From dfbdb024be89be408a66de5c68896316e9721dc1 Mon Sep 17 00:00:00 2001 From: Davit Potoyan Date: Wed, 23 Oct 2024 11:56:26 -0500 Subject: [PATCH] 'qhooo' --- ch04/note03.ipynb | 196 +++++++++++++++++++++++++----- ch04/note03B.ipynb | 297 +++++++++++++++++++++++++++++++++++++++++++++ ch04/note03B.md | 216 --------------------------------- 3 files changed, 462 insertions(+), 247 deletions(-) create mode 100644 ch04/note03B.ipynb delete mode 100644 ch04/note03B.md diff --git a/ch04/note03.ipynb b/ch04/note03.ipynb index 823a06fe..fce02739 100644 --- a/ch04/note03.ipynb +++ b/ch04/note03.ipynb @@ -74,37 +74,28 @@ "| 4 | $16x^4 - 48x^2 + 12$ |\n", "\n", "\n", - "- Hermite polynomials obey the following relations which are useful when evaluating integrals. Check that table above obeys these relations\n", + "Hermite polynomials obey the following relations which are useful when evaluating integrals. \n", "\n", - "$${H_v''(y) - 2yH_v'(y) + 2vH_v(y) = 0\\textnormal{ (characteristic equation)}}$$\n", + "**Characteristic Equation**\n", "\n", - "$${H_{v+1}(y) = 2yH_v(y) - 2vH_{v-1}(y)\\textnormal{ (recursion relation)}}$$\n", + "$${H_v''(y) - 2yH_v'(y) + 2vH_v(y) = 0}$$\n", + "\n", + "**Recursion Relation**\n", + "\n", + "$${H_{v+1}(y) = 2yH_v(y) - 2vH_{v-1}(y)}$$\n", + "\n", + "**Orthogonality and Normalization**\n", "\n", "$${\\int\\limits_{-\\infty}^{\\infty}H_{v'}(y)H_v(y)e^{-y^2}dy = \\left\\lbrace\\begin{matrix}\n", "0, & \\textnormal{ if }v' \\ne v\\\\\n", "\\sqrt{\\pi}2^vv!, & \\textnormal{ if }v' = v\\\\\n", "\\end{matrix}\\right.\n", - "}$$\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Odd/even symmetry of wavefunctions\n", - "\n", - "- Solutions $\\psi_v$ with $v = 0, 2, 4, ...$ are even: $\\psi_v(x) = \\psi_v(-x)$.\n", - "\n", - "- Solutions $\\psi_v$ with $v = 1, 3, 5, ...$ are odd: $\\psi_v(x) = -\\psi_v(-x)$.\n", - "\n", - "**Conseqeuences for evaluating integrals**\n", - "\n", - "- Integral of an odd function from $-a$ to $a$ ($a$ may be $\\infty$) is zero.\n" + "}$$" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "tags": [ "hide-input" @@ -113,15 +104,66 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import hermite, factorial\n", + "\n", + "# Hermite polynomial H_v(y)\n", + "def H_v(v, y):\n", + " return hermite(v)(y)\n", + "\n", + "# Harmonic oscillator wavefunction ψ_v(y)\n", + "def psi_v(v, y):\n", + " norm_factor = 1 / np.sqrt(2**v * factorial(v) * np.sqrt(np.pi))\n", + " return norm_factor * H_v(v, y) * np.exp(-y**2 / 2)\n", + "\n", + "# Define the y values\n", + "y_values = np.linspace(-5, 5, 1000)\n", + "\n", + "# Plot the first three Hermite polynomials\n", + "fig, axs = plt.subplots(1, 2, figsize=(12, 6))\n", + "\n", + "# Hermite polynomials H_0, H_1, H_2\n", + "axs[0].plot(y_values, H_v(0, y_values), label=r'$H_0(y)$', color='blue')\n", + "axs[0].plot(y_values, H_v(1, y_values), label=r'$H_1(y)$', color='green')\n", + "axs[0].plot(y_values, H_v(2, y_values), label=r'$H_2(y)$', color='red')\n", + "axs[0].set_title('First Three Hermite Polynomials')\n", + "axs[0].set_xlabel('y')\n", + "axs[0].set_ylabel(r'$H_v(y)$')\n", + "axs[0].legend()\n", + "\n", + "# Harmonic oscillator wavefunctions ψ_0, ψ_1, ψ_2\n", + "axs[1].plot(y_values, psi_v(0, y_values), label=r'$\\psi_0(y)$', color='blue')\n", + "axs[1].plot(y_values, psi_v(1, y_values), label=r'$\\psi_1(y)$', color='green')\n", + "axs[1].plot(y_values, psi_v(2, y_values), label=r'$\\psi_2(y)$', color='red')\n", + "axs[1].set_title('First Three Harmonic Oscillator Wavefunctions')\n", + "axs[1].set_xlabel('y')\n", + "axs[1].set_ylabel(r'$\\psi_v(y)$')\n", + "axs[1].legend()\n", + "\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "hide-input" + ] + }, + "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -131,12 +173,15 @@ "VMAX = 6\n", "QPAD_FRAC = 1.3\n", "SCALING = 0.7\n", - "COLOUR1 = (0.6196, 0.0039, 0.2588, 1.0)\n", - "COLOUR2 = (0.3686, 0.3098, 0.6353, 1.0)\n", + "COLOUR1 = 'blue'\n", + "COLOUR2 = 'red'\n", "\n", "# Normalization constant and energy for vibrational state v\n", - "N = lambda v: 1./np.sqrt(np.sqrt(np.pi)*2**v*factorial(v))\n", - "get_E = lambda v: v + 0.5\n", + "def N(v):\n", + " return 1. / np.sqrt(np.sqrt(np.pi) * 2**v * factorial(v))\n", + "\n", + "def