Maple's Quantum Chemistry Package in the Chemistry Classroom
MMaple’s Quantum Chemistry Package in theChemistry Classroom
Jason M. Montgomery † and David A. Mazziotti ∗ , ‡ † Department of Chemistry, Biochemistry, and Physics, Florida Southern College, Lakeland,FL 33801 ‡ Department of Chemistry and The James Franck Institute, University of Chicago,Chicago, IL 60637
E-mail: [email protected]
Abstract
An introduction to the Quantum Chemistry Package (QCP), implemented in thecomputer algebra system Maple, is presented. The QCP combines sophisticated elec-tronic structure methods and Maple’s easy-to-use graphical interface to enable compu-tation and visualization of the electronic energies and properties of molecules. Here wedescribe how the QCP can be used in the chemistry classroom using lessons providedwithin the package. In particular, the calculation and visualization of molecular or-bitals of hydrogen fluoride, the application of the particle in a box to conjugated dyes,the use of geometry optimization and normal mode analysis for hypochlorous acid, andthe thermodynamics of combustion of methane are presented.
With the advent of high-performance computing, sophisticated electronic structure meth-ods, and available quantum chemistry software packages, quantum calculations are now more1 a r X i v : . [ phy s i c s . e d - ph ] O c t owerful than ever. But to the undergraduate chemistry student, the abstractness of quan-tum chemistry and the technical nature of electronic structure methods can be dizzying.Introductory concepts on the quantum mechanical nature of atoms and molecules are intro-duced in first year courses and continue to be relevant throughout the chemistry curriculum,but exposure to quantum calculations may be very limited, if not absent, in part due to alack of access to affordable and easy-to-use electronic structure software.Here we discuss the Maple Quantum Chemistry Package (QCP), also known as the Quan-tum Chemistry Toolbox, for use in the chemistry or physics classroom. The QCP was specif-ically designed and developed for the computer algebra system Maple. Maple can be aninvaluable tool in the chemistry classroom that combines a symbolic computation engine,efficient numerical algorithms, and visualization tools, all accessible through a user-friendlygraphical interface.
Accordingly, the QCP adds sophisticated quantum chemistry func-tionality to Maple to provide an extensive, easy-to-use platform for the computation of theelectronic energies and properties of molecules.Included in the QCP is a set of
Curricula and
Lessons that represent the ways in whichthe QCP can be integrated in the classroom. Curricula are separated into General Chemistry,Physical Chemistry (both Quantum and Statistical Thermodynamics), Advanced PhysicalChemistry, and Physics. Each curriculum contains links to corresponding lessons that maybe imported as a Workbook and executed. In general, each lesson provides an overviewof learning objectives and already contains much of the required code and a narrative thatguides a student through the lesson.In what follows, we present portions of four lessons provided in the Quantum ChemistryPackage (QCP) to give the reader an idea of how the QCP might be exploited in the chemistryclassroom. The lessons are
Molecular Orbitals of Hydrogen Fluoride (Sec. 2.2),
Particlein a Symmetric Box (Sec. 2.3),
Geometry Optimization and Normal Modes (Sec. 2.4), and
Calculating Reaction Thermodynamics for Combustion of Methane (Sec. 2.5). It is importantto note that each activity can imported as a worksheet and can be modified as necessary by2tudents or instructor to fit the needs of the class or assignment.
Any application that utilizes the QCP begins with loading the package using the command with(QuantumChemistry) :Output of this command provides a list of the contents of the package. Using Maple’s
Search toolbar, the user can seek help on any function included in the package, including the variousoptions available for each function as well as examples.
One activity provided with the QCP involves the calculation and visualization of molecularorbitals (MOs) for hydrogen fluoride (HF). The activity might be useful for an upper-levelphysical chemistry course, in which students can make connections between an underlyinglevel of theory (electronic structure method and atomic orbital basis) and the resulting molec-ular orbital properties, or even organic chemistry or foundational general chemistry courses,in which students can make qualitative connections between atomic, molecular orbitals, andmolecular properties.After loading the QCP with the with(QuantumChemistry) command, the HF molecule is3efined as a list of lists, with distance units being angstroms by default: .The user can use the
GeometryOptimization function to find the minimum energy geometry:4n the input the user can specify through optional keyword arguments any method, basis,charge, spin, etc. In this case, we use Hartree-Fock method with the default STO-3Gbasis set. The output of the function provides an updated molecular geometry list as wellas calculation results, including total energy, molecular orbital energies, molecular orbitaloccupation numbers, molecular orbital coefficients, and even Mulliken charges on each atom.A powerful feature of the QCP is the ability to perform ab initio calculations and visualizeresults with simple Maple commands. For this activity, we visualize each of the five occu-pied MOs as well as the lowest unoccupied MO (LUMO) using the
DensityPlot3D command:5rom a pedagogical standpoint, the activity lends itself to simple visualization of anabstract concept, such as MOs, or to the ability for students to explore more complexconnections between a model chemistry (electronic structure method and underlying atomicorbital basis set) and the resulting energies and molecular properties.7 .3 A Particle in a Symmetric Box
