Exploring Potential Energy Surfaces Using Ab Initio Molecular Dynamics

1
Exploring Potential Energy Surfaces Using Ab
Initio Molecular Dynamics
Canadian Conference on Computational
Chemistry Halifax, July 19 - 24, 2009

• Prof. H. Bernhard Schlegel
• Department of Chemistry
• Wayne State University
• Current Research Group
• Dr. Peng Tao Dr. Barbara Munk
• Jia Zhou Jason Sonk
• Brian Psciuk Adam Birkholz
• Recent Group Members
• Prof. Xiaosong Li Dr. Hrant Hratchian Prof.
  Jason Sonnenberg Dr. Stan Smith
• Prof. Smriti Anand Dr. Jie (Jessy) Li
• Dr. John Knox Michael Cato

2
Overview

• AIMD study of non-statistical behavior acetone
  radical cation and 2,4-pentanedione radical
  cation dissociation
• AIMD study of a Coulomb explosion dissociation
  of CH2NHn, (n0,1,2,3)
• Electronic response of molecules in short,
  intense laser pulses

3
Applications of Ab Initio Molecular Dynamics
Jia Zhou Chemistry Wayne State U.
Prof. Smriti Anand Northern Virginia Community
College
Dr. Jie Li Genome Center UC Davis
4
Ab Initio Molecular Dynamics (AIMD)

• AIMD electronic structure calculations combined
  with classical trajectory calculations
• Every time the forces on the atoms in a molecule
  are needed, do an electronic structure
  calculation
• Born Oppenheimer (BO) method converge the
  wavefunction at each step in the trajectory
• Extended Lagrangian methods propagate the
  wavefunction along with the geometry
• Car-Parrinello plane-wave basis, propagate MOs
• ADMP atom centered basis, propagate density
  matrix

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Ab Initio Classical Trajectory on
theBorn-Oppenheimer Surface Using Hessians
Calculate the energy, gradient and Hessian
Solve the classical equations of motion on a
local 5th order polynomial surface
Millam, J. M. Bakken, V. Chen, W. Hase, W. L.
Schlegel, H. B. J. Chem. Phys. 1999, 111,
3800-5.
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Dissociation of Acetone Radical Cation

• Dissociation of C3H6O has been of interest for
  many years now
• The enol ion is produced via the McLafferty
  rearrangement.
• The enol form isomerizes to the keto form,
  activating the newly formed methyl group, and
  dissociates to form an acetyl cation and methyl
  radical
• Dissociation behaves in a non-statistical manner
  favoring the loss of newly formed methyl group by
  1.1-1.7 to 1

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Energy Dependence of the Branching Ratio
Osterheld, T. H. Brauman, J. I. J. Am. Chem.
Soc. 1993, 115, 10311-10316.
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Potential Energy Profile (CBS-APNO)
45
35
25
15
Relative Energy (kcal/mol)
5
Ketene/Methane complex
TS for Methane Elimination
-5
-15
Anand, S. Schlegel, H. B. Phys. Chem. Chem.
Phys. 2004, 6, 5166.
-25
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Improved Potential Energy Surfaces using Bond
Additivity Corrections (BAC)

• The most important corrections needed for acetone
  radical cation dissociation reaction are for C-C
  bond stretching potentials.
• BAC (bond additivity correction)
• add simple corrections to get better energetics
  for the reaction
• E E' ?E
• ?E AC-C Exp-aC-C RC-C1 AC-C Exp-
  aC-C RC-C2
• add the corresponding corrections to gradient and
  hessian
• G G' ?(?E)/?x
• H H' ?2(?E)/?x2
• A and a are parameters obtained by fitting to
  high level energies

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Branching Ratios for Microcanonical Ensemble
Initial Energy (kcal/mol) Branching Ratio Average Etranslation (kcal/mol) Average Dissociation Time (fs)
1 2 1.43 1.88 2.7 / 2.0 3.3 / 2.7 181 / 224 177 / 240
10 1.70 4.2 / 2.3 147 / 186
18 1.50 4.2 / 2.8 140 / 167
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Effect of Adding Energy to Specific Vibrational
Modes
Energy assigned 3rd mode 6th mode 8th mode
0 1.101 1.101 1.101
1 kcal/mol 1.591 1.581 1.541
2 kcal/mol 1.841 2.311 1.821
4 kcal/mol 1.461 1.851 2.361
8 kcal/mol 1.551 2.031 2.761
plus 0.5 kcal/mol in transition vector
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Dissociation of Chemically Activated
Pentane-2,4-dione Radical Cation

