Introduction to Geometry Optimizations, Functionals, and Basis Sets

Tutorial Created with Software Release: 2024-3
Topics: Catalysis & Reactivity, Energy Capture & Storage, Organic Electronics, Thin Film Processing
Methodology: Molecular Quantum Mechanics
Products Used: Jaguar, MS Maestro, Maestro

Tutorial files

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This tutorial is written for use with a 3-button mouse with a scroll wheel.
Words found in the Glossary of Terms are shown like this: Workspacethe 3D display area in the center of the main window, where molecular structures are displayed

 

Tip: You can hover over a glossary term to display its definition. You can click on an image to expand it in the page.
Abstract:

 

In this tutorial, we will learn to perform geometry optimizations on simple organic molecules. We will also introduce some basics regarding selecting density functionals and basis sets in Jaguar.

 

Tutorial Content

  1. Introduction to Geometry Optimizations

  1. Basis Sets and Density Functionals

  1. Creating Projects and Importing Structures 

  1. Predicting the Molecular Structure of SF2

  1. Predicting the Molecular Structure of Aniline

  2. Conformers of HONO

  1. Summary of Steps

  1. Conclusion and References

  1. Glossary of Terms

1. Introduction to Geometry Optimizations

Calculating the properties of a molecule or chemical system, such as vibrational frequencies and polarizability, typically starts by specifying where the atoms are located in the model, also known as giving a geometryThe 3D arrangement of atoms in a structure. Regardless of the method of calculation, properties will depend on the geometry given as an input to the calculation. However, in reality molecules are not immobile, so which configurations of atoms should one use to describe the system? It is usually best to use the geometryThe 3D arrangement of atoms in a structure that gives the lowest energy structure as this corresponds to the most stable structure and thus the molecule spends the most time in this configuration. To find this minimum-energy structure we perform geometry optimizations in which the input to the calculation is an initial guess structure that is similar to the minimum energy structure and then theoretical chemistry techniques are used to optimize the system.

However, the geometry optimization process is not perfect, the global minimum structure is not guaranteed to be found, and even sometimes it can be difficult to find a structure describing a local minimumA point on a potential energy surface that is lower in energy than all the points closely surrounding it, but there is another minimum on the surface that is even lower in energy. . An example of a potential energy surfaceA multi-dimensional surface that describes the energy of a structure as different features, such as bond lengths, change (PES) with global and local minima is shown in Figure 1. A potential energy surfaceA multi-dimensional surface that describes the energy of a structure as different features, such as bond lengths, change is a method-dependent plot of the energy of the system as a function of several parameters. In the case of Figure 1 you could imagine (as an example) that the surface is showing the energy of a water molecule as you stretch the OH bonds (x-axis) and change the HOH angle (y-axis). Using this PES as an example, the global minimum we are trying to find in our geometry optimization and a local minimum of the surface are labeled in Figure 1, below. Checking to see if the optimization procedure has found a local or global minimum is much more difficult, however, if the optimization is starting from a good guess geometry, the optimization procedure is likely to be closer to the global minimum rather than a local minimum. This is why giving a good starting point for the optimization is important.

Figure 1: Example of a potential energy surface. The darker the shade of blue the lower in energy the surface is.

In this tutorial we will be discussing the use of density functional theoryAbbreviated DFT, this method is one of the most widely used methods in computational chemistry for (ground state) quantum mechanical and solid state calculations. However, like all methods that attempt to solve the Schrödinger equation for more than one electron, this method is not exact. For density functional theory this is seen by having multiple choices of functionals to use in calculations depending on the properties you are trying to calculate and the types of molecules/systems you are working with. (DFT) for geometry optimizations. The nuances of this method are discussed in Section 2. There are many other methods that can be used to perform geometry optimizations, but DFT is one of the most widely used methods and is referenced throughout several of our other tutorials.

2. Basis Sets and Density Functionals

In this section we will describe how atomic and molecular orbitals are represented via the use of basis functionsA set of (typically gaussian functions) that are used to mathematically represent atomic and molecular orbitals and molecular wave functions. More information about basis sets in general and a list of the sets that Maestro supports can be found in the and how density functional theoryAbbreviated DFT, this method is one of the most widely used methods in computational chemistry for (ground state) quantum mechanical and solid state calculations. However, like all methods that attempt to solve the Schrödinger equation for more than one electron, this method is not exact. For density functional theory this is seen by having multiple choices of functionals to use in calculations depending on the properties you are trying to calculate and the types of molecules/systems you are working with. can be used to optimize those representations for different calculations. The goal of this section is to expose the reader to the terminology related to these topics, not to provide detailed information or recommendations. The Maestro suite automatically fills in recommended basis sets and functional choices in most panels, but the curious can look at the resources in the For Further Reading section for more information.

