{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [], "source": [ "__authors__ = [\"Tricia D Shepherd\" , \"Ryan C. Fortenberry\", \"Matthewy Kennedy\", \"C. David Sherril\"]\n", "__credits__ = [\"Victor H. Chavez\", \"Lori Burns\"]\n", "__email__ = [\"profshep@icloud.com\", \"r410@olemiss.edu\"]\n", "\n", "__copyright__ = \"(c) 2008-2019, The Psi4Education Developers\"\n", "__license__ = \"BSD-3-Clause\"\n", "__date__ = \"2019-11-18\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "The eigenfunctions solutions to the Schrödinger equation for a multielectron system depend on the coordinates of all electrons. The orbital approximation says that we can represent a many-electron eigenfunction in terms of individual electron orbitals, each of which depends only on the coordinates of a single electron. A *basis set* in this context is a set of *basis functions* used to approximate these orbitals. There are two general categories of basis sets: *minimal basis sets* that describe only occupied orbitals and *extended basis sets* that describe both occupied and unoccupied orbitals.\n", "\n", "### Part A. What is the calculated Hartree Fock energy using a minimal basis set?\n", "\n", "1. Import the required modules (**psi4** and **numpy**)\n", "\n", "2. Define a Boron atom as a ```psi4.geometry``` object. Be mindful of the charge and spin multiplicity. For a neutral B atom, the atom can only be a doublet (1 unpaired electron). \n", "\n", "3. Set psi4 options to select an **unrestricted** calculation (restricted calculation *won't* work with this electronic configuration).\n", "\n", "4. Run a **Hartree-Fock** calculation using the basis set **STO-3G**, store both the energy and the wavefunction object. The energy will be given in atomic units. \n", "\n", "5. Look at your results by printing them within a cell. It is possible to obtain information about the basis set from the wfn object. The number of basis functions can be accessed with: ```wfn.basiset().nbf()```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RESPONSE:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "### Part B. How does the Hartree Fock energy depend on the trial basis set?\n", "\n", "In computational chemistry, we focus on two types of functions: the Slater-type function and the Gaussian-type functions. Their most basic shape can be given by the following definitions. \n", "\n", "$$ \\Phi_{gaussian}(r) = 1.0 \\cdot e^{-1.0 \\cdot x^2} $$\n", "\n", "and\n", "\n", "$$ \\Phi_{slater}(r) = 1.0 \\cdot e^{-1.0 \\cdot |x|} $$\n", "\n", "\n", "Both functions can be visualized below:" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "r = np.linspace(0, 5, 100)\n", "sto = 1.0 * np.exp(-np.abs(r))\n", "gto = 1.0 * np.exp(-r**2)\n", "\n", "fig, ax = plt.subplots(ncols=2, nrows=1)\n", "\n", "p1 = ax[0]\n", "p2 = ax[1]\n", "\n", "fig.set_figheight(5)\n", "fig.set_figwidth(15)\n", "\n", "\n", "p1.plot(r, sto, lw=4, color=\"teal\")\n", "p1.plot(-r, sto, lw=4, color=\"teal\")\n", "\n", "p2.plot(r, gto, lw=4, color=\"salmon\")\n", "p2.plot(-r, gto, lw=4, color=\"salmon\")\n", "\n", "\n", "p1.title.set_text(\"Slater-type Orbital\")\n", "p2.title.set_text(\"Gaussian-type Orbital\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The STO is characterized by two features: 1) The peak at the nucleus and 2) the behavior far from the nucleus, which should tend to zero nice and smoothly. You can see that the GTO does not have those characteristics since the peak is smooth and the ends go to zero *too* quickly. \n", "\n", "You may remember that the ground state eigenfunction of the Hydrogen atom with a spin equal to zero has the same shape as the STO. This is true not only for Hydrogen but for every atomistic system. \n", "One may wonder then why are we not using STO in every calculation? The short answer is that we don't have the exact solution to each of the systems, and when it comes to handling approximations, the GTO are simply more efficient than the STO. Remember the theorem that states that the product of two Gaussians is also a Gaussian?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "In the first part of the lab, we used the smallest basis set available STO-3G, where STO stands for *Slater-type orbital* which is approximated by the sum of *3 Gaussian functions*. \n", "\n", "$$\\phi^{STO-3G} = \\sum_i^3 d_i \\cdot C(\\alpha_i) \\cdot e^{-\\alpha_i|r-R_A|^2} $$\n", "\n", "Where the $\\{ \\alpha \\}_i$ and $\\{ d \\}_i$ are the exponents and coefficients that define a basis set and are usually the components needed to create a basis set. \n", "\n", "STO-3G is an example of a minimal basis set, *i.e.