Electronic Properties of Flexible

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1



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Electronic Properties of Flexible
Systems


Tim Clark

Centre for Molecular Design

University of Portsmouth


Tim.Clark@port.ac.uk

Computer
-
Chemie
-
Centrum and

Excellence Cluster
“Engineering of
Advanced Materials”

Friedrich
-
Alexander
-
Universität

Erlangen
-
Nürnberg

Tim.Clark@chemie.uni
-
erlangen.de

2

Acknowledgements


Dr. Harry Lanig


Dr. Frank
Beierlein


Dr.
Catalin

Rusu


Dr. Matthias Hennemann


Dr. Christof
Jäger


Dr. Olaf
Othersen


Pavlo Dral M.Sc.



Prof. Siegfried Schneider (FRET)


Prof.
Carola

Kryschi

(SHG)


Prof. Nigel Richards (EMPIRE)


Prof. Markus Halik (SAMFETs)



Deutsche
Forschungsgemeinschaft

(DFG)


Bavarian State Government (KONWIHR
)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Can‘t do large systems

No good for charge transfer

Modeling

3


The Hamiltonian


Force field


no electronics, but good sampling
and geometries


Semiempirical MO/CI


CC
-
DFTB/TD
-
CC
-
DFTB


DFT/TDDFT


Ab

initio


SAMPLING !!!!


Molecular dynamics


QM/MM electronics



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Semiempirical MO Theory


Is very fast


Can therefore handle either very large systems or very
many smaller ones


Generally gives very good one
-
electron properties


because the semiempirical electron density is good


because the parameterization probably used a related
property


Because the MEP is good, solvent effects are also good


Semiempirical CI is good for excited states


Also better for frontier orbital energies than “higher” levels
of theory


Is therefore ideal for calculating the properties of many
“hot” geometries (snapshots) from MD simulations to
obtain ensemble properties

4



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Topics


UNO
-
CAS for Band Gaps


Simulating FRET in Biological Systems


Simulating SHG in Biological Membranes


EMPIRE


Very Large massively parallel
Semiempirical MO calculations


Self
-
Assembled Monolayer Field
-
Effect
Transistors (SAMFETs)


5



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Semiempirical UNO
-
CAS for
Optical Band Gaps

Pavlo Dral

6



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


UNO
-
CAS


U
HF
N
atural
O
rbital


C
omplete
A
ctive
S
pace configuration interaction



J. M.
Bofill

and P.
Pulay
,
J. Chem. Phys.
1989
,
90
, 3637.



Semiempirical UNO
-
CAS and UNO
-
CI: Method and
Applications in Nanoelectronics
, P. O. Dral and T. Clark,
J.
Phys. Chem. A,

2011
,
115
,
asap

(DOI: 10.1021/jp204939x).



7



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


UHF Natural Orbitals (UNOs)


Diagonalize

the total (


+

) UHF density
matrix


The eigenvectors are the UHF Natural
orbitals and the Eigenvalues are the UNO
occupation numbers (0 or 2 for RHF, partial
values between 0 and 2 for UHF)


S
ignificant
F
ractional
O
ccupation
N
umbers
(SFONs) between 0.02 and 1.98 define the
active space

8



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Advantages


The active space defined by the SFONs is
usually small enough to allow a full CI
calculation (UNO
-
CAS)


A CI
-
Singles (CIS) or CISD approach can
be used for larger active spaces


The active space is defined automatically


UNOs contain some multi
-
reference
information derived from the components of
the UHF wavefunction

9



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Disadvantages


It is sometimes very difficult to find the
correct UHF wavefunction (there may
be many solutions close in energy)


Only applicable for systems that
exhibit RHF/UHF instability (symmetry
breaking)

10



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Calculated Band Gaps: Polyynes

11



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Polyacene

band gaps

12



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Optical Properties



Two examples


Fluorescence resonant energy transfer (FRET) in
TetR

(S. Schneider)


Second
-
harmonic generation (SHG) by dyes in biological
membranes (C.
Kryschi
)



A Numerical Self
-
Consistent Reaction Field (SCRF) Model for
Ground and Excited States in NDDO
-
Based Methods
, G.
Rauhut
,
T. Clark and T. Steinke,
J. Am. Chem. Soc
., 1993,
115,

9174
.



NDDO
-
Based CI Methods for the Prediction of Electronic Spectra
and Sum
-
Over
-
States Molecular
Hyperpolarizabilities
, T. Clark and
J. Chandrasekhar,
Israel J. Chem.
, 1993,
33,

435.



