A density functional theory

8/7/2019 A density functional theory

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THEOCHEMELSEVIER Journal of Molecular Structure (Theochem) 417 (1997) 247-254

A density functional theory study on stability of carbonylmetallatemonoanions Mn(CO)& HFe(CO)i and Co(CO),

Zhida Chen*, Yuqing Deng, Lemin Ll, Guangxian XuDrpcumrrrt of Chemistry, State Key f.ahorato~ ofRare Earth Materials Chmictyv andApp/in~tion. Prkin,? lJniw,:\i~, Be(jirl,y 100871. Chino

Received 6 January 1997: accepted 6 January 1997

AbstractCalculations on optimized geometries, atomic net charges and interatomic Mulliken populations as well as relaxation

energies for the carbonylmetallate monoanions Mn(CO);, HFe(C0); and Co(C0); have been carried out by density functionaltheory at the local density approximation (LDA) level and at the LDAINL level with further non-local corrections for exchangeand correlation included self-consistently. On comparison with the corresponding hydrides, there were found to be shorter M-Cdistances and longer C-O separations in the carbonylmetallate anions. From Mulliken population analysis, it is shown that H+dissociation from hydride molecules leads the electronic charges on the carbonylmetallate anions to delocalize further on thecarbonyl groups, while the M-C bonding is strengthened and the C-O bonding is weakened. The relaxation energies calculatedare found to be - 63.01, - 82.00 and - 53.54 kJ mol- for Mn(CO);, HFe(C0); and Co(CO);, respectively. 8 1997 ElsevicrScience B.V.Kexxwrds: Density functional theory; Stability; Carbonylmetallate monoions; Molecular fragment

1. IntroductionA number of carbonylmetallate anionic species,

M(CO),- (where M is a transition metal and.r=3- -6. := 1 - -4), have been synthesized andcharacterized structurally. Thus, the chemistry of thecarbonylmetallate anions and their derivatives withtransition metals in low formal oxidation states hasbeen studied extensively over the past decades [ 1,2].With molecular fragment reagents as startingmaterials, molecular syntheses designed for inorganicmaterials and cluster compounds have recently beencarried out in our laboratory on the basis of molecularfragment chemistry [3]. in which a molecule is* Corresponding author

supposed to be composed of molecular fragments,sometimes with some bridging ligands. In fact, thecarbonylmetallates have been demonstrated to bequite useful molecular fragment reagents in molecularsyntheses designed for transition metal carbonylcluster compounds. It should be pointed out thatthese carbonylmetallate anions contain the transitionmetals in low formal oxidation states. even in theirlowest known oxidation states. The latter species haveoften been referred to as superreduced species. Thus,the study of the electronic structures of carbonyl-metallate monoanions has been a subject attractingintense attention [4]. In this paper, we are interestedin using molecular orbital calculations as a practicalguide for laboratory studies and shall put emphasisupon bonding energies and the delocalization ot

0166-12X0/97/$17.00 Q 1997 Elsevier Science B.V. All rights reservedP/I SOl66-1280(97)00016-X


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248 2. Chen et d/Journal of Molecular Structure (Theochem) 417 (1997) 247-254

negative charges on these highly reduced transitionmetal centers for the carbonylmetallate monoanionsMn(CO);, HFe(CO)i and Co(CO),.

Theoretical methods in quantum chemistry may, inprinciple, be applied in organometallic thermo-chemistry. However, calculations on large organo-metallic molecules with the ab initio method are stillimpractical. Thus, much attention has recently beenpaid to methods based on density functional theory asan alternative to the ab initio scheme. The applicationof approximate density functional theory to organo-metallic chemistry has recently been reviewed byZiegler and co-workers [5]. We shall, in the presentinvestigation, make use of approximate densityfunctional theory with non-local correction terms ofelectron exchange and correlation energies for geo-metry optimizations, bonding energy calculationsand electronic structures for Mn(CO);, HFe(C0);and Co(C0);.

