Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

III. Foldamer Research 3910 A. Overview 3910 B. Motivation 3910 C. Methods 3910 D. General Scope 3912 IV. Peptidomimetic Foldamers 3912 A. The R-Peptide Family 3913 1. Peptoids 3913 2. N,N-Linked Oligoureas 3914 3. Oligopyrrolinones 3915 4. Oxazolidin-2-ones 3916 5. Azatides and Azapeptides 3916 B. The â-Peptide Family 3917 1. â-Peptide Foldamers 3917 2. R-Aminoxy Acids 3937 3. Sulfur-Containing â-Peptide Analogues 3937 4. Hydrazino Peptides 3938 C. The γ-Peptide Family 3938 1. γ-Peptide Foldamers 3938 2. Other Members of the γ-Peptide Family 3941 D. The δ-Peptide Family 3941 1. Alkene-Based δ-Amino Acids 3941 2. Carbopeptoids 3941 V. Single-Stranded Abiotic Foldamers 3944 A. Overview 3944 B. Backbones Utilizing Bipyridine Segments 3944 1. Pyridine−Pyrimidines 3944 2. Pyridine−Pyrimidines with Hydrazal Linkers 3945

A field guide to foldamers.

One of the initial steps in the development of therapeutic agents is the identification of lead compounds that bind to the receptor or enzyme target of interest. Many analogs of these lead compounds are then synthesized to define the key recognition elements for maximal activity. In general, many compounds must be evaluated in both the lead identification and optimization steps. Increasing burdens have been placed on these efforts due to the large number of new therapeutic targets that continue to be identified thorough modern molecular biology methods.1 To address this demand, very powerful chemical and biological methods have been developed for the generation of large combinatorial libraries of peptides2 and oligonucleotides3 that are then screened against a receptor or enzyme to identify high-affinity ligands or potent inhibitors, respectively. While these studies have clearly demonstrated the power of library synthesis and screening strategies, peptides and oligonucleotides generally have poor oral activities and rapid in vivo clearance;4 therefore their utility as bioavailable therapeutic agents is often limited. Due to the favorable pharmacokinetic properties of many small organic molecules (<600-700 molecular weight),5 the design, synthesis, and evaluation of libraries of these compounds6 has rapidly become a major frontier in organic chemistry. Lorin A. Thompson was born in Lexington, KY, in 1970. He received the Bachelor of Science degree from the University of North Carolina, Chapel Hill, in 1992 where he worked under the guidance of Joseph Desimone. He is currently pursuing his doctorate in the laboratory of Jonathan Ellman at UC Berkeley where he is the 1994 Glaxo-Wellcome fellow. His research interests include the development of synthetic methodology for organic library construction.

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Synthesis and Applications of Small Molecule Libraries.

Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.

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Time-Dependent Density Functional Theory

Some of the challenges facing scientists in the area of the electronic structure and properties of solids are reviewed. At a time when computational advances have made possible high-quality calculations, not even conceivable 10 years ago, the article stresses the importance of going beyond the raw output of the calculation and understanding where the result originates. The areas selected for study include the Fermi surface and charge density waves, the stability of solids and the structures of solids under pressure, metal−insulator transitions, the method of moments, superconductivity, and the use of a relatively new technique for the study of chemical bonding, the electron localization function (ELF).

Electronic structure and properties of solids

The chemical bond is always considered from different points of view, depending or on the chemical and physical aspects to be examined. In both cases, description of the chemical bond are chosen that are appropriate for the particular research or application. Therefore, there are significant differences in the understanding as what constitutes chemical bonding. This is acceptable in practice but proves to be a hindrance for true interdisciplinarity. The concept of the chemical bond offer a firm basis upon which to forge links not only within chemistry but also to all related sciences. The general desire and the growing necessity for interdisciplinary collaboration requires a careful treatment of these concepts and, if possible, a tightening and standardization to a level that is widely acceptable and beneficial. In the age of tremendously fast development of computers and computer science, we believe that the electron localization function (ELF) provides a new description of the chemical bond for almost all classes of compounds. Its graphical language earns it the ultimate qualification for enhanced interdisciplinarity.

