Molecular Modeling inChemical Education and Research

Summer Tour 2005

Sean OhlingerWavefunction, Inc.

18401 Von Karman, Suite 370Irvine, CA 92612

sean@wavefun.comwww.wavefun.com

Professor Richard JohnsonChemistry Department

University of New Hampshirerpj@cisunix.unh.edu

What are we going to do today?

• Introduce you to molecular modeling and some of

its many applications in teaching and research.

• Introduce the newest versions of Spartan as tools in teaching.

• Introduce Odyssey, a new program for dynamic models.

• Demonstrate the Cambridge Crystal Structure Database

(CCSD) and its interface with Spartan.

• Give you plenty of time to have fun.

• Exchange ideas

What we won’t do today!

1. Overwhelm you.

2. Teach you the intricacies of Spartan and Odyssey.

3. Present the details of computational chemistry.

• Fast computers are now readily available. Today’s Pentium or PowerMac laptop is

much faster than yesterday’s mainframe computer.

• Sophisticated computational models are based on quantum mechanics and classical

mechanics.

• Recent development of the graphical user interface permits rapid construction of

models and spectacular visualization of the results. This has made molecular

modeling accessible to anyone.

The Essential Elements

Some things we often forget.....

• chemistry is about molecules

• molecules are three dimensional

• we can’t solve the Schrödinger equation exactly for molecules but the approximate solutions are excellent

Sir John Pople 1925-2004

"I could have done it in a much more complicated way," said the red Queen, immensely proud.- Lewis Carroll

“The essence of John Pople . . . to take what is, or what seems to be, intractable and make it so, so simple. Thank you, sincerely thank you, for sharing your precious gift with me, and with the scientific world. You will be sorely missed.”

Warren Hehre, President/CEO, Wavefunction, Inc.

Essentials of ModelingBuild Structures: Many programs are just visualizers. Spartan allows the rapid construction of virtually any structure in three dimensions. Odyssey allows you to build your own molecular dynamics simulations.

Perform Computations: Force-field and quantum mechanical models offer sophisticated descriptions of molecules, both known and unknown. We can’t solve the Schrödinger equation exactly for molecules but the approximate solutions are excellent.

Visualize and Interpret Results: Results include structure, energies, molecular orbitals, electron densities, vibrational modes, dynamics simulations, etc.

Recycle: Each answer often will lead to more questions and new calculations.

•Research in industry and academics.

•Design of new pharmaceuticals.

•College graduate level coursework.

•College undergraduate coursework.

•On the worldwide web!

•Even in high school classrooms.

Applications of molecular modeling and visualization

What can I do with modeling and visualization in my classroom and laboratory?

•Enhance teaching of selected concepts and content.•Emphasize the molecular nature of chemistry.•Move from two dimensions into three.•Show real 3 dimensional dynamic models – not just movies.•Prepare course material and WWW images.•Computational experiments in place of selected wet labs.•Motivate students to be excited about chemistry.•Research, enrichment and special projects.•Advanced courses.•Better prepare students for graduate school and future careers in chemistry.

What can I do with modeling and visualization in my research?

•Build and visualize complex structures in three dimensions.•Import/export structures from/to other sources or projects.•Use computations to model structure, conformation, energetics, thermodynamics and chemical reactivity.•Predict spectral properties: IR, UV-VIS, NMR shifts •Predict new chemical reactions.•Build and maintain a library of structures.•Prepare images for presentations, web pages, publications and proposals.•Enhance my own professional training and credentials.•Enhance my understanding of the literature.

Current WavefunctionWavefunction Software

SpartanModelSpartanModelan electronic model kitan electronic model kit

Spartan STSpartan STStudent EditionStudent Edition

Spartan ’04Spartan ’04

’06 is on the way….’06 is on the way….

What isA New Set of Programs + Associated

Chemistry Contentfor Teaching Concepts inIntroductory Chemistry

?

Odyssey is set to an accurate molecular scalewith time and molecular size greatly expanded.

An Introduction to Spartan

GraphicalUser

Interface

Semi-EmpiricalMolecular Orbital

Density Functional

Ab InitioMolecular orbital

External

Graphical Surfaces

Properties

MolecularMechanics

Spartan Architecture

Building and Visualizing Structures: Chemical evolution from methane to DNA

Current WavefunctionWavefunction Software

SpartanModelSpartanModel

Spartan ST Student EditionSpartan ST Student Edition

Spartan EssentialSpartan Essential

Spartan ’04Spartan ’04

’06 is on the way….’06 is on the way….

Now that we know how to buildmolecules, it’s time for bit of theory……

Theoretical ModelsMethods Based on Quantum Mechanics: These are approximate Solutions to the Schrodinger equation

•Semi–empirical :(CNDO, MNDO, ZINDO, AM1, PM3 etc.): based on the Hartree-Fock self-consistent field (HF-SCF) method, valence electrons only, approximations greatly simplify calculations, parameterized to fit experimental results; recent extension to many transition metals.