get_E(v):\n", + " return v + 0.5\n", "\n", "# Generate Hermite polynomials\n", "def make_Hr():\n", @@ -152,7 +197,7 @@ " return N(v) * Hr[v](q) * np.exp(-q**2 / 2)\n", "\n", "def get_turning_points(v):\n", - " qmax = np.sqrt(2 * get_E(v + 0.5))\n", + " qmax = np.sqrt(2 * get_E(v))\n", " return -qmax, qmax\n", "\n", "# Get potential energy\n", @@ -176,26 +221,115 @@ "\n", "# Plot potential and wavefunctions for both psi and |psi|^2\n", "for ax, prob_plot in zip(axs, [False, True]):\n", - " ax.plot(q, V, color='k', linewidth=1.5)\n", + " ax.plot(q, V, color='k', linewidth=1.5, label='Potential $V(q)$')\n", " for v in range(VMAX + 1):\n", " psi_v = get_psi(v, q)\n", " E_v = get_E(v)\n", " plot_func(ax, psi_v**2 if prob_plot else psi_v, q, scaling=SCALING * (1.5 if prob_plot else 1), yoffset=E_v)\n", - " ax.text(s=f'v={v}', x=qmin-0.2, y=E_v, va='center', ha='right')\n", + " ax.text(s=f'$E_{v} = {E_v:.1f}$', x=qmax + 0.2, y=E_v + 0.1, va='center', ha='left')\n", + " ax.axhline(y=E_v, color='gray', linestyle='--', alpha=0.7) # Draw energy levels as dashed lines\n", " ax.set_xlim(xmin, xmax)\n", " ax.set_ylim(0, E_v + 0.5)\n", " ax.set_yticks([])\n", " ax.spines['top'].set_visible(False)\n", " ax.spines['right'].set_visible(False)\n", " ax.spines['left'].set_position('center')\n", - " ax.set_xlabel('$q$')\n", + " ax.set_xlabel('$q$', fontsize=12)\n", " ylabel = r'$|\\psi(q)|^2$' if prob_plot else r'$\\psi(q)$'\n", - " ax.set_title(ylabel)\n", + " ax.set_title(ylabel, fontsize=14)\n", + " ax.legend()\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Odd/even symmetry of wavefunctions\n", + "\n", + "- Solutions $\\psi_v$ with $v = 0, 2, 4, ...$ are even: $\\psi_v(x) = \\psi_v(-x)$.\n", + "\n", + "- Solutions $\\psi_v$ with $v = 1, 3, 5, ...$ are odd: $\\psi_v(x) = -\\psi_v(-x)$.\n", + "\n", + "**Conseqeuences for evaluating integrals**\n", + "\n", + "- Integral of an odd function from $-a$ to $a$ ($a$ may be $\\infty$) is zero.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "tags": [ + "hide-input" + ] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import hermite\n", + "from scipy.integrate import quad\n", + "\n", + "# Hermite polynomial H_v(y) function\n", + "def H_v(v, y):\n", + " return hermite(v)(y)\n", + "\n", + "# Function to compute the product of H_v and H_v' for orthogonality check\n", + "def integrand(y, v1, v2):\n", + " return H_v(v1, y) * H_v(v2, y) * np.exp(-y**2)\n", + "\n", + "# Compute orthogonality integral\n", + "def check_orthogonality(v1, v2):\n", + " # Integral of the product of two Hermite polynomials with exp(-y^2)\n", + " integral, _ = quad(lambda y: integrand(y, v1, v2), -10, 10) # Using finite limits for stability\n", + " return integral\n", + "\n", + "# Define the y range for plotting\n", + "y_values = np.linspace(-5, 5, 1000)\n", + "\n", + "# Plot and check orthogonality for different pairs\n", + "def plot_orthogonality(v1, v2):\n", + " H1 = H_v(v1, y_values)\n", + " H2 = H_v(v2, y_values)\n", + " product = H1 * H2 * np.exp(-y_values**2)\n", + "\n", + " fig, ax = plt.subplots(figsize=(10, 6))\n", + " ax.plot(y_values, product, label=f'Product $H_{{{v1}}}(y) H_{{{v2}}}(y) e^{{-y^2}}$', color='purple')\n", + " ax.fill_between(y_values, 0, product, where=(product > 0), color='blue', alpha=0.5, label='Positive area')\n", + " ax.fill_between(y_values, 0, product, where=(product < 0), color='red', alpha=0.5, label='Negative area')\n", + " \n", + " # Orthogonality integral\n", + " integral_value = check_orthogonality(v1, v2)\n", + " ax.set_title(f'Orthogonality Check: $H_{{{v1}}}(y)$ and $H_{{{v2}}}(y)$ \\n Integral Value = {integral_value:.2e}')\n", + " ax.set_xlabel('y')\n", + " ax.set_ylabel(f'$H_{{{v1}}}(y) H_{{{v2}}}(y) e^{{-y^2}}$')\n", + " ax.axhline(0, color='black', linestyle='--')\n", + " ax.legend()\n", + " plt.show()\n", + "\n", + "# Plot orthogonality for different cases\n", + "plot_orthogonality(1, 2) # Odd vs Even: H_1(y) and H_2(y)\n", + "plot_orthogonality(0, 2) # Even vs Even: H_0(y) and H_2(y)\n", + "plot_orthogonality(1, 3) # Odd vs Odd: H_1(y) and H_3(y)\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "markdown", "metadata": {}, diff --git a/ch04/note03B.ipynb b/ch04/note03B.ipynb new file mode 100644 index 00000000..2b3812de --- /dev/null +++ b/ch04/note03B.ipynb @@ -0,0 +1,297 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Molecular Vibrations\n", + "\n", + ":::{admonition} **What you need to know**\n", + ":class: note\n", + "\n", + "- **Quantization of vibrations in molecules.