hydrogen bonding: ab initio accuracy from fast interatomic ...€¦ · hydrogen bonding: ab initio...

© 2018 Optibrium Ltd.Optibrium™, StarDrop™, Auto-Modeller™, Card View™ and Glowing Molecule™ are trademarks of Optibrium Ltd.

Mario Öeren, PhD – [email protected]

Hydrogen Bonding: Ab Initio Accuracy From Fast Interatomic Gaussian Approximation Potentials22nd August 2018

© 2018 Optibrium Ltd.

Introduction

• Gaussian Approximation Potential (GAP)

− A short introduction

− Practical example

− Ab initio accuracy without electrons

• The Hydrogen Bond Model

− How GAPs are applied

• Results

− Accuracy of the model

− Speed-up

− Improvements for the model

2


Gaussian Approximation Potential

3

B3LYP/def2-SVP



4

B3LYP/def2-SVP


• Input from an ab-initio calculation:

− Cartesian Coordinates

− Energy Values

− Force Values

• Representation of geometry

− Invariant with respect to permutational, rotational, reflectional and translational symmetry

• Smooth Overlap of Atomic Positions (SOAP)

− Finite cut-off

− Complicated environments

− Size of the system does not matter

• Interatomic potential fit using Gaussian Processes

− Gaussian Approximation Potential (GAP)


5

10.1103/PhysRevB.87.18411510.1002/qua.24927

B3LYP/def2-SVP


0

4

8

12

16

0 4 8 12 16

ΔE

kJ m

ol−1

(GA

P)

ΔE kJ mol−1 (DFT)

Test Set (251 Points)

Training Set (5 Points)


6

B3LYP/def2-SVP GAP (Energy, Forces)

R2 = 0.9997

ΔE is the relative energy value (compared to the conformation with the lowest energy value)

r

α


DFT

Train GAP

MD

New Data

GAP for Methanol

• How to explore the PES (obtain data points)

− Molecular dynamics simulation

− Single point calculations of MD snapshots

7

ΔE is the relative energy value

12 Degrees of Freedom!


GAP for Methanol




• Training and testing

− 100 initial points

− 1000 points for testing

8

-5

5

15

25

35

45

-5 5 15 25 35 45

ΔE

kJ m

ol−1

(GA

P)


Training with 9 Points

91 Points

9 Points

Average Error: 7.9 kJ mol−1

RMSE: 9.1 kJ mol−1

Maximum error: 18.9 kJ mol−1

R2 = 0.5895




GAP for Methanol







9

-5

5

15

25

35

45

-5 5 15 25 35 45

ΔE

kJ m

ol−1

(GA

P)


Training with 32 Points

68 Points

32 Points




R2 = 0.987




GAP for Methanol







• 46 training points

10

-5

5

15

25

35

45

55

-5 5 15 25 35 45 55

ΔE

kJ m

ol−1

(GA

P)


Testing the GAP

1000 Points




R2 = 0.987




Methanol Dimer

• Complicated PES

− 25 degrees of freedom

− Hydrogen bond

− Wide range of conformations

11


Methanol Dimer

• Complicated PES


− Hydrogen bond


o 3.5 × 1092

o 2.4 × 105

12

R2 = 0.9682



Methanol Dimer

• Complicated PES


− Hydrogen bond


13

• Simplifications


Methanol Dimer

• Complicated PES


− Hydrogen bond


14

0

5

10

15

20

25

30

0 5 10 15 20 25 30

ΔE

kJ m

ol−1

(GA

P)


10 000 Points For Testing




• Simplifications

• 1500 TrainingPoints

R2 = 0.9682



Interaction Potential

15

EHB = 34.65 kJ mol−1



16

• Form a fragment based system

EHB = 33.85 kJ mol−1



17


• Hydrogen bond energy

− Methanol molecules

− Methanol dimer

E1

E2

ETotal

EHB = ETotal – E1 – E2



18




− Methanol dimer

• Interaction potential

− Train potential with EHB

• Advantages

− More accurate

− Reduced time

• Atom types

EHB



19




− Methanol dimer



• Advantages

− More accurate

− Reduced time

• Atom types



20




− Methanol dimer



• Advantages

− More accurate

− Reduced time

• Atom types

-5

5

15

25

35

45

55

-5 5 15 25 35 45 55

Hyd

roge

n B

on

d k

J m

ol−1

(GA

P)

Hydrogen Bond kJ mol−1 (DFT)

10 000 Points For Testing




R2 = 0.7646



21




− Methanol dimer



• Advantages

− More accurate

− Reduced time

• Atom typesImage created with the SeeSAR™ module of StarDrop™.

PDB ID: 5FDQ

StarDrop™ is a trademark of Optibrium Ltd. SeeSAR™ is a trademark of BioSolveIT GmbH.


Summary

• Hydrogen bonding model – ab initio accuracy using GAPs

− Error (RMSE): 1.2 kJ mol−1

− Time gain: 120 seconds (DFT), 0.02 seconds (GAP)

22


Summary




− Big molecules (12)

Average Error: 0.54 kJ mol−1, RMSE: 0.66 kJ mol−1, Maximum Error: 1.28 kJ mol−1

23


Summary




− Big molecules (12)

Average Error: 0.54 kJ mol−1, RMSE: 0.66 kJ mol−1, Maximum Error: 1.28 kJ mol−1

• Applicability

− Other dimers

E.g.methanol : formaldehyde methanol : formic acid, methanol : formic acid anion formic acid : formic acid, methanol : primary amine primary amine : primary amine

− GAPs have a wide range of applications

− Any level of theory can be used with GAPs

24


Future Work

• Über potential

− Additional dimers found in and between drug molecules and proteins

− More charged species

− Combine atom types

− Reduce the amount of dimers

• Additional interactions

− Complex dimers

− Third monomer

• Predict errors of the model

25


Future Work

• Über potential






− Complex dimers

− Third monomer


26


Future Work

• Über potential






− Complex dimers

− Third monomer


27


Future Work

• Über potential






− Complex dimers

− Third monomer


28


Future Work

• Über potential






− Complex dimers

− Third monomer


29


Future Work

• Über potential






− Complex dimers

− Third monomer


30


Thank You

− Peter Hunt

− Gábor Csányi

− David Ponting

− Matthew Segall

31

GAPSOAP

10.1103/PhysRevB.87.18411510.1002/qua.24927

hydrogen bonding: ab initio accuracy from fast interatomic ...€¦ · hydrogen bonding: ab initio...

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