Colleagues, Given the increased interest in computational chemistry courses taught at the undergraduate and graduate levels, I have provided the computational chemistry archive at the Ohio State Supercomputer Center with an ASCII ftp file containing the majority of the materials used in the teaching of Chemistry 8003 here at the University of Minnesota. All chemistry graduate students are required to take at least two of three core courses during their first two years, and Chemistry 8003 is one of these. This core program is new this year. Similarly, this was the first time 8003 was taught. In this posting, I include only the general description. The ftp file is roughly twenty pages long (Microsoft Word single spaced text only file). If you access these materials, we would be very grateful to receive your comments. Christopher J. Cramer University of Minnesota Department of Chemistry 207 Pleasant St. SE Minneapolis, MN 55455-0431 cramer@staff.tc.umn.edu (612) 624-0859 ********** THE FOLLOWING MATERIALS WERE USED IN THE DEVELOPMENT AND TEACHING OF CHEMISTRY 8003 AT THE UNIVERSITY OF MINNESOTA. THE COURSE IS ONE OF THREE GRADUATE CORE COURSES OF WHICH THE CHEMISTRY DEPARTMENT REQUIRES ALL FIRST-YEAR GRADUATE STUDENTS TO TAKE TWO. ********** Chemistry 8003 was a one quarter, four credit course. It met 30 times in ten weeks for one hour each class. The classroom included a Mac IIsi on the ethernet hooked to a large-screen projector for demos. The course was taught for the first time in the Winter Quarter of 1992. Attached are the course syllabus, outline, problem sets, handouts, and the final exam and final assigned paper. Literature articles were used heavily for discussion; the references are included in the course outline. The attached materials are not copyrighted, and we encourage their use by any organization or individual so inclined. Certain handouts did not lend themselves to ASCII reproduction, and are not included. The 39 students (and roughly 15 auditors) had access 12 hours per day to a microcomputer lab. The software used in the course included PCModel, running on IBM 386 clones and Macintosh IIci's (we preferred the latter), AMSOL v.3.0.1 and Gaussian92. The latter two program suites were run on an IBM RS/6000 model 560. Communication with the workstation used NCSA Telnet v.2.5 for Macintosh. Students also had access to Microsoft Word 5.0, ChemDraw 3.0 and Chem3D 3.1 all running on Macs. All software was obtained under the appropriate license agreements except AMSOL and NCSA Telnet, which are currently public domain. Problem sets were completed by groups of two, the final exam and critical analysis paper were individual projects. Some overall impressions were: 1) our syllabus was a bit ambitious given the time constraints -- we cut a few things down, although we still tried to cover all topics. 2) We converted about 5-10% of the class to computational chemistry, inspired another 25-30% to start using some modeling software in their experimental research, left another 50% with a demonstrably larger (and perhaps even appreciated) understanding of computational chemistry, and the remainder left with the same prejudices against theory with which they came in. 3) As a rule, physical chemists thought there wasn't enough theory, organic chemists thought there was far, far too much theory, inorganic chemists felt slighted that so few techniques existed to treat metals effectively , and biological chemists wondered who cared about small molecules anyway. 4) More workstation power would have been nice. 5) As far as the course text(s), Clark is very out of date at this point with regard to ab initio HF theory, fairly out of date with regard to semiempirical MO theory, but still quite reasonable for molecular mechanics and technical issues like Z-matrices, etc. Hehre, Radom, Pople and Schleyer was placed on reserve for the class, but deemed a bit too expensive and technical to be a required textbook. The same was true for the Reviews in Computational Chemistry series edited by Boyd and Lipkowitz. -- With the exception of the conversion to comp. chem. rate (which we never expected to be so high!), all of these things were about what we expected, and we were pleased with the initial offering of the course. Obviously, we hope to improve on this in future years. Christopher J. Cramer Steven R. Kass _________ Chemistry 8003 Computational Chemistry COURSE DESCRIPTION This course will provide a broad survey of computational methods currently in use within the wider chemistry community. The intent is to familiarize the student in a hands-on fashion with currently available techniques (and software) used to model problems of chemical significance. Particular emphasis will be placed on practical methodologies which have become commonplace in modern research. Neither in- depth exploration of the underlying theories nor their mathematical implementations will be the object.. The class will address the ab initio self-consistent field (Hartree-Fock), and density functional (Kohn-Sham) approaches to solving the time-independent Schroedinger equation. Conformational analysis, estimation of one-electron properties and applications to molecular spectroscopy (UV, IR, NMR, ESR, microwave) will be