ELF: The Electron Localization Function

Die Gesichtspunkte, unter denen die Frage nach der chemischen Bindung gestellt wird, hangen davon ab, welche Verbindungsklassen oder welche chemisch-physikalischen Aspekte behandelt werden sollen, d.h. man wahlt jeweils die zum Forschungs- und Anwendungshintergrund passenden Beschreibungsschemata fur die chemische Bindung aus. So existieren bedeutende Unterschiede im Verstandnis dessen, was chemische Bindung ist. Dieser Umstand fuhrt zu Trennungen, die vielleicht aus praktischen Grunden verstandlich, aber im Sinne einer echten Interdisziplinaritat sehr hinderlich sind. Dabei bieten gerade die Konzepte der chemischen Bindung eine ungeheuer tragfahige Basis, um nicht nur innerhalb der Chemie, sondern auch zu allen benachbarten Wissenschaften Brucken zu schlagen. Der allgemeine Wunsch nach interdisziplinarer Zusammenarbeit und die zweifellos gewachsene Notwendigkeit hierfur erfordern eine pflegliche Behandlung dieser Konzepte und, wenn moglich, eine Straffung und Vereinheitlichung, die moglichst vielen akzeptabel erscheint und hilfreich wird. Wir glauben, das die Elektronenlokalisierungsfunktion (ELF) in der Ara einer lawinenartigen Computer- und Informatikentwicklung eine neue Beschreibung der chemischen Bindung fur nahezu alle Stoffklassen ermoglicht und durch ihre Bildsprache entscheidend zu einer erweiterten Interdisziplinaritat beitragen sollte.

