MOPAC workshop

Martin Peeks

21st April 2016

Course outline

2

Day one

1. What is MOPAC?(a) QM intro(b) What can you do with MOPAC?

2. Anatomy of a MOPAC job

3. Worked example: benzene: geometry, orbitals and vibrations

If time:4. Worked example: butane coordinate scan.

Day two

More advanced techniques:- Coordinate scans- Atomic charges- Transition states- Implicit solvent- Electronic spectra (UV)- Visualisation- FullMonte

The compchem hierarchy

3

Molecular mechanics

Semi-empirical

DFT

WFT

AMBER

OPLSMM+

MMFF94

HyperChem

MacromodelMolecular dynamics

RM1

AM1

Huckel

PM6

INDO

ZINDO

MOPAC

HyperChem

Gaussian

UFF

HFMP2

CASSCF

CCSD(T)

MNDO

DFTB

CISDB3LYP

PBE

M06-2X

wB97X-D

BP86

BLYP

Gaussian Turbomole OrcaGAMESS QChem NWChem

Molecular mechanics

4

Estr C-C Estr C-H Estr C-F Estr C-Cl

Ebend F-C-H Ebend F-C-C Ebend H-C-H (many) Ebend Cl-C-C

Ebend Cl-C-H Etor F-C-C-Cl Etor F-C-C-H Etor H-C-C-Cl

Etor H-C-C-H 1,3-/1,4- VdW VdW VdW

F = ma

Quantum mechanics

5

Born Oppenheimer approximation:Decouple electronic and nuclear motion

Electronic wavefunction described by QM: gives forces on nuclei, which then respond according to classical mechanics.

Hartree-Fock theory describes motion of electrons without reference to other electrons: electron correlation is neglected.

Coulomb and

exchange

Geometry optimisation

6

Solve SCF

Low forces on

atoms*?

Move atoms

Converged!Yes

No

* And predicted displacements

Semi-empirical methods

7

Replace many costly two-electron integrals in HF theory with parameters

Parameters from experimental and high-level calculations

Good parameters can give solutions with accuracy of HF theory

DFT and post-HF methods include more electron correlation, so are more accurate

Ignore core electrons: only consider valence electrons

Just because the computer gives you an answer, does not mean it’s the right answer!

Semi-empirical good for: Semi-empirical bad for:

Heavy atomsTransition metals (generally)Open-shell systemsSmall systems (DFT cheap)(Intermolecular interactions)

Quick geometry screeningBig systems before DFTCompromise: properties instead of DFT for big molecules

Semi-empirical methods

8

AM1(Austin)

Earliest model

Superseded by PM3 (then 6,7)

RM1(Recife)

Good for organics

Lacks heavier atoms (e.g. Si)

PM6(Parameterisation)

Heavily parameterised model. Wide applicability. Includes TMs Has dispersion and H-bond optimised versions

Bad for sp2 nitrogen planarity

PM7 Improvement on PM6

Nitrogens in amino acids still bad

ZINDO/S(Zerner’s intermediate neglect of differential overlap)(Hyperchem)

Good for electronic spectra: may beat B3LYP in many cases!

Bad for geometriesOften good to add empirical parameters for π and s overlap.

Semi-empirical methods

9

INDO/X New method (2014) for electronic spectroscopy

doi: 10.1021/ct500717u

OMx Improved accuracy: explicit orthogonalisation includes effects of Pauli exchange repulsion, improving conformational properties, non-covalents, and excited states

Limited parameters. For info see Thiel 2014 and refs

DFTBDensity functional tight binding

Approximate DFT. 100-1000 times faster than DFT. Minimal basis. Software: DFTB+. Can do periodic structures and electron transport

Bad for H-bonding, but can be corrected

HF-3c(v) HF theory in minimal basis with several empirical corrections

Available in CRYSTAL14 (see Grimme 2014 and refs)

Grimme 2014: 10.1021/jz5021313 (good comparison of performance for non covalents)

Thiel 2014: 10.1002/wcms.1161

Elstner, PCCP 2014 14368 (DFTB argument)

Some nice figures

10Grimme 2014: 10.1021/jz5021313

Practical considerations

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1. Look for examples in the literature

2. Benchmark to known properties or higher-level theory

3. Try different methods: see if the result is robust (and how much your choice matters)4. Avoid, or correct, known deficiencies in models

Balance your “tuning” effort against what you hope to learn: don’t spend so much time trying to match a DFT benchmark that you could have done a series of DFT calculations in the time.