emphasized. The advantages and disadvantages of semi-empirical approximations to the more rigorous ab initio formalism will be discussed (Huckel, INDO, MNDO, AM1, PM3, MNDO/D, SAM-1), as will be the development and application of classical force field approaches (MM2, MM3, AMBER, OPLS). The application of these various models to gas and condensed phase systems will be presented, with special emphasis on solvation issues. Additionally, the modeling of dynamical processes by classical, quantum and Monte Carlo type methodologies may be explored. CJC SRK _________ Chemistry 8003 Computational Chemistry SYLLABUS Chemistry 8003 Computational Chemistry 4 Credits Winter Quarter 1993 Prerequisites: Chemistry graduate student or instructorsÕ permission. Location: 331 Smith Hall. Instructors: Dr. Steven R. Kass (276 Kolthoff Hall, 625- 7513) and Dr. Christopher J. Cramer (215 Smith Hall, 624- 0859) TA: Khalid A. M. Thakur (70 Kolthoff, 624-7335). Office Hours: By arrangement -- you are welcome to look us up at any time. Textbook: Tim Clark, A Handbook of Computational Chemistry, Wiley-Interscience, New York, NY: 1985. Molecular Models: Chemistry is a science concerned with three dimensions while blackboards and writing paper are confined to two. A good set of molecular models can be tremendously useful for visualizing issues of stereochemistry and structure and we recommend them highly. Both the bookstore and the Organic Chemistry Teaching Stockroom offer a variety of model sets ranging in price from $10-25. There is no requirement to purchase a set, but we suspect many of you would find them helpful. Coursework: There will be four assigned laboratory projects during the quarter. The labs will be accomplished on either 386 PC's, Macs or on an IBM RS/6000 (students will be provided with accounts). There will be a requirement for an analysis of a computational paper within the student's area of interest due on the date of the final (approx. 4-8 pages). Lastly, there will be a final exam, which will be of the take home variety (open book, open library, etc.) There will be no exams prior to the final. Our intent is not to foster memorization of specific details within the field, but to provide the student with the background and resources necessary both to apply and to critically assess computational methodologies. Several classes will focus on discussion of recent applications and will involve the prior reading of journal articles and/or book chapters handed out previously in class. Grading: The four labs will each contribute 10% to your overall grade. The critical analysis will contribute an additional 30%, as will the final exam. The grading curve will reflect the graduate level of the course. Academic Misconduct: We rigorously adhere to the IT policy on scholastic conduct (IT Bulletin, p. 18). This is a challenging course affording significant opportunity for individual initiative. Inasmuch as all of the graded requirements are to be completed outside of class, you will have the opportunity to discuss them with your fellow students. This does not become inappropriate unless it is designed to arrive at the required results without actually performing the antecedent work. We have elected to adopt this grading scheme because we believe it will provide you with a particularly useful exposure to the field, and we trust you to act within what should be common-sense limits. CJC/SRK 12-31-92 _________ Chemistry 8003 Computational Chemistry COURSE OUTLINE Course Day 1 I. Introduction and Historical Perspectives (CJC,SRK) [Compendium of Software for Molecular Modeling, Rev. Comp. Chem., Vol. 3, Boyd and Lipkowitz, Eds., VCH, 1992.] II. Force Fields / Molecular Mechanics 2 A. Theory of classical mechanics. Parametrization of force fields. Bonded and non-bonded terms. MM2, MM3, AMBER, OPLS. Computer implementations -- hardware and software. (SRK) 3 B. Discussion of applications (to be chosen). (SRK) [Dorigo and Houk, JACS 1987, 109, 3698. Menger and Sherrod, JACS 1990, 112, 8071. 4 C. Discussion of applications (to be chosen). (CJC) [Nicholas, Hopfinger, Trouw and Iton, JACS 1991, 113, 4792. Still, Tempczyk, Hawley and Hendrickson, JACS 1990, 112, 6127. Dang, Rice, Caldwell and Kollman, JACS 1991, 113, 2481.] 5 D. Current frontiers. Extended force field terms. Hybrid QM/MM approaches. Polarized force fields. (CJC) Assign first lab. III. Semiempirical Theory 6-8 A. HŸckel MO theory. Hartree-Fock theory. MO-LCAO formalism. CNDO, INDO and NDDO approximations. Parameterization of semiempirical terms. Survey of modern Hamiltonians. Geometry optimization. General performance of the models. (CJC) 9 B. The IBM RS/6000 560 model. Unix. Vi editor. Memory and Disk space. General discussion of the interdependence of computational software and hardware. (SRK) 10-11 C. Molecular geometry representation. Z- matrices. Symmetry. Description of AMSOL and MOPAC. Keywords. Input and Output. (SRK) 12-13 D. Discussion of applications (to be chosen). (SRK) [Stewart, Semiempirical Molecular Orbital Methods, Rev. Comp. Chem., Vol. 1, Boyd and Lipkowitz, Eds., VCH, 1990. Dewar and Thiel, JACS 1977, 99, 4907. Dewar and Rzepa, JACS 1978, 100, 784.] 