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SOLUTION CHEMISTRY OF ELEMENT 105. PART I: HYDROLYSIS OF GROUP 5 CATIONS: Nb,Ta, Ha AND Pa
V. Pershina
29-13 ■D
Gesellschaft fur Schwerionenforschung mbH PlanckstraBe 1 • D-64291 Darmstadt • Germany Postfach 11 05 52 • D-64220 Darmstadt • Germany Solution Chemistry of Element 105. Part I: Hydrolysis of Group 5 Cations: Nb, Ta, Ha and Pa
V. Pershina Gesellschaft fur Schwerionenforschung, Planckstr.l, 64291 Darmstadt, Germany
Element 105/Hahnium/Transactinide chemistry/Relativistic molecular calculations/Hydrolysis
Summary
Relativistic molecular orbital calculations of the electronic structure of hydrated and hydrolyzed complexes have been performed for group 5 elements Nb, Ta, Ha and their pseudohomolog, Pa. On their basis, relative values of the free energy changes and constants of hydrolysis reactions were defined. These results show that hydrolysis decreases in the order Nb > Ta > Ha » Pa, which for Nb, Ta and Pa is in agreement with experiment. A decisive factor in the process turned out to be a predominant electrostatic metal-ligand interaction.
1. Introduction
A. Importance of hydrolysis
The importance of hydrolysis in chemistry of transition elements is known since long. For Nb and Ta, differences in their complex formation in aqueous acidic solutions and extraction by various organic media have often been explained by differences in their hydrolysis [1], Thus, e.g., in the absence of water, Nb(V) and Ta(V) form chlorocomplexes of the same type, MCle". In the presence of water, even in concentrated hydrochloric acid, Nb and Ta hydrolyze, but in different ways: Nb forms complexes containing Nb03+, like NbCOH^CU", NbOCU" or NbOCls2", while hydrolysis of Ta goes further with the formation of the polynuclear products (TaO^Cl^nCl)*, hindering its extraction [2],
1 For metals in trace concentrations, mononuclear hydrolysis products existing in wide range of pH can also profoundly affect the chemical behaviour of the metal. Generally, the composition and charge of these systems can control such important aspects of chemical behaviour as adsorption of the dissolved metals on surfaces of mineral particles, the solubility of hydroxides or oxides, the extent to which the metal can be complexed in solution or extracted from solutions by various agents, and transition to another valence state [3]. In trace concentrations, Nb and Ta show also differences toward the complex formation in HC1 solutions and extraction by various organic media as those found for macro concentrations of these elements. Thus, Nb is better extracted which means less hydrolyzed, while Ta is more hydrolyzed and hence less extracted [4]. How strong hydrolysis of their homolog, Ha (produced as single atoms in the “one-atom-at-a-time- experiments ” [5]), would be and how it would influence its extraction is an important question, especially if one takes into account that trends in properties observed within the lighter elements might not continue when going over to the 6d transition row where relativistic effects are so strong. Until now, hydrolysis of the transactinides has not been investigated. The only publication was that on hydrolysis of rutherfordium, Rf [6]. Studying sorption of the metal cations on glass surfaces coated with cobalt ferrocyanide, the authors of [6] have found rutherfordium to be much less adsorbed than Zr and Hf, which was interpreted as Rf being more hydrolyzed. This conclusion is, however, in contradiction with expectations based on the electrostatic model of the hydrolysis mechanism, which predicts that among ions with the same formal charge, the one with the larger ionic radius (like Rf in comparison with Zr and Hf) should be less hydrolyzed. Thus, to understand hydrolysis of transactinides and its influence on the complex formation, the present theoretical study has been undertaken in the particular case of the group 5 elements, Nb, Ta, Ha, and its pseudohomolog, Pa. Any theoretical consideration on this subject should be helpful, especially in the case of the very heavy elements, where the experimental study [5] is connected with difficulties caused by low production rates and short half-lives of their isotopes. Since the experiments on extraction of Nb, Ta, Ha
2 and Pa are performed with single atoms, all the further considerations will be related to mononuclear species. When discussing hydrolysis, one should distinguish between hydrolysis of cations and hydrolysis of salts (or compounds). In the second case, hydrolysis involves either the cation, the anion, or both and is a reversed process of the complex formation. In general, it can be expressed by the following equilibrium
xM(H20)w„z+ + yOH +aL <=> Mx0u(0H)y.2u(H20)wLa(xzya)+ + (xw° + u-w)H20 (i)
Another process known to most transition elements is the hydrolysis of cations, which takes place in the non-complexing media. In this case, each step in the formation of a series of mononuclear species can be described as a loss of successive protons [3]
