Determination of molar refractions and Abraham descriptors for tris ( acetylacetonato ) chromium ( III ) , tris ( acetylacetonato ) iron ( III ) and tris ( acetylacetonato ) cobalt ( III ) †

We have determined molar refractions of tris(acetylacetonato)chromium(III), tris(acetylacetonato)iron(III) and tris(acetylacetonato)cobalt(III). Although the d-electron structures of the three metal centres differ significantly, the three molar refractions are actually quite close to each other. We then used these molar refractions to determine the Abraham E-descriptor, we calculated the V-descriptor by McGowan’s method, and then used literature data on solubilities and water–solvent partitions to obtain the rest of the set of descriptors for the three tris(acetylacetonato) complexes. If we take E as the average of those for the chromium, iron and cobalt complexes, we can use limited literature data to obtain the full set of Abraham descriptors for the tris(acetylacetonates) of vanadium(III), yttrium(III), samarium(III), lanthanum(III) and neodymium(III). For the eight complexes, the descriptors vary regularly with complex molecular weight. These show that the complexes are quite polarizable, have zero hydrogen-bond acidity and significant hydrogen bond basicity. From the sets of Abraham descriptors, a very large number of physicochemical properties can be predicted for the eight acetonylacetonates.


Introduction
Methods are now available for the calculation or prediction of numerous physico-chemical properties of organic compounds.Water-octanol partition coefficients can easily be calculated through programs such as BioLoom, 1 the EPI Suite TM, 2 ACD ChemSketch, 3 the ACD Absolv suite 4 and SPARC. 5Some of these programs 2,5 can be used to calculate numerous other physicochemical properties.However, extension to compounds other than organic compounds is either very limited or non-existent.][8][9][10][11][12][13] These descriptors, together with a large set of equations we have constructed enables predictions to be made of all sorts of physicochemical, environmental and biological properties.Initially the system was applied to organic compounds and to a few simple inorganic compounds, but we have since applied it to organometallic compounds such mercury compounds 14 and the tetraphenyl derivatives of silicon, germanium, tin and lead. 15ecently we showed that the system could include derivatives of ferrocene. 16This suggests that we might be able to include inorganic complexes into our system.If so, this would mark a very significant extension of predictive methods into the vast area of inorganic complex chemistry.We start with the tris(acetylacetonato) complexes of chromium(III), cobalt(III) and iron(III) because there was a reasonable amount of data on the solubilities of these complexes that we could use.We refer to the complexes as Cr(acac) 3 , Co(acac) 3 and Fe(acac) 3 .One of the descriptors we need can be obtained from the refractive index or molar refractivity of a compound.No such data were available for the three tris(acetylacetonato) complexes, and so we decided to determine their molar refractions experimentally.

Compounds
The three tris(acetylacetonato) complexes, were purchased from Sigma-Aldrich.The purity of the iron compound was Z99.9%, while that of the chromium and cobalt was 99.99%.compound in 45 mL of solvent up to 200 mg, in 20 mg increments.The iron compound, a fine powder, dissolved readily and yielded a highly colored red solution.The chromium and cobalt compounds, in crystalline form, required sonication to completely dissolve the higher concentration solutions to give violet and green solutions, respectively.

Measurements
Density and refractive index were measured at 20.00 AE 0.01 1C with an Anton Paar DMA 4500 density meter mated to an Anton Paar RXA 170 refractometer through plastic tubing.The techniques, calibration, accuracy, and precision are given elsewhere. 17he ranges for the density and refractive index are 0.79101 to 0.79639 kg L À1 and 1.36135 to 1.36290, respectively.These ranges fall well within the manufacturer's recommendations for the calibration methods used here.The system was calibrated before each series of measurements with deionized water at 20 1C.For each case a value of 0.99821 g mL À1 were measured and agree with the accepted value for water at 20 1C of 0.998206 g mL À1 (one additional significant figure).

Data treatment
Table 1 reports the mole fractions, densities, and refractive index values for the ethanolic solutions of the complexes.
The molar volumes, V M , for each solution were calculated from where x i and M i are the mole fractions and molar masses of the solutions' components, respectively, and where i = 1, 2 refer to the solvent and solute, respectively.The molar refractions of the solutions, R, were calculated from the molar volumes and refractive indexes (n) according to The V M and R-values for each solution are also given in Table 1.Since V M is a homogeneous function of n 1 and n 2 , following Euler, one gets where V M 1 and V M 2 are the partial molar volumes for the solvent and solute, respectively.An analogous equation obtains for molar refraction (R). 18All V M and R-values exhibit nearly linear dependence on the mole fraction of solute.Consequently, intercepts and slopes were calculated employing Excel's linear regression routine, and standard deviations were determined from Excel's ANOVA routine.The refractive index (n 2 ) for each complex was calculated according to