14 E. Discussion of applications (to be chosen). (CJC) [Dewar, Zoebisch, Healy and Stewart, JACS 1985, 107, 3902. Bausch, Gregory, Olah, Prakash, Schleyer and Segal, JACS 1989, 111, 3633. Frau, Donoso, Munoz and Garcia Blanco, J. Comp. Chem. 1992, 13, 681.] 15 F. Current frontiers. NDDO fragment models. QM/MM models. Inclusion of d orbitals. Configuration interaction. (CJC) Assign second lab. IV. Ab Initio Hartree-Fock Theory 16 A. Derive HF equations, derive variational principle, discuss correlation techniques and implementation. (SRK) 17-18 B. Basis sets. Practical issues. Current software packages. Description of Gaussian 92. Keywords, input and output. (SRK) 19-20 C. Applicatons (to be chosen). Hypersurface construction. Closed shell and open-shell molecules. One- electron properties. Spectroscopy. Thermodynamics. (SRK) [Chou, Dahlke and Kass, JACS 1993, 115, 315. Curtiss, Raghavachari, Trucks and Pople, JCP 1991, 94, 7221.] 21 D. Applicatons (to be chosen). Current frontiers. Direct methods. Pseudo-spectral methods. (CJC) Assign third lab. [Foresman, Head-Gordon, Pople and Frisch, JPC 1992, 96, 135. Cramer, JOC 1991, 56, 5229.] V. Density Functional Theory 22 A. Derive Kohn-Sham equations with historical context. X-a. Basis sets. Software. (CJC) 23 B. Applications. Compare and contrast with HF type techniques. Current frontiers. (CJC) [Pudzianowski, Barrish and Spergel, Tet. Lett. 1992, 33, 293. Andzelm and Wimmer, JCP, 1992, 96, 1280.] VI. Solvation 24 A. Condensed phase effects in general. Thermodynamic and kinetic effects. (SRK) [General theory handout attached below.] 25-26 B. Continuum solvent models. Born and generalized- Born models. Kirkwood-Onsager model. Poisson-Boltzmann equations. Theory and implementation. Applications. Quantum and classical approaches. Software packages. (CJC) Assign fourth lab. [Cramer and Truhlar, JACS 1992, 114, 8794.] 27-28 C. Explicit solvent models. Monte Carlo and Molecular Dynamics simulations, theory and implementation. Software packages. Applications. (CJC) [Severance and Jorgensen, JACS 1992, 114, 10966.] 29 D. Current frontiers. Polarizable force fields. Correlated methods. Equilibrium and non-equilibrium considerations. (CJC) F Final Exam and Paper Analysis Due _________ Chemistry 8003 Computational Chemistry INITIAL SURVEY OF STUDENTS 1. Please describe yourself (e.g. undergrad, graduate student, etc.) and your research interests (e.g. physical, inorganic, etc.) 2. On a scale of 1-10, with 10 being very comfortable with, rate your familiarity with computers. 3. Of the scientific papers you read, approximately what percentage contain computational results? How well would you say you understand the applicability of the employed theory? 4. What do you expect to be the most difficult aspect of this class for you? 5. Is there any particular material/subject you would like to see covered in this class? 6. What do you want to take away from this class when you leave (other than an A, of course . . . )? _________ Chemistry 8003 Computational Chemistry COURSE HANDOUTS Some Commonly Used Force Fields Force Field Application Reference MM2 General purpose U. Burkert and N. L. Allinger, Molecular Mechanics, ACS Monograph 177. American Chemical Society, Washington D. C., 1982. MM3 General purpose (C, H, O, and N only) N. L. Allinger, Y. H. Yuh, and J.-H. Lii, J. Am. Chem. Soc., 111, 8551 (1989). MMX General purpose See PCMODEL (Serena Software) OPLS General Purpose / Proteins W. L. Jorgensen and J. Tirado-Rives, J. Am. Chem. Soc., 110, 1657 (1988). AMBER Proteins and Nucleic Acids S. J. Weiner, P. A. Kollman, D. T. Nguyen, and D. A. Case, J. Comput. Chem., 7, 230 (1986). CHARMM Proteins Nucleic Acids B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, and M. Karplus, J. Comput. Chem., 4, 187 (1983). L. Nilsson and M. Karplus, J. Comput. Chem., 7, 591 (1986). Sugars S. N. Ha, A. Giammona, M. Field, and J. W. Brady, Carbohydr. Res. 180, 207 (1988). Tripos Proteins M. Clark, R. D. Cramer III, and N. V. Opdenbosch, J. Comput. Chem., 10, 982 (1989). ECEPP Proteins F. A. Momany, R. F. McGuire, A. W. Burgess, and H. A. Scheraga, J. Phys. Chem., 79, 2361 (1975). ECEPP/2 Proteins G. NŽmethy, M. S. Pottle, and H. A. Scheraga, J. Phys. Chem., 87, 1883 (1983); M. J. Sippl, G. NŽmethy, and H. A. Scheraga, J. Phys. Chem., 88, 6231 (1984). CFF/VFF Proteins S. Lifson, A. T. Hagler, and P. Dauber, J. Am. Chem. Soc., 101, 5111 (1979). YETI Proteins A. Verdani, J. Comput. Chem., 9, 269 (1988). _________ Chemistry 8003 Computational Chemistry COURSE HANDOUTS Chemistry 8003 Computational Chemistry 4 Credits Winter Quarter 1993 KEY ASSUMPTIONS / FEATURES OF SEMIEMPIRICAL THEORY: 1. The overlap matrix elements in the secular determinant are set equal to the Kršnecker delta function, i.e., Sij = dij in | H - ES | = 0 2. Interactions of two electronic charge clouds are considered negligible if either cloud is spread over two orbitals with each on a different atom, i.e., < mn | ls > = 0 if either m and n, or l and s are not on the same atom. 3. Valence s and p orbitals comprise a sufficient basis set with which to form molecular orbitals. 4. van der Waals attractive forces are modeled by attractive Gaussian functions fit to reproduce experimental data. 5. The interactions of electronic charge clouds which are not ignored (see 2.) are approximated by the interactions of classical multipoles. 