•Ab Initio: (Non–empirical; from “first principles”): also HF-SCF but includes all electrons and uses minimal approximation, large collection of methods and levels of theory; increase in complexity for both basis functions and electron correlation.

•Density Functional: Based on electron density; includes electron correlation.

Methods Based on Classical Mechanics

•Force Field Methods: (MM2, MMFF, Amber, Sybyl, UFF etc.): based on Hooke's law, van der Waals interactions, electrostatics etc.; parameterized to fit experimental data. Also used to create dynamic models in Odyssey.

Schrodinger Equation

Nuclei don't move

Electronic Schrodinger equation

Guess how electrons affecteach other from idealized problem

1. Electrons move independently2. Molecular "solutions" written in terms of atomic solutions

Hartree-FockMolecular orbital methods

1. Atomic orbitals don't interact.2. Parameterization

SEMIEMPIRICAL MO MODELS

parameterization

DENSITY FUNCTIONALMODELS

Mix in excited statesto account for electron correlation

CONFIGURATIONINTERACTIONAND MOLLER-

PLESSET MODELS

AB INITIOHARTREE-FOCKMODELS

Basis Sets for Computational ModelsSemiempirical Methods: use Slater-type functions; one size fits all

Ab Initio methods: most commonly used are Gaussian functions; combination of Gaussians gives Slater-type orbitals.

Minimal basis set STO-3G

Split-Valence or Double-Zeta 3-21G(*)

Polarized basis sets 6-31G*

Extended basis sets 6-311+G**

Hartree-Fock limit: infinite basis set

unreliableenergetics

excellent results

for mostaccuratecalculations

Incr

eas i

ng C

ompl

exi ty

Example: Methane Basis Set 6-311G*Energy RelativeEnergy

(hartrees) (kcal/mol)----------------------------------------------------------------------E Hartree Fock -40.202409 0.0 kcal/molEMP2 -40.349308 -92.1EMP3 -40.365949 -102.6EMP4SDQ -40.369786 -105.0EMP4 -40.372940 -107.0B3LYP -40.527982 -204.2

Hartree Fock Energy

Exact Energy

Correlation Energy

Correlation energy: Electrons correlate their motion better than Hartree-Fock theory allows for. This is typically a small portion of the total energy. Inclusion of electron correlation lowers the energy of the wavefunction.

When do you really need electron correlation?

Important for the most accurate calculations.Essential for excited states, transition states, structures with unusual bonding schemes, high-spin molecules….

Which computational method do you need?

excited states, UV spectra, transition state energies, structures with unusual bonding schemes, most accurate predictions of structure and properties

Correlated methods(DFT, MP etc.

Ab Initio Hartree Fock(3-21G, 6-31G* etc)

Semiempirical(AM1, MNDO, PM3)

Force-Field(MMF, Syby)

Incr

easi

ng le

v el o

f the

ory

more accurate prediction of structureand properties, NMR spectra, relativeenergies of isomers, qualitative description of transition states and reactions

basic description of structure and bonding,vibrational spectra,, starting geometries for higher level calculations

conformational analysis, starting geometries for other calculations, basic questions of structure and shape

Modeling Carbohydrate Complexes at Multiple levels of Theory

MOLECULAR SIZE

AB INITIOMETHODS

SEMI-EMPIRICAL METHODS

FORCE-FIELDMETHODS

CPU

and

MEM

OR

Y D

EMA

ND

S

Approximate relationship between molecularsize and computational demands

Visualization

Vibrational Frequency Analysis

Stationary points on a potential surface are characterized by vibrational frequency analysis. Vibrational modes may becalculated and animated.

Energy minima will have all positive vibrational modes.

Energy maxima (first order transition states) will have a single negative or imaginary mode. This corresponds tothe reaction coordinate. Higher order transition states existbut they are rare. (Linear water for example!)

Calculated vibrational frequencies usually are ca. 10% toohigh relative to experiment.

What is the significance of this structure?

Back to work…….What can we calculate?

Sample calculations on a simple molecule.

• Optimized structure• Vibrational modes• Surfaces

Charge and Multiplicity

singlet doublet singlet

CH3+ CH3 CH3

-

Electrostatic Potential Maps

The electrostatic potential is the energy of interaction of a point positive charge (an electrophile) with the nuclei and electrons of a molecule. As a three dimensional isosurface, thiseasily shows lone pairs. Hydrazine is shown here.

The electrostatic potential can be mapped onto the electron density surface by using color to represent the value of the potential. The resulting model displays molecular size and shape (from the density map) and is colored to represent relative positive and negative regions of the surface. Colors toward red indicate negative values of the ESP, while colors toward blue represent positive potential values. Sodiumchloride is shown in this example.

