require any sophisticated equipment (one terminal per pair of students), and it can be completed i n one afternoon. We have used this experiment to introduce the concepts of bite size and by extension t h e hole size i n macrocycles. The exercise is designed also to give t h e students some understanding of molecular mechanics and to eliminate t h e "black box" approach. By making t h e students modify t h e force field, they get to see all the parameters that make u p t h e force field and, it is hoped, gain a n appreciation of their function. As with all molecular mechanical minimizations, it is important to find t h e global minimum and not t h e local minima. I n this experiment t h e students a r e instructed to enter the complexes i n t h e conformation that i s known to
The Differences in Binding Constants for EDTA and TMDTA as a Function of Metal Radius (5) Metal Ion
Ionic Radius (A) CuL+ 0.57 ~ i " 0.69 zn2+ 0.74 cd2' 0.95 ca2+ 1.XI ~ a ~ + 1.03 pb2+ 1.18
log Ki EDTA 18.70 18.52 16.44 16.36 10.61 15.46 17.88
log KI TMDTA
Alog K
18.82 18.07 15.23 13.83 7.26 11.28 13.70
4.12 0.45 1.21 2.53 3.35
4.18 4.18
be the global minimum. It is important to stress that the results-obtained from a mo1ec;lar mechanical analysis have to be analyzed carefully, especially i n molecules t h a t can adont more than one conformation. If the elobal minimum is not known, some type of conformational search has to be undertaken to find the global minimum.
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Literature Cited
In Memoriam: Henry Marshall Leicester (1906-1991) Henry Marshall Leicester, Professor Emeritus of Biochemistry at the Dental School of the University of the Pacific and an internationally renowned authority on the history of chemistry and the himhemistry of teeth, died April 29, 1991 at the age of 84. Born in San Francisco, California on December 22, 1906, he was the youngest of the three children. A pmoeious youth, he graduated early from San Francisco's Lowell High School and a t the age of 16 entered Stanford University from which he received his AB (19271, MA (1928), and PhD degrees (1930, in organic chemistry), the last a t the age of 24. Because of the scarcity of permanent positions during the Depression he spent the next eight years in a variety of activitiedtravel in Europe, including research in Zurich and London), a year as Instructor at Oberlin College, part of a year at the Cmegie Institution in Washingtan, and one and three years as Research Associate a t Stanford and the Midgley Foundation at Ohio State University, respectively. While at OSU, he found a complete net of the Journal of the Russian Physico-ChemicalSociety, which aroused his interest in the lives and works of Russian chemists, an area in which he became the undisputed American authority. He corresponded actively with colleagues in the Soviet Union, and he amassed a unique collection of Russian books on the history of science, which he later donated to the Stanford Library. In 1941 he began his permanent association with the College of Physicians and Surgeons, San Francisco (now the Dental School of the University of the Pacific),where he was Professor of Biochemistry, a position that he held until his retirement in 1977. He served as Chairman of the Department of Physiology and the Department of Biochemistry and Head of the Research Program, and he was honored far excellence in teaching in 1972. He served as a member of This Journal's Editorial Board from 1949to 1959. Since the 1940s he was active in the American Chemical Society's Division of History of Chemistry, presenting numerous papers, senring as Chairman (1947-19511, and being involved in Divisional affairs until his retirement. He was one of the founders and members of the Editorial Board of Chymia: Annual Studies in the History $Chemistry, to which he contributed three articles and sewed as Editor-&Chief from Volumes 3 (19501 through 12 (19601. He was also the author, editor, or translator of seven bwks: Biochemistry ofthe Teeth 1949-the standard textbook on the subject for two decades;A Source Bwk in Chemistry 1400-1900; The Historical Background of Chemistry; Source Book in Chemistry 190&1950; Discovery of the Elements, 7th ed; Mikhail Vosil'euich Lomonosov on the Corpuscular Theory: and Deuelopment of Biochemical Concepts from Ancient to Modern Times.He also published 118 articles in his lifetime, among them seven in the Encyclopaedia Britannica (19641, 21 biographies in the Dictionary of Scientific Biography (1970-19781, seven biographies in Wyndham Miles' American Chemists and ChemicalEngineers (19761, and a number of articles in the Academic Aneeriean Encyclopedia (1980). In addition to his historical studies, he was an authority on the biochemistry of teeth and was an active advocate of water fluoridation during the 1950's and 1960's, traveling around California to speak a t wmmunity meetings. His legacy endures in the hearts and minds of his students, colleagues, friends, and family and in his books and articles that have enriched the science of chemistry and its history.
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Journal of Chemical Education