6. The correlated motion of electrons is "built in" to some extent by fitting against experimental data (i.e., reality). Some General Performance Notes: 1. Sterics: MNDO overemphasized the effect of steric crowding (neopentane, for instance, gives a very high heat of formation). By contrast, 4-membered rings are much too stable with MNDO (cubane is overstabilized by 50 kcal/mol). AM1 and PM3 do much better with the energies of 4-membered rings, but still predict them to be planar as opposed to puckered. AM1 and PM3 also do poorly with 5-membered rings, which are predicted to be too flat -- furanoses are a prime example. The latter two methods are not bad for 6-membered rings. For a thorough comparison, see Ferguson et al., J. Comput. Chem. 1992, 13, 525. 2. Transition states: MNDO overestimates most reaction barriers because of its tendency to overestimate repulsions between atoms separated by van der Waals distances. AM1 and PM3 largely correct this problem. 3. Charged species are much less accurately treated than are neutrals. Anions are particularly difficult because the AO's used in the LCAO basis set are not very diffuse, they are simply valence orbitals. 4. Radicals tend to be overstabilized by all semiempirical methods. 5. Aromatics are consistently calculated as being too high in energy by MNDO, AM1 and PM3; the error is on the order of 4 kcal/mol. 6. Geometries: Average Errors Bond Bond Dihedrals Lengths Angles (few data) MNDO 0.054 4.3 21.6 AM1 0.050 3.3 12.5 PM3 0.036 3.9 14.9 7. Hypervalency is treated extremely poorly since d functions are not part of the basis. 8. Hydrogen bonding gives better gross geometries and energies with the PM3 Hamiltonian, but the oxygen-oxygen distance in the water dimer is better with AM1. For a thorough discussion and leading references on hydrogen bonding with the semiempirical methods, see Jurema and Shields, J. Comput. Chem. 1993, 14, 89. _________ Chemistry 8003 Computational Chemistry COURSE HANDOUTS Chemistry 8003 Ñ Solvation Handout February 26, 1993 1.1 Components of Solvation Prior to discussing different solvation models, it is appropriate to consider various terms which may contribute to the free energy of solvation. One key property of a solvent is its bulk dielectric. Upon passing from the vacuum (or dilute gas-phase) dielectric of unity into solution, the structure and charge distribution within a solute will generally relax to permit greater charge separation; this effect increases with increasing dielectric and is referred to as electronic polarization. The effect is mutual, insofar as the solute also polarizes the solvent (the latter effect usually distinguished from the former by the term electric polarization). Naturally, since it represents a distortion from the optimum gas-phase structure, polarization affects the free energy of the solute in a purely internal fashion as well, this being always a destabilizing effect. When the favorable intermolecular consequences of further polarization are overcome by the intramolecular costs of that distortion, relaxation is complete. While these energy terms, which we refer to as ENP, for Electronic, Nuclear, and Polarization, are primarily a function of the bulk dielectric, there are other terms which are more specifically associated with the first solvation shell. In particular, there is the cavitation energy required to fit the solute into the solvent. There are also attractive dispersion forces between the solute and the solvent molecules. Finally, there are local structural changes in the solvent as a result of the solute -- one key example is hydrogen bonding. While the electrostatic component of hydrogen bonding may be included to some degree in the dielectric interaction, it also has a directionality which can not be accounted for in a uniform dielectric. We refer to these latter energies as CDS terms, for Cavitation, Dispersion, and Solvent Structural rearrangement. In our analysis, we will have cause to assess the degree to which various models consider or ignore these terms. 1.2 Solvation Modeling We begin by noting that the current state of the art in solvation modeling in general follows one of two alternative approaches. The first involves the explicit construction of a solvent shell, consisting of hundreds or thousands of solvent molecules, about the solute of interest.4 This supermolecular system, which may be regarded as a microcanonical ensemble under suitable conditions, serves as a basis for simulations from which thermodynamic data related to solvation may be extracted. Simulations typically involve either a Monte-Carlo pseudo-random sampling approach5 or the solution of Newton's equations of motion to generate molecular dynamics phase- space trajectories.6 In either instance, the significant size of the system prohibits the analysis of forces and energies at the quantum mechanical level; instead a classical mechanical force field is generally employed. The classical approach almost always, therefore, ignores the contribution of polarization-relaxation to the ENP terms. While classically polarizable solvent models have been employed in specific simulations,7 they are not yet general. Classical polarization of the solute does