It is important to note that in order to directly compare the results of two quantum mechanical calculations, for example to find the energy difference between the reactants and products of a proposed reaction, the calculations need to use the same basis set and density functional.

Basis Sets

Many molecular quantum mechanical calculations rely on the LCAO (linear combination of atomic orbitals) method to transform atomic orbitals into molecular orbitals that can describe the system being studied. Once these molecular orbitals have been formed they can be used to find many useful properties for your system, such as excited state properties. However, atomic orbitals, and thus the molecular orbitals formed from them, tend to have complicated exponential forms that are especially difficult to integrate over, which is required for many calculations. To avoid the expense of integral computations, the wave functions for hydrogen-like atomic orbitals are expressed as linear combinations of functions that have known analytic formulas for their integrals, such as gaussians. There are many different ways to develop these linear combinations, leading to the many different types of basis sets that are offered in the Schrödginer suite of tools.

The basis sets used in this tutorial are a type of split-valence basis sets. In most quantum mechanical calculations the valence electrons are the ones participating in the chemistry being modeled, so they are the most important to accurately portray. In split-valence basis sets the valence electrons are modeled by using more basis functions to more accurately recreate the valence orbital shapes while keeping the total number of basis functions relatively low. Why not just use as many functions as possible for all the electrons in the system? The more basis functions that are used in the calculation, the more computationally expensive it is.

The particular type of split-valence basis sets that will be used in this tutorial, and many of the other quantum mechanics tutorials, are called the Pople basis sets. These are named in the form X-YZg where X, Y, and Z denote how many Gaussian functions are used to describe the core atomic orbitals and valence orbitals. For more information on Pople basis sets please see Ditchfield, et. al 1971, linked in the For Further Reading section. Pople basis functions can have additional diffuse - denoted with ‘+’ in the name - and polarization - denoted with ‘*’ in the name - functions to further improve the quality of the basis set for certain simulations. Polarization functions are used to better describe the polarizability of electrons in orbitals, which is especially important when describing chemical bonding. Diffuse basis functions are important for describing the portions of orbitals that are far from the atomic nucleus and are especially important for simulations involving ions, dipole moments, and bonding. For information about the other types of basis sets included in the Schrödinger Suite of tools, see the For Further Reading section at the end of this tutorial.

Density functionals

Density functional theoryAbbreviated DFT, this method is one of the most widely used methods in computational chemistry for (ground state) quantum mechanical and solid state calculations. However, like all methods that attempt to solve the Schrödinger equation for more than one electron, this method is not exact. For density functional theory this is seen by having multiple choices of functionals to use in calculations depending on the properties you are trying to calculate and the types of molecules/systems you are working with. relies on the use of density functionalsThe portion of density functional theory that describes the interactions between the electrons in the system. There are many choices for the functional, the best functional for each situation will depend on the level of accuracy needed for the result, the amount of computational resources available, the property being studied, and the types of molecules/systems being studied. For more information about the functionals offered in Maestro, see the to portray the interactions between electrons, as modeling the interactions between electrons is too complicated to be done exactly. Different density functionals are optimized for different types of molecules, levels of accuracy, and computational cost, so choosing the correct functional for your simulation requires knowledge of both the functional and the system you are trying to study. The Schrödinger suite of tools automatically loads a recommended functional for many of its calculations, but it may not be the best possible choice in all situations. In the table below we will give an overview of the categories of functionals and the vocabulary used to describe them. For more information and the full list of functionals that are available in Maestro, see the documentationThe portion of density functional theory that describes the interactions between the electrons in the system. There are many choices for the functional, the best functional for each situation will depend on the level of accuracy needed for the result, the amount of computational resources available, the property being studied, and the types of molecules/systems being studied. For more information about the functionals offered in Maestro, see the .

