Electronic properties of isolated molecules - Revision history

Daniele Varsano at 08:37, 1 April 2021

2021-04-01T08:37:05Z

← Older revision		Revision as of 08:37, 1 April 2021
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	[[File:Molecule cartoon.png\|none\|500px\|top\|]]		[[File:Molecule cartoon.png\|none\|500px\|top\|]]

	Prev:[[LabQSM#Module 2: DFT simulations of Molecules]]		Prev:[[LabQSM#Module 2: DFT simulations of Molecules (6h)]]

	==Calculation of molecules: Intro==		==Calculation of molecules: Intro==

Daniele Varsano at 08:35, 1 April 2021

2021-04-01T08:35:22Z

← Older revision		Revision as of 08:35, 1 April 2021
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	[[File:Molecule cartoon.png\|none\|500px\|top\|]]		[[File:Molecule cartoon.png\|none\|500px\|top\|]]

	Prev:[[LabQSM#~~Lecture~~ 2: DFT simulations of Molecules]]		Prev:[[LabQSM#Module 2: DFT simulations of Molecules]]

	==Calculation of molecules: Intro==		==Calculation of molecules: Intro==

Andrea Ferretti: /* Exercises */

2021-03-26T10:56:09Z

Exercises

← Older revision		Revision as of 10:56, 26 March 2021
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	*Density of states (dos.x tool)		*Density of states (dos.x tool)
	*The projected density of states (projwfc.x tool + sumpdos.x)		*The projected density of states (projwfc.x tool + sumpdos.x)

			[[Solution_LAB2_guanine_4 \| Hints]]

Andrea Ferretti: /* Exercises */

2021-03-26T10:44:42Z

Exercises

← Older revision		Revision as of 10:44, 26 March 2021
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	[[Solution_LAB2_guanine_3 \| Hints]]		[[Solution_LAB2_guanine_3 \| Hints]]


	===Exercise 4===		===Exercise 4===
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	*Density of states (dos.x tool)		*Density of states (dos.x tool)
	*The projected density of states (projwfc.x tool + sumpdos.x)		*The projected density of states (projwfc.x tool + sumpdos.x)


	===Exercise 5===		===Exercise 5===

Andrea Ferretti: /* Exercise 4 */

2021-03-26T10:42:23Z

Exercise 4

← Older revision		Revision as of 10:42, 26 March 2021
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	*Density, HOMO and LUMO orbitals and plot them (pp.x + xcrysden)		*Density, HOMO and LUMO orbitals and plot them (pp.x + xcrysden)
	*How the HOMO and LUMO orbitals ~~looks~~ like?		*How do the HOMO and LUMO orbitals look like?
	*Density of states (dos.x tool)		*Density of states (dos.x tool)
	*The projected density of states (projwfc.x tool,sumpdos.x)		*The projected density of states (projwfc.x tool + sumpdos.x)

	===Exercise 5===		===Exercise 5===

Andrea Ferretti: /* Exercise 1 */

2021-03-26T08:54:51Z

Exercise 1

← Older revision		Revision as of 08:54, 26 March 2021
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	*Use a molecular builder to find the initial molecular structure. (Avogadro)		*Use a molecular builder to find the initial molecular structure. (Avogadro)
	*Perform classical force field (FF) relaxation (using a built-in engine)		*Perform classical force field (FF) relaxation (using a built-in engine)
			*Setup a DFT calculation with the guanine structure obtained from Avogradro (check both the amount of vacuum and the kinetic energy cutoff to be used)
	*Perform a quantum mechanical (DFT based) refinement of the relaxation (using Quantum ESPRESSO, with thr=10^-3 on forces)		*Perform a quantum mechanical (DFT based) refinement of the relaxation (using Quantum ESPRESSO, with thr=10^-3 on forces)
	*Use the xcrysden software to visualize the relaxation path.		*Use the xcrysden software to visualize the relaxation path.