not appear to have been considered. By contrast, the simulation procedures necessarily include the CDS terms (within the force field formalism), by virtue of the explicit representation of the solvent. The main alternative to these simulation procedures replaces the explicit solvent molecules with a continuum having the appropriate bulk dielectric.8 Having simplified the system considerably, it is now possible to employ quantum mechanical approaches for the ENP relaxation of electronic and molecular structure within the continuum dielectric. Since this represents an effective averaging of solvent molecules, this is perhaps best referred to as a quantum- statistical model. Various methods for the incorporation of the bulk dielectric into the electronic structure calculation have been reported. The simplest approach, originally proposed by Kirkwood and Onsager,9 is to truncate at the dipole term the Taylor series for the classical multipolar expansion of the electronic structure; one thus includes only the monopole (charge) and dipole interaction with the continuum. That interaction is particularly simple to derive analytically if the solute is assumed to reside in a spherical cavity within the dielectric. This approach is somewhat restricted, given the limitations of the spherical cavity model. Moreover, the simplification of the electronic distribution does not permit non-zero ENP contributions to the solvation free energy for neutral molecules whose dipole moments vanish as a result of symmetry. Nevertheless, the model is particularly simple to implement and thus remains both widely available and employed.3i,10-12 Generalizations of the Kirkwood-Onsager model have appeared which carry out the Taylor series expansion to arbitrary classical multipole order, thereby overcoming many of the former's limitations. Efficient optimization of solvated geometries has prompted in some instances the retention of idealized cavities for the solutes,13 but the formalism has been applied extensively with multipolar expansions fitted to completely arbitrary surfaces.14 Finally, continuum approaches which adopt a generalized Born formalism for the interaction of atomic partial charges with the surrounding dielectric have appeared.15,16 The atom- centered monopoles in principle generate all of the required multipoles to describe the electronic distribution. We note this primarily for comparative purposes, since calculation of the ENP terms does not actually involve the multipole moments. As described above, the various quantum-statistical continuum models take account of the ENP solvation terms but in general make no effort to address the energetic effects implicit in the CDS terms. They are thus in some sense complementary to explicit solvent models insofar as each focuses on separate contributions to the solvation energy. In an effort to address these limitations, we developed the SMx aqueous solvation models.16 The most recent SM216b and SM316c models extend the Austin Model 1 (AM1)17 and Parameterized Model 3 (PM3)18 semiempirical gas-phase Hamiltonians respectively. This Neglect of Diatomic Differential Overlap (NDDO)19 level of theory permits us to treat even fairly large solutes quantum mechanically, and we employ an extended Born formalism to calculate the ENP solvation terms. In addition, however, we have added atomic parameters which account for the local CDS effects by assigning unique surface tensions to the solvent accessible surface areas of various functional groups within the solute. The relationship between solvent accessible surface area20 and the energetics of such phenomena as cavitation, dispersion and hydrogen bonding has been noted before in a variety of different contexts.21 The virtue of including all of these terms, however, is that it permits us to refine the SM2 and SM3 parameters by fitting against experimental22 free energies of solvation. Moreover, we specifically calculate absolute free energies of solvation -- a quantity not easily obtained with any of the aforementioned alternative approaches. The development and performance of these models has been recently reviewed.16d It suffices to note here that the mean unsigned error in predicted free energies of solvation is on the order of 0.8 kcal/mol for a data set of 150 molecules which spans a wide variety of functionalities. Additionally, since we are calculating absolute free energies of solvation, we must define our standard state, which we take as 1 M in both the gas phase and aqueous solution. In addition, we note that hybrid quantum mechanical/classical mechanical models have recently been explored which also permit the calculation of both the ENP and CDS solvation terms simultaneously.23 References 3. (a) J. S. Kwiatkowski, T. J. Zielinski, and R. Rein, Adv. Quantum Chem., 1986, 18, 85. (b) M. M. Karelson, A. R. Katritzky, M. Szafran, and M. C. Zerner, J. Org. Chem. 1989, 54, 6030. (c) M. M. Karelson, A. R. Katritzky, M. Szafran, and M. C. Zerner, J. Chem. Soc., Perkin Trans. 2, 1990, 195. (d) A. R. Katritzky and M. Karelson, J. Am. Chem. Soc., 1991, 113, 1561. (e) H. S. Rzepa, M. Y. Yi, M. M. Karelson, and M. C. Zerner, J. Chem. Soc., Perkin Trans. 