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Diatomic energy partition as a tool for bond analysis
Journal of Molecular Structure rTheochem), 254 (1992) 335-342 Elsevier Science Publishers B.V., Amsterdam
335
Diatomic energy partition as a tool for bond analysis Morella SAnchez’ and Fernando Ruette’ ‘Departamento de Quimica, IUT, Regibn Capital, IUT “F. River0 Palacio’: Apartado 40347, Caracas (Venezuela) ‘L&oratorio de Quimica Te6rica, Centro Quimica, IVIC, Apartado 21827, Caracas (Venezuela) (Received 14 September 1990)
Abstract The partitioning of the SCF total energy from the semiempirical method MINDO/SR into its physical and bond components was used to elucidate the nature of chemical bonds. This technique was applied to study the interaction of hydrogen with single iron atoms Feq (q = + 1,0, - 1) and with an Fell cluster. A detailed analysis of each physical component was carried out by splitting it into its s-s, p-p, d-d, s-p, s-d and p-d constituents, with the purpose of evaluating the participation of the atomic orbitals in the bond. Although the d orbitals of iron atoms show very little overlap with the s atomic orbit& of the hydrogen atom, they do contribute significantly to bonding through electrostatic diatomic interaction.
INTRODUCTION
Ruedenberg [ 11 devised a method for partitioning the electron density and electronic energy of a molecule into components, based upon the concepts of promotion, quasi-classical interaction, shared penetration, shared interference, and charge transfer. Other authors [ 2-41 have applied energy partition techniques to CNDO and MIND0 methods. Fischer and Kollmar [5] found that diatomic two center terms can be interpreted as a measure of the bond strength between two atoms. Kollmar [ 61 has further employed energy partition schemes in ab initio SCF, CNDO and MIND0/3 methods, finding that the two-center energy terms are of the same order of magnitude in the three methods. More recently, Ruette et al. [ 71 have studied the two-center integrals to analyze the role of the d orbit& in the diffusion of hydrogen over a nickel surface, and Rodriguez et al. [8] have made a similar analysis of the nature of the bonding in iron, silicon, and iron silicide clusters, with MINDO/SR calculations. The UHF MINDO/SR method [ 91 is a modification of MIND0/3 [lo] for transition metals. It includes selective molecular orbital occupancies and symmetries [ 111. The MINDO/SR method leads to a very reasonable description
0166-1260/92/$05.06
0 1992 Elsevier Science Publishers B.V. All rights reserved.
of catalytic systems containing transition metal compounds [ 121. Nevertheless, the success of this method is largelydependentupon the procedureused in estimatingthe ground state molecular parameters.These parametersare fitted in order to obtain reasonableequilibriumbond distancesand bond energies for the diatomic moleculesof interest (X-Y bond), obtained from experimental or sophisticatedab initio results. This paper deals with the application of a more specific partitioningenergy technique to the semiempiricalMINDO/SR method, to study hydrogen activation and Fe-H interactions with single iron atoms Feq (q = + l,O,- 1) and with Fe14clusters.One of the advantagesof this methodologyis that the qualitative information obtained for bond strengthstakes into account both ionic and covalentcontributionsand it is independentof the referenceatomic states. THElORJ3TICALPROCEDURE
In the MINDO/SR method, the total energy expression for a system of N electronscan be broken into monoatomic and diatomic contributions [ 121
(1)
E t&d=p4+*phB
The diatomic electronicenergyterm (Ed) can be partitionedaccordingto the differenttype of interactions (n) em=CE&
=E&+EV,+EJa+Ef.&+E&
(2)
E & representsthe contribution of the resonanceintegralsto the energy of the A-B bond
E&3=2 C
pEAYE %
P,~BAB&JRAB
(A-=B)
(3)
Here, BABis an empirical parameter, S,,, is the overlap matrix, and RAB is internucleardistance between the atoms A and B. Pcv= Pzy + P$, is a density matrix element,where PFy = ~c~ic~i and P$” = Cc$cffi i