The accuracy and cost shown in the table above are generalizations. Certain functionals within these categories can be more or less accurate or expensive than those in other categories. In order to choose the best functional for your system and the property you are trying to calculate you can look at resources describing how the functional was designed and benchmarking studies to determine if a given functional is a good choice. The list of functionals currently available in the Schrödinger suite can be found here and more information about density functional theory can be found in the For Further Reading section. 

3. Creating Projects and Importing Structures

At the start of the session, change the file path to your chosen Working DirectoryThe location where files are saved. in MS Maestro to make file navigation easier. Each session in MS Maestro begins with a default Scratch ProjectA temporary project in which work is not saved. Closing a scratch project removes all current work and begins a new scratch project., which is not saved. A MS Maestro project stores all your data and has a .prj extension. A project may contain numerous entries corresponding to imported structures, as well as the output of modeling-related tasks. Once a project is saved, the project is automatically saved each time a change is made.

Structures can be built in MS Maestro or can be imported using File > Import Structures (or drag-and-dropped), and are added to the Entry ListA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. and Project TableDisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data.. The Entry ListA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. is located to the left of the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed.. The Project TableDisplays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data. can be accessed by Ctrl+T (Cmd+T) or Window > Project Table if you would like to see an expanded view of your project data.

OR

  1. Double-click the Maestro or Materials Science icon

Note: This Jaguar workflow can be performed in Maestro or Materials Science Maestro. Use whichever interface you are comfortable with or typically use for your projects.

Figure 3-1. Change Working Directory option.

  1. Go to File > Change Working Directory
  2. Find your directory, and click Choose
  3. Pre-generated files are included for running jobs or examining output. Download the zip file here: https://www.schrodinger.com/sites/default/files/s3/release/current/Tutorials/zip/qm_go.zip
  4. After downloading the zip file, unzip the contents in your Working DirectoryThe location where files are saved. for ease of access throughout the tutorial

Figure 3-2. Save Project panel.

  1. Go to File > Save Project As
  2. Change the File name to GO_tutorial, and click Save
    • The project is now named GO_tutorial.prj

4. Predicting the Molecular Structure of SF2

As described above, numerous functionals and basis sets are available for Jaguar calculations. This section will teach how to set up a geometry optimization for a simple molecule, SF2, and will give a comparison of various results from evaluating functionals and basis sets.

Figure 4-1. Sketching and saving SF2.

To start optimizing a molecular geometry, you will need a starting molecule in your workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.. The molecule could be drawn in 2D or 3D using various MS Maestro tools, or can be imported from a file. In this case we will use the 2D Sketcher:

  1. Go to Edit > 2D Sketcher
    • The 2D Sketcher panel opens
  2. Draw the structure of SF2

Note: Use S and F on your keyboard for atom assignments

 

The 2D sketcher functions like many standard 2D molecular drawing tools. For a complete overview of using the sketcher panel, see the 2D Sketcher Panel documentation or watch the Building Small Molecules video in the Getting Going with Materials Science Maestro Video Series.

  1. Click on Save as New and for Input Entry Title write SF2. Click OK

Figure 4-2. Viewing and stylizing SF2.

  1. Close the 2D Sketcher panel
    • The SF2 molecule is selected(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. in the entry listA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. and includedthe entry is represented in the Workspace, the circle in the In column is blue in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.
  2. Change the representation to ball-and-stick by clicking on the Style menu and choosing Apply ball-and-stick representation

Figure 4-3. Measuring the S-F distance.

This molecule is not yet optimized. The 3D representation is simply generated from the 2D Sketcher as an approximate starting point. To learn more about measurement tools watch Getting Going with Materials Science Maestro Video Series: Measurements and Manual Adjustments. Let’s measure the S-F bond distance and the F-S-F angle to assess the starting point:

  1. Go to Workspace > Measure (or click Measure in the Favorites toolbar)
    • A banner appears at the top of the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed. for defining measurements
  2. With Distances selected for Measure, select one F atom and the S atom
    • The S-F distance is labeled

Figure 4-4. Measuring the F-S-F angle.

  1. Switch the Measure option to Angles and select one fluorine, then the sulfur and then the other fluorine
    • The F-S-F angle is labeled
  2. Click OK to close the measurement banner

We can see that the 2D Sketcher created this starting molecule with S-F bond lengths equal to 1.67Å and a bond angle of 109.5º

Figure 4-5. Force field minimization.

