Chemika Examenwiki - Gebruikersbijdragen [nl]

Density Functional Theory

2024-01-19T11:29:23Z

R0804512: /* Examenvragen */

[[Categorie:Machemie]]
==Vakinformatie==
Dit vak wordt gegeven door Frank de Proft en Paul Geerlings, en bestaat uit 4 delen (1. Basics of DFT 2. Computational DFT 3. Conceptual DFT 4. Time-dependant DFT). Het examen is mondeling met schriftelijke voorbereiding en bestaat uit 3 vragen.

==Examenvragen==

=== january 2024 ===
===morning===
# Give the definition of the exchange correlation functional, and describe the different levels of approximation (stress that the exact parts are larger than the approximated parts; LDA, GGA, meta GGA, hybrid)
# What is the linear response functional, what is the chemical significance in conceptual DFT and explain the connection with TDDFT (how it is used for determining excitation energies)
===afternoon===
# Discuss the variational principle in the context of DFT and compare it to wave-function QM (discuss all 3 types (HK, KS, TD))
# Explain what is the response function and describe it in the context of conceptual DFT (describe it with examples from the course notes, and stress the LRF with mesomeric and inductive effect)

=== Augustus 2022 ===
# Justify the use of the electron density as the central quality in quantum mechanics.
# What is the exchange-correlation functional? Discuss the levels of approximations. Is there an analogue for TDDFT?
# Compare Kohn-Sham and Hartree-Fock.

Quantum Chemistry

2024-01-16T18:43:24Z

R0804512: /* Question 1 (6 points) */

[[Categorie:Machemie]]
==Information on the course==
TBA

==Exam questions==

===15th January 2024===

====Question 1 (6 points)====
Given: a spectrum with 2 peaks (and their given energies in cm^(-1)(16978.0cm^-1 , 16960.9cm^-1) for Sodium (Z=11) with the caption: This is the spectrum for the first excitation of the sodium atom.
#Obtain all atomic terms and levels of both the ground state and the first excited state of the sodium atom.
#Use the selection rules to determine which transitions are allowed.
#Use the spectra to estimate the value of the spin-orbit coupling constant ζ for the 3p-orbital of sodium.

====Question 2 (8 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#What would a trial function of the form "exp(-kr)" look like? (Given: Hamiltonian of H atom, Laplacian in spherical coordinates, use variational perturbation theory to obtain k, it should probably be like 1s of hydrogen))

====Question 3 (6 points)====
By using Perturbation Theory, obtain the second-order energy correction due to the interaction of the 1D2 and 3P2 states of the oxygen atom.

===16th January 2023===
====Question 1 (6 points)====
Given: a spectrum with 2 peaks (and their given energies in cm^(-1) for Sodium (Z=11) with the caption: This is the spectrum for the first excitation of the sodium atom.
#Obtain all atomic terms and levels of both the ground state and the first excited state of the sodium atom.
#Use the selection rules to determine which transitions are allowed.
#Use the spectra to estimate the value of the spin-orbit coupling constant ζ for the 3p-orbital of sodium.
====Question 2 (8 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#What would a trial function of the form "exp(-kr)" look like?
====Question 3 (6 points)====
By using Perturbation Theory, obtain the second-order energy correction due to the interaction of the 1D2 and 3P2 states of the oxygen atom.

