introduction to computational quantum chemistryintroduction to computational quantum chemistry...
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Introduction to Computational Quantum Chemistry
Lesson 8: Population analysis
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Importance
Pictures of orbitals are informative, however numerical values aremuch easier to quantified and compared. For example σ vs π bondingin organic molecules.
What does a population analysis deliver?Determination of the distribution of electrons in a moleculeCreating orbital shapeDerivation of atomic charges and dipole ( multiple ) moments
Methods of calculationBased on the wave function ( Mulliken, NBO)Based on the electron density (Atoms in Molecules)Fitted to the electrostatic potential (CHELPG, MK)
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Mulliken Population Analysis
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Mulliken Population Analysis
AdvantagesMost popular methodStandard in program packages like GaussianFast and simple method for determination of electron distributionand atomic charged
DisadvantageStrong dependance of the results from the level of theory (basisset or kind of calculation)
Example: Li-charge in LiF
Population basis set q(Li,RHF) q(Li,B3LYP)Mulliken STO-3G +0.227 +0.078
6-31G +0.743 +0.5936-311G(d) +0.691 +0.558
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Natural Bond Orbital Analysis
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Natural Bond Orbital Analysis
Based on the theory of Natural Orbitals by Lowdin.
Two parts of the methodsNPA→ Natural population analysis to identify the populationnumbersNBO→ Analysis of the bond order based on the electronpopulation obtained by NPA
AdvantagesSmaller dependence on the basis setbetter reproducibility for different moleculesOrientates itself at the formalism for Lewis formulas
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Practical task
Draw HF molecule, optimize the geometry and generate G09input.Use pop=(nbo,savenbo) for NBO or Pop=Full for MullikenAfter Pop command, add a space and type ”FormCheck”Run the calculation
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Visualizing the orbitals
Open the *FChk file in AvogadroClick on Extensions→ Create SurfaceSelect ”Molecular Orbital” as surface typeChoose the MO you want to visualize and calculate
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You should be able to see something like these that shows the HOMOand LUMO of HF molecules
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Lesson 8: Solvation models
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Solvent effects
The solvent environment influences structure, energies, spectraetcShort-range effects
Typically concentrated in the first solvation sphereExamples: h-bonds, preferential orientation near an ion
Long-range effectsPolarization
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Imlicit vs. Explicit solvation
Implicit solvationDielectric continuumNo water molecules per seWavefunction of solute affected by dielectric constant of solventAt 20 °C: Water - ε = 78.4; benzene: ε = 2.3 ...
Explicit solvationSolvent molecules included (i.e. with electronic & nuclear structure)Used mainly in MM approachesMicrosolvation: only few solvent molecules placed around soluteCharge transfer with solvent can occur
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Basic assumptions
Solute characterized by QM wavefunctionBorn-Oppenheimer approximationOnly interactions of electrostatic originIsotropic solvent at equilibriumStatic model
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Cavity
Solute is placed in a void of surrounding solvent called “cavity”Size of the cavity:
Computed using vdW radii of atoms (from UFF, for example)Taken from the electronic isodensity level (typically ˜0.001 a.u.)
The walls of cavity determine the interaction interface (SolventExcluded Surface, SES)Size of the solvent molecule determines the Solvent AccessibleSurface (SAS)
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Visualizing cavity
Geomview software (in the modules)SCRF=(read) in the route section of the jobUse G03Defaults in SCRF command“geomview” in the SCRF specificationVisualize the “tesserae.off” file
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Electrostatic Interactions
Self-consistent solution of solute-solvent mutual polarizationsSolute induces polarization at the interface of cavityThis polarization acts back on the solute changing its wavefunctionVarious solvation models use different schemes for evaluation ofsolvation effectsProblems arise when electrostatics do not dominate solvent-soluteinteractions
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Polarizable Continuum Model (PCM)
Treats the solvent as polarizable dielectric continuumInduced surface charged represent solvent polarizationImplemented in Gaussian, GAMESS
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Solvation Model “Density” (SMD)
Full solute density is used instead of partial chargesLower unsigned errors against experimental data than othermodels
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COnductor-like Screening MOdel (COSMO)
Solute in virtual conductor environmentCharge q on molecular surface is lower by a factor f(ε):
q = f(ε)q∗ (1)
where f(ε) = (ε− 1)/(ε+ x); x being usually set to 0.5 or 0Implemented in Turbomole, ADF
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Beyond basic models
Anisotropic liquidsConcentrated solutions
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Two models:
MicrosolvationFew solvent molecules (1 to 3) put at chemically reasonable placeWater close to exchangeable protons (OH, NH2...)
MacrosolvationFirst (sometimes second) solvent layer around the whole moleculeUsually snapshots from MD
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Pros & Cons
+++ Modelling of real interactions with solvent (this can be crucialfor exchangeable protons in protic solvents)- Microsolvation lacks sampling- Computationally more demanding- For macrosolvation only single point calculations - the geometryis as good as forcefield
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Reaction
Model the Cl− + CH3Br→ CH3Cl + Br−
Find the energy barrier for the reactionSelect any solvent from Gaussian library (be not concerned aboutsolubility of species or chemical relevance)Assume Sn1 and Sn2 reaction pathwaysUse “SCRF=(solvent=XY)” in the route section of the calculation
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Procedure
Use B3LYP 6-31++g(d,p) methodUsage of difuse functions when dealing with anions is crucial!Use ultrafine integration gridUse Frequency calculations to be sure where on PES you areFor the scan use the distance between C and Cl as RCNegative value of step defines two atoms approaching
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Module “qmutil”
Extraction of values from gaussian runs:extract-gopt-ene logfileextract-gopt-xyz logfileextract-gdrv-ene logfileextract-gdrv-xyz logfileextract-xyz-str xyzfile framenumberextract-xyz-numstr xyzfile
Values ready for plotting in your favorite software
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Turbomole
Prepare job using define module (see presentation 6 for help)Setup COSMO using cosmoprep moduleSet epsilon to 78.4 and rsolv to 1.93
Leave all other values at their defaultDefine radii of atoms using “r all o” for optimized valuesOptimize all geometries
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