Combined QMMM Studies of the NO3 anion

1
Combined QM/MM Studies of the NO3- anion
Special Topic Literature Review Tongraar, A.,
Tangkawanwanit, P., and Rode, B. M. (2006). J.
Phys. Chem. A 11012918-26. Lebrero, M. C.,
Bikiel, D. E., Elola, B. M., Estrin, D. A., and
Roitberg, A. E. (2002). JCP 117(6)2718-2725.
Ramesh, S. G., Re, S., and Hynes, J. T. (2008).
J. Phys. Chem. A. 1123391-8.

• David M. Rogers
• Special Topics in QM
• Spring, 2008

2
Outline

• NO3- anion water
• Changes in resonance structures / pi system are
  quantum-mechanical!
• Properties of interest
• QM/MM Methods
• Results for NO3-
• Dependence on method?
• How to design your own QM/MM simulation.
• Ewald Summation Problem

3
The NO3- anion
How does antisymmetric stretch peak splitting
occur in water?
4
Important Properties of NO3-

• QM
• Proton affinity
• Charge density and MO structure
• Classical / QM
• Vibrational spectrum
• Geometry changes
• Influence on local liquid structure
• Di/quadru/octa/-pole moment
• Water dipole change

5
Major Effect of Solvation Ion stabilization

• Dissociated form of HNO3 kinetically unstable in
  vacuum or 8-water clusters.

Miller, Y. and Gerber, R. B. (2008). PCCP.
101091-3.
6
Major Effect of Solvation H-bonding

• What QM method can best describe
  hydrogen-bonding?
• HF tends to under-estimate water dimerization
  energy
• MP2 can over-estimate polarization, but
  accurately predicts vibrational spectra of NO3-
  and H2O
• DFT B3LYP can over-estimate electron correlation
  energies
• gt Method comparison must be done for each system!

7
Hydrogen Bonding Interactions

• What happens to water upon H-bonding?
• OH Bond lengthens
• Red-shift of OH-stretch frequency
• Acceptor's charge delocalizes into antibonding MO
  of water
• Charge re-distributed in acceptor molecule (anion)

8
Hydrogen Bonding Interactions
Ramesh studied NO3- solvation by analyzing
low-energy water cluster structures. How about
dynamical properties?
9
Continuum of Integration Methods

• Time-dependent QM
• B.O. dynamics
• Fictitious electron mass CPMD
• Overlapping boundary QM/MM
• M.O. based QM/MM
• QM partial charge MM
• Forcefield-based MM

10
Continuum of Integration Methods

• Time-dependent QM
• B.O. dynamics
• Fictitious electron mass CPMD
• Overlapping boundary QM/MM
• M.O. based QM/MM
• QM partial charge MM
• Forcefield-based MM

Tongraar et. al., JPC-A (2006).
11
Interface Region

• How does the QM region feel the influence of the
  solution environment?
• Point of disagreement between different QM/MM
  regions

• Overlapping boundary
• Do QM on a small cluster, but only use core.
• M.O. Based
• Frozen orbitals prevent electron density from
  leaking into vacuum
• Partial Charge based
• As above, no frozen orbitals

12
Lead Article
Tongraar, A., Tangkawanwanit, P., and Rode, B. M.
(2006). J. Phys. Chem. A 11012918-26.

• QM both HF and B3LYP/DZV
• MM flexible water model designed for IR spectra
  properties
• Cited Crucial factors for QM/MM
• Adequate electronic structure method
• Large enough basis set, calculation efficiency
• Adequate size of the QM region
• Overlapping boundary used core4.4 A, bound8.8
  A
• 0.2 A force switching gt outer 4.2 A discarded

13
Tests (1 pg.)

• Comparison of NO3- H2O heterodimer geometry
• N-OW rdf calculation
• QM region should get to second solvation shell

14
Results

• B3LYP over-estimates association energy, but
  accurately estimates H-bond lengthening
• HF under-estimates H-bond lengthening, but
  accurately estimates association energy
• HF suggested as giving better dynamical
  properties
• in line with a previous study using the same
  method for pure water

15
Aqueous NO3- H-Bond Strength Indicators

• Size of 1st and 2nd peaks in OHW RDF
• 0.9,1.3 (nitrate) vs. 1.5,1.7 (water)
• Diffusion constant near NO3-
• Higher than bulk by 25-80 (HF lower then B3LYP)
• Indicates cosmo/chao/ -tropic properties of ion
• Mean residence time of solvation water
• HF 0.11 vs. 0.33 ps
• B3LYP 0.14 vs. 1.07 ps
• DFT coordination number (HW within 3.5 A) is
  4.75-4.99 vs 3.74-3.78 for HF.