(4)
and where cFi is a coefficient that comes from the LCAO approach V=Cc~i$/4 P
(tl=W3
(5)
EJm is the repulsionenergybetween the electrons on atoms A and B, given by
the expression EL
=PAPBYAB
where
(6)
337
pA= zApw
and
&A
~~~=(ppluv)
and PeB)
(7)
EL is the attractive potential energy of the electrons on atom A by the B-core and vice versa EL=-PAVAB-PBVBA =
(8)
-PAZBhB-PBZAYhA
and zn are the core charges and yb differs from yABin that the Y orbital in eqn. (7) is the s orbital on B. In &A, fl is the s orbital on A. EL is the electronic exchange interaction of the electrons on atoms A and B given by
ZA
E&z-
ct )fi;A”;B( (P$
)2r,X+ (P&” )2%X)
(9)
where yeX= ( PV1wv) is the exchange integral. The expression for the nuclear repulsion energy between the cores A and B (EC) is E~=ZAZB[Y~+[(~/RAB)-Y~](YAB~-~~]
(10)
where LX- is another empirical parameter and yh is the Coulomb integral, considering only the s orbitals of A and B atoms. A more detailed analysis of diatomic energies can be performed taking into account the s-s, p-p, d-d, s-p, s-d and p-d components of the diatomic energy terms [8,11] E% =P;A V.BE~(~,v)
(A
(11)
EL (p,v) is the diatomic energy of Q-type as a function of their orbital components. Thus E!&(P,v)
=P,Y)BABS~vIR~~
EL(w)=
-p,,~B~:,(~,~)-p",~A~~A(~~v)
(12)
(13)
E~B(~,v)=P~~P,,YAB(~,~)
(14)
E%(W)
(15)
=
-(t)[(P~“)2y,,(~,y)+(P$Y)21/ex(H~)l
EL (p, v) represents the sum of the attractive energies between the electron p on atom A with the nucleus of B and vice versa, so we only consider the s-s, p-p and d-d attractive terms. The s-p, s-d, and d-p terms of the attractive energy are null in eqn. ( 13). This partition of the atomic orbital components permits us to discern the kind of interaction prevailing in the bond between two atoms and the role of the atomic orbitals (such as d orbitals) in the bond formation.
RESULTS AND DISCUSSION
Calculations for (FeH,)* (q=O,+ 1,-l) and Fe14H2systems were performed utilizingenergypartition per orbital, in order to evaluatethe hydrogen interactionwith one iron adsorption center. For ( FeHz )* (q= 0,+ 1,- 1) molecules, we only consider the side-bonded (Fe-(H,) ) geometry. The systems studiedare depicted in Fig. 1. Some of the most importantfeaturesin surfacereactionsarebond activation and bond formation (chemisorbed molecules). Therefore, for the above systems we first study the details of the H-H bond activation caused by Hz-Fe interactions,and secondly hydrogenchemisorptionby the formation of Fe-H bonds. The H-H components and the total electronic diatomic energies for Hz, (FeH2)* (q=O,+l,-l), and Fe14H2are shown in Table 1. The EL, EL, I&, EL and EL terms are denoted as AE, REE, EE, RE and RNN, respectively. A comparison of the total diatomic energy for the H-H bond in the isolated H2 molecule ( -0.4018 a.u.) with those in (FeH,)’ ( -0.3462 a.u.), ( FeHz)+ ( - 0.2999a.u. ), ( FeH2)- ( - 0.0631a.u. ) and Fe14H2( - 0.3272a.~. ) revealsthat only in the negativelycharged molecule is the H,H bond highly modified. (FeH, )Oexhibits a long Fe-H bond distance (2.01-A) and an H-H bond length (0.77 A) similarto that of the H2molecule (0.74 A). These values, taken with the fact that the H-H diatomic energyterm is close to that of the free H, molecule, indicate a weak iron-hydrogen interaction,typical of physiH-H \ / Fe
/
Y
(b)
Fig. 1. Geometry of the molecules studied (a) FeH2 with side-on geometry (b) Fe1,H2, H2 on atom 2.
TABLE 1 Diatomic energy partition into its physical components (a.u.) for the H-H bond of the Hz molecule and interacting with the [Felq (q=O,+ l,- 1) and Fell systems’ Energy type
Hz
[Fe&I0
[Fe&l+
[Fe& I-
F&-L
AEb REE” EEd RE” RNN’
- 0.7880 0.3940 -0.1970 -0.3115 0.5007
-0.7189 0.3316 -0.1655 - 0.2788 0.4854
-0.6812 0.2935 -0.1467 -0.2705 0.5050
- 1.0357 0.7155 - 0.0732 -0.1117 0.4420
-0.7026 0.3158 0.1567 - 0.2730 0.4893
Total
-0.4018
- 0.3462
- 0.2999
-0.0631
- 0.3272
“SeeFig. 1. bEL. “EL,. dEf&. “EL.
