Quantum Chemistry in the Age of Machine Learning

Front Cover
Quantum Chemistry in the Age of Machine Learning
Copyright
Contents
Companion website
Contributors
Preface
Reference
Part 1: Introduction
Chapter 1: Very brief introduction to quantum chemistry
Introduction-The foundations of quantum chemistry
Brief introduction of quantum mechanics
Basic concepts
Born-Oppenheimer approximation
Variational principle
Perturbation theory
Comparison of the variation principle and perturbation theory
Fundamentals of quantum chemistry
Categories of molecular electronic structure methods
Methods of molecular electronic structure computations
Hartree-Fock method
Post-Hartree-Fock methods
Configuration interaction
Møller-Plesset perturbation theory
Coupled-cluster method
MCSCF and post-MCSCF methods
Methods for excited states
Choice of the method
Methods of conceptional interpretation based on electronic structure calculations
Case studies
Case study 1
Case study 2
Conclusions and outlook
Acknowledgments
References
Chapter 2: Density-functional theory
Introduction
Theoretical foundations of DFT
Hohenberg-Kohn theorems
Kohn-Sham method
Spin density-functional theory
Density-functional approximations
Formal properties of Exc
Local density approximation
Generalized gradient approximations
Meta-GGA
Hybrid functionals
Hybrid functionals based on adiabatic connection
Long-range corrected hybrid functionals
Screened hybrid functionals
Hybrid functionals in the general form
Fifth-rung functionals
Doubly hybrid functionals
Exc based on adiabatic-connection fluctuation-dissipation theorem
Van der Waals dispersion interaction in DFT
Self-consistent equations for orbital-dependent functionals
Practical aspects of DFT implementations
Basis set
Atomic-type basis
Plane-wave basis
Augmented plane-wave (APW)-type basis
Core-valence interactions
Case studies
Basis set convergence
Molecular structures and vibrational spectra from different DFAs
Reaction energetics and transition state
Concluding remarks
Acknowledgments
References
Chapter 3: Semiempirical quantum mechanical methods
Introduction
Methods
Hückel method
Extended Hückel method
Approximations neglecting differential overlap
Zero-differential overlap
Complete neglect of differential overlap
Intermediate neglect of differential overlap
Neglect of diatomic differential overlap
DFT-based SQM methods
Non-covalent interactions in SQM methods
London dispersion correction
Hydrogen bonding
Accuracy of SQM methods applied to non-covalent interactions
Software implementations available
Case studies
Case study 1
Case study 2
Case study 3
Case study 4
Conclusions and outlook
Acknowledgments
References
Chapter 4: From small molecules to solid-state materials: A brief discourse on an example of carbon compounds
Introduction
Methods
Cluster model
QM/MM model
Periodic models
Electronic structures of carbon-based molecules
Electronic structures of graphene
Electronic structures of other carbon materials
Cycloaddition reactions
Case studies
Case study 1: Orbital analysis of C60
Case study 2: Understand the electronic structure of alkali metal-doped C60
Case study 3: Band structure of single-layer BN sheet
Conclusions and outlook
Acknowledgments
References
Chapter 5: Basics of dynamics
Introduction
Methods
Quantum dynamics of nuclei under Born-Oppenheimer approximation
From quantum dynamics to classical MD simulations
Propagating the MD simulations
Case studies
Case study 1: The HCl bond oscillation after photoexcitation from time-dependent quantum dynamics
Case study 2: Molecular dynamics simulation of naphthalene crystal
Conclusions and outlook
Acknowledgments
References
Chapter 6: Machine learning: An overview
Introduction
Methods
Supervised learning
Learning the pKa of substituted phenols
Supervised ML problems and methods
Applications in quantum chemistry
Unsupervised machine learning
Semi-supervised machine learning
Reinforcement learning
Basic concepts of machine learning
Optimization of the cost function
Presentation of data
Hyperparameter tuning and performance evaluation
Case study
Case study 1: Single-variable linear regression
Case study 2: Multivariable linear regression
Case study 3: Importance of feature selection
Case study 4: Beyond linear regression
Conclusions and outlook
Acknowledgment
References
Further reading
Chapter 7: Unsupervised learning
Introduction
Notation guide
Methods
Descriptors for encoding chemical information
What makes a good descriptor?