** Vibrational degrees of freedom are quantized in molecules. This which implications for infrared and raman spectroscopies. \n", + "- **Existence of Selection rules.** Not all vibrational transitions are observed. Quantum mechanics predicts that for transition to occur the trasnition probability needs to be non zero which is quantified via transition dipole moment. \n", + "- **Effects of unharmonicity.** Harmonic osccilator approximation captures the dominant transition frequency but is not fully accurate becasue harmonic shape of the potential descrimed the vicinity of potential energy minima which tends to become less accurate for excited vibrational states of molecules. \n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Harmonic Oscillator approximation\n", + "\n", + "- First let us write harmonic oscillator energies in a format used for spectroscopic analysis. This means converting to wavenumber units $\\tilde{\\nu}=\\frac{1}{\\lambda}$:\n", + "\n", + ":::{admonition} **Harmonic oscillator and spectroscopuc units**\n", + ":class: imporant\n", + "\n", + "$${\\tilde{E}_v = \\frac{E_v}{hc} = \\tilde{\\nu}\\left(v + \\frac{1}{2}\\right)}$$\n", + "\n", + "- **The vibrational quantum number** $v=0,1,2,...$ \n", + "- **The vibrational frequency** $\\tilde{\\nu} = \\frac{1}{2\\pi c}\\sqrt{k/\\mu}$, $cm^{-1}$ \n", + "- **Reduced mass of the diatomic molecule** $\\mu$. \n", + ":::\n", + "\n", + "- Note that $v$ and $\\nu$ look very similar but have different meaning! \n", + "- A typical value for vibrational frequency would be around $500 - 4000cm^{-1}$. Small values are associated with weak bonds whereas strong bonds have larger vibrational frequencies." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ":::{admonition} **Example**\n", + ":class: note\n", + "\n", + "A strong absorption of infrared radiation is observed for $^1H^{35}Cl$ at $2991 cm{-1}$.\n", + "\n", + "- Calculate the force constant k for this molecule\n", + "- By what factor do you expect this frequency to shift if deuterium is substituted for hydrogen in this molecule? The force constant is unaffected by this substitution.\n", + ":::\n", + "\n", + ":::{admonition} **Solution**\n", + ":class: dropdown\n", + "\n", + "- **part a**\n", + "\n", + "$$\\omega = 2\\pi \\nu = \\frac{2\\pi c}{\\lambda} =\\Big(\\frac{k}{\\mu}\\Big)^{1/2}$$\n", + "\n", + "\n", + "$$k = \\Big(\\frac{2\\pi c}{\\lambda}\\Big)^2\\mu=516 N \\cdot m^{-1}$$\n", + "\n", + "- **part b**\n", + "\n", + "$$\\frac{\\nu_{DCl}}{\\nu_{HCL}}=\\Big(\\frac{\\mu_{HCl}}{\\mu_{DCL}}\\Big)^{1/2}=0.717$$\n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Going beyond harmonic approximation\n", + "\n", + "\n", + "- Earlier when we have discussed the harmonic oscillator problem and we briefly mentioned that it can be used to approximate atom - atom interaction energy (*potential energy curve*) near the equilibrium bond length. \n", + "\n", + "- Harmonic potential would not allow for molecular dissociation and therefore it is clear that it would not be a realistic model when we are far away from the equilibrium geometry. The harmonic potential is given by:\n", + "\n", + "$${E(R) = \\frac{1}{2}k(R - R_e)^2}$$\n", + "\n", + "- $k$ is called the *force constant*, $R_e$ is the *equilibrium bond length*, and $R$ is the distance between the two atoms. The actual potential energy curve can be obtained from theoretical calculations or to some degree from spectroscopic experiments. \n", + "\n", + "- This curve has usually complicated form and hence it is difficult to solve the nuclear Schrodinger equation exactly for this potential. One way to see the emergence of the harmonic approximation is to look at *Taylor series expansion*:\n", + "\n", + "$${E(R) = E(R_e) + \\left(\\frac{dE}{dR}\\right)_{R = R_e}(R - R_e) + \\frac{1}{2}\\left(\\frac{d^2E}{dR^2}\\right)_{R = R_e}(R - R_e)^2 + ...