"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{4.96646801564063 e^{- 2.91093 r}}{\\sqrt{\\pi}}$"
],
"text/plain": [
" -2.91093⋅r\n",
"4.96646801564063⋅ℯ \n",
"────────────────────────────\n",
" √π "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1s_1 = hf.STO(zeta=1.45363, n=1)\n",
"f1s_2 = hf.STO(zeta=2.91093, n=1)\n",
"\n",
"display(Math('$\\chi_1 :'))\n",
"display(f1s_1)\n",
"display(Math('$\\chi_2 :'))\n",
"display(f1s_2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Note: More detail about this will be covered at part 2, but I want to point out the main idea at beginning. So it could remind you what's our final goal, when you feel distracted.\n",
"\n",
"By using Roothan equations below , which could be solved self-consistently for the orbital coefficient matrix **C** and orbital energy eigenvalues $\\epsilon_i$ by iterations, we could finally \n",
"1. get close to the real wavefunction (using improved Coefficients for Eq1).\n",
"2. get close to correct Molecular orbital energies (using $\\epsilon_i$), to get the real total energy\n",
"\n",
"$${\\mathbf {F}}{\\mathbf {C}}={\\mathbf {S}}{\\mathbf {C}}{\\mathbf {\\epsilon }}$$\n",
"\n",
" Note: \n",
" F (Fock matrix), S (Overlap matrix) are inputs. \n",
" S matrix is fixed, F matrix is changing every iteration because of the improved C. \n",
" C (Coefficient matrix) and $\\epsilon_i$ (eigenvalues) are results.\n",
" \n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### 2. Born–Oppenheimer approximation\n",
"Using Born–Oppenheimer approximation, molecular Hamiltonian could be expressed as \n",
"\n",
"$${\\displaystyle H=H_{\\text{e}}+T_{\\text{n}}}$$\n",
"
\n",
" Note: \n",
" e (electron), n (nuclear)\n",
" \n",
"
\n",
"Where\n",
"\n",
"$${\\displaystyle H_{\\text{e}}=-\\sum _{i}{{\\frac {1}{2}}\\nabla _{i}^{2}}-\\sum _{i,\\alpha}{\\frac {Z_{\\alpha}}{r_{i\\alpha}}}+\\sum _{i>j}{\\frac {1}{r_{ij}}}+\\sum _{\\beta>\\alpha}{\\frac {Z_{\\alpha}Z_{\\beta}}{R_{\\alpha \\beta}}}\\quad {\\text{and}}\\quad T_{\\text{n}}=-\\sum _{\\alpha}{{\\frac {1}{2M_{\\alpha}}}\\nabla _{\\alpha}^{2}}}$$\n",
"
\n",
" Note: \n",
" i, j (electron), $\\alpha$, $\\beta$ (nuclear)\n",
" \n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$H_e$: \n",
"1. sum of kinetic-energy operators for each electron\n",
"2. sum of nuclear–electronic Coulombic attraction terms\n",
"3. sum of electron-electron repulsion energy\n",
"4. sum of nuclear-nuclear repulsion energy ($V_{NN}$)\n",
"\n",
"$T_n$: \n",
"1. sum of kinetic-energy operators for each nuclear"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Classically, during the time of a cycle of electronic motion, the change in nuclear configuration is negligible. Thus, considering the nuclei as fixed, we omit the nuclear kinetic-energy terms $T_n$. So commonly when we say hartree fock energy, we are only talking about $H_e$ term.\n",
"\n",
"$${\\displaystyle H_{\\text{e}}=-\\sum _{i}{{\\frac {1}{2}}\\nabla _{i}^{2}}-\\sum _{i,\\alpha}{\\frac {Z_{\\alpha}}{r_{i\\alpha}}}+\\sum_{i} \\sum_{j>i}{\\frac {1}{r_{ij}}} + V_{NN}}$$\n",
"\n",
"The first 3 terms together is purely electronic Hamiltonian. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### 3. Hartree fock approximation\n",
"\n",
"Because of the inter-electronic repulsion term $\\frac{1}{r_{i j}}$, the Schrödinger equation for a molecule wavefunction is not separable. So the true wave function cannot be written as the product of n one-electron functions. \n",
"\n",
"The essence of hartree-fock approximation is to treat electron-electron repulsion in an average way, so this complicated many-electron problem could be solved as one-electron problem. \n",
"\n",
"Then the molecular wavefunction could be written as a product of all one-electron wavefunctions. \n",
"The functions chosen to represent each electron is based on the hydrogen-like atomic wavefunction. ( Note: This is the reason why we use Slater type Orbital (STO), because it's transformed from exact wavefunction for an electron around a hydrogen atom)\n",
"\n",
"$$\n",
"\\Psi({r_1 r_2})=\\phi_{1}\\left(\\boldsymbol{r}_{1}\\right) \\phi_{2}\\left(\\boldsymbol{r}_{2}\\right)\n",
"$$\n",
"\n",
"However this product does not satisfy antisymmetric requirements (which means if you swap electrons the sign of the wavefunction should invert). This problem can be overcome by taking a linear combination of both products:\n",
"$$\n",
"\\begin{aligned} \\Psi\\left(\\mathbf{r}_{1}, \\mathbf{r}_{2}\\right) &=\\frac{1}{\\sqrt{2}}\\left\\{\\phi_{1}\\left(\\mathbf{r}_{1}\\right) \\phi_{2}\\left(\\mathbf{r}_{2}\\right)-\\phi_{1}\\left(\\mathbf{r}_{2}\\right) \\phi_{2}\\left(\\mathbf{r}_{1}\\right)\\right\\} \\\\ &=\\frac{1}{\\sqrt{2}}\\left|\\begin{array}{ll}{\\phi_{1}\\left(\\mathbf{r}_{1}\\right)} & {\\phi_{2}\\left(\\mathbf{r}_{1}\\right)} \\\\ {\\phi_{1}\\left(\\mathbf{r}_{2}\\right)} & {\\phi_{2}\\left(\\mathbf{r}_{2}\\right)}\\end{array}\\right| \\end{aligned}\n",
"$$\n",
"\n",
"In this way, the Schrödinger equation would then be separated into n one-electron hydrogenlike equations.\n",
"\n",
"Suppose there is an operator called Fock operator $\\hat F$, the eigenvalue corresponding to $\\hat F$ on a one-electron wavefunction is the energy related to this electron.\n",
"\n",
"Each electron energy $\\varepsilon_{i}$ will include \n",
"1. kinetic-energy for this electron\n",
"2. sum of coulombic attraction between this electron and all nuclears\n",
"3. the potential of this electron interacting with an averaged distribution of other electrons, (which is calculated by treating all of the other electrons within the molecule as a smooth distribution of negative charge, and this is the major simplification inherent in the Hartree–Fock method). \n",
"(What does this means? explained at below )\n",
"\n",
" Note: If we take$\\sum_{i}^{n} {\\varepsilon_{i}}$, we will count each interelectronic repulsion twice, which needs to be subtracted when calculating total energy of molecule. \n",
"\n",
"What's the meaing of the potential of this electron interacting with an averaged distribution of other electrons?\n",
"suppose we want to find the electron-electron repulsion potential ($\\text{Vee}$) of electron 1 with electron 2.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\text{Vee}_{1 2}=\\left\\langle\\phi (1)^*|\\frac{1}{r_{1 2}} | \\phi (1)\\right\\rangle$$\n",
"This is not solvable, because we don't know the location of electron (2).\n",
"\n",
"And hartree fock simplify this to: \n",
"(recall that $\\left|\\phi(2)\\right|^{2}$ is the probability density of electron (2)\n",
"\n",
"$$\\text{Vee}_{1 2}=\\left\\langle\\phi (1)^*|\\;\\;\\; \\int \\frac{\\left|\\phi(2)\\right|^{2}}{r_{12}} d v_{2} \\;\\;\\; | \\phi (1)\\right\\rangle \\tag{Eq2}$$\n",
"\n",
"By using the probability density of electron (2) $\\left|\\phi(2)\\right|^{2}$, \n",
"\n",
"$$\\text{infinitesimal charge density} * \\text{infinitesimal volume} = \\text{infinitesimal charge}$$\n",
"\n",
"and integrate over all space, we could get the repulsion energy above. \n",
"It could be also rewritten as, which is more commonly used: \n",
