1. Introduction Role of Calculations Calculations are much like experiments in that both may be employed in two different ways: 1. Data collection. 2. Looking for the unusual.
Advantages of Calculations Calculations can be performed on unstable molecules and reaction transition states; Experiments are very difficult on such molecules and can not be performed on transition states.
Calculations are becoming less and less costly; Experiments are becoming more and more costly.
Advantages of Calculations (Cont.)
Calculations are safe; Experiments are sometimes dangerous.
Calculations are now easy to perform; Experiments are sometimes more difficult. Calculations are now performed by not only computational chemists but also experimental chemists.
Disadvantages of Calculations
The cost of calculations increases rapidly with molecular size; The cost of experiments is generally independent of the molecular size.
Calculations sometimes yield different results depending on the employed model; Experiments usually provide only one result.
1. Basic Guide to Computational Chemistry
Molecular mechanics (MM) methods
Quantum mechanics (QM) methods
Ab Initio Hartree-Fock
Ab Initio correlated (Møller-Plesset)
Differences Between Molecular Mechanics and Quantum Methods
Molecular mechanics are restricted to the description of equilibrium structure and conformation. Quantum methods also provide information about non-equilibrium forms, e.g., transition states, and about electron charge distributions.
Differences Between Molecular Mechanics and Quantum Methods (Cont.)
Molecular mechanics are based on use of experimental information (=parameters), and thus can not be applied outside the range of parameterization. Quantum methods are not based on use of experimental information, and thus can be applied to areas where there is little or no prior experience.
Differences Between Molecular Mechanics and Quantum Methods (Cont.)
Molecular mechanics methods are much less costly than even the simplest quantum methods such as semi-empirical methods.
Range of Molecular Mechanics and Quantum Methods Method Range (heavy atoms) Molecular Mechanics > 1000 Semi-Empirical < 200 Ab initio Hartree-Fock(HF) < 50 Ab initio Correlated < 20 Density Functional (DFT) < 100
Relative Computation Times Methylcyclohexane (C H ) 7 14 Level of Calculation Single-Point Energy Geometry Optimization MMFF94 (MM) f f AM1 (Semi-Empirical) f .06 HF/3-21G (Ab initio) 1 8 HF/6-31G* (Ab initio) 7 54 MP2/6-31G* - 100 (Ab initio Correlated) pBP/DN* (DFT) 2 14
Comparison of the Performance of Molecular Mechanics(MM) and Quantum Methods(QM) Task MM Semi- Ab initio DFT Empirical HF Correlated Geometry S S S S S Transition-state - S S S S Geometry Conformation S U S S S
Thermochemistry - U S S S S= satisfactory; U= unsatisfactory
References of MM and QM
Review of MM: U. Burkert and N. L. Allinger, molecular mechanics, ACS monograph 177, American chemical society, Washington D.C., 1982.
Reviews of basic QM: I. N. Levine, quantum chemistry, 4th ed., Prentice hall, Englewood cliffs, NJ, 1991; P.W. Atkins and R.S. Friedman, molecular quantum mechanics, 3rd ed., Oxford Univ. Press, oxford, 1997.
Review of semi-empirical methods: T. Clark, A handbook of computational chemistry, Wiley, new York 1986.
Review of Hartree-Fock and Møller-Plesset models: W.J. Hehre, L. Radom, P.V.R. Schleyer and J.A. Pople, Ab Initio molecular orbital theory, Wiley, new York 1986.
Reviews of density functional theory: R.G. Parr and W. Yang, density functional theory of atoms and molecules, oxford Univ. Press, oxford, 1989; J.K. Labanowski and J.W. Andzelm, eds., Density functional methods in chemistry, Spriger-Verlag, new York, 1991.
Widely Used Software Packages for MM, QM Chem3D (CambridgeSoft, Corp. www.camsoft.com : Mac, PC) Gaussian (Gaussian, Inc. www.gaussian.com : Unix, PC) MOPAC (Fujitsu CCS www.winmopac.com : Unix, PC) Sybyl (Tripos, Inc. www.tripos.com : Unix) SPARTAN (Wavefunction, Inc.: Unix, Mac, PC) Each software has different user interface, operating feature, price, manual and so on.
