Computational Chemistry at TCU Benjamin G. Janesko TCU 2010.02.19 - - PowerPoint PPT Presentation

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Computational Chemistry at TCU Benjamin G. Janesko TCU 2010.02.19 Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 1 / 45 Outline Computational Chemistry 1 Drug design 2 Visualizing molecules 3 Quantum chemistry and

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Computational Chemistry at TCU

Benjamin G. Janesko

TCU

2010.02.19

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 1 / 45

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SLIDE 2

Outline

1

Computational Chemistry

2

Drug design

3

Visualizing molecules

4

Quantum chemistry and computing

5

Applying computational chemistry

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 2 / 45

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SLIDE 3

What is computational chemistry?

Predicting how atoms, molecules, and solids will behave in new situations Designing new molecules and solids to do new jobs

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 3 / 45

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SLIDE 4

Three areas where computational chemistry is useful

Designing drug candidates to cure diseases

▶ Need to predict how individual molecules will stick together

Designing molecules with new properties

▶ High-energy-density materials (explosives)

Designing catalysts to make products (fuel, plastics, etc) using renewable sources, with less energy

▶ Need to predict how chemical bonds are formed and broken Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 4 / 45

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SLIDE 5

Outline

1

Computational Chemistry

2

Drug design

3

Visualizing molecules

4

Quantum chemistry and computing

5

Applying computational chemistry

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 5 / 45

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SLIDE 6

Designing drugs with computational chemistry

http://www.rcsb.org/pdb/explore/jmol.do?structureId=3K2P&bionumber=1 Crystal structure of a drug molecule bound to HIV-1 reverse transcriptase [View in web browser with Jmol applet]

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 6 / 45

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SLIDE 7

How do drugs work?

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 7 / 45

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SLIDE 8

How do drugs work?

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 8 / 45

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SLIDE 9

Drug docking in computational chemistry

Determine the structure of a protein target to block Guess several (105) structures of possible drugs Simulate the binding between drug and protein with ball-and-spring molecular mechanics Take the 5 − 10 best candidates and test in the lab

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 9 / 45

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SLIDE 10

A simple example of drug docking

Met-enkephalin pentapeptide structure from http://www.rcsb.org/pdb/explore/explore.do?structureId=1PLX

▶ Endogeneous opioid peptide neurotransmitter ▶ Blocking enkephalins could change pain tolerances

Molecular mechanics simulation with ”Avogadro” open-source molecular mechanics package, http://avogadro.openmolecules.net/wiki/Main Page Real-time ”docking” simulation possible [Illustrate drug docking onto met-enkephalin with Avogadro]

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 10 / 45

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SLIDE 11

Outline

1

Computational Chemistry

2

Drug design

3

Visualizing molecules

4

Quantum chemistry and computing

5

Applying computational chemistry

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 11 / 45

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SLIDE 12

Chemists visualize molecules with stereo views. . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 12 / 45

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SLIDE 13

. . . or with molecular models. . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 13 / 45

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. . . and most recently with computers

Software like Avogadro could be a valuable classroom tool Build chemical intuition into something you can’t see Electron density maps, charge distributions, etc. are all useful Sometimes it’s enough just to see the molecule in 3-D

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 14 / 45

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Example: Adamantane, and other diamandoid hydrocarbons

[view in Avogadro]

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 15 / 45

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Another fun example: Octanitrocubane

[view in Avogadro]

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 16 / 45

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Another fun example: Octanitrocubane

C8(NO2)8 Decomposes into 8 CO2 and 4 N2 This decomposition releases an enormous amount of energy, as your students can see from a simple bond energy calculation Count Bond DE (kJ/mol) 12 C-C 348 8 C-N 308 16 N-O 201 16 C=O 805 4 N[triple]N 941 Total energy change is 9856 - 16644 = 6788 kJ/mol

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 17 / 45

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Synthesis of octanitrocubane

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 18 / 45

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SLIDE 19

Outline

1

Computational Chemistry

2

Drug design

3

Visualizing molecules

4

Quantum chemistry and computing

5

Applying computational chemistry

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 19 / 45

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SLIDE 20

Molecular mechanics

Force on atom i at position ⃗ ri is Fi =

Bound to i

∑

j

−kij ( ∣⃗ ri −⃗ rj∣ − r0

ij

) +

close to i

∑

jk

−Tijk(휃ijk − 휃0

ijk

+

all atoms

∑

j

ZiZj ⃗ ri −⃗ rj ∣⃗ ri −⃗ rj∣3 + . . . Atom i accelerates via Newton’s equation Fi = miai Let each atom move at its new velocity for a short time Δt, then re-evaluate all the forces Repeat until the atoms have stopped, and you’re at an energy minimum

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 20 / 45

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Ball-and-spring models

Molecular mechanics is fine for normal molecules . . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 21 / 45