• The enol radical cation can be produced via the
  McLafferty rearrangement
• Energy is localized in terminal C-C bond, but
  can flow to the other C-C bonds

Zhou, J. Schlegel, H. B. J. Phys. Chem. A 2009,
113, 1453
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Potential Energy Surface for Pentanedione Radical
Cation
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Kinetic Scheme for Pentanedione Radical Cation
Number of trajectories
Time (fs)
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Dissociation of Methanimine and its Cations,
CH2NHn (n0,1,2,3)

• Simplest example of a molecule with a CN double
  bond, also known as methyleneimine and
  formaldimine
• As electrons are removed, bonding should become
  weaker, finally leading to a Coulomb explosion
• CH2NH formed by pyrolysis of amines and azides,
  and seen in interstellar clouds
• Monocation also well studied experimentally, but
  little or no experimental information on higher
  cations
• Many theoretical studies over the years, but at
  many different levels of theory
• Structures and energetics calculated by CBS-APNO
• Ab initio molecular dynamics by B3LYP/6-311G(d,p)

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Dissociation of H2CNH
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Dissociation of H2CNH
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Dissociation of H2NCH2
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Dissociation of H2NCH3
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Direct vs Indirect Dissociation of H2CNH
Direct (no hydrogen rearrangement before
dissociation)
Indirect (hydrogen migration before dissociation)
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Ab Initio Molecular Dynamicsof CH2NHn
Dissociation

• Neutral H2CNH (200 kcal/mol initial energy)
• CH dissociation (28 direct, 4 indirect)
• NH dissociation (13 direct, 3 indirect)
• Triple dissociation (22 HCNHH, 9 HNCHH)
• Molecular dissociation (9 HCNH2, 10 HNCH2)
• Monocation H2CNH (150 kcal/mol initial energy)
• HCNH H (68 direct, 13 indirect)
• H2CN H ? HCNH H (10)
• Molecular dissociation (3 HCNH2, 3 HNCH2)
• Dication H2NCH2 (120 kcal/mol initial energy)
• HCNH H (51 direct, 24 indirect)
• H2NC H (10)
• No reaction (13)

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Time Dependent Simulations of Molecules in
Strong Fields
Prof. Xiaosong Li University of Washington
Jason Sonk, WSU
Prof. Robert Levis, Temple U.
Dr. Stan Smith, Temple U.
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Electronic Response of Molecules Short, Intense
Laser Pulses

• For intensities of 1014 W/cm2, the electric field
  of the laser pulse is comparable to Coulombic
  attraction felt by the valence electrons strong
  field chemistry
• Need to simulate the response of the electrons to
  short, intense pulses
• Time dependent Schrodinger equations in terms of
  ground and excited states
• ? ? Ci(t) ?i i h dCi(t)/dt
  ? Hij(t) Ci(t)
• Requires the energies of the field free states
  and the transition dipoles between them
• Need to limit the expansion to a subset of the
  excitations TD-CIS, TD-CISD
• Time dependent Hartree-Fock equations in terms of
  the density matrix
• i h dP(t)/dt F(t), P(t)
• For constant F, can use a unitary transformation
  to integrate analytically
• P(ti1) V ? P(ti) ? V V exp i ?t F
  
• Fock matrix is time dependent because of the
  applied field and because of the time dependence
  of the density (requires small integration step
  size 0.05 au)