1. Applications to Investigation of Molecular Structure and Property
Investigation of Molecular Structure by use of MM and/or QM a. Geometry b. Absolute Configuration
Investigation of Molecular Property (Electron Charge Distributions) by use of QM
I. Investigation of Molecular Structure by use of MM and/or QM a. Geometry (bond distance, angle, energy of molecules etc.) Conformational Energy Differences in 1,3- Butadiene; Investigation of Order of Stability H H H H H H H H H H H s-trans H s-cis twisted Dihedral angle 0 90 180
Relation between Dihedral Angle and Relative Conformer Energy in 1,3-Butadiene twisted s-trans s-cis Order of stability: s-trans > s-cis > twisted
a. Absolute Configuration Physical Methods X-ray Crystallography CD Spectroscopy Chemical Methods Total Synthesis NMR Spectroscopy (2D-NMR, 1D-NMR with Chiral Derivatizing Agents such as Mosher’s Method) Computational Chemistry (MM and/or QM)
Advantage and Disadvantage of X- ray and CD Method Advantage These methods have high reliability. Disadvantage These methods have limitation of application. Preparation of single crystal (X-ray) Molecules where -electron chromophores exist or can be introduced (CD method)
Advantages and Disadvantages of Total Synthesis Advantage This method has high reliability. Disadvantage
Many Synthetic Organic Chemists
Advantages and Disadvantages of NMR (2D-NMR, 1D-NMR with Chiral Derivatizing Agents ) Advantage NMR is widely used and easy to perform. Disadvantage Low Reliability on Acyclic Systems as well as Macrocyclic Systems (2D-NMR) Preparation of Derivatives by use of Chiral Derivatizing Agents (Mosher’s Method etc.)
Advantages and Disadvantages of Computational Chemistry Advantage This method does not require preparation of specific samples in contrast to X-ray and Mosher’s method etc. Disadvantage This method requires combination with another method such as NMR. QM has limitation of molecular size.
Determination of Absolute Configuration in A Macrocyclic System by a Combination of Computational Chemistry and Another Method H O O H O O SeO2 O O OH at room temp. 13 Sarcophine HMBC 20 CH3 NOESY H O O 2 O H OH (R) ?
H O O The distance between H-2 and H-13 is 4.0 Å in 13(R)configuration. O H OH (R) configration This is not consistent with information based on NOESY.
The distance between H-2 and H-13 is H O O 2.4 Å in 13(S)configuration. O H OH This is consist s e tent with informa information (S) configuration based on NOESY o . n NOESY
H O O Cl CD Spectrum O H O (S) O - Negative Cotton Effect CD also supports 13(S)co configuration.
• Investigation of Molecular Property (Electron Charge Distributions) by use of QM Electrostatic Potential Atomic Charges Dipole Moment Enthalpy, Entropy, and Free Energy Salvation Energy etc. Investigatio tion of Basicity (Proton Affinity), Acidity, and More… re…
4-Aminopyridine: Where is the Basic Site ? NH2 Quantitative Investigation N NH + NH NH 3 2 2 + H2O + H3O+ + H2O N N N H+ A B H(A) = 193.6, H(B) = 169.1 kcal/mol B is s more stable than A, and thus s the ring N is more basic.
Qualitative Investigation (Electrostatic Potential Map) Colors near red represent more negati ent more negative charge, while colors near blue rep represent more positive charge. NH2 N Th T e h e r irng n g N
N i s mo s m re o re n e n g e a g t a itve v l e y ch y a ch r a g r e g d e , d ,a n a d n d t h t u h s u i s s likel ke y t y o t o b e b e m o m r o e r e b a b si a c. si
Imidazole: Where is the Basic Site ? 3 N N 1 H Electrostatic Potential Map Th e Th e N - N 3 - 3 i s s n e n g e a g t a itve v l e y y c h c a h r a g r e g d e , d ,a n a d n d t h t u h s u i s s s t h t e h e b a b s a i s c c s i s te t . e
Electrostatic Potential (ESP) Map for the Alcohols CH3CH2OH CF3CH2OH OH O OH 2N
E S E P S P m a m p a p s ho sh w o s w s t h t a h t a tt h t e h e a c a id ci i d c c s i s te t s e s a r a e r e p o p s o i s titv i el ve y y c h c a h r a g r e g d e , d a n a d n d i ti tr e r f e lfec e t c s t s t h t e h e r e r l e a l t a itve v e a c a i c d i i d tites e ( s l(ig i h g t h tv s v . s .d a d r a k r b k l b u l e u ) e . ) .
• Applications to Investigation of Chemical Reactivity and Selectivity (Investigation of Molecular Orbital by use of QM) a. When there are more than one reagent, which reagent will react first ? b. When a molecule contains multiple reactive sites, which site will react first ? Examination of frontier molecul ecular orbi bital (HOMO and LUMO) is an impo portant method because most chemical reactions ons involve electron movement between them.
References of Frontier Molecular Orbital (FMO) Theory and Reaction
I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, New York, 1976.