HAVE CLEAR GOALS AND A HYPOTHESIS

Remember, the computer is stupid. It might give an answer,

but you need to decide if that answer is correct.

MOPAC

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MNDOAM1PM3PM6RM1MNDO-dPM7

Software by James J. P. Stewart

Free for academic use

Actively developed

Widely used

Good manual

Solvent effects

Symmetry

Electrostatic methods

Powerful SCF convergers

Vibrations

Orbitals

Thermochemistry

Electronic excitations (caveat)

Transition states

Proteins

Issues:Some methods not implemented“Black box”

Anatomy of a MOPAC job

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PM7 EF GNORM=0.01 XYZ

Water

For workshop

O 0.000000 +1 0.000000 +1 0.000000 +1

H 0.758602 +1 0.000000 +1 0.504284 +1

H 0.758602 +1 0.000000 +1 -0.504284 +1

Job instructionswater.mop

Comment linesCan be blank

Molecule coordinates (Cartesian, Gaussian zmat, Turbomole, or

internal)

Essential blank line! Atom type

zx y

Optimisation flag:+1: optimise

+0: freeze-1: Use as reaction coordinate (see later)

If you omit the flag, +1 is default

MOPAC files

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Input file: water.mop MOPAC

water.arcArchive file: job results and final coords

water.outOutput log file: shows calculation input, progress,

results and errors

water.resRestart file: written for long jobs; can restart job by passing ”restart” command in original job input file

water.endThis file is empty. If you put text into it, MOPAC will

save restart and density files and will stop the calculation

water.mgfGenerated with GRAPHF keyword, and gives orbitals

which can be viewed in Jmol.

water.auxGenerated with AUX keyword. Gives extra info which can be viewed with some visualisers (e.g. GABedit)

water.denDensity file: contains density matrix You’ll never need

this

A practical example

Goal: optimise the geometry of benzene using MOPAC, calculate the vibrational frequencies, and view the frontier orbitals using Jmol

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Huckel theory

benzene.mop

PM7 EF GNORM=0.01 GRAPHF ESP

C -4.461121 1.187057 -0.028519

C -3.066650 1.263428 -0.002700

C -2.303848 0.094131 0.041626

C -2.935547 -1.151550 0.059845

C -4.330048 -1.227982 0.034073

C -5.092743 -0.058655 -0.010193

H -1.203506 0.154419 0.062012

H -2.568481 2.246445 -0.017380

H -5.063248 2.109543 -0.063538

H -2.333618 -2.074158 0.094513

H -4.828415 -2.210938 0.048462

H -6.193085 -0.118286 -0.030823

Check the output file

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CYCLE: 19 TIME: 0.000 TIME LEFT: 2.00D GRAD.: 0.007 HEAT: 22.95651

GRADIENT = 0.00727 IS LESS THAN CUTOFF = 0.01000

In a few minutes we’ll look at the orbitals and ESP, but first let’s calculate the vibrations

Geometry optimisation takes us to a location on the 3N-6 dimensional potential energy surface where the gradient is low.

But this point isn’t necessarily a minimum. A FORCE calculation gives us the vibrations and tells us about the shape of the potential energy surface

The FORCE calculation provides the Hessian matrix, which is the second derivative of energy w.r.t. atomic displacement (cf. gradient is first derivative).