2. Computational detailsAll reported calculations are carried out by utilizing

the Amsterdam density functional (ADF) package,version 1.1.3. The local density approximation(LDA) with local exchange and correlation potentialsmakes use of the parametrization of Vosko et al. [6].Non-local corrections (NL) with Beckes non-localexchange correction [7] and Perdews non-localcorrelation correction [8] are added in each SCF-consistent cycle. Convergence is achieved once themaximum number of elements of the commutator ofboth the Fock matrix and the density matrix is smallerthan lo- and the norm of the commutator is underlo4 in absolute value. The numerical integration pro-cedure applied for the calculations is the polyhedronmethod developed by Velde and co-workers [9]. Theelectronic configurations of the molecular systems aredescribed by an uncontracted triple-c ST0 basis set[lo] on Mn 3d,4s, Fe 3d,4s, and Co 3d,4s as well as adouble-r ST0 basis set on 0 2s,2p, C 2s,2p, and H 1s.The 0, C and H atoms are given an extra polarizationfunction: 0 3d ({3d =2.00); C 3d ({3d =2.20); H 2p({+ = 1.25). The inner core shells for all atoms exceptthe H atom are treated by the frozen core approxima-tion. A set of auxiliary s, p, d, f and g ST0 functions,centered on all nuclei, is introduced to fit the

molecular density and to represent Coulomb andexchange potentials accurately [ 1 I]. All the calcula-tions are carried out with a spin-restricted scheme.The geometry optimization procedure is based onthe analytic gradient method implemented at theLDA level by Versluis et al. and at the LDA/NLlevel by Fan et al. [12]. The optimization uses theNewton-Raphson method and Hessian is updatedwith the Broyden-Fletcher-Goldfarb-Shannostrategy [ 131. Convergence is achieved once changesin coordinate values are less than 0.01 unit (distancesare given in atomic units and angles in radians) andthe norm of all gradient vectors is smaller than 0.01.

We have fully optimized the geometries ofMn(CO);, HFe(C0); and Co(CO), by LDA andLDA/NL. The geometry of Mn(C0); has beenoptimized respectively within the CA,,, Cjv and D1,symmetry constraints. The geometry optimization ofHFe(CO)i is within the Cjv symmetry constraint. Thegeometry of CO(CO), has been optimized respect-ively within the Cjy and Td symmetry constraints.For a comparison of the differences in electronicstructure between Mn(C0); and HMn(CO)s, HFe(CO), and H2Fe(C0)4, and Co(CO)i andHCO(CO)~, the hydrides HMn(CO)S, H2Fe(CO)_,and HCo(CO)d are also calculated by density func-tional theory with the LDA and LDA/NL approxima-tions. Structure parameters of these hydrides in ourcalculations are taken from experimental dataobtained by gas-phase electron diffraction [ 131. Inour work, the calculated relaxation energies [5]a forMn(CO);, HFe(C0); and Co(CO), represent theenergies gained when the Mn(CO);, HFe(C0); andCo(CO), anions rearrange from the geometriestaken up in their hydrides HMn(CO)s, H2Fe(CO)$and HCo(CO)+

3. Results and discussion3.1. Optimized structures3.1.1. Mrl(CO)~

The optimized structures of Mn(C0); under theCd,,, Cl and Djh symmetry constraints are presentedin Table 1. The crystal structure data from X-rayanalysis are available for the trigonal-bipyramidalMn(C0); in ]Ni( 1, lo-phen) 31[Mn(CO)tI 2 (see


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Table IOptimized geometries

Z. Chrn et al.Nournal of Molecular Structure (Throchern) 417 (1997) 247-254 219

Symmetry Method M-C,, M-C,, G-O,, C,,,-0,X M-H C,i,-M-C;q O,,-C,,-Mh

HCo(CO),c-3,

LDA I .7x)LDA/NL 1.837LDA I .77 ILDA/NL 1.825LDA 1.771LDAML I .824exptl I.798

LDA/NLd I.855 I.854 I.155 I.155 I .589 91.8 I X0.0Exptl 1.856 1.854 1.142 1.142 I.576 94.53 I Xl. I

LDA 1.738 1.748 I.166 I.165 I.518 9Y.5 173.3LDAPJL I.738 1.797 1.176 I.173 1.533 9Y.S 177.5Exptl I .75 1.72 1.15 1.18 I .57 YY.07 Ill.2

Exptl 1.802 I .832 1.145

LDALDA/NLLDALDA/NLExptl

LDA/NLExptl

I.742I .794I .8031.7861.847I.8321.7951.839I.820

I.1651.174I I67

I.155I.176I.163I.164I.169I.170I.163I.172I.153

101.7 178.5102.3 177. I8Yl.5 177.6

1.175 91.3I.1671.177I.155

90.090.090.0

I.145

I.166I.173

I.556 96.Oh 16.5148.5 176.2

I.737I.791I .736I .789I .825( I .76)

(1.89)

I .730I.784I .7361.789

1.167I.174I.164I.174

_

1.23(1.17)( I .29)

_

107.8108.4lOY.5109.5lOY.S(l I?)