M(H20)„z+ « MOH(H20)n ., In this way, species containing O2", OH and H20 ligands can be generally produced. In the present publication, we will be concerned primarily with the hydrolysis of cations. The hydrolysis of salts will be considered in a forthcoming paper. B. Hydrolysis products of Nb, Ta and Pa Though the class of mononuclear species has recently received growing attention, these simpler hydrolysis products have not been well characterized. In most cases the stepwise formation of hydroxide complexes is poorly established by available data. The reason for that is the fact that hydrolysis is normally studied at the higher metal concentrations where polynuclear complexes are predominant. As a result, our knowledge of the hydrolysis products of many cations is poor. Potentiometric measurements of the hydrogen ion concentration for Nb and Ta in aqueous media at small concentrations (10"6 M) indicate the dominance of pentavalent 3 species which are limited in concentration by the solubility of the +5 oxides. Nb is found to be more hydrolyzed than Ta (Fig. 1). From relatively uncertain data on solubilities, the following equilibria have been derived for mononuclear species of Nb and Ta in 1M KNO3 at 19° [3] Nb(OH)5 (aq) + H+ <=> Nb(OH)/ + H20 log Q = -0.6 Ta(OH)5 (aq) + H+ o Ta(OH)/ + H20 log Q = 1.0 Nb(OH)5 (aq) + H20 Nb(OH)6 " + H+ log Q = -7.4 Ta(OH)s (aq) + H20 <=> Ta(OH)6 " + H+ log Q = -9.6 confirming, in addition to the data of the potentiometric measurements, a stronger hydrolysis of Nb in comparison with Ta. The data of Fig. 1 also show that hydrolysis of Nb and Ta is strong and proceeds fast to the formation of the ultimate products M(OH)5(aq) and M(OH)6 ". Since almost no intermediate hydrolysis compounds are known, the equlibria that have to be studied here are: Nb(H20)6 5+ Nb(OH)s <=> Nb(OH)6 " (3) Ta(H20)6 5+ o Ta(H20)2(0H)4+ <=> Ta(OH)5 o Ta(OH)6 " (4) Hydrolysis of Pa has been relatively well investigated and the species (in perchloric acid solutions) have been characterized [7] (Fig. 1). In comparison with Nb and Ta, hydrolysis of Pa is much weaker. The presence of small amounts of weakly complexing anions is not changing the results. The following hydrolysis products were shown to exist also in HC1 solutions [8]: Pa(OH)/ <=> PaO(OH)2+ (< 1M HC1) Pa(OH)32+ o PaO(OH)2+ (1-2 M HC1) 4 Pa(OH)23+ <=> Pa03+ (4-6 M HC1) The equilibria describing the hydrolysis of Pa are the following: Pa(H20)6 5+ <=> PaO(OH)2+ <=> PaO(OH)2+ <=> Pa(OH)5 <=> Pa(OH)6 " (5) Since the present study is comparative (hydrolysis of Ha as compared to that of Nb, Ta and Pa under the same conditions), we will concentrate here on a comparative prediction of the stability of the hydrolysis products. Luckily enough, all the known reactions for Nb, Ta and Pa belong to the same type where the utmost hydrolysis product M(OH)& is formed: M(H20)6 5+ M(OH)6 > 6H + (M = Nb, Ta and Pa) (6) (7) <2/6 = [ M(OH)6 -][ H+]6 /[ M(H2o)6 5+] The same type of reaction (6) can be supposed for hahnium. For Pa, the following step M(H20)6 5+ <=> M(OH)2(H20)43+ + 2H+ (M = Pa) (8) showing stability of the intermediate hydrolysis product might be also of interest. Reactions (6) will be considered in the following sections. (M(OH)s complexes known as precipitants will not be analyzed here, since their real coordination number, CN, as soluble mononuclear species is not known). 5 2. Models for mononuclear species A. The simple electrostatic model Generally, the stability of a hydrolysis product Mx0u(0H)v(H20)w -AGf (u,v,w)l23RT=^ai+'£ja ij +logQ-log(«!v!vv!2w)+(2M+v+l)log555 (9) and log K = -AGr/2.3RT, (10) where AGr is the free energy change of a hydrolysis reaction. The first term on the right hand side of Eq. (9), J/t,, is the nonelectrostatic contribution from M, O, OH, and H20. The next term, , is a sum of each pairwise electrostatic interactions: a tJ = -Bq,q/d,j, 01) 6 where d/j is the distance between moieties i and j, and qj are their formal charges; and B is an independent constant. In the case of ionic bonding, the formal charge was supposed to be equal to the maximum ionic charge z on a moiety, and in the case of covalent bonding - to the maximum ionic charges on each moiety plus/minus a number of electrons (one for each ligand) which is supposed to be on the bonding with other moieties. Q is the partition function: G=l+%exp(-AG,/aT) (12) representing the contribution of structural isomers, which differ in free energy by AGs. The last two terms in Eq. (9) are statistical: one is a correction for the indistinguishable configurations of the species, and the other is a conversion to the molar scale of concentration. The main approximations of this model are the following: (1) the assumption that the effective dielectric constant in the vicinity of ligands is constant, (2) the neglect of multipolar nature of OH and H2O, and (3) the neglect of the contribution of hydration effect beyond the first coordination sphere. Using Eq. (9), and assuming that the M-OH and M-H2O bonds are ionic, one obtains for the first hydrolysis constant (reaction 2) (13) M-OH Provided the difference uoh-«h2o is not too variable, log K\, is expected to change linearly with the ratio of the cation charge to the M-OH distance (or the radius of the cation). Constants for the subsequent hydrolysis steps are found to decrease as the number of OH groups increases [3]. This ionic model has been applied to the description of hydrolysis of many metal cations. Experimental data on A"n for many cations of similar type show, in agreement with Eq. (13), an increase in these values almost linearly with the ratio of the cation charge z to the M-OH interatomic distance (see Fig. 18.4 in Ref. [3]). 