We can improve upon this starting structure by using a force field minimization. The molecule will still not be optimized by quantum mechanics, but it will improve the starting geometry, which we recall is helpful for navigating the PES during an optimization 

  1. Select all three atoms in the workspace (there are many approaches to do so: Main Menu, Select > All; Toolbar, Quick Select > All, Shift + Click + Drag and more)
  2. In the Build dropdown from the toolbar (3D Builder panel), select Minimize selected atoms
    • The molecule is minimized, and the parameters adjust slightly

We can see that now the starting molecule has equivalent S-F bond lengths equal to 1.66Å and a bond angle of 101.0º

Actually, the experimental bond length is 1.587Å and bond angle is 98.048º. Thus, the force field optimization improves the structure, but is still somewhat far from being experimentally accurate

 

Note: Force fields are usually good at generating structures of molecules with common functional groups and elements. When it comes to more exotic atomic arrangements and less frequent elements (such as transition metals) or simply large molecules, force fields can yield structures with inaccurate or even unphysical geometries, and in those cases, quantum mechanical geometry optimizations become absolutely indispensable.

Figure 4-6. Setting the QM Multistage Workflow panel to optimization.

Now let us optimize the molecule at the quantum mechanical level

  1. With the SF2 entry selected(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includedthe entry is represented in the Workspace, the circle in the In column is blue, go to Tasks > Materials > Quantum Mechanics > Molecular Quantum Mechanics > QM Multistage Workflow
  2. Change the Stage Type to Optimization

Note: The task of performing a single geometry optimization can be performed in the QM Multistage Workflow panel or the Jaguar Optimization panel. Feel free to use either panel for this task.

Note: Herein, we are optimizing one molecule. By selecting many molecules in the entry list, we can optimize as many molecules as we would like concurrently with the same QM settings.

Figure 4-7. Setting the QM parameters.

Various settings can be altered depending on the specific use case. We will only adjust the Input tab for this example.

  1. For Theory, retain B3LYP-D3
  2. For Basis set, retain 6-31G**

A few additional comments about preparing for an optimization calculation:

  • If you hover the mouse over the basis set in the table, you can see the number of basis functions associated with the basis set. This is useful to know since the quality of the basis set usually improves as the number of functions increases, noting again the trade-off between quality and computational expense.
  • Always make sure the charge and the spin multiplicity are correct (in this case, SF2 is a neutral, singlet, so charge = 0 and spin multiplicity = 1). Multiplicity is defined as 2S + 1, where S is the total spin quantum number. For instance, a system with one unpaired electron is a doublet (multiplicity = 2), since the total spin quantum number S = ½.
  • Use the Atom-Level Settings button, located in the bottom left corner of the stage section, to define per-atom basis sets.
  • Constraints can be defined on the Optimization tab. Constraints are used to define sections of the system that are not touched by the optimization and are useful for running calculations on large systems or on systems where a portion of the geometry needs to be in a certain configuration.
  • Properties, such as atomic charges, vibrational frequencies, surfaces and more can be requested on the Properties tab.
  • Solvent can be defined via several implicit solvation models on the Solvation tab. Note that this example is a gas-phase geometry optimization.
  • Read more about geometry optimizations and learn more about using the QM Multistage Workflow panel in the Introduction to Multistage Quantum Mechanical Workflows tutorial.

Figure 4-8. Naming and running the job.

  1. Change the Job name to SF2_B3LYP-D3_6-31GSS
    • Usually we incorporate stars (*) and pluses (+) into files names with S and P, respectively
  2. Adjust the job settings () as needed
    • This job requires a CPU host and should complete in under 5 minutes. For some general timings of typical Jaguar jobs, see: Timings for Typical Jaguar Jobs
  3. Click Run

Note: It is advised to also add in a Vibrational frequencies calculation (from the Properties tab). This involves a bit more computational expense, but is a useful way to be sure that your output is a minimum (as opposed to a maximum) on the PES. For more detail, see the Locating Transition States: Part 1 tutorial.

Figure 4-9. The output molecule.

When the job finishes, a banner will appear indicating that the result has been incorporated. A new entry group is added to the entry listA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. titled SF2_B3LYP-D3_6-31GSS (1) containing one entry named SF2

  1. Select(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includethe entry is represented in the Workspace, the circle in the In column is blue SF2 from the entry list
    • The molecule with the optimized geometry is now shown in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.
  2. Repeat the measurement steps 6-9 from above

We can see that the optimized molecule has equivalent S-F bond lengths equal to 1.63Å and a bond angle of 100.2º (remember, your values may not correspond perfectly with these.)