Running force calculation

• Open benzene.arc

• Save as.. benzene-force.mop

• Delete frontmatter until job line and coordinates, and change job line to:

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PM7 FORCE

C (……)

Force output

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NORMAL COORDINATE ANALYSIS (Total motion = 1 Angstrom)

Root No. 1 2 3 4 5 6 7 8

1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A

349.1 349.5 593.9 600.3 600.5 759.4 901.9 902.3

Let’s open this in Jmol to see the vibrations:• Right click in Jmol window, File>Load>Open Local File…• Find .out file, open it. Admire benzene.• Right click, model 1/31 > (choose a vibration)• Right click, Vibration>On• Look at other vibrations

All vibrations are positive, so we’re at a minimum in the 3N-6 dimensional surface

Force output: a counter example

• Run the MOPAC job benzene-disp.mop.

• One C-H bond has been arbitrarily lengthened (we need the LET keyword because we’re not at a region of low gradient, so MOPAC doesn’t (quite rightly) want to do the FORCE calculation). LET tells it to trust that we know what we’re doing.

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PM7 FORCE LET GRAPHF

C (……)

NORMAL COORDINATE ANALYSIS (Total motion = 1 Angstrom)

Root No. 1 2 3 4 5 6 7 8

1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 A

-1093.6 356.2 402.4 593.6 601.1 606.3 789.2 885.1

Open benzene-disp.out in Jmol and look at the imaginary (negative) vibrational mode

It corresponds to the un-optimised C-H bond.

If you have an imaginary frequency after geom. opt., the vibrational mode suggests which atoms to move to resolve it. Often a manual movement is necessary. Or the explicit vibrational matrix (Hessian) can be used in optimisation with the RECALC=n keyword.

Looking at the benzene orbitals

• Right click in Jmol and load the (original) benzene.mgffile

• Right click, Surfaces>Molecular electrostatic potential (range ALL)

• Consider what this means with reference to C-H π bonding, and π-π stacking (offset-stack)

• Right click, Surfaces>Off

• Right click, Surfaces>Molecular Orbitals(…) – Look at the occupied (2.0) and unoccupied (0.0) orbitals.

Notice that the orbital energy is given by the eigenvalues. You can see which are degenerate (same energy) orbitals. Compare to the Huckel picture on an earlier slide.

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n-butane conformational scan

• Optimise n-butane – Add PM7 EF GNORM=0.01 to top of XYZ

coordinates. Check blank lines!

• Convert XYZ to internal coordinates– Take optimised geometry from .arc file, and use

job line: 0SCF INT in a new job

• Take internal coordinates from .arc file, and create a new job file. Choose coordinate for optimisation (-1), and use PM7 EF GNORM=0.01 STEP=10 POINT=36

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A quick look at internal coordinates and scans

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PM7 EF POINT=36 STEP=10

C 0.00000000 +0 0.0000000 +0 0.0000000 +0 0 0 0

C 1.52900685 +1 0.0000000 +0 0.0000000 +0 1 0 0

C 1.53604856 +1 112.2754272 +1 0.0000000 +0 1 2 0

C 1.52890789 +1 112.2729499 +1 -70.0119025 -1 3 1 2

H 1.10665225 +1 109.8084276 +1 -122.3909147 +1 1 2 3

H 1.10700465 +1 109.5858133 +1 121.7969671 +1 1 2 3

H 1.09540072 +1 111.1872638 +1 179.7201334 +1 2 1 3

H 1.09552157 +1 111.4078034 +1 -60.2155832 +1 2 1 3

H 1.09566835 +1 111.4985953 +1 59.8005705 +1 2 1 3

H 1.10577596 +1 109.6659220 +1 52.4123128 +1 3 1 2

H 1.10777503 +1 109.4390512 +1 168.0924601 +1 3 1 2

H 1.09532734 +1 111.2167199 +1 179.0356396 +1 4 3 1

H 1.09533828 +1 111.3620139 +1 -60.8698033 +1 4 3 1

H 1.09579159 +1 111.5045425 +1 59.1256365 +1 4 3 1

+0 = Do nothing+1 = Optimise-1 = Scan: do 36 points in 10 unit (degree, here) integrals.