(107)

I.801 1.803 I.151 I.148 I .499 98.2I.818 I .764 I.141 I.141 I.556 99.7 -

177.7180.0180.017x.2

177.2178.0180.0I80.0167.5(155)

(IX())

179.9172.6_

Key: eq. equatorial: ax, axial. Interatomic distances are given in AngstrGm\.h Bond angles are given in degrees. Ref. [15]. Ref. [S]a. Ret. 1141. Average value.p Ref. [ Ih].h C,,-Fe-C,,. Fe+C,,AO,,.C,,--Fe-C .I\, Fe-C,,PC,i,.

Ref [171.


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250 2. Chen et ai./Journal of Molecular Structure (Theochem) 417 (1997) 247-254Table 1). For the purpose of comparison, both themolecular structure for HMn(CO)S obtained by gas-phase electron diffraction [14] and the calculatedgeometry [5]a of this molecule obtained by DFT atthe LDA/NL level are listed in Table 1. It is found inTable 1 that the geometries optimized by LDA/NL, ingeneral, agree better with experimental structures thanthose optimized by LDA, which is consistent withZieglers calculations [5]a. Thus, in this text weshall mainly discuss the results calculated by LDA/NL. Our calculations show that for the structures ofMn(C0); under the Cd, CjV and Djh symmetries, theDjh geometric configuration is the most stable one interms of energy. The calculated total bonding energiesare found to be 12.63 kJ mol- and 4.19 kJ mol-lower than those for the Cd, and CjV geometries,respectively. The calculated geometry is ingood agreement with the experimental data [ 151obtained from X-ray diffraction analysis for the[Ni(l,lO-ghen)j][Mn(CO)s]~ crystal, with deviationsof 0.02 A (bond distance) and 2 (bond angle). Itshould be remembered that our calculations haveignored the role of the counterion [Ni( l,lO-phen)]in the crystal field. On the other hand, the calculatedMn-C,, distance of 1.839 .$ is slightly longer than theMn-C,, distance (1.824 A), which correctly repro-duces the experimental measurements [ 141. Hencethe calculated geometry for Mn(C0); using DFT-LDA/NL is satisfactory in our studies.

It is worth pointing out that there is one notabledifference in the corresponding Mn-C and C-Odistances between HMn(CO)s and Mn(C0);. It isshown from the experimental data in Table 1 thatafter the dissociation of H+ ions in HMn(CO)S, theMn-C,, and Mn-C,, separations are shorter by0.058 A and 0.034 A, respectively, while, in contrast,the C,,-O,, and C,-O,, distances are longer by0.013 A and 0.011 A, respectively. It is interestingto remark here that this trend in bond distance changesis important in understanding the stability of thecompounds studied.3.1.2. HFe(C0):

The experimental geometry of the HFe(CO)i anionhas been found to be a configuration with CjVsymmetry [ 161. The geometry optimization in our cal-culations has been carried out within the CjV sym-metry constraint. All bond distances are calculated

within 0.02 A from the crystal structure data [16]obtained from X-ray diffraction analysis, except Fe-C,, which has a deviation of 0.07 A and Fe-H with adeviation of 0.04 A. We are not able to rationalize thelarge deviations between experiment and theory forthis Fe-C,, distance. For the Fe-H distance, weexpect that at least some of the deviation might bedue to experimental uncertainties in the position ofthe H atom. On the other hand, the calculated bondangles are within 0.5 from experimental observationsand reproduce well the experimental fact that theequatorial CO groups are slightly leaning toward theaxial hydrogen atom [ 151. Again, it is interesting tonote the differences in the corresponding bond distancesbetween H2Fe(CO)1 and HFe(CO)i. It is found inTable 1 that the Fe-C,, and Fe-C, experimentaldistances are shortened from 1.802 A and 1.832 Ain H11Fe(C0)4 to 1.75 A and 1.72 A in HFe(CO);,respectively, while the C,,-O,, and C,,-O,, experi-mental separations are lengthened from 1.145 A inH*Fe(CO)., to 1.15 A and 1.18 A in HFe(CO)i,respectively. These changes in the bond distancesindicate the effect of the dissociation of H+ ions onthe Fe-C and C-O chemical bonds.3.1.3. Co(CO),