You should feel free to explore rerunning this optimization with various functionals and basis sets and investigating the impact. Below we list results for such an evaluation. Note that the quality of results generally improves as we move from smaller basis sets to larger ones. Indeed, the smallest basis sets perform similarly to a force field optimization. Also note that M06-2X generally performs better than B3LYP, but recall that it is more computationally expensive. If you compare the basis sets with polarization functions (**) to those without (6-31G) you will also notice a large difference in results, showing that when possible polarization functions should be included.

 

Level of theory

# functions

S-F bond length, Å *

F-S-F angle, º *

2D Sketcher

-

1.67

109.5

Force field

-

1.66

101.0

 

B3LYP/STO-3G

19

1.70

94.9

B3LYP/6-31G

31

1.74

99.0

B3LYP/6-31G**

49

1.63

100.1

B3LYP-D3/6-31G**

49

1.63

100.2

B3LYP/cc-pVDZ

46

1.65

99.2

B3LYP/cc-pVTZ(-f)

73

1.62

99.2

B3LYP/cc-pVTZ

94

1.61

99.2

 

M06-2X/STO-3G

19

1.67

94.2

M06-2X/6-31G

31

1.71

97.0

M06-2X/6-31G**

49

1.61

98.5

M06-2X/cc-pVDZ

46

1.62

97.7

M06-2X/cc-pVTZ(-f)

73

1.60

97.9

M06-2X/cc-pVTZ

94

1.60

98.0

 

Experiment

-

1.587

98.048

*quantitative results will vary slightly depending on operating system, version of MS Maestro and other variables

 

To visualize the accuracy of the predicted geometry versus the number of basis functions, see the plot below:

5. Predicting the Molecular Structure of Aniline

Now that we have learned the fundamental steps for a geometry optimization, let’s look at an example where a routine quantum mechanical optimization does not yield the global minimum geometry. Such is the case when we take the molecule aniline and follow the same steps outlined in Section 4. 

Figure 5-1. Creating a new entry.

  1. Right-click in any empty space in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed. and choose Create New Entry > Create Empty Entry
  2. In the dropdown banner, for Entry title input aniline and click the green checkmark
    • A new entry is created. It is selected(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includedthe entry is represented in the Workspace, the circle in the In column is blue

Figure 5-2. Aniline in the 2D Sketcher.

Proceed to draw aniline in the 2D Sketcher:

  1. Go to Edit > 2D Sketcher
    • The 2D Sketcher panel opens
  2. Draw the structure of aniline
  3. Click Update Entry

Figure 5-3. Aniline in the workspace.

  1. Close the 2D Sketcher panel
    • The aniline molecule is selected(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. in the entry listA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. and includedthe entry is represented in the Workspace, the circle in the In column is blue in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.
  2. Change the representation to ball-and-stick by clicking on the Style menu () and choosing Apply ball-and-stick representation

Notice that the molecule is completely flat. Specifically, the NH2 group is level with the phenyl ring, representing a planar geometry. If you wish to confirm, you can measure the HNCC dihedral angle (0º).

Figure 5-4. Parameterizing the QM Multistage panel for the geometry optimization.

If we did not know any better, we might assume that this is a perfectly good starting point, and proceed to a geometry optimization. Let’s do so, just for the sake of example:

  1. With the aniline entry selected(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includedthe entry is represented in the Workspace, the circle in the In column is blue, go to Tasks > Materials > Quantum Mechanics > Molecular Quantum Mechanics > QM Multistage Workflow
  2. Make sure that the Stage Type is set to Optimization
  3. Set the Theory to M06-2X and the Basis set to 6-31G**
  4. Change the Job name to aniline_M06-2X_6-31GSS
  5. Adjust the job settings () as needed
    • This job requires a CPU host and should complete in under 5 minutes
  6. Click Run

Note: It is advised to also add in a Vibrational frequencies calculation (from the Properties tab). This involves a bit more computational expense, but is a useful way to be sure that your output is a minimum (as opposed to a maximum) on the PES. For more detail, see the Locating Transition States: Part 1 tutorial.