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Hydrogen Molecule aug-cc-pVTZ basis plus 3 sets
of diffuse sp shells Emax 0.07 au (1.7 ? 1014
W/cm2), ? 0.06 au (760 nm)
(b)
(a)
(c)
TD-CIS TD-CISD TD-HF
Instantaneous dipole response
(b)
(d)
Time (0.05au)
(c)
Fourier transform of the residual dipole
response
(e)
Energy (au)
(f)
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Butadiene
Laser pulse
Dipole
Charges
8.751013 W/cm2 760 nm HF/6-31G(d,p) Dt 0.0012
fs
Populations of occupied orbitals
Populations of unoccupied orbitals
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Butadiene, Hexatriene and NaphthaleneTD-CIS/6-31G
(d,p), ? 0.06 au (760 nm)
Excited state weights in the final wavefunction
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Excited State Energies of Butadiene
RPA CIS CIS(D) CISD EOM-CCSD
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??? Transition Dipoles for Butadiene (6-31G(d,p)
basis)
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Response of 2 and 3 Level Systemsto a 3 Cycle
Gaussian Pulse
0.25
0.00
0.35
0.25
0.00
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Response of the ? States of Butadieneto a 3
Cycle Gaussian Pulse
TD-CIS 1Ag (gs) 1Bu
1Ag 1Bu
TD-EOMCC
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TD-CIS response vs number of states

• A large number of states are needed for the
  response to be stable
• Lowest states are well separated
• Higher states form a quasi-continuum
• Most of the higher lying states are needed
  primarily to represent the polarization of the
  molecule in the field

Energy (au)
State Number
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TD-CIS in a Reduced Space

• Perturbation theory for the effective
  polarizability of the low lying states
• Finite difference method for the effective
  polarizability
• where D' is the matrix of transition dipoles
  with the elements between the low lying states
  set to zero
• Integrate TD-CI equations with polarizability

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TD-CIS in a Reduced SpaceButadiene,
TD-CIS/6-31G(d,p)Emax 0.05 au (8.75 ? 1013
W/cm2), ? 0.06 au (760 nm)

• Large CIS space

• Small CIS space with polarizability

Instantaneous Dipole
Instantaneous Dipole
Time (fs)
Time (fs)
Wavefunction Coefficients
Wavefunction Coefficients
Energy (au)
Energy (au)
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Response of Butadieneto a 3 Cycle Gaussian
Pulse(?0.6 au, 6-31G(d,p) basis)
RPA
TD-CIS
TD-CIS(D)
TD-EOMCC
(c)
(f)
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Transition Dipoles for Butadiene(CIS)
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Response of Butadieneto a 3 Cycle Gaussian
Pulse(?0.6 au, TD-CIS)
6-31G(d,p)
6-31G(d,p)
6-311G(2df,2pd)
(c)
(f)
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Acknowledgements

• Collaborators
• Dr. T. Vreven, Gaussian Inc.
• Dr. M. J. Frisch, Gaussian Inc.
• Prof. John SantaLucia, Jr., WSU
• Raviprasad Aduri (SantaLucia group)
• Prof. G. Voth, U. of Utah
• Prof. David Case, Scripps
• Prof. Bill Miller, UC Berkeley
• Prof. Thom Cheatham, U. of Utah
• Prof. S.O. Mobashery, Notre Dame U.
• Prof. R.J. Levis, Temple U.
• Prof. C.H. Winter, WSU
• Prof. C. Verani, WSU
• Prof. E. M. Goldfield, WSU
• Prof. D. B. Rorabacher, WSU
• Prof. J. F. Endicott, WSU
• Prof. J. W. Montgomery, U. of Michigan
• Prof. Sason Shaik, Hebrew University
• Prof. P.G. Wang, Ohio State U.

Current Research Group Dr. Peng Tao Dr. Barbara
Munk Jia Zhou Jason Sonk Brian Psciuk Adam
Birkholz Recent Group Members Prof. Jason
Sonnenberg, Stevenson University, Prof. Xiaosong
Li, U. of Washington Prof. Smriti Anand, Northern
Virginia College Dr. Hrant Hratchian, Gaussian,
Inc. Dr. Jie Li, U. California, Davis (Duan
group) Dr. Stan Smith, Temple U. (Levis
group) Dr. John Knox, GlaxoSmithKline
(Singapore) Michael Cato, Jackson State U.
(Leszczynski group) Funding and
Resources National Science Foundation Office of
Naval Research NIH Gaussian, Inc. Wayne State
U.
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Recent Group Members
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Current Group Members