Ammm:QM/MM

Introduction

What is QM/MM?

• Hybrid method that QM (Quantum mechanics) and MM (molecular mechanics) calculation schemes
• The system is divided into two regions
  • QM and MM regions
  • Regions are designed based on compromise in calculation time and accuracy

Why use QM/MM?

• The system is too large to use ab initio calculations
  
• MM calculations do not give the "correct" answer
• Processes involving change in electronic structure

How QM/MM methods differ?

Treatment of the junction between QM and MM regions

Use of link atoms

• Hydrogen is “inserted” along the bond contained in the QM/MM junction
  
  • Placed closed to the MM atom
    
  • Behavior is changed based on the identity of the MM atom
    

Localized orbitals

• Specially designed local orbitals assigned to boundary QM and MM atoms
  
  • maintain closure of QM system
  • local orbitals are designed and tested based on empirical data
  • no need for extra atoms

Pseudopotential methods

• MM-bounded boundary QM atoms are assigned a special basis set and potential
  • mimic correct covalent bonding scheme
  • designed from small system models
  • no need for extra atoms

Methods of energy calculations

Subtraction Scheme

ONIOM - (our own n-layered integrated molecular orbital and molecular mechanics)

Method developed by Morokuma and co-workers which allows for different regions of a system to be calculated at different levels of theory and combine to produce a consistent energy expression. 

E(ONIOM2) = E(High, region 1) + E(low, regions 1 and 2) – E(low, region1)
E(ONIOM3) = E(High, region A) +E(Medium, regions A and B) + E(Low, regions A, B and C) – E(Medium, region A) – E(Low, region A and B) www.gaussian.com/g_tech/g_ur/k_oniom.htm

Summation scheme

Example:

E_total(1 and 2) = E_QM(1 and 2) + E_{QM/MM, ele}(1 and 2) + E_QM/MM,nucl(1 and 2) + E_QM/MM,vdw(1 and 2) + E_{QM/MM,covalent}(1 and 2) + E_MM(2)

The way in which the electrostatic interaction between the QM and MM regions are described

Mechanical embedding

Polarization from MM electrostatics comes from interpolation scheme used to combine energy terms. 

Electronic embedding

QM polarization form MM electrostatics is explicitly considered.

Linear-scaled Eward Method

Particle-mesh Eward technique with periodic boundary conditions

GSBP - generalized solvent boundary potential

Small region of the system surround QM region is treated explicitly. The remainder of the system is fixed and described in terms of solvent-shielded static field and a Poisson–Boltzmann reaction field.

Case study

Project Introduction

Goals

• Simulate the ¹H and ²⁰⁵Tl NMR spectra based MM and QM/MM refined x-ray crystallographic and NMR structures
• Understand how differences in the structure lead to different chemical shifts
• Gain insight into molecular structural information directly from experimental chemical shifts

The G-quardruplex Model System

                                  

• Model System for the development of ²⁰⁵Tl NMR
  • All classes of biomacromolecules bind monovalent cations
  • Na⁺ and K⁺ are poor spectroscopic nuclei
  • Tl⁺ is an excellent mimic of K⁺
  • ²⁰⁵Tl⁺ is a spin ½ nucleus with a large gyromagnetic ratio
    • ¹H > ¹⁹F > ²⁰⁵Tl > ³¹P
• G₄T₄G₄ is the telomeric sequence from the ciliate Oxytricha Nova
  • Homodimeric G-quadruplex with diagonal loops
  • Contains four G-quartets, each composed of four guanine bases
  • Exceptionally stable and structures have been solved by NMR and X-ray crystallography
  • Binds 3-5 monovalent cations
    

Experimental NMR Spectra

Quantum Mechanics / Molecular Mechanics (QM/MM) Hybrid Methodology

www.gaussian.com/g_tech/g_ur/k_nmr.htm

www.gaussian.com/g_tech/g_ur/k_oniom.htm

¹H NMR simulations

²⁰⁵Tl simulations

²⁰⁵Tl benchmarks

¹⁵N simulation of NH₄⁺ bound G-quadruplex

Case study conclusions

• We have completed NMR simulations of G-quadruplet at the QM/MM level where the influence of the surrounding environment is explicitly considered
• ¹H-NMR is found to be extremely sensitive to the configuration of the system, useful for gaining structural insight
• Stacking greatly impacts the¹H NMR Spectra
• The ions most exposed to the loops have different magnetic environments most likely due to structural disorder
• All-electron (UGBS) simulations of ²⁰⁵Tl NMR spectra provide valuable insight on the origin of chemical shifts
  
  

Further Reading

H. Hu, W. Yang / Journal of Molecular Structure: THEOCHEM 898 (2009) 17–30

H. M. Senn, W. Thiel. Current Opinion in Chemical Biology 2007, 11:182–187

M. Svensson, S. Humbel, R.D.J. Froese, T. Mastubara, S. Sieber, and K. Morokuma, J.Phys.Chem., 100, 19357 (1996).

R. A. Friesner and V. Guallar, Annu. Rev. Phys. Chem. 2005. 56:389–427