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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Conformational Analysis

Scanning the PES with Gaussian

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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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