*EL,.
sorbed states. In Fei4H2, the H-H diatomic energy is slightly smaller than in the preceding case. Therefore, the cooperative effect of other atoms in the cluster in the activation of the H-H bond on one center site is small. Experimental evidence confirms the existence of physisorbed states which are precursors for dissociation [ 131 and several stable dihydrogen complexes with iron [ 141, such WI, WW2) U-U(&wMBPh4 [I61 and as [FeH(HA (dm=Ll+ [Fe(H),) (H,) (PEtPhz)3] [17] have been reported. In the ( FeHz) - molecule, the lower value of the H-H diatomic energy and the longer H-H bond distance (0.86 A) than in the diatomic molecule, suggest that H, has been activated by interaction with the negatively charged iron. If we assume that the electronic repulsion between electrons (REE), the electron-nucleus attraction ( AE ) and the nucleus-nucleus repulsion (RNN ) are electrostatic terms, and that the resonance energy (RE) and the exchange energy (EE) can be considered as covalent terms, we find that the covalent terms are responsible for the H-H activation. The change of the electrostatic terms in (FeH,) - compared to the same terms in Hz is quite small (0.0151 a.u. ) when compared to the correspondent change in the covalent terms (0.3236 a.u. ). This result is in agreement with the fact that the electronic transfer from Fe- to the H, (8) molecular orbital causes the H-H weakening. The values of the diatomic energy per orbital for the Fe-H bond in FeH, (FeH# (q = 0, + 1, - 1 ), Fe,,H and Fe14H2systems are shown in Table 2. The d-d and p-p terms correspond to the attractive energy between the Fe (d) and Fe(p) orbitals and the hydrogen nucleus. The s-s terms includes the electron attraction between the Fe (4s) electron density and the hydrogen nucleus, and between the H (1s) electron density and the iron nucleus. We can see that the total diatomic energies are a complicated combination of attractive and repulsive energies, with some important contribution from resonance energy. The covalent participation of the d orbitals in the Fe-H bond is indeed negligible, as can be seen from the small values for the resonance and exchange energies
340 TABLE 2 Partitioning of diatomic energy (in a.u. ) for the Fe-H bond in the orbital components Energy type
Component s-s
P-P
d-d
- 3.0359 0.1522 - 0.0741 -0.1891 -3.1469
-0.0803
- 2.0762
- 0.0803
- 2.0762
1.9369 0.2093 -0.0031 -0.0221 - 1.7528
- 0.0385
- 1.6609
- 0.0385
- 1.6609
1.6878 0.0273 -0.0136 - 0.0544 - 1.7285
- 0.0321
- 1.7242
REE EE RE Total [Fe&IAE REE EE RE Total
FeH AE REE EE RE Total
W&Jo m
-
RRE RE RR Total [Fe&
AE
I+
&Ji (H-&r, AE REE EE RE Total Fe& fw REE EE RE Total
-
1
(H&re(I,
-0.0321
- 1.7242
- 2.5451 0.2787 -0.0035 - 0.0188 - 2.2887
-0.0574
- 1.5126
- 0.0574
- 1.5126
- 3.0225 0.1825 -0.0387 -0.1219 -3.0006
-0.1364
- 1.9631
1 - 1.9157 0.1430 - 0.0048 - 0.0337 - 1.8112
-0.1364
- 1.9631
- 0.0963
- 1.7536
- 0.0963
- 1.7536
UThecore repulsion energy for Fe-H has been added.
