C o m p u te r M o d e lin g o f M o le c u la r E le c tro n ic S tru c tu re

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1 C o m p u te r M o d e lin g o f M o le c u la r E le c tro n ic S tru c tu re P e te r P u la y D e p a rtm e n t o f C h e m is try a n d B io c h e m is try, U n iv e rs ity o f A rk a n s a s, F a y e tte v ille

2 C h e m ic a l m a tte r: e v e ry th in g a ro u n d u s e x c e p t lig h t (o r p a rtic le b e a m s ) T h e a to m ic a n d m o le c u la r th e o ry o f m a tte r w a s c o n c lu s iv e ly p ro v e n o n ly in th e e a rly 1 9 th c e n tu ry. B y , a ll d e ta ils h a v e b e e n w o rk e d o u t. A to m s c a n s tic k to g e th e r a n d fo rm d is tin c t m o le c u le s, ra n g in g in s iz e fro m a fe w a to m s to th o u s a n d s. A lte rn a tiv e ly, th e y c a n fo rm la rg e, m a c ro s c o p ic a g g re g a te s o f u n lim ite d s iz e (m e ta ls, o rd in a ry s a lt). E v e ry th in g w e d e a l w ith, e x c e p t lig h t, c o n s is ts o f c h e m ic a l m a tte r. T h is is w h y c h e m is try is s o im p o rta n t 5 /1 7 /

3 T h e p h y s ic a l b a s is o f c h e m is try w h y d o a to m s fo rm b o n d s? re m a in e d a c o m p le te m y s te ry u n til th e d is c o v e ry o f q u a n tu m m e c h a n ic s in * T h e S c h rö d in g e r e q u a tio n fo r s ta tio n a ry s ta te s : HΨ = E Ψ is d e c e p tiv e ly s im p le, e v e n if w ritte n o u t fu lly. H o w e v e r, its fu ll s o lu tio n is v e ry d iffic u lt b e c a u s e o f th e c a t-a n d -m o u s e p la y o f th e e le c tro n s. C o n s id e rin g th e e le c tro n s in d iv id u a lly in th e a v e ra g e e le c tric fie ld o f th e o th e r e le c tro n s is d o a b le b u t d o e s n o t re a c h c h e m ic a l a c c u ra c y. Chemistry is a science of small energy differences. * P. A. M. Dirac, Proc. Roy. Soc.(London) 1926, 79, 361 The underlying physical laws necessary for the mathematical theory of the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. 3

4 The changing face of chemistry Chemical systems are virtually inexhaustible. The number of stable organic (only C,H,, and S!) molecules with M<750 daltons is estimated to be *! This is impossible to cover, experimentally or computationally, but the latter offers more hope Effective computational prediction of chemical properties and phenomena will open a new chapter in chemistry, biochemistry and materials science. * Mathematical Challenges from Theoretical/ Computational Chemistry, U.S. ational Research Council, ational Academy Press, Washington, D.C

5 10 10 improvement in the efficiency of electronic structure methods since 1970 Main contributors: Improvement in computer technology Price/performance ratio of processors Parallelization ovel theoretical methods analytical derivative techniques forces vs energy Density Functional Theory (DFT) low-scaling methods (linear in molecular size)

6 Computer price/performance ratios $/Mflops

7 Chlorinated benzodioxins 7

8 Matrix isolation and simulated IR spectra of porphine isotopomers J. Phys. Chem. 1996, 100,

9 Porphyrins are important biological molecular molecules that often bind metals. The green of the leaves and the red of the blood are due to metallo-porphyrins. The picture shows nickel porphyrin, a model for biological porphyrins, and its experimental and computer simulated infrared spectra. The experimental spectrum (top) was taken by X. Y. Li at the Hongkong University of Science and Technology. The calculated spectrum was produced in P. Pulay s lab at the Chemistry Department of the University of Arkansas. Comparison of the experimental and simulated spectrum in the 400 cm 1 region (inset lower right) proves that this molecule is not perfectly flat but ruffled.

10 Calculation of MR chemical shifts (with Prof. J. Hinton) MR is the most important structural method Prediction of MR shifts in unusual bonding situations: e.g. nonclassical asymmetric versus classical structure of carbocations (7-norbornadienyl chloride hydrolyses time faster than the saturated 7-norbornyl chloride) + C7 σ=219 ppm + (calculated) C7 σ=34 ppm (experiment) C7 σ= 30 ppm (calculated) Department of Chemistry and Biochemistry, U. of Arkansas 10

11 Proton chemical shifts in proteins (Bing Wang, A. Chuma) Proton chemical shifts in small molecules can be predicted to about 0.05 ppm H α chemical shifts change about 2.5 ppm if the torsional angles ϕ, ψ change Determination of protein backbone structure by comparing calculated and experimental proton chemical shifts? 100 atom fragments of proteins can be calculated straightforwardly Department of Chemistry and Biochemistry, U. of Arkansas 11

12 Peptide analogues H1 H23 H20 H21 H19 H22 H2 H24 Average absolute deviation: H3 H25 H26 H4 H5 H27 in dimethylsulfoxide: 0.06 ppm in D 2 : H6 H7 H8 H28 H10 H11 H9 H12 H ppm H15 H16 H17 H14 Department of Chemistry and Biochemistry, U. of Arkansas H30 H13 H H31 H18 12

13 Experimental vs. calculated aliphatic proton chemical shifts in amides Fig exp.(ppm) DMS D calc.(ppm) Department of Chemistry and Biochemistry, U. of Arkansas 13

14 Carbon-based materials: sheets, spheres (fullerenes) and nanotubes are assuming increasing importance in technology, in particular in nanotechnology. Some fundamental questions, like the mechanism of graphite sheets sliding over each other, and the interaction of water with hydrophobic (water repelling) surfaces like graphite can be best addressed by accurate computer simulations. The pictures show two graphite segments sliding over each other (left) and the interaction between a water molecule and a small graphite sheet (coronene). (Alan Ford and Estelle Huff at the University of Arkansas, Fayetteville)

15 Accurate computer simulation led to the surprising result that π stacking contributes more to the energy of DA than hydrogen bonding (P. Hobza et al., Science). This conclusion was based on accurate calculations of π interactions between DA bases by Dr. Janowski at the U. of Arkansas, Fayetteville. The picture shows a methyladenine methylthymine pair

16 A localized occupied orbital in C 192 H 48 An inherently delocalized system 16

17 18 Fig 3 Experimental pka vs calculated pka (6-311+G**//3-21G(d)) y = x R 2 = Experimental pka acids phenols alcohols amines anilines pyridines together Calculated pka Department of Chemistry and Biochemistry, U. of Arkansas 17

18 Structures Zn 6 S 6 Ligand Average Binding Energy (kcal/mol) -Formic acid Acetic Acid Ammonia Methylamine Methylmercaptan TMP Department of Chemistry and Biochemistry, U. of Arkansas

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