From 2ae639e7a1d15741a4422c959aa5ec48caef0081 Mon Sep 17 00:00:00 2001
From: Quarto GHA Workflow Runner <quarto-github-actions-publish@example.com>
Date: Wed, 13 Dec 2023 19:15:05 +0000
Subject: [PATCH] Built site for gh-pages

---
 .nojekyll                                     |   2 +-
 examples/chemistry/excited_states.html        |   6 +
 .../chemistry/qchem_modelling_basics.html     |   6 +
 examples/fault_tolerant/qsp_state_prep.html   |   6 +
 .../berylium_ibm_quantum.html                 |   6 +
 .../overview_endtoend.html                    |   6 +
 ...ist_cloud_hardware_experiments_braket.html |   6 +
 .../umbrella_inversion.html                   |   6 +
 examples/img/cluster_glycine.png              | Bin 0 -> 58009 bytes
 examples/img/glycine_forms.png                | Bin 0 -> 37960 bytes
 .../classical_shadows.html                    |   6 +
 examples/problem_decomposition/dmet.html      |   6 +
 examples/problem_decomposition/dmet_uhf.html  |   6 +
 .../problem_decomposition/ifci_mifno.html     |   6 +
 examples/problem_decomposition/oniom.html     |   6 +
 examples/problem_decomposition/qmmm.html      | 974 ++++++++++++++++++
 examples/variational_methods/adapt.html       |   6 +
 .../iqcc_using_clifford.html                  |   6 +
 examples/variational_methods/vqe.html         |   6 +
 .../vqe_custom_ansatz_hamiltonian.html        |   6 +
 examples/workflow_basics/1.the_basics.html    |   6 +
 .../workflow_basics/2.qpu_connection.html     |   6 +
 .../workflow_basics/3.noisy_simulation.html   |   6 +
 .../workflow_basics/symbolic_simulator.html   |   6 +
 hands_on/T1_circuits.html                     |   6 +
 hands_on/T1_circuits_solved.html              |   6 +
 hands_on/T2_simulators.html                   |   6 +
 hands_on/T2_simulators_solved.html            |   6 +
 hands_on/T3_VQE.html                          |   6 +
 hands_on/T3_VQE_solved.html                   |   6 +
 hands_on/T4_hardware_experiments.html         |   6 +
 hands_on/T4_hardware_experiments_solved.html  |   6 +
 hands_on/T5_fault_tolerant_build_blocks.html  |   6 +
 ...T5_fault_tolerant_build_blocks_solved.html |   6 +
 index.html                                    |   7 +
 search.json                                   |  37 +-
 sitemap.xml                                   |  66 +-
 37 files changed, 1233 insertions(+), 33 deletions(-)
 create mode 100644 examples/img/cluster_glycine.png
 create mode 100644 examples/img/glycine_forms.png
 create mode 100644 examples/problem_decomposition/qmmm.html

diff --git a/.nojekyll b/.nojekyll
index c92dff3..569169d 100644
--- a/.nojekyll
+++ b/.nojekyll
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diff --git a/examples/chemistry/excited_states.html b/examples/chemistry/excited_states.html
index 12e8376..9e1d9eb 100644
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/chemistry/qchem_modelling_basics.html b/examples/chemistry/qchem_modelling_basics.html
index 6eb0b4f..074399c 100644
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/fault_tolerant/qsp_state_prep.html b/examples/fault_tolerant/qsp_state_prep.html
index 9c8adbf..9506a8b 100644
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/hardware_experiments/berylium_ibm_quantum.html b/examples/hardware_experiments/berylium_ibm_quantum.html
index 56c7b94..c483905 100644
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+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
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diff --git a/examples/hardware_experiments/overview_endtoend.html b/examples/hardware_experiments/overview_endtoend.html
index 9b4c967..0dc622b 100644
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   </div>
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+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
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 </li>
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diff --git a/examples/hardware_experiments/qemist_cloud_hardware_experiments_braket.html b/examples/hardware_experiments/qemist_cloud_hardware_experiments_braket.html
index a0b6848..842220c 100644
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+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/hardware_experiments/umbrella_inversion.html b/examples/hardware_experiments/umbrella_inversion.html
index f0ecf06..b0702fa 100644
--- a/examples/hardware_experiments/umbrella_inversion.html
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+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
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diff --git a/examples/img/cluster_glycine.png b/examples/img/cluster_glycine.png
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diff --git a/examples/measurement_reduction/classical_shadows.html b/examples/measurement_reduction/classical_shadows.html
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   <a href="../../examples/problem_decomposition/oniom.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/problem_decomposition/dmet.html b/examples/problem_decomposition/dmet.html
index 53e3ee9..19376ed 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/problem_decomposition/dmet_uhf.html b/examples/problem_decomposition/dmet_uhf.html
index ea6ba57..985d774 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
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diff --git a/examples/problem_decomposition/ifci_mifno.html b/examples/problem_decomposition/ifci_mifno.html
index 8558ff3..fc4a7ab 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
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+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
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diff --git a/examples/problem_decomposition/oniom.html b/examples/problem_decomposition/oniom.html
index f143be5..d6b3ad8 100644
--- a/examples/problem_decomposition/oniom.html
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
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diff --git a/examples/problem_decomposition/qmmm.html b/examples/problem_decomposition/qmmm.html
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+<header id="title-block-header" class="quarto-title-block default">
+<div class="quarto-title">
+<h1 class="title">The QM/MM method: Solvation of the Glycine Amino Acid</h1>
+</div>
+
+
+
+<div class="quarto-title-meta">
+
+    
+  
+    
+  </div>
+  
+
+</header>
+
+<section id="introduction" class="level2">
+<h2 class="anchored" data-anchor-id="introduction">Introduction</h2>
+<section id="principles-of-the-qmmm-method" class="level3">
+<h3 class="anchored" data-anchor-id="principles-of-the-qmmm-method">Principles of the QM/MM method</h3>
+<p>In 2013, the Nobel Prize in Chemistry was awarded to Martin Karplus, Michael Levitt, and Arieh Warshel for their groundbreaking work in advancing the understanding of complex chemical systems. Their achievement was centered around the development of multiscale models, a significant milestone in the field of computational chemistry. Specifically, their work highlighted the QM/MM method, an abbreviation for Quantum Mechanics/Molecular Mechanics. Introduced in 1976 in the <a href="https://doi.org/10.1016/0022-2836(76)90311-9">Journal of Molecular Biology</a>, it amalgamates quantum mechanics, which describes the behavior of particles at the electronic level, with molecular mechanics, a classical approach that uses forcefields to model interatomic interactions. The introduction of this method became a cornerstone in biochemical simulation workflows, allowing scientists to simulate and understand complex chemical reactions occurring within biological contexts with remarkable accuracy. Its primary objective remains the reduction of computational cost in modeling intricate chemical systems, useful in the study of biochemical entities like DNA/RNA strands, proteins, and organic molecules.</p>
+<p>Consider protein simulations as a case in point: the majority of proteins consist of 50 to 200 amino acids (<a href="https://www.ncbi.nlm.nih.gov/books/NBK26830/">source</a>). With an average of approximately 19 atoms per amino acid, a solitary protein system might necessitate the consideration of anywhere between 950 to 3800 atoms. This estimate however does not take into account solvents, ions, and other vital molecular species that could be important in the simulation model.</p>
+<p>This problem size is quite typical in many molecular mechanics workflows. Nonetheless, handling interactions like charge transfers or hydrogen bonds, which are pivotal in protein/drug interactions, can pose challenges when using forcefield-based methods. In such scenarios, the nuanced description of these molecular interactions is better represented via quantum mechanics. However, the problem size becomes intractable for quantum mechanics methods alone. Hence, the fusion of both realms has been beneficial for the computational chemistry community and forms the essence of the QM/MM approach.</p>
+</section>
+<section id="quantum-mechanical-methods" class="level3">
+<h3 class="anchored" data-anchor-id="quantum-mechanical-methods">Quantum mechanical methods</h3>
+<p>Molecules reside within the microscopic realm and adhere to the principles of the Schrödinger equation. For more introductory material on modeling molecular systems, please refer to our <a href="https://goodchemistryco.github.io/Tangelo-Examples/examples/chemistry/qchem_modelling_basics.html">previous notebook</a>.</p>
+<p>Quantum computing research is rapidly advancing on both software and hardware fronts. Chemistry stands out as a promising application for these devices, propelling an active research field, exemplified further in the paper reviews by <a href="https://doi.org/10.1146/annurev-physchem-032210-103512">Kassal et al.</a> and <a href="https://doi.org/10.1021/acs.chemrev.8b00803">Cao et al.</a>. Harnessing QM/MM methodologies within quantum computing simulations holds promise in capturing crucial environmental effects, such as solvent interactions, enriching the accuracy and realism of computational models [1, 2].</p>
+</section>
+<section id="computing-solvation-energies" class="level3">
+<h3 class="anchored" data-anchor-id="computing-solvation-energies">Computing solvation energies</h3>
+<p>We apply this approach to the explicit solvation of a simple amino acid (glycine) in water through electrostatic embedding. To determine solvation energies for chemical compounds, the following steps are taken in this notebook: 1. Compute the molecular energies of isolated compounds using a quantum algorithm. For the sake of simplicity, the quantum algorithm used here is the Variational Quantum Eigensolver (VQE). Other quantum solvers available in Tangelo have already been or can be integrated with QM/MM. 2. Calculate the molecular energies of solvated compounds. In this step, the QM/MM problem decomposition method models the glycine amino acid using VQE, similar to the previous step. Meanwhile, explicit water molecules are modeled through molecular mechanics. 3. Determine the energy differences that signify solvation energy. A more negative energy denotes a stronger interaction between the solvent and the molecule.</p>