}$$\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"DeD0\"\n", + "\n", + "One has to distinguish between two kinds of dissociation energies: *equilibrium dissociation energy* $D_e$ and *spectroscopic dissociation energy* $D_0$. Show are Harmonic vs Morse potential\n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Morse potential and dissociation energy \n", + "\n", + "- Morse potential proisde more accurate description for molecular vibrations and predicts dissociation and changing spacing between energy levels. \n", + "\n", + "$$V(R)=D_e(1-e^{-a(R-R_e)^2})$$\n", + "\n", + "- $D_e$ is measured from the bottom of the potential to the dissociation limit whereas $D_0$ is measured from the lowest vibrational level to the dissociation limit. \n", + "\n", + "$$D_0 = D_e-\\frac{1}{2}h\\nu$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Unharmonic oscillator\n", + "\n", + "- We attempt to account for the deviation from the harmonic behavior by adding higher order polynomial terms $\\tilde{E}_v$:\n", + "\n", + "$${\\tilde{E}_v = \\tilde{\\nu}_e(v + \\frac{1}{2}) - \\tilde{\\nu}_ex_e(v + \\frac{1}{2})^2 + \\tilde{\\nu}_ey_e(v + \\frac{1}{2})^3}$$\n", + "\n", + "- where $\\tilde{\\nu}_e$ is the vibrational wavenumber, $x_e$ and $y_e$ are anharmonicity constants, and $v$ is the vibrational quantum number. Usually the third term is ignored and we can write the vibrational transition frequencies as ($v\\rightarrow v+1$):\n", + "\n", + "$${\\tilde{\\nu}_{v\\rightarrow v+1} = \\tilde{E}_{v+1} - \\tilde{E}_v = \\tilde{\\nu}_e[1- 2x_e (v+1)] }$$\n", + "\n", + "- As we will see soon that by adding the 2nd order polynomial term to the eigenvalues, we actually imply the use of a potential function that allows for dissociation. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overtone transitions\n", + "\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"DeD0\"\n", + "\n", + "Illustration of overtone transitions\n", + ":::\n", + "\n", + "\n", + "- The higher order terms are small but they give rise to overtone transitions with $\\Delta v = \\pm 2, \\pm 3, ...$ with rapidly decreasing intensities.\n", + "\n", + "$${\\tilde{\\nu}_{0\\rightarrow v} = \\tilde{E}_{v} - \\tilde{E}_0 = \\tilde{\\nu}_e \\cdot v - \\tilde{\\nu}_ex_e \\cdot v (v+1)}$$\n", + "\n", + ":::{admonition} **Example**\n", + ":class: note\n", + "\n", + "Given $\\tilde{\\nu}=536 cm^{-1}$ and $x_e\\tilde{\\nu}=3.4 cm^{-1}$ for $^{23}Na^{19}F$ molecule, calculate frequencies of first two overtones.\n", + ":::\n", + "\n", + ":::{admonition} **Solution**\n", + ":class: note, dropdown\n", + "\n", + "We make use of the equation ${\\tilde{\\nu}_{0\\rightarrow v} = \\tilde{\\nu}_e \\cdot v - 2\\tilde{\\nu}_ex_e v (v+1)}$ to compute transitions to levels 1 (fundamental), 2 (first overtone) and 3 (second overtone)\n", + "\n", + "- $\\tilde{\\nu}_{0\\rightarrow 1} = 1\\tilde{\\nu}_e - 2\\tilde{\\nu}_ex_e= 1\\cdot536-2\\cdot3.4=529 cm^{-1}$\n", + "- ${\\tilde{\\nu}_{0\\rightarrow 2} = 2\\tilde{\\nu}_e - 6\\tilde{\\nu}_ex_e= 2\\cdot536-6\\cdot3.4}=1059 cm^{-1}$\n", + "- ${\\tilde{\\nu}_{0\\rightarrow 3} = 3\\tilde{\\nu}_e - 12\\tilde{\\nu}_ex_e= 3\\cdot536-12\\cdot3.4}=1567 cm^{-1}$\n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Population of vibrational states\n", + "\n", + "- Out of all possible vibrational states which states do molecules occupy at room temperature? For harmonic oscillator, the Boltzmann distribution gives the statistical weight for the $v$ level:\n", + "\n", + "$${f_v = \\frac{e^{-(v + 1/2)h\\nu/(k_BT)}}{\\sum\\limits_{v=0}^\\infty e^{-(v+1/2)h\\nu/(k_BT)}}}\n", + "{= \\frac{e^{-vh\\nu/(k_BT)}}{\\sum\\limits_{v=0}^\\infty e^{-vh\\nu/(k_BT)}}}$$\n", + "\n", + "- Note that the degeneracy factor is identically one because there is no degeneracy in one dimensional harmonic oscillator. To proceed, we recall geometric series:\n", + "\n", + "$${\\sum\\limits_{v=0}^\\infty x^v = \\frac{1}{1 - x}\\textnormal{ with }x < 1}$$\n", + "\n", + "\n", + "$${\\sum\\limits_{v=0}^\\infty e^{-vh\\nu/(k_BT)} = \\frac{1}{1 - e^{-h\\nu/(k_BT)}}}$$\n", + "\n", + "\n", + "$${f_v = \\left(1 - e^{-h\\nu/(k_BT)}\\right)e^{-vh\\nu/(k_BT)}}$$\n", + "\n", + "- For example, for $H^{35}Cl$ the thermal population of the first vibrational level $v = 1$ is very small about $9\\times$ $10^{-7}$.