5097
J. Phys. Chem. 1991,95, 5097-5103
Electronlc and Oeometrlc Structures of Varlous Products of the Sc+
+ H20Reaction
J. L. Tilson and J. F. Harrison* Department of Chemistry, Michigan State University, East Lansing, Michigan 48824- I322 (Received: October 18. 1990) The products of the Sc+ + H 2 0 reaction were investigated by constructing ab initio multiconfiguration self-consistent-field (MCSCF) and configuration interaction (MCSCF+l+2) wave functions for three states of +ScO, two states of +%OH and the ground states of H2-+Sc0 and H - W H . All geometries were optimized and a Mulliken population analysis was performed for each system. The two reaction products, H2.-+Sc0 and H-+ScOH, are nearly degenerate (Al? = 5 kcallmol) and are both the result of an exoergic reaction. The H2-+Sc0 product is the ground-state +ScO molecule electrostatically bound to H2and is 35 kcallmol below the reactants, The insertion product, H-+ScOH, assumes a cis conformation and is 40 kcallmol below the reactants.
Introduction We are interested in characterizing possible products of the gas-phase reaction of the monopositive ions of the early transition metals with H20. In this study we focus on the simplest of these ions, Sc+, and report the results of ab initio electronic structure calculations on the systems +ScO, +ScOH, the insertion product H-+%-OH, and the complex H2-.+Sc0. These results are compared with experiment and previous calculations on the complex Sc+-0H2. The basis set used, molecular codes, and other technical details are collected in the Appendix. Experimental Results There has been extensive experimental and theoretical work on the reactions of transition-metal ions with small ligands. Pertinent to this work are the +MO (M = Sc, Ti, etc.) bond strengths' (in particular +ScO Do = 159 f 7 kcal/mol) and the several experimental +M-OH and +MO-H (M = Sc, Ti, V, Cr, etc.) bond strengths.2 Recent results indicate a +Sc-OH bond strength of 87.8 kcal/mol and further suggests the reaction of Sc+ with H 2 0 yields the products Sc+-.H20 with an interaction energy (Do) of 31.4 kcal/moL3 +ScOGeneral Considerations. If the two valence electrons on Sc+ form two bonds with the two unpaired electrons in the ground state of 0, the resulting molecule is a singlet of ll symmetry and is represented by the Lewis structure +
"
SC=O
5'
Po*pl
P, orientation
.A&= T-
4s
L z
PY
OR 2' orientation
The local symmetry of 0 in the first approach is II and in the second,E-. If 0 is in the II orientation, Sc+must also be locally II and this may be accomplished by using either the ground 4s3d configuration (4s3drx or 4s3dxJ or the low-lying 3d2configuration ( I ) (a) Murad, E. J. J. Geophys. Res. 1978, 83, 5525. (b) Kang, H.; Beauchamp, J. L. 1. Am. Chem. Soc. 1986. 108, 5663. (c) Aristov, N.; Armentrout, P. E. J. Am. Chem. Soc. 1984, 106,4065. (2) (a) Murad, E. J . Chem. Phys. 1980, 73, 1381. (b) Kang, H.; Beauchamp, J. L. J . Am. Chem. Soc. 1986,108,7502. (c) Cassady, C. J.; Freiser, 9. S.J . Am. Chem. Soc. 1984,106, 6176. (3) Magnera, T. F.;David, D. E.; Michl, J. J . Am. Chem. Soc. 1989, I l l , 4100.
0022-3654191/2095-5091S02.50/0
u
where one of the u bonds results from the singlet coupling of the Sc d r and 0 2pr and the second r bond is a dative bond formed from the lone pair in the 2 p r orbital on 0 and the empty dx on Sc. In the calculations the A bonds are of course equivalent. The Sc u electron is asymptotically either a 4s or 3da. If, however, 0 is in the Z-orientation, Sc+ must also be locally Z-.This may be achieved by using the d2 configuration, in particular dr, d r y This results in the Lewis structure
where the u electrons are formally from 0. Clearly the equilibrium structure will be a mixture of the two Lewis structures. MCSCF Results. The character of both Lewis structures may be incorporated into a three-pair generalized valence bond4 (GVB) wave function of the form $
where we suppress the explicit representation of the 0 2s electrons. The ground-state oxygen atom may approach the Sc+ in either of two orientations, according to whether the oxygen 2pa orbital is singly or doubly occupied.
