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Calculate bond dissociation energies and apply Morse potential equations to predict molecular stability. Explore bond length-energy correlations, hybridization effects, and bond order relationships from single σ bonds to triple bonds. Quantitative analysis of C-C, C=O, and N≡N systems using R computational tools in CoCalc.

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Advanced Chemical Bonding with R in CoCalc - Chapter 3

Bond Energy and Molecular Stability

This notebook contains Chapter 3 from the main Advanced Chemical Bonding with R in CoCalc notebook.

For the complete course, please refer to the main notebook: Advanced Chemical Bonding with R in CoCalc.ipynb

# Setup: Load essential R packages for chemical analysis # Avoid interactive CRAN prompts options(repos = c(CRAN = "https://cloud.r-project.org")) required_packages <- c("ggplot2", "dplyr", "plotly", "corrplot", "reshape2", "RColorBrewer") # Install missing packages quietly missing <- required_packages[!vapply(required_packages, requireNamespace, logical(1), quietly = TRUE)] if (length(missing)) install.packages(missing, quiet = TRUE) # Attach packages without printing list results or masking chatter suppressPackageStartupMessages({ for (pkg in required_packages) { suppressWarnings(library(pkg, character.only = TRUE, quietly = TRUE, warn.conflicts = FALSE)) } }) # Alternatively: # invisible(lapply(required_packages, function(pkg) # suppressWarnings(library(pkg, character.only = TRUE, quietly = TRUE, warn.conflicts = FALSE)) # )) # Theme fix: use linewidth instead of size to avoid ggplot2 deprecation warning chemistry_theme <- ggplot2::theme_minimal() + ggplot2::theme( plot.title = ggplot2::element_text(size = 16, face = "bold", color = "#2E86AB"), plot.subtitle = ggplot2::element_text(size = 12, color = "#A23B72"), axis.title = ggplot2::element_text(size = 12, face = "bold"), axis.text = ggplot2::element_text(size = 10), legend.title = ggplot2::element_text(size = 11, face = "bold"), panel.grid.minor = ggplot2::element_blank(), panel.border = ggplot2::element_rect(color = "gray80", fill = NA, linewidth = 0.5) ) cat("Chemical Analysis Toolkit Loaded Successfully!\n") cat("Ready to explore the molecular world with R\n")

Chapter 3: Bond Energy and Molecular Stability

3.1 Bond Energy Fundamentals

Bond energy (or bond dissociation energy) is the energy required to break one mole of bonds in the gas phase:

A-B(g) → A(g) + B(g) ΔH = Bond Energy

  1. Bond Order: Triple > Double > Single bonds

  2. Atomic Size: Smaller atoms form stronger bonds

  3. Electronegativity: Moderate differences optimize bond strength

  4. Hybridization: sp > sp² > sp³ bond strength

3.3 Bond Length-Energy Relationship

Morse Potential: E(r) = De[1 - e^(-a(r-re))]²

Where:

  • De = dissociation energy

  • re = equilibrium bond length

  • a = controls curve steepness

# Comprehensive bond energy and length database bond_properties <- data.frame( bond_type = c("H-H", "C-C", "C=C", "C≡C", "C-H", "C-O", "C=O", "C≡O", "O-H", "N-H", "C-N", "C=N", "C≡N", "O=O", "N≡N", "F-F", "Cl-Cl"), bond_energy = c(436, 348, 614, 839, 413, 358, 743, 1072, 463, 391, 293, 615, 891, 495, 941, 159, 242), # kJ/mol bond_length = c(74, 154, 134, 120, 109, 143, 120, 113, 96, 101, 147, 129, 117, 121, 110, 142, 199), # pm bond_order = c(1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 3, 2, 3, 1, 1), hybridization = c("s-s", "sp3-sp3", "sp2-sp2", "sp-sp", "sp3-s", "sp3-sp3", "sp2-sp3", "sp-sp3", "sp3-s", "sp3-s", "sp3-sp3", "sp2-sp3", "sp-sp3", "sp2-sp2", "sp-sp", "sp3-sp3", "sp3-sp3"), common_in = c("H2 gas", "Alkanes", "Alkenes", "Alkynes", "Hydrocarbons", "Alcohols", "Carbonyls", "CO gas", "Water", "Amines", "Amines", "Imines", "Nitriles", "O2 gas", "N2 gas", "F2 gas", "Cl2 gas") ) # Compute robust starts for nls from log-log linearization: log(E) = log(a) - b*log(r) start_lm <- lm(log(bond_energy) ~ log(bond_length), data = bond_properties) a0 <- exp(coef(start_lm)[1]) b0 <- -coef(start_lm)[2] # Advanced bond energy visualization with stable nls fit p_bond_energy <- ggplot(bond_properties, aes(x = bond_length, y = bond_energy)) + geom_point(aes(size = bond_order, color = bond_order), alpha = 0.8) + geom_text(aes(label = bond_type), hjust = -0.1, vjust = -0.1, size = 3) + geom_smooth( inherit.aes = FALSE, aes(x = bond_length, y = bond_energy, group = 1), method = "nls", formula = y ~ a * x^(-b), method.args = list(start = list(a = a0, b = b0), control = list(maxiter = 200, warnOnly = TRUE)), se = FALSE, color = "red" ) + scale_size_continuous(range = c(3, 8), name = "Bond\nOrder") + scale_color_gradient(low = "blue", high = "red", name = "Bond\nOrder") + labs( title = "Universal Bond Energy-Length Relationship", subtitle = "Morse-like inverse trend: shorter bonds are stronger", x = "Bond Length (pm)", y = "Bond Energy (kJ/mol)", caption = "Data approximates E ∝ 1/r^b (b estimated from data)" ) + chemistry_theme print(p_bond_energy) # Calculate key correlations correlation_length_energy <- cor(bond_properties$bond_length, bond_properties$bond_energy) correlation_order_energy <- cor(bond_properties$bond_order, bond_properties$bond_energy) cat(sprintf("\n Bond Length - Energy Correlation: %.3f\n", correlation_length_energy)) cat(sprintf(" Bond Order - Energy Correlation: %.3f\n", correlation_order_energy)) cat("\n Strong negative correlation confirms quantum mechanical predictions!\n") # Create bond order analysis bond_order_stats <- bond_properties %>% group_by(bond_order) %>% summarise( avg_energy = mean(bond_energy), avg_length = mean(bond_length), count = n(), .groups = 'drop' ) cat("\nBond Order Analysis:\n") print(bond_order_stats)
📈 Bond Length - Energy Correlation: -0.393 📈 Bond Order - Energy Correlation: 0.936 Strong negative correlation confirms quantum mechanical predictions! Bond Order Analysis: # A tibble: 3 × 4 bond_order avg_energy avg_length count <dbl> <dbl> <dbl> <int> 1 1 345. 129. 9 2 2 617. 126 4 3 3 936. 115 4
Image in a Jupyter notebook

From Bond Energy and Molecular Stability to VSEPR Theory and Molecular Geometry

We’ve explored bond energy and molecular stability, gaining insights into how these fundamental concepts govern molecular interactions and chemical behavior.

But how do these principles extend to VSEPR theory and molecular geometry? In Chapter 4, you'll see how the ideas we’ve covered underpin our understanding of three-dimensional molecular shapes and real-world chemical properties.


Journey Forward

The move from Chapter 3 to Chapter 4 is a natural progression in your chemical education. The foundational knowledge gained here will illuminate the advanced concepts ahead.