Molecular Quantum Chemistry

Gaussian and all that…

Herbert Früchtl

Overview

Using Gaussian on the clusterComputational methods overviewBasis setsCalculation of different propertiesGaussview on cluster and PC

A typical calculation

1. Get initial geometry

2. Edit input

3. Run calculation

4. Analyse results

Geometry in Gaussian Input Format

Convert known geometry from different formatbabel –i<fmt> <inputfile> -og03 <input>.gjfbabel –H

Build molecule with builder softwareMolden, Maestro, Gaussview

Don’t run long calculations from Gaussview oncluster!

Notation: replace <something> with actual argument

Elements of G09 Input

Checkpoint file (for restart or orbital analysis)

Memory requirement (too much may slowcalculation down)

Number of processors (12 on wardlaw node)

Keywords

Title (must be present, but has no effect)

Charge and multiplicity

Geometry (Cartesian or Z-matrix)

Empty lines (required)

There could be additional information for

some methods

Running SLURM Batch Jobs

Submit script to batch queuefor execution when acompute node is available

Job script with SLURMdirectives at the start:

Name of job

Request one nodeUse 12 coresRun for 48h maxUse complete nodesScript to run Gaussian

SLURM directives

Commands toexecute when jobstarts

Analysis of Results

Text output: <input>.logEnergy, final geometry, …

Checkpoint file (name specified in input)Additional information (orbitals, …)

formchk <file>.chkCreates “formatted checkpoint” for transfer to differentcomputer

cubegen <file>.fchkCreates density map to be displayed with various otherprograms

.log, .chk, .fchk can be viewed with Gaussview

Gaussview / File Transfer Caveats

Text files (.log, .fchk) may need conversion to Windows format(dos2unix, unix2dos)

Only formatted checkpoint files (.fchk) are transferablebetween machines. Create them with formchk.

Gaussview 4 can not read frequencies from Gaussian 09 logfiles. Translate to G03 format with g09tog03.

Modelling Methods for Molecules

1 10 100 1000 10000 100000 1000000

Number of Atoms

Accu

racy

FCI

CCSD(T)

DFT

Hartree-Fock

Molecular Mechanics

QM/MM

Semiempirical Methods

MP2

Molecular Mechanics

Parametrised forces betweenatoms or groups

No description of electronicstructure

Cheap large systems and/orlong dynamics simulations

Not good for change in bondstructure

Often problems associating atomtypes

Force fields optimised for certainclass of molecule

Force Fields:UFFAMBERCHARMMOPLSDreiding

For dynamics usean MD program(AMBER, DL_POLY, …)

Semiempirical Methods

Fastest electronic structure method!

Electronic structure with severeapproximations and parametrisedintegrals

Originally optimised for small(ish)organic molecules

Only PM6/7 (not in Gaussian)parametrised for all elements.

Methods:AM1PM3PM6PM7

Often good forinitial optimisation.

For many purposesa good Force Fieldis better.

Consider QM/MM

Density Functional Theory

All ground state properties can bedetermined as a functional of the electrondensity (Hohenberg-Kohn Theorem)

This functional is not known. Many modelfunctionals in use.

Current functionals do not describe staticcorrelation (London dispersion), althoughsome are parametrised to experimentalresults. Empirical corrections for forcesavailable.

Density Functionals

LDAlocal density

GGAgradient corrected

Meta-GGAkinetic energy densityincluded

Hybrid“exact” HF exchangecomponent

Hybrid-meta-GGA

VWN5

BLYPHCTHBP86

TPSSM06-L

B3LYPB97/2MPW1K

MPWB1KM05-2XM06-2X

Better scaling with system

size

Allow density fitting for even

better scaling

Meta-GGA is “bleeding

edge”, but M06-2X slowlyreplacing B3LYP as “goldstandard”

Hybrid makes bigger

difference in cost andaccuracy than meta-GGA

Look at literature if

somebody has comparedfunctionals for systemssimilar to yours!

Incr

easi

ng

qualit

yand

com

puta

tionalco

st

Post-HF Methods

MP2

Similar to DFT in total accuracy

Describes all kinds of correlationenergy

Scales n5 with basis functions

CCSD(T)

Best feasible black-box methodfor small molecules

Scaling n7

Many more Methods:MP3, MP4QCISD, BDCCSDT(Q)

MP2 may be necessaryin case of dispersiondominated interactions(e.g. -)

QM/MM

Treat “interesting” region withhigher accuracy

Anything not part of the reactiontreated on lower level (typicallyMM)

Boundary atoms saturated with Hatoms

Careful where you cut!