We have fully optimized two geometries ofCo(CO), with C3 and Td symmetries. The calculatedCjV configuration is 0.87 kJ mall higher in energythan the Td structure. This agrees well with the experi-mental Td geometry obtained by X-ray analysis of thecrystal structure for TICO(CO)~ [17]. It should bepointed out that there are no discrete T~CO(CO)~moieties in the solid state. Thus, the counterion Tlin the TlCo(C0)4 crystal affects significantly the bonddistances in Co(C0);. The experimental Td geometryfor Co(CO), is in fact slightly distorted. The three-fold-related carbonyl group has a Co-C-O angle of155, not 180. Therefore, there are two sets of corre-sponding bond distances and bond angles. The experi-mental structural data for the two sets are given inparentheses in Table 1. The calculated Co-C distanceof 1.789 A is found to be 0.036 A shorter than theexperimental average value of 1.825 A [ 171. Also, thetheoretical estimate of the C-O distance agrees withthe experimental average data to within 0.056 A.However these theoretical values are within thecorresponding experimental bond distances of the


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% Chen ct ul./Journul oJMoleculnr Structure (Them-hem) 417 (1097) 247-254 251

two sets mentioned above. In this case, a direct com-parison of the bond distances calculated by LDA/NLbetween HCO(CO)~ and Co(CO), might help tounderstand the change in chemical bonding due tothe H dissociation in HCo(CO)+It is found in Table 1 that the calculated Co-Cdistance in Co(C0); is 0.013 i shorter than theaverage calculated value of Co-C in HCo(CO)+ Incontrast, the C-O separation in Co(CO), is calculatedto be larger than the average calculated distance of C-O in HCo(CO)+ It should be noted that the trend in thedecrease of the M-C (where M is Mn, Fe, Co) dis-tances upon an increase in the C-O separationbecomes obvious. These structural changes showthat when H+ ions in Mn(CO);, HFe(CO)4 andCo(CO)i are removed by dissociation, the interactionbetween the central metal atom and the coordinatingcarbon atom at the carbonyl groups becomes strongerwith a concomitant weakening of the bondingbetween the carbon and oxygen atoms in the carbonylgroups.

3.2. Mulliken population analysis3.2.1. Atomic net churges

For the Mn(CO);, HFe(C0); and Co(W), speciesas well as their hydrides, the central transition metalatom is in a low formal oxidation state. Hence, theproblem of electronic charge distribution in the mole-cules or anions has been a subject of intense interest.On the basis of Mulliken population analysis, atomicnet charges for the species mentioned above are givenin Table 2. It is found in Table 2 that the calculatedatomic net charges on the central metal atoms and thecarbon atoms of the carbonyl groups are all positive,but not too high, while all the oxygen atoms of thecarbonyl groups have negative net charges. To avoidconfusion in the charge signs. we prefer herein todiscuss electronic charges on atoms rather than netcharges. It is interesting to note that the electroniccharges on the central metal atoms in the hydridemolecules are greater than those in the correspondinganions. The dissociation of H- ions in the hydride

Table 2Atotmc net chargesSymmetry Method M C,, C,, a, O,k H C -0

LDA 0.4384LDA/NL 0.45 IS

I,DA -0.0464LDA/NL 0.1764

LDA 0.I8-uLDA/NL 0.2380

LDA -0.1380LDA/NL 0.063 I

LDA 0.082 ILDA/NL 0.1209

LDA -0.06 I7LDA/NL 0.0893

0.2383 0.2703 -0.54050.2534 0.2835 -0.557 I -0.5361-0.ss37

_ -0.2840-0.2X69

0.4294 0.4332 -0.45000.4092 0.4095 -0.464 I

-0.464 I-0.4778

0.1597 -0.025x0.1 I I5 -0.06I6

0.2416 0.2675 -0.547 I 4.55230.2578 0.2772 -0.5648 -0.5670

0.0136 -0.2 187-0.027 I -0.29x4

0.4235 0.43820.406 I 0.4240

-0.4503 -0.4448 0.1023 -0.0 I67-0.4640 -0.4581 0.0606 -0.0460

0.2787 0.2787 0.5492 4.5492 _ -0.270s0.2853 0.2853 0.5655 -0.5655 -0.2802

0.4298 0.4546 -0.4494 -0.452 I0.4144 0.4384 -0.4629 -0.4650

0. I 182 -0.00860.0829 -0.0376

Average value.