"\n",
"$$\n",
"\\text{Vee}_{1 2}= \\int \\int \\frac{\\left|\\phi(2)\\right|^{2} \\phi (1)^* \\phi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$\n",
"$$\n",
"= \\int \\int \\frac{\\phi(2)^*\\phi(2) \\phi (1)^* \\phi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
Fock operator \n",
"The operator corresponding to one electron energy $\\varepsilon_{i}$ is fock operator. (For the restricted case which assumes closed-shell orbitals and single- determinantal wavefunctions)\n",
"\n",
"$$\\hat{F}(i)=-\\frac{1}{2} \\nabla_{i}^{2}-\\sum_{\\alpha} \\frac{Z_{\\alpha}}{r_{1 \\alpha}} + \\sum_{j=1}^{n / 2}\\left[2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)\\right]$$\n",
"\n",
"where:\n",
"\n",
"- ${\\displaystyle {\\hat {F}}(i)}$ is the Fock operator for the i-th electron in the system, \n",
"- $-\\frac{1}{2} \\nabla_{i}^{2}-\\sum_{\\alpha} \\frac{Z_{\\alpha}}{r_{1 \\alpha}} $ are kinetics energy and sum of nuclear-electron attraction respectively. \n",
"These two terms are often considered as the core terms, and refered as $\\hat{H}^{\\mathrm{core}}_i$\n",
"\n",
"So Fock operator could be rewritten as \n",
"$$\\hat{F}(i)=\\hat{H}_{core}(i)+\\sum_{j=1}^{n / 2}\\left[2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)\\right]$$\n",
"\n",
"- ${\\displaystyle n}$ is the number of electrons and ${\\displaystyle {\\frac {n}{2}}}$ is the number of occupied orbitals in the closed-shell system, \n",
"- ${\\displaystyle {\\hat {J}}_{j}(i)}$ is the Coulomb operator, defining the repulsive force between the j-th and i-th electrons in the system, (explained at Eq2)\n",
"$$\n",
"\\hat{J}_{j}(1) f(1) =f(1) \\int\\left|\\phi_{j}(2)\\right|^{2} \\frac{1}{r_{12}} d v_{2}\n",
"$$\n",
"\n",
"\n",
"\n",
" Note: \n",
" ${\\displaystyle f(1)}$, ${\\displaystyle f(2)}$ are the one-electron wavefunctions acted upon by the exchange operator as functions of the electron positions, and ${\\displaystyle \\phi _{j}(1)}$ and ${\\displaystyle \\phi _{j}(2)}$ are the one-electron wavefunction of the jth electron as functions of the positions of the electrons.\n",
" \n",
"
\n",
" \n",
"- ${\\displaystyle {\\hat {K}}_{j}(i)}$ is the exchange operator, defining the quantum effect produced by exchanging two electrons. \n",
"\n",
"$$\\hat{K}_{j}(1) f(1) =\\phi_{j}(1) \\int \\frac{\\phi_{j}^{*}(2) f(2)}{r_{12}} d v_{2}$$\n",
"\n",
"The Coulomb operator is multiplied by two since there are two electrons in each occupied orbital. The exchange operator is not multiplied by two since it has a non-zero result only for electrons which have the same spin as the i-th electron.\n",
"\n",
"
Roothan equation \n",
"The eigenvalue corresponding to the fock operator is the molecular orbital energies, electrons will occupy start from the lowest level, since we are dealing closed shell molecule, each orbital will has 2 or 0 electrons. \n",
"\n",
"The Roothaan equations are a representation of the Hartree–Fock equation in a non orthonormal basis set (molecular orbitals represented by linear combination of atomic orbitals), which could be solved in matrix way that computer is good at.\n",
"\n",
"$${\\mathbf {F}}{\\mathbf {C}}={\\mathbf {S}}{\\mathbf {C}}{\\mathbf {\\epsilon }}$$\n",
"\n",
" Note: \n",
" F (Fock matrix), S (Overlap matrix) are inputs. \n",
" S matrix is fixed, F matrix is changing every iteration because of the improved C. \n",
" C (Coefficient matrix) and $\\epsilon_i$ (eigenvalues) are results.\n",
" \n",
"
\n",
"\n",
"\n",
"
Why iterations? \n",
"\n",
"Since the Fock operator depends on the orbitals used to construct the corresponding Fock matrix, the eigenfunctions of the Fock operator are in turn new orbitals, which can be used to construct a new Fock operator. In this way, the Hartree–Fock orbitals are optimized iteratively until the change in total electronic energy falls below a predefined threshold. In this way, a set of self-consistent one-electron orbitals is calculated. The Hartree–Fock electronic wave function is then the Slater determinant constructed from these orbitals. Following the basic postulates of quantum mechanics, the Hartree–Fock wave function can then be used to compute any desired chemical or physical property within the framework of the Hartree–Fock method and the approximations employed."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"### 4. Why build matrix and how to solve secular equation?\n",
"Because in this way, computer could solve it efficiently. \n",
"\n",
"\n",
"\n",
" Why build matrix? Click to uncollapse \n",
"(This part is from Calculating Orbital Energies and Expansion Coefficients - Chemistry LibreTexts \n",
" \n",
"\n",
"Solving secular equation is actually calculating orbital energies and coefficients based on **variation principle**, which states that any approximate wavefunction must have a higher energy than the true wavefunction. \n",
"(This part is from [Calculating Orbital Energies and Expansion Coefficients - Chemistry LibreTexts](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Symmetry_(Vallance)/20%3A_Calculating_Orbital_Energies_and_Expansion_Coefficients) .)\n",
"\n",
"Let's ignore the coulomb $\\hat J$ and exchange $\\hat K$ operator in fock operator, what's left is one electron Hamiltonian core operator $\\hat H_{core}$. So how to calculate eigenvalue of Hamiltonian core operator and it's corresponding wavefunction of Helium with double zeta basis? \n",
"(Fock operator could be used as the same way.)\n",
"\n",
"$$\n",
"E=\\frac{\\langle\\phi|\\hat{H}| \\phi\\rangle}{\\langle\\phi | \\phi\\rangle}\n",
"$$\n",
"Where \n",
"$$\\phi = c_{1} \\chi_1 + c_{2} \\chi_2 \\quad \\text{(unnormalized)} $$\n",
"Plug in $\\phi$ and expand\n",
"\n",
"$$\n",
"\\begin{aligned} E &=\\frac{\\left\\langle c_{1} \\chi_{1}+c_{2} \\chi_{2}|\\hat{H}| c_{1} \\chi_{1}+c_{2} \\chi_{2}\\right\\rangle}{\\left\\langle c_{1} \\chi_{1}+c_{2} \\chi_{2} | c_{1} \\chi_{1}+c_{2} \\chi_{2}\\right\\rangle} \\\\ &=\\frac{\\left\\langle c_{1} \\chi_{1}|\\hat{H}| c_{1} \\chi_{1}\\right\\rangle+\\left\\langle c_{1} \\chi_{1}|\\hat{H}| c_{2} \\chi_{2}\\right\\rangle+\\left\\langle c_{2} \\chi_{2}|\\hat{H}| c_{1} \\chi_{1}\\right\\rangle+\\left\\langle c_{2} \\chi_{2}|\\hat{H}| c_{2} \\chi_{2}\\right\\rangle}{\\left\\langle c_{1} \\chi_{1}| c_{1}\\chi_{1}\\right\\rangle+\\left\\langle c_{1} \\chi_{1}| c_{2} \\chi_{2}\\right\\rangle+\\left\\langle c_{2} \\chi_{2} | c_{1} \\chi_{1}\\right\\rangle+\\left\\langle c_{2} \\chi_{2} | c_{2} \\chi_{2}\\right\\rangle} \\\\ &=\\frac{c_{1}^{2}\\left\\langle\\chi_{1}|\\hat{H}| \\chi_{1}\\right\\rangle+ c_{1} c_{2}\\left\\langle\\chi_{1}|\\hat{H}| \\chi_{2}\\right\\rangle+ c_{2} c_{1}\\left\\langle\\chi_{2}|\\hat{H}| \\chi_{1}\\right\\rangle+ c_{2}^{2}\\left\\langle\\chi_{2}|\\hat{H}| \\chi_{2}\\right\\rangle}{c_{1}^{2}\\left\\langle\\chi_{1} | \\chi_{1}\\right\\rangle+ c_{1} c_{2}\\left\\langle\\chi_{1} | \\chi_{2}\\right\\rangle+ c_{2} c_{1}\\left\\langle\\chi_{2} | \\chi_{1}\\right\\rangle+ c_{2}^{2}\\left\\langle \\chi_{2}|\\chi_{2}\\right\\rangle} \\end{aligned}\n",
"$$\n",
"\n",
"If define\n",
"$$\n",