* it represents the orbitals of each occupied subshell with one basis function. While basis sets of the form STO-nG were popular in the 1980's, they are not widely used today. For the same reason that multiple Gaussian functions better approximate a Slater type orbital, multiple STO-nG functions are found more efficient to approximate atomic orbitals. In practice, inner shell (core) electrons are still described by a single STO-nG function and only valence electrons are expressed as the sum of STO-nG type functions. \n", "\n", "You will see that the approximation performs really well. Look at the following example$^1$:" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def sto(r, coef, exp):\n", " return coef * (2*exp/np.pi)**(3/4) * np.exp(-exp*(r)**2)\n", "\n", "slater = (1/np.pi)**(0.5) * np.exp(-1.0*np.abs(r))\n", "\n", "sto_1g = sto(r, 1.00, 0.270950)\n", "sto_2g = sto(r, 0.67, 0.151623) + sto(r, 0.43, 0.851819)\n", "sto_3g = sto(r, 0.44, 0.109818) + sto(r, 0.53, 0.405771) + sto(r, 0.154, 2.22766)\n", "\n", "\n", "plt.figure(figsize=(15,5))\n", "\n", "plt.plot(r, sto_1g, lw=4, c=\"c\")\n", "plt.plot(-r, sto_1g, label=\"STO-1G\", lw=4, c=\"c\")\n", "\n", "plt.plot(r, sto_2g, lw=4, c=\"orchid\")\n", "plt.plot(-r, sto_2g, label=\"STO-2G\", lw=4, c=\"orchid\")\n", "\n", "plt.plot(r, sto_3g, lw=4, c=\"gold\" )\n", "plt.plot(-r, sto_3g, label=\"STO-3G\", lw=4, c=\"gold\" )\n", "\n", "plt.plot(r, slater, ls=\":\", lw=4, c=\"grey\")\n", "plt.plot(-r, slater, label=\"Slater-type function\", ls=\":\", lw=4, c=\"grey\")\n", "\n", "plt.legend(fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see that with the addition of each new Gaussian, our linear combination behaves more and more like a STO. Each of these Gaussians is commonly knon as *primitive*. \n", "\n", "###### $^1$ Szabo, Attila, and Neil S. Ostlund. Modern quantum chemistry: introduction to advanced electronic structure theory. Courier Corporation, 2012." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "___" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand how to read each basis set, let's consider the next available basis set: 3-21G basis set. The number before the dash, \"3\" represents the 3 Gaussian primitives (i.e. a STO-\"3\"G) use to represent the inner shell electrons. The next two numbers represent the valence shell split into two sets of STO-nG functions--One with\"2\" Gaussian-type orbitals (GTOs) and one with \"1\" GTO. Let us see how this other basis set performs. \n", "\n", "1. With the previously defined Boron atom. Run a new HF calculation using the basis set \"3-21G\".\n", "\n", "2. Rationalize the number of basis functions used for the STO-3G and 3-21G calculations. \n", "\n", "3. Compare the STO-3G and 3-21G HF energies. WHich basis set is more accurate? (Recall the variational principle states that for a given Hamiltonian operator, any trial wavefunction will have n average energy that is greater than or equal to the \"true\" corresponding ground state wavefunction. Because of this, the Hartree Fock energy is an upper bound to the ground state energy of a given molecule. )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RESPONSE:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "### Part C. How can we improve the accuracy of the HF energy?\n", "\n", "To make an even better approximation to our trial function, we may need to take into account the two following effects:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Polarization:\n", "Accounts for the unequal distribution of electrons when two atoms approach each other. We can include these effects by adding STO's of higher orbital angular momentum, i.e., d-type functions are added to describe valence elctrons in 2p orbitals. \n", "\n", "We can if there is presence of polarization functions with the use of asterisks:\n", "\n", "* One asterisk (*) refers to polarization on heavy atoms.\n", "* Two asterkisks (**) is used for polarization on Hydrogen (H-Bonding).\n", "\n", "\n", "#### Difusse Functions:\n", "These are useful for systems in an excited state, systems with low ionization potential, and systems with some significant negative charge attached. \n", "\n", "The presence of diffuse functions is symbolized by the addition of a plus sign:\n", "\n", "* One plus sign (+) adds diffuse functions on heavy atoms.\n", "* Two plus signs (++) add diffuse functions on Hydrogen atoms.