\n", + "- **This is why generally the excited vibrational levels do not contribute to the (IR) spectrum.**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Vibrational modes of molecules\n", + "\n", + "A molecule has translational and rotational motion as a whole while each atom has it's own motion. The vibrational modes can be IR or Raman active. For a mode to be observed in the IR spectrum, changes must occur in the permanent dipole (i.e. not diatomic molecules). Diatomic molecules are observed in the Raman spectra but not in the IR spectra. This is due to the fact that diatomic molecules have one band and no permanent dipole, and therefore one single vibration. An example of this would be $O_2$ or $N_2$.\n", + "\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"co2-mode\"\n", + "\n", + "Normal modes of $CO_2$ with associated vibrational frequencies\n", + ":::\n", + "\n", + "\n", + "- However, unsymmetric diatomic molecules (i.e. CN do absorb in the IR spectra. Polyatomic molecules undergo more complex vibrations that can be summed or resolved into normal modes of vibration. The normal modes of vibration are: asymmetric, symmetric, wagging, twisting, scissoring, and rocking for polyatomic molecules.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Calculating number of modes\n", + "\n", + "- The degrees of vibrational modes for linear molecules can be calculated using the formula:\n", + ":::{admonition}\n", + ":class: important\n", + "\n", + "- **Linear** Molecules with N atoms:\n", + "\n", + "$$N_{modes} = 3N−5$$\n", + " \n", + "- **Non-linear** molecules with N atoms\n", + "\n", + "$$N_{modes} = 3N−6$$\n", + "\n", + ":::" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Selection rules\n", + "\n", + "- Selection rules in spectroscopy are fundamental principles that dictate whether a transition is allowed or forbidden during the absorption or emission of electromagnetic radiation, such as infrared (IR) or Raman spectroscopy. The origins of these rules lie in the quantum mechanical description of molecular vibrations and the interactions of molecules with electromagnetic radiation.\n", + "\n", + "- Molecular symmetry plays a crucial role in determining the allowed transitions.\n", + "Symmetry considerations, especially in molecules, come from group theory, which helps in predicting whether a certain vibrational mode will be IR or Raman active.\n", + "\n", + "- Not all diatomic molecules have vibrational absorption spectrum. To see this, we have to calculate the electric dipole transition moment. We will learn more about whu To proceed, we expand $\\mu_0^{(e)}$ in a Taylor series about $R = R_e$:\n", + "\n", + "$${\\mu_0^{(e)}(R) = \\mu_e + \\left(\\frac{\\partial\\mu}{\\partial R}\\right)_{R = R_e}(R - R_e) + \\frac{1}{2}\\left(\\frac{\\partial^2\\mu}{\\partial R^2}\\right)_{R = R_e}(R - R_e)^2 + ...}$$\n", + "\n", + "- Next we integrate over the vibrational degrees of freedom and obtain:\n", + "\n", + "$${\\int\\psi^*_{v''}\\mu_0\\psi_{v'}dR = \\mu_e\\int\\psi^*_{v''}\\psi_{v'}dR + \\left(\\frac{\\partial\\mu}{\\partial R}\\right)_{R = R_e}\\int\\psi_{v''}^*(R - R_e)\\psi_{v'}dR}\\\\\n", + "{ + \\frac{1}{2}\\left(\\frac{\\partial^2\\mu}{\\partial R^2}\\right)_{R = R_e}\\int\\psi_{v''}^*(R - R_e)^2\\psi_{v'}dR + ...}$$\n", + "\n", + "- The first term above is zero since the vibrational eigenfunctions are orthogonal. The second term is nonzero if the dipole moment depends on the internuclear distance $R$. Therefore we conclude that the selection rule for pure vibrational transition is that the dipole moment must change as a function of $R$. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Application of selection rules\n", + "\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"amide-ir\"\n", + "\n", + "Example of 2D IR spectorsocpy used to study protein by detecting amide group $C=0$ vibrations in different parts of the molecules.