S-P
s-d
Total
0.1023 -0.0507 -0.1918 - 0.1402
2.6441 - 0.0012 -0.0051 2.6378
-5.1925 2.8985 -0.1260 -0.3860 - 0.3666”
0.0355 -0.0125 -0.0669 -0.0439
1.5307 -0.0001 -0.0002 1.5304
- 3.6363 1.7756 -0.0157 - 0.0893 -0.0683’
0.0276 - 0.0138 -0.0756 -0.0618
1.4860 -0.0001 -0.0004 1.4855
-3.4441 1.5410 -0.0275 -0.1303 - 0.0871”
0.0794 -0.0179 -0.0641 - 0.0026
2.0899 0.0000 0.0000 2.0899
-4.1152 2.4479 -0.0214 -0.0829 - 0.05w
0.1810 -0.0539 -0.1845 -0.0574
2.6050 -0.0007 - 0.0029 2.6014
-5.1220 2.9685 - 0.0934 -0.3094 - 0.2730’
0.0866 -0.0149 -0.0811 -0.0094
1.5770 -0.0002 - 0.0005 1.5763
- 3.7655 1.8066 -0.0199 -0.1153 - 0.0830”
341 TABLE 3 Total electronic diatomic energy contribution per orbital (TE(j); j=s,p,d), core-core repulsion (RNN) and total diatomic energy (DE)” Molecule
TE(s)
TE(P)
m(d)
RNN
DE
FeH FeH, FeH,+ FeH,
-
-0.1078 - 0.0456 -0.0413 - 0.0578
0.1894 - 0.3083 -0.4014 0.2329
2.4394 1.8974 1.9738 1.7207
- 0.3666 - 0.0683 - 0.0871 -0.0509
2.8074 1.6118 1.6185 1.9465
“Values in a.u.
of the s-d terms, as shown in Table 2. The small participation of the d orbitals in the covalent terms, even for the chemisorbed bonds (Fe14H and FeH), is due to the overlap between the d orbitals of iron and the s orbital of hydrogen being very small. Nevertheless, two important energetic contributions of the d orbitals in the Fe-H bond; the attractive interaction between the d orbitals of iron and the H nucleus, and the s-d repulsive term, are present in Table 2. In order to estimate the specific contribution to the diatomic energy of a particular orbital, we follow the same procedure used in ref. 8. The total diatomic energy contribution (TE (_j)) of the j orbital is based on the relative weight given by the orbital occupation TE (s ) = TE,_, + cu,_,TE,_, + CX,_~TE~_~ TE (p ) = Tl&
+ c+~TE,_, + CY~-~TE,-,-~
TE (d ) = TEd-d + q_sTEs_d + cu~_PTEp_~ with cyi_k=nj/ (nj+ nk) (nj is the j orbital population). The results for FeH, (FeH,)q (q=O, + 1, - 1) shown in Table 3 indicate that the most important contribution to the Fe-H bond comes from the s orbitals, with some participation (attractive or repulsive) of the d orbitals. These d terms, in spite of their smc!l values, can be important in the stabilization of the side-on system because of the small values of the total diatomic energy. For example, in neutral (FeH,)O and in positively charged (FeH,) + molecules, the d orbit& play a stabilizing role. In contrast, however, in Fe-H and (FeH,) - molecules, the d electron effect is in the opposite direction. Therefore, the d electrons can be of fundamental importance in the formation of an Fe-H bond, because they generate a net electrostatic interaction that is a balance between electron-core attraction and electron-electron repulsion.
342 REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12
13
14 15 16 17
K. Ruedenberg, Rev. Mod. Phys., 34 (1962) 326. J.A. Pople, D.P. Santry and G.A. SegaI, J. Chem. Phys., 43 (1965) 5129. M.J.S. Dewar and D.H. Lo, J. Am. Chem. Sot., 93 (1975) 7201. J.B. Moffat and H.E. Popkie, Int. J. Quantum. Chem., 2 (1968) 565. J.B. Moffat and K.F. Tang, J. Phys. Chem., 79 (1975) 654. H. Fischer and H. Kolhnar, Theor. Chim. Acta, 16 (1970) 163. H. Kolhnar, Theor. Chim. Acta, 50 (1978) 235. F. Ruette, E.V. Ludeiia and A.J. Hemandez, Int. J. Quantum. Chem., 29 (1986) 1351. L.J. Rodriguez, F. Ruette, G.R. Castro, E.V. Ludefia and A.J. HemBndez, Theor. Chim. Acta, 77 (1990) 39. G. Blyholder, J. Head and F. Ruette, Theor. Chim. Acta, 60 (1982) 429. R.C. Bingham, M.J.S. Dewar and