Visualizing Biomolecules:

Carboxypeptidase from a PDB File

Getting the word out….

Images and structures are easily transferred to:• Powerpoint presentations like this one• Word-processing programs• JPEG files www pages• AVI animations• PDB files www pages and other programs• Browser plugins like Chime (MDLI) offer

structure visualization on and off the WWW.

This is cool, but is there a version

for

Macintosh?

What is

A New Set of

Programs + Associated Chemistry Content

for Teaching Concepts in

Introductory Chemistry

?

Run Odyssey

…in the Introductory/GeneralChemistry/High School Curriculum:

• Thermochemistry• Gases• Liquids/Solids/Intermolecular Forces• Solutions• Kinetics• Chemical Thermodynamics

...

SPARTAN vs.SPARTAN vs.

Molecules / Small Clusters Bulk Matter

Energy Minimization(T = 0)

Dynamics at Given Temperature

Small Molecule Chemistry (Organic / Inorganic / Medicinal / Biological)

Introductory / General / Physical Chemistry

Quantum MechanicsEngine

Classical Molecular Dynamics

SImulation Engine

Integrated (DHTML) Chemistry Content

Also:

…is interactive:

• Stop-’N-Go Dynamics• Sample Manipulation• Property Queries• Plotting

…all “on-the-fly”, initiated and controlledby the student

Molecular DynamicsSimulation Engine:

Newton: F = m • a

dE (x1,y1,z1,…)dx1

= m1 •dvx1

dt Run Odyssey

Customization:

…annotate pages

…change sample(s)

…change text

…even create your own page !

Models can be created in Spartan and brought directly into Odyssey to create new molecular dynamics simulations.

MD Simulations: Input

3. Force field force field:MMFF with extensions,~ sufficient for pedagogical purposes

2. Velocities vx1 , vy1

, vz1 , … basically temperature !

1. Positions x1,y1,z1,… but really output in“equilibrium” situations

E (x1,y1,z1,…)

MD Simulations: Output• Equilibrium structure• Hydrogen bonds• Spontaneous changes• Response to perturbations

• Energetics / Thermodynamics

• Particle trajectories• Diffusive behavior• Rotational motion

…for thechosen

temperature

Searching the Cambridge Structure Database (CSD)

Wavefunction is now responsible for distribution of the Cambridge Structural Database (CSD) System (on Windows and Unix) to academic institutions in the United States.

The CSD currently contains more than 280,000 published X-ray crystal structures for organic and organometallic compounds. About 20,000 new structures are added annually. New versions of the CSD are released every six months. The CSD System includes the ConQuest search software used to interrogate all CSD information fields (bibliographic, chemical and crystallographic), and also includes IsoStar, a knowledge-base of intermolecular interactions and Mercury, a visualization and analysis program.

Structure searching can be done directly through Spartan and structures are easily imported.

Searching the Cambridge Database

Searching the Spartan Database

Applications of Spartan

•Teaching basic concepts: atomic orbitals, acidity, resonance, chemical bonding

•Using lists •Conformational analysis•Coordinate driving•Transition state searching•Visualizing reactions•Examples from inorganic chemistry

Atomic Orbitals: The Bromide Ion HF/3-21G Results

Atomic configuration: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6

Atomic Orbital Energies

eigenvalues: -486.69845 1s

-64.66592 -57.85828 -57.85828 -57.85828 2s,2p

-9.52913 -7.10100 -7.10100 -7.10100 3s,3p-2.83570 -2.83570 -2.83570 -2.83570 -2.8357 3d

-0.63114 -0.08504 -0.08504 -0.08504 4s,4p

1s

2s

2p

3s

3p

3d

4s

4p

ENER

GY

Acidity: Oxoacids of Halogens

HClO4 ↔ H+ + ClO4-

Ka = 1x1010

(strong)

HClO3 ↔ H+ + ClO3-

Ka = 1.6x101HClO2 ↔ H+ + ClO2

-

Ka = 1.0x10-2HClO ↔ H+ + ClO-

Ka = 3.0x10-8

(weak)

perchloric acid(perchlorate ion)

chloric acid(chlorate ion)

chlorous acid(chlorite ion)

hypochlorous acid(hypochlorite ion)

Ionic vs. Covalent Bonding: Salt

Calculate sodium chloride at the ab initio HF/3-21G(*)level of theory.

Visualize electron density, electrostatic potential mapsAnd charges.