A
Semiempirical

QM/MM Implementation and its Application to the
Absorption of Organic Molecules in
Zeolites
, T. Clark, A. Alex, B.
Beck, P.
Gedeck

and H.
Lanig
,
J. Mol. Model.

1999,
5
, 1.



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


FRET in the Tetracycline
Repressor

Frank Beierlein, Prof. Siegfried Schneider,
Harry Lanig, Olaf
Othersen

14

Simulating FRET from Tryptophan: Is the
Rotamer

Model Correct? ,


F. R. Beierlein, O. G.
Othersen
, H. Lanig, S. Schneider and T. Clark,

J. Am. Chem. Soc. ,
2006
, 128 , 5142
-
5152.



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


FRET (SFB 473)

Tryptophan





Tetracycline





One monomer of the Tetracycline
Repressor (
TetR
) Protein



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


The Experimental Problem


Fluorescence decay in the protein is
biexponential


Usually treated using the “
rotamer

model”


Each individual exponential decay process can
be attributed to a corresponding tryptophan
rotamer


Differences in distance and, above all
orientation, relative to the acceptor
(tetracycline) give different decay rates (
Förster

theory)


Is this model correct?



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Chromophores

Tryptophan

Two low
-
lying excited states

1
L
a
, polar, solvent sensitive,
usually the emitting state
(~350nM)

1
L
b
, non
-
polar

Tetracycline:Mg
2+

“BCD”
Chromopohore

Absorption overlaps with
tryptophan emission, making
FRET possible



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Glycyltryptophan

Absorbance Spectra (H
2
O)

-

Experimental

-

SCRF (


= 78.36)

-

QM/MM (explicit
water)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Tryptophan Transition Dipoles

From above the ring

In the ring plane

10% of the calculated snapshots shown



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Rotamer Distribution



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Einstein Coefficients

(no FRET)

-

Total

-

Rotamer 1

-

Rotamer 2




Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


FRET Rate Constants (
Förster

theory)

-

Total

-

Rotamer 1

-

Rotamer 2




Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Exponential Fits

Total
without
FRET

Rotamer

1
with

FRET

Rotamer 2
with

FRET

Total

with

FRET

No. of Exponentials

1

2

2

2



(ns)

4.65

4.03, 1.76

3.65, 1.70

3.94, 1.74

Coefficient(s) (%)

100

57, 43

66, 33

59, 41

Fit for the total is approximated well by the weighted average of
the parameters for the individual
rotamers
,
not as two
individual decay components
.



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


FRET Conclusions


Individual
rotamers

with significant lifetimes can be
identified in the MD simulations


Including FRET makes the decay curves
biexponential

for each
rotamer


Biexponentiality

is caused by the distribution of the
FRET rates, rather than by individual
rotamers


“Spectroscopic Ruler” distances may be in error by
as much as 6 Å if the orientation factor is not
considered explicitly




Simulating FRET from Tryptophan: Is the
Rotamer

Model
Correct?
, F. R.
Beierlein
, O. G.
Othersen
, H.
Lanig
, S.
Schneider and T. Clark,
J. Am. Chem. Soc.
,
2006
,
128
,
5142
-
5152.



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


SHG in Biological Membranes

Catalin
Rusu
, Prof. Carola
Kryschi
,
Harry Lanig

25

Monitoring Biological Membrane
-
Potential
Changes: a CI QM/MM Study


C.
Rusu
, H. Lanig, T. Clark and C.
Kryschi
,

J. Phys. Chem. B ,
2008
, 112 , 2445
-
2455



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


SHG in Membranes


Second
-
harmonic generation (SHG)
has been used recently to monitor
action potentials (AP) in
cardiomyocytes

or neurons


The intensity of the SHG (
I
SHG
) is
monitored as a function of the trans
-
membrane potential


Di
-
8
-
ANEPPS was used as a typical
lipophilic

dye that is incorporated into
the membrane


The simulation system consisted of
one dye molecule, 63 DPCC lipid
molecules and 3,840 water molecules




Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


The Simulation System



Water: blue



Lipids: green (head groups bold)



Dye: red



GROMOS force field with optimized
Lennard
-
Jones parameters for lipids



Periodic boundary conditions



PME electrostatics, NPT ensemble



10 ns equilibration + 10 ns production MD



700 snapshots per trajectory (last 7 ns of
the production phase)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


QM
-
CI/MM Snapshots


Di
-
8
-
ANEPPS used as the QM
-
part
(
chromophore
, 91 atoms)