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Ball-and-spring models

Molecular mechanics is fine for normal molecules . . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 21 / 45

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Quantum mechanical models

Electrons in a molecule really obey Schr¨

  • dinger’s equation from

quantum mechanics iℏ ∂ ∂t Ψ(⃗ x1,⃗ x2 . . .⃗ xN) = ˆ HΨ(⃗ x1,⃗ x2 . . .⃗ xN) Closed-form (paper and pencil) solutions to Schr¨

  • dinger’s equation

are available for the hydrogen atom Every other atom, molecule, and solid must be approximated! Those approximations can readily be evaluated by a computer

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 22 / 45

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Approximating the wave function of one electron

Stationary states of Schr¨

  • dinger’s equation become

− ℏ2 2me ∇2휙i(⃗ x) + V (⃗ x)휙i(⃗ x) = 휖i휙i(⃗ x) Everything we need to know about that electron can be obtained from its wave function We can approximate the wavefunction as a sum of “basis functions” 휙i(⃗ x) =

M

∑

휇=1

ci휇휒휇(⃗ x) Select the basis functions so that the math becomes easy

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 23 / 45

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A basis set for the electron in H+

2

2 1 1 2 3 0.0 0.2 0.4 0.6 0.8 1.0 Zcoordinate Basis function amplitude

휒휇(⃗ r) = (2훼 휋 )1/4 exp ( −훼∣⃗ r − ⃗ R휇∣2)

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 24 / 45

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Approximating the wave function of one electron

Describe the wavefunction as a vector ⃗ 휙. Element 휇 of the vector is the coefficient ci휇 in 휙i(⃗ r) =

M

∑

휇=1

ci휇휒휇(⃗ r) Substituting that expression into Schr¨

  • dinger’s equation

− ℏ2 2me ∇2휙i(⃗ r) + V (⃗ r)휙i(⃗ r) = 휖i휙i(⃗ r) gives a new matrix equation ∑

휈

H휇휈휙휈 = 휖휙휇 H휇휈 = ∫ d3⃗ r휒∗

휇(⃗

r) [ − ℏ2 2m∇2 + V (⃗ r) ] 휒휈(⃗ r) The coefficients ci휇, which are all we need to describe the wave function, are eigenvectors of the matrix H

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 25 / 45

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Computers are great for diagonalizing matrices

BLAS/LAPACK (Basic Linear Algebra Subprograms / Linear Algebra PACKage) suite of matrix diagonalization algoritms in FORTRAN/C/C++ Jacobi eigenvalue algorithm, Cholesky decomposition, LU factorization . . . Algorithms specific to sparse matrices (most elements are zero) Quantum chemistry codes are really just front-ends to BLAS/LAPACK!

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 26 / 45

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Our H+

2 example

2 basis functions, one on each atom H is a 2x2 matrix 휓 is a 2-element vector that obeys ( 훼 훽 훽 훼 ) ( c1 c2 ) = 휖 ( c1 c2 ) The 2 eigenvalues of H correspond to occupied and unoccupied

  • rbitals

Realistic calculations will use hundreds or thousands of basis functions

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 27 / 45

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Approximating the wavefunction of many electrons

Approximate as a product of one-electron functions Ψ(⃗ r1,⃗ r2 . . .⃗ rn) = 휙1(⃗ r1)휙2(⃗ r2) . . . 휙N(⃗ rN)

▶ Detail: Add ”exchange” terms to ensure Ψ changes sign when 2

electrons are interchanged

Each electron obeys − ℏ2 2me ∇2휙i(⃗ r) + V (⃗ r)휙i(⃗ r) = 휖i휙i(⃗ r) where V (⃗ r) is the interaction with the average electron distribution

▶ Nonlocal ”exchange” contributions avoid self-interaction

Now we occupy the N lowest-energy eigenvectors of H Iterate to self-consistency

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 28 / 45

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Density functional theory

Again, approximate as a product of one-electron wavefunctions Ψ(⃗ r1,⃗ r2 . . .⃗ rn) = 휙1(⃗ r1)휙2(⃗ r2) . . . 휙N(⃗ rN) Each electron obeys − ℏ2 2me ∇2휙i(⃗ r) + V eff (⃗ r)휙i(⃗ r) = 휖i휙i(⃗ r) The ”effective” interaction V eff (⃗ r) corrects for many-body effects The hard part is devising this interaction!