Popular descriptors for machine learning
Kernels
Dimensionality reduction/mapping
Dimensionality reduction for data compression
Principal components analysis
Multidimensional scaling
Kernel principal components analysis
Principal covariates regression
Dimensionality reduction for visualization and pattern recognition
t-distributed stochastic neighbor embedding
UMAP
Feature selection: Feature-preserving dimensionality reduction
Clustering
Motivation
Theory and examples
Hierarchical clustering
Partition-based clustering
Density-based clustering
Evaluation of clustering results
Case studies
Cyclohexane molecular dynamics simulation
Construct a PCA
Construct a kernel PCA
t-SNE and UMAP
Performing clustering analysis on the t-SNE embedding
Exploring surface structural motifs
Problem description
Constructing surface atom descriptors
Reducing dimensionality with PCA
Advantages of non-linear dimensionality reduction
Experiment with other clustering algorithms
Conclusions
References
Chapter 8: Neural networks
Introduction
Methods
Feed-forward neural network
Activation functions
Training a neural network
Neural networks for learning time series
One-dimensional convolutional neural network
Recurrent neural network
Long short-term memory
Gated recurrent unit
Bidirectional recurrent neural network
Case study
Conclusions and outlook
Acknowledgments
References
Chapter 9: Kernel methods
Introduction
Methods
Kernel methods explained for chemists
From linear regression to kernel methods
Fitting kernel methods: Kernel ridge regression
On a choice of the kernel function
Other kernel methods: Support vector regression
Other kernel methods: Gaussian process regression
Including derivative information for training
Computational resources requirements
Unsupervised learning
Kernel principal component analysis-KPCA
Kernel K-means
Case studies
Case study 1: Fitting with kernel ridge regression
Case study 2: Kernel principal component analysis
Conclusions and outlook
IntroductionKernel methods correspond to a learning paradigm that goes beyond simple linear approximations to model or extract
References
Chapter 10: Bayesian inference
Introduction
Basic concepts of Bayesian statistics
What is probability
Bayes theorem
Prior distribution
Likelihood function
Posterior distribution
Bayesian inference for parameter estimation and confidence interval
Bayesian regression
Bayesian linear regression
Gaussian process regression
GPR model based on Bayesian linear regression
Estimation of f(x)
Bayesian explanation of the GPR model
Bayesian inference in machine learning: Bayesian neural networks
Case study
Gaussian process regression
Conclusions and outlook
Acknowledgments
References
Part 2: Machine learning potentials
Chapter 11: Potentials based on linear models
Introduction
Methods
From ordinary least squares to sparse linear regression
Ordinary least square (OLS) method
Ridge regression
Lasso regression
Lasso 1D
Lasso, general case
Coordinate descent
Least angle regression selection
Geometrical interpretations
Lasso vs Ridge
LassoLars vs Lasso coordinate descent
Different approaches to obtain linear model of machine-learning interaction potentials
Spectral neighbor analysis potential and developments
The original approach from A. P. Thompson and coworkers
A hybrid approach proposed by M-C. Marinica and coworkers
Generalization of the modified embedded atom method potential and Physical LassoLars Interaction Potential (PLIP)
The original approach proposed by A. Seko and coworkers
Physical LassoLars interaction potential
Case studies
Case study 1: Learning an arbitrary function using a set of Gaussian functions.
Case study 2 Learning the potential from Lennard-Jones binary simulations.