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252 Z. Chen et aL/Journal of Molecular Structure (Themhem) 417 ( 1997) 247-254

molecule will certainly increase the electronic chargefor the anion by one; however, the electronic chargeon the central metal atom in fact does not increase, onthe contrary, it decreases by 0.2751 e, 0.1749 e and0.0316 e for the Mn, Fe and Co atoms, respectively.On the other hand, the dissociation of H+ ions in thehydride molecule leads the electronic charges on theoxygen and carbon atoms in the carbonyl groups toincrease. Table 2 shows that the electronic charge oneach carbonyl group increases by 0.2253 e, 0.2524 eand 0.2426 e on average for Mn(Co);, HFe(C0)4 andCo(CO),, respectively. It is obvious that the electroniccharges for this species of carbonylmetallate anion arefurther delocalized on the coordinating carbonylgroups after the dissociation of H+ ions in the hydridemolecule.3.2.2. Interatomic M&liken populations

The calculated interatomic Mulliken populationsare listed in Table 3. On comparison with the hydridemolecules, the Mulliken populations between thecentral metal atom M and the carbon atom C (bothC,, and C,,) for the Mn(CO);, HFe(CO)i andCo(CO), anions increase significantly. In Table 3,the increment of the Mulliken populations betweenMn-C,, and Mn-C,, are found to be 0.1168 and0.0800, respectively, and 0.1118 and 0.1360 for Fe-C,, and Fe-C,,, respectively. In the case of Co(CO),,the Mulliken population on the average for Co-C,,and Co-C,, increases by 0.1420. While it is shownin Table 3 that the Mulliken populations for carbonylgroups in the carbonylmetallate anions decrease

Table 3Interatomic Mulliken populations

slightly, for Mn(CO);, HFe(C0)4_ and Co(CO), thesituations differ from each other. The decrease ofthe C-O Mulliken population for Mn(C0); is thesmallest, being calculated to be 0.0382 and 0.0002for C,,-O,, and C,,-O,, respectively. In the case ofHFe(CO)i, the Mulliken populations of C,,-O,, andC,,-O,, decrease by 0.0398 and 0.0562, respectively.For Co(CO);, the Mulliken population reductions forC,,-O,, and C,,-O,, are calculated to be 0.0854 and0.0936, respectively.

The change in the interatomic Mulliken populationmight be rationalized on the basis of chemical valencetheory. It is well known that in transition metalcarbonyl compounds there is both CO - M donationbonding and M - CO donation back bonding. Thelatter is formed from d electrons on the metal atom,back bonding to a a* molecular orbital of the carbonylgroup. The two types of chemical bonding, CO - Mand M - CO, allow the metal atom to combine withcarbonyl group ligands. Thus, when more valenceelectrons transfer from the central metal atom to thecarbonyl groups, the M-CO bond will be strength-ened, resulting in weakening of the C-O bond ofthe carbonyl group. Therefore, the carbonyl groupsplay an important role in stabilizing carbonylmetallateanions.3.3. Relaxation energy

Recently Folga and Ziegler [5]a have investigatedmetal-carbon and metal-hydrogen bond energies forcertain metal carbonyl compounds by DFT-LDA!NL.

