Maple Quantum Chemistry Toolbox
The Maple Quantum Chemistry Toolbox from RDMChem, a separate add-on product to Maple, is a powerful environment for the computation and visualization of the electronic structure of molecules. In Maple 2023, this toolbox has significant new features and enhancements that enable:
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Searching the scientific literature for new journal articles and preprints without leaving Maple.
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Exploring algorithms and computations for quantum computers with the new QuantumComputing subpackage.
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Flying through a molecule or an orbital in 3-D with new fly-though molecular animations.
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Importing molecular geometries and skeletal structures for nearly 100 million chemical structures using SMILES formulas.
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Customizing your own Hamiltonian in variational calculations of the 2-RDM.
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Teaching with a new lesson on Fermi's Golden Rule, in addition to the other ≈30 builtin lessons for classroom learning and self-study, in undergraduate-to-graduate courses in chemistry and physics.
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Additional enhancements throughout the package.
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Note: The Maple Quantum Chemistry Toolbox (QCT) is required in order to execute the examples in this worksheet.
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Literature Search
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In Quantum Chemistry Toolbox 2023 a new command, LiteratureSearch, has been added that searches the scientific literature for you without ever leaving Maple. Just add some keywords to define your search and let Maple do the rest. By default QCT searches a collection of more than 40 million science articles and preprints from the EuropePMC database including the complete PubMed and PubMed Central collections. But QCT can also search the more than 2.2 million preprints on the arXiv server including the latest in physics from quantum physics to biophysics. Before we begin we load the QuantumChemistry package,
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Find articles on the methylation of RNA.
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By default, the page size is ten entries per page. Here we selected two entries per page to facilitate the demonstration. Upon executing the command again, the Quantum Chemistry Toolbox automatically gives you the next page of entries. The command can be reset to the first page of entries with the keyword resetpage. Search results can be simultaneously printed to the screen and a file with the filename keyword. We can search by keyword, author, and journal separately or all at once. Next, search the arXiv for the most recently posted preprints on quantum tunneling in molecules.
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Quantum Computing
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Use Quantum Chemistry Toolbox 2023 to explore quantum computing with the power of computer algebra. Perform simulations of a quantum computer in Maple. Unlike most simulators, Maple can compute with both exact arithmetic (i.e. rational and irrational numbers) and symbolic variables. The wave function is printed using an easy-to-understand Dirac-like notation. First, load the new QuantumComputing subpackage
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Maple knows the standard 1- and 2-qubit gates. For example, Pauli Z gate
or the Pauli X and Y gates
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or the most general 1-qubit gate, known as the U (universal) gate, that depends on 3 angles that we keep symbolic,
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or a 2-qubit gate like the CNOT gate.
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We can initialize a state of 4 qubits on our simulated quantum computer with the InitialState command
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The initial wave function has each of its 4 qubits in the lower state of the qubit, denoted by 0. To illustrate preparing a state on the quantum computer, use a product of gates (unitary transformations), known as a circuit, to prepare a Schrodinger cat state in which the state of all qubits down becomes entangled with the state of all qubits up. In the Quantum Chemistry Toolbox, the circuit is readily assembled as a Maple list of equations. The left side of an equation indicates the qubit or qubits on which the gate acts and the right side provides the gate itself.
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To prepare the new state, we act on the initial state state0 with our circuit.
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The new state entangles a state of 4 "down" qubits with a state of 4 "up" qubits. Like Schrodinger's cat, our state is half up and half down. The probability of being "up" in each qubit 1/2 as we can see from the QubitPopulationsPlot command
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SMILES
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Entering a molecule's geometry can be tedious. That is why in the Quantum Chemistry Toolbox there are unconventional ways to import geometries, such as retrieving them by chemical name from a database of nearly 100 million molecules. Now in Quantum Chemistry Toolbox 2023 you can also import molecular geometries and skeletal structures by their SMILES (Simplified Molecular-Input Line-Entry System) formula. Import some molecular geometries with SMILES and make some molecular plots
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and
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Similarly, we can import the skeletal structures of these molecules from SMILES formulas
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and
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Fly-through Molecular 3-D Animations
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It's a bird ... it's a plane ... it's Superman. Now you can fly through molecules with the new fly-though molecular 3-D animations in QCT 2023. We can make fly-through animations by adding the viewpoint keyword in PlotMolecule, DensityPlot3D, ChargesPlot, DipolePlot, TransitionDipolePlot, and ExcitonDensityPlot. The user can choose the strings "flythrough", "flythrough2", "flythrough3", "flythrough4", "circleright", or "circleleft" to obtain six different 3-D fly-through animations. For example, consider the molecule 1,3-dibromobenzene
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With the PlotMolecule command we have
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or the DipolePlot command
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or the LUMO from the DensityPlot3D command
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Custom Hamiltonians in Variational2RDM
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While the Quantum Chemistry Toolbox allows any molecule to be computed, sometimes it is useful to be able to solve a custom Hamiltonian, i.e. for a spin model. In Quantum Chemistry Toolbox 2023 any custom Hamiltonians can be used with the Variational2RDM method. Additional details and an example are available in the Help pages.
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Using the Package in the Classroom
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The Maple Quantum Chemistry Toolbox includes approximately 30 lessons that can be used in chemistry and physics courses from advanced high school courses through the graduate level. These lessons and associated curricula provide instructors and students with real-time quantum chemistry computations and visualizations that quickly deepen understanding of molecular concepts. Detailed lesson plans and curricula are provided for Introductory (General) Chemistry, Physical Chemistry (Quantum Mechanics and Thermodynamics), Thermodynamics (Physics), Quantum Mechanics (Physics), Computational Chemistry, and Quantum Chemistry as well as Advanced Placement (AP) and International Baccalaureate (IB) chemistry courses. Topics include atomic structure, chemical bonding, the Maxwell-Boltzmann distribution, heat capacity, enthalpy, entropy, free energy, particle-in-a-box, vibrational normal modes, infrared spectroscopy, as well as advanced electronic structure methods. Use of the Quantum Chemistry Toolbox in the classroom is described in a recent paper in J. Chem. Ed. Quantum Chemistry Toolbox 2023 includes a new lesson on Fermi's Golden Rule. The Maple environment allows us to seamlessly combine analytical work with electronic structure calculations and visualizations from the Quantum Chemistry Toolbox .
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