7 B. A model based on the real distribution of the charge density Due to the assumed electrostatic nature of the metal-OH interaction, Eq. (13) is working well for the cations, which form ionic bonds with OH. Since the CN as well as the bonding character of the heavier transition metals is more variable, Eq. (13) may not be reliable any more. The more covalent the metal-ligand bond is, the more complicated is the dependence of K on distances and charge distributions [3], Thus, e.g., though the ionic radius (IR) of Zr4* (0.84 A for CN=8 [10]) is slightly larger than IR of Hf4* (0.83 A), Zr is more hydrolyzed than Hf. Eq. (13) does not explain a stronger hydrolysis of Nb5+ in comparison with that of Ta5+ either, though both cations have equal formal charges and equal IR = 0.64 A for CN=6 [10]. In compounds of the transactinides, covalent bonding was shown [11] to be predominant, so that the ionic model will be probably even less applicable. Thus, estimates of hydrolysis constants for the very heavy elements should be made on the basis of the knowledge of the real charge distribution in their compounds. This knowledge can be obtained from molecular orbital calculations which will be described in the following section. 3. Method and details of the calculations A. Dirac-Slater Discrete Variational (DS-DV) method To calculate both and from Eq. (9), the DS-DV method [12] proved to be the most suitable, since it includes the Mulliken population analysis procedure [13], allowing for direct estimates of the chemical bonding in the two (ionic and covalent) terms. The method has been extensively used by us for description of bonding in transactinide compounds [14], so that here only its main features will be outlined. The DS-DV method is a fully relativistic all-electron (or frozen core, EC, if necessary) method with the spin-orbit coupling explicitely included. The method uses four- component basis functions which are transformed into molecular symmetry orbitals using 8 double point groups. Molecular integrals between these functions are calculated in a numerical, three-dimentional grid. The most recent version of the method includes minimization of the error in the total energy [12b] and the integration scheme of Boerrigter et al. [15], which altogether gives much more accurate results for total energies. The Dirac Hamiltonian is hD = ca7t + (P- l)c2 + V, (14) where the potential is the sum of three parts y= %, + % + %, (15) with V„ the nuclear, Vc the Coulomb and Vx = -3a(3p/87t) the exchange-correlation potential. Most of the correlation effects are included in the exchange-correlation term. The present calculations have been performed within the FC and full-electron approximations. The number of integration points was 104. B. Mulliken population analysis and parameters used in the calculations Analysis of bonding has been done using the Mulliken theory of bonding [13], based on the corresponding numbers. The used quantities are effective charges: Qi = N°i-Ni, (16) where A'0, is the total number of electrons in the ground state of the free neutral atom z, and N, = lN(cr2 + CrcsS n); 07) and overlap populations (OP) between orbitals r and s on centers z and j 9 %(Wj) = = 'L2N(kK,cks,sr,Sl ■ (18) k k Here ckr are MO coefficients on the MO orbital k, S rs is an overlap integral between orbitals r and s, N(k) is the number of electrons on the molecular orbital k. The total OP is OP = n = ^tn(ri’sj) ■ (19) The Mulliken equation for the binding energy of a molecule without non-bonded electron pairs is [13a] D0 = Ec + Eop - P. (20) Here Ec is the ionic (Coulomb) part of the binding energy, Eop is the covalent contribution and P is the sum of valence state excitation energies. As one can see, Eq. (20) lies in the basis of Eq. (9) so that -AGr contains ADo (e.g., for compounds of the right and left parts of reaction 6). In Eq. (20), the ionic part Ec =2.3RTa,y can be calculated in the following way Ec = -B'QiQ/djjE , (21) where B' transforms the energy in eV. (In a solution, an effective dielectric constant e must be introduced). The total number of the Ec terms is then (h+l)h/2, where h is the total number of atoms in a molecule. Thus, for MfHzO^ with h= 18, there are (18+1)18/2= 171 terms. The source of uncertainty in calculating Ec is e. In practice, its approximate value can be estimated from experimental data. For example, e of 20 was given by