Descriptor methodology
Our method for the determination of descriptors for neutral solutes uses two linear free energy relationships, eqn ( 5) and (6).
Eqn ( 5) is used when the dependent variable, log SP, refers to condensed phase processes, such as the water-solvent partition coefficient for a series of solutes in a given system; then SP itself is the water-solvent partition coefficient.Eqn ( 6) is used when log SP refers to a gas to system partition, where SP is the gas to system partition coefficient.
The independent variables in eqn ( 5) and ( 6) are solute descriptors as follows: [6][7][8][9][10][11][12][13] E is the solute excess molar refractivity in units of (cm 3 mol À1 )/10, S is the solute dipolarity/polarizability, A and B are the overall or summation hydrogen bond acidity and basicity, V is the McGowan characteristic volume in units of (cm 3 mol À1 )/100 and L is the logarithm of the gas-hexadecane partition coefficient, at 298 K.The coefficients in eqn ( 5) and ( 6) are obtained by multiple linear regression analysis, and serve to characterize the system under consideration.
In order to apply eqn (5) or (6), values of the dependent variable are needed.The most direct source is a directly determined water-solvent partition coefficient, P, as log P.However, most of the relevant data consists of solubilities in (dry) solvents and in water.Then partition coefficients can be Table 1 x 2 , r(g cm À3 ), n, V M (cm 3 mol À1 ), and R (cm 3 mol À1 ) for ethanolic solutions of M(acac) 3 [M = Cr, Fe, and Co] obtained indirectly through eqn (7), where C w and C s are solubilities in mol dm À3 , in water and a given solvent.If a value of C w is not known, or is perhaps doubtful, then log C w can be allowed to float, and becomes another unknown parameter to deduce.
We can greatly increase the number of simultaneous equations, by converting every log P value from eqn (7) into a corresponding log K s value through eqn ( 8), where K s is the gas to solvent partition coefficient and K w is the gas to water partition coefficient.Now log K w itself is another variable to be determined.
This leaves E, S, A, B, V, L, and possibly log C w and log K w to be determined through a set of simultaneous equations with log P and log K s as the dependent variables in eqn ( 5) and ( 6).The Microsoft 'Solver' add-on is particularly useful, and any number of simultaneous equations can be solved to give a 'best-fit' solution.
Since we have as many as eight variables to obtain, it is useful to be able to deduce one or more variables independently, and so reduce the number that have to be obtained through the set of simultaneous equations.For organic compounds, E can be calculated through two programs 4,19 and can also be obtained from a calculated liquid refractive index at 293 K. 3 Now that we have experimental molar refractions there is no problem in obtaining values of E.
The volume descriptor, V, can very easily be calculated for organic compounds through McGowan's method, 20 but as we showed in the case of ferrocene, it is not straightforward to use McGowan's method for inorganic complexes.
The McGowan volume, V x = 100 Â V, is calculated from atomic increments, as shown in Table 2, 16,20,21  We can resolve this by using the equations we have constructed 16 for the correlation of V x against the partial molal volumes, , of a series of organic and inorganic compounds in acetonitrile solvent, 22 eqn ( 5) and ( 6).For Co(acac) 3 we have that V M 2 (MeCN) = 256.6 cm 3 mol À1 in acetonitrile, 22 and so calculated values of V x are 233.1 AE 6.2 on eqn (9) and 228.2 AE 7.9 on eqn (10), very close to the McGowan volume of 228.0 cm 3 mol À1 as calculated for the non-cyclic structure in Fig. 2. Similar calculations for Cr(acac) 3 and Fe(acac) 3 confirm the use of the non-cyclic structure in the calculation of V x .We make it clear that the structure in Fig. 2 is only for the purpose of calculating V x and is not intended as the representation of the actual structure of Co(acac) 3 .However, now that we have shown that the structure in Fig. 2 can be used to calculate V for M(acac) 3 complexes, we can use the same method to calculate V for complexes of various substituted acetylacetones.

Molar refractions
The molar volumes, molar refractions, and refractive indices are listed in Table 3.The molar volumes of the three tris-acac metal compounds follow the trend of Co o Fe E Cr, which inversely follows the molecular masses of the three compounds.This observation is in accord with the results of crystal structures [23][24][25] of the compounds in which the metal oxygen bond distances increase in roughly the same direction: Co    ligand itself do not vary appreciably, then the cobalt compound would be expected to have the smallest volume.
The d-electron structures of the three metal centers also differ significantly with the chromium(III) and iron(III) centers being paramagnetic high-spin d 3 and d 5 , respectively, while the cobalt(III) center is diamagnetic low-spin d 6 .