2, 1991, 635. (f) C. J. Cramer and D. G. Truhlar, J. Am. Chem. Soc., 1991, 113, 8552. (g) M. W. Wong, K. B. Wiberg, M. J. Frisch, J. Am. Chem. Soc., 1992, 114, 1645. (h) C. J. Cramer and D. G. Truhlar, Chem. Phys. Lett., 1992, 198, 74. (i) S. Woodcock, D. V. S. Green, M. A. Vincent, I. H. Hillier, M. F. Guest, and P. Sherwood, J. Chem. Soc., Perkin Trans. 2, 1992, 2151. 4. (a) M. P. Allen and D. J. Tildesley, ÔComputer Simulations of Liquids,Õ Oxford University Press, London, 1987. (b) J. M. Haile, ÔMolecular Dynamics Simulation,Õ Wiley-Interscience, New York, 1992. (c) A. Warshel, ÔComputer Modeling of Chemical Reactions in Enzymes and Solutions,Õ Wiley-Interscience, New York, 1991. 5. (a) W. L. Jorgensen, Acc. Chem. Res., 1989, 22, 184. (b) D. L. Beveridge and F. M. DiCapua, Annu. Rev. Biophys. Chem., 1989, 18, 431. 6. (a) P. A. Kollman and K. M. Merz, Acc. Chem. Res., 1990, 23, 246. (b) T. P. Straatsma and J. A. McCammon, J. Chem. Phys., 1991, 95, 1175. 7. (a) G. King and A. Warshel, J. Chem. Phys., 1989, 91, 3647. (b) L. X. Dang, J. E. Rice, J. Caldwell, and P. A. Kollman, J. Am. Chem. Soc., 1991, 113, 2481. (c) Y. W. Xu, C. X. Wang, and Y. Y. Shi, J. Comput, Chem., 1992, 13, 1109. (d) F. S. Lee, Z. T. Chu, and A. Warshel, J. Comput. Chem., 1993, 14, 161. 8. (a) O. Tapia, in ÔQuantum Theory of Chemical Reactions,Õ R. Daudel, A. Pullman, L. Salem, and A. Viellard, Eds., Reidel, Dordrecht, 1980, Vol. 2, p. 25. (b) J. Tomasi, G. Alagona, R. Bonaccorsi and C. Ghio, in ÔModelling of Structure and Properties of Molecules,Õ Z. B. Maksic, Ed., Horwood, Chichester, 1987, p. 330. 9. (a) L. Onsager, J. Am. Chem. Soc., 1936, 58, 1486. (b) J. G. Kirkwood, J. Chem. Phys., 1939, 7, 911. (c) O. Tapia and O. Goscinski, Mol. Phys., 1975, 29, 1653. 10. M. J. Frisch, G. W. Trucks, M. Head-Gordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defrees, J. Baker, J. J. P. Stewart, and J. A. Pople, Gaussian 92, Gaussian, Inc., Pittsburgh PA, 1992. 11. M. Karelson, T. Tamm, A. R. Katritzky, S. J. Cato, and M. C. Zerner, Tetrahedron Comput. Methodol., 1989, 2, 295. 12. M. F. Guest and J. Kendrick, GAMESS CCP1/86/1, Daresbury Laboratory, 1986. 13. (a) J. L. Rivail, in ÔNew Theoretical Concepts for Understanding Organic Reactions,Õ J. Bertr‡n and I. G. Czismadia, Eds., Luwer, Dordrecht, 1989, pp. 219-230. (b) R. R. Pappalardo, E. S‡nchez-Marcos, M. F. Ruiz-L—pez, D. Rinalds, and J. L. Rivail, J. Phys. Org. Chem., 1991, 4, 148. (c) D. Rinaldi, J. L. Rivail, and N. Rguini, J. Comput. Chem., 1992, 13, 675. 14. (a) J. Tomasi, R Bonaccorsi, R. Cammi, and F. J. Olivares del Valle, J. Mol. Struct. THEOCHEM, 1991, 234, 401. (b) M. Negre, M. Orozco, and F. J. Luque, Chem. Phys. Lett., 1992, 196, 27. (c) B. Wang and G. P. Ford, J. Chem. Phys., 1992, 97, 4162. (d) G. E. Chudinov and D. V. Napolov, Chem. Phys. Lett., 1993, 201, 250. 15 (a) R. Costanciel and R. Contreras, Theor. Chim. Acta, 1984, 65, 1. (b) T. Kozaki, M. Morihasi, and O. Kikuchi, J. Am. Chem. Soc., 1989, 111, 1547. (c) S. C. Tucker and D. G. Truhlar, Chem. Phys. Lett., 1989, 157, 164. (d) W. C. Still, A. Tempczak, R. C. Hawley and T. Hendrickson, J. Am. Chem. Soc., 1990, 112, 6127. 16. (a) C. J. Cramer and D. G. Truhlar, J. Amer. Chem. Soc., 1991, 113, 8305, 9901(E). (b) C. J. Cramer and D. G. Truhlar, Science, 1992, 256, 213. (c) C. J. Cramer and D. G. Truhlar, J. Comput. Chem., 1992, 13, 1089. (d) C. J. Cramer and D. G. Truhlar, J. Comput.-Aided Mol. Design, 1992, 6, 629. 17. (a) M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. Am. Chem. Soc., 1985, 107, 3902. (b) M. J. S. Dewar and E. G. Zoebisch, J. Mol. Struct. (Theochem), 1988, 180, 1. (c) M. J. S. Dewar and C. Jie, J. Mol. Struct. (Theochem), 1989, 187, 1. (d) M. J. S. Dewar and Y. C. Yuan, Inorg. Chem., 1990, 29, 3881. 18. (a) J. J. P. Stewart, J. Comput. Chem., 1989, 10, 209, 221. (b) J. J. P. Stewart, J. Comput.-Aided Mol. Des., 1990, 4, 1. 19. J. A. Pople and D. L. Beveridge, ÔApproximate Molecular Orbital Theory,Õ McGraw-Hill, New York, 1970. 20. R. B. Hermann, J. Phys. Chem., 1972, 76, 2754. 21. (a) D. Eisenberg and A. D. McLachlan, Nature, 1986, 319, 199. (b) T. Ooi, M. Oobatake, G. Nemethy, and H. A. Scheraga, Proc. Natl. Acad. Sci. USA, 1987, 84, 3086. 22. (a) J. Hine and P. K. Mookerjee, J. Org. Chem., 1975, 40, 287. (b) S. Cabani, P. Gianni, V. Mollica, and L. Lepori, J. Solution Chem., 1981, 10, 563. (c) A. Ben-Naim and Y. Marcus, J. Chem. Phys., 1984, 81, 2016. 23. (a) M. J. Field, P. A. Bash, and M. Karplus, J. Comput. Chem., 1990, 11, 700. (b) O. Tapia, F. Colonna, J. G. Angyan, J. Chim. Phys., 1990, 87, 875. (c) V. Luzhkov and A. Warshel, J. Comput. Chem., 1992, 13, 199. (d) J. Gao, J. Phys. Chem., 1992, 96, 537. (e) J. Gao and J. J. Pavelites, J. Am. Chem. Soc., 1992, 114, 1912. _________ Chemistry 8003 Computational Chemistry PROBLEM SETS Problem Set 1 1/15/93 (Due 1/27/93) Using PCModel, answer the questions below. 1. What is the difference in energy between 1- methylcyclobutene (A) and methylenecyclobutane (B)? Does your result seem reasonable (briefly explain)? 2. What is the Sn-Csp3 stretching force constant and equilibrium bond length parameter in MMX? Calculate the structure of (CH3)3SnF and compare the SnÐC bond length with the equilibrium parameter. 