+</section>
+</section>
+<section id="use-case-solvation-of-the-glycine-animo-acid" class="level2">
+<h2 class="anchored" data-anchor-id="use-case-solvation-of-the-glycine-animo-acid">Use-case: Solvation of the glycine animo acid</h2>
+<section id="preparation-for-the-notebook" class="level3">
+<h3 class="anchored" data-anchor-id="preparation-for-the-notebook">Preparation for the notebook</h3>
+<p>The next cells ensure that the appropriate packages are installed and imported into the Python environment to successfully execute this notebook.</p>
+<div class="cell" data-execution_count="1">
+<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="cf">try</span>:</span>
+<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>    <span class="im">import</span> tangelo</span>
+<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="cf">except</span> <span class="pp">ModuleNotFoundError</span>:</span>
+<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>    <span class="op">!</span>pip install git<span class="op">+</span>https:<span class="op">//</span>github.com<span class="op">/</span>goodchemistryco<span class="op">/</span>Tangelo.git<span class="op">@</span>develop <span class="op">--</span>quiet</span>
+<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>    <span class="op">!</span>pip install qulacs pyscf rdkit openbabel<span class="op">-</span>wheel <span class="op">--</span>quiet</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="cell" data-execution_count="2">
+<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Tangelo common imports.</span></span>
+<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo <span class="im">import</span> SecondQuantizedMolecule</span>
+<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.algorithms.variational <span class="im">import</span> VQESolver, BuiltInAnsatze</span>
+<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.toolboxes.molecular_computation.frozen_orbitals <span class="im">import</span> get_orbitals_excluding_homo_lumo</span>
+<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.toolboxes.molecular_computation.molecule <span class="im">import</span> atom_string_to_list</span>
+<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a><span class="co"># QM/MM-related imports.</span></span>
+<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.problem_decomposition.qmmm.qmmm_problem_decomposition <span class="im">import</span> QMMMProblemDecomposition</span>
+<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.problem_decomposition.oniom._helpers.helper_classes <span class="im">import</span> Fragment, Link</span>
+<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> tangelo.toolboxes.molecular_computation.mm_charges_solver <span class="im">import</span> MMChargesSolverRDKit</span>
+<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a><span class="co"># Basis set used in this notebook.</span></span>
+<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>basis <span class="op">=</span> <span class="st">"cc-pvdz"</span></span>
+<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a><span class="co"># Constants.</span></span>
+<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a>ha_to_kcalmol <span class="op">=</span> <span class="fl">627.509</span></span>
+<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a>cal_to_j <span class="op">=</span> <span class="fl">4.184</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+</section>
+<section id="amino-acid-tautomers" class="level3">
+<h3 class="anchored" data-anchor-id="amino-acid-tautomers">Amino acid tautomers</h3>
+<p>Amino acids form the basic building blocks of polypeptides and proteins within living organisms. While nature encompasses about 500 variations, only 22 are encoded in the genetic blueprint of life. These molecules are characterized by their end-capping functional groups: an amine (NH<span class="math inline">\(_3\)</span>) and a carboxylic acid (COOH), with a central functional group denoted as ‘R’ that defines the unique properties of each amino acid.</p>
+<p>This notebook primarily focuses on employing computational techniques that integrate quantum mechanics with molecular mechanics (QM/MM). This method allows researchers to explore interactions among molecules within aqueous solutions, providing essential insights into the behaviors and functionalities of proteins at a reasonable computational cost.</p>
+<p>Our initial step involves defining the atomic coordinates of glycine, the simplest amino acid with a ‘R’ functional group consisting solely of a hydrogen atom. Given the extensive computational requirements for running a full quantum algorithm on the entire system, this notebook opts to freeze certain molecular orbitals, therefore simplifying the simulation to manage its complexity.</p>
+<div class="cell" data-execution_count="4">
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>xyz_glycine <span class="op">=</span> <span class="st">"""</span></span>
+<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="st">  C          2.05388        0.61558        0.07379</span></span>
+<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="st">  O          1.96483       -0.57096       -0.21241</span></span>
+<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="st">  O          3.19750        1.18239        0.43269</span></span>
+<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a><span class="st">  H          3.96112        0.54040        0.42260</span></span>
+<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a><span class="st">  C          0.91678        1.61052        0.03784</span></span>
+<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a><span class="st">  H          0.94914        2.17916        0.95644</span></span>
+<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a><span class="st">  H          1.13065        2.30136       -0.76945</span></span>
+<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a><span class="st">  N         -0.39578        0.99717       -0.14991</span></span>
+<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -0.70125        0.48980        0.67086</span></span>
+<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -0.41063        0.36439       -0.94717</span></span>
+<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
+<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Creating a molecule object from the coordinates.</span></span>
+<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a>glycine <span class="op">=</span> SecondQuantizedMolecule(xyz_glycine, basis<span class="op">=</span>basis)</span>
+<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a><span class="co"># Setting the active space to HOMO-1 to LUMO+1.</span></span>
+<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a>frozen_orbitals_gly <span class="op">=</span> get_orbitals_excluding_homo_lumo(glycine, homo_minus_n<span class="op">=</span><span class="dv">1</span>, lumo_plus_n<span class="op">=</span><span class="dv">1</span>)</span>
+<span id="cb3-19"><a href="#cb3-19" aria-hidden="true" tabindex="-1"></a>glycine.freeze_mos(frozen_orbitals_gly, inplace<span class="op">=</span><span class="va">True</span>)</span>
+<span id="cb3-20"><a href="#cb3-20" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The neutral form of GLY will be described by an active space of </span><span class="sc">{</span>glycine<span class="sc">.</span>n_active_mos<span class="sc">}</span><span class="ss"> molecular orbitals and </span><span class="sc">{</span>glycine<span class="sc">.</span>n_active_electrons<span class="sc">}</span><span class="ss"> electrons."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The neutral form of GLY will be described by an active space of 4 molecular orbitals and 4 electrons.</code></pre>
+</div>
+</div>
+<p>One might wonder why this amino acid dissolves in water despite being a neutral organic compound. The reason lies in its behavior when in water; evidences show that amino acids adopt a <a href="https://en.wikipedia.org/wiki/Zwitterion">zwitterionic</a> form [3-6]. Although the entire molecule remains electrically neutral, a hydrogen atom shifts from the carboxylic acid group to the amine group, showcasing a form of <a href="https://en.wikipedia.org/wiki/Tautomer">tautomerism</a>. Thus, to precisely model the interaction of water with glycine, it is crucial to include the equivalent tautomer in the calculations of solvation properties.</p>
+<p>In the next cell, we construct this chemical structure while using the same approach of freezing certain molecular orbitals.</p>
+<div class="cell" data-execution_count="5">
+<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>xyz_zwitterion <span class="op">=</span> <span class="st">"""</span></span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="st">  C         -0.72588       -0.48930       -0.87995</span></span>
+<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -0.40429       -0.99901        0.24400</span></span>
+<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -1.71249       -0.74617       -1.57606</span></span>
+<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="st">  C          0.24065        0.58647       -1.40746</span></span>
+<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="st">  H          0.94067        0.15610       -2.10976</span></span>
+<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -0.32329        1.37177       -1.87959</span></span>
+<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a><span class="st">  N          0.99940        1.14332       -0.24215</span></span>
+<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="st">  H          1.19967        0.36262        0.37817</span></span>
+<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="st">  H          1.91733        1.52621       -0.51811</span></span>
+<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="st">  H          0.35328        1.80600        0.26884</span></span>
+<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
+<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a><span class="co"># Creating a molecule object from the coordinates.</span></span>
+<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a>zwitterion <span class="op">=</span> SecondQuantizedMolecule(xyz_zwitterion, basis<span class="op">=</span>basis)</span>