fitting the parameter B of Eq. (13) to experimental data for first hydrolysis constants of many transition metal cations [3]. For the hydrolysis steps considered here, none of hydrolysis constants is, unfortunately, known so that z cannot be estimated. Thus, in order not to 10 introduce an uncertainty, the energy of the Coulomb interaction will be calculated in vacuum, though some estimates of K for solutions with £=20 will be also given. In Eq. (20), P = IPh, the sum of the valence-state promotion energies taken over all the atoms involved. For Nb, Ta and Ha this is an s2d 3 —> d 2sp3 excitation energy corresponding to the octahedral hybridisation. In defining AGr , or log/f AP=0, since atoms and their hybridisation in the left and right parts of reaction (6) are the same. Estimates of EOP = 2.3RTa; are the most uncertain. According to Mulliken [13], the overlap energy E°P = A.I^nir^Sj), (22) where AT is an empirically determined constant, and Irs is the mean valence-state ionization energy from the valence shells of the atoms to which atomic orbitals %r and belong. In Eq. (22), only n(ritSj) can be directly calculated using the DS-DV method (Eqs. 18-19). ln can in principal be defined from spectroscopic data. For fractional electronic configurations, which metal atoms have in a molecule, Irs, or It, can be determined from energies of configurations with a full number of electrons, e.g. l[d*‘S‘'-p<']=i\-qs-qr)l[d’} + q,l[d-'!:\ + qpl[d-'p\ (23) Unfortunately, there are no such data for the transactinides. Also atomic calculations giving those values are absent. Another problem is to define Ax. For simple neutral molecules Ax can be estimated from dissociation energies [13]. For complexes in solutions, this is not possible, so that absolute values of Eop cannot be obtained. For the purpose of the present investigation (to define -AGr), it would be, however, enough to estimate differences in Eop, AEOP, between the components of the right and left parts of reaction (6): 11 ( i X 1 I AUOH)6 M(H20)6 f 1 M(Otf>6 ~ _1_ z J M o o V A" M A" y AE0P = \ AOP X -ly/*M(0H)1 fM(H20)l* A'^ w i u where A' and A" are the total numbers of atoms in M(OH)6 and M(H20>6 5+, respectively. By analogy with aoH-amo (see Eq. 13 and Eq. 18-6 in [3]), one can assume the differences in the parentheses to be also not too variable from metal to metal. Thus, we can write AE0P = r AOP, (24) where K' is a coefficient, which could be roughly estimated as it is shown further. Eq. (24) means that differences in the E0P are well defined by differences in OP, and the latter will be used in the analysis of the covalent energy changes. It would also be possible to define K' and then AEOP for an element of interest if a corresponding hydrolysis constant for any other analogous element were known (see Eq. 29 further). Unfortunately, for the hydrolysis steps considered here, such knowledge is absent, and we can only try to give rough estimates of K' on the basis of the knowledge of the bonding in a similar type of compound. Such a compound must be a neutral molecule where the binding energy (or Edi SS) is known, or can be calculated from some other data (e.g. from enthalpies of formation via the Born-Haber cycle). Unfortunately, binding energies for the studied hydrated and hydrolyzed complexes in solutions cannot be estimated even from the Born-Haber cycle and some other assumptions have to be made. Thus, furthermore, the metal-OH bonding has been supposed to be similar to that of the metal-fluorine one in the MFn " complexes. This has a reason: As was shown [3,16], some mononuclear hydrolysis products exhibit trends in stability with cation charge and size that are similar to those of the fluoride complexes. Further, the M-F bonding in MFn z" has been supposed to be similar to that of gaseous MF5 (M = Nb and Ta), where AHf is known and Edi SS can be calculated from the Born-Haber cycle. Then knowing Ec and OP (from the DS DV calculations), Eop can be 12 obtained (see procedure, which was applied earlier by us to estimates of bonding in other transactinide-compounds [14]). By correlating the change in E0P in going from NbFs to TaF5 with a change in OP, K’ of 1.51 eV has been obtained. In the hydrolysis process, the metal is, however, the same, but the ligand changes. Thus, a couple of compounds of the same metal with different ligands has to be chosen where Edj ss can be calculated. The only “available” couple is ME; —> MCI5 giving K' of 0.37 eV. The latter has been used in calculating AE0P, though this is a very rough approximation, since Eop[M(H20)6 5+]-Eop[M(OH)6"] is probably smaller than Eop[MFs]- E°p[MCls]. (AEop for AT'= 1.51 eV will also be given for comparison to find out whether such a large change in the covalent contribution to AGr will influence the situation). The last contribution to AGr would be the change in the hydration energy AGhydr beyond the first coordination sphere. Being a reverse function of the radii of the large species, this hydration energy should be small. Besides, since reaction (6) has the same metal atom in the left and right parts, and the IR of OH" (1.37 A) is very similar to the IR of O2" (1.40 A [10]), the differences AGhydr should be very similar for all the elements in discussion and will not change the relative values of AGr. C. Geometrical configurations and bond distances By analogy with other transition element hexa-aquometal ions [17,18], M(H%0)6^ (M= Nb, Ta, Ha and Pa) were assumed to have an octahedral coordination of oxygen atoms around the metal ion. Due to the +5 ionized state of the metal formally having no filled d orbitals, there is no reason to suppose any distortion, so that a regular coordination has been accepted. Position of the hydrogen atoms has been discussed in a number of publications [17,18] and shown in Fig. 2. An entire molecule belongs to the Th symmetry group. Metal-oxygen distances in many aqua-cations determined by different physical methods were shown [19] to be very close to the sum of the IR. Thus, bond lengths equal 13 to IR(M5+)+IR(02') for CN=6 have been taken. The standard water molecule data are Roh=0.958 A and Z 104.5°. Analogously, M(OH)e" complexes have been assumed to have a structure of a regular octahedron (Oh symmetry group), with the metal-oxygen bond lengths being IR(M5+)+IR(OH"), where Rq h =102 A. The IR(Ha5+) has been accepted to be 0.7-0.71 A taking into account the IR extrapolated from the multiconfiguration Dirac-Fock calculations [20] minus the relativistic contraction of the bond lengths (see Ref. [14]). Table 1 summarizes the interatomic distances utilized in the calculations. 4. Results of the calculations and discussion A. Energy levels and electronic density distribution The energies of the highest occupied molecular orbital (HOMO), the lowest unoccupied MO (LUMO), the energy gap, AE, between them and of other unoccupied levels of d-character for MfHzO)^ obtained as a result of the calculations are given in Table 2. The electronic density distribution data are presented in Tables 3 and 4. The data of Tables 3 and 4 show that MfHzO)^ are rather ionic. The value of the total OP parameter is very high, but it results from the O-H covalent interaction of the water molecules: the partial OP(M-Oh2o) are low (see Table 4). The covalence increases from the Nb to the Ha compound. Ha has the strongest covalent bonding with oxygen of the water molecules, mainly due to the largest overlap 7s(Ha)-2p(0), 6d.i/2(Ha)-2p(0) and 6ds/2(Ha)-2p(0). Pa(H20)6 5+ is the most ionic compound in the considered group. An increase in the energy gap between the HOMO and LUMO is a reason to think about a regular octahedron structure of the complexes under consideration, and especially that of Ha having the largest AE (Fig. 3). A tetragonal distortion of the Ha complex which could have been supposed due to a second-order Jahn-Teller effect, will not take place since AE is large (AE > 2a'/K, where K is the force constant and a=dV7d/? 0, with V being the molecular potential and R0 the intemuclear distance at the point of equilibrium [21]). Thus, all the water molecules are equally bound to the Ha ion. 14 Energies of the HOMO, LUMO, AE, and of unoccupied levels of d-character for M(OH)g, obtained as a result of the calculations are given in Table 5. One can see that the values of AE in M(OHV are larger than those in M(H20)6 5+, with AE of the Ha complex being the largest. This is evidence for a stronger interaction of the metal ions with OH groups than with water molecules. A strong relativistic stabilization of the 7pi/2- valence electrons in the Ha compound results in the lowering in energy of the 6g antibonding level (shown in the parentheses in Table 5), mixing into the group of the crystal-field and spin-orbit splitted d-levels. The electronic density distribution data for M(OH)& are given in Table 6. The data in Tables 3, 4 and 6 show that M(OH)& are more covalent than the corresponding M(H20)6 5+. Although the latter compounds have larger total OP, due to the O-H covalent bonding in the water molecules (Table 4), the covalence of the metal- oxygen bond in M(H20>6 5+ is smaller than that in the corresponding M(OH)e. The covalence increases from Nb to Ha. (There are also smaller effective charges in M(OH)& than in M(H20)6 5+). It is interesting, that Pa(H20)6 5+ is the most ionic compound among all M(H20)6 5+ under consideration, while Pa(OHV is the most covalent among all M(OH)&. This will be shown to be reflected in a specific position of Pa in the hydrolysis. B. Prediction of hydrolysis For the present comparative study, it would be sufficient to give relative values of AGr, as well as those of log K (Eq. 10). They can be obtained as differences in total energies of the species on the right hand side of reaction (6) and those on the left hand side. As shown in section 3.B, the differences in the total energies can be replaced by the differences in the first two terms, a, and atj, (the right part of Eq. 9), i.e. as differences in both the ionic and covalent contributions to bonding. In turn, these terms can be calculated from Eqs. (21) and (24) using Q, and OP. It seems also reasonable to estimate these two parts separately in order to elucidate their influences on the hydrolysis process. Rough estimates of changes in the total energies will be also given. 