Density Functional Theory Calculations of the Barrier to Atropisomerism of aDibenzo[d,f][1,3,2]dioxaphosphepin Moiety: a Tool for Rational Ligand Design

Robert Frankea,*, Cornelia Borgmannb, Dieter Hessb, Klaus-Diether Wieseb

Marl, a Infracor GmbH and b Oxeno Olefinchemie GmbH, Degussa Gruppe

Received September 1st, 2003.

Abstract. Density functional theory calculations yield reasonablevalues for the barrier to atropisomerism in a dibenzo[d,f]-[1,3,2]dioxaphosphepin moiety of diphosphite ligands and thus

Dichtefunktionalrechnungen zur Höhe der Atropisomerie-Barriere in einerDibenzo[d,f][1,3,2]dioxaphosphepin-Einheit: ein Werkzeug für das rationale Design vonLiganden

Inhaltsübersicht. Dichtefunktionalrechnungen ergeben zufrieden-stellende Ergebnisse für die Höhe der Barriere in Atropisomerenvon Diphosphit-Liganden, die Dibenzo[d,f][1,3,2]dioxaphosphe-

Introduction

Highly enantioselective hydroformylation catalysed by chi-ral metal complexes has been obtained with only a few cata-lytic systems. One example is a rhodium catalyst modifiedby BINAPHOS � a phosphine-phosphite ligand � that re-aches enantiomeric excess (ee) up to 96 % [1]. Diphosphitesare important alternatives for the industry because of theirsimple and therefore cost-efficient synthesis. Chiral diphos-phites show higher ee’s and higher regioselectives if theyhave rigid structures and bulky substituents [2]. RecentlyBriggs and Whiteker reported different regioselectivities fordiastereomers of rhodium-diphosphite catalysts in propyl-ene hydroformylation [3]. They performed molecular mech-anics calculations and found different natural bite angles [4]and cone angles for the diastereomers and concluded thatthe hydroformylation regioselectivity of this catalyst isdominated by steric effects.

Since the discovery of highly regioselective catalysts con-taining chelating diphosphines and diphosphites for therhodium-catalysed hydroformylation of olefins, researchhas been done to establish theoretical means of enabling a-priori ligand development (see e.g. [4, 5]). The critical evalu-ation of these theoretical models is a prerequisite for theirproper application. Despite the progress made in recent ye-ars, the kinetics and energetics of the hydroformylation se-

* Dr. R. FrankePaul-Baumann-Str. 1D-45764 MarlTelephone: �49 2365 49 9892e-mail: robert.franke@infracor.de

Z. Anorg. Allg. Chem. 2003, 629, 2535�2538 DOI: 10.1002/zaac.200300296 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 2535

provide an energetic criterion for falsification of hypothetical stablestereoisomers in rational ligand design.Keywords: Density functional calculations; Atropisomerism; Di-oxaphosphepin

pin-Einheiten enthalten. Sie stellen somit ein energetisches Krite-rium zur Falsifikation hypothetisch stabiler Stereoisomere für dasrationale Design von Liganden zur Verfügung.

quence with rhodium diphosphites still remain quite un-clear. Therefore, direct comparison of calculated properties,such as energetic barrier heights, with experimental valuesis not possible. In this article, we present quantum chemicalinvestigations of barriers to rotation in diphosphite ligandsand their comparison with experimental data in order toexplore the possibility of predicting the stereochemistry ofsuch systems.

Results and Discussion

Optically-active diphosphites containing biaryl moities areaxially chiral compounds with trigonal centres linked byrotationally-restricted single bonds. Depending on the bar-rier to rotation, interconversion of conformers is possible ata certain temperature; this could lead to the formation ofseveral stereoisomers of the diphosphite in a steady stateequilibrium. Whiteker et al. [6] report on variable tempera-ture NMR spectroscopy studies which enable the directmeasurement of the life-time of atropisomers and the calcu-lation of the barrier to interconversion of two dia-stereomeric disphosphite ligands. For facile atropisomerismof the dibenzo[d,f][1,3,2]dioxaphosphepin moiety in diphos-phite 1 a barrier height of ∆G��10 kcal/mol (1 cal �4.1840 J) was determined. The occurrence of an intercon-version of the atropisomeric stereoisomers by biaryl ro-tation under catalytic conditions was deduced to be likely.Assuming that one is able to calculate barriers to rotationby theoretical methods with reasonable accuracy, this ob-servation leads to an energetic criterion for falsification ofhypothetical stable stereoisomeric diphosphites in rational

R. Franke, C. Borgmann, D. Hess, K.-D. Wiese

Fig. 1 Structural representation of diphosphite 1

ligand design. We present here density functional theory(DFT) calculations of the energy barrier for interconversionin atropisomers for selected biphenyl fragments.

To model the atropisomer in 1 we considered the biphe-nyl epimerization depicted in Scheme 1. From the datagiven in Table 1 it can be seen that the results for the barrierheight are in reasonable agreement with the experimentallydeduced value of Whiteker et al. The DFT-BP86 calculationfor the molecule in the gas phase shows the minimum devi-ation of 1.9 kcal/mol. The functionals BP86 and B3LYPlead to very similar energy barriers. The DFT calculationsincluding the COSMO dielectric continuum solvationmodel show that the barrier height is not significantly alt-ered by the influence of a solution phase (assuming a highdielectric constant of the solvent). Calculations using theCOSMO-RS model yield the Gibbs free activation energyin solution by means of a statistical thermodynamic treat-ment of the solute-solvent interaction. The calculationsdocumented in Table 1 show that finite temperature effectsare negligible, as are also the influence of the solvent tolu-ene and entropic effects. Results for various other solvents(e.g. cyclohexene, hexen, octen, tetrahydrofurane, styrene,ethyl acrylate), not documented here, indicate that the bar-rier to atropisomerism in 2 is not influenced by solvent ef-fects, or that such influence is weak (differences smallerthan 1 kcal/mol in the Gibbs free activation energy). Okiapplies the term atropisomer to refer to conformers thatinterconvert with a half-life greater than 1000 s (0.28 h) [7].