Descriptors
Water-solvent partition coefficients into water-methanol mixtures, dimethylsulfoxide (DMSO) and dioxane for Cr(acac) 3 have been listed by Alousy and Burgess. 26Watarai et al., 27 have determined partitions into dodecane, tetrachloromethane and benzene.Solubilities of Cr(acac) 3 are known in water-ethanol mixtures 28 but only in those of low ethanol content, and we did not use any of these values.Solubilities are also known in the solvents dimethylformamide 29,30 dichloromethane, 1,1,1-trichloroethane and tetrahydrofuran. 30The solubility of Cr(acac) 3 in water at 298 K is given as log C w = À2.55, 29with C w in mol dm À3 , and so the various solubilities can be converted into values of log P through eqn (7).Then if we take log K w as unknown to be determined, we can convert all the log P values into log K s values through eqn (8).We can calculate V x = 2.2830 by McGowan's method, and from the refractive index in Table 3 calculate that E = 2.222.This leaves the descriptors S, A, B, L and log K w to be obtained from a set of simultaneous equations in log P. In Table 4 are the values of log P that we used.A preliminary analysis showed that three values were out of line, leaving 14 values of log P and 14 values of the corresponding log K s .We also had two equations in log K w giving a total of 30 simultaneous equations.The equation coefficients 16,[31][32][33] for eqn (5) and ( 6) are collected in Tables 5 and 6.The best fit solution of the 30 simultaneous equations yielded the descriptors shown in Table 7, and the calculated values of log P from these descriptors are in Table 4.
The 14 calculated and observed values of log P for Cr(acac) 3 in Table 4 yield an average error AE of 0.042, an average absolute error AAE of 0.094 and a standard deviation of 0.125 log units.For the total of 30 simultaneous equations the SD is 0.123 log units.This is shown in Table 7, where N is the total number of equations used.We left out data in three solvents in Table 4, where the difference between log P(calc) and log P(obs) was very large.
For Fe(acac) 3 , water-solvent partition coefficients are known into propan-2-ol, DMSO, and various water-methanol mixtures. 26olubilities have been determined in several solvents 30,34 but apparently not in water itself.However, we can take log C w as another descriptor to be determined through our analysis.We find that with log C w = À2.38, the observed values of log P and those These 46 equations yielded the descriptors shown in Table 7 and log C w = À2.37, with a standard deviation between calculated and observed dependent variables of 0.136 log units.The calculated and observed values of log P are in Table 8.For the 22 used values, AE = 0.018, AAE = 0.117 and SD = 0.140 log units.
In the case of Co(acac) 3 , solubilities are known in water (log C w = À2.41), 29dimethylformamide, 29 dodecane, 27 various ethanol-water mixtures 28 and alkoxyethanols. 35Alousy and Burgess. 26have listed partition coefficients into methanolwater mixtures and into a large number of pure solvents.The solubilities were converted into log P values, and we were able to use 33 such values.We also had 33 of the corresponding log K s values, and two equations in log K w giving a total of 68 simultaneous equations.These were solved to yield the descriptors in Table 7 with an SD between the 68 calculated and observed values of 0.205 log units.The observed and calculated values of log P are in Table 9.For the 33 calculated and observed values that we used, AE = 0.006, AAE = 0.136 and SD = 0.158 log units.
The determined descriptors for the complexes of Cr, Fe and Co, Table 7, do not very greatly between the three.All the complexes are quite polarizable, with S ranging from 1.67 to 2.25, as evidenced also by their dipole moments that vary from 0.95 to 1.10. 36There is little variation in hydrogen bond basicity, and all the complexes have A as zero.It might have been expected that a concentrated positive charge in the middle of the molecule would induce some hydrogen bond acidity for the -CHQ hydrogen atom, but there is no doubt that A = 0.
There are limited data for other M(acac) 3 complexes, but only in a few cases are there enough to attempt to deduce descriptors.Even then, without a knowledge of E and V, little can be done.Values of V can be calculated exactly as for Fe(acac) 3 with the atomic increments for M 3+ atoms as shown in Table 2, 21 but without any experimental values of molar refraction, E cannot be determined.However, E does not seem to alter very much with the nature of the M 3+ atom, and in the case of the Cr, Fe and Co complexes, values of the obtained descriptors vary only slightly with change in the taken value of E. We therefore took E as 2.48, the average of the Cr, Fe and Co complexes, Imura and N. Suzuki 37 have determined log P values for V(acac) 3 , and there is just enough information to obtain the descriptors given in Table 7.There is a little more data for the M(acac) 3 complexes of yttrium, samarium, lanthanum and neodymium 38 and these yield the descriptors in Table 7.The descriptors S, B, L and log K w for these extra five complexes fall into the same pattern as shown by the Cr, Fe and Co complexes.All four descriptors alter regularly with increase in the complex molecular weight, MW, over the eight complexes.The Bdescriptor varies the most regularly, see eqn (11).This equation might be useful in the assignment of descriptors to other M(acac) 3 complexes.B = À0.904+ 0.00750MW N = 8, SD = 0.087, R 2 = 0.937, F = 89.72 (11)   By comparison to organic compounds, there have been comparatively few studies on physicochemical properties of inorganic complexes.Analysis of solubilities has provided estimates of the solubility parameter of complexes, 27,34,39 but the various predictive methods that have been so useful for organic compounds [1][2][3][4][5] have not been applied to inorganic complexes.Now that we have descriptors for the three complexes, Table 7, these can be used to predict log P values from the gas phase and from water to a very large number of both dry and wet solvents, as well as to several ionic liquids.We can illustrate this by the calculation of the water to wet octanol partition coefficient, as log P oct , commonly used as a measure of hydrophobicity.It is a simple matter to combine the descriptors in Table 7 with the equation coefficients given in Table 5 to yield the values given in Table 10.Our calculated log P oct values vary regularly with complex molecular weight, from the somewhat hydrophobic Cr(acac) 3 to the decidedly hydrophilic Sm, La and Nd complexes, as shown in eqn (12) and by Fig. 3.
Log P oct = 13.989À 0.0345MW N = 8, SD = 0.230, The quite good statistics of eqn (12) suggest that our assignment of E = 2.48 for five of the complexes is at least reasonable.We can compare the values of log P oct for the complexes with those for organic compounds with around 15 carbon atoms.This indicates that all the M(acac) 3 complexes are much less hydrophobic than even glycerol tributanoate, which also has six oxygen atoms.Indeed, several of the complexes are hydrophilic.