K. Fukui, Theory of Orientation and Stereoselection, Springer, Berlin, 1975.
T. L. Gilchrist and R. C. Storr, Organic Reactions and Orbital Symmetry, 2nd. Ed., Cambridge University Press, 1979.
T. A. Albright, J. K. et al., Orbital Interactions in Chemistry, Wiley, New York, 1985.
• Investigation of Chemical Reactivity Examination of FMO Energies A reagent with the highest HOMO energy will give its electrons most easily and thus be the most reactive donor. A reagent with the lowest LUMO energy should be able to accept electrons most easily and thus be the most reactive accepter.
Acrolein/BF : What is the role of Lewis Acids ? 3 Lewis acids are commonly used to accelerate chemical reactions; the BF3 adduct of acrolein more rapidly undergoes nucleophilic attack than acrolein itself. H H H H H O H O H H BF3 Acrolein Acrolein/BF3
H H H H H O H O H H BF3 LUMO Energy -0.19 eV -2.01 eV acrolein LUMO Orbital acrolein/BF3 Energy HOMO nucleophile smaller gap (more reactive)
L e L w e i w s a s c a id ci d co mp co l mp ex e at xa iton o n r e r d e u d c u e c s e s th e th e e n e e n r e g r y g y o f o f LU L MO U
MO o n o n a cr a o cr l o ei e n, n ,m a m ki a n ki g n g i t tmo
r mo e re a cce a ss cce ib ssi l b e e t o t o t h t e h e HO H MO O
MO o n o n n u n c u le cl o e p o h p i h le. e
a. Investigation of Chemical Selectivity Examination of FMO Shape (Value) The regions where LUMO shape (value) is large will be reactive sites toward attack by a nucleophile. The regions where HOMO shape (value) is large will be reactive sites toward attack by a electrophile.
Ester Enolate: Where is the reactive site ? The ester enolate has two possible sites, which may react with electrophiles; the anion and the terminal carbon. - E O O O E E E C CH2 C CH2 C CH CH 2 2 O CH3 H2C O CH3 H2C O CH3 The site where HOMO shape (value) is larger wil be more reactive toward attack by a electrophile.
- O The c he color near r near red indicates minimum value, and the the C CH2 H color near r near blue lue indicates 2C O CH3 maximum value of HOMO. HOMO of the Enolate HOMO Map of the Enolate The terminal carbon,where HOMO shape (value) is larger, genera ral y reacts with electrophile.
Electrophilic Substitution of Indole; What should be favorite position for electrophilic attack ? 4 3 5 2 6 N H 7
H O H M O O M O m a m p ap r ev r eal evea s t s hat t
hat 3- posi 3- t posi iton i on s s the t
he m o m st os tl ikel i y kely si t si e t of e of el ect el r ect ophi r l ophi ic c at t at ack t . ack.
Stereochemistry of Nucleophilic Additions to Carbonyl Compounds Cyclohexanones has two possible faces, which may undergo nucleophilic attack; the axial and the equatorial face. Nu axial O X X X=CH2, O, S equatorial Nu The face where LUMO shape (value) is larger wil be more reactive toward attack by y a nucleophile.
Nucleophilic Additions to Dioxanone Ring Nu LUMO map axial O LUMO map for for O the equatorial O the axial face face equatorial Nu Nucleophililes prefere rential y attack from the axial face.
Nucleophilic Additions to Dithianone Ring Nu axial O LUMO map for LUMO map for S the axial face S the equatorial face equatorial Nu Nucleophililes pre referential y attack ck from m the equatorial face.
1. Future Direction I. Calculation in Solution
Although calculation in gas phase usually provides a reliable account, it in solution is still unsatisfactory for investigation of some tasks. The development of seve veral methods is in progress for the ca calculation in so solution.
References of Recently Developed Methods for Calculation in Solution
Supramolecular method: A. Abotto et al., J. Am. Chem. Soc., 119, 11255 (1997).
MC and MD method: M. Aida et al., Chem. Phys. Lett., 292, 474 (1998).
QM/MM method: J. Gao et al., J. Am. Chem. Soc., 115, 9667 (1993).
RISM-SCF method: H. Sato et al., J. Chem. Phys., 105, 1546 (1996).
I. Extension of Application Field of Computational Organic Chemistry MM and QM calculations have been used mainly in the field of investigation of molecular structure and chemical reaction so far. Explosive developments in computer hardware and software They have recently y begun to be widely applied in not only organic chemistry y but also biochemistry and closely related fields such as drug design.
References of Drug Design by use of QM R1 R3 N R1 R2 R2
R. R. Squires et al., J. Phys. Chem. A, 102, 9072 (1998).
J. Hoffner et al., J. Am. Chem. Soc., 120, 376 (1998).
P. R. Schreiner, ibid., 120, 4184 (1998). Quantum chemi mical calculations (QM) are exp xpected to become an important method for r drug design in the future.