Scheme 1 Schematic representation of interconversion of atropisomers for the bisphenol fragment of 2

2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 2535�25382536

Table 1 Barriers to rotation about the chiral axis of bisphenolfragment of 2 (Scheme 1)

Method Medium Temperature/°C ∆G�/kcal/mol

Energy GeometryDFT-B3LYP DFT-B3LYP Gas Phase �273.15 12.2DFT-BP86 DFT-BP86 Gas Phase �273.15 11.9DFT-BP86 DFT-BP86 Dielectric �273.15 11.9COSMO COSMO Continuum

ε � �DFT-BP86 DFT-BP86 Toluene 25 12.1COSMO-RS COSMODFT-BP86 DFT-BP86 Toluene 120 12.1COSMO-RS COSMO

Following this definition one can estimate via the Eyringequation a minimum barrier height of 22 kcal/mol at roomtemperature and 29 kcal/mol at 120 °C for the existence ofatropisomerism. In view of the experimental results docu-mented in ref. [6] we conclude that, in cases where DFTcalculations predict energy barriers to atropisomerism in di-phosphite ligands containing biaryl moities of about12 kcal/mol, an interconversion of resulting sterioisomersshould take place.

To extend our investigations towards systems with highbarriers to rotation, we studied the biaryl rotation in frag-ment 3. It is well-known that the presence of 6,6�-methylsubstituents prevents the interconversion of conformers byrotation in biphenyl systems containing substituents in theremaining ortho positions different from hydrogen atoms.The barrier yielded by the DFT treatment (functional:BP86) amounts 34 kcal/mol. Using the Eyring equation wehence estimate a half life τ1/2 > 2.5*108 h at room tempera-ture. Although a direct comparison with experimental val-ues is not possible, the qualitative conclusion of this resultis in perfect agreement with experimental observations [3].

Briggs and Whiteker published results for the half-life ofRRR and RSR diastereomers in diphosphite 4 [3]. Theirchiral HPLC studies revealed that the interconversion viathe rotation about the central tert-butyl substituted biphe-nyl axis is slow. The half-life amounts τ1/2 � 3180 s at T�34 °C which yields an energy barrier of 23.1 kcal/mol�. Wehave computed the barrier height for this rotation by DFT(functional: BP86). Our value of 22.5 kcal/mol (τ1/2 �

Density Functional Theory Calculations of the Barrier to Atropisomerism

Fig. 2 Structural representation of phosphite 3

Fig. 3 Structural representation of diphosphite 4

1107 s at T�34 °C) is in reasonable agreement with the ex-perimental value.

The DFT calculations reported in this article indicatethat an a priori prediction of atropisomerism of phosphitemoities is possible. This is particularly helpful for the fine-tuning of catalysts by ligand modification. It is beyond thescope of this article to discuss technical issues of our quan-tum chemical calculations but a few remarks concerninglimitations should be made. Specifically, attention must bedrawn to two potentially serious drawbacks. Consideringthat the number of minima and saddle points of the poten-tial energy surface typically grows exponentially with thenumber of nuclear coordinates there is in principle noguarantee that calculations for the rotational barriers in

Z. Anorg. Allg. Chem. 2003, 629, 2535�2538 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 2537

complex molecular fragments such as 4 are based on the’relevant’ conformers. An inadequate conformational searchmight produce predicted barrier heights in bulky and con-formationally flexible fragments which are too large. Fur-thermore, because the half-life is related exponentially tothe value of the barrier height, relatively small errors in thequantum chemical calculations cause large deviations fromexperimental data, as can be seen in our calculations for 4.Therefore we recommend a focus on the investigation ofsmall molecular fragments and the use of the calculatedbarrier heights as a criterion for the falsification of hypo-thetical stable stereoisomers in the process of rational li-gand design.

Details of the Calculations

All quantum chemical calculations were performed with the TUR-BOMOLE [8] suite of programs using on all atoms a valence triplezeta basis including one set of polarisation functions [9]. The DFTcalculations were performed with the B3LYP functional [10] andthe BP86 functional (exchange functional B88 [11], correlationfunctional P86) [12]. In the case of the DFT-BP86 calculations theresolution-of-identity approximation for the two-electron-integralsemploying the corresponding auxiliary basis sets [13] was used. TheCOSMO solvation model [14] implemented in TURBOMOLE wasused for the calculation in the condensed phase. The Gibbs freeenergies in the multicomponent mixtures at finite temperatureswere calculated using the COSMO-RS model [15]. The COSMO-RS calculations were carried out with the COSMOTHERM pro-gram, version C1.2, revison 07/02; COSMOlogic GmbH & Co. KG,Leverkusen, Germany, 2002. The molecular mechanics calculationsfor generating start structures were carried out with the modellingpackage Cerius2 of Accelrys Inc. employing the force field COM-PASS.

The Eyring equation reads: ∆G� � �R ·T · ln � h · ln(2)

kB ·T ·τ1/2� , with

the gas constant R, temperature T, Planck constant h, Boltzmannconstant kB and half-life τ1/2.

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