"H_{i j}=\\left\\langle\\chi_{i}|\\hat{H}| \\chi_{j}\\right\\rangle\n",
"\\quad and \\quad \n",
"S_{i j}=\\left\\langle\\chi_{i} | \\chi_{j}\\right\\rangle \n",
"\\tag {Eq3}\n",
"$$\n",
"\n",
" Note: This is where H matrix (same to Fock matrix) and S matrix comes from! We will come build these matrix at part 5.\n",
" \n",
"
\n",
"and note that $H_{ij} = H_{j}$ and $S_{ij} = S_{ji}$ , \n",
"\n",
"$$\n",
"E=\\frac{c_{1}^{2} H_{11}+2 c_{1} c_{2} H_{12}+c_{2}^{2} H_{22}}{c_{1}^{2} S_{11}+2 c_{1} c_{2} S_{12}+c_{2}^{2} S_{22}}\n",
"$$\n",
"\n",
"\n",
"$$\n",
"E\\left(c_{1}^{2} S_{11}+2 c_{1} c_{2} S_{12}+c_{2}^{2} S_{22}\\right)=c_{1}^{2} H_{11}+2 c_{1} c_{2} H_{12}+c_{2}^{2} H_{22}\n",
"$$\n",
"\n",
"To minimize the energy with respect to c1 and c2, we require\n",
"\n",
"$$\n",
"\\frac{\\partial E}{\\partial c_{1}}=0\n",
"\\quad and \\quad\n",
"\\frac{\\partial E}{\\partial c_{2}}=0\n",
"$$\n",
"\n",
"If we differentiate the above equation through separately by c1 and c2 and apply this condition, we will end up with two equations in the two unknowns c1 and c2 , which we can solve to determine the coefficients and the energy.\n",
"\n",
"$$\n",
"\\begin{array}{l}{E\\left(2 c_{1} S_{11}+2 c_{2} S_{12}\\right)=2 c_{1} H_{11}+2 c_{2} H_{12}} \\\\ {E\\left(2 c_{1} S_{12}+2 c_{2} S_{22}\\right)=2 c_{1} H_{12}+2 c_{2} H_{22}}\\end{array}\n",
"$$\n",
"\n",
"These are normally rewritten slightly, in the form\n",
"$$\n",
"\\begin{array}{l}{c_{1}\\left(H_{11}-E S_{11}\\right)+c_{2}\\left(H_{12}-E S_{12}\\right)=0} \\\\ {c_{1}\\left(H_{12}-E S_{12}\\right)+c_{2}\\left(H_{22}-E S_{22}\\right)=0}\\end{array} \\tag{Eq4}\n",
"$$\n",
"Write this in matrix form gives\n",
"$$\n",
"\\left(\\begin{array}{cc}{H_{11}-E S_{11}} & {H_{12}-E S_{12}} \\\\ {H_{12}-E S_{12}} & {H_{22}-E S_{22}}\\end{array}\\right)\\left(\\begin{array}{c}{c_{1}} \\\\ {c_{2}}\\end{array}\\right)=\\left(\\begin{array}{l}{0} \\\\ {0}\\end{array}\\right)\n",
"$$\n",
"For the equations to have a solution, the determinant of the matrix must be equal to zero. Which means\n",
"$$\n",
"\\left(H_{11}-E\\right)\\left(H_{22}-E\\right)-\\left(H_{12}-E S_{12}\\right)^{2}=0\n",
"$$\n",
"Now, there is only one unkown variable E, solve the equation will commonly give us two E (eigenvalue). \n",
"And put this two E back to Eq4 will give us two set of (c1, c2), which corresponding to \n",
"$$\\phi_1 = c_{11} \\chi_1 + c_{21} \\chi_2 \\quad (\\varepsilon_{1})$$\n",
"$$\\phi_2 = c_{12} \\chi_1 + c_{22} \\chi_2 \\quad (\\varepsilon_{2})$$\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thanks for powerful scipy, secular equation could be solved simply by calling \n",
"`eigenvalue, C = scipy.linalg.eigh(H, S)`"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:22.919377Z",
"start_time": "2019-11-18T21:39:22.907722Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-1.97961968 1.03859384]\n",
"[[-0.66167682 1.70635833]\n",
" [-0.37818627 -1.79065634]]\n"
]
}
],
"source": [
"# H and S are calculated from next part\n",
"H = np.array([[-1.85073991, -1.88346692], \n",
" [-1.88346692, -1.58510327]])\n",
"S = np.array([[1. , 0.83752358],\n",
" [0.83752358, 1. ]])\n",
"\n",
"e, Co = scipy.linalg.eigh(H, S)\n",
"\n",
"print(e)\n",
"print(Co)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test if whether the eigenvalue and coefficient satisfy Eq4. \n",
"Note: `[-0.66167682, -0.37818627]` is the eigenvector corresponding to eigenvalue `-1.97961968` \n",
"`[1.70635833, -1.79065634]` is the eigenvector corresponding to eigenvalue `1.03859384` \n",
"The result below $e^{-17}$ and $e^{-16}$ are so close to 0, there is no much difference with 0."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:23.458233Z",
"start_time": "2019-11-18T21:39:23.449378Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.7755575615628914e-17\n",
"8.881784197001252e-16\n"
]
}
],
"source": [
"tmp1 = Co[0, 0] * (H[0, 0] - e[0] * S[0, 0]) + Co[1, 0] * (H[0, 1] - e[0] * S[0, 1])\n",
"tmp2 = Co[0, 1] * (H[0, 1] - e[1] * S[0, 1]) + Co[1, 1] * (H[1, 1] - e[1] * S[1, 1])\n",
"print(tmp1)\n",
"print(tmp2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 5. How to build matrix\n",
"\n",
"Note: To avoid confusion, letters `r`, `s`, `t`, `u` are used to label matrix element and the basis functions $\\chi$, and the letters `i`, `j` are used to label the MOs $\\phi$.\n",
"\n",
"Back to Eq3, $H_{rs}$ in H matrix and $S_{rs}$ in S matrix are defined as \n",
"$$\n",
"H_{r s}=\\left\\langle\\chi_{r}|\\hat{H}| \\chi_{s}\\right\\rangle\n",
"\\quad and \\quad \n",
"S_{r s}=\\left\\langle\\chi_{r} | \\chi_{s}\\right\\rangle \n",
"$$\n",
"\n",
"(a) Hamiltonian core matrix H \n",
"\n",
"Where Hamiltonian core operator $\\hat H$ is \n",
"$$\\hat{H}^{\\mathrm{core}}_i \\equiv-\\frac{1}{2} \\nabla_{i}^{2}-\\sum_{\\alpha} \\frac{Z_{\\alpha}}{r_{i \\alpha}}$$\n",
"\n",
"$$H_{r s}=\\left\\langle\\chi_{r}|\\hat{H}| \\chi_{s}\\right\\rangle\n",
"\\quad $$\n",
"\n",
"$$=\\int_{0}^\\infty \\chi_r \\hat{H} \\chi_s \\; 4\\pi r^2dr$$\n",
"\n",
"$$= \\int_{0}^\\infty \\chi_r ((-\\dfrac{1}{2}) \\nabla^2 -\\sum_{\\alpha} \\frac{Z_{\\alpha}}{r_{i \\alpha}})\\chi_s \\; 4\\pi r^2 dr$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Where $\n",
"{\\text { Laplace operator: } \\nabla^{2}} {=\\frac{1}{r^{2}} \\frac{\\partial}{\\partial r}\\left(r^{2} \\frac{\\partial f}{\\partial r}\\right)=\\frac{1}{r} \\frac{\\partial^{2}}{\\partial r^{2}}(r f)}$\n",
"(For wavefunction which only has radial part.) \n",
"\n",
"And since we are calculating atom, there is only one nuclear $\\alpha$\n",
"\n",
"$$\\therefore H_{rs}= \\int_{0}^\\infty \\chi_r ((-\\dfrac{1}{2}) \\dfrac{1}{r} \\dfrac{\\partial}{\\partial r} \\dfrac{\\partial}{\\partial r} r \\chi_s - \\dfrac{Z_{\\alpha}}{r} \\chi_s )4\\pi r^2 dr$$ \n",
"\n",
"Let's write this in sympy. \n",
"For easy reading, the code below seperate equation above into\n",
"$ H_{rs}= \\int_{0}^\\infty \\chi_r (T - V )4\\pi r^2 dr$ "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:24.224451Z",
"start_time": "2019-11-18T21:39:24.219965Z"
}
},
"outputs": [],
"source": [
"def H_int(fr, fs, Z):\n",
" \"\"\"\n",
" Compute H_core integral between two STO functions.\n",
" H_core = electron kinetics energy + electron nuclear potential energy\n",
"\n",
" INPUT:\n",
" Z: Nuclear charge\n",
" \"\"\"\n",
" T = - ((1 / 2) * (1 / r) * diff(diff(r * fs, r), r))\n",
" V = - (Z / r) * fs\n",
" return sp.integrate(fr * (T + V) * 4 * sp.pi * r * r, (r, 0, +oo))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`H_int` function calculate $H_{rs}$ element in H matrix. To build H matrix, we just need to go over `r` from (1, 2, 3 ... num_bfs), and go over `s` also from (1, 2, 3 ... num_bfs), where `num_bfs` is number of basis functions, we will see this more at below."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:24.816269Z",
"start_time": "2019-11-18T21:39:24.803528Z"
}
},
"outputs": [],
"source": [
"def H_matrix(bfs, Z):\n",
" \"\"\"\n",
" Compute the core hamiltonian matrix H.\n",
" H_core = electron kinetics energy + electron nuclear potential energy\n",
"\n",
" INPUT:\n",
" bfs: basis functions\n",
