# Presentation: 336179

## Towards Fundamental Understanding and Rational Control of Crystal Growth

- Tonglei Li, University of Kentucky, DMR-0449633

***Poking fun at University of Iowa****.  The group traveled to Iowa City and attended the Midwest Organic Solid State Chemistry Symposium XVI June 9-10, 2006.  From left to right, Sihui Long (postdoctoral student), Tonglei Li (PI), Clare Aubrey (graduate student), Hongxia Guo (graduate student), Christin Hollis (graduate student), Yuxin Yang (graduate student), and Matt Swadley (undergraduate student).*

## The three graphics are electronic structures calculated of form YN of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (aka ROY for its red, orange and yellow colors of at least 10 polymorphs reported to date).  The larger graphics shows isosurfaces of electron density in gray (0.04 e/bohr^3), nucleophilic electronic Fukui function in red (0.002 e/bohr^3), and electrophilic electronic Fukui function in blue (0.002 e/bohr^3).  The top right graphics shows the nuclear Fukui functions, indicated by arrows whose lengths and colors are mapped to their values respectively, in addition to the isosurfaces of nucleophilic electronic Fukui function.  The bottom right graphics shows the electrophilic nuclear Fukui functions in addition to the isosurfaces of electrophilic electronic Fukui function.
The study is to understand intermolecular interactions with regard to molecular packing and polymorphism.  Electronic Fukui functions are believed to reveal the locality of intermolecular interactions between organic molecules.  It has been shown the electronic Fukui function determines the local polarizability:
where  and S are global polarizability and softness, respectively, f (r) is electronic Fukui function, and r and  are polar coordinates.  Moreover, nuclear Fukui function may be regarded as a “condensed” form of electronic Fukui function, perhaps providing a simpler representation of the local, intermolecular interactions.
where  and R are the nuclear Fukui function and position of nucleus , respectively, v (r) is the external potential defined by nuclear charges nuclear positions, and N is the number of electrons in the system.

- The study is to understand intermolecular interactions with regard to molecular packing and polymorphism.  Electronic Fukui functions are believed to reveal the *locality* of intermolecular interactions between organic molecules.  It has been shown the electronic Fukui function determines the local polarizability:
- where ** and *S* are global polarizability and softness, respectively, *f** *(**r**) is electronic Fukui function, and **r** and ** are polar coordinates.  Moreover, nuclear Fukui function may be regarded as a “condensed” form of electronic Fukui function, perhaps providing a simpler representation of the local, intermolecular interactions.
- where **** and **R**** are the nuclear Fukui function and position of nucleus **, respectively, *v** *(**r**) is the external potential defined by nuclear charges nuclear positions, and *N* is the number of electrons in the system.

- Tonglei Li, University of Kentucky, DMR-0449633

- Towards Fundamental Understanding and Rational Control of Crystal Growth