Figure 5-5. The output molecule.

When the job finishes, a banner will appear indicating that the result has been incorporated. A new entry group is added to the entry list titled aniline_M06-2X_6-31GSS (1) containing one entry named aniline

  1. Select(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includethe entry is represented in the Workspace, the circle in the In column is blue aniline from the entry listA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.
    • The geometry optimized molecule is now shown in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.

Notice that the molecule remains planar!

We know from a general chemistry background that aniline should not be flat. The nitrogen should be somewhat puckered, approaching a more trigonal pyramidal geometry.

Here we have demonstrated one of many possible pitfalls that may occur when performing QM geometry optimizations. The explanation of this unexpected under-performance of the supposedly accurate DFT calculation lies in the nature of the initial guess structure. The flat configuration of the amino group corresponds to a saddle point on the potential energy surface. See below for illustration:

A quantum chemical geometry optimization appears to have nothing left to do when it comes to optimizing the dihedral angle coordinates of the flat amino-group in aniline. Geometry optimizations proceed by computing a gradient on the potential energy surface and then stepping in the direction opposite the gradient, approaching a stationary point. However, for the saddle shown, the energy gradient is already zero. So, the geometry optimization has no reason to alter the corresponding coordinate. Of course, a tiny perturbation in any direction away from the flat geometry or simply the breaking of symmetry would make the corresponding gradient non-zero and would induce the geometry optimizer to collapse the structure into one with a puckered amino-group. A perturbation in plane (such as extending one of the N-H bonds) would also make the gradient non-zero, but its subsequent minimization would bring us back to the saddle point. To arrive at a minimum, it is important to make a perturbation in the right direction.

How can we deal with such situations in practice? When working with a simple molecule, it is usually not a problem to spot a suspiciously flat functional group (such as the amino-group), perturb it a little by moving atoms manually out of the plane, and optimize the symmetry-broken structure. But when optimizing more complicated and larger molecules, especially in batches, then inspecting every structure and perturbing every suspicious atomic arrangement, just in case, becomes unmanageable.

Jaguar has an efficient automatic solution to this problem, which is demonstrated in the following section. The most important lesson, though, is to always check your input and output structures! 

Figure 5-6. Adding the check_min keyword.

  1. Select(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includethe entry is represented in the Workspace, the circle in the In column is blue the starting aniline molecule from the entry list
  2. Reopen the QM Multistage Workflow panel
  3. Keep all of the settings the same except:
    • Change the Job name to aniline_M06-2X_6-31GSS_2, and
    • In the Additional keywords section at the bottom of the panel, input check_min=2
  4. Adjust job settings if needed, and click Run

The keyword check_min analyzes a structure and attempts to perturb it in the relevant directions to break symmetry and move away from a saddle point. It is an example of a Jaguar keyword. For a complete list of geometry optimization and transition state keywords, refer to the help documentation

Local saddle points, like the one we have discovered in the case of the flat aromatic amine, can be spotted after analyzing the quantum mechanical Hessian matrix (a matrix of energy second derivatives with respect to coordinate displacements), which corresponds to the setting check_min=1. However, this is a computationally expensive procedure, and less expensive solutions like check_min=2 are available. In particular, check_min=2 breaks the initial symmetry by perturbing all rotatable torsion.

Figure 5-7. The output molecule.

When the job finishes, a banner will appear indicating that the result has been incorporated. A new entry group titled aniline_M06-2X_6-31GSS_2 (1)  is added to the entry listA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.. It contains one entry named aniline

  1. Select(1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries. and includethe entry is represented in the Workspace, the circle in the In column is blue aniline from the entry list
    • The optimized molecule is now shown in the workspaceThe 3D display area in the center of the main window, where molecular structures are displayed.

Notice that the molecule is now the expected puckered geometry

  1. Open the Project Table and compare the relative energies of this output and the previous output. You will notice that the puckered output is more stable

Optionally: Repeat this procedure for 2-amino-furan, 2-amino-pyrrole, 2-amino-thiophene and 2-aminothiazole. You will notice similar pitfalls.

 

To move on to more advanced practice, e.g. automating quantum mechanical calculations on many input molecules simultaneously, see the Introduction to Multistage Quantum Mechanical Workflows tutorial.