" Z: nuclear charge\n",
" OUTPUT:\n",
" H: core hamiltonian matrix\n",
" \"\"\"\n",
" num_bfs = len(bfs)\n",
" H = np.zeros((num_bfs, num_bfs))\n",
"\n",
" for r in range(num_bfs):\n",
" for s in range(num_bfs):\n",
" H[r, s] = H_int(bfs[r], bfs[s], Z)\n",
"\n",
" return H"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-16T23:46:32.213610Z",
"start_time": "2019-11-16T23:46:32.193048Z"
}
},
"source": [
"(b) Overlap matrix S \n",
"\n",
"If you understand H matrix, S (Overlap) matrix will be very easy.\n",
"\n",
"$$S_{rs} = \\int_{0}^\\infty \\chi_r^* \\chi_s \\; 4 \\pi r^2dr$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:25.430921Z",
"start_time": "2019-11-18T21:39:25.425617Z"
}
},
"outputs": [],
"source": [
"def S_int(fr, fs):\n",
" \"\"\"\n",
" Compute overlap integral between two STO functions.\n",
" \"\"\"\n",
" return sp.integrate(fr * fs * 4 * sp.pi * r * r, (r, 0, +oo))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:25.742399Z",
"start_time": "2019-11-18T21:39:25.737856Z"
}
},
"outputs": [],
"source": [
"def S_matrix(bfs):\n",
" \"\"\"\n",
" Compute overlap matrix S.\n",
"\n",
" INPUT:\n",
" fs: basis functions\n",
" OUTPUT:\n",
" S: Overlap matrix\n",
" \"\"\"\n",
" num_bfs = len(bfs)\n",
" S = np.zeros((num_bfs, num_bfs))\n",
"\n",
" for r in range(num_bfs):\n",
" for s in range(num_bfs):\n",
" S[r, s] = S_int(bfs[r], bfs[s])\n",
"\n",
" return S"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(c) Fock matrix F \n",
"Fock matrix F = H matrix + G matrix \n",
"\n",
"Fock matrix could be generated similarly like H, where Fock operator is \n",
"$$\\hat{F}(i)=\\hat{H}_{core}(i)+\\sum_{j=1}^{n / 2}\\left[2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)\\right]$$\n",
"\n",
"The second term is often denoted as $\\hat G$.\n",
"\n",
"$$\\hat{F}(i)=\\hat{H}_{core}(i)+\\hat G$$\n",
"\n",
"Because we already have **H matrix** above, so we only need to build **G matrix**, add them together will generate **Fock matrix**. \n",
"\n",
"G matrix \n",
"\n",
"The defination of $J$ (Coulomb operator) and $K$ (exchange operator) are. (1) (2) below simple means they are different electron.\n",
"\n",
"$$\n",
"\\begin{aligned} \\hat{J}_{j}(1) f(1) &=f(1) \\int\\left|\\phi_{j}(2)\\right|^{2} \\frac{1}{r_{12}} d v_{2} \\\\ \\hat{K}_{j}(1) f(1) &=\\phi_{j}(1) \\int \\frac{\\phi_{j}^{*}(2) f(2)}{r_{12}} d v_{2} \\end{aligned}\n",
"$$\n",
"\n",
"\n",
" Note: \n",
" ${\\displaystyle f(1)}$, ${\\displaystyle f(2)}$ are the one-electron wavefunctions acted upon by the exchange operator as functions of the electron positions, and ${\\displaystyle \\phi _{j}(1)}$ and ${\\displaystyle \\phi _{j}(2)}$ are the one-electron wavefunction of the jth electron as functions of the positions of the electrons.\n",
" \n",
"
\n",
"\n",
"\n",
"Let's see the result first, we will walk through an example ($G_{12}$ of helium) below explain how to get here. (Basically, it's just expand $\\phi_i$ into linear combination of the basis functions.)\n",
"$$\n",
"\\left\\langle\\chi_{r}(1) | \\hat{J}_{j}(1) \\chi_{s}(1)\\right\\rangle=\\sum_{t} \\sum_{u} c_{t j}^{*} c_{u j} \\iint \\frac{\\chi_{r}^{*}(1) \\chi_{s}(1) \\chi_{t}^{*}(2) \\chi_{u}(2)}{r_{12}} d v_{1} d v_{2}\n",
"$$\n",
"$$\n",
"\\left\\langle\\chi_{r}(1) | \\hat{K}_{j}(1) \\chi_{s}(1)\\right\\rangle=\\sum_{t} \\sum_{u} c_{t j}^{*} c_{u j} \\iint \\frac{\\chi_{r}^{*}(1) \\chi_{u}(1) \\chi_{t}^{*}(2) \\chi_{s}(2)}{r_{12}} d v_{1} d v_{2}\n",
"$$\n",
"If define\n",
"\n",
"$$\n",
"(r s | t u) \\equiv \\iint \\frac{\\chi_{r}^{*}(1) \\chi_{s}(1) \\chi_{t}^{*}(2) \\chi_{u}(2)}{r_{12}} d v_{1} d v_{2}\n",
"$$\n",
"\n",
"It could be rewritten as\n",
"$$\n",
"\\left\\langle\\chi_{r}(1) | \\hat{J}_{j}(1) \\chi_{s}(1)\\right\\rangle=\\sum_{t=1}^{b} \\sum_{u=1}^{b} c_{t j}^{*} c_{u j}(r s | t u)\n",
"$$\n",
"\n",
"$$\n",
"\\left\\langle\\chi_{r}(1) | \\hat{K}_{j}(1) \\chi_{s}(1)\\right\\rangle=\\sum_{t=1}^{b} \\sum_{u=1}^{b} c_{t j}^{*} c_{u j}(r u | t s)\n",
"$$\n",
"And final $G_{rs}$ will be\n",
"$$\n",
"G_{r s}=\\sum_{t=1}^{b} \\sum_{u=1}^{b} \\sum_{j=1}^{n / 2} c_{t j}^{*} c_{u j}[2(r s | t u)-(r u | t s)]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-17T02:31:33.798505Z",
"start_time": "2019-11-17T02:31:33.787851Z"
}
},
"source": [
"\n",
"\n",
" Example: \n",
"Let's take $G_{12}$ element in G matrix (Helium atom) as an example to see how this comes out. (click to uncollapse)\n",
" \n",
"\n",
"\n",
"$$G_{r s}=\\left\\langle\\chi_{r}|\\hat{G}| \\chi_{s}\\right\\rangle$$\n",
"$$G_{1 2}=\\left\\langle\\chi_{1}|\\hat{G}| \\chi_{2}\\right\\rangle$$\n",
"\n",
"$$G_{1 2}= \\sum_{j=1}^{n / 2} \\left\\langle\\chi_{1}|2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle$$\n",
"\n",
"For helium atom, num of electron (n) is 2, there is only one 1s orbital.\n",
"\n",
"$$G_{1 2}= \\left\\langle\\chi_{1}|2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle$$\n",
"$$G_{1 2}= 2\\left\\langle\\chi_{1}| \\hat{J}_{j}(i)| \\chi_{2}\\right\\rangle - \\left\\langle\\chi_{1}|\\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle$$\n",
"\n",
"Let's do $\\left\\langle\\chi_{1}| \\hat{J}_{j}(i)| \\chi_{2}\\right\\rangle$ first \n",
"\n",
"$$\\left\\langle\\chi_{1}(1)| \\hat{J}_{1}| \\chi_{2}(1)\\right\\rangle $$ \n",
"$$= \\left\\langle\\chi_{1}(1)| \\;\\;\\; \\int \\frac{\\left|\\phi_1(2)\\right|^{2}}{r_{12}} d v_{2} \\;\\;\\; | \\chi_{2}(1)\\right\\rangle $$ \n",
"$$\n",
"= \\int \\int \\frac{\\phi_1(2)^*\\phi_1(2) \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$\n",
"\n",
"$$\n",
"= \\int \\int \\frac{[c_{11}\\chi_{1}^*(2) + c_{21}\\chi_{2}^*(2)][c_{11}\\chi_{1}(2) + c_{21}\\chi_{2}(2)] \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$\n",
"\n",
"\n",
"$$\n",
"= \\int \\int \\frac{c_{11}\\chi_{1}^*(2)c_{11}\\chi_{1}(2) \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"+ \\int \\int \\frac{c_{11}\\chi_{1}^*(2)c_{21}\\chi_{2}(2) \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$\n",
"$$\n",
"+ \\int \\int \\frac{c_{21}\\chi_{2}^*(2)c_{11}\\chi_{1}(2) \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"+ \\int \\int \\frac{c_{21}\\chi_{2}^*(2)c_{21}\\chi_{2}(2) \\chi (1)^* \\chi (1)}{r_{12}} d v_{2}d v_{1}\n",
"$$\n",
"\n",
"Use \n",
"$\n",
"(r s | t u) \\equiv \\iint \\frac{\\chi_{r}^{*}(1) \\chi_{s}(1) \\chi_{t}^{*}(2) \\chi_{u}(2)}{r_{12}} d v_{1} d v_{2}\n",
"$ to simplify the representation.\n",
"\n",
"$$\n",
"\\left\\langle\\chi_{1}| \\hat{J}_{j}(i)| \\chi_{2}\\right\\rangle\n",
"= c_{11}c_{11}(1 2 | 1 1) + c_{11}c_{21}(1 2 | 1 2) + c_{21}c_{11}(1 2 | 2 1) + c_{21}c_{21}(1 2 | 2 2)\n",
"$$\n",
"$$\n",
"=\\sum_{t=1}^{2} \\sum_{u=1}^{2} \\sum_{j=1}^{2 / 2} c_{t j}^{*} c_{u j} (1 \\;2 | t \\;u)\n",
"$$\n",
"\n",
"Similar $\\left\\langle\\chi_{1}| \\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle$ could also be inferred, \n",
"$$\n",
"\\left\\langle\\chi_{1}| \\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle\n",
"= c_{11}c_{11}(1 1 | 1 2) + c_{11}c_{21}(1 2 | 1 2) + c_{21}c_{11}(1 1 | 2 2) + c_{21}c_{21}(1 2 | 2 2)\n",
"$$\n",
"$$\n",
"=\\sum_{t=1}^{2} \\sum_{u=1}^{2} \\sum_{j=1}^{2 / 2} c_{t j}^{*} c_{u j} (1 \\;u | t \\;2)\n",