D.H. Lo, J. Am. Chem. Sot., 97 (1975) 1285. J. Head, G. Blyholder and F. Ruette, J. Comput. Phys., 45 (1982) 255. F. Ruette, A.J. Hemandez and E.V. Ludefia, Surf. Sci., 151 (1985) 103. F. Ruette, G. Blyholder and J.D. Head, Surf. Sci., 137 (1984) 491. G. Blyholder, J. Head and F. Ruette, Surf. Sci., 131 (1983) 403. F. Ruette, G. Blyholder and J.D. Head, J. Chem. Phys., 80 (1984) 2042. F. Rue&, E.V. Ludeiia, A.J. Hemandez and G.R. Castro, Surf. Sci., 167 (1986) 393. F. Ruette and G. Blyholder, Theor. Chim. Acta, 74 (1988) 137. M.R. Shanabarger, Surf. Sci., 150 (1985) 451. G. Ertl, in J.R. Anderson and M. Boudart (Eds. ) , Catalysis Science and Technology, Springer, Berlin, 1985, p. 209. E. Nowicka and R. Dus, Surf. Sci., 144 (1984) 665. G.J. Kubas, Act. Chem. Res., 21 (1988) 120. R.H. Morris, J.F. Sawyer, M. Shirahan and J.D. Zubkowski, J. Am. Chem. Sot., 107 (1985) 5581. J.S. Ricci, T.F. Koetzle, M.T. Bautista, T.M. Hofstede, R.H. Morris and J.F. Sawyer, J. Am. Chem. Sot., 111 (1989) 8823. L.S. Van Der Sluys, J. Eckert, 0. Eisenstein, J.H. HalI, J.C. Huffman, S.A. Jackson, T.F. Koetzle, G.J. Kubas, P.J. Vergamini and K.G. Caulton, J. Am. Chem. Sot., 112 (1990) 4831.
335
Diatomic energy partition as a tool for bond analysis Morella SAnchez’ and Fernando Ruette’ ‘Departamento de Quimica, IUT, Regibn Capital, IUT “F. River0 Palacio’: Apartado 40347, Caracas (Venezuela) ‘L&oratorio de Quimica Te6rica, Centro Quimica, IVIC, Apartado 21827, Caracas (Venezuela) (Received 14 September 1990)
Abstract The partitioning of the SCF total energy from the semiempirical method MINDO/SR into its physical and bond components was used to elucidate the nature of chemical bonds. This technique was applied to study the interaction of hydrogen with single iron atoms Feq (q = + 1,0, - 1) and with an Fell cluster. A detailed analysis of each physical component was carried out by splitting it into its s-s, p-p, d-d, s-p, s-d and p-d constituents, with the purpose of evaluating the participation of the atomic orbitals in the bond. Although the d orbitals of iron atoms show very little overlap with the s atomic orbit& of the hydrogen atom, they do contribute significantly to bonding through electrostatic diatomic interaction.
INTRODUCTION
Ruedenberg [ 11 devised a method for partitioning the electron density and electronic energy of a molecule into components, based upon the concepts of promotion, quasi-classical interaction, shared penetration, shared interference, and charge transfer. Other authors [ 2-41 have applied energy partition techniques to CNDO and MIND0 methods. Fischer and Kollmar [5] found that diatomic two center terms can be interpreted as a measure of the bond strength between two atoms. Kollmar [ 61 has further employed energy partition schemes in ab initio SCF, CNDO and MIND0/3 methods, finding that the two-center energy terms are of the same order of magnitude in the three methods. More recently, Ruette et al. [ 71 have studied the two-center integrals to analyze the role of the d orbit& in the diffusion of hydrogen over a nickel surface, and Rodriguez et al. [8] have made a similar analysis of the nature of the bonding in iron, silicon, and iron silicide clusters, with MINDO/SR calculations. The UHF MINDO/SR method [ 91 is a modification of MIND0/3 [lo] for transition metals. It includes selective molecular orbital occupancies and symmetries [ 111. The MINDO/SR method leads to a very reasonable description
0166-1260/92/$05.06
0 1992 Elsevier Science Publishers B.V. All rights reserved.
