Development of Machine-Learned Potential Energy Surfaces with Application to the Reactive and Vibrational Dynamics of High Dimensional Molecular Systems Öffentlichkeit
Nandi, Apurba (Summer 2022)
Abstract
The potential energy surfaces (PESs) play a significant role in quantum chemistry calculations; such as kinetics and dynamics of chemical reactions, reactive and non-reactive scattering, and molecular spectroscopy. Developing a robust mathematical model for the generation of high dimensional PESs is a challenging work in theoretical and computational research, mainly for large molecules and molecular clusters. There are several bottlenecks as the molecular size increases, such as dimensionality of PES, the number of appropriate basis functions to t the dataset, and the appropriate fitting method.
In this work, a software has been developed to incorporate both electronic energies and gradients generating high-dimensional PES using limited numbers of training configurations employing a permutationally invariant polynomial (PIP) basis. Our main goal of this work was to demonstrate a procedure that can produce a very good PES of a molecule without sacrificing quantitative accuracy using a small training dataset. We showed that a precisely fitted potential surface of CH4 can be obtained using energies and gradients with only 100 or even just 50 widely scattered configurations and that was successfully applied to quantum calculations.
Next, a fragment-based PIP approach has been developed to extend our fitting method for more than 10-12 atom systems. This was the first time we were able to develop a PES of 12 atom peptide molecule, N-methyl acetamide, which described both cis and trans isomers and their two isomerization TS accurately, which was a great achievement. Rigorous diffusion Monte-Carlo (DMC) calculations were successfully performed to compute quantum ZPE of N-methyl acetamide.
Recently, a fascinating method has been developed based on -Machine Learning approach to achieve CCSD(T) level accuracy (energies and gradients) from low-level DFT or MP2 level of theory using a very limited number of data sets and successfully applied to 9-atom Ethanol, 12-atom N-methyl acetamide (NMA), and 15-atom Acetylacetone molecules. This Machine Learning approach provides a solid ground for future innovation in fields like materials science and computational biology by means of highly accurate simulations currently out of reach.
These analytical potential surfaces were also employed in chemical reaction dynamics study and anharmonic vibrational calculations. Quasi-classical trajectory (QCT) calculations were performed to investigate the "Zero-point energy leak" and "Isomerization" of syn-Criegee. The adiabatic switching method was applied to prepare the initial conditions for these quasi-classical trajectories. Quantum ZPEs of methanol and its all isotopologs and isotopomers and the D/H exchange probability in their zero-point state have been investigated which was great interest in astrochemical research. A fascinating work was done by establishing a vibration-facilitated roaming mechanism in the isomerization of CO molecule on NaCl(100) surface by considering a (CO-NaCl)n finite cluster models. The novelty of this work is the isomerization was seen for highly excited CO vibrational states, in excellent agreement with the experiment. Recently, quantum nuclear simulations have been performed on a newly developed CCSD(T) machine-learned PES and revealed the equivalence of gas-phase trans and gauche conformers of ethanol when accurate vibrational zero-point energies and dynamical e ects were taken into consideration. This conclusion is drawn on the basis of agreeing on diffusion Monte-Carlo and semiclassical (SC) calculations of the two isomers' zero-point energies, and upon DMC determination of the ground-state vibrational wave-function.
Molecular vibrational properties of N-methyl acetamide (NMA), and ethanol have been investigated. Diffusion Monte Carlo calculations were applied to characterize the vibrational ground state properties and wave-function, while the vibrational eigenenergies and eigenstates were calculated employing the vibrational self-consistent eld (VSCF) and virtual-state configuration interaction (VCI) method using our home-built MULTIMODE software.
Additionally, I developed a software to train and predict bimolecular thermal rate constants over a large temperature range with the use of the Machine Learning technique. Several quantum mechanical methods are there to compute the tunneling rate constant, however, each method has some bottleneck, and a remedy is suggested by this new approach. The approach uses Gaussian process (GP) regression to predict the rate constant values. Clustering and training are done over 52 different reactions and predictions are made for the new reactions that are not included into the training data.