15 In Table 7, Ec, OP, and their differences for M(OH)6 and M(H20)6 5+ as a result of the calculations are given. Estimates of AEOP along with the total energy differences, AE1, are also shown. (As mentioned above, the values are given for the species in vacuum. In a solution with a specific dielectric constant, Ec will be by a factor of e less. All the other values, Eop or El, will be reduced respectively, but their relative values, for a given compound with respect to another, will stay the same). From Table 7, one can see that Ec for M(OHV and M(H20)6 5+ of Nb, Ta and Ha are similar, while those of Pa are different. Ec (absolute value) of Pa(OH)& is lower than those of Nb, Ta and Ha, while Ec of Pa(H20)e5+ is much higher. Obviously, Pa holds water molecules stronger than Nb, Ta and Ha. The differences AEC also show a strong resistance of Pa against hydrolysis. The negative changes in the energy of the Coulomb interaction when water molecules are replaced by OH groups then decrease in the order: (25) -AEC: Nb>Ta>Ha»Pa In contrast to AEC, the differences in the OP values (Table 7) are very small and similar for Nb, Ta and Ha. (Negative AOP means a decrease in the covalent interaction energy from M(H20)6 5+ to M(OH)& , so that a positive energy change AEOP occurs). They follow the sequence -AEop: Pa > Nb > Ta > Ha (26) Here, Pa has a preference to form Pa(OH)& . The values of AEC are, however, much larger than those of AEop, so that even the highest value of K' =1.51 giving AEop listed in Table 7 cannot influence the order of hydrolysis of the cations established by the electrostatic interaction, so that quite definitely: -AE1, or -AG : Nb > Ta > Ha » Pa (27) 16 Thus, in agreement with experiment [3] (Fig. 1), Nb is more hydrolyzed than Ta, and both of them are much more hydrolysed than Pa. Ha is less hydrolyzed than Nb and Ta, but much more than Pa. It is interesting to note here, that although an increasing covalent interaction might influence the electrostatic nature of hydrolysis [3], the present data show that still changes in the Coulomb part of the metal-ligand interaction define the process. Of course, the electrostatic interaction calculated here is based on the real electronic density distribution, and not on the assumption of formal charges used in the simple ionic model. Thus, the present data show clearly the difference between Nb and Ta, which was not explained by the electrostatic model. They also explain a unique position of Pa in the considered row. They show, that a smaller effective charge of Ha in comparison with those of Nb and Ta and smaller changes in the electrostatic part of the binding energy are a reason for a weaker hydrolysis of Ha. It would also be possible to give absolute values of log K provided some experimental data were known. Thus, using the data of Table 7 and Eq. (9), log K can be expressed in the following way: log K = -AGr/2.3RT = AEc/2.3RTe + AE0P/2.3RT +14.51. (28) For the elements of interest, with K'=0.37 and £=20 one has: Nb log Kl6= -5.42k -0.15+ 14.51 Ta log Km = -5.42k - 1.74 + 14.51 (29) Ha log Kl6 = -5.256-3.29+ 14.51 Pa log KI6 = -3.226 - 7.77 + 14.51 Here, the first term on the right hand side of each of Eqs. (29) corresponds to the first term of the right part of Eq. (9), with parameter 6 being a correction factor for the real value of log K in solution. (Experimental data [3] for the first hydrolysis step have shown 17 that aoH-aH2o for transition elements with partially filled d-shells is about -20). The second term on the right part has been calculated directly for e=20. If one had a value of log K for at least one lighter homolog of Ha, one could define k and then the exact value of log tf(Ha). Knowledge of the hydrolysis constants for a couple of (lighter) elements would enable one to give both the correct value of the second term (or the dielectric constant) and k. Unfortunately, for reactions (6) considered here, none of the hydrolysis constants is known so that only relative values of log K can be given. In principal, any hydrolysis step, where log K is known for any homolog of Ha, could be described in a similar way. Then, by calculating AEC, AE0P and defining k, the exact value of log K for Ha could be obtained 5. Conclusions To summarize, relativistic MO calculations of the electronic structure of hydrated and hydrolysed species of the Nb, Ta, Ha and Pa cations in aqueous solutions and derived free energy changes of reactions (6) have shown that the hydrolysis decreases in the order: Nb > Ta > Ha » Pa. For Nb, Ta and Pa the results are in full agreement with experiment. A decisive factor turned out to be the predominant changes in the electrostatic interaction energy when water molecules in the first coordination sphere are replaced by OH. Thus, in going in the Periodic Table over to the transactinides, electrostatics will still define the nature of the metal-OH and metal-HzO interactions, and finally the hydrolysis process. Nevertheless, both the electrostatic and non-electrostatic interactions must be determined on the basis of relativistic MO calculations. Using formal effective charges can result in erroneous results. In the case of the transactinides, the non-relativistic calculations (see [14]) would give a more ionic character of bonding than that of the 4d and 5d elements, which would result in a stronger hydrolysis of the 6d elements in comparison with that of lighter homologs. 