Gaussian keyword:ONIOM(HF/6-31G(d):AM1:UFF)Up to 3 layers

Gaussian Basis Sets

Pople splitvalence

6-31g

6-31+g*

6-31++g**

Poplevalence triplezeta

6-311g

6-311+g*

6-311++g**

Dunning correlationconsistent

cc-pvdz aug-cc-pvdz

cc-pvtz aug-cc-pvtz

cc-pvqz aug-cc-pvqz

Diffuse functions

long-distance interactionsanions

Polarisation functions

Flexibility in angularcharge distribution

Many more basis sets

Post-HF methods need larger basis than DFT

Geometry Optimisation

• Find (local) minimum (equilibriumstructure) or saddle point (transitionstate) on potential energy surface

• No guarantee to find “correct”minimum or TS

• TS considerably more difficult

• Most methods are quasi-Newton withupdated Hessian Need good initial guess of curvature

– Frequency calculation at lower level

– Optimisation at lower level (ReadFC)

– In extreme cases, calculate Hessian inevery stepOpt=CalcFC in GaussianExpensive!

Transition State Optimisation

Transition state:1st order saddle point onpotential energy surface

Method:follow Eigenvector of negativeEigenvalue uphillall other directions downhill

Considerably more difficultthan minimisation

Need good Hessian

Need starting point where Hessianhas correct structure: one negativeEigenvalue

Solvation

Explicit Solvent

Expensive

Solvent may be treated at lowerlevel (QM/MM)

Continuum Solvation Models

In Gaussian:SCRF=(PCM,Solvent=H2O)(various models and solventsavailable)

++

-

+

--

Solvent treatment is essential for Zwitterions and many ionsGeometry optimisation more difficult with both approaches

Infrared Spectroscopy

Frequencies are

Eigenvalues of mass-weighted force constantmatrix (Hessian)

Harmonic approximation(and therefore too high)

Anharmonic frequenciespossible, but expensive(Gaussian keyword

Frequency=Anharmonic)

UV/Visible SpectroscopyElectronically excited states vertical excitation

energies HOMO-LUMO gap (Koopman’s Theorem)

Bad; virtual HF/DFT orbital energies unreliable,no orbital relaxation

ZINDOsemiempirical, limited selection of atoms;fast, qualitatively OK

CISHF based; rather inaccurate (but better than Koopman)

TD-DFTDFT equivalent of CIS (but founded in different theory);better than CIS

CIS(D)CIS with approximate doublesbased on MP2; accurate but expensive

NMR Properties

Shielding Tensor(keyword NMR)

Spin-Spin couplings(NMR=SpinSpin)

Expensive!

Requires good basis setat nucleus

Consider uncontracting basisfunctions orNMR=(SpinSpin,Mixed)(uncontracts basis and addsfunctions around nucleus for partof the calculation)

Atom Isotropic shielding in ppm

Needs to be compared to valuefrom TMS optimised andcalculated with same methodand basis set

Thermochemistry

Frequency calculation gives zero-point correctionto Energy, Enthalpy and Gibbs Free Energy

Properties calculated at 298.15K (default) oruser-specified temperature

Thermodynamic reaction properties can bedetermined in a “model chemistry” (CBS-QB3,G2, …)(expensive!)

Atomic Charges

There is no suchthing as anatom…

Mulliken

Projection of electrondensity on AO basis

Calculated by default

Not very reliable

Diffuse basis functionsmake things worse!

NBO

Natural Bond Orbitals

Better…

AIM

Atoms in Molecules

Cut molecule at surface of“minimum flux”

Requires separateprogram to calculate

Gaussview

Graphical user interface for Gaussian

Can be used to

build molecules

analyse results

run calculations (not on cluster!)

Have site licence for any University-owned PC(Windows or Linux)

Problems with cygwin seem to be resolved. Tell me ifthat’s not the case…

Gaussview Screenshot

And Finally

Gaussian is not the only program

B3LYP is not the only functional

6-31g* is not the only basis set

More information:

http://www.gaussian.com/g_tech/1.htmhttp://www.gaussian.com/g_ur/g03mantop.htm

(we have G03 on PCs, but G09 on clusters)

Ask me! (or TvM, or MBuehl, or any of our postgrads)

Postgrad course on computational chemistry

Email your name and supervisor to Tanja van Mourik

tvm22@st-andrews.ac.uk

Not only for postgrads!

Other Lectures and Seminars

Lectures on

Introduction to using the EaStCHEM cluster (previous)

DFT on Periodic Systems (next)

Available on School website (Current Students -> Undergrads -> Course resources)

Computation in Chemistry Seminars

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