16
Earlier Study
Lebrero, M. C., Bikiel, D. E., Elola, B. M.,
Estrin, D. A., and Roitberg, A. E. (2002). JCP
117(6)2718-2725.

• QM DFT, Gaussian Basis
• MM TIP4P fixed and fluctuating charge
• Cited crucial factor for solution study
• Enough waters to fill first few solvation shells
• Antisymmetric stretch peak splitting observed
• Partial Charge method used, only NO3- treated
  quantum mechanically.
• Results too focused on changes in IR spectrum
  upon solvation.

17
Later Study
Ramesh, S. G., Re, S., and Hynes, J. T. (2008).
J. Phys. Chem. A. 1123391-8.

• QM MP2/DZP... energy calculations on small
  clusters.
• Focus on electronic structure and hydrogen bond
  strength of NO3-(aq)
• Results
• Water's OH stretch frequency red-shifts (lower
  freq.) when H-bonding occurs.
• Magnitude is positively correlated with proton
  affinity of acceptor, water OH bond lengthening,
  and extent of charge transfer gt indicates
  relative hydrogen bond strength

18
Results (cont.)

• Relative hydrogen-bond interaction strength (1
  water)
• F- gt Cl- gt NO3- Br- gt I- gt H2O
• Relative strength decreases as more waters are
  added
• OH freq. shift is -214 (theor.) / -181 (expt.)
  cm-1 _at_ 6 waters (up from -534 cm-1 at 1), and
  less strong than other halide clusters.
• Less water polarization at larger coordination
  numbers
• Pi orbital resonance prevents large localization
  of negative charge, and decreases hydrogen
  bonding ability

19
Design Your Own QM/MM Sim.

• What are the important properties of my solute?
• Gauge of changing electronic structure?
• How does the solution environment make a
  difference?
• Role of solvent motion
• Symmetry breaking, hydrophobic effects,
  diffusion, etc.
• What hypotheses can I reasonably expect to
  confirm from short MD simulations?

20
Design Your Own QM/MM Sim.

• Test and Validate
• Compare known, static, and gas phase properties.
• Rationalize the difference between alternate
  electronic structure methods.
• Choose a QM/MM boundary treatment that minimizes
  artificial side-effects.
• Perform the Simulation
• Effectively Present Your Results!
• Large, legible charts and graphs
• Write a concise explanation to someone who hasn't
  spent the last year (or 3) on your project.

21
Ewald Summation

• What is the potential due to a point charge? 1/r
• This potential should be screened at large
  distances, and periodic with respect to box
  repeats. -gt add in some terms to make this happen
• Solve and write for efficient summation

Equations from The Potential Distribution Theorem
and Models of Molecular Solutions.
22
A Numerical Example

• The total electrostatic potential is
  pairwise-additive with one caveat
• Calculating the caveat
• erfc term disappears for large enough h
• K-space sum approx. zero for large enough k

23
Python Numpy Source
gtgtgt calc_eps(ones(3)10.0, .54, 10) Error
4.04980576401e-16 mad -2.83729748 -2.83729748
-2.83729748
24
What about the usual MD Codes?

• System
• 1 sodium ion in a (32 A)3 box
• PME grid size 643
• x/2L -61.594 kJ/mole
• NAMD 2.6 E 0.0 kJ/mole
• Gromacs 3.3.1 E -61.595734 kJ/mole
• Despite citation of Darden's (traditional)
  method, the total charge correction is
  implemented in Gromacs!

U. Essman, L. Perela, M. L. Berkowitz, T. Darden,
H. Lee and L. G. Pedersen (1995). J. Chem. Phys.
103 8577-92.