===Monday 13th January 2020 (8:30 am)===
The exam is open book, you can have your course notes, your exercises and the book "Quantum Chemistry" by Levine with you. You get 4 hours to make the exam. You write everything down and then you go to the professor for oral examination.
====Question 1 (8 of 20 points)====
#Obtain all atomic terms and levels of a d9 configuration.
#Rank them in order of energy and give their relative energies in terms of the one-electron spin-orbit coupling constants.
====Question 2 (4 of 20 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#For the ground state of a hydrogenlike atom, show that <R> = 3a/2Z. (Given: value of some difficult integral that you will need to calculate <R>)
====Question 3 (4 of 20 points)====
Given: all atomic states of the ground state configuration of a carbon atom and their energies, and all atomic states of the 1s22s2p3 configuration and their relative energies.
#Comment on the order of the atomic states. (''He expects that you talk about Hund’s rules, when are these valid, when not, talk about order of atomic states with different J values but from the same term…'')
#From the given energy values, estimate the value for ζ2p.
#What spectral transitions are allowed between the ground state and the given excited state? Give the energies of these transitions.
====Question 4 (4 of 20 points)====
By using second-order perturbation theory, obtain the second-order energy correction due to interaction of the 1S0 and 3P0 states of a p2 configuration.
(''You should find the wave functions for both states in form of Slater determinants and calculate the matrix elements of ĤSO using the Condon-Slater rules'')

Quantum Chemistry

2024-01-16T18:38:46Z

R0804512: /* Question 2 (8 points) */

[[Categorie:Machemie]]
==Information on the course==
TBA

==Exam questions==

===15th January 2024===

====Question 1 (6 points)====
Given: a spectrum with 2 peaks (and their given energies in cm^(-1) for Sodium (Z=11) with the caption: This is the spectrum for the first excitation of the sodium atom.
#Obtain all atomic terms and levels of both the ground state and the first excited state of the sodium atom.
#Use the selection rules to determine which transitions are allowed.
#Use the spectra to estimate the value of the spin-orbit coupling constant ζ for the 3p-orbital of sodium.
====Question 2 (8 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#What would a trial function of the form "exp(-kr)" look like? (Given: Hamiltonian of H atom, Laplacian in spherical coordinates, use variational perturbation theory to obtain k, it should probably be like 1s of hydrogen))

====Question 3 (6 points)====
By using Perturbation Theory, obtain the second-order energy correction due to the interaction of the 1D2 and 3P2 states of the oxygen atom.

===16th January 2023===
====Question 1 (6 points)====
Given: a spectrum with 2 peaks (and their given energies in cm^(-1) for Sodium (Z=11) with the caption: This is the spectrum for the first excitation of the sodium atom.
#Obtain all atomic terms and levels of both the ground state and the first excited state of the sodium atom.
#Use the selection rules to determine which transitions are allowed.
#Use the spectra to estimate the value of the spin-orbit coupling constant ζ for the 3p-orbital of sodium.
====Question 2 (8 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#What would a trial function of the form "exp(-kr)" look like?
====Question 3 (6 points)====
By using Perturbation Theory, obtain the second-order energy correction due to the interaction of the 1D2 and 3P2 states of the oxygen atom.

===Monday 13th January 2020 (8:30 am)===
The exam is open book, you can have your course notes, your exercises and the book "Quantum Chemistry" by Levine with you. You get 4 hours to make the exam. You write everything down and then you go to the professor for oral examination.
====Question 1 (8 of 20 points)====
#Obtain all atomic terms and levels of a d9 configuration.
#Rank them in order of energy and give their relative energies in terms of the one-electron spin-orbit coupling constants.
====Question 2 (4 of 20 points)====
#Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
#For the ground state of a hydrogenlike atom, show that <R> = 3a/2Z. (Given: value of some difficult integral that you will need to calculate <R>)
====Question 3 (4 of 20 points)====
Given: all atomic states of the ground state configuration of a carbon atom and their energies, and all atomic states of the 1s22s2p3 configuration and their relative energies.
#Comment on the order of the atomic states. (''He expects that you talk about Hund’s rules, when are these valid, when not, talk about order of atomic states with different J values but from the same term…'')
#From the given energy values, estimate the value for ζ2p.
#What spectral transitions are allowed between the ground state and the given excited state? Give the energies of these transitions.
====Question 4 (4 of 20 points)====
By using second-order perturbation theory, obtain the second-order energy correction due to interaction of the 1S0 and 3P0 states of a p2 configuration.
(''You should find the wave functions for both states in form of Slater determinants and calculate the matrix elements of ĤSO using the Condon-Slater rules'')