6. Conformers of HONO

As an example of how impactful the starting guess geometry can be for these types of calculations we can study HONO. HONO has two low energy conformers that form local minimum on our potential energy surface, cis-HONO and trans-HONO. For more details about the geometry of the HONO molecule, see ‘Ab Initio Molecular Orbital Calculation of the HONO Torsional Potential.’

In this section setting up the calculations is largely left as an exercise to the reader, the steps to set up the calculations are similar to those in the previous sections. Starting structures and output files are included in the project files in the folder labeled Section_06.

Figure 6-1. Importing the starting structures.

  1. Go to File > Import Structures
  2. Navigate to where you downloaded the provided files and choose Section_06/HONO_structures.mae
  3. Click Open
  4. A new entry group is added containing three structures: cis-HONO, trans-HONO, and barrier_HONO_85
    • Feel free to visualize these as you wish
    • The barrier_HONO_85 structure has a dihedral angle of 85° to match the angle of the rotational barrier given in the paper linked above

Figure 6-2. Setting up geometry optimizations on the imported HONO molecules.

  1. Ensure the three structures are selected, then go to Tasks > Materials > Quantum Mechanics > Molecular Quantum Mechanics > QM Multistage Workflow
  2. Change the Stage type to Optimization
  3. Change the Theory and Basis set options to any functional and basis set combination of your choice
    • You can try several combinations in one job by appending stages to the workflow, just make sure to change the settings, stage type, and deselecting geometry from stage
    • You can change the Name of the stage to help distinguish your results later
    • You can also change the settings in the Properties tab to calculate vibrational frequencies
  4. When you are ready, rename your job to jaguar_workflow_HONO
  5. Adjust your job settings and hit Run
    • Alternatively, example job files have been included with the tutorial files, go to File > Import Structures and navigate to Section_06 >
    • These calculations were done with a combination of B3LYP-D3 or M06-2X for the density functional and 6-31G** or cc-pVTZ for the basis set

Figure 6-3. Example of geometry optimization results.

  1. When the job finishes or after importing visualize your results
    • If you calculated vibrational frequencies, you can check them to ensure an energy maximum or minimum has been reached
    • Did all of the structures converge to the same geometry?
    • For the given jobs, only the structures starting from the trans conformer optimized to the trans conformer

 

Figure 6-4. Gas Phase Energy results shown in the Project Table.

  1. Open the project table ( in the top right corner of the Maestro window)
  2. Look at the Gas Phase Energy column
    • These energies are in Hartrees, 1 Hartree = 627.509 kcal/mol
    • How different are the energies of the optimized structures? (It is best to compare within each basis set and functional combination)

The cis-HONO and trans-HONO are practically the same in energy, when comparing the outputs of the same functional and basis set choice to each other the energies of the optimized structures are only different by less than 1 kcal/mol. The different basis set and functional combinations have different predictions for which conformer is lower in energy, showing what is already well known in the literature: DFT results are not known for being accurate to within 1 kcal/mol. When comparing structures with energies this close it is best to look towards a higher level of theory. It is also important to note that even though the B3LYP-D3/cc-pVTZ combination predicted the trans conformer was more stable, using these settings with the barrier_HONO_85 structure still led to the cis conformer, showing just how important having a good starting structure for your optimization is.

7. Summary of Steps

  1. Import or draw (using the 2D or 3D sketcher) a guess geometry for the system.
  2. Open the QM Multistage Workflow Panel and change the Stage Type to Optimization.
  3. Select the basis set and density functional that will work best for your accuracy needs and molecule type. See the documentation for more guidance on choosing a functional and choosing a basis set.
  4. To check if your molecular geometry is actually at a minimum on the PES, add the check_min=2 to the Additional keywords section of the panel
  5. Run the job
  6. Use the project table to view the calculated quantities for the molecule once the job has finished.

8. Conclusion and References

This tutorial covered the basics of selecting basis sets and functionals in Jaguar. We showed that the larger the basis set, the more accurate the result, which is a typical observation in many calculations. However, the computational expense grows sharply with the size of the basis set, usually as the third power of the number of basis functions. Since the number of basis functions also increases with the size of the system being studied, this cost might not have been seen for the examples in this tutorial, but would be exacerbated in larger systems. Therefore, it is important to select the basis set judiciously – not too small to compromise the quality of the results, and not too big to make the calculation too computationally expensive without gaining anything additional in the quality of the result. In general, we strongly recommend validating the functional/basis combination on systems similar to what is to be studied.