of catalytic systems containing transition metal compounds [ 121. Nevertheless, the success of this method is largelydependentupon the procedureused in estimatingthe ground state molecular parameters.These parametersare fitted in order to obtain reasonableequilibriumbond distancesand bond energies for the diatomic moleculesof interest (X-Y bond), obtained from experimental or sophisticatedab initio results. This paper deals with the application of a more specific partitioningenergy technique to the semiempiricalMINDO/SR method, to study hydrogen activation and Fe-H interactions with single iron atoms Feq (q = + l,O,- 1) and with Fe14clusters.One of the advantagesof this methodologyis that the qualitative information obtained for bond strengthstakes into account both ionic and covalentcontributionsand it is independentof the referenceatomic states. THElORJ3TICALPROCEDURE
In the MINDO/SR method, the total energy expression for a system of N electronscan be broken into monoatomic and diatomic contributions [ 121
(1)
E t&d=p4+*phB
The diatomic electronicenergyterm (Ed) can be partitionedaccordingto the differenttype of interactions (n) em=CE&
=E&+EV,+EJa+Ef.&+E&
(2)
E & representsthe contribution of the resonanceintegralsto the energy of the A-B bond
E&3=2 C
pEAYE %
P,~BAB&JRAB
(A-=B)
(3)
Here, BABis an empirical parameter, S,,, is the overlap matrix, and RAB is internucleardistance between the atoms A and B. Pcv= Pzy + P$, is a density matrix element,where PFy = ~c~ic~i and P$” = Cc$cffi i
(4)
and where cFi is a coefficient that comes from the LCAO approach V=Cc~i$/4 P
(tl=W3
(5)
EJm is the repulsionenergybetween the electrons on atoms A and B, given by
the expression EL
=PAPBYAB
where
(6)
337
pA= zApw
and
&A
~~~=(ppluv)
and PeB)
(7)
EL is the attractive potential energy of the electrons on atom A by the B-core and vice versa EL=-PAVAB-PBVBA =
(8)
-PAZBhB-PBZAYhA
and zn are the core charges and yb differs from yABin that the Y orbital in eqn. (7) is the s orbital on B. In &A, fl is the s orbital on A. EL is the electronic exchange interaction of the electrons on atoms A and B given by
ZA
E&z-
ct )fi;A”;B( (P$
)2r,X+ (P&” )2%X)
(9)
where yeX= ( PV1wv) is the exchange integral. The expression for the nuclear repulsion energy between the cores A and B (EC) is E~=ZAZB[Y~+[(~/RAB)-Y~](YAB~-~~]
(10)
where LX- is another empirical parameter and yh is the Coulomb integral, considering only the s orbitals of A and B atoms. A more detailed analysis of diatomic energies can be performed taking into account the s-s, p-p, d-d, s-p, s-d and p-d components of the diatomic energy terms [8,11] E% =P;A V.BE~(~,v)
(A
(11)
EL (p,v) is the diatomic energy of Q-type as a function of their orbital components. Thus E!&(P,v)
=P,Y)BABS~vIR~~
EL(w)=
-p,,~B~:,(~,~)-p",~A~~A(~~v)
(12)
(13)
E~B(~,v)=P~~P,,YAB(~,~)
(14)
E%(W)
(15)
=
-(t)[(P~“)2y,,(~,y)+(P$Y)21/ex(H~)l
EL (p, v) represents the sum of the attractive energies between the electron p on atom A with the nucleus of B and vice versa, so we only consider the s-s, p-p and d-d attractive terms. The s-p, s-d, and d-p terms of the attractive energy are null in eqn. ( 13). This partition of the atomic orbital components permits us to discern the kind of interaction prevailing in the bond between two atoms and the role of the atomic orbitals (such as d orbitals) in the bond formation.
RESULTS AND DISCUSSION
Calculations for (FeH,)* (q=O,+ 1,-l) and Fe14H2systems were performed utilizingenergypartition per orbital, in order to evaluatethe hydrogen interactionwith one iron adsorption center. For ( FeHz )* (q= 0,+ 1,- 1) molecules, we only consider the side-bonded (Fe-(H,) ) geometry. The systems studiedare depicted in Fig. 1. Some of the most importantfeaturesin surfacereactionsarebond activation and bond formation (chemisorbed molecules). Therefore, for the above systems we first study the details of the H-H bond activation caused by Hz-Fe interactions,and secondly hydrogenchemisorptionby the formation of Fe-H bonds. The H-H components and the total electronic diatomic energies for Hz, (FeH2)* (q=O,+l,-l), and Fe14H2are shown in Table 1. The EL, EL, I&, EL and EL terms are denoted as AE, REE, EE, RE and RNN, respectively. A comparison of the total diatomic energy for the H-H bond in the isolated H2 molecule ( -0.4018 a.u.) with those in (FeH,)’ ( -0.3462 a.u.), ( FeHz)+ ( - 0.2999a.u. ), ( FeH2)- ( - 0.0631a.u. ) and Fe14H2( - 0.3272a.~. ) revealsthat only in the negativelycharged molecule is the H,H bond highly modified. (FeH, )Oexhibits a long Fe-H bond distance (2.01-A) and an H-H bond length (0.77 A) similarto that of the H2molecule (0.74 A). These values, taken with the fact that the H-H diatomic energyterm is close to that of the free H, molecule, indicate a weak iron-hydrogen interaction,typical of physiH-H \ / Fe
/
Y
(b)
Fig. 1. Geometry of the molecules studied (a) FeH2 with side-on geometry (b) Fe1,H2, H2 on atom 2.