Chemistry in Motion

2024-01-16T18:35:06Z

R0804512: /* Examenvragen */

[[Categorie:Machemie]]

==Vakinformatie==
Vak van 6 stp gedoceerd door Koen Clays en Jérôme Loreau. Bestaat uit 2 delen: Advanced Chemical Kinetics en Dynamics of Chemical and Biochemical Systems, het laatste deel wordt gedoceerd door Clays en was voordien een vak op zichzelf (kijk naar die examenwikipagina voor oudere vragen).
Dynamics of Chemical and Biochemical Systems is een mondeling examen, bevattende hoofdstukken over (1) stabiliteit, (2) fluctuaties, (3) diffusie, (4) Langevin, (5) relaxatie, (6) evolutie. Het laatste hoofdstuk werd de laatste 2 jaar weggelaten.

==Examenvragen==

===12th of January 2024, Afternoon===
=====Loreau's part=====

Given a Sn1 reaction M-A + B -> M + B + A -> M-B

#Give the order of the reaction and the units of the rate coefficient (he wants you to change your answer depending on the pressure)
#Give rate law and what is the dependence on the concentration of B
#Draw the energy profile of this reaction, and describe the geometry of the transition state
#given eryings equation describe the entropy and enthalpy profile of the transition state
#what method can be used to evaluate the rate coefficient (he just expects you to talk about all the methods)

What are the advantages and disadvantages of quantum methods and (explain how to obtain the rate coefficient, compare TD and TI)

Compare the rate coefficients for Hard sphere, TST and Arrhenius equation (he also wants you to know how they are obtained and explain the different parts of the equations)

====Clays' part====

Show how you can derive Einstein equation from Fick's law and Langevin equation

Given is the Master Equation of Fluctuation Theory, for both P(delta P, delta S) and P(delta T, delta V). Derive the amplitude of fluctuations for one of the four possible fluctuations.

===12th of January 2024, Morning===

=====Loreau's part=====

Given a reaction OH+CH3OH -> CH3O+H2O, Figure of ln(k(T) w.r.t. 1/T
# Does this reaction follow Arrhenius behaviour.
# Why might this reaction deviate from Arrhenius behaviour.
# Which methods could we use to predict k(T).
# Assume we use TST what would we need to determine k(T).
# What are the limitations when using TST.

Lindemann’s theory about unimolecular reaction.
# Describe this theory, write the expression of rate coefficient.
# What is the problem of this theory and how to fix it?

====Clays' part====

# Prove that for stability conditions in terms of entropy can be related to a minimum in "energy".
# Given is the Master Equation of Fluctuation Theory, for both P(delta P, delta S) and P(delta T, delta V). Derive the amplitude of fluctuations for one of the four possible fluctuations.

===29th August 2023===
====Advanced Chemical Kinetics====
=====First question=====
Given a Diels-Alder reaction of A+B->C, elementary, exothermic.
* H2C=CH-CH=CH2 (1,3-butadiene) + H2C=CH2 (ethylene) -> H2C=CH-CH2-CH2-CH=CH2 (cyclohexene)
# Give the order of the reaction, and the unit of the rate coefficient.
# Describe entropy and enthalpy profile of this reaction.
# Would you expect the transition state to be more like the reactants or the product?
# Based on your answer of the previous question, which type of energy is more suitable before the transition state?
# What methods could be used to describe the rate coefficient? What information do we need to know for each method?
# If the product further undergoes isomerization or fragmentation, what method should we use for it?
=====Second question=====
Lindemann’s theory about unimolecular reaction.
# Describe this theory, write the expression of rate coefficient.
# What is the problem of this theory and how to fix it?
====Dynamics of Chemical and Biochemical Systems====
# Prove that for stability conditions in terms of entropy can be related to a minimum in "energy".
# Explain the relation between Fick's laws, Langevin equation and the Einstein equation.