Table of Contents
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
I Theories and Methods 5
Chapter 2 Potential Energy Surface . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Born-Oppenheimer Approximation . . . . . . . . . . . . . . . . . . . . . 6
2.2 Permutationally Invariant Potential Energy Surface . . . . . . . . . . . . 8
2.2.1 Monomial symmetrization . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Invariant polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Dipole Moment Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Chapter 3 Molecular Vibrations . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 Normal Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Vibrational Self-Consistent Field and Virtual-state Configuration Interaction 22
3.3 The Software ''Multimode" . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.1 Watson Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3.2 n-Mode representation of Potential . . . . . . . . . . . . . . . . . 26
3.3.3 VCI excitation space and matrix pruning . . . . . . . . . . . . . . 26
3.3.4 Infrared intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Diffusion Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 4 Classical Trajectory Simulations . . . . . . . . . . . . . . . . . 32
4.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Microcanonical Sampling (NV E) . . . . . . . . . . . . . . . . . . 33
4.1.2 Normal Mode Sampling . . . . . . . . . . . . . . . . . . . . . . . 34
4.2 Final Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2.1 Translations and Rotations . . . . . . . . . . . . . . . . . . . . . . 36
4.2.2 Vibration and Zero-point Energy Constraint . . . . . . . . . . . . 37
II Systematic Developments in PIP Method for Generating High-dimensional PESs 38
Chapter 5 Implementation of Simultaneous Energy-Gradients Fitting in Permutationally Invariant Polynomial Approach . . . . . 39
5.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3 Theory and software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3.2 MSA software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4.1 1d potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4.2 CH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.5.1 Training and testing precision . . . . . . . . . . . . . . . . . . . . 53
5.5.2 Normal mode analyses . . . . . . . . . . . . . . . . . . . . . . . . 57
5.5.3 Diffusion Monte Carlo Zero Point Energy . . . . . . . . . . . . . . 58
5.5.4 PES-EG from AIMD direct dynamics . . . . . . . . . . . . . . . . 61
5.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Chapter 6 Implementation of Fragmented basis in Permutationally In-
variant Polynomial Approach for PES Fitting . . . . . . . . . 66
6.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.4 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.5.1 Full PIP PES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.5.2 Fragmented PIP PES . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Chapter 7 Implementation of -Machine Learning in Permutationally Invariant Polynomial Fitting to Obtain CCSD(T) Level Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.3 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.4.1 CH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.4.2 H3O+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.4.3 N-methyl acetamide . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.4.4 Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Chapter 8 Rapid and Accurate Construction of CCSD(T)-level PES of large molecules using Fragmented Method . . . . . . . . . . . 124
8.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.3 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.4.1 New PES for Acetylacetone at CCSD(T)/aVTZ Level . . . . . . . 141
8.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Chapter 9 Development of a CCSD(T)-based 4-body Potential forWater147
9.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
9.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.4 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 170
III Reaction Dynamics and Molecular Vibrations 172
Chapter 10 Implications of \Zero-Point Leak" and Isomerization of syn-
CH3CHOO in Quasiclassical Trajectory Calculations via Adi-
abatic Switching . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
10.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
10.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
10.3 Theory and Computational Details . . . . . . . . . . . . . . . . . . . . . 179
10.3.1 Adiabatic switching . . . . . . . . . . . . . . . . . . . . . . . . . . 179
10.3.2 Quantization of H0 . . . . . . . . . . . . . . . . . . . . . . . . . . 180
10.3.3 Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
10.3.4 Computational details . . . . . . . . . . . . . . . . . . . . . . . . 182
10.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
10.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Chapter 11 Quantum Zero-point Energies of Methanol and Deuterated
Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
11.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
11.3 Theory and Computational Details . . . . . . . . . . . . . . . . . . . . . 195
11.3.1 Potential Energy Surface of CH3OH . . . . . . . . . . . . . . . . . 195
11.3.2 Diffusion Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . 197
11.3.3 Computational details . . . . . . . . . . . . . . . . . . . . . . . . 200
11.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
11.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 204
Chapter 12 Vibration-facilitated roaming in the isomerization of CO adsorbed on NaCl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
12.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
12.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
12.3 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
12.3.1 Potential Energy Surface for CO-NaCl . . . . . . . . . . . . . . . 209
12.3.2 (CO-NaCl) Cluster . . . . . . . . . . . . . . . . . . . . . . . . . . 214
12.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
12.4.1 Normal mode CO-stretch Potentials, and Vibrational Energies for C and O-down isomers . . . . . . . . . . . . . . . . . . . . . . . . 229
12.4.2 Quasiclassical Trajectory Calculations . . . . . . . . . . . . . . . 231
12.4.3 IR emission Spectra for C and O-down isomers . . . . . . . . . . . 238
12.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Chapter 13 Nuclear quantum dynamics reveal the leaky nature of gas phase trans and gauche Ethanol conformers . . . . . . . . . 242
13.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
13.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
13.3 Theory and Computational Details . . . . . . . . . . . . . . . . . . . . . 247
13.3.1 Machine Learning for PES construction . . . . . . . . . . . . . 247
13.3.2 Diffusion Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . 249
13.3.3 Adiabatically Switched Semiclassical Initial Value Representation 252
13.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
13.4.1 The starting low level PES (VLL) . . . . . . . . . . . . . . . . . . 255
13.4.2 The correction PES ( VCC-LL) . . . . . . . . . . . . . . . . . . . 256
13.4.3 The New CCSD(T) Ethanol PES (VLL!CC) . . . . . . . . . . . . 258
13.5 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 279
Chapter 14 Semiclassical and Multimode Calculations for the Vibrational Energies of Trans and Gauche Ethanol . . . . . . . . . 282
14.1 Chapter Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
14.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
14.3 Theory and Computational Details . . . . . . . . . . . . . . . . . . . . . 287
14.3.1 CCSD(T) PES of Ethanol . . . . . . . . . . . . . . . . . . . . . . 287
14.3.2 MULTIMODE Calculations . . . . . . . . . . . . . . . . . . . . . 288
14.3.3 Semiclassical Theory . . . . . . . . . . . . . . . . . . . . . . . . . 291
14.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
14.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 299
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