+<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a><span class="co"># Setting the active space to HOMO-1 to LUMO+1.</span></span>
+<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a>frozen_orbitals_zwit <span class="op">=</span> get_orbitals_excluding_homo_lumo(zwitterion, homo_minus_n<span class="op">=</span><span class="dv">1</span>, lumo_plus_n<span class="op">=</span><span class="dv">1</span>)</span>
+<span id="cb5-19"><a href="#cb5-19" aria-hidden="true" tabindex="-1"></a>zwitterion.freeze_mos(frozen_orbitals_zwit)</span>
+<span id="cb5-20"><a href="#cb5-20" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The zwitterion form of GLY will be described by an active space of </span><span class="sc">{</span>zwitterion<span class="sc">.</span>n_active_mos<span class="sc">}</span><span class="ss"> molecular orbitals and </span><span class="sc">{</span>zwitterion<span class="sc">.</span>n_active_electrons<span class="sc">}</span><span class="ss"> electrons."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The zwitterion form of GLY will be described by an active space of 4 molecular orbitals and 4 electrons.</code></pre>
+</div>
+</div>
+<p>With the molecules now encoded as Tangelo objects, we’re ready to perform quantum chemistry calculations. Below is a visual representation illustrating the two distinct tautomers of the glycine amino acid that we previously constructed.</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="../img/glycine_forms.png" class="img-fluid figure-img"></p>
+<figcaption class="figure-caption">Glycine forms</figcaption>
+</figure>
+</div>
+</section>
+<section id="using-quantum-algorithms-on-the-glycine-molecule" class="level3">
+<h3 class="anchored" data-anchor-id="using-quantum-algorithms-on-the-glycine-molecule">Using quantum algorithms on the glycine molecule</h3>
+<p>The following code cell defines the options passed to our quantum solver (for simplicity, the well-known Variational Quantum Eigensolver (VQE) with a UCCSD ansatz). These settings are applied in subsequent energy computations.</p>
+<div class="cell" data-execution_count="6">
+<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>vqe_options<span class="op">=</span> {</span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>    <span class="st">"ansatz"</span>: BuiltInAnsatze.UCCSD,</span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>    <span class="st">"qubit_mapping"</span>: <span class="st">"scBK"</span>,</span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>    <span class="st">"up_then_down"</span>: <span class="va">True</span></span>
+<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a> }</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<p>We then run the quantum solver for both forms of glycine. We are particularly interested in the total molecular energies obtained, as they are necessary to calculate the hydration energy later on (see step 1 outlined in the “Computing solvation energies” section above).</p>
+<div class="cell" data-execution_count="7">
+<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>quantum_solver_gly <span class="op">=</span> VQESolver({<span class="st">"molecule"</span>: glycine, <span class="op">**</span>vqe_options})</span>
+<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a>quantum_solver_gly.build()</span>
+<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>e_quantum_gly <span class="op">=</span> quantum_solver_gly.simulate()</span>
+<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The gas phase molecular energy of glycine (neutral) is </span><span class="sc">{</span>e_quantum_gly<span class="sc">:.5f}</span><span class="ss"> Ha."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The gas phase molecular energy of glycine (neutral) is -282.85661 Ha.</code></pre>
+</div>
+</div>
+<div class="cell" data-execution_count="8">
+<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>quantum_solver_zwit <span class="op">=</span> VQESolver({<span class="st">"molecule"</span>: zwitterion, <span class="op">**</span>vqe_options})</span>
+<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>quantum_solver_zwit.build()</span>
+<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a>e_quantum_zwit <span class="op">=</span> quantum_solver_zwit.simulate()</span>
+<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The gas phase molecular energy of glycine (zwitterion) is </span><span class="sc">{</span>e_quantum_zwit<span class="sc">:.5f}</span><span class="ss"> Ha."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The gas phase molecular energy of glycine (zwitterion) is -282.79736 Ha.</code></pre>
+</div>
+</div>
+<p>Since tautomers have the same set of atoms, comparing the two molecular energies indicates that the neutral form of the glycine amino acid is more stable than the zwitterion. This outcome aligns with the fact that formal charges on atoms in the gas phase are difficult to generate due to the lack of an environment for stabilization.</p>
+<p>We now have access to the molecular energies of each tautomer. We now sample the energy of the molecular system consisting of a cluster of water around the molecules (see step 2 outlined in the “Computing solvation energies” section above). The energy differences <span class="math inline">\(\Delta E_{\text{solv}}\)</span> (after removing the water molecule potential energy contributions) should be proportional to the free energies of solvation <span class="math inline">\(\Delta H_{\text{solv}}\)</span> or <span class="math inline">\(\Delta G_{\text{solv}}\)</span> measured in laboratories.</p>
+<p>The remaining steps taken in this notebook are revolving around computing the molecular energies of those clusters using the QM/MM method, which is a simplified version of a more complete study as reported in [7].</p>
+</section>
+<section id="preparing-the-qmmm-calculation-get-the-partial-charges-for-h_2o" class="level3">
+<h3 class="anchored" data-anchor-id="preparing-the-qmmm-calculation-get-the-partial-charges-for-h_2o">Preparing the QM/MM calculation: get the partial charges for <span class="math inline">\(H_2O\)</span></h3>
+<p>The supported QM/MM framework in Tangelo needs the partial charges for the part of the system described via molecular mechanics. This is what we do in the next code cell. Here, in summary: - A mean-field calculation is performed for a single water molecule; - The Mulliken atomic charges are retrived from the <code>analyze</code> method; - A function is defined to construct an array in the <code>[(partial_charge, (x, y, z)), ...]</code> format.</p>
+<div class="cell" data-execution_count="9">
+<div class="sourceCode cell-code" id="cb12"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>xyz_h2o <span class="op">=</span> <span class="st">"""</span></span>
+<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -2.08448       -2.25652       -0.22848</span></span>
+<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -2.35312       -3.17615       -0.12238</span></span>
+<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.83562       -1.85666        0.64078</span></span>
+<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
+<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>h2o <span class="op">=</span> SecondQuantizedMolecule(xyz_h2o, basis<span class="op">=</span>basis)</span>
+<span id="cb12-8"><a href="#cb12-8" aria-hidden="true" tabindex="-1"></a>(_, mulliken_atomic_charges), _ <span class="op">=</span> h2o.mean_field.analyze()</span>
+<span id="cb12-9"><a href="#cb12-9" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb12-10"><a href="#cb12-10" aria-hidden="true" tabindex="-1"></a><span class="kw">def</span> get_charges(water_molecule_coords):</span>
+<span id="cb12-11"><a href="#cb12-11" aria-hidden="true" tabindex="-1"></a>    xyz_h2os <span class="op">=</span> atom_string_to_list(water_molecule_coords)</span>
+<span id="cb12-12"><a href="#cb12-12" aria-hidden="true" tabindex="-1"></a>    mulliken_charges_waters <span class="op">=</span> [<span class="op">*</span>mulliken_atomic_charges] <span class="op">*</span> (<span class="bu">len</span>(xyz_h2os) <span class="op">//</span> <span class="bu">len</span>(mulliken_atomic_charges))</span>
+<span id="cb12-13"><a href="#cb12-13" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb12-14"><a href="#cb12-14" aria-hidden="true" tabindex="-1"></a>    <span class="cf">return</span> [(q, xyz_h2os[i][<span class="dv">1</span>]) <span class="cf">for</span> i, q <span class="kw">in</span> <span class="bu">enumerate</span>(mulliken_charges_waters)]</span>
+<span id="cb12-15"><a href="#cb12-15" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb12-16"><a href="#cb12-16" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The Mulliken partial charges computed from an Hartree-Fock calculation in </span><span class="sc">{</span>basis<span class="sc">}</span><span class="ss"> are</span><span class="ch">\n</span><span class="ss">O = </span><span class="sc">{</span>mulliken_atomic_charges[<span class="dv">0</span>]<span class="sc">}</span><span class="ch">\n</span><span class="ss">H1 = </span><span class="sc">{</span>mulliken_atomic_charges[<span class="dv">1</span>]<span class="sc">}</span><span class="ch">\n</span><span class="ss">H2 = </span><span class="sc">{</span>mulliken_atomic_charges[<span class="dv">2</span>]<span class="sc">}</span><span class="ss">."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The Mulliken partial charges computed from an Hartree-Fock calculation in cc-pvdz are
+O = -0.6346652155730794
+H1 = 0.3194372332962432
+H2 = 0.31522798227682913.</code></pre>
+</div>
+</div>
+</section>
+<section id="computing-the-solvation-energies-using-qmmm-with-charge-embedding" class="level3">
+<h3 class="anchored" data-anchor-id="computing-the-solvation-energies-using-qmmm-with-charge-embedding">Computing the solvation energies using QM/MM with charge embedding</h3>
+<p>The next task involves computing solvated molecule energies using the QM/MM electrostatic embedding method. Using the previously calculated water atomic charges, the <code>QMMMProblemDecomposition</code> class consolidates necessary information for this calculation. This includes: - “geometry”: Coordinates of the molecule in a list format. - “mmpackage”: Molecular mechanics package utilized. - “charges”: Electrostatic charges and their coordinates. - “qmfragment”: A <code>Fragment</code> object defining the solver and related options for computing the molecular energy in quantum mechanics.</p>