\n", + ":::\n", + "\n", + "- All homonuclear diatomic molecules (e.g., $H_2$, $O_2$, etc.) have zero dipole moment, which cannot change as a function of $R$. Hence these molecules do not show vibrational spectra. \n", + "- In general, all molecules that have dipole moment have vibrational spectra as change in $R$ also results in change of dipole moment. We still have the integral present in the second term. \n", + "- For harmonic oscillator wavefunctions, this integral is zero unless $v'' = v'\\pm 1$ . This provides an additional selection rule, which says that the vibrational quantum number may either decrease or increase by one." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### IR spectra\n", + "\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"ir\n", + "\n", + "IR spectral frequencies observed due to different vibrational frequencies of bonds in organic molecules. \n", + ":::\n", + "\n", + "\n", + ":::{figure-md} markdown-fig\n", + "\"amide-ir\"\n", + "\n", + "Example of 2D IR spectorsocpy used to study protein by detecting amide group $C=0$ vibrations in different parts of the molecules.\n", + ":::" + ] + } + ], + "metadata": { + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/ch04/note03B.md b/ch04/note03B.md deleted file mode 100644 index d9a22805..00000000 --- a/ch04/note03B.md +++ /dev/null @@ -1,216 +0,0 @@ -## Molecular Vibrations - -:::{admonition} What you need to know -:class: note - -- **Quantization of vibrations in molecules.** Vibrational degrees of freedom are quantized in molecules. This which implications for infrared and raman spectroscopies. -- **Existence of Selection rules.** Not all vibrational transitions are observed. Quantum mechanics predicts that for transition to occur the trasnition probability needs to be non zero which is quantified via transition dipole moment. -- **Effects of unharmonicity.** Harmonic osccilator approximation captures the dominant transition frequency but is not fully accurate becasue harmonic shape of the potential descrimed the vicinity of potential energy minima which tends to become less accurate for excited vibrational states of molecules. -::: - - -### Harmonic Oscillator - -- First let us write harmonic oscillator energies in a format used for spectroscopic analysis. This means converting to wavenumber units $\tilde{\nu}=\frac{1}{\lambda}$: - -$${\tilde{E}_v = \frac{E_v}{hc} = \tilde{\nu}\left(v + \frac{1}{2}\right)}$$ - -- **The vibrational quantum number** is denoted as $v$ -- **The vibrational frequency** expressed in wavenumber units $cm^{-1}$ units is $\tilde{\nu} = \frac{1}{2\pi c}\sqrt{k/\mu}$ -- **Reduced mass of the diatomic molecule** $\mu$. - -- Note that $v$ and $\nu$ look very similar but have different meaning! A typical value for vibrational frequency would be around $500 - 4000cm^{-1}$. Small values are associated with weak bonds whereas strong bonds have larger vibrational frequencies. - -:::{admonition} **Example** -:class: note - -A strong absorption of infrared radiation is observed for $^1H^{35}Cl$ at $2991 cm{-1}$. - -- Calculate the force constant k for this molecule -- By what factor do you expect this frequency to shift if deuterium is substituted for hydrogen in this molecule? The force constant is unaffected by this substitution. -::: - -:::{admonition} **Solution** -:class: dropdown - -- **part a** - -$$\omega = 2\pi \nu = \frac{2\pi c}{\lambda} =\Big(\frac{k}{\mu}\Big)^{1/2}$$ - - -$$k = \Big(\frac{2\pi c}{\lambda}\Big)^2\mu=516 N \cdot m^{-1}$$ - -- **part b** - -$$\frac{\nu_{DCl}}{\nu_{HCL}}=\Big(\frac{\mu_{HCl}}{\mu_{DCL}}\Big)^{1/2}=0.717$$ -::: - -### Going beyond harmonic approximation - - -- Earlier when we have discussed the harmonic oscillator problem and we briefly mentioned that it can be used to approximate atom - atom interaction energy (*potential energy curve*) near the equilibrium bond length. - -- Harmonic potential would not allow for molecular dissociation and therefore it is clear that it would not be a realistic model when we are far away from the equilibrium geometry. The harmonic potential is given by: - -$${E(R) = \frac{1}{2}k(R - R_e)^2}$$ - -- $k$ is called the *force constant*, $R_e$ is the *equilibrium bond length*, and $R$ is the distance between the two atoms. The actual potential energy curve can be obtained from theoretical calculations or to some degree from spectroscopic experiments. - -- This curve has usually complicated form and hence it is difficult to solve the nuclear Schrodinger equation exactly for this potential. One way to see the emergence of the harmonic approximation is to look at *Taylor series expansion*: - -$${E(R) = E(R_e) + \left(\frac{dE}{dR}\right)_{R = R_e}(R - R_e) + \frac{1}{2}\left(\frac{d^2E}{dR^2}\right)_{R = R_e}(R - R_e)^2 + ...