{
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      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "#**Química Computacional - Aula Prática 11**\n",
        "\n",
        "---\n",
        "Bibliografia de Suporte:\n",
        "\n",
        "Mike P. Allen and Dominic J. Tildesley, ”Computer Simulation of Liquids”,\n",
        "Clarendon Press, Oxford, 1997\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "8crRlPgWWMi6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Mecânica Estatística, Simulação e Modelação Molecular**\n",
        "\n",
        "\\\\\n",
        "\n",
        "**Exercício 1**\n",
        "\n",
        "No contexto dos **potenciais de par efectivos**, um potencial intermolecular de esferas rígidas (*hard spheres*) é modelo não realístico permitindo apenas estudar propriedades gerais de um líquido ou um sólido de forma aproximada.\n",
        "\n",
        "\\\\\n",
        "\\begin{equation}\n",
        "U \\approx \\sum_{i}^{N} \\sum_{j>i}^{N} u_2^{eff} (r_{ij}) =\n",
        "\\begin{cases}\n",
        "\\infty \\ (r < \\sigma)\\\\\n",
        "0 \\ \\ (r \\geq \\sigma)  \\\\\n",
        "\\end{cases}\n",
        "\\end{equation}\n",
        "\n",
        "\\\\\n",
        "Escreva um programa para representar o potencial $U$ em função da distância $r_{ij}$ para partículas com diâmetro $σ = 2 Å$. Faça a representação para $0 \\leq r \\leq 10~Å$ e $-1 \\leq U(r) \\leq 10~Å$. Não se esqueça de indicar as unidades.\n",
        "\n",
        "Nota: Use o exercício 2 da Aula 6 como ponto de partida para representar a função. Embora a biblioteca numpy contenha a \"constante\" infinito através de `np.inf`, para uma representação eficiente pode usar um número muito grande, e.g. `1e6`"
      ],
      "metadata": {
        "id": "CXoD_3r1u7QB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n"
      ],
      "metadata": {
        "id": "QW2V0XMgsREQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 2**\n",
        "\n",
        "O potencial de Lennard-Jones\n",
        "\n",
        "\\\n",
        "\\begin{equation}\n",
        "u(r) = 4 \\epsilon \\left[ \\left(\\frac{\\sigma}{r}\\right)^{12} - \\left(\\frac{\\sigma}{r}\\right)^{6}\\right]\n",
        "\\end{equation}\n",
        "\n",
        "\\\n",
        "é muito utilizado em simulações de dinâmica molecular para representar as interacções intermoleculares.\n",
        "\n",
        "\\\\\n",
        "Em vários campos de forças as simulações de moléculas de água são realizadas usando o modelo TIP3P (Transferable Intermolecular Potential with 3 Points of interaction) cujos parâmetros são:\n",
        "\n",
        "\\begin{equation}\n",
        "\\sigma_{OO} = 3.1507~Å\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "ϵ_{OO} = 0.1521 \\ \\text{kcal mol}^{-1}\n",
        "\\end{equation}\n",
        "\n",
        "Represente o potencial de par efectivo utilizando o potencial de Lennard-Jones para dois átomos de oxigénio para valores de $0 \\leq r \\leq 10 Å$"
      ],
      "metadata": {
        "id": "DjbSliM5lTbG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "ZIEevtteuqli"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 3**\n",
        "\n",
        "Mostre que o valor de $r_{min} = 2^{1/6}\\sigma$.\n",
        "\n",
        "\n",
        "Nota 1: Vai necessitar da regra dos expoentes $\\frac{d}{dr} (r^{n}) = n r^{n-1}$\n",
        "\n",
        "Nota 2: $r_{min}$ é muitas vezes designado por $r_0$\n",
        "\n",
        "\\\\\n",
        "\n",
        "**Exercício 4**\n",
        "\n",
        "Calcule o valor de $r_{min}$ para o potencial de de Lennard-Jones de dois átomos de oxigénio usando o modelo TIP3P"
      ],
      "metadata": {
        "id": "n5U01KrcaKXO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 5**\n",
        "\n",
        "Use agora o exercício 4 da Aula 4 como base para encontrar o valor de $r$ para o qual o potencial de Lennard-Jones para os dois átomos de oxigénio no modelo de água TIP3P é mínimo ($r_{min}$ ou $r_0$). Compare com o valor obtido no exercício anterior. Verifique também o valor de $u(r_{min})$ e compare com os parâmetros fornecidos no exercício 2. Não se esqueça de indicar as unidades."