Conclusions
We have shown that it is possible to employ the same methodology used to obtain Abraham descriptors for organic compounds to obtain Abraham descriptors for inorganic complexes.Then the various equations we have constructed for organic compounds can be used to predict a very large range of physicochemical properties for inorganic complexes.We have already shown 40 that the methods used here can be extended to obtain descriptors for electrolytes and there is no fundamental reason why our extended method cannot be used to obtain descriptors for charged inorganic complexes (electrolytes) as well as for inorganic complexes that are nonelectrolytes, The main difficulty in obtaining descriptors for the inorganic complexes is in the estimation of the E-descriptor.In the present work we have determined the E-descriptor from our experimentally determined molar refractions for the tris(acetylacetonato)chromium(III), tris-(acetylacetonato)iron(III) and tris(acetylacetonato)cobalt(III) complexes.This is a time-consuming procedure and at the moment is a limiting factor on the determination of the Abraham descriptors.

Conflicts of interest
There are no conflicts to declare.
with 6.56 subtracted for each bond (single, double and triple bonds all counting as one bond).If the structure of an acac derivative of cobalt(III) is as shown in Fig. 1, then for tris(acetylacetonato)Co(III) there are 15 Â 3 = 45 bonds.Then with V x for Co(3+) = 0.78 mL mol À1 , for the complex we have V x = 21 Â 8.71 + 15 Â 16.35 + 6 Â 12.43 + 0.78 À 6.56 Â 45 = 208.3cm 3 mol À1 .However, the CQO -Co coordinate bond is not a 'McGowan' bond, and the oxygen atom in QOhas three bonds instead of two.So there is a difficulty in calculating the McGowan volume for the cyclic structure.Suppose we use the non-cyclic structure, Fig. 2. Now the number of bonds is 14 Â 3 = 42, and V x = 21 Â 8.71 + 15 Â 16.35 + 6 Â 12.43 + 0.78 À 6.56 Â 42 = 228.0cm 3 mol À1 , substantially larger than that calculated for the cyclic structure.

Fig. 1 A
Fig. 1 A possible configuration of Co(acac) 3 for the calculation of McGowan's volume, illustrated for just one of the acac molecules.

Fig. 2
Fig. 2 A possible 'open chain' configuration of Co(acac) 3 for the calculation of McGowan's volume.

Fig. 3 A
Fig.3A plot of calculated values of the water-octanol partition coefficient, as log P oct , for the eight M(acac) 3 complexes against the complex molecular weight.

Table 3 V
M  2, R 2 , and n 2 for M(acac) 3 complexes a a Standard deviations in parentheses.Table 4Calculated and observed values of water-solvent partition coefficients, as log P, for Cr(acac) 3

Table 5
Coefficients in eqn (5) for water-solvent partitions as log P

Table 2
, we calculate E = 2.524; then the unknowns to be found by solution of the set of simultaneous equations in log P are S, A, B, L, log K w and log C w .We used a total of 22 values of log P, 22 values of the corresponding log K s through eqn(8)and two equations in log K w leading to a set of 46 simultaneous equations.

Table 8
Calculated and observed values of water-solvent partition coefficients, as log P, for Fe(acac) 3

Table 9
Calculated and observed values of water-solvent partition coefficients, as log P, for Co(acac) 3

Table 10
Values of log P oct for acetylacetonate complexes and some organic compounds