This code and these plots explore Molecular Modelling for Beginners, 2nd Ed. by Alan Hinchliffe Section 12.6, pages 181 to 184. In this Section, the author explores the concepts of particle indistinguishability, symmetric, and antisymmetric wavefunctions. I recommend you read the text for a complete treatment of these concepts. However, I cover the essentials here.
We can write a wavefunction and total energy for two non-interacting particles in a one-dimensional box as:
This post explores the simplest quatnum mechanical system: the particle in a one-dimensioanl infinite potential well, also known as the one-dimensional particle in a box.
\[ \psi_{n}(x) = \sqrt{\frac{2}{L}} \sin\Bigl(\frac{n \pi x}{L}\Bigr) \]
\[ E_n = U_0 + \frac{n^2 h^2}{8 m L^2} \]
\[ n = 1, 2, 3, \dots \]
Particle in a one-dimensional box This Python code on this page explores Section 11.3.1 in Molecular Modeling for Beginners, 2nd Ed.
In my prior aqueous solubility regression study, I did an exploratory data visualization and found intriguing plots of solubility versus other variables in the study. I didn’t perform any experimental modeling of those relationships in that study. Here, I followup by performing a cluster analysis of solubility relationships to help future regression modeling efforts. My question is: do clusters within each of these relationships explain each feature’s effect on solubility?
Aqueous solubility (ability to dissolve in water) is an essential property of a chemical compound important in the laboratory. Can the solubility of a compound be predicted based on a chemical structure alone? John Delaney posed this predictions question in 2004 (Delaney 2004) and wrote a paper with numerous citations in the chemistry literature. This study will take a dataset similar to that study and use linear and random forest regression to predict the compounds’ solubilities.
Molecular dynamics models the motion of atoms within molecules using classical mechanics. Many resources exist online and in print on molecular mechanics. I wanted to learn more about molecular mechanics by implementing it in Python code. Yet, when I searched for resources to lead me in writing my code, I found them scattered online. Pulling them together into a cohesive whole was difficult. In this post, I make a simple molecular dynamics simulation using velocity Verlet integration in Python and compare its results to empirical and analytical values.
Introduction Convolutional neural networks (CNNs) are a deep learning technology to use for classifying images. For this demonstration I used images from an introductory organic chemistry class. My problem was one of binary classification: could the CNN distinguish images with a structure called a benzene ring from images without a benzene ring? While I encountered challenges of working with a small dataset (with 205 images in each class), I did train the CNN to 73% accuracy of test data.
Aqueous solubility (ability to dissolve in water) is an important property of a chemical compound that is important in the laboratory. While it is possible to determine these solubilities through physical experiments, let’s assume for this tiny project that such experiments are prohibitively expensive. This presents an interesting predictive modeling problem: given a known chemical structure, can the aqueous solubility of a compound be predicted without physical experiments? This was the question proposed by Delaney in 2004 (Delaney, 2004) in a study that created a simple regression model that took SMILES strings (a data format to store the structure of chemical compounds), extracted features from these data and created a regression model to predict solubility.