===13th January 2023===
====Advanced Chemical Kinetics====
=====First question=====
# Give the rate constant described by TST and explain the different elements.
# Given are the expressions for Qrot and Qtrans. Qelec and Qvib can be neglected. Describe the temperature dependence for the following reactions:
#* F + H2 --> HF + H
#* C2H4 + HCl --> C2H5Cl
# What becomes the temperature dependence if we include Qvib.
# Compare with the result obtained from the Arrhenius equation (A in Arrhenius equation is obtained via experiment whereas with TST the pre-exp. factor is obtained via direct calculation)
# Can we do quantum calculations for these reactions. Explain

=====Second question=====
# Unimolecular reaction that shows first order behavior at high pressure and second order behavior at low pressure. Write down the reaction rates and the dimensions of the rate constants for these two cases.
# Prove qualitatively and quantitative the rates at high and low pressure.

====Dynamics of Chemical and Biochemical Systems====
# Given is the Master Equation of Fluctuation Theory, for both P(delta P, delta S) and P(delta T, delta V). Derive the amplitude of fluctuations for one of the four possible fluctuations.
# The reaction is: A+B <-> C+D. Derive and describe the relaxation for an instantaneous T-jump. What are the minimal conditions/requirements and which ones are optimal? (see page 10 of the relaxation pdf)

===29th August 2022===
====Advanced Chemical Kinetics====
# Given the ozone reaction that happens in the earths stratosphere. What method would be the most accurate to describe the rate constant? (justify)
# Question about TST
1) Write down the expression for the rate constant in TST. Explain the different elements.
2) Given are Qtrans and Qrot equations (Qel and Qvib can be neglected). Describe the temperature dependency of the rate constant for the following reactions (both have non-linear TS):
*F + H2 --> HF + H
*non-linear molecule + linear molecule --> non-linear molecule (Was specific, but don't remember the molecules)
3. Exercise 2.3

====Dynamics of Chemical and Biochemical Systems====
# Explain how we get from the entropy maximum of the second law of thermodynamics to the minimum in energy. Explain what role fluctuations play here and explain the probability.
# Explain the relation between Fick's laws, Langevin equation and the einstein equation. (He said no derivation was necessary) Explain correlation between the diffusion constant and temperature and friction.

===14 januari 2022 - Voormiddag===
====Advanced Chemical Kinetics====
1. [NO3] + [CO] --(fast)-> [NO2] + [CO2] bij T hoger dan 255°C; [NO2] + [NO2] --(slow)-> [NO3] + [NO] en [NO3] + [CO] --(fast)-> [NO2] + [CO2] bij T lager dan 255°C (exotherme reacties)
1) Leid voor beide reacties de reactie rate af (tweede met steady state approximation)
2) Wat is de orde van elke reactie en de bijboherende units (2de orde; unit = cm^-3/s)
3) Teken het energieprofiel ifv reactie coordinaat
4) Welke quantum dynamische techniek verkies je: time independent of time dependent? (Time dependent wegens reacties met meer dan 4 atomen. Dit is niet doenbaar voor time independent)
5) Welke technieken zou je nog kunnen gebruiken voor de k te berekenen? (hard sphere, tst, capture theory, classical)
6) Stel de reactie, die exotherm is, heeft een late barrière. Welke energie is nodig voor deze te overbruggen? (Polanyi's rules, E(vibratie) nodig)
2. Oefening 3 van Chapter 2 met als extra vraag de delen van de k(hard sphere) uit te leggen.

==== Dynamics of Chemical and Biochemical Systems====
# Gegeven de Master Equation of Fluctuation Theory, voor zowel P(delta P, delta S) als P(delta T, delta V). Leid de amplitude van de fluctuaties van een van deze 2 vergelijkingen af.
# Reactie A+B <-> C+D. Leid de relaxatieformule af. Wat zijn de minimale condities/voorwaarden en wat zijn de optimale?