A survey of wave function effects on theoretical calculation of gas phase 19 F NMR chemical shifts using factorial design H. Shaghaghi, H. Ebrahimi, M. Tafazzoli *, M. Jalali-Heravi Department of Chemistry, Sharif University of Technology, P. O. Box 11155-9516, Tehran, Iran 1. Introduction 19 F NMR is one of the most delicate and practical branches of nuclear magnetic resonance (NMR) spectroscopy. It has been widely used in many fields particularly in biological systems due to the fact that the F nucleus, as proved by experiments, enjoys the advantage of having a naturally occurring single isotope with one- half spin. As indicated in several recent investigations, the 19 F chemical shift is very sensitive to the environment and this facilitates the study of structure and dynamics in simple fluorine compounds [1–4] and biological systems [5–8]. The intermolecular effects present in condensed phases can be almost eliminated in gas phases [9]. Therefore, the gas phase properties can be considered as a zero point in many fields of research such as dynamics, solvent effects and hydrogen bonding studies. Although there are very limited reports on gas phase 19 F nuclear magnetic resonance properties [10–13], fortunately, the properties of molecules in dilute gases more closely resemble those obtained from the theoretical calculations for single molecules. The Gauge-independent atomic orbital (GIAO) method [14] has been successfully applied to the calculations performed for NMR parameters using ab initio computation methods. The simplest type of ab initio computation is Hartree–Fock (HF) scheme, in which the instantaneous coulombic electron–electron repulsion is not speci- fically taken into account and only its average effect (mean field) is included in the calculation [14,15]. There are methods such as density functional theory (DFT) and Moller–Plesset perturbation theory (Mpn) [14,15] in which correction for electron–electron repulsion is also included. Theoretical results of shielding constants are very sensitive to the selected calculation method as well as the basis sets. Fukaya and Ono [16] have calculated 19 F chemical shifts for different kinds of perfluoro compounds in different levels of theories, but they have compared their results with the experimental data of 19 F chemical shifts in solution phase. These researchers also have reported that B3LYP/6-31++G(d,p) with 10 ppm deviation is the best level for the 19 F chemical shifts calculation. The factorial design has been utilized in many surveys as a multivariate method to find the best level of theory [17–22]. This statistical method allows discovering the most significant variables for a certain system with only few experiments [23,24]. In the present study, a factorial design was used for studying the effects of calculation methods and basis sets on 19 F chemical shifts. The main aim of the present contribution was developing a general optimum level of theory for calculating 19 F chemical shifts. This can be justified due to limited availability of experimental values for 19 F chemical shifts in gas phase. The results are promising and a level of theory with a minimum absolute deviation is proposed for each molecule. 2. Results and discussion 2.1. 2 4 factorial designs In order to determine the optimum wave functions and calculational methods two 2 4 factorial designs were considered. Journal of Fluorine Chemistry 131 (2010) 47–52 ARTICLE INFO Article history: Received 22 August 2009 Received in revised form 26 September 2009 Accepted 28 September 2009 Available online 3 October 2009 Keywords: Gas phase 19 F chemical shift GIAO Factorial design MP2 DFT ABSTRACT The wave functions for calculating gas phase 19 F chemical shifts were optimally selected using the factorial design as a multivariate technique. The effects of electron correlation, triple-j valance shell, diffuse function, and polarization function on calculated 19 F chemical shifts were discussed. It is shown that of the four factors, electron correlation and the polarization functions affect the results significantly. B3LYP/6-31 + G(df,p) wave functions have been proposed as the best and the most efficient level of theory for calculating 19 F chemical shifts. An additional series of fluoro compounds were used as a test set and their predicted 19 F chemical shifts values confirmed the validity of the approaches. ß 2009 Elsevier B.V. All rights reserved. * Corresponding author. Tel.: +98 21 66005718; fax: +98 21 66012983. E-mail address: tafazzoli@sharif.edu (M. Tafazzoli). Contents lists available at ScienceDirect Journal of Fluorine Chemistry journal homepage: www.elsevier.com/locate/fluor 0022-1139/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jfluchem.2009.09.020