MM surroundings (DCCP + water)
consisted of 14,700 atoms


18 active orbitals


18 active electrons


Single + pair
-
double excitations



QM/MM

= 4.0


Excitation energy = 1.17
eV

(for sum
-
over
-
states

)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Trans
-
Membrane Potential


External potential applied to the QM
-
CI/MM
calculations


Change in dye dipole moment
in
vacuo

used to calibrate the system


External potential then adjusted to give a
local potential at the dye of



0.1 V


Three calculations at +0.1, 0.0 and

0.1 V
for each snapshot


Total simulated AP is therefore 0.2 V (about
twice as large as in the experiment)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Dye


Vertical Stability



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Calculated

I
SHG

(

V = 0.2V)

Simulation 1:


I
SHG

= 41.6


11.1 %

Simulation 2:


I
SHG

= 43.2


13.0
%

Experiment:

I
SHG



40 %



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


SHG Conclusions


The qualitative picture of the dye in the
membrane is correct



The MD simulations give lateral diffusion rates
several orders of magnitude higher than those
deduced from experiment


Force
-
field problem (van
der

Waals)?


Experimental interpretation ?



SHG enhancement of the order found in the
experimental studies is also found in the
simulations



C. F.
Rusu
, H. Lanig, O. G.
Othersen
, C.
Kryschi

and T.
Clark, to be submitted to
J. Am. Chem. Soc.

(
2007
)



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


EMPIRE: A Very Large Scale
Parallel Semiempirical SCF
Program

Matthias Hennemann

33



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Develop a completely new semiempirical MO Program
(EMPIRE) ; design specifications:


Neither LMO nor D&C


Need to treat conjugated systems


Massively parallel:


SCF

50,000 Atoms using 1,000 cores


Configuration Interaction (CI)

5,000 Atoms using 1,000 cores


Program


Direct
on
-
the
-
fly

calculation of the 2
-
electron integrals and the
one
-
electron matrix


Avoid matrix
diagonalization



34

The Big Hammer Approach



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Comparison with VAMP

35

910 Atoms

1,960 Orbitals


VAMP

11
Cycles

59
Seconds

(1
Core
)


EMPIRE

16
Cycles

58
Seconds

(1
Core
)

7.8
Seconds

(12
Cores
)








Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Scaling on one Node

36

Dual
-
Hex
-
Core Xeon 5650 “
Westmere
” 2.66 GHz (@ 2.93 GHz)

with 12 MB cache per chip und 24 GB RAM.



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Benchmark results:
Adamantane

6

6

6











37

11,232 Atoms

24,192
Orbitals


4

12 Cores:

78.4 Minutes


8

12 Cores:

44.3
Minuten


16

12 Cores:

25.6
Minuten


22 Cycles



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Benchmark
-
Results
: HLRB II

38

HLRB II:

9,728 Cores
-

512 per Partition: 1.6 GHz dual core Itanium 2 “Montecito”, 4
GB RAM per Core,
NUMAlink

4 with 6,4
GByte
/s per link und direction



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Hard
Scaling

(
LiMa
)

39

LiMa

500 Dual
-
Hex
-
Core

Xeon 5650 “
Westmere


2,66 GHz (@ 2.93 GHz)

12 MB Cache per Chip

24 GB RAM per
Node

Infiniband

with 40
Gbit
/s

per link and direction



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


40

0



molecular scale electronic devices with pure and mixed SAMs



relation of device characteristics on molecular
structure
and
SAM composition



SAMs as important
dielectric and
bifunctional

layers
in
condensers and FETs

Application: Organic Field
-
Effect Transistors



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Application:

Organic Field
-
Effect Transistors

41


Constructed of self
-
assembled
monolayers (SAMs)


Head groups such as fullerenes can
function as the semiconductor


No additional semiconductor layer
necessary


Properties vary widely


Can an adequate permanent
semiconductor layer be attained?


Classical MD simulations with AM1
single
-
points on snapshots


Prof. Marcus Halik

C10PA + C60C18PA

C60C18PA



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


C
10
PA + C
60
C
18
PA
-

Monolayer









42


6,050 Atoms

15,950 Orbitals


25 Minutes

(8

12 Cores)


36 Cycles


At the moment:

50 Snapshots



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Local Electron Affinity (EA
L
)









43



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Section through the SAM (EA
L
)









44



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs


Section through the SAM (EA
L
)

45



Introduction



UNO
-
CAS



FRET



SHG in
membranes



Very large
scale MO



SAMFETs