Die Elektronenlokalisierungsfunktion ELF

Carlet. J. Clement. H. Demarne, M. Mellet. J.-P. Richaud, D. Segondy. M. Vedel, J:P. Gagnol. R. Roncucci, B. Castro. P. Corvol. G. Evin. B. P. Roques, ibid. 1986, 29, 1152-1159: d) H . Mazdiyasni. D. B. Konopacki, D. A. Dickman, T. M. Zydowsky, Tetruhedron Lett. 1993, 34, 435-438. [4] a) M . Frankel. P. Moses. Tetrahedron 1960.9.289-294: h) W. F. Gilmore, H.-J. Lin. J. Org. Chem. 1978, 43. 4535 4537; c) G. R. Moe. L. M. Sayre. P. S. Portoghese. E,trrrhedron Lei). 1981.22. 537-540: d) B. Garrigues. M. Mulliez, Swthesis 1988, 810-813; e) D. Merricks. P. G. Sammes. E. R. H . Walker. K. Henrrck, M. M. McPartlin. J. Chcm. Soc. Pwkin Puns. 1 1991, 2169-2176. (51 a) P. Garner. J. M. Park. J . Org. Chem. 1987.52. 2361 -2364; h) W. D. Luhell. H. Rapoport, J. Am. Chenr. Soc. 1987, 109, 236-239; c) N. J. Miles, P. G. Sammes. P. D. Kennewell, R. Westwood, J . Chem. Sue. Perkin Truns. 1 1985. 2299-2305; d) J. Jurczak, A. Golehiowski, Chenz. Rev. 1989, R9. 149-164: e) M. T. Reetz, Angeu.. Chem. 1991. 103, 15591573; A n p c . . Chem. In[. Ed. Engl. 1991. 30, 1531 -1546: f) M. T. Reetz, J. Kanand, N. Griehenow. K. Harms, ibrd. 1992, 104. 1638 and 1992. 31. 1626-1629: g) M. R. Leanna. T. J. Sowin. H. E. Morton. Telrulierlron Lett. 1992. 33, 5029-5032. a) J. C. Carretero. L. Ghosez. Tetruhedrori Letr. 1987. 28. 1101-1104: h) J. C. Carretero. M. Demillequand. L. Ghosez, Tetrahedron 1987, 43. 5125-5134; c ) J. C. Carretero, J. Davies, J. Marchand-Brynaert. L. Ghosez, Bull. So(,. Chiin. Fr. 1990. 127, 835-842. a) B. Musicki. T. S. Widlanski. Tutruhedron Lefr. 1991. 32, 1267-1270; b) B. Musicki. T. S. Widlanski, J Org. Chein. 1990, 55, 4231-4233; c) R. G. Henriques, T. S. Widlanski, T. Xu, J. D. Lamheth, J . Am. Chem. Soc. 1992. / 2 4 , 7311 -7333; d) M. Kovacevic. Z. Brkic. 2. Mandic, M. Tomic. M. Luic. B. K. Prodic, Crout. Chem. Actu 1992, 65, 817-S33. J. Huang. T. S. Widlanski, Tetruhedron Lrit. 1992, 33, 2657-2660. R. C. Reynolds, P. A. Crooks, J. A. Maddry, M. S. Akhtar, J. A. Montgomery, J. A. Secrist 111, J . Org. Chem. 1992. 57, 2983-2985. H. McIlwain. J. Chem. Soc. 1941, 75-77. J. A. Dale, H. S. Mosher, J. Am. Chem. Soc. 1973. 95. 512-519. Starting from noncrystallized 3, NMR analysis of the Mosher's amides revealed a 2 9 8 : 2 ratio of diastereoisomers. while starting from recrystallized 3, the Mosher's amides were obtained as single compounds within the limits of NMR detection ( > 9 9 : 1). NMR analysis of dimers 7 revealed them to he single diastereomers. a) I . M. Gordon. H. Maskill, M. F. Ruasse, Chem. So(. Rev. 1989, 18. 123 ~ 151 : h) J. F. King, R. Rathore in The Chemimy ofSulphonic Acid.7, Esters and their Deriwfiles (Eds. : S . Patai. 2. Rappoport). Wiley. Chichester, 1991. pp. 697766. K. Hori, H. Kazuno. K. Nomura, E. Yoshii. Telruhedron Lerl. 1993. 34, 21832186. a) S. H. Gellman. G. P. Dado, G.-B. Liang, B. R. Adams, J . Am. Cheni. Soc. 1991, 113, 1164-1173: h) G. P. Dado, S. H. Gellman. ibid. 1993, 115. 42284245; c) V. Dupont, A. Lecoq, J.-P. Mangeot, A. Auhry, G. Boussard. M. Marraud. ibicl. 1993, 1f5. 8898-8906. and references therein.: d) E. A. Gallo, S. H. Gellmdn, rbid. 1993, 115. 9774-9788; e )G. P. Dado, S. H. Gellman. ibid. 1994. 116, 1054-1062. Usage-directed Still-Chang--Guida torsional Monte Carlo method 119 a], as a part of BATCHMIN-MacroModel3.1 molecular mechanics program 119 h]. was used for the conformational search on a Silicon Graphics Iris workstation. The conformers were minimized in chloroform using the GBiSA model included in BATCHMIN [19c]. MM2* parameters were used as implemented in MacroModel [19b]. with the addition of suitable parameters for the sulfonamide group [19d]. For a conformational analysis of vinylogous polypeptides, see: M. Hagihara, N. J. Anthony, T. J. Stout, J. Clardy. S. L. Schreiher, J Am. Cheni Soc. 1992. 114,6568 6570. a) G. Chang, W. C. Guida. W. C. Still. J . A m . C/ieni. So<. 1989. / / I . 4379-4386; b) F. Mohamadi, N. G. J Richards. W. C. Guida, R. Liskamp, M. Lipton. C. Caufield, G. Chang, T. Hendrickson. W. C. Still. J . Compur. Chem. 1990. 11, 440-467; c) W. C. Still. A. Tempczyk, R. C. Hawley, T. Hendrickson. J . Am. Chen?. Soc. 1990, 112. 61276129; d) L. Belvisi. 0. Carugo, G . Poli. J. Mol. Struct. 1994. 318. 189-202 Localization of Electrons in Intermetallic Phases Containing Aluminum**

Steffen Wengert

Papers

ELF: The Electron Localization Function

Die Elektronenlokalisierungsfunktion ELF

Localization of Electrons in Intermetallic Phases Containing Aluminum

ELF: The Electron Localization Function

Unequivocal Partitioning of Crystal Structures, Exemplified by Intermetallic Phases Containing Aluminum†‡