vibrational spectroscopy of large moleculescassam/workshop10/presentations/...vibrational...
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Vibrational Spectroscopy Vibrational Spectroscopy of Large Molecules:of Large Molecules:Anharmonic Algorithms Anharmonic Algorithms and Applicationsand Applications
R. Benny GerberThe Hebrew University of Jerusalem, Israeland University of California at Irvine, USA
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Importance:Importance:
Vibrational spectroscopy is a major tool for studying properties of large molecules.
In some cases, it is a unique tool.
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Determination of Structure by Determination of Structure by Spectroscopy : Spectroscopy : (SO(SO44--22))--(H(H22O)O)nn
Miller, Y.; Chaban, G.M.; Zhou, J.;Asmis,K.R.; Neumark,D.M.; Gerber,R.B., J.C.P. 127, 9 (2007).
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Determination of Structure by Determination of Structure by Spectroscopy : Spectroscopy : The complex GThe complex G--C of C of nucleic acid basesnucleic acid bases
B.Brauer, R. B. Gerber, M. Kabeláč, P. Hobza, J. M. Bakker, A. G. Abo Riziq, M. S. de Vries, JPC A, 109, 6924, (2005).
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Identification of intermediates in Identification of intermediates in processes : processes : The photocycle of Photoactive The photocycle of Photoactive Yellow Protein (PYP)Yellow Protein (PYP)
AA Adesokan, DH Pan, E AA Adesokan, DH Pan, E Fredj, RA Mathies, RB Gerber J. Am. Chem. Soc.(2007).
Hellingwerf et al. J Phys Chem A 2003.
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Testing potential functions (Force Testing potential functions (Force Fields) for large moleculesFields) for large molecules
(A) The native state globular structure of ubiquitin. (B) The A state conformation, stable at low pH methanol water stable at low pH methanol water solution.
Moil MD simulation package with the AMBER force field
Segev, E; Wyttenbach, T; Bowers, MT, Gerber RB. P.C.C.P. 10, 21 (2008)
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Outline of LectureOutline of Lecture
I. The challenges
II. Principles of the method
III. Algorithms, and how they scale with N (no. of atoms)atoms)
IV. Applications
V. Structures of sugars
VI. Spectra of long chains of hydrocarbons and imaging of Lipids
VII. Conclusions and future directions
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The Harmonic ApproximationThe Harmonic Approximation
W
21 2
1),...,( jj
N
joN qkWqqW ∑+= jq - Normal modes
...........)2
1()
2
1( 2211.....1 ++++=Ε vvnvv ωω hh
q1
q2
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The Challenges of Anharmonic The Challenges of Anharmonic CalculationsCalculations
A Quantum Mechanical Problem for Many Interacting Degrees of Freedom
� Find method to solve it
� Develop algorithm that scales well with N
� Apply for realistic potentials
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VSCFVSCF, , First Step: Separable First Step: Separable ApproximationApproximation
Assume :
),...,( 1 NxxΨ - Vibrational wavefunction
)()....()(),...,( 22111 NNN xxxxx ϕϕϕ=Ψ )()....()(),...,( 22111 NNN xxxxx ϕϕϕ=ΨJ. M. Bowman, J.Chem.Phys. (1978)G. D. Carney, L. Sprandel, C.W. Kern, Adv.Chem.Phys. (1978)M. Cohen, S. Gretia, R.M. McEachran, Chem.Phys.Lett. (1979)R. B. Gerber, M. A. Ratner, Chem.Phys.Lett. (1979)
Key question: Which coordinates to use? Key question: Which coordinates to use?
R.B. Gerber, M. A. Ratner, Adv.Chem.Phys 70, 92 (1988)
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Vibrational SelfVibrational Self--Consistent Consistent Field in Normal CoordinatesField in Normal Coordinates
nnn ΨΕ=ΗΨ
To solve:
(1)
),...,(2 12
2
1
2
Nj
N
j j
qqVqm+
∂∂
−=Η ∑=
h
)(),...,(1
1 j
N
jjN qqq ∏
=
=Ψ ϕ
VSCF (or Hartree) Approximation:
(2)
(3)
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)()()(2 2
22
jjjjjjjj
qqqVqm
ϕεϕ =
+
∂∂
−h
(4)
(5)
SCF equations:
(4) , (5) are solved by iteration.
Total Energy is:
(6)
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VSCFVSCF--PTPT22: Correcting SCF by : Correcting SCF by Perturbation TheoryPerturbation Theory
J. O. Jung and R. B. Gerber JCP 105,10332 (1996)
),...,( 1 NSCF qqV∆+Η=Η (7)
)(qVqqVV jN
jjN ∑
=
−=∆1
1 ),...,(
Treat ∆V as a small perturbation
(8)
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Ab initio Anharmonic Ab initio Anharmonic SpectroscopySpectroscopy
Direct VSCF, VSCF – PT2 Calculations Using Electronic
Dr. G.M. Chaban
Dr. J.O. Jung
Structure Codes
G.M. Chaban, J.O. Jung, R.B. Gerber J.Chem.Phys. 111, 1823, (1999)
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The Pairwise Coupling The Pairwise Coupling ApproximationApproximation
),q(qW)(qVV),...,qV(q jii ij
coupijj
N
j
diagjN ∑∑∑
>=
++=1
01i ijj >=1
Satisfactory in most cases for our system
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Scaling of VSCFScaling of VSCF--PTPT2 2 with Nwith N
N = 3 Natoms -6(no. of vibrational modes)
Liat Pele Dr. Brina Brauer
L. Pele, B. Brauer, and R.B. Gerber, Theor. Chem. Acc. (2007)
VSCF-PT2 computing time is of O(N3).