Plotting Data: Constraints, Lists and Spreadsheets

Animating the Inversion Barrier in Ammonia

3D Plots may also be useful

Using Lists and Spreadsheets: Conformations of Cyclohexane

Other examples: shapes, radicals, HX polarization, alkane series, forms of carbonbenzene MO’s, covalent vs. ionic bonding, ozonolysis energetics, polyene UV, benzene isomers, benzonitrile nitration, hydroboration

NMR Spectral Calculation

Another example

Example: Conformations of Octane

Visualizing Chemical Reactions

Locate the transition state

Calculate the intrinsic reaction coordinate

Animate the transition state “imaginary” vibrational mode

To find a transition stateyou MUST start with a guessed geometry in this region of space

Starting anwhere inthis region of space will usually find the minimum.

REACTANT

PRODUCT

TRANSITIONSTATE

ENER

GY

REACTION COORDINATE

Stationary point: a molecular geometry where all forces on atoms are zero (or minimized to tolerances set in programs.)

1) Energy minimum: easy to find but there are often many conformations. Frequency analysis will give all positive vibrational frequencies.

2) First order saddle point or transition state: more difficult to find becauseyou must start with a guessed geometry that is close to the answer.Frequency analysis will give one “imaginary” frequency which corresponds to the reaction coordinate.

3) Higher order saddle point: a transition state in more than one direction.Frequency analysis will give two or more imaginary frequencies. Simplest example may be linear water.

Modeling Transition States

Diels-Alder TS Migratory insertion in CH3Mn(CO)5

Strategies for Finding Transition State Structures

If you can find one TS, you have them all.

Find the simplest TS for the reaction first; then build on the rest of your moleculeand partially optimize with the important structural components frozen.

To examine regio- and stereochemical issues, build as many copies as you needin a spreadsheet and optimize them all in one job. This is an extraordinarilypowerful technique.

Strategies for Finding Transition State StructuresUse bond lengths or other constraints to pre-optimize a guess.

Bonds that are being broken or made usually are 20 – 50% longer intransition state structures. Look at related structures for guidance. Dataoften are highly transferable from related TS structures.

This is almost always MUCH easier to accomplish in Spartan.

H

TS bond C--H bond length is ca. 1.4 - 1.5 Angstroms

Diels-Alder TS usually hasC----C bond lengths of1.9 - 2.3 Angstroms

H

C

H H

ClNC

2.397

2.126

SN2 has pentacoordinatecarbon and two long bonds

B3LYP/6-31G*

Strategies for Finding Transition State Structures

Use the transition state library in Spartan: draw arrows corresponding tothe mechanism. The library includes thousands of transition states.

Hints: 1) Draw arrows in a continuous direction 2) Use the INSERT key to place several molecules on screen3) Some arrows are drawn bond to bond4) To draw arrows to a space, hold down the

shift key and click on two atoms separating the new bond.5) You can begin on either side of a reaction.

A Research Example: Synthesis of Panepophenanthrin (2003)

O

O

OOH

RR

O

H

HO

H

R = C(OH)(CH3)2

O

O

O

OMe

Me

OHH

HOH

MeMe

OH

OH

panepophenanthrin

O

OH

Me

Me OHO

O

O

O

HOMe

Me

OHH

H

MeMe

OH

OH

X. Lei., R. P. Johnson and J. A. Porco Jr.Angew. Chem. Internat. Edit. 2003,42, 3913.

Eight possible modes of cycloaddition

Intrinsic Reaction Coordinate (IRC) Searches

An IRC calculation starts with the TS geometry and Hessian, then locates theminima connected to this TS. This begins by following the “imaginary” vibrational mode. IRC calculations are time consuming since each point must be optimized on the surface.

IRC calculations are the most reliable way to prove that you have found the correct TS.

Examples from Inorganic Chemistry

Zr benzyne complexethylene insertion

Berry pseudorotation in PCl5

Migratory insertion inCH3Mn(CO)5

Visualizing a chemical reaction: Nucleophilic Substitution

Visualization of the HOMO best shows the negativecharge location. This begins on the nucleophile and migrates to the leaving group. The animation alsoshows the inversion of stereochemistry. Drawing electron density slices shows bonds forming and breaking.

HC

HHNC Br

H

C

HH

NC BrH

C

HHNC Br- -

Stereocenter inversion , SN2 examples

HOMO

Electron Density Slice

Visualizing an SN2 Reaction

Molecular Recognition.

Base Pairing

Nonactin-Potassium Complex

Wrapping up: What can you do with molecular modeling and visualization in your classroom and laboratory?

•Enhance teaching of selected concepts and content.•Emphasize the molecular nature of chemistry.•Move from two dimensions into three.•Show real 3-D dynamic models – not just movies.•Prepare course material and WWW images.•Computational experiments in place of selected wet labs.•Motivate students to be excited about chemistry.•Research, enrichment and special projects.•Advanced courses.•Better prepare students for graduate school and future careers in chemistry.

Now it’s up to you….