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 29 / 45

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SLIDE 31

Outline

1

Computational Chemistry

2

Drug design

3

Visualizing molecules

4

Quantum chemistry and computing

5

Applying computational chemistry

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 30 / 45

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SLIDE 32

Reversible hydrogen storage

Hydrogen gas H2 is a clean way to store energy

▶ Combine with oxygen O2 to get back energy and water

Storing hydrogen in a tank isn’t practical. You need a big tank Goal: A material that binds a lot of H2, holds it tightly (and safely), and releases it on heating

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 31 / 45

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Frustrated Lewis pairs

Coordinate covalent bonds involve an electron pair being donated from a Lewis base to a Lewis acid ”Frustrated Lewis pairs” are a strong Lewis acid and a strong Lewis base, that are too bulky to bind together Very strong frustrated Lewis pairs can reversibly split H2 into H+ (bound to the Lewis base) and H− (bound to the Lewis acid) [Show (C6F5)3B-P(t-Bu)3 frustrated Lewis pair in Avogadro]

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 32 / 45

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Frustrated Lewis pairs in the chemistry classroom

Lewis acids (electron acceptors like BR3) and Lewis basies (electron donors like :NR3, :PR3) are staples of acid-base chemistry Dative bonds between Lewis acids and Lewis bases are a nice way of understanding these systems Frustrated Lewis pairs illustrate how these might be useful

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 33 / 45

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SLIDE 35

Can quantum chemistry predict the degree of ”frustration”?

There are three components to the interaction

▶ Direct B ← P electron transfer ▶ Steric repulsion between the large C6F5 and C(CH3)3 side groups ▶ Donor-acceptor and van der Waals interactions between the side groups

B ← P bond length and bond strength is a sensitive function of those three interactions

▶ Example: Replacing C6F5 with a smaller electron-widthdrawing group

C(CF3)3 predicted to increase bond strength from negligible to 69 kcal/mol

▶ C-C bonds are only around 80 kcal/mol! Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 34 / 45

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Problem: Van der Waals interactions

2 2 4 6 0.0 0.2 0.4 0.6 0.8 1.0 Position Average electron density

Helium dimer electron density

”Mean-field” approximations give reasonable average probabilities of finding an electron at a point . . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 35 / 45

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Problem: Van der Waals interactions

e1 e2

2 2 4 6 0.0 0.2 0.4 0.6 0.8 1.0 Position Average electron density

Helium dimer electron density

. . . but when electron 1 is on the right, electron 2 is generally on the right. . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 36 / 45

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SLIDE 38

Problem: Van der Waals interactions

e1 e2

2 2 4 6 0.0 0.2 0.4 0.6 0.8 1.0 Position Average electron density

Helium dimer electron density

. . . and when electron 1 is on the right, electron 2 is generally on the left. . .

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 37 / 45

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Van der Waals interactions

Explicitly many-body interaction between electron pairs Hard to model with our mean-field and DFT methods Calculations to date either

▶ Include many parameters fit to experiment ▶ Include explict (and expensive) many-body corrections ▶ Predict the wrong answer! Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 38 / 45

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SLIDE 40

How do we model these frustrated Lewis pairs?

Simple approach: Add ball-and-spring corrections to an electronic structure calculation Van der Waals interactions between atoms are relatively transferable Mathematically, we have E = EDFT −

atoms

∑

ij

CiCj R6

ij

(1 − fdamp[Rij]) Stefan Grimme, 2003

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 39 / 45

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SLIDE 41

Damping correction

0.0 0.5 1.0 1.5 2.0 70 60 50 40 30 20 10 Internuclear Separation Energy Damped Undamped

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 40 / 45

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SLIDE 42

Is this any use?

Calculate errors in B-N bond dissociation energies for several sets of well-characterized coordinate covalent bonds

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Average error (kcal/mol)

Semilocal DFT State-of-the-art hybrid DFT Highly parameterized DFT DFT with dispersion corrections

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 41 / 45

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SLIDE 43

Computational speedups

Time to calculate the energy of (C6F5)3B − P(tBu)3 0.5 1 1.5 2 2.5 3

Relative calculation time

Semilocal DFT State-of-the-art hybrid DFT Highly parameterized DFT DFT with dispersion corrections

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 42 / 45

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What predictions do these new methods make?

Binding energies (kcal/mol) of a frustrated Lewis pair and a (predicted) very strong Lewis pair Method (C6F5)3B − P(tBu)3 (CF3)3B − P(tBu)3 Literature 19 69 Standard DFT 27 State-of-the-art 1 30 Highly parameterized DFT 10 44 DFT with dispersion corrections 11 45 Some of those literature results may need reinvestigated

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 43 / 45

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SLIDE 45

Dechlorination of groundwater contaminants

Trichloroethylene molecule [simulate in Avogadro] Good degreaser/dry cleaning solvent Relatively nonflammable, thus safer in the short term Carcinogen and groundwater contaminant Significant problem near military bases, old dry-cleaning stores

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 44 / 45

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SLIDE 46

Benjamin G. Janesko (TCU) Computational Chemistry at TCU 2010.02.19 45 / 45