}$$ - -:::{figure-md} markdown-fig -DeD0 - -One has to distinguish between two kinds of dissociation energies: *equilibrium dissociation energy* $D_e$ and *spectroscopic dissociation energy* $D_0$. Show are Harmonic vs Morse potential -::: - -### Morse potential and dissociation energy - -- Morse potential proisde more accurate description for molecular vibrations and predicts dissociation and changing spacing between energy levels. - -$$V(R)=D_e(1-e^{-a(R-R_e)^2})$$ - -- $D_e$ is measured from the bottom of the potential to the dissociation limit whereas $D_0$ is measured from the lowest vibrational level to the dissociation limit. - -$$D_0 = D_e-\frac{1}{2}h\nu$$ - - - -### Unharmonic oscillator - -- We attempt to account for the deviation from the harmonic behavior by adding higher order polynomial terms $\tilde{E}_v$: - -$${\tilde{E}_v = \tilde{\nu}_e(v + \frac{1}{2}) - \tilde{\nu}_ex_e(v + \frac{1}{2})^2 + \tilde{\nu}_ey_e(v + \frac{1}{2})^3}$$ - -- where $\tilde{\nu}_e$ is the vibrational wavenumber, $x_e$ and $y_e$ are anharmonicity constants, and $v$ is the vibrational quantum number. Usually the third term is ignored and we can write the vibrational transition frequencies as ($v\rightarrow v+1$): - -$${\tilde{\nu}_{v\rightarrow v+1} = \tilde{E}_{v+1} - \tilde{E}_v = \tilde{\nu}_e[1- 2x_e (v+1)] }$$ - -- As we will see soon that by adding the 2nd order polynomial term to the eigenvalues, we actually imply the use of a potential function that allows for dissociation. - - -### Overtone transitions - - -![](./images/vib_modes.jpeg) - -- The higher order terms are small but they give rise to overtone transitions with $\Delta v = \pm 2, \pm 3, ...$ with rapidly decreasing intensities. - -$${\tilde{\nu}_{0\rightarrow v} = \tilde{E}_{v} - \tilde{E}_0 = \tilde{\nu}_e \cdot v - \tilde{\nu}_ex_e \cdot v (v+1)}$$ - -:::{admonition} **Example** -:class: note - -Given $\tilde{\nu}=536 cm^{-1}$ and $x_e\tilde{\nu}=3.4 cm^{-1}$ for $^{23}Na^{19}F$ molecule, calculate frequencies of first two overtones. -::: - -:::{admonition} **Solution** -:class: note, dropdown - -We make use of the equation ${\tilde{\nu}_{0\rightarrow v} = \tilde{\nu}_e \cdot v - 2\tilde{\nu}_ex_e v (v+1)}$ to compute transitions to levels 1 (fundamental), 2 (first overtone) and 3 (second overtone) - -- $\tilde{\nu}_{0\rightarrow 1} = 1\tilde{\nu}_e - 2\tilde{\nu}_ex_e= 1\cdot536-2\cdot3.4=529 cm^{-1}$ -- ${\tilde{\nu}_{0\rightarrow 2} = 2\tilde{\nu}_e - 6\tilde{\nu}_ex_e= 2\cdot536-6\cdot3.4}=1059 cm^{-1}$ -- ${\tilde{\nu}_{0\rightarrow 3} = 3\tilde{\nu}_e - 12\tilde{\nu}_ex_e= 3\cdot536-12\cdot3.4}=1567 cm^{-1}$ -::: - - -### Population of vibrational states - -- Out of all possible vibrational states which states do molecules occupy at room temperature? For harmonic oscillator, the Boltzmann distribution gives the statistical weight for the $v$ level: - -$${f_v = \frac{e^{-(v + 1/2)h\nu/(k_BT)}}{\sum\limits_{v=0}^\infty e^{-(v+1/2)h\nu/(k_BT)}}} -{= \frac{e^{-vh\nu/(k_BT)}}{\sum\limits_{v=0}^\infty e^{-vh\nu/(k_BT)}}}$$ - -- Note that the degeneracy factor is identically one because there is no degeneracy in one dimensional harmonic oscillator. To proceed, we recall geometric series: - -$${\sum\limits_{v=0}^\infty x^v = \frac{1}{1 - x}\textnormal{ with }x < 1}$$ - - -$${\sum\limits_{v=0}^\infty e^{-vh\nu/(k_BT)} = \frac{1}{1 - e^{-h\nu/(k_BT)}}}$$ - - -$${f_v = \left(1 - e^{-h\nu/(k_BT)}\right)e^{-vh\nu/(k_BT)}}$$ - -- For example, for $H^{35}Cl$ the thermal population of the first vibrational level $v = 1$ is very small about $9\times$ $10^{-7}$. -- **This is why generally the excited vibrational levels do not contribute to the (IR) spectrum.