Conclusion and outlook
Acknowledgments
References
Chapter 12: Neural network potentials
Introduction
Methods
Atomic-centered symmetry functions
SchNet
DeepPot-SE
Example of simulation with neural network potentials
Case studies
Simulation of the oxidation of methane
Step 1: Preparing the reference dataset
Step 2. Training the NN PES
Step 3: Freeze the model
Step 4: Running MD simulation based on the NNP
Step 5: Analysis of the trajectory
Conclusions and outlook
Acknowledgment
References
Chapter 13: Kernel method potentials
Introduction
Methods
KRR-CM
Descriptor
Fitting function
KREG model
Descriptor
pKREG model
GDML model
Descriptor
Fitting function
sGDML model
GAP-SOAP model
Descriptor: SOAP
Sparsification
Linear combination of unknown values
Fitting function: GAP
Operator learning
Guidelines for choosing an appropriate kernel method potential
Case study
Step 1. Training the KREG potential
Step 2. Geometry optimization with the trained KREG model
Conclusions and outlook
Acknowledgments
References
Chapter 14: Constructing machine learning potentials with active learning
Introduction
Methods
Uncertainty sampling
Query-by-committee
Failure collection
Stochastic surface walking method
Steinhardt-type order parameter
Case study
Conclusion and outlook
Acknowledgments
References
Chapter 15: Excited-state dynamics with machine learning
Introduction
Methods
Hierarchical equations of motion
ML-assisted HEOM
Trajectory surface hopping
Fewest switches surface hopping
Nonadiabatic couplings
ML-assisted TSH
Learning potential energy surfaces
Hopping in ML-assisted TSH: Internal conversion
Learning spin-orbit couplings
Training set generation
Case studies
Case study 1: Hierarchical equations of motion
Case study 2: HEOM with machine learning
Case study 3: Trajectory-surface hopping with machine learning
Step 1: Create the training set
Step 2: Model training (MLatom/KREG)
Step 3: Run the ML-NAMD simulation (Newton-X/MLatom)
Conclusions and outlook
Acknowledgments
References
Chapter 16: Machine learning for vibrational spectroscopy
Introduction
Vibrational spectroscopies: Workhorse characterization technique in many applications
Case for machine learning-assisted spectroscopy
Methods
Introduction to computational vibrational spectroscopy
Machine learning in vibrational spectroscopy
Specifics of machine-learned potential energy surfaces for computational vibrational spectroscopy
Learning the mapping among the structure, potential, and spectrum
Machine learning to solve the vibrational Schrödinger equation
Case studies
Quantum dynamics-friendly neural network potential energy surface
The code
Solving the Schrödinger equation with the help of Gaussian process regression
The code
Conclusions and outlook
References
Chapter 17: Molecular structure optimizations with Gaussian process regression
Introduction
Methods
Established methods for molecular optimizations
Quasi-Newton methods
Step restriction
Approximate Hessian
Hessian-update methods
Choice of coordinates
Constrained geometry optimization
Geometry optimization in the direct inversion of the iterative subspace
Machine learning methods for structure prediction
Machine learning-based surrogate PES
The restricted variance optimization method
Hessian approximation
Coordinates
The trend function
The characteristic length scales
Restricted-variance optimization
Case studies
One-dimensional system (H2)
Two-dimensional system (H2O)
Transition state optimization (CH3-CH=OCH2=CH-OH)
Conclusions and outlook
Acknowledgments
References
Part 3: Machine learning of quantum chemical properties
Chapter 18: Learning electron densities
Introduction
A property to rule them all
Topology
Methods
Prediction of the electron density
Numerical methods
Analytical methods
Symmetry-adapted Gaussian process regression
A2MDnet and A3MDnet
Methods targeting DFT
KH-maps
XC functionals
Wave function prediction
Electron density methods
3D space integration
Electron density
Case studies
Case study 1: Using PySCF to obtain reference electron densities
Case study 2: Training an A3MDnet predictor
Case study 3: Predicting valence electron densities with DeepDFT
Conclusions and outlook
Acknowledgments
References
Chapter 19: Learning dipole moments and polarizabilities
Introduction
Methods
Learning permanent and transition dipole moments
Learning polarizabilities
Other relevant approaches
Learning tensorial properties with embedded atom neural networks
Case studies
Conclusions and outlook
Acknowledgments
References
Chapter 20: Learning excited-state properties
Introduction
Methods
Absorption spectra
Case study 1: KREG for learning energy gaps and oscillator strengths of a single compound
Case study 2: SchNarc for learning transition dipole moments and energy levels of one or more compounds simultaneously