TABLE 1 Diatomic energy partition into its physical components (a.u.) for the H-H bond of the Hz molecule and interacting with the [Felq (q=O,+ l,- 1) and Fell systems’ Energy type
Hz
[Fe&I0
[Fe&l+
[Fe& I-
F&-L
AEb REE” EEd RE” RNN’
- 0.7880 0.3940 -0.1970 -0.3115 0.5007
-0.7189 0.3316 -0.1655 - 0.2788 0.4854
-0.6812 0.2935 -0.1467 -0.2705 0.5050
- 1.0357 0.7155 - 0.0732 -0.1117 0.4420
-0.7026 0.3158 0.1567 - 0.2730 0.4893
Total
-0.4018
- 0.3462
- 0.2999
-0.0631
- 0.3272
“SeeFig. 1. bEL. “EL,. dEf&. “EL.
*EL,.
sorbed states. In Fei4H2, the H-H diatomic energy is slightly smaller than in the preceding case. Therefore, the cooperative effect of other atoms in the cluster in the activation of the H-H bond on one center site is small. Experimental evidence confirms the existence of physisorbed states which are precursors for dissociation [ 131 and several stable dihydrogen complexes with iron [ 141, such WI, WW2) U-U(&wMBPh4 [I61 and as [FeH(HA (dm=Ll+ [Fe(H),) (H,) (PEtPhz)3] [17] have been reported. In the ( FeHz) - molecule, the lower value of the H-H diatomic energy and the longer H-H bond distance (0.86 A) than in the diatomic molecule, suggest that H, has been activated by interaction with the negatively charged iron. If we assume that the electronic repulsion between electrons (REE), the electron-nucleus attraction ( AE ) and the nucleus-nucleus repulsion (RNN ) are electrostatic terms, and that the resonance energy (RE) and the exchange energy (EE) can be considered as covalent terms, we find that the covalent terms are responsible for the H-H activation. The change of the electrostatic terms in (FeH,) - compared to the same terms in Hz is quite small (0.0151 a.u. ) when compared to the correspondent change in the covalent terms (0.3236 a.u. ). This result is in agreement with the fact that the electronic transfer from Fe- to the H, (8) molecular orbital causes the H-H weakening. The values of the diatomic energy per orbital for the Fe-H bond in FeH, (FeH# (q = 0, + 1, - 1 ), Fe,,H and Fe14H2systems are shown in Table 2. The d-d and p-p terms correspond to the attractive energy between the Fe (d) and Fe(p) orbitals and the hydrogen nucleus. The s-s terms includes the electron attraction between the Fe (4s) electron density and the hydrogen nucleus, and between the H (1s) electron density and the iron nucleus. We can see that the total diatomic energies are a complicated combination of attractive and repulsive energies, with some important contribution from resonance energy. The covalent participation of the d orbitals in the Fe-H bond is indeed negligible, as can be seen from the small values for the resonance and exchange energies
340 TABLE 2 Partitioning of diatomic energy (in a.u. ) for the Fe-H bond in the orbital components Energy type
Component s-s
P-P
d-d
- 3.0359 0.1522 - 0.0741 -0.1891 -3.1469
-0.0803
- 2.0762
- 0.0803
- 2.0762
1.9369 0.2093 -0.0031 -0.0221 - 1.7528
- 0.0385
- 1.6609
- 0.0385
- 1.6609
1.6878 0.0273 -0.0136 - 0.0544 - 1.7285
- 0.0321
- 1.7242
REE EE RE Total [Fe&IAE REE EE RE Total
FeH AE REE EE RE Total
W&Jo m
-
RRE RE RR Total [Fe&
AE
I+
&Ji (H-&r, AE REE EE RE Total Fe& fw REE EE RE Total
-
1
(H&re(I,
-0.0321
- 1.7242
- 2.5451 0.2787 -0.0035 - 0.0188 - 2.2887
-0.0574
- 1.5126
- 0.0574
- 1.5126
- 3.0225 0.1825 -0.0387 -0.1219 -3.0006
-0.1364
- 1.9631
1 - 1.9157 0.1430 - 0.0048 - 0.0337 - 1.8112
-0.1364
- 1.9631
- 0.0963
- 1.7536
- 0.0963
- 1.7536
UThecore repulsion energy for Fe-H has been added.
