1.021 , 3.021, 10.333, 22.00 : Introduction to Modeling and Simulation : Spring 2012 Part II – Quantum Mechanical Methods : Lecture 5

More QM Modeling for Solar Thermal Fuels, Plus a Little H-Storage

Jeffrey C. Grossman

Department of Materials Science and Engineering

Massac husetts Institute of T ec hnology

Par t II T opics

1. It ’ s a Quantum W orld: The Theor y of Quantum Mechanics

2. Quantum Mechanics: Practice Mak es P erf ect

3. Fr om Man y-Body to Single-Par ticle; Quantum Modeling of Molecules

4. Application of Quantum Modeling of Molecules: Solar Thermal Fuels

5. Application of Quantum Modeling of Molecules: Hydr ogen Storage

6. Fr om Atoms to Solids

7. Quantum Modeling of Solids: Basic Pr oper ties

8. Advanced Pr op . of Materials: What else can w e do?

9. Application of Quantum Modeling of Solids: Solar Cells Par t I

10. Application of Quantum Modeling of Solids: Solar Cells Par t II

11. Application of Quantum Modeling of Solids: Nanotechnolog y

Lesson outline

• F eeling g ood about energ y le v els

• Contin ued discussion of solar thermal fuels

• Interactiv e calculations and discussion on candidate fuels

• Hyd r ogen storage

Let ’ s l ook at a sing le element:

carbo n

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Ca rbon in Ene r g y to Date

One Bar r el of oil (159 liters) =

1.73 MWh of energ y .

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Sa me C: 10 5 X Imp r o v ement

That same 1 barrel could be used to make the plastic needed for thin-­‐film solar cells.

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The solar cells could generate ~16,000 MWh of energy over their lifetime, or 10,000 X as much.

Ene r g y Le v els a nd Basis Sets

L et ’ s pause and f eel our oneness with these things.

H G ( → r ) = E G ( → r )

Energ y L e v els

The S. Eq. leads to w a v efunctions

Which squar ed lead to pr obability distributions

Which once spin is ta k en into account

Image adapted from Wikimedia Commons, http://commons.wikimedia.org .

Courtesy of David Manthey. Used with permission. Source: http://www.orbitals.com/orb/orbtable.htm .

T ells us about energ y le v els!

Energ y L e v els

Courtesy of Mark R. Leach on meta- synthesis.com .

http://ww w .meta- synthesis.com/w ebbook/39_diatomics/diatomics.html

R e vi e w: Basis functions

Matrix eigen value equation: G = Σ c i ф i

i

H G = E G

H Σ c i ф i = E Σ c i ф i

expansion in or thonormalized basis functions

∫ d → r ф H

i i

c i ф i = E

i i

Σ H j i c i = E c j

i

H ⇤ c = E ⇤ c

Basis Set Con v e r gence

When is a basis set con v erged?

• Man y basis sets h a v e been made f or diff er ent elements.*

• Y ou can ma k e y our o wn one to o .

• This can lead to big tables (but chemists lo v e big tables!).

* see , e .g., bse .pnl.g o v

Basis Set Con v e r gence

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What else?

After the basis set is con v erged, is the calculation “right”?

example: what is the most stable structur e of 20 carbon atoms?

Hmmmm....

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Back to our fi r st

a p p l i c a t i o n e x a m p l e : S o l ar Chemical Fuels

Sola r - Chemical :

Heat sto r ed in chemical bonds

Cha r ging

Heat

Discha r ging

A no v el a pp r oach to sola r thermal f uels

There are many, many photoactive molecules...

h 



DHA/VHF

...that are terrible solar thermal fuels.

E/Z−

h   Stilbene



spiropyran/merocyanine

Ca n w e tur n the m int o goo d ones ?

Role of the CNT template

Intermolecular Separation (A)

h 

h 



Ne w Mate r ials for Sola r Thermal Fuels

Template Materials + Photoactive Molecules

=

So Why do W e Need QM?

h 

E a

 H

Solar radiation spectrum © Robert A. Rohde/Global Warming Art . License: CC-BY-SA. This content is excl uded from our Creative Commons license. For more information, see http://ocw.mit.edu/help/faq-fair-use/ .

excited state

19

In-Class Calculations of Sola r Thermal Fuels

K ey Conce pt: Density of States (DOS)

20

F r om The Ba nd Ga p to Stor a ge Efficiency

• Assume that all photons that h a v e higher energ y than the band ga p get absorbed b y the molecule AND lead to photo- isomerization.

• Let the fraction of molecules in the excited state (cis state) be x.

• Then, f or a solar spectrum I(lamda):

λ max ,ci s

x

0

I ( λ ) d λ = ( 1 —

x )

0

λ max ,t r an s

I ( λ ) d λ

λ max = E

hc

bandg ap

F r om Absor ption Spectr a to Stor a ge Efficiency

• Assume that all absorbed photons lead to photo- isomerization.

• Let the fraction of molecules in the excited state (cis state) be x.

• Then, f or a solar spectrum I(lamda):

x Z abs

( λ ) I ( λ ) d λ = ( 1 — x ) Z abs

I ( λ )

( λ ) d λ

cis

( hc )

tr ans

( hc )

λ λ

But how do w e g e t this “ abs” f unc ti on?

-­‐-­‐> from the energy levels!!

Summar y/Reading

• What is con v ergence in a Quantum Mechanical Calculation?

• F eeling f or what those energ y le v els mean!

• Connection of energ y le v els to light absorption, and connection of that to charging efficiency in

solar fuels.

• Extra r eading: g oogle “atomic orbitals , ” “molecular orbital theor y , ” etc .

• A bit on h yd r ogen storage .

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