Post on 04-Dec-2021
Computational Module ITutorial day-3
Department of ChemistryUniversity of Zurich, Switzerland, 2021
Thermochemistry
Thermochemistry
Thermochemistry is the study of energy (heat) associated withchemical reactions.
⇒ Switching from microscopic to macroscopic picture:Thermal energy corrections based on statistical thermodynamics.
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Frequency calculations
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Calculating the gradient, Hessian and frequenciesfor a harmonic potential:
E(R) =12
kR2
dE(R)
dR= kR
d2E(R)
dR2= k
Frequencies:
ω =
√km
⇒ Classification of stationary states based on harmonic frequencies.
Transition states (TS)
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Calculating the gradient, Hessian and frequenciesfor a harmonic potential:
⇐ Transition state
E(R) = −12
kR2
dE(R)
dR= −kR
d2E(R)
dR2= −k
Frequencies:
ω =
√−km
⇒ N imaginary frequencies indicate an N-th order transition state.⇒ Visualization of TS in terms of the normal mode of the imaginary frequency.
Intrinsic Reaction Coordinates
Calculating an intrinsic reaction coordinate (IRC):Gaussian: optimize -> frequency -> IRC
• determines which minima on PES are connected by TS structure
• starts at TS and optimizes the geometry to find minima
• Be careful: Most often more than one reaction path!
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Conformational Analysis
Scanning the PES with Gaussian
• using Rigid Scan is keeping coordinates frozen while scanning a particular one
⇒ Single-point energy calculations
• using Relaxed Scan is keeping scanned coordinate frozen while optimizingthe remaining ones
⇒ Geometry optimizations
• In constrast to IRC no lowest energy paths!
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Thermal energy corrections
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⇒ Exothermic / endothermic reaction?
⇒ How large is the activation energy?
Thermal energy corrections
Thermal energy correction Ethermby exploiting connection of state functions (free energy G, enthalpy H, entropy S) andpartition functions:
Gaussian: optimize -> frequency
• Accounting for the effects of molecular translation, rotation and vibration
Etherm = ZPE + Evib + Erot + Etrans + Eelectr
• Zero-point energy (ZPE) to account for molecular vibrations present at 0 K
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← ZPE← Etherm
Thermal energy corrections
• Thermal correction Etherm accounting for the effects of molecular translation,rotation and vibration
Etherm = ZPE + Evib + Erot + Etrans + Eelectr
• Enthalpy correction Hcorr = Etherm + kBT• Gibbs free energy correction Gcorr = Hcorr − TS
• Total Gibbs free energy Gtot = εelectr + Gcorr
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⇐ Gtot = εelectr + Gcorr
⇐ εelectr
Thermal energy corrections
• Vibrational partition function depends on frequencies⇒ Minimum energy or saddle point structures required!
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⇒ Activation energies can be obtainedby calculating ∆G of reactants and TS
Solvent effects
• Electrostatic interaction betweensolute and solvent:mutual electric polarization
• Classical electrostatics:Polarization function P defined bypermittivity ε and electric field E
P =ε− 14π
E
• Explicit vs. implicit solvation
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Continuum solvation models
Continuous dielectric medium characterized by dielectric constant εIn Gaussian:
• Onsager model is the simplest
• Iso-density polarizable continuum model (PCM) defines the cavity as a surfaceat constant electronic density
• Self-consistent iso-density PCM accounts for coupling between cavity andelectron density
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Bibliography I
James B. Foresman and Aeleen FrischExploring Chemistry with Electronic Structure Methods - Third EditionGaussian, 2015
Tomasi, J., Mennucci, B. and Cammi, R.Quantum Mechanical Continuum Solvation ModelsChemical Reviews, 105(8):2999–3094, 2005
Pictures:https://gaussian.com/wp-content/uploads/dl/thermo.pdfhttps://en.wikipedia.org/wiki/Energy_profile_(chemistry)http://doktori.bme.hu/bme_palyazat/2018/Honlap/Radai_Zita_en.html
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