"$$\n",
"\n",
"So $G_{1 2}$ is \n",
"$$G_{1 2}= \\left\\langle\\chi_{1}|2 \\hat{J}_{j}(i)-\\hat{K}_{j}(i)| \\chi_{2}\\right\\rangle$$\n",
"$$\n",
"=\\sum_{t=1}^{2} \\sum_{u=1}^{2} \\sum_{j=1}^{2 / 2} c_{t j}^{*} c_{u j}[2(1 \\;2 | t \\;u)-(1\\; u | t \\;2)]\n",
"$$\n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Build G matrix in python\n",
"\n",
"recall $G_{rs}$ is\n",
"$$\n",
"G_{r s}=\\sum_{t=1}^{b} \\sum_{u=1}^{b} \\sum_{j=1}^{n / 2} c_{t j}^{*} c_{u j}[2(r s | t u)-(r u | t s)]\n",
"$$\n",
"\n",
"If define $P_{rs}$ (density matrix) as \n",
"$$\n",
"P_{t u} \\equiv 2 \\sum_{j=1}^{n / 2} c_{t j}^{*} c_{u j}, \\quad t=1,2, \\ldots, b, \\quad u=1,2, \\ldots, b\n",
"$$\n",
"\n",
"Then $G_{rs}$ could be simplified again as \n",
"$$\n",
"G_{r s}=\\sum_{t=1}^{b} \\sum_{u=1}^{b} P_{t u}\\left[(r s | t u)-\\frac{1}{2}(r u | t s)\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we built a matrix **R** which is 4 dimension, and save all the posible $(r s | t u)$, then we could build G matrix like below."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:27.304275Z",
"start_time": "2019-11-18T21:39:27.297301Z"
}
},
"outputs": [],
"source": [
"def G_matrix(P, R):\n",
" \"\"\"\n",
" Compute G matrix.\n",
" G = coulombic repulsion energy + exchange energy\n",
"\n",
" INPUT:\n",
" P: density matrix\n",
" R: electron repulsion matrix\n",
" OUTPUT:\n",
" G: repulsion matrix\n",
" \"\"\"\n",
" num_bfs = P.shape[0]\n",
" G = np.zeros((num_bfs, num_bfs))\n",
"\n",
" for r in range(num_bfs):\n",
" for s in range(num_bfs):\n",
" g = 0\n",
" for t in range(num_bfs):\n",
" for u in range(num_bfs):\n",
" int1 = R[r, s, t, u]\n",
" int2 = R[r, u, t, s]\n",
" g += P[t, u] * (int1 - 0.5 * int2)\n",
" G[r, s] = g\n",
"\n",
" return G"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
P matrix \n",
"\n",
"And also P (density) matrix\n",
"$$\n",
"P_{t u} \\equiv 2 \\sum_{j=1}^{n / 2} c_{t j}^{*} c_{u j}, \\quad t=1,2, \\ldots, b, \\quad u=1,2, \\ldots, b\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:27.989772Z",
"start_time": "2019-11-18T21:39:27.983154Z"
}
},
"outputs": [],
"source": [
"def P_matrix(Co, N):\n",
" \"\"\"\n",
" Compute density matrix P.\n",
"\n",
" INPUT:\n",
" Co: coefficents matrix\n",
" N: num of electrons\n",
" OUTPUT:\n",
" P: repulsion matrix\n",
" \"\"\"\n",
" P = np.zeros([Co.shape[0], Co.shape[0]])\n",
"\n",
" for t in range(Co.shape[0]):\n",
" for u in range(Co.shape[0]):\n",
" for j in range(int(N/2)):\n",
" P[t, u] += 2 * Co[t, j] * Co[u, j]\n",
" return P"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-17T01:14:10.661943Z",
"start_time": "2019-11-17T01:14:10.654184Z"
}
},
"source": [
"R matrix \n",
"\n",
"R matrix (4 dimenstion), which is the most computation-expensive part in hartree-fock method. (In principle, there are a lot of elements in R matrix are equal by symmetry, but for code simplicity, we didn't implemented this.)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:28.716995Z",
"start_time": "2019-11-18T21:39:28.708282Z"
}
},
"outputs": [],
"source": [
"def R_matrix(bfs):\n",
" \"\"\"\n",
" Compute the electron repulsion integral matrix R.\n",
"\n",
" INPUT:\n",
" fs: basis functions\n",
" OUTPUT:\n",
" R: repulsion matrix\n",
" \"\"\"\n",
" start = time.time()\n",
" num_bfs = len(bfs)\n",
" R = np.zeros((num_bfs, num_bfs, num_bfs, num_bfs))\n",
"\n",
" for r in range(num_bfs):\n",
" for s in range(num_bfs):\n",
" for t in range(num_bfs):\n",
" for u in range(num_bfs):\n",
" R[r, s, t, u] = R_int([bfs[r], bfs[s], bfs[t], bfs[u]])\n",
"\n",
" stop = time.time()\n",
" print('time Repu: {:.1f} s'.format(stop-start))\n",
" return R"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-17T01:17:53.730961Z",
"start_time": "2019-11-17T01:17:53.724470Z"
}
},
"source": [
"Recall the element $R_{rstu}$ in R matrix is \n",
"$$\n",
"(r s | t u) \\equiv \\iint \\frac{\\chi_{r}^{*}(1) \\chi_{s}(1) \\chi_{t}^{*}(2) \\chi_{u}(2)}{r_{12}} d v_{1} d v_{2}\n",
"$$\n",
"\n",
"For 1s or 2s orbital which only has radial part, this could be calculated approximately in sympy. However, for the orbitals which has angular part, how to solve two-electron Repulsion integral of Slater Type Orbital (STO) is still slow and difficult. This is the main reason why Gaussian Type Orbital (GTO) is more frequently used, and we will try GTO in next chapter.\n",
"\n",
"$$(rs|tu) = \\int_{0}^\\infty \\int_{0}^\\infty \\dfrac{\\chi_r^*(1) \\chi_s(1) \\chi_t^*(2) \\chi_u(2)}{r_{12}} \\; 4 \\pi r_1^2dr_1\\; 4 \\pi r_2^2dr_2 $$\n",
"\n",
"$$(rs|tu) = \\int_{0}^\\infty \\chi_r^*(1) \\chi_s(1) \\; 4 \\pi r_1^2dr_1\\int_{0}^\\infty \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{12}}\\; 4 \\pi r_2^2dr_2 $$\n",
"\n",
"$r_{12}$ here is tricky to deal with, from problem 9.14 in quantum_chemistry by levine\n",
"\n",
"$$(rs|tu) = \\int_{0}^\\infty \\chi_r^*(1) \\chi_s(1) \\; 4 \\pi r_1^2dr_1\\int_{0}^\\infty \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{>}}\\; 4 \\pi r_2^2dr_2 $$\n",
"\n",
" Note: \n",
" $r_{>}$ is the larger one between $r1$ and $r2$\n",
" \n",
"
\n",
"$$(rs|tu) = \\int_{0}^\\infty \\chi_r^*(1) \\chi_s(1) \\; 4 \\pi r_1^2dr_1(\\int_{0}^{r_1} \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{1}}\\; 4 \\pi r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{2}}\\; 4 \\pi r_2^2dr_2) $$\n",
"\n",
"Let$ \\; B= \\int_{0}^{r_1} \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{1}}\\; 4 \\pi r_2^2dr_2 + \\int_{r_1}^\\infty \\frac{ \\chi_t^*(2) \\chi_u(2)}{r_{2}}\\; 4 \\pi r_2^2dr_2$\n",
"\n",
"$$(rs|tu) = \\int_{0}^\\infty \\chi_r^*(1) \\chi_s(1) B \\; 4 \\pi r_1^2 dr_1 $$\n",
"\n",
"So the element $R_{rstu}$ in R matrix could be calculated by"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:29.702699Z",
"start_time": "2019-11-18T21:39:29.694802Z"
}
},
"outputs": [],
"source": [
"def R_int(four_bfs):\n",
" \"\"\"\n",
" Compute electron-electron repulsion integral.\n",
"\n",
" INPUT:\n",
" four_bfs: an array contain 4 basis functions\n",
" \"\"\"\n",
" f1, f2, f3, f4 = four_bfs\n",
"\n",
" f1 = f1.subs(r, r1)\n",
" f2 = f2.subs(r, r1)\n",
" f3 = f3.subs(r, r2)\n",
" f4 = f4.subs(r, r2)\n",
"\n",
" B = (1 / r1) * sp.integrate(f3 * f4 * 4 * sp.pi * r2 * r2, (r2, 0, r1)) + sp.integrate((1 / r2) * f3 * f4 * 4 * sp.pi * r2 * r2, (r2, r1, +oo))\n",
" return sp.integrate(f1 * f2 * 4 * sp.pi * r1 * r1 * B, (r1, 0, +oo))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is basically all the matrixes we will need to use, and we already solved the most difficult part of hartree fock!! \n",
"\n",
"### 6. Secular Equation\n",
"\n",
"**Fock matrix** is the sum of **H matrix** and **G matrix**. \n",
"F = H + G\n",
"\n",
"Then, Roothan equation could be solved simply by calling \n",
"`eigenvalue, C = scipy.linalg.eigh(F, S)` \n",
"eigenvalues are MO orbital energies.\n",
"\n",
"$${\\mathbf {F}}{\\mathbf {C}}={\\mathbf {S}}{\\mathbf {C}}{\\mathbf {\\epsilon }}$$\n",
"
\n",
" Note: \n",
" F (Fock matrix), S (Overlap matrix) are inputs. \n",
" S matrix is fixed, F matrix is changing every iteration because of the improved C. \n",