Species Symmetry Method M-C,, M-C,, c,,-o,, C&J ,, M-H

MWO); DlhHMnKO)s C4

HFe(C0); Ci,

HzFe(C0J4 CZ,,

co(c0); TdHCo(CO), C?,

LDA 0.2070 0.2548 0.8510 0.8802LDA/NL 0.3108 0.3326 0.7814 0.8054LDA 0.2352 0.2892 0.8696 0.8540LDA/NL 0.1940 0.2526 0.8196 0.8056LDA 0.3240 0.3674 0.8424 0.8554LDA/NL 0.3952 0.4346 0.7728 0.7760LDA 0.3236 0.3382 0.8628 0.8806LDA/NL 0.2834 0.2986 0.8 I26 0.8322LDA 0.5328 0.5328 0.8 130 0.8130LDAAL 0.5696 0.5696 0.7350 0.7350LDA 0.4458 0.4668 0.8640 0.8730LDAJTiL 0.4192 0.4360 0.8204 0.8286

_0.44260.44360.41040.20280.39300.3912_0.44080.4344


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Z. Chrn rt ul./Journ al of Molrcular Structure (Throchem) 417 I 1097) 247-254 15.7Table 4Relaxation energiesMethod Mn(C0);LDA -77.14LDA/NL. -63.01I In kilojoules per mole.

HFe(C0); Co(CO)i-88.88 -58.55-82.00 -53.54

The results. calculated with quite a high accuracy,have aroused our interest in the calculation of relaxa-tion energies for the species of carbonylmetallateanions. The relaxation energies for the speciesMn(CO)& HFe(CO)i and Co(CO), are referred to asthe amounts of energy released when these anions arereorganized from the geometry taken up by theirhydride species to the geometry having a stable stateof the anions. From the total bonding energies cal-culated at the DFT-LDA/NL and LDA levels beforeand after relaxation, we obtained relaxation energiesfor these anions, which are given in Table 4. Therelaxation energies from the LDA/NL calculationsare slightly lower than those obtained by LDA. Weshall only discuss here the relaxation energies cal-culated by LDA/NL. It is shown in Table 4 that therelaxation energies are -63.01 kJ mol-, -82.00 kJmolJ and -53.54 kJ mol- for Mn(CO);, HFe(C0);and Co(C0):. respectively. The percentage of thetotal bonding energy for the anions in the stablestate is a small value (0.68% for Mn (CO);, 1.02%for HFe(CO)J and 0.70% for Co(CO),). The relaxa-tion energies for the (CO)5Mn. and (CO)&o. radicalsare calculated to be -36.13 kJ mol- and -1.86 kJmolJ at the DFT-LDA/NL level by Folga and Ziegler[5]a. Our relaxation energy calculated for theMn(C0); anion is comparable with that for the corre-sponding (CO)sMn. radical. However, the calculatedrelaxation energy for Co(C0); is remarkably largerthan that for the (CO)JCo. radical. Thus, it can beseen that the relaxation energies calculated for theanions in question are within an order of magnitudeof a few tens of kilojoules per mole.

4. ConclusionsIn general, the carbonylmetallate anions in question

adopt a geometry with higher symmetry. On com-parison with the corresponding hydride molecules,

shorter M-C distances and longer C-O separationsare found in the carbonylmetallate anions. Fromchemical bonding theory, Ht ion dissociation leadselectronic charges in the anion to further delocalizeon carbonyl groups, and the M-C bonds strengthen,while the C-O bonding weakens. Our calculatedresults show that the relaxation energy for the anionsin question are within an order of magnitude of a fewtens of kilojoules per mole.

AcknowledgementsThis work was supported by the National Natural

Science Foundation of China.

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[3] G. Xu. Chem. J. Chin. Umv. I (1984) 100. G. Xu, Ahstr. Paperof the 23nd Int. Conf. in Coordination Chemistry. CO. USA,1984. p. 526. Cr. Xu, in: Yaozeng Huang (Ed. ), New Frontiersin Organometullic and Inorganic Chemistry. Science Press,Beijmp, China. 1984, p. 73.

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[13] (a) H.B. Schlegel, in: K.P. Lawley (Ed.) Ab Initio Methods inQuantum Chemistry, Adv. Chem. Phys. Vol. 67, Wiley NewYork, 1987. (b) J.D. Head, M.C. Zemer, Adv. Quantum Chem.20 (1988) 1.

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[15] B.A. Frenz, J.A. Ibers, Inorg. Chem. 11 (1972) 1109.[16] M.B. Smith, R. Bau, .I. Am. Chem. Sot. 95 (1973) 3288.[171 D.P. Schussler, W.R. Robinson, W.F. Edgell, Inorg. Chem. 13

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A density functional theory