+<p>It’s worth noting the various methods available for generating water cluster geometries. The following geometries were created by randomly positioning three water molecules around each terminal and subsequently optimized using the AMBER94 force field. This optimization step can be done with any molecular mechanics package, like <a href="https://openmm.org/">OpenMM</a> or <a href="https://www.rdkit.org/">RDKit</a>. An illustration showcasing one of the generated conformations is presented in the figure below.</p>
+<div class="quarto-figure quarto-figure-center">
+<figure class="figure">
+<p><img src="../img/cluster_glycine.png" class="img-fluid figure-img"></p>
+<figcaption class="figure-caption">Cluster of water molecules and glycine</figcaption>
+</figure>
+</div>
+<div class="cell" data-execution_count="10">
+<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>xyz_waters_gly <span class="op">=</span> <span class="st">"""</span></span>
+<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -2.08448       -2.25652       -0.22848</span></span>
+<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -2.35312       -3.17615       -0.12238</span></span>
+<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.83562       -1.85666        0.64078</span></span>
+<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -0.29165       -1.17766       -1.97014</span></span>
+<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a><span class="st">  H          0.55770       -1.31516       -1.52416</span></span>
+<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -0.98020       -1.66830       -1.47470</span></span>
+<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a><span class="st">  O          4.62948       -0.92998        0.20740</span></span>
+<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a><span class="st">  H          5.09272       -1.49221        0.83838</span></span>
+<span id="cb14-10"><a href="#cb14-10" aria-hidden="true" tabindex="-1"></a><span class="st">  H          3.79167       -1.33448       -0.07876</span></span>
+<span id="cb14-11"><a href="#cb14-11" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -2.80676        2.14474       -0.62525</span></span>
+<span id="cb14-12"><a href="#cb14-12" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.85118        1.90309       -0.45829</span></span>
+<span id="cb14-13"><a href="#cb14-13" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -2.93359        2.38421       -1.55080</span></span>
+<span id="cb14-14"><a href="#cb14-14" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -1.81568       -0.72927        1.87434</span></span>
+<span id="cb14-15"><a href="#cb14-15" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.84048       -0.80009        2.83473</span></span>
+<span id="cb14-16"><a href="#cb14-16" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -2.66617       -0.33065        1.49202</span></span>
+<span id="cb14-17"><a href="#cb14-17" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -3.76770        0.00135        0.46835</span></span>
+<span id="cb14-18"><a href="#cb14-18" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -3.57200        0.87852        0.03795</span></span>
+<span id="cb14-19"><a href="#cb14-19" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -3.59648       -0.71670       -0.16049</span></span>
+<span id="cb14-20"><a href="#cb14-20" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
+<span id="cb14-21"><a href="#cb14-21" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb14-22"><a href="#cb14-22" aria-hidden="true" tabindex="-1"></a>qmmm_model_gly <span class="op">=</span> QMMMProblemDecomposition({</span>
+<span id="cb14-23"><a href="#cb14-23" aria-hidden="true" tabindex="-1"></a>    <span class="st">"geometry"</span>: atom_string_to_list(xyz_glycine),</span>
+<span id="cb14-24"><a href="#cb14-24" aria-hidden="true" tabindex="-1"></a>    <span class="st">"mmpackage"</span>: <span class="st">"rdkit"</span>,</span>
+<span id="cb14-25"><a href="#cb14-25" aria-hidden="true" tabindex="-1"></a>    <span class="st">"charges"</span>: get_charges(xyz_waters_gly),</span>
+<span id="cb14-26"><a href="#cb14-26" aria-hidden="true" tabindex="-1"></a>    <span class="st">"qmfragment"</span>: Fragment(solver_high<span class="op">=</span><span class="st">"vqe"</span>,</span>
+<span id="cb14-27"><a href="#cb14-27" aria-hidden="true" tabindex="-1"></a>        options_high<span class="op">=</span>{<span class="st">"basis"</span>: basis, <span class="st">"frozen_orbitals"</span>: frozen_orbitals_gly, <span class="op">**</span>vqe_options})</span>
+<span id="cb14-28"><a href="#cb14-28" aria-hidden="true" tabindex="-1"></a>})</span>
+<span id="cb14-29"><a href="#cb14-29" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb14-30"><a href="#cb14-30" aria-hidden="true" tabindex="-1"></a>e_qmmm_gly <span class="op">=</span> qmmm_model_gly.simulate()</span>
+<span id="cb14-31"><a href="#cb14-31" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The hydration energy for glycine (neutral) is </span><span class="sc">{</span>(e_qmmm_gly<span class="op">-</span>e_quantum_gly) <span class="op">*</span> ha_to_kcalmol <span class="op">*</span> cal_to_j<span class="sc">:5.0f}</span><span class="ss"> kJ/mol."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The hydration energy for glycine (neutral) is  -136 kJ/mol.</code></pre>
+</div>
+</div>
+<div class="cell" data-execution_count="11">
+<div class="sourceCode cell-code" id="cb16"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a>xyz_waters_zwit <span class="op">=</span> <span class="st">"""</span></span>
+<span id="cb16-2"><a href="#cb16-2" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -2.33478        0.43459        1.56814</span></span>
+<span id="cb16-3"><a href="#cb16-3" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.65671       -0.25663        1.45580</span></span>
+<span id="cb16-4"><a href="#cb16-4" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -3.11977        0.14754        1.04111</span></span>
+<span id="cb16-5"><a href="#cb16-5" aria-hidden="true" tabindex="-1"></a><span class="st">  O          3.57502        1.26874       -0.76381</span></span>
+<span id="cb16-6"><a href="#cb16-6" aria-hidden="true" tabindex="-1"></a><span class="st">  H          3.59649        0.47309       -0.17203</span></span>
+<span id="cb16-7"><a href="#cb16-7" aria-hidden="true" tabindex="-1"></a><span class="st">  H          4.40577        1.75433       -0.74479</span></span>
+<span id="cb16-8"><a href="#cb16-8" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -0.93902        2.44112        0.89259</span></span>
+<span id="cb16-9"><a href="#cb16-9" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.06155        3.25709        1.38776</span></span>
+<span id="cb16-10"><a href="#cb16-10" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -1.58516        1.71621        1.19305</span></span>
+<span id="cb16-11"><a href="#cb16-11" aria-hidden="true" tabindex="-1"></a><span class="st">  O         -3.99606       -0.58515       -0.21107</span></span>
+<span id="cb16-12"><a href="#cb16-12" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -4.64697       -0.10084       -0.73262</span></span>
+<span id="cb16-13"><a href="#cb16-13" aria-hidden="true" tabindex="-1"></a><span class="st">  H         -3.23854       -0.83634       -0.78921</span></span>
+<span id="cb16-14"><a href="#cb16-14" aria-hidden="true" tabindex="-1"></a><span class="st">  O          3.12434       -0.68537        0.90701</span></span>
+<span id="cb16-15"><a href="#cb16-15" aria-hidden="true" tabindex="-1"></a><span class="st">  H          3.33270       -0.62390        1.84641</span></span>
+<span id="cb16-16"><a href="#cb16-16" aria-hidden="true" tabindex="-1"></a><span class="st">  H          2.63054       -1.54344        0.73112</span></span>
+<span id="cb16-17"><a href="#cb16-17" aria-hidden="true" tabindex="-1"></a><span class="st">  O          1.55389       -2.64818        0.61476</span></span>
+<span id="cb16-18"><a href="#cb16-18" aria-hidden="true" tabindex="-1"></a><span class="st">  H          0.69747       -2.15400        0.51558</span></span>
+<span id="cb16-19"><a href="#cb16-19" aria-hidden="true" tabindex="-1"></a><span class="st">  H          1.54074       -3.48659        0.14319</span></span>
+<span id="cb16-20"><a href="#cb16-20" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
+<span id="cb16-21"><a href="#cb16-21" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb16-22"><a href="#cb16-22" aria-hidden="true" tabindex="-1"></a>qmmm_model_zwit <span class="op">=</span> QMMMProblemDecomposition({</span>
+<span id="cb16-23"><a href="#cb16-23" aria-hidden="true" tabindex="-1"></a>    <span class="st">"geometry"</span>: atom_string_to_list(xyz_zwitterion),</span>
+<span id="cb16-24"><a href="#cb16-24" aria-hidden="true" tabindex="-1"></a>    <span class="st">"mmpackage"</span>: <span class="st">"rdkit"</span>,</span>
+<span id="cb16-25"><a href="#cb16-25" aria-hidden="true" tabindex="-1"></a>    <span class="st">"charges"</span>: get_charges(xyz_waters_zwit),</span>
+<span id="cb16-26"><a href="#cb16-26" aria-hidden="true" tabindex="-1"></a>    <span class="st">"qmfragment"</span>: Fragment(solver_high<span class="op">=</span><span class="st">"vqe"</span>,</span>
+<span id="cb16-27"><a href="#cb16-27" aria-hidden="true" tabindex="-1"></a>        options_high<span class="op">=</span>{<span class="st">"basis"</span>: basis, <span class="st">"frozen_orbitals"</span>: frozen_orbitals_zwit, <span class="op">**</span>vqe_options})</span>
+<span id="cb16-28"><a href="#cb16-28" aria-hidden="true" tabindex="-1"></a>})</span>
+<span id="cb16-29"><a href="#cb16-29" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb16-30"><a href="#cb16-30" aria-hidden="true" tabindex="-1"></a>e_qmmm_zwit <span class="op">=</span> qmmm_model_zwit.simulate()</span>
+<span id="cb16-31"><a href="#cb16-31" aria-hidden="true" tabindex="-1"></a><span class="bu">print</span>(<span class="ss">f"The hydration energy for glycine (zwitterion) is </span><span class="sc">{</span>(e_qmmm_gly<span class="op">-</span>e_quantum_zwit) <span class="op">*</span> ha_to_kcalmol <span class="op">*</span> cal_to_j<span class="sc">:5.0f}</span><span class="ss"> kJ/mol."</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell-output cell-output-stdout">
+<pre><code>The hydration energy for glycine (zwitterion) is  -292 kJ/mol.</code></pre>
+</div>
+</div>
+<p>It’s important to note that we haven’t deducted the potential energy contribution of water molecules. This omission is intentional based on the PySCF backend used in this study, as outlined in its <a href="https://pyscf.org/user/qmmm.html">QM/MM documentation</a>. In PySCF’s implementation, the calculated total energy doesn’t include the static Coulomb interactions of MM point charges, MM energy, vdw interaction, or other bonding/non-bonding effects between QM and MM particles. Tangelo supports other chemistry backends, including Psi4, and users should refer to the relevant backend documentation to confirm energy contributions and understand the output.</p>