3. How many conformations of cycloheptane are there? What are their relative energies? At room emperature what would the equilibrium contribution of each conformer be (assume DG = DH)? 4. Calculate the structure and heat of formation of butadiene. How do they compare with experiment? Using the rigid rotor approximation, calculate the rotational barrier for this compound. Forgetting about the rigid rotor approximation, what is the barrier to rotation? 5. Answer one of the following two questions: i) How do the experimental and calculated structures of Fe(CO)5 compare? Are they in quantitative or qualitative accord? ii) Compare the geometries of (CH3)2S, (CH3)3P and (CH3)4Si. Explain any trends you can discern. 6. Answer one of the following two questions: i) What is the lowest energy structure of the dipeptide H2N-alanine-glycine-CO2H? ii) Calculate the heats of reaction for the following series of transformations and rationalize the results. SiH4 + CH3CH3 -----> CH3SiH3 + CH4 CH3SiH3 + CH3CH2CH3 -----> (CH3)2SiH2 + CH3CH3 (CH3)2SiH2 + (CH3)3CH -----> (CH3)3SiH + CH3CH2CH3 (CH3)3SiH + (CH3)4C -----> (CH3)4Si + (CH3)3CH 7. Answer one of the following two questions: i) Explain how you would calculate the lowest energy structure for 3-methoxycylclohexene and then calculate it. How reliable do you think the geometry is (explain/defend your answer)? How reliable do you think the calculated heat of formation is (explain/defend your answer)? ii) Calculate the structure for cobalt tris(ethylenediamine) [Co(NHCH2CH2NH)3], cobalt tris(acetylenediamine) [Co(NHCH=CHNH)3], and compare them to each other and with related experimental data. _________ Chemistry 8003 Computational Chemistry PROBLEM SETS Chem 8003 2/1/93 Problem Set 2 (Due 2/17/93) 1. Identify all of the symmetry elements and give the point groups for the given molecules. [Graphics deleted] 2. Supply a Z-matrix (internal coordinates) which takes advantage of the full symmetry of each molecule. a. Cyclobutene (c-C4H6) b. PCl5 c. Naphthalene 3. Semiempirical methods provide electronic energies and nuclear repulsion energies for input molecules e. g. cyclopropane. Explain for this molecule how the the heat of formation is derived from these quantities. 4. Calculate the heat of formation of naphthalene using AM1 and PM3, and compare the results with experiment. In addition, sketch the HOMO and LUMO for this compound and rationalize where you would expect an electrophile to attack this substrate. Is your expectation borne out experimentally? 5. Compute at the MINDO/3, MNDO, AM1 and PM3 levels the enthalpy difference between glycine and its zwitterion. What conformational issues must be considered for this calculation? Comment on the results. Explain how you might accomplish this calculation for L-alanine -- what factors make the latter a more difficult calculation? 6. Calculate the inversion barriers for ammonia and aziridine (c-C2H5N) and compare the results to experiment. 7. Taking as many points as you feel necessary, graph the enthalpy of C-C bond rotation in fluoroacetic acid at the AM1 and PM3 semiempirical levels, as well as with the MMX force field. Do the curves conform to your expectations? Why or why not? Do the same thing for the fluoroacetate anion, and compare to the results for the neutral acid. 8. Calculate the reaction profile for the SN2 reaction of chloride anion with chloromethane at the MNDO, AM1 and PM3 levels (Use [rC-Cl(1) - rC-Cl(2)] as your reaction coordinate). Which is in best agreement with experiment? How would you do this problem differently if the reactants were chloride anion and bromomethane? 9. 1,3-Butadiene reacts with ethylene in the gas phase at elevated temperatures to afford cyclohexene. Calculate the heat of reaction and the reaction barrier (i.e. activation energy) using AM1. Compare your results to experiment. 10. Calculate the equilibrium structures for cyclohexanone, cyclopentanone, cyclobutanone and cyclopropanone at the AM1 level. What are the carbonyl bond dipoles in each case (calculated as [ qC - qO ] * r[CO])? Calculate the IR stretch for each carbonyl. How do they compare to each other and experiment? _________ Chemistry 8003 Computational Chemistry PROBLEM SETS Chem 8003 2/17/93 Problem Set 3 (Due 3/3/93) 1. Calculate the structures and energies of the important conformers of methanol using the ST0-3G, 3-21G, and 6-31G* basis sets. Be sure to take full advantage of symmetry. In addition, give the rotational barrier about the C-O bond and compare your results to experiment. 2. What is the zero point energy of acetonitrile (CH3CN)? Use the 3-21G and 6-31G(d) basis sets to answer this question, and compare your results to experiment. 