1. Veracity through variety (of methods): Simulating dipeptides with little volume Tanja van Mourik

2. Overview Why study peptides with computational methods? What is computational quantum chemistry? 1. Background 2. Application The shape of a small peptide little “volume”

3. 1. Background theory

4. Why study peptides with computational methods? the shape of biomolecules is important for their function it is difficult to deduce the shape unambiguously from experiments computational data can help experimental assignment function shape ?

5. What is computational quantum chemistry? Quantum chemistry is based on quantum mechanics Particles are completely characterised by their wavefunction  Wavefunction can be obtained from the Schrödinger equation: H  =E 

6. However, the Schrödinger equation cannot be solved exactly Need to use approximate methods in general: more precise methods == higher computational demand

7. larger basis sets => more precise results => higher computational demand more precise methods == higher computational demand Level of theory depends on method and basis set Method: approximate way to solve the Schrödinger equation Basis set: representation of the wavefunction H  =E 

8. 2. Application

9. The shape of the Tyr-Gly dipeptide N O O O- H HH CC CC C C = carbon O = oxygen N = nitrogen H = hydrogen N H -O C C C C C C H H H H 2 x 2 x 2 x 3 x 6 x 6 x 12 x 12 = 124416 conformers

10. single-point calculations HF/3-21G* 33433 geometry optimisations HF/3-21G* 300 single-point MP2/6-31+G* 20 Hierarchical Selection Scheme geometry optimisations MP2/6-31+G* selected conformers: create structures of all possible conformers sort according to their number of H-bond interactions 124416 geometry optimisations B3LYP/6-31+G* 20

11. 0.03.43.63.94.2 4.55.6 5.75.8 6.5 7.07.1 7.410.5 10.611.0

12. conf 1conf 2conf 3 conf 4conf 5conf 6 Geometries from B3LYP/6-31+G(d)

13. Structures were computed with two different levels of theory: B3LYP/6-31+G* MP2/6-31+G* method basis set MP2 and B3LYP generally assumed to be of similar accuracy. However, the MP2 and B3LYP structures differ considerably!

14.  Gly B3LYP structure MP2 structure missing dispersion? BSSE? Dispersion: physical attraction between atoms BSSE: artificial attraction between atoms B3LYP, MP2: two different quantum-chemical methods

15. rotation around  Gly MP2/6-31+G* B3LYP/6-31+G*  Gly  E [kJ/mol] MP2B3LYP minimum MP2 minimum MP2 minimum

16. Possible reasons for the different geometries obtained with B3LYP and MP2: MP2 results may be affected by BSSE (unphysical attraction) B3LYP results may be affected by missing dispersion (physical attraction) We can reduce the BSSE in the MP2 calculations by using larger basis sets

17. rotation around  Gly MP2B3LYP minimum MP2 minimum MP2 minimum MP2/6-31+G* B3LYP/6-31+G* MP2/6-31+G* MP2/avdz MP2/avtz MP2/avqz  Gly  E [kJ/mol] veracity through variety

18. MP2/avdz MP2/avtz MP2/avqz BSSE (kJ/mol) BSSE not the same over the  Gly range

19. Summary Using computational quantum chemistry one can predict almost any molecular property, without prior knowledge of the molecular system But: to obtain reliable results, high levels of theory need to be used, requiring large computational resources Results obtained with high-level methods can be used to verify/calibrate more approximate methods Here: shape of a small peptide “little volume” => “veracity through variety” Static structures => no velocity

20. Problem Hierarchical selection scheme is not guaranteed to select the most stable conformers (Even high-level methods may miss conformers) Can data science help to select most relevant conformers?

21. Acknowledgements Engineering and Physical Sciences Research Council (EPSRC) The Royal Society EaStCHEM Leo Holroyd (UCL and St Andrews) Ashley Shields (St Andrews) EaStCHEM Research Computing Facility Dimitrios Toroz (UCL) Jie Cao (St Andrews)

22. “Tyrosine-glycine revisited: Resolving the discrepancy between theory and experiment” Leo F. Holroyd and Tanja van Mourik, Phys. Chem. Lett. 621, 124-129 (2015). “Performance of the M06-L density functional for a folded Tyr-Gly conformer” J. Cao and T. van Mourik, Chem. Phys. Lett. 485, 40-44 (2010). “Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers” L. F. Holroyd and T. van Mourik, Chem. Phys. Lett. 442, 42-46 (2007). “The structure of the gas-phase tyrosine-glycine dipeptide” D. Toroz and T. van Mourik, Mol. Phys. 104, 559-570 (2006). “Comparison of ab initio and DFT electronic structure methods for peptides containing an aromatic ring: The effect of dispersion and BSSE” A. E. Shields and T. van Mourik, J. Phys. Chem. A 111, 13272 – 13277 (2007). “Conformational structure of tyrosine, tyrosyl-glycine and tyrosyl-glycyl-glycine by double resonance spectroscopy” A. Abo-Riziq, L. Grace, B. Crews, M.P. Callahan, T. van Mourik and M.S. de Vries, J. Phys. Chem. A 115, 6077-6087 (2011). Publications