" C (Coefficient matrix) and $\\epsilon_i$ (eigenvalues) are results.\n",
" \n",
"
\n",
"\n",
"We could wrap `scipy.linalg.eigh` into a function"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:30.403598Z",
"start_time": "2019-11-18T21:39:30.399630Z"
}
},
"outputs": [],
"source": [
"def secular_eqn(F, S):\n",
" \"\"\"\n",
" Slove secular equation, return the MO energies (eigenvalue) and improved coeffients (eigenvector)\n",
"\n",
" INPUT:\n",
" F: fock matrix or h_core matrix\n",
" S: overlap integral\n",
" OUTPUT:\n",
" ei: eigenvalue\n",
" C: eigenvector\n",
" \"\"\"\n",
" ei, C = scipy.linalg.eigh(F, S)\n",
" return ei, C"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 7. Total Energy\n",
"Finally, hartree fock total energy is \n",
"$$\n",
"E_{\\mathrm{HF}}=2 \\sum_{i=1}^{n / 2} \\varepsilon_{i}-\\sum_{i=1}^{n / 2} \\sum_{j=1}^{n / 2}\\left(2 J_{i j}-K_{i j}\\right)+V_{N N}\n",
"$$\n",
"
\n",
" Note: \n",
" i, j are electron (only r, s, t, u are used for matrix element)\n",
" \n",
"
\n",
"\n",
"Where every term is \n",
"1. Energy of all the electrons (in closed shell condition, every orbital is doubly-occupied)\n",
"2. Recall that when we build F operator and calculat electron energy, electron-electron repulsion is counted twice when you sum all the electrons energy. This is the remove the extra count.\n",
"3. Nuclear-Nuclear repulsion term, which is not included in F operator. (because we are calculating Atom, this term is always 0)\n",
"\n",
"half sum of the all the electrons $({n / 2})$ could also be written as \n",
"$$\n",
"\\sum_{i=1}^{n / 2} \\varepsilon_{i}=\\sum_{i=1}^{n / 2} H_{i i}^{\\mathrm{core}}+\\sum_{i=1}^{n / 2} \\sum_{j=1}^{n / 2}\\left(2 J_{i j}-K_{i j}\\right)\n",
"$$\n",
"\n",
"So $E_{\\mathrm{HF}}$ could be simplifed as \n",
"$$\n",
"E_{\\mathrm{HF}}=\\sum_{i=1}^{n / 2} \\varepsilon_{i}+\\sum_{i=1}^{n / 2} H_{i i}^{\\mathrm{core}}+V_{N N}\n",
"$$ \n",
"
\n",
" Note: \n",
" i, j are electron (only r, s, t, u are used for matrix element) \n",
" H here is not H matrix, which is $\n",
"H_{i i}^{\\text {core }}=\\left\\langle\\phi_{i}\\left|\\hat{H}^{\\text {core }}\\right| \\phi_{i}\\right\\rangle\n",
"$\n",
" \n",
"
\n",
"\n",
"Expand $\\phi_{i}$ into basis functions and simplify, we could calculate total energy using the matrix we have built before.\n",
"$$\n",
"E_{\\mathrm{HF}}=\\sum_{i=1}^{n / 2} \\varepsilon_{i}+\\frac{1}{2} \\sum_{r=1}^{b} \\sum_{s=1}^{b} P_{r s} H_{r s}^{\\mathrm{core}}+V_{N N}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:31.050893Z",
"start_time": "2019-11-18T21:39:31.045024Z"
}
},
"outputs": [],
"source": [
"def energy_tot(e, N, P, H, Vnn=0):\n",
" \"\"\"\n",
" Compute the total energy.\n",
"\n",
" INPUT:\n",
" e: MO energies\n",
" N: num of electrons\n",
" P: density matrix\n",
" H: h_core matrix\n",
" Vnn: nuclear nuclear repulsion energy, for atom is 0\n",
" \"\"\"\n",
" e_tot = 0\n",
"\n",
" for i in range(int(N/2)):\n",
" e_tot += e[i].real\n",
"\n",
" e_tot = e_tot + 0.5 * (P * H).sum() + Vnn\n",
" return e_tot"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-17T17:58:53.611565Z",
"start_time": "2019-11-17T17:58:53.606125Z"
}
},
"source": [
"### 8. Utils"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And also some utils function to print information and compare our result with reference"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:32.284994Z",
"start_time": "2019-11-18T21:39:32.273100Z"
}
},
"outputs": [],
"source": [
"def print_info(S, H, e, Co, P, hf_e, start, stop, delta_e=0, verbose=False):\n",
" \"\"\"\n",
" Print information while doing SCF interations.\n",
" \"\"\"\n",
" if(verbose):\n",
" # overlap\n",
" print('Overlap:')\n",
" print(S)\n",
"\n",
" # hamiltonian\n",
" print('Core hamiltonian:')\n",
" print(H)\n",
"\n",
" # Co\n",
" print('Coefficients:')\n",
" print(Co)\n",
"\n",
" # density\n",
" print('Density matrix:')\n",
" print(P)\n",
"\n",
" # MOs\n",
" print('MO energies:')\n",
" message = ', '\n",
" m_list = ['e{} = {:0.3f}'.format(i+1, x) for i, x in enumerate(e)]\n",
" message = message.join(m_list)\n",
" print(message)\n",
"\n",
" print('HF energy: {:0.5f} (hartree) = {:0.5f} (eV)'.format(hf_e, hf_e*27.211))\n",
" if delta_e != 0:\n",
" print('dE : {:.2e}'.format(delta_e))\n",
" print('time used: {:.1f} s'.format(stop-start))\n",
"\n",
"\n",
"def compare(cal, ref, tol=1.0e-4):\n",
" \"\"\"\n",
" Compare calculated result with reference data.\n",
" \"\"\"\n",
" delta = np.abs(ref - cal)\n",
" if delta < tol:\n",
" message = '\\33[32m' + 'PASSED' + '\\x1b[0m'\n",
" else:\n",
" message = '\\033[91m' + 'FAILED' + '\\033[0m'\n",
" print('-' * 32, message, '-' * 33)\n",
" print('cal: {:.7f}, ref: {:.7f}\\n\\n'.format(cal, ref))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 9. Run Hartree Fock\n",
"\n",
"Steps to run hartree fock\n",
"\n",
"1. Initialization\n",
" - Let Fock matrix = H_core matrix, without considering electron repulsion\n",
" - Solve secular equation with H and S to get initial Co (means initial guessed molecular orbitals) and build inital P (density) matrix\n",
" - Prepare Repulsion matrix R (take time)\n",
"2. Iteration\n",
" - Using P matrix and R matrix to calculate G matrix\n",
" - F matrix = H matrix + G matrix\n",
" - Solve secular equation with F and S to get improved Co (means improved molecular orbitals)\n",
" - Using improved Co to build improved P matrix\n",
" - check whether converged (the change of total energy smaller than converge requirement)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:33.472759Z",
"start_time": "2019-11-18T21:39:33.461574Z"
}
},
"outputs": [],
"source": [
"def run_hf(bfs, Z):\n",
" \"\"\"\n",
" Run restricted hartree fock for a single atom.\n",
"\n",
" INPUT:\n",
" bfs: basis functions\n",
" Z: nuclear charge of the atom\n",
" \"\"\"\n",
" print('------------------------------', \"Initialization\", '------------------------------')\n",
" print('-------------------------', \"Ignore repulsion integral\", '------------------------')\n",
" N = Z # num of electron = nuclear charege (since it's atom)\n",
" start = time.time()\n",
"\n",
" # initialization\n",
" H = H_matrix(bfs, Z)\n",
" S = S_matrix(bfs)\n",
" e, Co = secular_eqn(H, S)\n",
" P = P_matrix(Co, N)\n",
" Vnn = 0 # A single atom does not have nuclear repulsion\n",
" hf_e = energy_tot(e, N, P, H, Vnn)\n",
"\n",
" stop = time.time()\n",
" print_info(S, H, e, Co, P, hf_e, start, stop, verbose=verbose)\n",
" print('-----------', \"Caculating Electron Repulsion Integral (takes time)\", '------------')\n",
" R = R_matrix(bfs)\n",
" delta_e = 1\n",
" ITER = 0\n",
" previous_e = hf_e\n",
"\n",
" # Iterations\n",
" while(delta_e > E_conv and ITER < MAXITER):\n",
" print('------------------------------', \"Iteration\", ITER + 1, '------------------------------')\n",
" start = time.time()\n",
"\n",
" # important scf steps\n",
" G = G_matrix(P, R)\n",
" F = H + G\n",
" e, Co = secular_eqn(F, S)\n",
" P = P_matrix(Co, N)\n",
" hf_e = energy_tot(e, N, P, H, Vnn)\n",
"\n",
" delta_e = np.abs(hf_e - previous_e)\n",
" previous_e = hf_e\n",
" ITER += 1\n",
" stop = time.time()\n",