We have also learned how to perform simple geometry optimizations. The tutorial demonstrated that there might be unexpected difficulties in geometry optimizations when working with deceptively simple structures, like aniline and that choosing a good starting structure is important. Even straightforward quantum chemical optimizations might fail to produce optimal geometries in some cases. In this case, a special Jaguar keyword helped to move away from a saddle point on the potential energy surface and arrive at a true minimum.

For further learning:

For introductory content, focused on navigating the Schrödinger Materials Science interface, an Introduction to Materials Science Maestro tutorial is available. Please visit the materials science training website for access to 70+ tutorials. For scientific inquiries or technical troubleshooting, submit a ticket to our Technical Support Scientists at help@schrodinger.com.

For self-paced, asynchronous, online courses in Materials Science modeling, including access to Schrödinger software, please visit the Schrödinger Online Learning portal on our website.

If you are interested in running Jaguar calculations from the command line, please visit the documentationThe portion of density functional theory that describes the interactions between the electrons in the system. There are many choices for the functional, the best functional for each situation will depend on the level of accuracy needed for the result, the amount of computational resources available, the property being studied, and the types of molecules/systems being studied. For more information about the functionals offered in Maestro, see the for example files and guidance.

For some related practice, proceed to explore other relevant tutorials:

For further reading:
  • See the Jaguar help documentation
  • For example of Jaguar input files, see here
  • R. Ditchfield; W. J. Hehre; J. A. Pople. “Self‐Consistent Molecular‐Orbital Methods. IX. An Extended Gaussian‐Type Basis for Molecular‐Orbital Studies of Organic Molecules” J. Chem. Phys. 54, 724–728 (1971). doi.org/10.1063/1.1674902
  • Dunning, Thomas H. "Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen" J. Chem. Phys. 90,2 (1989), 1007–1023. doi.org/10.106/2F1.456153
  • Thompson, D. L. and Darsey, J. A. “Ab Initio Molecular Orbital Calculation of the HONO Torsional Potential” J. Phys. Chem. 91 (1987), 3168-3171. do.org/10.1021/j100296a013

9. Glossary of Terms

Basis functions - A set of (typically gaussian functions) that are used to mathematically represent atomic and molecular orbitals and molecular wave functions. More information about basis sets in general and a list of the sets that Maestro supports can be found in the Documentation.

Computational cost - A combination of the amount of time and computational resources needed to run a computation. A method with high computational cost will take more time and/or processing units (CPUs or GPUs) than a method with a lower computational cost.

Density functional theory - Abbreviated DFT, this method is one of the most widely used methods in computational chemistry for (ground state) quantum mechanical and solid state calculations. However, like all methods that attempt to solve the Schrödinger equation for more than one electron, this method is not exact. For density functional theory this is seen by having multiple choices of functionals to use in calculations depending on the properties you are trying to calculate and the types of molecules/systems you are working with.

Density functionals - The portion of density functional theory that describes the interactions between the electrons in the system. There are many choices for the functional, the best functional for each situation will depend on the level of accuracy needed for the result, the amount of computational resources available, the property being studied, and the types of molecules/systems being studied. For more information about the functionals offered in Maestro, see the Documentation.

Entry List - A simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.

Geometry - The 3D arrangement of atoms in a structure

Included - the entry is represented in the Workspace, the circle in the In column is blue

Local minimum - A point on a potential energy surface that is lower in energy than all the points closely surrounding it, but there is another minimum on the surface that is even lower in energy.

Potential energy surface - A multi-dimensional surface that describes the energy of a structure as different features, such as bond lengths, change

Project Table - Displays the contents of a project and is also an interface for performing operations on selected entries, viewing properties, and organizing structures and data.

Scratch Project - A temporary project in which work is not saved. Closing a scratch project removes all current work and begins a new scratch project.

Selected - (1) The atoms are chosen in the Workspace. These atoms are referred to as "the selection" or "the atom selection." Workspace operations are performed on the selected atoms. (2) The entry is chosen in the Entry List (and Project Table) and the row for the entry is highlighted. Project operations are performed on all selected entries.

Working Directory - The location where files are saved.

Workspace - The 3D display area in the center of the main window, where molecular structures are displayed.