+<p>The results indicate negative energy differences, suggesting stabilization for both forms of the glycine amino acid in aqueous solutions. Experimental <span class="math inline">\(\Delta H_{\text{solv}}\)</span> is approximately 122 kJ/mol (Russian Journal of General Chemistry, 2008, 78, 6, 1155 - 1160). While we’re not directly computing free energy differences (for example, we didn’t include entropic effects), our results fall within a similar order of magnitude. Notably, the zwitterion form exhibits enhanced stabilization by the water shell, attributed to water’s polar nature, which enhances its ability to solvate polar molecules.</p>
+</section>
+</section>
+<section id="closing-words" class="level2">
+<h2 class="anchored" data-anchor-id="closing-words">Closing words</h2>
+<p>This notebook serves as an introductory exploration of the QM/MM method applied to biochemical systems within aqueous environments, demonstrating how quantum algorithms in Tangelo can be applied to such applications.</p>
+<p>By examining glycine tautomers and stability differences, it showcases the potential of QM/MM for studying solvated systems. We demonstrated that QM/MM + VQE calculations are able to show both forms of the glycine amino acid are stabilized in aqueous solutions. Although we didn’t directly compute free energy differences, our results roughly align with experimental data, notably indicating the zwitterion’s enhanced stabilization by the water shell due to water’s inherent polarity.</p>
+<p>Like other problem decomposition techniques available in Tangelo (ONIOM, DMET, etc), the QM/MM implementation gives users the freedom to select and integrate quantum algorithms tailored to their research needs. In this tutorial, we simply used VQE as the fragment solver, but the QM/MM method can be paired with other quantum or classical solvers in Tangelo. Users can tailor quantum algorithms to their biochemical systems, optimizing their computational approach based on the nature and complexity of the problem at hand.</p>
+<p>What will you do with QM/MM and Tangelo ?</p>
+</section>
+<section id="references" class="level2">
+<h2 class="anchored" data-anchor-id="references">References</h2>
+<ol type="1">
+<li>Liu, H.; Low, G.H.; Steiger, D.S.; Häner, T.; Reiher, M.; Troyer, M. Prospects of quantum computing for molecular sciences. Materials Theory. 2022, 6, 11.</li>
+<li>Izsák, R.; Riplinger, C.; Blunt, N.S.; de Souza, D.; Holzmann, N.; Crawford, O.; Camps, J.; Neese, F.; Schopf, P. Quantum computing in pharma: A multilayer embedding approach for near future applications. J. Comput. Chem. 2023, 44(3), 406.</li>
+<li>Jensen, J.H.; Gordon, M.S. On the Number of Water Molecules Necessary To Stabilize the Glycine Zwitterion. J. Am. Chem. Soc. 1995, 117, 8159-8170.</li>
+<li>Fernandez-Ramos, A.; Smedarchina, Z.; Siebrand, W.; Zgierski, M.Z. A direct-dynamics study of the zwitterion-to-neutral interconversion of glycine in aqueous solution. J. Chem. Phys. 2000, 113, 9714-9721.</li>
+<li>Valverde, D.; da Costa Ludwig, Z.M.; da Costa, C.R.; Ludwig, V.; Georg, H. C. Zwitterionization of glycine in water environment: Stabilization mechanism and NMR spectral signatures. J. Chem. Phys. 2018, 148, 024305.</li>
+<li>Bhate, M.P.; Woodard, J.C.; Mehta M.A.&nbsp;Solvation and Hydrogen Bonding in Alanine- and Glycine-Containing Dipeptides Probed Using Solution- and Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2009, 131, 27, 9579-9589.</li>
+<li>Takenaka, N.; Kitamura, Y.; Koyano, Y.; Asada, T.; Nagaoka, M. Reaction path optimization and vibrational frequency analysis via ab initio QM/MM free energy gradient (FEG) method: Application to isomerization process of glycine in aqueous solution. Theor. Chem. Acc. 2011, 130, 215-226.</li>
+</ol>
+
+
+</section>
+
+</main> <!-- /main -->
+<script id="quarto-html-after-body" type="application/javascript">
+window.document.addEventListener("DOMContentLoaded", function (event) {
+  const toggleBodyColorMode = (bsSheetEl) => {
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+      try { href = new URL(href).hash; } catch {}
+      const id = href.replace(/^#\/?/, "");
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diff --git a/examples/variational_methods/adapt.html b/examples/variational_methods/adapt.html
index 1fecf3d..a04bc2f 100644
--- a/examples/variational_methods/adapt.html
+++ b/examples/variational_methods/adapt.html
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/variational_methods/iqcc_using_clifford.html b/examples/variational_methods/iqcc_using_clifford.html
index a3fa28e..4e53069 100644
--- a/examples/variational_methods/iqcc_using_clifford.html
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/variational_methods/vqe.html b/examples/variational_methods/vqe.html
index a81c44f..c401036 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/variational_methods/vqe_custom_ansatz_hamiltonian.html b/examples/variational_methods/vqe_custom_ansatz_hamiltonian.html
index 1de5d82..49e22d1 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/workflow_basics/1.the_basics.html b/examples/workflow_basics/1.the_basics.html
index 130f4d1..efcb203 100644
--- a/examples/workflow_basics/1.the_basics.html
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/workflow_basics/2.qpu_connection.html b/examples/workflow_basics/2.qpu_connection.html
index c56b0b5..1bf4ffa 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/workflow_basics/3.noisy_simulation.html b/examples/workflow_basics/3.noisy_simulation.html
index 4c8dfd7..11f2e40 100644
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/examples/workflow_basics/symbolic_simulator.html b/examples/workflow_basics/symbolic_simulator.html
index b407a0a..669096c 100644
--- a/examples/workflow_basics/symbolic_simulator.html
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T1_circuits.html b/hands_on/T1_circuits.html
index 1c1ca6a..e930c45 100644
--- a/hands_on/T1_circuits.html
+++ b/hands_on/T1_circuits.html
@@ -269,6 +269,12 @@
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T1_circuits_solved.html b/hands_on/T1_circuits_solved.html
index c2ba2df..a3cef2f 100644
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T2_simulators.html b/hands_on/T2_simulators.html
index bcb7d9e..2cd8233 100644
--- a/hands_on/T2_simulators.html
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@@ -271,6 +271,12 @@
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T2_simulators_solved.html b/hands_on/T2_simulators_solved.html
index ca05e4a..7e16b4a 100644
--- a/hands_on/T2_simulators_solved.html
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@@ -271,6 +271,12 @@
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T3_VQE.html b/hands_on/T3_VQE.html
index d5ff311..6f02530 100644
--- a/hands_on/T3_VQE.html
+++ b/hands_on/T3_VQE.html
@@ -271,6 +271,12 @@
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  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T3_VQE_solved.html b/hands_on/T3_VQE_solved.html
index 53702c9..4d2355e 100644
--- a/hands_on/T3_VQE_solved.html
+++ b/hands_on/T3_VQE_solved.html
@@ -271,6 +271,12 @@
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T4_hardware_experiments.html b/hands_on/T4_hardware_experiments.html
index 7f75138..20fc24a 100644
--- a/hands_on/T4_hardware_experiments.html
+++ b/hands_on/T4_hardware_experiments.html
@@ -271,6 +271,12 @@
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T4_hardware_experiments_solved.html b/hands_on/T4_hardware_experiments_solved.html
index ebc7eab..653c66d 100644
--- a/hands_on/T4_hardware_experiments_solved.html
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T5_fault_tolerant_build_blocks.html b/hands_on/T5_fault_tolerant_build_blocks.html
index e349a25..4047f0b 100644
--- a/hands_on/T5_fault_tolerant_build_blocks.html
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   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/hands_on/T5_fault_tolerant_build_blocks_solved.html b/hands_on/T5_fault_tolerant_build_blocks_solved.html
index 641935c..ea57477 100644
--- a/hands_on/T5_fault_tolerant_build_blocks_solved.html
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+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="../examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
diff --git a/index.html b/index.html
index eba776a..1deb2cf 100644
--- a/index.html
+++ b/index.html
@@ -235,6 +235,12 @@
   <a href="./examples/problem_decomposition/oniom.html" class="sidebar-item-text sidebar-link">
  <span class="menu-text">ONIOM Problem Decomposition - A use case for an acetic acid molecule in water</span></a>
   </div>
+</li>
+          <li class="sidebar-item">
+  <div class="sidebar-item-container"> 
+  <a href="./examples/problem_decomposition/qmmm.html" class="sidebar-item-text sidebar-link">
+ <span class="menu-text">The QM/MM method: Solvation of the Glycine Amino Acid</span></a>
+  </div>
 </li>
       </ul>
   </li>
@@ -428,6 +434,7 @@
 <li><a href="examples/problem_decomposition/dmet_uhf.html">DMET Unrestricted Hartree-Fock</a></li>
 <li><a href="examples/problem_decomposition/ifci_mifno.html">iFCI - MIFNO</a></li>
 <li><a href="examples/problem_decomposition/oniom.html">ONIOM</a></li>
+<li><a href="examples/problem_decomposition/qmmm.html">QMMM</a></li>
 </ul></li>
 <li>Hardware Experiments
 <ul>
diff --git a/search.json b/search.json
index d0d1162..de78f25 100644
--- a/search.json
+++ b/search.json
@@ -123,7 +123,7 @@
     "href": "index.html",
     "title": "",
     "section": "",
-    "text": "Welcome !\nThis website contains the jupyter notebooks for Tangelo. This includes tutorial notebooks and research-related notebooks. Anyone can contribute a notebook to the repository!\nIf you are new to Tangelo, we suggest you start with 1. The basics, and Quantum Chemistry Basics. After that, what you are most interested in determines where you go next !\nThere are multiple ways to run and play with these notebooks: through Binder, Google Colab, a local install (…).\nAn overview of the many notebooks so far (there may be more, including example scripts as well):\n\nWorkflow Basics\n\n1. The basics\n2. QPU Connection\n3. Noisy Simulation\nSymbolic Simulation\n\nChemistry\n\nQuantum Chemistry Basics\nExcited State methods\n\nVariational Methods\n\nVQE\nVQE with user defined ansatz\nAdapt VQE Solver\nIterative Qubit Coupled Cluster using only Clifford Circuits\n\nMeasurement Reduction\n\nClassical Shadows\n\nProblem Decomposition\n\nDensity Matrix Embedding Theory\nDMET Unrestricted Hartree-Fock\niFCI - MIFNO\nONIOM\n\nHardware Experiments\n\nEnd-to-End hardware experiment\nHardware Experiment using QEMIST Cloud\nBerylium IBM quantum experiment\nUmbrella inversion Braket\n\nFault Tolerant\n\nState Preparation using Quantum Signal Processing"
