Electronic Properties of Flexible
Systems
• Introduction
•UNO-CAS
Tim Clark
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Computer-Chemie-Centrum and
Excellence Cluster “Engineering of
Advanced Materials”
Friedrich-Alexander-Universität
Erlangen-Nürnberg
Tim.Clark@chemie.uni-erlangen.de
Centre for Molecular Design
University of Portsmouth
Tim.Clark@port.ac.uk
1
Acknowledgements
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
•
•
•
•
•
•
•
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)
2
Modeling
• The Hamiltonian
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
– Force field – no electronics, but good sampling
and geometries
– Semiempirical MO/CI
– CC-DFTB/TD-CC-DFTB No good for charge transfer
– DFT/TDDFT
– Ab initio
Can‘t do large systems
• SAMPLING !!!!
– Molecular dynamics
– QM/MM electronics
3
Semiempirical MO Theory
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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
Topics
• UNO-CAS for Band Gaps
• Introduction
• Simulating FRET in Biological Systems
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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
Semiempirical UNO-CAS for
Optical Band Gaps
Pavlo Dral
•SHG in
membranes
•Very large
scale MO
•SAMFETs
6
UNO-CAS
• UHF Natural Orbital – Complete Active
Space configuration interaction
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
– 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).
•SAMFETs
P U  U
T
7
UHF Natural Orbitals (UNOs)
• Diagonalize the total ( + ) UHF density
matrix
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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)
• Significant Fractional Occupation Numbers
(SFONs) between 0.02 and 1.98 define the
active space
8
Advantages
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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
Disadvantages
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
• 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)
•SAMFETs
10
Calculated Band Gaps: Polyynes
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
11
Polyacene band gaps
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
12
Optical Properties
• Two examples
– Fluorescence resonant energy transfer (FRET) in TetR
(S. Schneider)
– Second-harmonic generation (SHG) by dyes in biological
membranes (C. Kryschi)
• Introduction
•UNO-CAS
•FRET
•
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.
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
FRET in the Tetracycline
Repressor
Frank Beierlein, Prof. Siegfried Schneider,
Harry Lanig, Olaf Othersen
Simulating FRET from Tryptophan: Is the Rotamer Model Correct? ,
•SAMFETs
F. R. Beierlein, O. G. Othersen, H. Lanig, S. Schneider and T. Clark,
J. Am. Chem. Soc. , 2006 , 128 , 5142-5152.
14
FRET (SFB 473)
Tetracycline
Tryptophan
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
One monomer of the Tetracycline
Repressor (TetR) Protein
The Experimental Problem
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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?
Chromophores
Tryptophan
Two low-lying excited states
• Introduction
1L ,
a
polar, solvent sensitive,
usually the emitting state
(~350nM)
•UNO-CAS
•FRET
1L ,
b
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Tetracycline:Mg2+
“BCD” Chromopohore
Absorption overlaps with
tryptophan emission, making
FRET possible
non-polar
Glycyltryptophan Absorbance Spectra (H2O)
• Introduction
- Experimental
•UNO-CAS
- SCRF ( = 78.36)
•FRET
- QM/MM (explicit
water)
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Tryptophan Transition Dipoles
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
From above the ring
In the ring plane
10% of the calculated snapshots shown
Rotamer Distribution
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Einstein Coefficients
(no FRET)
• Introduction
- Total
•UNO-CAS
- Rotamer 1
•FRET
- Rotamer 2
•SHG in
membranes
•Very large
scale MO
•SAMFETs
FRET Rate Constants (Förster theory)
• Introduction
- Total
•UNO-CAS
- Rotamer 1
•FRET
- Rotamer 2
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Exponential Fits
Total
without
FRET
• Introduction
•UNO-CAS
No. of Exponentials
•FRET
•SHG in
membranes
Rotamer 1 Rotamer 2
with
with
FRET
FRET
Total
with
FRET
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
•Very large
scale MO
•SAMFETs
Fit for the total is approximated well by the weighted average of
the parameters for the individual rotamers, not as two
individual decay components.