Daniele Varsano: /* Janak's theorem, Piece-wise Linearity, Ionization potential */

2021-03-25T10:56:42Z

Janak's theorem, Piece-wise Linearity, Ionization potential

← Older revision		Revision as of 10:56, 25 March 2021
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	Viceversa for the LUMO (too deep). These behaviours are also connected to an over-delocalization (then leading eg also to over-hybridisation)		Viceversa for the LUMO (too deep). These behaviours are also connected to an over-delocalization (then leading eg also to over-hybridisation)
	error of the orbitals and of the charge density.		error of the orbitals and of the charge density.

			For a review on the topic see: [https://pubs.rsc.org/de/content/articlelanding/2020/cp/d0cp02564j#!divAbstract L. Krnoik and S: Kummel Piecewise linearity, freedom from self-interaction, and a Coulomb asymptotic potential: three related yet inequivalent properties of the exact density functional. Phys. Chem. Chem. Phys. 22, 16467 (2020)]

	==Exercises==		==Exercises==

Andrea Ferretti: /* Exercise 3 */

2021-03-18T22:14:08Z

Exercise 3

← Older revision		Revision as of 22:14, 18 March 2021
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	===Exercise 3===		===Exercise 3===
	'''Electronic properties of the Guanine molecule'''		'''Electronic properties of the Guanine molecule'''
	What does IP mean? [ IP = Etot(N-1)-Etot(N) ]
			What does IP mean? [ IP = Etot(N-1)-Etot(N) ]

	*Let’s do this calculation explicitly (the ∆-scf procedure)		*Let’s do this calculation explicitly (the ∆-scf procedure)

Andrea Ferretti: /* Janak's theorem, Piece-wise Linearity, Ionization potential */

2021-03-18T22:13:38Z

Janak's theorem, Piece-wise Linearity, Ionization potential

← Older revision		Revision as of 22:13, 18 March 2021
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	The total energy can also be extended to fractional number of electrons (making a statistical mixture of systems at N and N-1		The total energy can also be extended to fractional number of electrons (making a statistical mixture of systems at N and N-1
	electrons), and should be piece-wise linear.		electrons), and should be piece-wise linear (PWL).

	The ionisation potential is defined as		The ionisation potential is defined as
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	IP = E[N-1] -E[N]		IP = E[N-1] -E[N]

	~~and, because~~ of Janak's theorem, one should also have:		Computing the IP following the above expression takes the name of Delta-scf.

			Because of Janak's theorem, one should also have:

	IP = -eps_HOMO		IP = -eps_HOMO

	While the two methods should give the same result in exact KS-DFT, when approximate functionals are used this is		While the two methods should give the same result in exact KS-DFT, when approximate functionals are used this is
	no longer true. In particular, the total energy is no longer piece-wise-linear ~~(PWL)~~ but convex (for standard local and semi local functionals).		no longer true. In particular, the total energy is no longer piece-wise-linear but convex (for standard local and semi local functionals).
	This is depicted in the figure below.		This is depicted in the figure below.

	[[File:PWL plot.png\|none\|350px\|top\|]]		[[File:PWL plot.png\|none\|350px\|top\|]]

			Here the slope of the PWL total energy curve between N-1 and N electrons correspond to the IP computed as a finite difference of total energy.
			Instead the slope at integer occupations corresponds to the negative of the HOMO eigenvalue.

			When convexity due to, e.g., LDA or PBE, is present, the HOMO eigenvalue turns out to be less negative (i.e. higher in energy) than it should.
			Viceversa for the LUMO (too deep). These behaviours are also connected to an over-delocalization (then leading eg also to over-hybridisation)
			error of the orbitals and of the charge density.

	==Exercises==		==Exercises==

Andrea Ferretti: /* Janak's theorem, Piece-wise Linearity, Ionization potential */

2021-03-18T22:06:28Z

Janak's theorem, Piece-wise Linearity, Ionization potential

← Older revision		Revision as of 22:06, 18 March 2021
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	This is depicted in the figure below.		This is depicted in the figure below.

	[[File:PWL plot.png\|none\|~~500px~~\|top\|]]		[[File:PWL plot.png\|none\|350px\|top\|]]

	==Exercises==		==Exercises==