** - - -### Vibrational modes of molecules - -A molecule has translational and rotational motion as a whole while each atom has it's own motion. The vibrational modes can be IR or Raman active. For a mode to be observed in the IR spectrum, changes must occur in the permanent dipole (i.e. not diatomic molecules). Diatomic molecules are observed in the Raman spectra but not in the IR spectra. This is due to the fact that diatomic molecules have one band and no permanent dipole, and therefore one single vibration. An example of this would be $O_2$ or $N_2$. - - -:::{figure-md} markdown-fig -co2-mode - -Normal modes of $CO_2$ with associated vibrational frequencies -::: - - -- However, unsymmetric diatomic molecules (i.e. CN do absorb in the IR spectra. Polyatomic molecules undergo more complex vibrations that can be summed or resolved into normal modes of vibration. The normal modes of vibration are: asymmetric, symmetric, wagging, twisting, scissoring, and rocking for polyatomic molecules. - - -### Calculating number of modes - -- The degrees of vibrational modes for linear molecules can be calculated using the formula: - -$$3N−5$$ - -- The degrees of freedom for nonlinear molecules can be calculated using the formula: - -$$3N−6$$ - -- Determine if the molecule is linear or nonlinear (i.e. Draw out molecule using VSEPR). If linear, use Equation 1 If nonlinear, use Equation 2 -Calculate how many atoms are in your molecule. This is your N value. -Plug in your N value and solve. - -### Selection rules - -- Selection rules in spectroscopy are fundamental principles that dictate whether a transition is allowed or forbidden during the absorption or emission of electromagnetic radiation, such as infrared (IR) or Raman spectroscopy. The origins of these rules lie in the quantum mechanical description of molecular vibrations and the interactions of molecules with electromagnetic radiation. - -- Molecular symmetry plays a crucial role in determining the allowed transitions. -Symmetry considerations, especially in molecules, come from group theory, which helps in predicting whether a certain vibrational mode will be IR or Raman active. - -- Not all diatomic molecules have vibrational absorption spectrum. To see this, we have to calculate the electric dipole transition moment. We will learn more about whu To proceed, we expand $\mu_0^{(e)}$ in a Taylor series about $R = R_e$: - -$${\mu_0^{(e)}(R) = \mu_e + \left(\frac{\partial\mu}{\partial R}\right)_{R = R_e}(R - R_e) + \frac{1}{2}\left(\frac{\partial^2\mu}{\partial R^2}\right)_{R = R_e}(R - R_e)^2 + ...}$$ - -- Next we integrate over the vibrational degrees of freedom and obtain: - -$${\int\psi^*_{v''}\mu_0\psi_{v'}dR = \mu_e\int\psi^*_{v''}\psi_{v'}dR + \left(\frac{\partial\mu}{\partial R}\right)_{R = R_e}\int\psi_{v''}^*(R - R_e)\psi_{v'}dR}\\ -{ + \frac{1}{2}\left(\frac{\partial^2\mu}{\partial R^2}\right)_{R = R_e}\int\psi_{v''}^*(R - R_e)^2\psi_{v'}dR + ...}$$ - -- The first term above is zero since the vibrational eigenfunctions are orthogonal. The second term is nonzero if the dipole moment depends on the internuclear distance $R$. Therefore we conclude that the selection rule for pure vibrational transition is that the dipole moment must change as a function of $R$. - -### Application of selection rules - - -:::{figure-md} markdown-fig -amide-ir - -Example of 2D IR spectorsocpy used to study protein by detecting amide group $C=0$ vibrations in different parts of the molecules. -::: - -- All homonuclear diatomic molecules (e.g., $H_2$, $O_2$, etc.) have zero dipole moment, which cannot change as a function of $R$. Hence these molecules do not show vibrational spectra. -- In general, all molecules that have dipole moment have vibrational spectra as change in $R$ also results in change of dipole moment. We still have the integral present in the second term. -- For harmonic oscillator wavefunctions, this integral is zero unless $v'' = v'\pm 1$ . This provides an additional selection rule, which says that the vibrational quantum number may either decrease or increase by one. - -### IR spectra - - -:::{figure-md} markdown-fig -ir spectra - -IR spectral frequencies observed due to different vibrational frequencies of bonds in organic molecules. -::: - - -:::{figure-md} markdown-fig -amide-ir - -Example of 2D IR spectorsocpy used to study protein by detecting amide group $C=0$ vibrations in different parts of the molecules. -::: -