FRET Conclusions
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
• 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
•SAMFETs
• 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
SHG in Biological Membranes
Catalin Rusu, Prof. Carola Kryschi,
Harry Lanig
Monitoring Biological Membrane-Potential
Changes: a CI QM/MM Study
•SAMFETs
C. Rusu, H. Lanig, T. Clark and C. Kryschi,
J. Phys. Chem. B , 2008 , 112 , 2445-2455
25
SHG in Membranes
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• Second-harmonic generation (SHG)
has been used recently to monitor
action potentials (AP) in
cardiomyocytes or neurons
• The intensity of the SHG (ISHG) is
monitored as a function of the transmembrane 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
SO3-
N+
(H2C)7
CH3
N
(CH2)7
CH3
The Simulation System
• Introduction
•UNO-CAS
• Water: blue
• Lipids: green (head groups bold)
• Dye: red
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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)
QM-CI/MM Snapshots
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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-overstates )
Trans-Membrane Potential
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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)
Dye – Vertical Stability
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
z-coordinate of simulation cell [nm]
8
5
2
3
4
5
6
7
time [ns]
8
9
10
Calculated ISHG (V = 0.2V)
30
25
• Introduction
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Counts
•UNO-CAS
20
15
10
5
0
15
20
25
30
35
40
45
50
55
Delta I SHG [%]
MD1
MD2
Simulation 1: ISHG = 41.6  11.1 %
Simulation 2: ISHG = 43.2  13.0 %
Experiment: ISHG  40 %
60
65
70
75
80
SHG Conclusions
• The qualitative picture of the dye in the
membrane is correct
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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
EMPIRE: A Very Large Scale
Parallel Semiempirical SCF
Program
Matthias Hennemann
•SHG in
membranes
•Very large
scale MO
•SAMFETs
33
The Big Hammer Approach
• 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
Comparison with VAMP
910 Atoms
1,960 Orbitals
VAMP
11 Cycles
59 Seconds
(1 Core)
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
EMPIRE
16 Cycles
58 Seconds
(1 Core)
7.8 Seconds
(12 Cores)
•Very large
scale MO
•SAMFETs
35
Scaling on one Node
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
Dual-Hex-Core Xeon 5650 “Westmere” 2.66 GHz (@ 2.93 GHz)
with 12 MB cache per chip und 24 GB RAM.
36
Benchmark results: Adamantane 666
11,232 Atoms
24,192
Orbitals
• Introduction
412 Cores:
78.4 Minutes
•UNO-CAS
•FRET
•SHG in
membranes
812 Cores:
44.3 Minuten
•Very large
scale MO
1612 Cores:
25.6 Minuten
•SAMFETs
22 Cycles
37
Benchmark-Results: HLRB II
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
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
38
Hard Scaling (LiMa)
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
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
39
Application: Organic Field-Effect Transistors
• Introduction
•UNO-CAS
0
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
• 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
40
Application:
Organic Field-Effect Transistors
• Constructed of self-assembled
monolayers (SAMs)
• Introduction
•UNO-CAS
•FRET
• Head groups such as fullerenes can
function as the semiconductor
• No additional semiconductor layer
necessary
•SHG in
membranes
• Properties vary widely
•Very large
scale MO
• Can an adequate permanent
semiconductor layer be attained?
•SAMFETs
C10PA + C60C18PA
• Classical MD simulations with AM1
single-points on snapshots
• Prof. Marcus Halik
C60C18PA
41
C10PA + C60C18PA - Monolayer
6,050 Atoms
15,950 Orbitals
• Introduction
25 Minutes
(812 Cores)
•UNO-CAS
•FRET
36 Cycles
•SHG in
membranes
At the moment:
50 Snapshots
•Very large
scale MO
•SAMFETs
42
Local Electron Affinity (EAL)
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
43
Section through the SAM (EAL)
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
44
Section through the SAM (EAL)
• Introduction
•UNO-CAS
•FRET
•SHG in
membranes
•Very large
scale MO
•SAMFETs
45