      ],
      "metadata": {
        "id": "dvFTBmhV_aUY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n"
      ],
      "metadata": {
        "id": "Vjlj6Idx_uni"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 6**\n",
        "\n",
        "Se as particulas do sistema forem carregadas, pode usar-se também um potencial de potencial de Coulomb para descrever as interações electrostáticas de longo alcance:\n",
        "\n",
        "\\begin{equation}\n",
        "    u(r_{ij})^{Coul}= \\frac{1}{4 \\pi \\epsilon_{0}} \\frac{q_i q_j}{r_{ij}}\n",
        "\\end{equation}\n",
        "\n",
        "O modelo TIP3P (Transferable Intermolecular Potential with 3 Points of interaction) para a molécula de água usa os seguintes parâmetros para as cargas atómicas:\n",
        "\n",
        "\\begin{equation}\n",
        "q_O = -0.834e\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "q_H = 0.417e\n",
        "\\end{equation}\n",
        "\n",
        "Faça um programa para representar o potencial de Coulomb (em kcal mol$^{-1}$) dos pares O$\\cdots$H, H$\\cdots$H e O$\\cdots$O em função da distância $r$, para valores de $0 \\leq r \\leq 10 Å$.\n",
        "\n",
        "Nota: O potencial de Coulomb é muitas vezes escrito na seguinte forma\n",
        "\n",
        "\\begin{equation}\n",
        "    u(r_{ij})^{Coul}= C \\frac{q_i q_j}{r_{ij}}\n",
        "\\end{equation}\n",
        "\n",
        "Onde a constante C devolve o valor do potencial na unidade desejada. Quando queremos expressar a energia em kcal mol$^{-1}$ e usamos distâncias em Angstroms (Å) com cargas elementares ($e$), o valor de C é aproximadamente 332 kcal Å mol$^{-1}$ e$^2$"
      ],
      "metadata": {
        "id": "IdDjzbqmO0BS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n",
        "#\n"
      ],
      "metadata": {
        "id": "MZ7NY_kHQbK3"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 7**\n",
        "\n",
        "Sem realizar nenhum cálculo e apenas por inspecção visual do gráfico e da função, indique para cada par qual o mínimo do potencial (se existir).\n",
        "\n",
        "**Exercício 8**\n",
        "\n",
        "Considere agora os parâmetros completos para o modelo de água TIP3P\n",
        "\n",
        "\\begin{equation}\n",
        "\\sigma_{OO} = 3.1507~Å\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "ϵ_{OO} = 0.1521 \\ \\text{kcal mol}^{-1}\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "\\sigma_{HH} = 1~Å\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "ϵ_{HH} = 0 \\ \\text{kcal mol}^{-1}\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "\\sigma_{OH} = 1~Å\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "ϵ_{OH} = 0 \\ \\text{kcal mol}^{-1}\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "q_O = -0.834e\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "q_H = 0.417e\n",
        "\\end{equation}\n",
        "\n",
        "Represente o potencial total para cada par (O$\\cdots$H, H$\\cdots$H e O$\\cdots$O)."
      ],
      "metadata": {
        "id": "uNC_1CCAVYXq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n",
        "#\n",
        "#\n"
      ],
      "metadata": {
        "id": "_qs_vGccYhHT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Exercício 9**\n",
        "\n",
        "Considere o seguinte dímero da molécula de água\n",
        "\n",
        "\n",
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)\n",
        "\n",
        "Cujas distâncias entre os pares são\n",
        "\n",
        "$r_{15} = 1.942$\n",
        "\n",
        "$r_{14} = 2.894$\n",
        "\n",
        "$r_{16} = 3.336$\n",
        "\n",
        "$r_{24} = 3.333$\n",
        "\n",
        "$r_{25} = 2.446$\n",
        "\n",
        "$r_{26} = 3.867$\n",
        "\n",
        "$r_{34} = 3.333$\n",
        "\n",
        "$r_{35} = 2.446$\n",
        "\n",
        "$r_{36} = 3.867$\n",
        "\n",
        "Calcule o potencial total para o dímero de água usando os parâmetros do modelos TIP3P. Despreze o termos intermoleculares. Se preferir, pode escrever um programa em Python para calcular o valor. Obtenha também as contribuições do potencial de Lennard-Jones e do potencial de Coulomb. Comente os resultados com base no peso e contribuição de cada termo para a estabilização do dímero de água."
      ],
      "metadata": {
        "id": "ez42XyEdczg4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#\n",
        "#\n",
        "#\n",
        "#\n",
        "#\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "6kYa0IXaeNvI"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}