Computing Atomic Charges

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

Tutorial files

3.6 MB
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:

 

This tutorial demonstrates the use of Jaguar and Maestro for computing and displaying three types of atomic charges – Mulliken, ESP, and Stockholder.

 

Tutorial Content

  1. Introduction to Atomic Charges 

  1. Creating Projects

  1. Optimizing the Geometry and Computing the Atomic Charges for Mafenide

  1. Viewing and Analyzing Results for Mafenide

  2. Optimizing the Geometry and Computing the Atomic Charges for TFSI
  3. Extra examples

  1. Conclusion and References

  1. Glossary of Terms

1. Introduction to Atomic Charges

Atomic chargesWhile not physically observable, these quantities help describe the distribution of electron density in a molecule or system. They are often used to quantify other molecular properties, such as reactivity. are useful quantities for understanding the distribution of electrons in a molecule. In addition to providing insights about the reactivity of a system, atomic chargesWhile not physically observable, these quantities help describe the distribution of electron density in a molecule or system. They are often used to quantify other molecular properties, such as reactivity. are also useful for parameterizing electrostatic components of classical force fields or for seeing how the distribution of electrons change during chemical processes. It is worth noting that individual atomic charges are not physical observables, only the total charge of a system can be deduced from experiment. Atomic charge calculations divide the total charge of the system based on different properties, such as the electronegativity of the atoms, to provide insights into the chemical properties and reactivity of the molecule(s).

Jaguar can compute several types of atomic charges. Among the charge types that Jaguar can compute are Mulliken chargesA set of partial charges that are calculated using a population matrix and the atomic basis functions that contribute to the representation of the orbitals for a given atom., electrostatic potentialA function that describes the electron density throughout the molecule. While it is a continuous quantity, in practice the potential is calculated at grid points defined throughout the system and then extrapolated. Charges are calculated during the process of creating the electrostatic potential to define where the electron density is in the system. (ESP) charges, and Stockholder chargesAtomic charges that are calculated via a Hirshfeld partitioning of the electron density, it is less sensitive to choice of basis set than Mulliken charges. . These different types of atomic charge calculations vary in the systems they are most accurate for, so choosing which one to use requires both knowledge of the computational method and the system you are studying. Luckily calculating all of them is relatively inexpensive, though since atomic charges are not physically observable, they cannot be directly compared to experimental values to determine which computational method is ‘best.’ Instead one can look at physically observable properties that are calculated using these atomic charges or see if there are any recommendations for a particular method based on literature on the type of system being studied.

In this tutorial, we will learn to calculate the Mulliken, ESP, and Stockholder charges for mafenide and bis(trifluoromethanesulfonyl)imide (TFSI), which is a key Schrödinger capability for studying any type of molecule. Mafenide is a prototypical small molecule drug and TFSI is a widely used anion, for example, in battery materials. The tutorial files also include extra examples for the other charge types that are available in Jaguar and will be discussed briefly in Section 6.

Specifically, we will perform a QM geometry optimization in a solvent continuum model and subsequent atomic charge property calculation for mafenide and TFSI using the QM Multistage Workflow panel and then visualize the resulting atomic charges.

For more practice on performing geometry optimizations, visit the Introduction to Geometry Optimizations, Functionals and Basis Sets tutorial for a foundational lesson or the Introduction to Multistage Quantum Mechanical Workflows tutorial for a more advanced lesson.

Note that the charges calculated in the workflow demonstrated here could be used for parameterizing the electrostatic component of a classical forcefield. For an example of this complete workflow, see the Diffusion tutorial. Predicting diffusivity is useful in many application areas, including pharmaceutical formulations and battery design.

2. Creating Projects

At the start of the session, change the file path to your chosen Working DirectoryThe location where files are saved. in MS Maestro (or Maestro) to make file navigation easier. Each session in MS Maestro (or 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 (or 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 Maestro) 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 to start Maestro or MS Maestro
    • (No icon? See Starting Maestro)
    • This tutorial uses MS Maestro, but 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 2-1. Change Working Directory option.

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

Figure 2-2. Save Project panel.

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

3. Optimizing the Geometry and Computing the Atomic Charges for Mafenide

In this section, we perform a geometry optimization of mafenide using the B3LYP-D3/6-31G** level of theory and PCM solvation model. We also calculate ESP charges, Mulliken charges, and Stockholder charges of the optimized structure. For more information about performing geometry optimizations and the various parameters see the Introduction to Geometry Optimizations, Functionals and Basis Sets or the Introduction to Multistage Quantum Mechanical Workflows tutorials.