18 The present relativistic calculations have shown Ha to be less hydrolysed than its homologs, Nb and Ta, but more than Pa. Both Ha(H20)6 5+ and Ha(OH)e are more covalent than the analogous compounds of Nb and Ta. They have strong bonding with the ligands due to strong 7s-2p(0), as well as 6d]/2-2p(0), 6ds/2-2p(0) interactions. The large energy gap in Ha(H20)6 5+ prevents any distortion of a regular structure. Our earlier calculations [14] have shown that groups 4 and 5 are very similar, and bonding changes in a similar way within the groups. This is quite in contrast to the results of Ref. [6] interpreted in terms of a stronger hydrolysis of Rf in comparison with Zr and Hf. As an explanation of a stronger hydrolysis, a lower coordination of water molecules (only 6) in contrast to 8 of Zr and Hf has been given. The lower CN was attributed [6] to relativistic effects which split the 6d orbitals into two 6d3/2 and three strongly destabilized 6d 5/2 orbitals. The destabilization of the 6d 5/2 orbitals was believed to cause the promotion energy involving 7s, 7p and 6ds/2 orbitals to be too high for the sp3d 4 hybridization. This was believed to give Rf a coordination number 6 rather than 8 in aqueous solutions because 6-coordination requires only the 6ds/2 orbitals while 8-coordination requires in addition the 6ds/ 2 orbitals. However, data on energies of the valence-shell electrons show, that the difference between the 6d3 /2 and 6ds/2 orbitals [22] is too small to cause such an effect, smaller than the 7pi/2-7p3/2 separation, though both the 7p,/2 and orbitals were assumed [6] to participate in the hybridization. Thus, a conclusion about a reduction of the CN due to this reason cannot be maintained. On the contrary, it is known [23] that increasing relativistic effects in the transactinides result in a close location of all the valence levels (the difference between the 7s, 6d and 7p levels is only 1-2 eV for Rf), so that higher CN are easily reached. Analogously to Ha(H20)6 5+ with respect to Nb(H20)6 5+ and Ta(H%0)6 3^, and to RfCl4 with respect to ZrCl4 and HfCl4 [14], Rf(H20)g4+ will probably also have a larger energy gap between the occupied and vacant MO than the corresponding compounds of Zr and Hf, so that no second-order Jahn-Teller effect becomes active resulting in a distortion of a regular structure and hence a loss of some water molecules. 19 In the case of group 4, one can also expect, that effective charges and overlap populations for Hf(H:0)g4^ will change in a similar way relative to those for Zr(H20)g4+, as Ta(H20>6 5+ relative to Nb(H20)6 5+. Thus, the stronger hydrolysis of Hf in comparison with Zr is probably due to larger changes in the Coulomb part of the metal-ligand interaction when water molecules are replaced by OH. This would be in agreement with the experiment [3], By applying the same arguments for the case of Rf, one can expect a weaker hydrolysis in comparison with that of Zr and Hf (similar to the hydrolysis of Ha relative to that of Nb and Ta). Nevertheless, exact calculations of the electronic structure of the hydrated and hydrolysed complexes of Zr, Hf and Rf will be of course of high interest. Acknowledgements The calculations were performed on the IBM-AIX Cluster of the Gesellschaft fur Schwerionenforschung, which the author thanks for the financial support. She is also grateful to Dr. T. Bastug for the help with some routines of the calculations. References 1. Treatise on Analytical Chemistry, eds. Kolthoff, I. M. and Elvins, P. J., Part II, Vol. 6, John Wiley and Sons (Interscience Publ.), New York, 1964. 2. Schafer, H.: Angew. Chem. 71, 153 (1959). 3. Baes, Jr, C. F. and Mesmer, R. E.: The Hydrolysis of Cations, John Wiley, New York, 1976. 4. Scherff, H.-L. and Herrmann, G.: Z Electrochemie, 64, 1022 (1960). 5. Kratz, J. V., Zimmermann, H. P., Scherer, U. W., Schadel, M., Briichle, W., Gregorich, K. E., Gannett, C. M., Hall, H. L., Henderson, R. A., Lee, D. M., Leyba, J. D., Nurmia, M„ Hoffman, D. C., Gaggeler, H. W., Jost, D„ Baltensperger, U., Ya Nai-Qi, Tiirler, A., Lienert, Ch.: Radiochim. Acta, 48, 121 (1989). 20 6. Bilewicz, A., Siekerski, S., Kacher, C. D., Gregorich, K. E., Lee, D. M., Stoyer, N. J., Kadkhodayan, B., Kreek, S. A., Lane, M. R„ Sylwester, E. R., Neu, M. P., Mohar, M. F. , Hoffman, D. C.: Radiochim. Acta, 75, 121 (1996). 