Liat Pele Dr. Brina Brauer
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Scaling of VSCFScaling of VSCF--PTPT2 2 with Nwith N
N = 3 Natoms -6(no. of vibrational modes)
Liat Pele Dr. Brina Brauer
L. Pele, B. Brauer, and R.B. Gerber, Theor. Chem. Acc. (2007)
New version reduces VSCF-PT2 computing time from O(N6) to O(N3).
Liat Pele Dr. Brina Brauer
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How Many Pairwise Couplings How Many Pairwise Couplings Do We need ?Do We need ?
Numerical experiments of series of peptides:
Liat Pele
of series of peptides:
NlogN couplings Wij(Qi,Qj) suffice for good accuracy !
Pele and Gerber J. Chem. Phys. (2008)
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Numerical Experiments: Mean Numerical Experiments: Mean Accuracy of (separable) VSCFAccuracy of (separable) VSCF
Improves with N!Improves with N!
Liat Pele
Tests for: Di- , Tri and Tetra – Peptides.
Deviations of VSCF from VSCF-PT2 are computed.
Pele and Gerber J. Phys. Chem. C (2010)
computed.
Deviations decrease as logN.
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The Protonated ImidazoleThe Protonated Imidazole--Water Water Cluster, (ImHCluster, (ImH++))--HH22OO
CC-VSCF calculations with MP2/DZP and IRPD
Experiments for (ImH+)-H2O-N2:
AA Adesokan, GM Chaban, O Dopfer and RB GerberIR Photodissociation experiments by Prof. O. Dopfer
Yemi Adesokan
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(ImH+)(H2O)-N2. Assignment and comparison of theoreticalharmonic and anharmonic frequencies in wave numbers tothose obtained from experiments.
NH stretch (towards water)289728903217
Water asym stretch372336964011
Water sym stretch3639 36483884
MODE DESCRIPTIONIRPDCC-VSCF(Ab initio)
Harmonic(Ab initio)
Ab initio = MP2/DZP
Mean VSCF- experiment deviation : 0.6%
Mean harmonic – experiment deviation: 7.1%
C5-H stretchapp 317232213392
C3-H stretchapp 317231653372
C1-H stretch, C2-H stretchapp 317232053380
NH stretch (towards N2)340433883587
NH stretch (towards water)289728903217
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Approach:
Improving “Low Level” Improving “Low Level” Potentials for Potentials for
Spectroscopy CalculationsSpectroscopy CalculationsDr. BrinaBrauer
Dr. G.M. Chaban
Modify the PM3 potential by:
VNEW(q1,...,qn)=VPM3(λ1q1 ,... λnq)
( )
( 3)
harmonicj
j harmonicj
abinitio
PM
ωλ
ω=
Where
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The Structures of The Structures of αα –– Glucose in a MatrixGlucose in a Matrix
Agreement with IR experiments supports the structures
MP2/TZP Energies
Dr. B. Brauer
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Expt Calcd "A" Expt Calcd "B" Expt Calcd "X" Conf A G+g- Conf B G-g+ Conf X T
3632 3644 3634 3640 3604 35603634 3657 3636 3645 3627 36373641 3660 3640 3665 3640 36493645 3682 3645 3671 3645 3655
OH Stretch Vibrational Frequencies in cm-1
PhenylPhenyl--ββ--Glucose in the Gas PhaseGlucose in the Gas Phase
Average Deviation from Experiment < 1%!
Prof. J. P. Simons Dr. B. Brauer
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Vibrational Spectroscopy and Imaging of Biological Membranes
in vivo tissue imaging of a mouse skin
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Dodecane Dodecane –– Model Molecule for Model Molecule for Lipid MembranesLipid Membranes
Liat Pele Dr. Jiří Šebek
Prof. Eric O. Potma
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Modeling Temperature and Modeling Temperature and Environment EffectsEnvironment Effects
Dodecane - VSCF (scaled PM3 level)
0.8
1R
elat
ive
Ram
an In
ten
sity smoothed spectrum
VSCF lines
2600 2800 3000 32000
0.2
0.4
0.6
Wavenumber [cm-1]
Rel
ativ
e R
aman
Inte
nsi
ty
VSCF lines
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Spectroscopy of DodecaneSpectroscopy of DodecaneH-Dodecane - VSCF (scaled PM3 level)
0.2
0.4
0.6
0.8
1
Rel
ativ
e R
aman
Inte
nsi
ty
experimentVSCF
2600 2800 3000 32000
Wavenumber [cm-1]D-Dodecane - VSCF (scaled PM3 level)
1800 2000 2200 24000
0.2
0.4
0.6
0.8
1
Wavenumber [cm-1]
Rel
ativ
e R
aman
Inte
nsi
ty
experimentVSCF
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Summary: State of the ArtSummary: State of the Art
1. Many successful applications for systems up to ~50 atoms
2. Method is most suitable for: isolated molecules, low temperatures
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Collaborations with Experimental Collaborations with Experimental GroupsGroups
Prof. J.P. Prof. M.S. de Prof. G.Meijer and Prof. J.P. Simons
Prof. M.S. de Vries
Prof. G.Meijer and Prof. G. Von Helden
Prof. T. Rizzo
Prof. I.BarProf. D. M. Neumark
Prof. O. Dopfer
Prof. R. A. Mathies
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The Present FrontierThe Present Frontier
1) Methods and algorithm for 103 atoms and more (e.g. for protein structure by spectroscopy )
2) Systems at room temperature, interacting with environment : Can VSCF be used ? How extensive is the applicability ?