DistanceA-B

Angle ABC Torsion ABCDA B C D

1

2

3

4

5

6

7

8

9

10

11

12

13

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The result

• List of geometries at each step in .out

• Then energies vs. coordinate at end. Plot that in Excel (or similar) to get torsion profile

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POINTS ON REACTION PATH

AND CORRESPONDING HEATS

-70.01190250 -60.01190250 -50.01190250 -40.01190250 -30.01190250 -20.01190250

-27.44919287 -27.21056585 -26.79589606 -26.25478124 -25.63120502 -25.03018671

9.98809750 19.98809750 29.98809750 39.98809750 49.98809750 59.98809750 69.98809750 79.

-24.56061695 -24.98003323 -25.58139116 -26.24270245 -26.83699398 -27.26119750

89.98809750 99.98809750 109.98809750 119.98809750 129.98809750 139.98809750 149.98809750 159.

-27.21915750 -26.93590742 -26.70516254 -26.62856640 -26.75059520 -27.04844007

169.98809750 179.98809750 189.98809750 199.98809750 209.98809750 219.98809750 229.98809750 239.

-28.10805101 -28.20323473 -28.09606365 -27.81314828 -27.42827277 -27.03920458

249.98809750 259.98809750 269.98809750 279.98809750

-26.72085983 -26.96632388 -27.26072586 -27.45857030

Was our start structure a minimum?

Was it the global minimum?

Take-home message

• Every torsion adds to the conformational space which must be sampled to find the global minimum.

• With lots of rotors, a “conformational explosion” results

• Quick screening of torsions in MOPAC can be powerful. More sophisticated tools (using MOPAC) exist. Can also use MM.

• Your geometry optimisation might complete, but you still need to check:– Is it a minimum? Always do a force calculation– Is it a global minimum? Consider checking torsions.

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What next?

• Play around with MOPAC

• Try examples for your own curiosity. Maybe dissociation of methyl iodide (lengthen the C-I bond and look at the energy profile). Or anything

• Try to fix problems yourself: use the MOPAC website and manual http://openmopac.net/manual/

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Other visualisation methods

1. MOLDEN: popular tool for visualising results. Very powerful, but weird interface. Installation on OS X is not for the faint of heart. Windows is easy. ftp://ftp.cmbi.ru.nl/pub/molgraph/molden/bin

2. Jmol: powerful and portable program for visualisation of results. Actively developed. Lots of features. At time of writing, MOPAC support is poor (.arc and .aux files can’t be opened, symmetry in .mgf files is ignored, and there’s a 256 atom limit). I’ve reported the bugs and have fixed the 256 atom limit myself, locally. Overall, though, is it the best tool at the moment for most users http://jmol.sourceforge.net/

3. Avogadro 2 (> v 0.9): lots of potential and somewhat-actively developed. However, doesn’t yet have a full feature-set. Avogadro 1 is impossible to use with MOPAC in my experience: it’s as buggy as an entomology lecture. http://www.openchemistry.org/

4. Chimera, Pymol, Crystalmaker: good for making pretty pictures from xyz files. They can each do much more too!

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(all of this is ”just my opinion”: decide for yourself which you prefer!)

Important acronyms

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SCF Self consistent field: used to calculate electronic wavefunction

RHF Restricted Hartree Fock: formulation of HF theory where all electrons pair (spin-up/spin-down)

UHF Unrestricted Hartree Fock: spin-up and spin-down (alpha and beta) electrons and orbitals treated separated. Used to open shell systems and complex cases

EF Eigenvector Following: geometry optimisation method

ESP Electrostatic potential

XYZ Cartesian coordinates (.xyz file)

ZMAT Z-matrix: another way of representing atomic coordinates