" print_info(S, H, e, Co, P, hf_e, start, stop, delta_e, verbose=verbose)\n",
"\n",
" return hf_e"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Set converge criterion"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:34.613355Z",
"start_time": "2019-11-18T21:39:34.609672Z"
}
},
"outputs": [],
"source": [
"MAXITER = 40 # Maximum SCF iterations\n",
"E_conv = 1.0e-6 # Energy convergence criterion\n",
"verbose = False # whether to print matrix information while iterating"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 10. Test\n",
"\n",
"
Run hartree fock for Helium "
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-19T03:01:59.843709Z",
"start_time": "2019-11-19T03:01:59.771743Z"
},
"scrolled": true
},
"outputs": [],
"source": [
"def test1():\n",
" # Use 2 Slater Type ourbital to represent Helium 1s orbital.\n",
" # The final Helium 1s orbital is a linear combination of these two STO.\n",
" f1s_1 = STO(zeta=1.45363, n=1)\n",
" f1s_2 = STO(zeta=2.91093, n=1)\n",
"\n",
" # all basis functions\n",
" fs = [f1s_1, f1s_2]\n",
"\n",
" # nuclear charge of He\n",
" Z = 2\n",
"\n",
" # run hartree fock\n",
" hf_e = run_hf(fs, Z)\n",
"\n",
" # compare result with reference\n",
" ref_hf_e = -2.8616726\n",
" compare(hf_e, ref_hf_e)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:39.253712Z",
"start_time": "2019-11-18T21:39:35.764456Z"
},
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------------------------------ Initialization ------------------------------\n",
"------------------------- Ignore repulsion integral ------------------------\n",
"HF energy: -3.95924 (hartree) = -107.73486 (eV)\n",
"time used: 0.2 s\n",
"----------- Caculating Electron Repulsion Integral (takes time) ------------\n",
"time Repu: 3.2 s\n",
"------------------------------ Iteration 1 ------------------------------\n",
"HF energy: -2.78457 (hartree) = -75.77099 (eV)\n",
"dE : 1.17e+00\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 2 ------------------------------\n",
"HF energy: -2.85860 (hartree) = -77.78532 (eV)\n",
"dE : 7.40e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 3 ------------------------------\n",
"HF energy: -2.86152 (hartree) = -77.86490 (eV)\n",
"dE : 2.92e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 4 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86877 (eV)\n",
"dE : 1.42e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 5 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86896 (eV)\n",
"dE : 7.01e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 6 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86897 (eV)\n",
"dE : 3.45e-07\n",
"time used: 0.0 s\n",
"-------------------------------- \u001b[32mPASSED\u001b[0m ---------------------------------\n",
"cal: -2.8616726, ref: -2.8616726\n",
"\n",
"\n"
]
}
],
"source": [
"test1()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Run hartree fock for Beryllium "
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:39:39.271108Z",
"start_time": "2019-11-18T21:39:39.256567Z"
}
},
"outputs": [],
"source": [
"def test2():\n",
" \"\"\"\n",
" Test of Be (1s, 2s)\n",
" \"\"\"\n",
" # Use 2 STO to represent Be 1s orbital and another 2 STO for 2s orbital\n",
" # The final 1s orbital is a linear combination of these 4 STO.\n",
" # Same for 2s orbital.\n",
" f1s_1 = STO(zeta=5.59108, n=1)\n",
" f1s_2 = STO(zeta=3.35538, n=1)\n",
" f2s_1 = STO(zeta=1.01122, n=2)\n",
" f2s_2 = STO(zeta=0.61000, n=2)\n",
"\n",
" # all basis functions\n",
" fs = [f1s_1, f1s_2, f2s_1, f2s_2]\n",
"\n",
" # nuclear charge of Be\n",
" Z = 4\n",
"\n",
" # run hartree fock\n",
" hf_e = run_hf(fs, Z)\n",
"\n",
" # compare result with reference\n",
" ref_hf_e = -14.572369\n",
" compare(hf_e, ref_hf_e)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T21:40:37.419340Z",
"start_time": "2019-11-18T21:39:39.274384Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------------------------------ Initialization ------------------------------\n",
"------------------------- Ignore repulsion integral ------------------------\n",
"HF energy: -19.51846 (hartree) = -531.11686 (eV)\n",
"time used: 1.0 s\n",
"----------- Caculating Electron Repulsion Integral (takes time) ------------\n",
"time Repu: 56.9 s\n",
"------------------------------ Iteration 1 ------------------------------\n",
"HF energy: -14.28744 (hartree) = -388.77544 (eV)\n",
"dE : 5.23e+00\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 2 ------------------------------\n",
"HF energy: -14.50425 (hartree) = -394.67518 (eV)\n",
"dE : 2.17e-01\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 3 ------------------------------\n",
"HF energy: -14.55105 (hartree) = -395.94867 (eV)\n",
"dE : 4.68e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 4 ------------------------------\n",
"HF energy: -14.56616 (hartree) = -396.35976 (eV)\n",
"dE : 1.51e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 5 ------------------------------\n",
"HF energy: -14.57061 (hartree) = -396.48075 (eV)\n",
"dE : 4.45e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 6 ------------------------------\n",
"HF energy: -14.57187 (hartree) = -396.51521 (eV)\n",
"dE : 1.27e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 7 ------------------------------\n",
"HF energy: -14.57223 (hartree) = -396.52493 (eV)\n",
"dE : 3.57e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 8 ------------------------------\n",
"HF energy: -14.57233 (hartree) = -396.52766 (eV)\n",
"dE : 1.01e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 9 ------------------------------\n",
"HF energy: -14.57236 (hartree) = -396.52843 (eV)\n",
"dE : 2.83e-05\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 10 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52865 (eV)\n",
"dE : 7.94e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 11 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52871 (eV)\n",
"dE : 2.23e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 12 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52872 (eV)\n",
"dE : 6.27e-07\n",
"time used: 0.0 s\n",
"-------------------------------- \u001b[32mPASSED\u001b[0m ---------------------------------\n",
"cal: -14.5723687, ref: -14.5723690\n",
"\n",
"\n"
]
}
],
"source": [
"test2()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 11. Excise - Plot the charge density of orbitals\n",
"Write a function based on the code of `run_hf()`, plot the charge density $4 \\pi r^2 |\\phi_i|^2$ of all the orbitals (final iteration).\n",
"\n",
"For example, Beryllium:\n",
"Note: You only need to plot the final one (most bottom) \n",
"Hint see below.\n",
"![](https://yyrcd-1256568788.cos.na-siliconvalley.myqcloud.com/yyrcd/2019-11-18-221449.png)"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:29:23.052587Z",
"start_time": "2019-11-18T22:29:23.048102Z"
}
},
"source": [
"Hint: convert a sympy expression to python function by using [sp.lambdify()](https://docs.sympy.org/latest/modules/numeric-computation.html#lambdify) \n",
"For example, to plot $\\chi_1$, which is the 1st wavefunction of Beryllium Basis set."