+    "text": "Welcome !\nThis website contains the jupyter notebooks for Tangelo. This includes tutorial notebooks and research-related notebooks. Anyone can contribute a notebook to the repository!\nIf you are new to Tangelo, we suggest you start with 1. The basics, and Quantum Chemistry Basics. After that, what you are most interested in determines where you go next !\nThere are multiple ways to run and play with these notebooks: through Binder, Google Colab, a local install (…).\nAn overview of the many notebooks so far (there may be more, including example scripts as well):\n\nWorkflow Basics\n\n1. The basics\n2. QPU Connection\n3. Noisy Simulation\nSymbolic Simulation\n\nChemistry\n\nQuantum Chemistry Basics\nExcited State methods\n\nVariational Methods\n\nVQE\nVQE with user defined ansatz\nAdapt VQE Solver\nIterative Qubit Coupled Cluster using only Clifford Circuits\n\nMeasurement Reduction\n\nClassical Shadows\n\nProblem Decomposition\n\nDensity Matrix Embedding Theory\nDMET Unrestricted Hartree-Fock\niFCI - MIFNO\nONIOM\nQMMM\n\nHardware Experiments\n\nEnd-to-End hardware experiment\nHardware Experiment using QEMIST Cloud\nBerylium IBM quantum experiment\nUmbrella inversion Braket\n\nFault Tolerant\n\nState Preparation using Quantum Signal Processing"
   },
   {
     "objectID": "examples/chemistry/qchem_modelling_basics.html",
@@ -468,6 +468,41 @@
     "section": "Closing words",
     "text": "Closing words\nThis feature allows us to bring together the state-of-the-art MI problem decomposition schemes available at scale in QEMIST cloud, and quantum workflows written with Tangelo. It facilitates exploring larger, more industrially-relevant use cases with a combination of classical and quantum workflows of your choice, on subproblems that are more ammenable to current devices.\nBoth iFCI and MI-FNO implement the method of increments. They differ in how they truncate the virtual orbital space (SNO vs FNO) and the inclusion of a correction factor for MI-FNO fragments (which is not required for iFCI fragments).\nFor now, this exploration is manual, as we believe the current state of the field does not benefit from a fully automated and streamlined platform… yet! In the future, platforms such as QEMIST Cloud will be able to directly use Tangelo to run entire workflows on cloud infrastructure, using both quantum and classical devices.\nMaybe your discoveries can contribute to advancing the field, and bring that future a bit sooner.\nWhat will you do with Tangelo?"
   },
+  {
+    "objectID": "examples/problem_decomposition/qmmm.html",
+    "href": "examples/problem_decomposition/qmmm.html",
+    "title": "The QM/MM method: Solvation of the Glycine Amino Acid",
+    "section": "",
+    "text": "In 2013, the Nobel Prize in Chemistry was awarded to Martin Karplus, Michael Levitt, and Arieh Warshel for their groundbreaking work in advancing the understanding of complex chemical systems. Their achievement was centered around the development of multiscale models, a significant milestone in the field of computational chemistry. Specifically, their work highlighted the QM/MM method, an abbreviation for Quantum Mechanics/Molecular Mechanics. Introduced in 1976 in the Journal of Molecular Biology, it amalgamates quantum mechanics, which describes the behavior of particles at the electronic level, with molecular mechanics, a classical approach that uses forcefields to model interatomic interactions. The introduction of this method became a cornerstone in biochemical simulation workflows, allowing scientists to simulate and understand complex chemical reactions occurring within biological contexts with remarkable accuracy. Its primary objective remains the reduction of computational cost in modeling intricate chemical systems, useful in the study of biochemical entities like DNA/RNA strands, proteins, and organic molecules.\nConsider protein simulations as a case in point: the majority of proteins consist of 50 to 200 amino acids (source). With an average of approximately 19 atoms per amino acid, a solitary protein system might necessitate the consideration of anywhere between 950 to 3800 atoms. This estimate however does not take into account solvents, ions, and other vital molecular species that could be important in the simulation model.\nThis problem size is quite typical in many molecular mechanics workflows. Nonetheless, handling interactions like charge transfers or hydrogen bonds, which are pivotal in protein/drug interactions, can pose challenges when using forcefield-based methods. In such scenarios, the nuanced description of these molecular interactions is better represented via quantum mechanics. However, the problem size becomes intractable for quantum mechanics methods alone. Hence, the fusion of both realms has been beneficial for the computational chemistry community and forms the essence of the QM/MM approach.\n\n\n\nMolecules reside within the microscopic realm and adhere to the principles of the Schrödinger equation. For more introductory material on modeling molecular systems, please refer to our previous notebook.\nQuantum computing research is rapidly advancing on both software and hardware fronts. Chemistry stands out as a promising application for these devices, propelling an active research field, exemplified further in the paper reviews by Kassal et al. and Cao et al.. Harnessing QM/MM methodologies within quantum computing simulations holds promise in capturing crucial environmental effects, such as solvent interactions, enriching the accuracy and realism of computational models [1, 2].\n\n\n\nWe apply this approach to the explicit solvation of a simple amino acid (glycine) in water through electrostatic embedding. To determine solvation energies for chemical compounds, the following steps are taken in this notebook: 1. Compute the molecular energies of isolated compounds using a quantum algorithm. For the sake of simplicity, the quantum algorithm used here is the Variational Quantum Eigensolver (VQE). Other quantum solvers available in Tangelo have already been or can be integrated with QM/MM. 2. Calculate the molecular energies of solvated compounds. In this step, the QM/MM problem decomposition method models the glycine amino acid using VQE, similar to the previous step. Meanwhile, explicit water molecules are modeled through molecular mechanics. 3. Determine the energy differences that signify solvation energy. A more negative energy denotes a stronger interaction between the solvent and the molecule."
+  },
+  {
+    "objectID": "examples/problem_decomposition/qmmm.html#introduction",
+    "href": "examples/problem_decomposition/qmmm.html#introduction",
+    "title": "The QM/MM method: Solvation of the Glycine Amino Acid",
+    "section": "",
+    "text": "In 2013, the Nobel Prize in Chemistry was awarded to Martin Karplus, Michael Levitt, and Arieh Warshel for their groundbreaking work in advancing the understanding of complex chemical systems. Their achievement was centered around the development of multiscale models, a significant milestone in the field of computational chemistry. Specifically, their work highlighted the QM/MM method, an abbreviation for Quantum Mechanics/Molecular Mechanics. Introduced in 1976 in the Journal of Molecular Biology, it amalgamates quantum mechanics, which describes the behavior of particles at the electronic level, with molecular mechanics, a classical approach that uses forcefields to model interatomic interactions. The introduction of this method became a cornerstone in biochemical simulation workflows, allowing scientists to simulate and understand complex chemical reactions occurring within biological contexts with remarkable accuracy. Its primary objective remains the reduction of computational cost in modeling intricate chemical systems, useful in the study of biochemical entities like DNA/RNA strands, proteins, and organic molecules.\nConsider protein simulations as a case in point: the majority of proteins consist of 50 to 200 amino acids (source). With an average of approximately 19 atoms per amino acid, a solitary protein system might necessitate the consideration of anywhere between 950 to 3800 atoms. This estimate however does not take into account solvents, ions, and other vital molecular species that could be important in the simulation model.\nThis problem size is quite typical in many molecular mechanics workflows. Nonetheless, handling interactions like charge transfers or hydrogen bonds, which are pivotal in protein/drug interactions, can pose challenges when using forcefield-based methods. In such scenarios, the nuanced description of these molecular interactions is better represented via quantum mechanics. However, the problem size becomes intractable for quantum mechanics methods alone. Hence, the fusion of both realms has been beneficial for the computational chemistry community and forms the essence of the QM/MM approach.\n\n\n\nMolecules reside within the microscopic realm and adhere to the principles of the Schrödinger equation. For more introductory material on modeling molecular systems, please refer to our previous notebook.\nQuantum computing research is rapidly advancing on both software and hardware fronts. Chemistry stands out as a promising application for these devices, propelling an active research field, exemplified further in the paper reviews by Kassal et al. and Cao et al.. Harnessing QM/MM methodologies within quantum computing simulations holds promise in capturing crucial environmental effects, such as solvent interactions, enriching the accuracy and realism of computational models [1, 2].\n\n\n\nWe apply this approach to the explicit solvation of a simple amino acid (glycine) in water through electrostatic embedding. To determine solvation energies for chemical compounds, the following steps are taken in this notebook: 1. Compute the molecular energies of isolated compounds using a quantum algorithm. For the sake of simplicity, the quantum algorithm used here is the Variational Quantum Eigensolver (VQE). Other quantum solvers available in Tangelo have already been or can be integrated with QM/MM. 2. Calculate the molecular energies of solvated compounds. In this step, the QM/MM problem decomposition method models the glycine amino acid using VQE, similar to the previous step. Meanwhile, explicit water molecules are modeled through molecular mechanics. 3. Determine the energy differences that signify solvation energy. A more negative energy denotes a stronger interaction between the solvent and the molecule."