Figure 3-1. 2D Sketcher panel with the drug mafenide drawn.

We will begin with sketching the mafenide molecule

  1. Go to Edit > 2D Sketcher
  2. Draw the 2D structure of mafenide as shown in the Figure
  1. Click Save as New
  2. Change the name of the Entry Title dialog that appears to Mafenide
  3. Close the 2D Sketcher panel

Figure 3-2. View of the unoptimized 3D structure of mafenide with the corresponding entry in the Entry List.

The 3D structure of mafenide is shown in the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed. and the corresponding entry is available in the Entry ListA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion. on the left. Stylize as you wish, here we show the ball-and-stick representation.

This 3D structure was created by the 2D to 3D structure converter utilizing a force field. The geometry in the 3D structure may not be optimal. We recommend that you always act on quantum mechanical energy-minimized structures when you compute atomic and molecular properties, especially when high prediction accuracy is desirable.

Figure 3-3. Jaguar Optimization panel with the mafenide entry included.

In order to optimize the geometry, we will use the Jaguar Optimization panel

  1. Go to Tasks > Materials > Quantum Mechanics > Molecular Quantum Mechanics > Optimization
  2. Go to the Solvation Tab

 

Figure 3-4. Choosing the PCM implicit solvent model in the Jaguar Optimization panel.

By default, Jaguar geometry optimizations are performed in gas-phase. Here, we would like to optimize the geometry of our molecule in a water solvent continuum

  1. For the Solvent model, choose PCM.
    • PCM is the Polarizable Continuum Model implicit solvent model
  2. Go to the Properties Tab

 

Note: The Optimize in gas phase option can be used if we wish to compute the solvation energy as a difference between the gas phase energy and solution phase energy since the charge distribution will differ with and without solvent

Figure 3-5. Selecting the Properties in the Jaguar Optimization panel.

  1. For Properties check the boxes for Atomic electrostatic potential charges (ESP), Mulliken populations, and Stockholder charges
    • Here we will keep the default settings, but further specifications for the calculation can be made by clicking on the Property name and changing the settings below
  2. Keep the Job name jag_Mafenide_opt_B3LYP-D3_6-31Gss
  3. Adjust the job settings () as needed
    • This job requires a CPU host and can be completed in about 10 minutes on 8 processors
  4. Click Run

4. Viewing and Analyzing Results for Mafenide

In this section, we will view the three types of atomic charges calculated in the previous section.

Figure 4-1. Optimized mafenide molecule.

Once the geometry optimization and property calculations are complete, the newly optimized molecule with its computed atomic charges is automatically incorporatedOnce a job is finished, output files from the working directory are added to the project and shown in the Entry List and Project Table. in the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed. and is available in the Entry ListA simplified view of the Project Table that allows you to perform basic operations such as selection and inclusion.

  1. IncludeThe entry is represented in the Workspace, the circle in the In column is blue. the output from the optimization calculation in the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed.

Figure 4-2. Opening the Edit Custom Label panel.

  1. Go to > > Edit Custom Label, as shown in the Figure
    • The Edit Custom Label panel opens
    • Different label fields are shown

Figure 4-3. The current available custom labels.

  1. Search for the three atomic charges in the list. If a charge is missing, click the Add Label Fields icon ( )
    • Some calculated charges may already be in the Edit Custom Label field. For example, this calculation automatically detected ESP and Stockholder Charges. Only Mulliken Charges need to be added to the list. Note that your Edit Custom Label menu may look different.

Figure 4-4. Picking ESP Charges, Mulliken Charges, and Stockholder Charges in the Edit Custom Label window.

  1. Scroll down the label fields,choose ESP Charges, Mulliken Charges, and Stockholder Charges in the list and click OK

Figure 4-5. Picking ESP Charges, Stockholder  Charges, and Mulliken charges in the Edit Custom Label panel.

  1. Click the ESP Charges, Stockholder Charges, and Mulliken Charges checkboxes to include the label fields
    • Note that all three charges can be viewed at once or each type of charge can be viewed individually. Checking all three will result in viewing all three charges simultaneously in the workspace
  2. Click OK

Figure 4-6. ESP charges, Stockholder charges, and Mulliken charges for Mafenide.

The atomic charges appear as atomic labels in the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed. and their order is defined by the order in which they are listed in the Edit Custom Label panel: ESP charges; Stockholder charges; Mulliken charges. The order can be changed by dragging and dropping the entries in the Edit Custom Label panel.

 

For example, observe the yellow sulfur atom (see red arrow). It has an ESP charge of 0.89, a Stockholder charge of 0.47, and a Mulliken charge of 1.18 as shown in the figure. 