7. (a) The Chemistry of the Actinide Elements, 2d edition, editors Katz, J. J., Seaborg, G. T. and Morss, L. R.: Chapman and Hall, London, Vol. 1, (1986), p. 142; (b) Bouissieres, G. In: Tagungsber. 3 Int. Pa-Konference (ed. Bom, H.-J.), Schloss- Elmau, April 1969, German Perort BMBW-FBK 71-17, Paper No. 26 (1971). 8. Scherff, H. L., Herrmann, G.: Radiochim. Acta 6, 53 (1966). 9. Kassiakoff, A., and Harker, D.: J. Am. Chem. Soc. 60, 2047 (1938). 10. Shannon, R. D.: Acta Crystallogr. Sect. A 32, 751 (1976). 11. Pershina, V.: Chem. Rev. 96, 1977 (1996). 12. (a) Rosen, A., Ellis, D. E.: J. Chem. Phys. 62, 3039 (1975); (b) Basing, T.: doctoral thesis, University of Kassel, 1994. 13. (a) Mulliken, R. S.: J. Phys. Chem. 56, 295 (1952); (b) Mulliken, R. S.: J. Chem. Phys. 23, 1841 (1955). 14. (a) Pershina, V., Sepp. W.-D., Fricke, B., Rosen, A.: J. Chem. Phys. 96, 8367 (1992); (b) Pershina, V. and Fricke, B.: J. Phys. Chem. 98, 6468 (1994). 15. Boerrigter, P. M., te Velde, G., Baerends, E. J.: Int. J. Quantum Chem. 33, 87 (1988). 16. ref. 3, p. 398; Ahrland, S., Liljenzin, J. O. and Rydberg, J. In: Comprehensive Inorganic Chemistry, ed. Bailar, J. C. et al., Pergamon Press, Oxford, 1973, Vol. 5, p. 465. 17. Clark, D. W., Farrimond, M. S.: J. Chem. Soc. (A), 299 (1971). 18. Stromberg D., Sandstrom, M., Wahgren, U.: Chem. Phys. Lett. 172, 49 (1990). 19. Burgess, J.: Ions in Solution, Ellis Horwood Limited, New York, 1988, p. 40. 20. Fricke, B., Johnson, E., Rivera, G. M.: Radiochim. Acta 62, 17 (1993). 21. (a) Jahn H. A., Teller, E.: Proc. Roy. Soc., 161, 220 (1937); (b) Renner, R.: Z. Phys. 92, 172 (1934); (c) Englman, R.: The Jahn-Teller Effect in Molecules and Crystals, Wiley-Interscience, London, 1972. 22. Glebov, V. A., Kasztura, L., Nefedov, V. S., Zhuikov, B. L.: Radiochim. Acta, 46, 117 (1989). 21 23. Fricke, B.: Struct. Bond. 21, 89 (1975). Table 1. Metal-oxygen interatomic distances (in A), used for the calculations of the electronic structure of M(H?0)6 5+ and M(OH)6 , where M = Nb, Ta, Ha and Pa Molecule Nb Ta Ha Pa M(H20)6 5+ 2.04 2.04 2.105 2.18 M(OH)6 - 2.10 2.01 2.075 2.15 Table 2. Energies of the HOMO, LUMO, vacant levels of d-character and AE (in eV) for M(H20)6 5+, where M = Nb, Ta, Ha and Pa MO Nb Ta Ha MO Pa - - - - 6u, 7u -25.02 - - - - 5u -25.12 6g, 7g -25.96 -24.75 -23.47 5u -28.59 5g -30.26 -29.35 -28.10 6u, 7u -28.93 ?g,6g" -30.40 -29.82 -29.23 5u -29.16 6u,7u b -33.87 -33.88 -33.48 7u -33.06 AE 3.47 4.06 4.25 AE 3.90 aLUMO;bHOMO 23 Table 3. Atomic orbital populations (qO and effective charges (Q) for M(H20)6 5+, where M = Nb, Ta, Ha and Pa Parameter Nb Ta Ha Pa ns 0.17 0.30 0.44 0.12 npi/2 0.06 0.01 0.08 0.06 np3/2 0.13 0.11 0.12 0.15 (n-l)d 3/2 1.19 1.12 1.14 0.59 (n- 1 )ds/2 1.70 1.49 1.28 0.73 (n-2)fs/2 - - - 0.61 (n-2)f?/2 - - - 0.65 Qm 2.15 2.23 2.20 2.50 Qo -0.66 -0.68 -0.68 -0.69 Qh 0.56 0.57 0.57 0.55 24 Table 4. Partial overlap populations for M(OH)& and M(H20)6 5+, where M = Nb, Ta, Ha and Pa Compound OP Nb Ta Ha Pa M(OHV ZOP(M-O) 3.09 3.41 3.58 3.24 ZOP(O-O) -0.49 -0.53 -0.45 -0.15 ZOP(M-H) -0.96 -0.92 -0,96 -1.14 ZOP(O-H) 3.79 3.80 3.75 3.68 OP(tot) 5.43 5.78 5.92 5.63 M(H20)6 5+ EOP(M-O) 1.42 1.80 1.96 0.95 ZOP(O-O) -0.14 -0.19 -0.18 -0.04 ZOP(M-H) -1.12 -1.10 -1.12 -1.22 ZOP(H-H) -0.47 -0.47 -0.49 -0.43 ZOP(O-H) 6.63 6.60 6.60 6.81 OP(tot) 6.32 6.67 6.77 6.14 25 Table 5. Energies of the HOMO, LUMO, vacant levels of d-character and AE (in eV) for M(OH)6 , where M = Nb, Ta, Ha and Pa MO Nb Ta Ha MO Pa - - - - 6u 6.10 (6g) - - (6.03) 8u 4.95 8g(2) 6.13 7.02 7.16 6u 4.62 7g 4.68 5.84 6.25 8u 4.16 8g'(2) 4.55 5.36 5.22 7u 3.94 8g"(2) 0.37 0.51 0.18 8g, 6g -0.36 AE 4.18 4.84 5.03 AE 4.30 a LUMO; b HOMO: (2) stands for a double degenerate orbital. 26 Table 6. Atomic orbital populations (q,) and effective charges (Q) for M(OH)& , where M = Nb, Ta, Ha and Pa Parameter Nb Ta Ha Pa ns 0.22 0.32 0.42 0.17 npi/2 0.18 0.23 0.28 0.15 nps/2 0.33 0.37 0.31 0.20 (n-l)d 3/2 1.30 1.26 1.28 0.92 (n-l)ds/2 1.90 1.72 1.67 1.29 (n-2)fs/2 - - - 0.58 (n-2)f?/2 - - - 0.70 Qm 1.09 1.17 1.06 1.02 Qo -0.61 -0.62 -0.61 -0.59 Qh 0.26 0.26 0.27 0.26 27 Table 7. Energies of Ec, OP, differences in these values (A), as well as in Eop and in the total binding energies, AE', between M(OH)o and M(H20)^ Parameter Compound Nb Ta Ha Pa Ec, eV M(OH)6 - -21.74 -23.33 -21.48 -19.53 M(H20)6 5+ -21.92 -25.38 -25.37 -29.71 AEC, eV 0.18 2.05 3.89 9.18 OP M(OH)6 5.43 5.78 5.92 5.63 M(H20)6 5+ 6.32 6.67 6.77 6.14 AOP -0.89 -0.89 -0.85 -0.51 AEop, eV K'=0.37 0.32 0.32 0.31 0.19 K'=1.51 1.34 1.34 1.28 0.77 AE1, eV K'=0.37 0.50 2.37 4.20 9.37 K'=1.51 1.52 3.39 5.17 9.95 28 Figures Fig. 1. Predominance diagram for the mononuclear species of pentavalent Nb, Ta and Pa (adopted from [3]). Fig. 2. The hexahydrated complex in Th symmetry. Fig. 3. A scheme of the MO energies (the HOMO, LUMO and other valence d-orbitals) for M(H20)6 5+, where M = Nb, Ta, Ha and Pa (g - even and u - odd wave function with respect to the center of symmetry). 29 f Z y,d -20 Ta Ha -22 6g, 7g -24 - - 6g, 7g 6g, 7g -26 > -34 HOMO 7u 6u, 7u 6u, 7u 6u, 7u -36 Fig. 3