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papers/A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.md

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+___
+author: Anagha Aneesh
+date: 2024-11-20
+title-block-banner: ![[bpm_title.webp]]
+bibliography: ../references.bib
+___
+# A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra
+# Why I chose this paper
+- Reconstructing IR/Raman spectra is interesting to me
+- Applications of ML to electronic structure theory (outside of potential) is cool
+# Introduction
+- Machine learning force fields (ML FF) have accelerated the field of molecular simulations – specifically for systems where there is not an established force field
+- ML FFs are significantly more cost-efficient
+- Learning molecular properties like dipole moment (IR) and polarizability (Raman) can help in interpreting spectra signals and benchmarking ML accuracy against experiment
+- Neural network algorithms v.s. kernel algorithms
+	- NN: better performance + lower cost for larger systems
+	- kernel: requires less data + high cost for large systems
+## Existing Work on ML Models for Electric Polarizability
+- Equivariant neural networks, response formalism, Applequists's dipole interaction model
+- Two kernel-based methods
+	- align structures in training data and treat tensor components as scalars
+		- requires lots of data
+	- symmetry-adapted Gaussian regression
+		- generalization of scalar kernel ridge regression (KRR)
+### Goal of this work
+- KRR on bond polarizability model (BPM)
+	- molecular polarizability is a sum over bond contributions
+# Theory
+## Bond Polarizability Model
+- total molecular polarizability, $\alpha$ is the sum of bond polarizabilities
+$$
+\alpha = \sum_b{\alpha^b}
+$$
+- elements of individual bond polarizability tensors
+$$
+\alpha_{ij}^{b} = \frac{1}{3}(2\alpha_p^b + \alpha_l^b)\delta_{ij} + (\alpha_l^b + \alpha_p^b)(\hat{R}_i^b\hat{R}_j^b - \frac{1}{3}\delta_{ij})
+$$
+- assumes bonds are cylindrically symmetric and typically assumes total polarizability only depends on bond length
+## ML Model
+- Separate polarizability tensor into isotropic and anisotropic components so the ML task is to infer these
+$$
+\alpha = \alpha_{\text{iso}}\bf{1}+\beta
+$$
+- Rewrite elements of tensor in terms of components
+$$
+\alpha_{ij}^{b} = \alpha_{\text{iso}}^b\delta_{ij} + \beta^b(\hat{R}_i^b\hat{R}_j^b - \frac{1}{3}\delta_{ij})
+$$
+- KRR used to evaluate isotropic component, summed over bonds instead of atoms
+$$
+\alpha_{\text{iso}} = \sum_b{\alpha_{\text{iso}}^b} = \sum_n{\sum{K(\textbf{q}^b},\textbf{q}^{b'})w_n}
+$$
+- Using a Gaussian kernel
+$$
+K(\textbf{q}^b,\textbf{q}^{b'}) = \text{exp}(-\gamma||\textbf{q}^b-\textbf{q}^{b'}||^2)
+$$
+- The same can be done for anisotropic component
+$$
+\beta_{ij} = \sum_b{\beta^bQ_{ij}^b} = \sum_n{\sum_{b,b'}{K(\textbf{q}^b},\textbf{q}^{b'})Q_{ij}^bv_n}
+$$
+- loss function
+$$
+\mathcal{L} = \frac{1}{2}\sum_{i,j}{||\beta_{ij} - \textbf{K}_{ij}\textbf{v}||^2}
+$$
+## Raman Spectra
+- Calculating the anharmonic IR and Raman spectra
+$$
+I_{\text{iso}}(\omega) \propto v(\omega) \int{dt \ e^{i\omega t}\langle\dot{\alpha}_{\text{iso}}(\tau)\dot{\alpha}_{\text{iso}}(t-\tau)}\rangle_\tau
+$$
+$$
+I_{\text{aniso}}(\omega) \propto v(\omega) \int{dt \ e^{i\omega t}\langle Tr[\dot{\beta}_{\text{iso}}(\tau)\dot{\beta}_{\text{iso}}(t-\tau)}]\rangle_\tau
+$$
+# Biphenyl
+
+![[bpm_fig1.webp]]
+# Raman spectra evaluation
+![[bpm_fig2.webp]]
+# Malonaldehyde
+- keto and enol forms---
+author: Martiño Ríos-García
+date: 2024-11-13
+title-block-banner: core_bench_papers/ai_agents_blog_pic.jpg 
+bibliography: ../references.bib
+---
+![[bpm_fig3.webp]]
+# Future Directions
+- Deep neural network implementation of BPM
+- Consider all bonds within a cutoff region