For this activity, we use Maple’s built-in plotting functions to visualize the energies andwavefunctions of a symmetric particle-in-a-box (PB). We then apply the PB model to twochemistry applications, one a toy model and one that corresponds to the ubiquitous conju-gated dye lab. 8he advantage of having students use Maple’s plotting functions to visualize PB energiesand wavefunctions is to provide the necessary background and understanding of the relation-ship between higher energy states and their corresponding nodal structure. To reinforce thenotion that the PB model can be useful in understanding real chemical systems, we use theQCP to calculate the energies and wavefunctions of a chain of H-atoms. As seen in Sec. 2.2,the user can input the geometry using a list of lists (output suppressed) and visualize themolecule using the
PlotMolecule function. 9n this activity, we use the Hartree-Fock method with a minimal STO-3G basis to calculatethe energy and molecular orbitals. The output here has been suppressed, but an examplefor the HF molecule is provided in Sec. 2.2.The user can visualize molecular orbitals using the
DensityPlot3D command and comparethe nodal structures to those expected based on the simple PB model.101n another application of the PB model, we again use the Hartree-Fock method and aminimal basis to calculate the energies and MOs for a series of cyanine dyes, the structuresof which are provided. Here we show the 3,3’-diethylthiacarbocyanine iodide dye and theresulting HOMO. 12he nodal structure along the conjugated chain can again be compared to the n = 4 PBwavefunction, which would correspond to the HOMO for a PB system with 8 π -electrons.In the activity, students can also approximate peak absorption wavelength by approximating∆ E = E LUMO − E HOMO . Upon completion, students can see that 1) peak wavelengthscalculated using electronic structure methods are in qualitative agreement with experiment,and 2) higher level electronic structure models, such as density functional theory (DFT) and 6-31G basis set, can improve accuracy. 13 .4 Geometry Optimizations and Normal Modes
Another important concept for students, from general to organic to physical chemistry, is thenotion of an optimum molecular geometry and associated vibrational modes. In this activity,students calculate the optimum geometry and normal modes of hypochlorous acid (HClO).Students can specify a starting geometry in bond-angle coordinates (for example r HO = 1 . r OCl = 1 . θ (HOCl) = 104 . BondDistances and
BondAngles functions.A follow-up calculation for the normal modes is accomplished using the
VibrationalModes command. Students can animate each vibration using the
VibrationalModeAnimation com-mand. (Here, we have modified output to show three frames of the animation for printingpurposes.) 14tudents can compare calculated frequencies with literature values (3609 cm − (OH stretch),1239 cm − (bend), and 724 cm − (Cl-O stretch)) and can explore higher level model chemistriesto get better agreement with experiment. It is important to note that the utility of the QC package extends beyond only explicitelectronic structure applications. For example, in one activity provided with the package,we use the
Thermodynamics function to calculate the thermodynamics of combustion for15ethane:CH (g) + O (g) −→ CO (g) + H O(g) ∆ H rxn =? , ∆ G rxn =? , ∆ S rxn =? (1)For a given reaction specie in Rxn 1, for example CH , the user specifies the name andcorresponding label, symmetry number, electronic structure method and basis with whichto calculate energies, electronic structure and basis with which to calculate the vibrationalfrequencies (usually the same as energy but not required), a scaling factor, and molecularspin corresponding to singlet, doublet, triplet, etc.:Once a given molecular specie has been specified, the user can load the molecule using the MolecularData function, which retrieves a 3D geometry from PubChem based on the nameor CID provided and execute the
Thermodynamics function to calculate the thermodynamicvariables S , H , and G : 16he above input and subsequent calculation output would be updated for each of themolecules in Rxn 1. Once thermodynamic variables for each of the reactant and productspecies is calculated, the entropy of combustion (∆ S ), enthalpy (∆ H ), and Gibbs free energy(∆ G ) can be calculated using Hess’s Law:∆ F = (cid:88) i n i F product,i − (cid:88) j n j F reactant,j (2)where F is the desired thermodynamic variable, and n i and n j are the molar coefficients inRxn 1: 17hese results can be compared with predictions using Hess’s law and tabulated standardentropy and standard enthalpy and free energy of formation values. In this paper, we have introduced the Quantum Chemistry Package, implemented in Maple,and have shown how it can be used in the chemistry classroom. It is important to emphasizethat the QCP contains both wavefunction and density functional methods. Electronic struc-ture methods highlighted above include the Hartree-Fock and DFT methods, but a diverseset of electron correlation methods are also included in the QCP, such as 2nd-order Møller-Plesset perturbation theory (MP2), coupled cluster, full and active space variants ofconfiguration interaction (CI). Furthermore, unique to the package are two-electronreduced density matrix (2RDM) methods, parametric 2RDM (P2RDM) and variational2RDM (V2RDM), which are well-suited for strongly correlated molecules where theycan accurately describe quantum effects that are difficult to treat by conventional methods.The breadth of methods available in the package also make it suitable for research gradecalculations.It is our hope that instructors from all levels of chemistry use the imbedded lessons as18ell as create their own to share with the chemistry and Maple communities in order to helpintegrate quantum calculations throughout the chemistry curriculum!
Acknowledgement
D.A.M. gratefully acknowledges the United States Army Research Office (ARO) GrantsW911NF-16-C-0030 and W911NF-16-1-0152 and the United States National Science Foun-dation Grant CHE-1565638.
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