# Optimization of Algorithms for Ion Mobility Calculations

## Abstract

Ion mobility spectrometry (IMS) is increasingly employed to probe the structures of gas-phase ions, particularly those of proteins and other biological macromolecules. This process involves comparing measured mobilities with those computed for potential geometries, which requires evaluation of orientationally averaged cross sections using some approximate treatment of ion-buffer gas collisions. Two common models are the Projection Approximation (PA) and Exact Hard-Spheres Scattering (EHSS) that represent ions as collections of hard spheres. Though calculations for large ions and/or conformer ensembles take significant time, no algorithmic optimization had been explored. Previous EHSS programs were dominated by ion rotation operations that allow orientational averaging. We have developed two new algorithms for PA and EHSS calculations: one simplifies those operations and greatly reduces their number, and the other disposes of them altogether by propagating trajectories from a random origin. The new algorithms were tested for a representative set of seven ion geometries including diverse sizes and shapes. While the best choice depends on the geometry in a non-obvious way, the difference between the two codes is generally modest. Both are much more efficient than the existing software, for example faster than the widely used Mobcal (implementing EHSS) ~10 - 30 fold.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 902680

- Report Number(s):
- PNNL-SA-52282

400412000; TRN: US200717%%610

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Physical Chemistry A, 111(10):2002-2010; Journal Volume: 111; Journal Issue: 10

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 59 BASIC BIOLOGICAL SCIENCES; ALGORITHMS; APPROXIMATIONS; CROSS SECTIONS; EVALUATION; GEOMETRY; ION MOBILITY; OPTIMIZATION; ORIGIN; PROBES; PROTEINS; ROTATION; SCATTERING; SPECTROSCOPY; TRAJECTORIES

### Citation Formats

```
Shvartsburg, Alexandre A., Mashkevich, Stefan V., Baker, Erin Shammel, and Smith, Richard D.
```*Optimization of Algorithms for Ion Mobility Calculations*. United States: N. p., 2007.
Web. doi:10.1021/jp066953m.

```
Shvartsburg, Alexandre A., Mashkevich, Stefan V., Baker, Erin Shammel, & Smith, Richard D.
```*Optimization of Algorithms for Ion Mobility Calculations*. United States. doi:10.1021/jp066953m.

```
Shvartsburg, Alexandre A., Mashkevich, Stefan V., Baker, Erin Shammel, and Smith, Richard D. Thu .
"Optimization of Algorithms for Ion Mobility Calculations". United States.
doi:10.1021/jp066953m.
```

```
@article{osti_902680,
```

title = {Optimization of Algorithms for Ion Mobility Calculations},

author = {Shvartsburg, Alexandre A. and Mashkevich, Stefan V. and Baker, Erin Shammel and Smith, Richard D.},

abstractNote = {Ion mobility spectrometry (IMS) is increasingly employed to probe the structures of gas-phase ions, particularly those of proteins and other biological macromolecules. This process involves comparing measured mobilities with those computed for potential geometries, which requires evaluation of orientationally averaged cross sections using some approximate treatment of ion-buffer gas collisions. Two common models are the Projection Approximation (PA) and Exact Hard-Spheres Scattering (EHSS) that represent ions as collections of hard spheres. Though calculations for large ions and/or conformer ensembles take significant time, no algorithmic optimization had been explored. Previous EHSS programs were dominated by ion rotation operations that allow orientational averaging. We have developed two new algorithms for PA and EHSS calculations: one simplifies those operations and greatly reduces their number, and the other disposes of them altogether by propagating trajectories from a random origin. The new algorithms were tested for a representative set of seven ion geometries including diverse sizes and shapes. While the best choice depends on the geometry in a non-obvious way, the difference between the two codes is generally modest. Both are much more efficient than the existing software, for example faster than the widely used Mobcal (implementing EHSS) ~10 - 30 fold.},

doi = {10.1021/jp066953m},

journal = {Journal of Physical Chemistry A, 111(10):2002-2010},

number = 10,

volume = 111,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}