3. Using all appropriate symmetry to simplify the problem, optimize the geometries of ammonia and the planar barrier to lone pair inversion for ammonia at the following levels: HF/STO-3G, HF/3-21G, HF/6-31G, HF/6-31G*, HF/6-311G, HF/6- 311G*, HF/6-311G** and MP2/6-31G*. Describe any effects the following have on both geometries and barrier height: 1) d functions on nitrogen, 2) p functions on hydrogen, and 3) electron correlation. What is the experimental barrier? Which level appears to give the best answer? Why do you think that level does as well as it does? Could the calculation be improved? How? 4. Locate the transition state for the reaction HCN --> HNC at both the HF/6-31G* and MP2/6-31G* levels. Plot the energetics for these two levels against a reaction coordinate of the HXC angle, where X is the midpoint of the C-N bond. Take as many points as you feel necessary. _________ Chemistry 8003 Computational Chemistry PROBLEM SETS Chem 8003 2/24/93 Problem Set 4 (Due 3/10/93) 1. CH3CH2CN + CH2=CH2 -----> CH3CH3 + CH2=CHCN (1) CH2=CHCN + HCCH -----> HCCCN + CH2=CH2 (2) a. Calculate the reaction enthalpies for equations 1 and 2 at the 6-31G*//3-21G level. b. Sketch the HOMO and LUMO for CH2=CHCN and HCCCN. c. Explain why equations 1 and 2 are exothermic or endothermic in qualitative terms. 2. At the HF/6-31+G* level, calculate the following for formaldehyde (H2CO): 1) principle moments of inertia, 2) IR spectrum, and 3) the wavelength and oscillator strengths for the n --> pi* and pi --> pi* excitations (hint: use CI singles). For which of these calculations do you think it was important to include diffuse functions on the heavy atoms? Why? Which frequencies will only be visible in the Raman spectrum and not the standard IR absorption spectrum? Why? 3. Using the HF/3-21+G basis set and the AM1-SM2 method calculate the reaction profile for the SN2 reaction of chloride and methyl chloride. Plot this as an overlay on the AM1 gas phase results taking the infinitely separated reactants as the energy zero. What is the aqueous reaction barrier? What qualitative changes are there in mechanism upon going from the gas phase to solution? How do the ab initio results compare to those obtained with AM1? Would you expect this reaction to take place rapidly in the gas phase or solution? 4. Consider oxalaldehyde (CHO-CHO). Calculate the PM3-SM3 free energies of aqueous solvation for the s-cis and s-trans forms. How are they different and why? Perform the same calculation at the SCRF/3-21G level using Gaussian92. How are the results different and why? _________ Chemistry 8003 Computational Chemistry FINAL PAPER GUIDELINES Chemistry 8003 Computational Chemistry 3 Credits Winter Quarter 1993 Guidelines for Final Critical Analysis of a Paper 0. This is not a group project. Each individual is responsible for this requirement. 1. The paper should be chosen from the literature. Any work dated 1990 or beyond is permissible -- earlier papers will be considered on a case by case basis. You are not merely allowed, but encouraged to pick a paper germane to your own research interests. Simultaneous presentation of experimental results is fine, however more than 50% of the paper must be devoted to computation/theory. 2. The chosen paper must be approved by one of the instructors. 3. The deadline for choosing a paper is Friday, February 26th. 4. The form of your analysis should be five ± one pages in length excluding references, figures, etc. (double-spaced, 12 point Times font, one inch margins). You should address the following areas at a minimum: a. What are the objectives of the study? b. What are the most significant conclusions drawn from the study? c. How does the employed level of theory impact on the research? Were there issues which could not be adequately addressed? Are the conclusions dependent on assumptions implicit to the theory? d. What comparisons are made to experiment, if any? What is the overall trustworthiness of the paper in your opinion? e. How could you improve on the current results? [Don't assume you have infinite computational resources! Put yourself in the authors' place and try to design either improvements or extensions of their work which could reasonably be carried out.] 5. This analysis will be due, together with the final exam, to one of the instructors by Friday, March 19th at 10:00 AM _________ Chemistry 8003 Computational Chemistry FINAL EXAM This exam is to be completed individually. It is due at 10:00 AM on Friday, March 19th. The completed exam should be turned in to either Steven or myself. If you wish to turn the exam in early, we will accept it at any time. Please double space all responses, and use font sizes no smaller than 12. Unless you dabble in calligraphy to earn extra pocket change, we would prefer word-processed/typed submissions. 1. Compare molecular mechanics to semiempirical molecular orbital theory to ab initio Hartree Fock molecular orbital theory. In particular, identify key assumptions implicit in each. Give examples of situations where one or more may be either particularly appropriate or alternatively proscribed. Assess the expected success of each with respect to prediction of such experimental observables as structure, energetics and spectra. (500 words maximum). 2. Comment on the following statement: "The higher the level of theory, the more trustworthy the answer." (150 words maximum). 3. How does symmetry affect a calculation at various levels of theory? When, if ever, is it dangerous to impose symmetry, and what can you do to avoid problems? (150 words maximum). 4. Explain in a general way, and illustrate with examples as you feel appropriate, how computational chemistry can be used as a tool in an experimental program. You need not confine yourself to the academic environment -- feel free to consider government and industrial research programs as well. (500 words maximum).