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Let us look at how the addition of these effects will improve our energy:\n", "\n", "1. Repeat the boron atom energy calculation for each of the basis sets listed: \n", " ``['6-31G', '6-31+G', '6-31G*', '6-31+G*', '6-311G*', '6-311+G**', 'cc-pVDZ', 'cc-pVTZ']``\n", " \n", "2. Using `print(f\"\")` statements, builld a table where for each basis you identify the type and number of STO-nG function used for the core and valence electrons. \n", "3. For each basis, identify the type and number of STO-nG functions used for the core and valence electrons. \n", "4. On the same table, specify wether polarized or difusse functions are included. \n", "5. Record the total number of orbitals. For the Boron atom, which approximation (choice of basis set) is the most accurate? How does the accuracy relate to the number of basis functions used?\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RESPONSE:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part D. How much \"correlation energy\" can we recover" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the Hartree Fock level of theory, each electron experiences an average potential field of all the other electrons. In essence, it is a \"mean field\" approach that neglects individual electron-electron interactions or \"electron correlation\". Thus, we define t he difference between the self-consistent field energy and the exact energy as the correlation energy. Two fundamentally different approaches to account for electron correlation effects are available by selecting a Correlation method: Moller Plesset (MP) Perturbation theory and Coupled Cluster (CC) theory. \n", "\n", "1. Based on the calculated SCF energy for the *6-311+G** basis set, determine the value of the correlation energy for boron assuming an \"experimental\" energy of **-24.608 hartrees$^2$**\n", "\n", "2. Using the same basis set, perform an energy calculation with MP2 and MP4. \n", " (You may recover the MP2 energy from the MP4 calculation but you will have to look at the output file). \n", " MP4 will require the use of the following options:\n", " ```psi4.set_options({\"reference\" :\"rohf\", \"qc_module\":\"detci\"})```\n", "\n", "3. Using the same basis set, perform an energy calculation with CCSD and CCSD(T). \n", " (You may recover the CCSD energy from the CCSD(T) calculation but you will have to look at the output file). \n", "\n", "4. For each method, determine the percentage of the correlation energy recovered. \n", "\n", "
\n", "\n", "\n", "###### $^2$. H. S. Schaefer and F. Harris, (1968) Phys Rev. 167, 67" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RESPONSE:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part E. Can we use DFT(B3LYP) to calculate the electron affinity of boron?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The electron affinity of atom A is the energy released for the process:\n", " \n", "$$ A + e^{-} \\rightarrow A^{-} $$\n", "\n", "Or simply the energy difference between the anion and the neutral forms of an atom. These are reported in positive values:\n", " \n", "$$ EA = - (E_{anion} - E_{neutral}) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It was reported$^3$ that the electron affinity of Boron at the B3LYP 6-311+G** level of theory is **-0.36 eV**. In comparison to the experimental value of **0.28 eV** this led to the assumption that B3LYP does not yield a reasonable electron affinity. \n", "|" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "1. Define a Boron atom for two different configurations:\n", " For the anion, set the charge to **-1**. Once we do that, the charge and spin multiplicity are no longer compatible. For 2 electrons in a set of *p* orbitals, the multiplicity can only be 3 (triplet state, unpaired spins) or 1 (singlet state, paired spins). Here, by Hund's rules, we expect the spins will remain unpaired, leading to a triplet. Run the calculation and record the energy for boron anion. \n", " \n", "2. Calculate the electron affinity. Is this literature result consistent with your calculation? (Remember 1 hartree = 27.2116 eV)\n", "\n", "3. Repeat the electron affinity calculation of boron, but this time, assume the anion is a singlet sate. Whata is the reason$^4$ for the reporte failure of the B3LYP method?\n", "\n", "
\n", "\n", "###### $^3$C. W. Bauschlicher, (1998) Int. J. Quantum Chem. 66, 285\n", "###### $^4$ B. S. Jursic, (1997) Int. J. Quantum Chem. 61, 93" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "RESPONSE:" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 4 }