]
},
{
"cell_type": "code",
"execution_count": 88,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:33:27.002531Z",
"start_time": "2019-11-18T22:33:26.952113Z"
}
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{13.2203684670961 e^{- 5.59108 r}}{\\sqrt{\\pi}}$"
],
"text/plain": [
" -5.59108⋅r\n",
"13.2203684670961⋅ℯ \n",
"────────────────────────────\n",
" √π "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f1s_1 = STO(zeta=5.59108, n=1)\n",
"display(f1s_1)\n",
"f = sp.lambdify(r, f1s_1, \"numpy\")"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:35:40.036531Z",
"start_time": "2019-11-18T22:35:39.880792Z"
}
},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(0, 5, 300)\n",
"y = f(x)\n",
"plt.figure(figsize=(16,2))\n",
"plt.plot(x, y, label='$\\chi_{}$'.format(1))\n",
"plt.legend()\n",
"plt.xlim(0, x[-1])\n",
"plt.xlabel('r')\n",
"plt.ylabel('$\\chi_1$')\n",
"plt.title('Wavefunction of $\\chi_1$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Code below is example solution "
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:19:08.517819Z",
"start_time": "2019-11-18T22:19:08.503756Z"
}
},
"outputs": [],
"source": [
"def run_hf(bfs, Z):\n",
" \"\"\"\n",
" Run restricted hartree fock for a single atom.\n",
"\n",
" INPUT:\n",
" bfs: basis functions\n",
" Z: nuclear charge of the atom\n",
" \"\"\"\n",
" print('------------------------------', \"Initialization\", '------------------------------')\n",
" print('-------------------------', \"Ignore repulsion integral\", '------------------------')\n",
" N = Z # num of electron = nuclear charege (since it's atom)\n",
" start = time.time()\n",
"\n",
" # initialization\n",
" H = H_matrix(bfs, Z)\n",
" S = S_matrix(bfs)\n",
" e, Co = secular_eqn(H, S)\n",
" P = P_matrix(Co, N)\n",
" Vnn = 0 # A single atom does not have nuclear repulsion\n",
" hf_e = energy_tot(e, N, P, H, Vnn)\n",
"\n",
" stop = time.time()\n",
" print_info(S, H, e, Co, P, hf_e, start, stop, verbose=verbose)\n",
" print('-----------', \"Caculating Electron Repulsion Integral (takes time)\", '------------')\n",
" R = R_matrix(bfs)\n",
" delta_e = 1\n",
" ITER = 0\n",
" previous_e = hf_e\n",
"\n",
" densities = [] # [[d1, d2], [d1, d2], [d1, d2]]\n",
" # plot \n",
" x = np.linspace(0, 5, 300)\n",
" tmp_density = get_density(bfs, Co, x)\n",
" densities.append(tmp_density)\n",
"\n",
" # Iterations\n",
" while(delta_e > E_conv and ITER < MAXITER):\n",
" print('------------------------------', \"Iteration\", ITER + 1, '------------------------------')\n",
" start = time.time()\n",
"\n",
" # important scf steps\n",
" G = G_matrix(P, R)\n",
" F = H + G\n",
" e, Co = secular_eqn(F, S)\n",
" P = P_matrix(Co, N)\n",
" hf_e = energy_tot(e, N, P, H, Vnn)\n",
"\n",
" delta_e = np.abs(hf_e - previous_e)\n",
" previous_e = hf_e\n",
" ITER += 1\n",
" stop = time.time()\n",
" print_info(S, H, e, Co, P, hf_e, start, stop, delta_e, verbose=verbose)\n",
"\n",
" # plot\n",
" tmp_density = get_density(bfs, Co, x)\n",
" densities.append(tmp_density)\n",
"\n",
" plot_density(densities, x)\n",
"\n",
"\n",
" return hf_e"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:01:15.924387Z",
"start_time": "2019-11-18T22:01:15.918349Z"
}
},
"outputs": [],
"source": [
"def get_density(bfs, Co, x):\n",
" r = sp.Symbol('r')\n",
" density = []\n",
" \n",
" # all orbitals\n",
" for i in range(Co.shape[0]):\n",
" tmp_orbital = 0\n",
" # all basis functions\n",
" for j, f in enumerate(bfs):\n",
" tmp_orbital += Co[j][i] * bfs[j]\n",
" tmp_d_function = tmp_orbital * tmp_orbital * r * r * 4 * np.pi\n",
" tmp_f = sp.lambdify(r, tmp_d_function, \"numpy\")\n",
" tmp_d = tmp_f(x)\n",
" density.append(tmp_d)\n",
" return density"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:10:54.844928Z",
"start_time": "2019-11-18T22:10:54.833778Z"
}
},
"outputs": [],
"source": [
"def plot_density(densities, x):\n",
" num_orbitals = len(densities[0])\n",
" num_iterations = len(densities)\n",
"\n",
" for i in range(num_orbitals):\n",
" plt.figure(figsize=(16,2))\n",
" for j, d in enumerate(densities):\n",
" if j == 0 or j == (num_iterations - 1):\n",
" plt.plot(x, d[i], label='iteration {}'.format(j+1))\n",
" else:\n",
" plt.plot(x, d[i])\n",
" plt.legend()\n",
" plt.xlim(0, x[-1])\n",
" plt.xlabel('r')\n",
" plt.ylabel('$4 \\pi r^2 |\\phi_{}|^2$'.format(i+1))\n",
" plt.title('charge density of $\\phi_{}$'.format(i+1))\n",
" plt.show()\n",
" \n",
" plt.figure(figsize=(16,2))\n",
" for i, d in enumerate(densities[-1]):\n",
" plt.plot(x, d, label='$\\phi_{}$'.format(i+1))\n",
" plt.legend()\n",
" plt.xlim(0, x[-1])\n",
" plt.xlabel('r')\n",
" plt.ylabel('$4 \\pi r^2 |\\phi_i|^2$')\n",
" plt.title('charge density of all orbitals $\\phi_i$ (final iteration)')\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:10:59.934397Z",
"start_time": "2019-11-18T22:10:56.168713Z"
},
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------------------------------ Initialization ------------------------------\n",
"------------------------- Ignore repulsion integral ------------------------\n",
"HF energy: -3.95924 (hartree) = -107.73486 (eV)\n",
"time used: 0.2 s\n",
"----------- Caculating Electron Repulsion Integral (takes time) ------------\n",
"time Repu: 2.7 s\n",
"------------------------------ Iteration 1 ------------------------------\n",
"HF energy: -2.78457 (hartree) = -75.77099 (eV)\n",
"dE : 1.17e+00\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 2 ------------------------------\n",
"HF energy: -2.85860 (hartree) = -77.78532 (eV)\n",
"dE : 7.40e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 3 ------------------------------\n",
"HF energy: -2.86152 (hartree) = -77.86490 (eV)\n",
"dE : 2.92e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 4 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86877 (eV)\n",
"dE : 1.42e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 5 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86896 (eV)\n",
"dE : 7.01e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 6 ------------------------------\n",
"HF energy: -2.86167 (hartree) = -77.86897 (eV)\n",
"dE : 3.45e-07\n",
"time used: 0.0 s\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"-------------------------------- \u001b[32mPASSED\u001b[0m ---------------------------------\n",
"cal: -2.8616726, ref: -2.8616726\n",
"\n",
"\n"
]
}
],
"source": [
"test1()"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T22:12:17.757743Z",
"start_time": "2019-11-18T22:11:22.213856Z"
},
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"------------------------------ Initialization ------------------------------\n",
"------------------------- Ignore repulsion integral ------------------------\n",
"HF energy: -19.51846 (hartree) = -531.11686 (eV)\n",
"time used: 0.7 s\n",
"----------- Caculating Electron Repulsion Integral (takes time) ------------\n",
"time Repu: 52.7 s\n",
"------------------------------ Iteration 1 ------------------------------\n",
"HF energy: -14.28744 (hartree) = -388.77544 (eV)\n",
"dE : 5.23e+00\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 2 ------------------------------\n",
"HF energy: -14.50425 (hartree) = -394.67518 (eV)\n",
"dE : 2.17e-01\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 3 ------------------------------\n",
"HF energy: -14.55105 (hartree) = -395.94867 (eV)\n",
"dE : 4.68e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 4 ------------------------------\n",
"HF energy: -14.56616 (hartree) = -396.35976 (eV)\n",
"dE : 1.51e-02\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 5 ------------------------------\n",
"HF energy: -14.57061 (hartree) = -396.48075 (eV)\n",
"dE : 4.45e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 6 ------------------------------\n",
"HF energy: -14.57187 (hartree) = -396.51521 (eV)\n",
"dE : 1.27e-03\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 7 ------------------------------\n",
"HF energy: -14.57223 (hartree) = -396.52493 (eV)\n",
"dE : 3.57e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 8 ------------------------------\n",
"HF energy: -14.57233 (hartree) = -396.52766 (eV)\n",
"dE : 1.01e-04\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 9 ------------------------------\n",
"HF energy: -14.57236 (hartree) = -396.52843 (eV)\n",
"dE : 2.83e-05\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 10 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52865 (eV)\n",
"dE : 7.94e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 11 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52871 (eV)\n",
"dE : 2.23e-06\n",
"time used: 0.0 s\n",
"------------------------------ Iteration 12 ------------------------------\n",
"HF energy: -14.57237 (hartree) = -396.52872 (eV)\n",
"dE : 6.27e-07\n",
"time used: 0.0 s\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"-------------------------------- \u001b[32mPASSED\u001b[0m ---------------------------------\n",
"cal: -14.5723687, ref: -14.5723690\n",
"\n",
"\n"
]
}
],
"source": [
"test2()"
]
},
{
"cell_type": "markdown",
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-18T19:57:17.522866Z",
"start_time": "2019-11-18T19:57:17.516024Z"
}
},
"source": [
"### 12. Limitations\n",
"Limitations of this implementation: \n",
"1. Because of the coordinate system (Spherical coordinate system), this implementation can only deal with atom.\n",
"1. Because angular part is not included in current STO function, only atoms which only have s orbital could be represented by STO.\n",
"1. For restricted hartree fock, could only run closed shell atom.\n",
"1. Integral calculated by sympy, which is slow but easy to understand.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 13. Reference\n",
"[1] Levine, Quantum Chemistry, 7th Edition, chapter 14 \n",
"[2] Wikipedia\n",
"[Hartree–Fock method](https://en.wikipedia.org/wiki/Hartree%E2%80%93Fock_method#Hartree%E2%80%93Fock_algorithm), \n",
"[Fock matrix](https://en.wikipedia.org/wiki/Fock_matrix), \n",
"[Roothaan equations](https://en.wikipedia.org/wiki/Roothaan_equations), \n",
"[Coulomb operator](https://en.wikipedia.org/wiki/Coulomb_operator), \n",
"[Exchange operator](https://en.wikipedia.org/wiki/Exchange_operator) \n",
"[3] Clementi, Enrico, and Carla Roetti. [Roothaan-Hartree-Fock atomic wavefunctions: Basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms, Z≤ 54.](https://www.sciencedirect.com/science/article/pii/S0092640X74800161) Atomic data and nuclear data tables 14.3-4 (1974): 177-478. \n",
"[4] Acosta C R. [Restricted closed shell Hartree Fock Roothaan matrix method applied to Helium atom using Mathematica[J].](https://files.eric.ed.gov/fulltext/EJ1051495.pdf) European Journal of Physics Education, 2017, 5(1): 1-14. \n",
"[5] Jacob Martin, [Simple Quantum Chemistry: Hartree-Fock in Python](http://nznano.blogspot.com/2018/03/simple-quantum-chemistry-hartree-fock.html), 2018 \n",
"[6] Claire Vallance, [Calculating Orbital Energies and Expansion Coefficients](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Symmetry_(Vallance)/20%3A_Calculating_Orbital_Energies_and_Expansion_Coefficients), 2019"
]
}
],
"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": "3.6.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
}