 

Note: Even though we chose the 6-31G** basis set, for our calculation, Stockholder charges are always computed using the 6-31G basis set in Jaguar.

Figure 4-7. The original and the ionic representations of the sulfonamide group, the latter being an interpretation of the atomic charges calculation.

With respect to formal charges for representing the molecule, according to these computed charges, the sulfur in the sulfonamide group has the positive charge on it and the two oxygen atoms bear the negative charge. The three atomic charge methods produced three different values but they all resulted in a sulfur bearing the positive charge and oxygen bearing the negative charge. Therefore, the sulfonamide group might be best represented by the ionic Lewis structure on the right in the Figure. The resonance structure for the oxygen atoms is similar to that in a carboxylate group.

Figure 4-8. Accessing the MS Maestro Preferences panel on a Mac.

Optional: The label sizes, font, and color for atomic charges can be controlled

  1. Choose Edit > Preferences on a Linux/Windows machine or Materials Science > Preferences on a Mac

Figure 4-9. Altering the Atom/Bond Label preferences.

Optional:

  1. Select Atom/Bond Labels
    • Alter the label preferences to your liking
  2. Close the Preferences menu when finished

5. Optimizing and Computing the Atomic Charges for TFSI

In this section, we will repeat the steps from Section 3 and Section 4 on the bis(trifluoromethylsulfonyl)imide (TFSI) anion. First an optimization and charge calculation will be performed on TFSI in the PCM solvent model with acetonitrile as the solvent, then the three charge labels will be applied. For detailed steps refer back to Section 3 and Section 4. We will briefly go over the main steps for calculating the atomic charges of TFSI.

Figure 5-1. 2D Sketcher panel with TFSI drawn.

  1. Open the 2D Sketcher panel : Edit > 2D Sketcher
  2. Draw the 2D structure of TFSI
    • Be sure to include the formal charge on the nitrogen atom. To do this, first click the decrease charge icon (shown by the red box) then click on the nitrogen atom. This formal charge does not affect the atomic charge calculation other than indicating that the overall charge on the molecule is -1.
  3. Click Save as New
  4. Type TFSI in the Entry Title dialog that appears
  5. Close the 2D Sketcher panel and stylize the molecule as you wish

 

Figure 5-2. Jaguar Optimization panel with the TFSI entry included.

  1. Go to Tasks > Materials > Quantum Mechanics > Molecular Quantum Mechanics > Optimization
    • The Optimization panel opens, make sure the TFSI entry is includedThe entry is represented in the Workspace, the circle in the In column is blue.
  2. Click on the Solvation Tab

Figure 5-3. Choosing the PCM implicit solvent model in the Jaguar Optimization panel.

  1. For the Solvent model, choose PCM
  2. For the Solvent, choose acetonitrile
    • Other solvent choices besides water or acetonitrile are available as well
  3. Click on the Properties Tab    

Figure 5-4. Selecting the Properties in the Jaguar Optimization panel.

  1. For Properties check the box for Atomic electrostatic potential charges (ESP), Milliken populations, and Stockholder charges
  2. Keep the Job name jag_TFSI_opt_B3LYP-D3_6-31Gss
  3. Adjust the job settings () as needed
    • This job requires a CPU host and can be completed in about 10 minutes on 8 processors
  4. Click Run

Figure 5-5. Optimized TFSI molecule.

 

  1. IncludeThe entry is represented in the Workspace, the circle in the In column is blue. the structure resulting from the optimization calculation in the WorkspaceThe 3D display area in the center of the main window, where molecular structures are displayed.
  2. Go to > > Edit Custom Label

 

Figure 5-6. The Edit Custom Label panel.

 

  1. The ESP Charges, Stockholder Charges, and Mulliken Charges should already be options in the menu since we used them with the Mafenide molecule
    • If the three charges are not currently listed click the Add Label Fields icon ( ) to add the label
    • Scroll down the label fields,choose ESP Charges, Mulliken Charges, and Stockholder Charges in the list and click OK
  2. Click the ESP Charges, Stockholder Charges, and Mulliken Charges checkbox to include the label field.
  3. Click OK

Figure 5-7. ESP Charges, stockholder Charges, and Mulliken charges for TFSI.

Analyze, for example, the blue nitrogen atom (see red arrow). It has an ESP charge of -0.69, a Stockholder charge of -0.33, and a Mulliken charge of -0.75 as shown in the Figure.

6. Extra Examples

In this section we will briefly discuss the other properties that can be calculated in the Jaguar panel that can give insights into atomic charges. While there are many ways to compute atomic charges, this tutorial will only touch on the ones that can be calculated via the Jaguar panel.