S-P
s-d
Total
0.1023 -0.0507 -0.1918 - 0.1402
2.6441 - 0.0012 -0.0051 2.6378
-5.1925 2.8985 -0.1260 -0.3860 - 0.3666”
0.0355 -0.0125 -0.0669 -0.0439
1.5307 -0.0001 -0.0002 1.5304
- 3.6363 1.7756 -0.0157 - 0.0893 -0.0683’
0.0276 - 0.0138 -0.0756 -0.0618
1.4860 -0.0001 -0.0004 1.4855
-3.4441 1.5410 -0.0275 -0.1303 - 0.0871”
0.0794 -0.0179 -0.0641 - 0.0026
2.0899 0.0000 0.0000 2.0899
-4.1152 2.4479 -0.0214 -0.0829 - 0.05w
0.1810 -0.0539 -0.1845 -0.0574
2.6050 -0.0007 - 0.0029 2.6014
-5.1220 2.9685 - 0.0934 -0.3094 - 0.2730’
0.0866 -0.0149 -0.0811 -0.0094
1.5770 -0.0002 - 0.0005 1.5763
- 3.7655 1.8066 -0.0199 -0.1153 - 0.0830”
341 TABLE 3 Total electronic diatomic energy contribution per orbital (TE(j); j=s,p,d), core-core repulsion (RNN) and total diatomic energy (DE)” Molecule
TE(s)
TE(P)
m(d)
RNN
DE
FeH FeH, FeH,+ FeH,
-
-0.1078 - 0.0456 -0.0413 - 0.0578
0.1894 - 0.3083 -0.4014 0.2329
2.4394 1.8974 1.9738 1.7207
- 0.3666 - 0.0683 - 0.0871 -0.0509
2.8074 1.6118 1.6185 1.9465
“Values in a.u.
of the s-d terms, as shown in Table 2. The small participation of the d orbitals in the covalent terms, even for the chemisorbed bonds (Fe14H and FeH), is due to the overlap between the d orbitals of iron and the s orbital of hydrogen being very small. Nevertheless, two important energetic contributions of the d orbitals in the Fe-H bond; the attractive interaction between the d orbitals of iron and the H nucleus, and the s-d repulsive term, are present in Table 2. In order to estimate the specific contribution to the diatomic energy of a particular orbital, we follow the same procedure used in ref. 8. The total diatomic energy contribution (TE (_j)) of the j orbital is based on the relative weight given by the orbital occupation TE (s ) = TE,_, + cu,_,TE,_, + CX,_~TE~_~ TE (p ) = Tl&
+ c+~TE,_, + CY~-~TE,-,-~
TE (d ) = TEd-d + q_sTEs_d + cu~_PTEp_~ with cyi_k=nj/ (nj+ nk) (nj is the j orbital population). The results for FeH, (FeH,)q (q=O, + 1, - 1) shown in Table 3 indicate that the most important contribution to the Fe-H bond comes from the s orbitals, with some participation (attractive or repulsive) of the d orbitals. These d terms, in spite of their smc!l values, can be important in the stabilization of the side-on system because of the small values of the total diatomic energy. For example, in neutral (FeH,)O and in positively charged (FeH,) + molecules, the d orbit& play a stabilizing role. In contrast, however, in Fe-H and (FeH,) - molecules, the d electron effect is in the opposite direction. Therefore, the d electrons can be of fundamental importance in the formation of an Fe-H bond, because they generate a net electrostatic interaction that is a balance between electron-core attraction and electron-electron repulsion.
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