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+    "title": "The QM/MM method: Solvation of the Glycine Amino Acid",
+    "section": "Use-case: Solvation of the glycine animo acid",
+    "text": "Use-case: Solvation of the glycine animo acid\n\nPreparation for the notebook\nThe next cells ensure that the appropriate packages are installed and imported into the Python environment to successfully execute this notebook.\n\ntry:\n    import tangelo\nexcept ModuleNotFoundError:\n    !pip install git+https://github.com/goodchemistryco/Tangelo.git@develop --quiet\n    !pip install qulacs pyscf rdkit openbabel-wheel --quiet\n\n\n# Tangelo common imports.\nfrom tangelo import SecondQuantizedMolecule\nfrom tangelo.algorithms.variational import VQESolver, BuiltInAnsatze\nfrom tangelo.toolboxes.molecular_computation.frozen_orbitals import get_orbitals_excluding_homo_lumo\nfrom tangelo.toolboxes.molecular_computation.molecule import atom_string_to_list\n\n# QM/MM-related imports.\nfrom tangelo.problem_decomposition.qmmm.qmmm_problem_decomposition import QMMMProblemDecomposition\nfrom tangelo.problem_decomposition.oniom._helpers.helper_classes import Fragment, Link\nfrom tangelo.toolboxes.molecular_computation.mm_charges_solver import MMChargesSolverRDKit\n\n# Basis set used in this notebook.\nbasis = \"cc-pvdz\"\n\n# Constants.\nha_to_kcalmol = 627.509\ncal_to_j = 4.184\n\n\n\nAmino acid tautomers\nAmino acids form the basic building blocks of polypeptides and proteins within living organisms. While nature encompasses about 500 variations, only 22 are encoded in the genetic blueprint of life. These molecules are characterized by their end-capping functional groups: an amine (NH\\(_3\\)) and a carboxylic acid (COOH), with a central functional group denoted as ‘R’ that defines the unique properties of each amino acid.\nThis notebook primarily focuses on employing computational techniques that integrate quantum mechanics with molecular mechanics (QM/MM). This method allows researchers to explore interactions among molecules within aqueous solutions, providing essential insights into the behaviors and functionalities of proteins at a reasonable computational cost.\nOur initial step involves defining the atomic coordinates of glycine, the simplest amino acid with a ‘R’ functional group consisting solely of a hydrogen atom. Given the extensive computational requirements for running a full quantum algorithm on the entire system, this notebook opts to freeze certain molecular orbitals, therefore simplifying the simulation to manage its complexity.\n\nxyz_glycine = \"\"\"\n  C          2.05388        0.61558        0.07379\n  O          1.96483       -0.57096       -0.21241\n  O          3.19750        1.18239        0.43269\n  H          3.96112        0.54040        0.42260\n  C          0.91678        1.61052        0.03784\n  H          0.94914        2.17916        0.95644\n  H          1.13065        2.30136       -0.76945\n  N         -0.39578        0.99717       -0.14991\n  H         -0.70125        0.48980        0.67086\n  H         -0.41063        0.36439       -0.94717\n\"\"\"\n\n# Creating a molecule object from the coordinates.\nglycine = SecondQuantizedMolecule(xyz_glycine, basis=basis)\n\n# Setting the active space to HOMO-1 to LUMO+1.\nfrozen_orbitals_gly = get_orbitals_excluding_homo_lumo(glycine, homo_minus_n=1, lumo_plus_n=1)\nglycine.freeze_mos(frozen_orbitals_gly, inplace=True)\nprint(f\"The neutral form of GLY will be described by an active space of {glycine.n_active_mos} molecular orbitals and {glycine.n_active_electrons} electrons.\")\n\nThe neutral form of GLY will be described by an active space of 4 molecular orbitals and 4 electrons.\n\n\nOne might wonder why this amino acid dissolves in water despite being a neutral organic compound. The reason lies in its behavior when in water; evidences show that amino acids adopt a zwitterionic form [3-6]. Although the entire molecule remains electrically neutral, a hydrogen atom shifts from the carboxylic acid group to the amine group, showcasing a form of tautomerism. Thus, to precisely model the interaction of water with glycine, it is crucial to include the equivalent tautomer in the calculations of solvation properties.\nIn the next cell, we construct this chemical structure while using the same approach of freezing certain molecular orbitals.\n\nxyz_zwitterion = \"\"\"\n  C         -0.72588       -0.48930       -0.87995\n  O         -0.40429       -0.99901        0.24400\n  O         -1.71249       -0.74617       -1.57606\n  C          0.24065        0.58647       -1.40746\n  H          0.94067        0.15610       -2.10976\n  H         -0.32329        1.37177       -1.87959\n  N          0.99940        1.14332       -0.24215\n  H          1.19967        0.36262        0.37817\n  H          1.91733        1.52621       -0.51811\n  H          0.35328        1.80600        0.26884\n\"\"\"\n\n# Creating a molecule object from the coordinates.\nzwitterion = SecondQuantizedMolecule(xyz_zwitterion, basis=basis)\n\n# Setting the active space to HOMO-1 to LUMO+1.\nfrozen_orbitals_zwit = get_orbitals_excluding_homo_lumo(zwitterion, homo_minus_n=1, lumo_plus_n=1)\nzwitterion.freeze_mos(frozen_orbitals_zwit)\nprint(f\"The zwitterion form of GLY will be described by an active space of {zwitterion.n_active_mos} molecular orbitals and {zwitterion.n_active_electrons} electrons.\")\n\nThe zwitterion form of GLY will be described by an active space of 4 molecular orbitals and 4 electrons.\n\n\nWith the molecules now encoded as Tangelo objects, we’re ready to perform quantum chemistry calculations. Below is a visual representation illustrating the two distinct tautomers of the glycine amino acid that we previously constructed.\n\n\n\nGlycine forms\n\n\n\n\nUsing quantum algorithms on the glycine molecule\nThe following code cell defines the options passed to our quantum solver (for simplicity, the well-known Variational Quantum Eigensolver (VQE) with a UCCSD ansatz). These settings are applied in subsequent energy computations.\n\nvqe_options= {\n    \"ansatz\": BuiltInAnsatze.UCCSD,\n    \"qubit_mapping\": \"scBK\",\n    \"up_then_down\": True\n }\n\nWe then run the quantum solver for both forms of glycine. We are particularly interested in the total molecular energies obtained, as they are necessary to calculate the hydration energy later on (see step 1 outlined in the “Computing solvation energies” section above).\n\nquantum_solver_gly = VQESolver({\"molecule\": glycine, **vqe_options})\nquantum_solver_gly.build()\ne_quantum_gly = quantum_solver_gly.simulate()\nprint(f\"The gas phase molecular energy of glycine (neutral) is {e_quantum_gly:.5f} Ha.\")\n\nThe gas phase molecular energy of glycine (neutral) is -282.85661 Ha.\n\n\n\nquantum_solver_zwit = VQESolver({\"molecule\": zwitterion, **vqe_options})\nquantum_solver_zwit.build()\ne_quantum_zwit = quantum_solver_zwit.simulate()\nprint(f\"The gas phase molecular energy of glycine (zwitterion) is {e_quantum_zwit:.5f} Ha.\")\n\nThe gas phase molecular energy of glycine (zwitterion) is -282.79736 Ha.\n\n\nSince tautomers have the same set of atoms, comparing the two molecular energies indicates that the neutral form of the glycine amino acid is more stable than the zwitterion. This outcome aligns with the fact that formal charges on atoms in the gas phase are difficult to generate due to the lack of an environment for stabilization.\nWe now have access to the molecular energies of each tautomer. We now sample the energy of the molecular system consisting of a cluster of water around the molecules (see step 2 outlined in the “Computing solvation energies” section above). The energy differences \\(\\Delta E_{\\text{solv}}\\) (after removing the water molecule potential energy contributions) should be proportional to the free energies of solvation \\(\\Delta H_{\\text{solv}}\\) or \\(\\Delta G_{\\text{solv}}\\) measured in laboratories.\nThe remaining steps taken in this notebook are revolving around computing the molecular energies of those clusters using the QM/MM method, which is a simplified version of a more complete study as reported in [7].\n\n\nPreparing the QM/MM calculation: get the partial charges for \\(H_2O\\)\nThe supported QM/MM framework in Tangelo needs the partial charges for the part of the system described via molecular mechanics. This is what we do in the next code cell. Here, in summary: - A mean-field calculation is performed for a single water molecule; - The Mulliken atomic charges are retrived from the analyze method; - A function is defined to construct an array in the [(partial_charge, (x, y, z)), ...] format.\n\nxyz_h2o = \"\"\"\n  O         -2.08448       -2.25652       -0.22848\n  H         -2.35312       -3.17615       -0.12238\n  H         -1.83562       -1.85666        0.64078\n\"\"\"\n\nh2o = SecondQuantizedMolecule(xyz_h2o, basis=basis)\n(_, mulliken_atomic_charges), _ = h2o.mean_field.analyze()\n\ndef get_charges(water_molecule_coords):\n    xyz_h2os = atom_string_to_list(water_molecule_coords)\n    mulliken_charges_waters = [*mulliken_atomic_charges] * (len(xyz_h2os) // len(mulliken_atomic_charges))\n\n    return [(q, xyz_h2os[i][1]) for i, q in enumerate(mulliken_charges_waters)]\n\nprint(f\"The Mulliken partial charges computed from an Hartree-Fock calculation in {basis} are\\nO = {mulliken_atomic_charges[0]}\\nH1 = {mulliken_atomic_charges[1]}\\nH2 = {mulliken_atomic_charges[2]}.