Mulliken charges, charges from Electrostatic Potential Fitting (ESP), and Stockholder charges were discussed in the earlier examples. These charge types, as seen in the previous sections allow you to add labels to the workspace to easily visualize the calculated atomic charges. The method discussed here, natural chargesNatural charges are the calculation of the electron density on different atoms based on a natural bond order analysis. Natural orbitals are thought to be the orbitals that are best at representing the system, and can often recreate predicted Lewis structures. , cannot be shown as atom labels. The information can only be found in the output files of the calculations, as will be shown in this section.

Natural chargesNatural charges are the calculation of the electron density on different atoms based on a natural bond order analysis. Natural orbitals are thought to be the orbitals that are best at representing the system, and can often recreate predicted Lewis structures. , discussed in more detail here, are calculated based on natural bond orbitals. They are the ‘intrinsic’ description of the electron density based on the wave function that describes the system.  Natural chargesNatural charges are the calculation of the electron density on different atoms based on a natural bond order analysis. Natural orbitals are thought to be the orbitals that are best at representing the system, and can often recreate predicted Lewis structures. are known for being less basis set dependent than Mulliken charges, though also more computationally expensive, and often replicate the expected Lewis structures of a system.

Figure 6-1. Selecting NBO analysis and Atomic Fukui indices in the Properties tab.

  1. Set up the same calculations as in  Section 3 and Section 5 but with the following changes:
    • In the Properties tab select Atomic Fukui indices and Stockholder charges
    • Adjust the job names to jag_molecule_opt_B3LYP-D3_6-31Gss_extra, where molecule is replaced by either Mafenide or TFSI
  2. The same job settings as the previous sections can be used, the additional charge calculations will not greatly impact the computational cost
  3. If you would like to run the job yourself, click Run. Otherwise go to File > Import Structures, navigate to where you downloaded the tutorial files, and Open Section_06 > jag_TFSI_opt_B3LYP-D3_6-31Gss_extra > jag_TFSI_opt_B3LYP-D3_6-31Gss_extra.01.mae
    and
    Section_06 > jag_Mafenide_opt_B3LYP-D3_6-31Gss_extra.01.mae

 

 

Figure 6-2. Looking at the results for the natural charges.

The results of these charge calculations cannot be viewed by adding labels to our structures in the workspace. Instead we will need to read the output files.

  1. If you ran the jobs, open a file manager, navigate to your workspace and open jag_TFSI_opt_B3LYP-D3_6-31Gss_extra > jag_TFSI_opt_B3LYP-D3_6-31Gss_extra.out
    • If you are using the provided tutorial files go to the same folder that you imported the files from in the last step and open jag_TFSI_opt_B3LYP-D3_6-31Gss_extra.out
  2. Search for the ‘Summary of Natural Population Analysis’ there will be a table underneath with a column labeled ‘Natural Charges’
    • This column contains the charge predictions obtained from the natural bond order calculation
  3. Repeat for the file jag_Mafenide_opt_B3LYP-D3_6-31Gss_extra > jag_Mafenide_opt_B3LYP-D3_6-31Gss_extra.out

7. Conclusion and References

This tutorial demonstrated how to compute, display, and interpret atomic charges using Jaguar and Maestro. In doing so, we also learned how to optimize molecular structures using the PCM solvation model.

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 documentation for example files and guidance.

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

8. Glossary of Terms

Atomic charges - While not physically observable, these quantities help describe the distribution of electron density in a molecule or system. They are often used to quantify other molecular properties, such as reactivity.

Electrostatic potential - A function that describes the electron density throughout the molecule. While it is a continuous quantity, in practice the potential is calculated at grid points defined throughout the system and then extrapolated. Charges are calculated during the process of creating the electrostatic potential to define where the electron density is in the system.

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

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

Incorporated - Once a job is finished, output files from the working directory are added to the project and shown in the Entry List and Project Table.

Mulliken charges - A set of partial charges that are calculated using a population matrix and the atomic basis functions that contribute to the representation of the orbitals for a given atom.

Natural charges - Natural charges are the calculation of the electron density on different atoms based on a natural bond order analysis. Natural orbitals are thought to be the orbitals that are best at representing the system, and can often recreate predicted Lewis structures.

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 - The entry is chosen in the Entry List (and Project Table), the row is highlighted; project operations are performed on all selected entries.

Stockholder charges - Atomic charges that are calculated via a Hirshfeld partitioning of the electron density, it is less sensitive to choice of basis set than Mulliken charges.

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.