Case studies
Case study 1: ML-NEA spectrum for a single molecule
Case study 2: UV/Vis absorption spectra predicted with SchNarc trained on two different molecules
UV/visible spectra of learned molecules
Interpretation of the spectrum
Transferability in chemical compound space
Electrostatic potentials
Conclusions and outlook
Challenges ahead
Acknowledgments
References
Part 4: Machine learning-improved quantum chemical methods
Chapter 21: Learning from multiple quantum chemical methods: Delta-learning, transfer learning, co-kriging, and
Introduction
Methods
Delta-learning
LFAF: Low-level QC predictions as features of machine learning models
Combination of Delta-learning and LFAF
Transfer learning
Combination of Delta-learning and transfer learning
Learning multifidelity and multioutput data with kernel methods: Co-kriging
Hierarchical machine learning
Case studies
Case study 1: Delta-learning vs direct learning
Case study 2: Hierarchical machine learning
Case study 3: Transfer learning
Conclusions and outlook
IntroductionModern quantum chemistry (QC) offers a vast selection of different methods, each with its advantages and d
References
Chapter 22: Data-driven acceleration of coupled-cluster and perturbation theory methods
Introduction
Methods
Data-driven coupled cluster
Basic theory
Data-driven coupled-cluster singles and doubles
DDCCSD and transferability
Data-driven multiconfigurational methods
Basic theory
Data-driven CASPT2
Case studies
Water as a case study for DDCCSD
DDCASPT2: Ozone case study
Conclusions and outlook
Acknowledgment
References
Chapter 23: Redesigning density functional theory with machine learning
Introduction
Methods
Global electron density formulation of ML-DFTXC
Quasi-local electron density formulation of ML-DFTXC: The ML XC potential model
The holographic electron density theorem (HEDT) and its implications on ML-DFTXC
Pre-calculating XC potential as the target
Model building, training, and SCF explained with a successful story
Quasi-local Electron density formulation of ML-DFTXC: The ML XC energy density model
Theory
Implementation and illustrative examples
Quasi-local electron density formulation of ML-DFTXC: The ML XC fragment energy model
Theory
Implementation and illustrative examples
General quasi-local electron density formalism of ML-DFTXC
Additional ML models: ML For van der Waals interaction
Case study
An example for the ML-DFTXC potential model
Conclusions and outlook
References
Chapter 24: Improving semiempirical quantum mechanical methods with machine learning
Introduction
Methods
Correcting predictions by semiempirical quantum mechanical methods with machine learning
Delta-learning
General-purpose ML-NDDO method AIQM1
General-purpose ML-DFTB methods
ML-improved SQM methods for heats of formation
Improving semiempirical Hamiltonian parameters with machine learning
Automatic parameterization technique: ML-OM2
ML-EHM
The extended Hückel theory
ML effective Hamiltonian
ML-EHM loss function and training
The ML-EHM learnable parameters
ML-improved DFTB Hamiltonians
Case study
Conclusions and outlook
Acknowledgments
References
Chapter 25: Machine learning wavefunction
Introduction
Methods
Variational Monte Carlo in a nutshell
Modeling the wavefunction in Fock space
Neural-network quantum state
Gaussian process state
Modeling the wavefunction in real space
FermiNet
PauliNet
Supervised machine learning of the wavefunction
SchNOrb
Case studies
Particle in a box
Bayesian learning of the wavefunction with a Gaussian process
Variational optimization of the Gaussian process wavefunction
Ground state energies from PauliNet
PauliNet training
CCSD(T) calculations
Comparison of PauliNet and CCSD(T)
Conclusions and outlook
Acknowledgments
References
Part 5: Analysis of big data
Chapter 26: Analysis of nonadiabatic molecular dynamics trajectories
Introduction
Theoretical methods
Descriptor or feature selection
TSH dynamics
MM-SQC dynamics
Dimensionality reduction approaches
Principal component analysis
Multidimensional scaling
Isometric feature mapping (ISOMAP)
Diffusion map
Trajectory similarity
Examples
Case studies
Case study 1: Classical MDS analysis of CH2NH2+ dynamics
Case study 2: Fréchet distance analysis of phytochromobilin
Case study 3: PCA of site-exciton model dynamics
Conclusions and outlook
References
Chapter 27: Design of organic materials with tailored optical properties: Predicting quantum-chemical polarizabilities an ...
Introduction
Rational design strategies for materials
Data-driven design protocol
Methods
Molecular polarizability
Refractive index
Computational protocol
Case studies: Implementing the rational design protocol
Standard DNNs for α, nr, and N
Physics infused model
Transfer learning
Conclusions and outlook
References
Index
Back Cover