### Abstract

The procrystal calculation of the electron density is a very rapid procedure that offers a quick way to analyze various bonding properties of a crystal. This study explores the extent to which the positions, number, and properties of bond-critical points determined from the procrystal representations of the electron density for minerals are similar to those of first-principles ab initio model distributions. The purpose of the study is to determine the limits imposed upon interpretation of the procrystal electron density. Procrystal calculations of the electron density for more than 300 MO bonds in crystals were compared with those previously calculated using CRYSTAL98 and TOPOND software. For every bond-critical point found in the ab initio calculations, an equivalent one was also found in the procrystal model, with similar magnitudes of electron density, and at similar positions along the bonds. The curvatures of the electron densities obtained from the ab initio and the procrystal distributions are highly correlated. It is concluded that the procrystal distributions are capable of providing good estimates of the bonded radii of the atoms and the properties of the electron-density distributions at the bond-critical points. Because the procrystal model is so fast to compute, it is especially useful in addressing the question as to whether a pair of atoms is bonded or not. If the Bader criteria for bonding are accepted, then the successful generation of the bond- critical points by the procrystal model demonstrates that bonding is an atomic feature. The main difference between the critical-point properties of the procrystal and the ab initio model is that the curvature in the electron density perpendicular to the bond path of the ab initio model is sharper than for the procrystal model. This is interpreted as indicating that the electrons that migrate into a bond originate from its sides, and not from the regions closer to the nuclei. This observation also suggests that ab initio optimization routines could see an improvement in speed if the parameters relating to the angular components of atomic wave functions were to vary before the radial components.

Original language | English (US) |
---|---|

Pages (from-to) | 369-385 |

Number of pages | 17 |

Journal | Physics and Chemistry of Minerals |

Volume | 29 |

Issue number | 5 |

DOIs | |

State | Published - 2002 |

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### Keywords

- Bond-critical points
- Electron density
- Feldspar
- Procrystal
- Pyroxene
- Topology

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Materials Science(all)

### Cite this

*Physics and Chemistry of Minerals*,

*29*(5), 369-385. https://doi.org/10.1007/s00269-001-0236-0

**A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals.** / Downs, Robert T; Gibbs, G. V.; Boisen, M. B.; Rosso, K. M.

Research output: Contribution to journal › Article

*Physics and Chemistry of Minerals*, vol. 29, no. 5, pp. 369-385. https://doi.org/10.1007/s00269-001-0236-0

}

TY - JOUR

T1 - A comparison of procrystal and ab initio model representations of the electron-density distributions of minerals

AU - Downs, Robert T

AU - Gibbs, G. V.

AU - Boisen, M. B.

AU - Rosso, K. M.

PY - 2002

Y1 - 2002

N2 - The procrystal calculation of the electron density is a very rapid procedure that offers a quick way to analyze various bonding properties of a crystal. This study explores the extent to which the positions, number, and properties of bond-critical points determined from the procrystal representations of the electron density for minerals are similar to those of first-principles ab initio model distributions. The purpose of the study is to determine the limits imposed upon interpretation of the procrystal electron density. Procrystal calculations of the electron density for more than 300 MO bonds in crystals were compared with those previously calculated using CRYSTAL98 and TOPOND software. For every bond-critical point found in the ab initio calculations, an equivalent one was also found in the procrystal model, with similar magnitudes of electron density, and at similar positions along the bonds. The curvatures of the electron densities obtained from the ab initio and the procrystal distributions are highly correlated. It is concluded that the procrystal distributions are capable of providing good estimates of the bonded radii of the atoms and the properties of the electron-density distributions at the bond-critical points. Because the procrystal model is so fast to compute, it is especially useful in addressing the question as to whether a pair of atoms is bonded or not. If the Bader criteria for bonding are accepted, then the successful generation of the bond- critical points by the procrystal model demonstrates that bonding is an atomic feature. The main difference between the critical-point properties of the procrystal and the ab initio model is that the curvature in the electron density perpendicular to the bond path of the ab initio model is sharper than for the procrystal model. This is interpreted as indicating that the electrons that migrate into a bond originate from its sides, and not from the regions closer to the nuclei. This observation also suggests that ab initio optimization routines could see an improvement in speed if the parameters relating to the angular components of atomic wave functions were to vary before the radial components.

AB - The procrystal calculation of the electron density is a very rapid procedure that offers a quick way to analyze various bonding properties of a crystal. This study explores the extent to which the positions, number, and properties of bond-critical points determined from the procrystal representations of the electron density for minerals are similar to those of first-principles ab initio model distributions. The purpose of the study is to determine the limits imposed upon interpretation of the procrystal electron density. Procrystal calculations of the electron density for more than 300 MO bonds in crystals were compared with those previously calculated using CRYSTAL98 and TOPOND software. For every bond-critical point found in the ab initio calculations, an equivalent one was also found in the procrystal model, with similar magnitudes of electron density, and at similar positions along the bonds. The curvatures of the electron densities obtained from the ab initio and the procrystal distributions are highly correlated. It is concluded that the procrystal distributions are capable of providing good estimates of the bonded radii of the atoms and the properties of the electron-density distributions at the bond-critical points. Because the procrystal model is so fast to compute, it is especially useful in addressing the question as to whether a pair of atoms is bonded or not. If the Bader criteria for bonding are accepted, then the successful generation of the bond- critical points by the procrystal model demonstrates that bonding is an atomic feature. The main difference between the critical-point properties of the procrystal and the ab initio model is that the curvature in the electron density perpendicular to the bond path of the ab initio model is sharper than for the procrystal model. This is interpreted as indicating that the electrons that migrate into a bond originate from its sides, and not from the regions closer to the nuclei. This observation also suggests that ab initio optimization routines could see an improvement in speed if the parameters relating to the angular components of atomic wave functions were to vary before the radial components.

KW - Bond-critical points

KW - Electron density

KW - Feldspar

KW - Procrystal

KW - Pyroxene

KW - Topology

UR - http://www.scopus.com/inward/record.url?scp=0036071946&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036071946&partnerID=8YFLogxK

U2 - 10.1007/s00269-001-0236-0

DO - 10.1007/s00269-001-0236-0

M3 - Article

VL - 29

SP - 369

EP - 385

JO - Physics and Chemistry of Minerals

JF - Physics and Chemistry of Minerals

SN - 0342-1791

IS - 5

ER -