\")\n\nThe Mulliken partial charges computed from an Hartree-Fock calculation in cc-pvdz are\nO = -0.6346652155730794\nH1 = 0.3194372332962432\nH2 = 0.31522798227682913.\n\n\n\n\nComputing the solvation energies using QM/MM with charge embedding\nThe next task involves computing solvated molecule energies using the QM/MM electrostatic embedding method. Using the previously calculated water atomic charges, the QMMMProblemDecomposition class consolidates necessary information for this calculation. This includes: - “geometry”: Coordinates of the molecule in a list format. - “mmpackage”: Molecular mechanics package utilized. - “charges”: Electrostatic charges and their coordinates. - “qmfragment”: A Fragment object defining the solver and related options for computing the molecular energy in quantum mechanics.\nIt’s worth noting the various methods available for generating water cluster geometries. The following geometries were created by randomly positioning three water molecules around each terminal and subsequently optimized using the AMBER94 force field. This optimization step can be done with any molecular mechanics package, like OpenMM or RDKit. An illustration showcasing one of the generated conformations is presented in the figure below.\n\n\n\nCluster of water molecules and glycine\n\n\n\nxyz_waters_gly = \"\"\"\n  O         -2.08448       -2.25652       -0.22848\n  H         -2.35312       -3.17615       -0.12238\n  H         -1.83562       -1.85666        0.64078\n  O         -0.29165       -1.17766       -1.97014\n  H          0.55770       -1.31516       -1.52416\n  H         -0.98020       -1.66830       -1.47470\n  O          4.62948       -0.92998        0.20740\n  H          5.09272       -1.49221        0.83838\n  H          3.79167       -1.33448       -0.07876\n  O         -2.80676        2.14474       -0.62525\n  H         -1.85118        1.90309       -0.45829\n  H         -2.93359        2.38421       -1.55080\n  O         -1.81568       -0.72927        1.87434\n  H         -1.84048       -0.80009        2.83473\n  H         -2.66617       -0.33065        1.49202\n  O         -3.76770        0.00135        0.46835\n  H         -3.57200        0.87852        0.03795\n  H         -3.59648       -0.71670       -0.16049\n\"\"\"\n\nqmmm_model_gly = QMMMProblemDecomposition({\n    \"geometry\": atom_string_to_list(xyz_glycine),\n    \"mmpackage\": \"rdkit\",\n    \"charges\": get_charges(xyz_waters_gly),\n    \"qmfragment\": Fragment(solver_high=\"vqe\",\n        options_high={\"basis\": basis, \"frozen_orbitals\": frozen_orbitals_gly, **vqe_options})\n})\n\ne_qmmm_gly = qmmm_model_gly.simulate()\nprint(f\"The hydration energy for glycine (neutral) is {(e_qmmm_gly-e_quantum_gly) * ha_to_kcalmol * cal_to_j:5.0f} kJ/mol.\")\n\nThe hydration energy for glycine (neutral) is  -136 kJ/mol.\n\n\n\nxyz_waters_zwit = \"\"\"\n  O         -2.33478        0.43459        1.56814\n  H         -1.65671       -0.25663        1.45580\n  H         -3.11977        0.14754        1.04111\n  O          3.57502        1.26874       -0.76381\n  H          3.59649        0.47309       -0.17203\n  H          4.40577        1.75433       -0.74479\n  O         -0.93902        2.44112        0.89259\n  H         -1.06155        3.25709        1.38776\n  H         -1.58516        1.71621        1.19305\n  O         -3.99606       -0.58515       -0.21107\n  H         -4.64697       -0.10084       -0.73262\n  H         -3.23854       -0.83634       -0.78921\n  O          3.12434       -0.68537        0.90701\n  H          3.33270       -0.62390        1.84641\n  H          2.63054       -1.54344        0.73112\n  O          1.55389       -2.64818        0.61476\n  H          0.69747       -2.15400        0.51558\n  H          1.54074       -3.48659        0.14319\n\"\"\"\n\nqmmm_model_zwit = QMMMProblemDecomposition({\n    \"geometry\": atom_string_to_list(xyz_zwitterion),\n    \"mmpackage\": \"rdkit\",\n    \"charges\": get_charges(xyz_waters_zwit),\n    \"qmfragment\": Fragment(solver_high=\"vqe\",\n        options_high={\"basis\": basis, \"frozen_orbitals\": frozen_orbitals_zwit, **vqe_options})\n})\n\ne_qmmm_zwit = qmmm_model_zwit.simulate()\nprint(f\"The hydration energy for glycine (zwitterion) is {(e_qmmm_gly-e_quantum_zwit) * ha_to_kcalmol * cal_to_j:5.0f} kJ/mol.\")\n\nThe hydration energy for glycine (zwitterion) is  -292 kJ/mol.\n\n\nIt’s important to note that we haven’t deducted the potential energy contribution of water molecules. This omission is intentional based on the PySCF backend used in this study, as outlined in its QM/MM documentation. In PySCF’s implementation, the calculated total energy doesn’t include the static Coulomb interactions of MM point charges, MM energy, vdw interaction, or other bonding/non-bonding effects between QM and MM particles. Tangelo supports other chemistry backends, including Psi4, and users should refer to the relevant backend documentation to confirm energy contributions and understand the output.\nThe results indicate negative energy differences, suggesting stabilization for both forms of the glycine amino acid in aqueous solutions. Experimental \\(\\Delta H_{\\text{solv}}\\) is approximately 122 kJ/mol (Russian Journal of General Chemistry, 2008, 78, 6, 1155 - 1160). While we’re not directly computing free energy differences (for example, we didn’t include entropic effects), our results fall within a similar order of magnitude. Notably, the zwitterion form exhibits enhanced stabilization by the water shell, attributed to water’s polar nature, which enhances its ability to solvate polar molecules."
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+    "title": "The QM/MM method: Solvation of the Glycine Amino Acid",
+    "section": "Closing words",
+    "text": "Closing words\nThis notebook serves as an introductory exploration of the QM/MM method applied to biochemical systems within aqueous environments, demonstrating how quantum algorithms in Tangelo can be applied to such applications.\nBy examining glycine tautomers and stability differences, it showcases the potential of QM/MM for studying solvated systems. We demonstrated that QM/MM + VQE calculations are able to show both forms of the glycine amino acid are stabilized in aqueous solutions. Although we didn’t directly compute free energy differences, our results roughly align with experimental data, notably indicating the zwitterion’s enhanced stabilization by the water shell due to water’s inherent polarity.\nLike other problem decomposition techniques available in Tangelo (ONIOM, DMET, etc), the QM/MM implementation gives users the freedom to select and integrate quantum algorithms tailored to their research needs. In this tutorial, we simply used VQE as the fragment solver, but the QM/MM method can be paired with other quantum or classical solvers in Tangelo. Users can tailor quantum algorithms to their biochemical systems, optimizing their computational approach based on the nature and complexity of the problem at hand.\nWhat will you do with QM/MM and Tangelo ?"
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+    "href": "examples/problem_decomposition/qmmm.html#references",
+    "title": "The QM/MM method: Solvation of the Glycine Amino Acid",
+    "section": "References",
+    "text": "References\n\nLiu, H.; Low, G.H.; Steiger, D.S.; Häner, T.; Reiher, M.; Troyer, M. Prospects of quantum computing for molecular sciences. Materials Theory. 2022, 6, 11.\nIzsák, R.; Riplinger, C.; Blunt, N.S.; de Souza, D.; Holzmann, N.; Crawford, O.; Camps, J.; Neese, F.; Schopf, P. Quantum computing in pharma: A multilayer embedding approach for near future applications. J. Comput. Chem. 2023, 44(3), 406.\nJensen, J.H.; Gordon, M.S. On the Number of Water Molecules Necessary To Stabilize the Glycine Zwitterion. J. Am. Chem. Soc. 1995, 117, 8159-8170.\nFernandez-Ramos, A.; Smedarchina, Z.; Siebrand, W.; Zgierski, M.Z. A direct-dynamics study of the zwitterion-to-neutral interconversion of glycine in aqueous solution. J. Chem. Phys. 2000, 113, 9714-9721.\nValverde, D.; da Costa Ludwig, Z.M.; da Costa, C.R.; Ludwig, V.; Georg, H. C. Zwitterionization of glycine in water environment: Stabilization mechanism and NMR spectral signatures. J. Chem. Phys. 2018, 148, 024305.\nBhate, M.P.; Woodard, J.C.; Mehta M.A. Solvation and Hydrogen Bonding in Alanine- and Glycine-Containing Dipeptides Probed Using Solution- and Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2009, 131, 27, 9579-9589.\nTakenaka, N.; Kitamura, Y.; Koyano, Y.; Asada, T.; Nagaoka, M. Reaction path optimization and vibrational frequency analysis via ab initio QM/MM free energy gradient (FEG) method: Application to isomerization process of glycine in aqueous solution. Theor. Chem. Acc. 2011, 130, 215-226."
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