n
(3du3drx or 3du3dxy). These options result in the Lewis structure
-
(c0re)~(8u~ - X9$)(3x? - u4x?)(3r;
- v4~,2)
An MCSCF function of this form which includes all possible spin couplings consists of 37 configuration state functions (CSFs). The energy predicted by this function is shown in Figure 1 as a function of Sc-0 separation. This function predicts an equilibrium separation of 3.095 au and a dissociation energy, De of 134 kcal/mol. Also shown in Figure 1 are various low-lying triplet states. The 3Pstate obtains by triplet coupling the u-bonding electrons in the 'Z+state. The d6+ symmetry orbitals were eliminated from the 3Z+calculation to prevent collapsing to the 6+ component of the lower energy 3A state. This forces dissociation to the higher energy asymptote seen in Figures 1 and 2. One of the tripletcoupled electrons becomes localized on Sc in an orbital of 3du symmetry with some 4s character while the companion electron settles into an oxygen 2pu orbital. The bond length in this state is longer than in the lZ+state (3.454 au versus 3.095 au) and the molecule contains two equivalent r bonds and no u bond. This molecular state should dissociate to the ground' 3D state of Sc+ and the ground5 'P state of 0 and its De relative to this asymptote (4) (a) Goddard, 111, W. A.; Dunning, Jr., T. H.; Hunt, W. J.; Hay, P. J. Ace. Chem. Res. 1973,6, 368. (b) Goddard, 111, W. A.; Harding, L. 9. Annu. Rev. Phys. Chem. 1978,29, 363. (5) Moore, C. E. Nad. Stand. Re! Data Ser., Narl. Bur. Stand. No. 35.
0 1991 American Chemical Society
5098 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
V,,,,,au MCSCF MCSCF+I+2 MCSCF -834.56442 -834.63270 3.0953 -834.43800 -834.50591 3.5008 -834.41312 -834.47419 3.4537
state '2+
'A 32+ '2+ *Z+(SCO)
Tilson and Harrison we, cm-I
re, au
MCSCF+ 1+2 MCSCF 3.1196 1067 743 3.4941 3.4361 592 3.153'
De, kcal/mol
MCSCF+ 1+2 MCSCF 1134 134.2 734 54.8 622 39.2
MCSCF+1+2 146.0 66.4 46.5 159 h l b 162 h 3b
965'
'Experimental value, from ref 27. bExperimentalvalue, from ref la. ScO+ MCSCF Potential Energy
100,
so:
:;i; 1;
,
,
,
,
,
,
50
60
70
8.0
90
'OC
ScO+ MCSCF+1+2
Potential Energy
-180
-200 - .
2.0
-220 20
30
40
r(Sc-0)au
Figure 1. MCSCF potential energies of the XIZt, 3A, and 'Et states of +ScO relative to the ground-state asymptote. Energy is in millihartrees, where I mhartree equals 0.6275 kcal/mol. The atomic structures at the asymptotes are indicated on the plot by both atomic symmetry and valence configuration.
is 39 kcal/mol. If we imagine forming this state from the asymptotic ground-state fragments we must triplet couple the spatially extensive Sc 4s and the 0 2pu electrons and singlet couple the Sc 3da and singly occupied 0 2pa orbital. At large Sc-0 separations the * , A bond would be very weak and the repulsive triplet coupling ion the u system dominant. Consequently we anticipate that this state would be repulsive at large separations and would have to overcome a barrier to obtain the electronic structure we see at equilibrium. This equilibrium structure obtains when this repulsive curve intersects the attractive SF curve which 3du) 0-(2P;2pu) asymptote. The separates to the Sc2+(2D; second triplet is of 'A symmetry and is obtained from the %+by moving the unpaired u electron on Sc into a d orbital. Both of these states have A,A bonds and no u bond. Exciting an unpaired electron from the u orbital on Sc to its 6- orbital puts more electron density on Sc in the a region and weakens the a,a bonds. This results in the bond length increasing to 3.50 au as compared to 3.45 au in the state. This u to 6- excitation also reduces the repulsion between the unpaired electron on Sc and the 0 2pu electron. That the total energy of the state drops by 15 kcal/mol relative to the 3Z+state suggests the reduced repulsion more than compensates for the slight reduction in the r,a bond strength. The absolute energies ( Vmin),dissociation energies (De),bond lengths (re),and vibrational frequencies (we) are collected in Table I. Configuration Interaction Results. The three states of +ScO described above were also studied by using multireference configuration interaction (CI) techniques. For each state we constructed a C1 wave function containing all single and double substitutions from the MCSCF configuration space. For example,
+
5.0
4'0
5:O
610
7:O
El0
9j0
ld.0
r(Sc-0)au
Figure 2. MCSCF+I+2 potential energies of the XIZt, 'A, and 'Z+ states of +ScO relative to the ground-state asymptote. Energy is in mhartrees, where 1 mhartree equals 0.6275 kcal/mol. The atomic structures at the asymptote are indicated on the plot by both atomic symmetry and valence configuration. for the state, the MCSCF space consisted of 37 CSF's and all singles and doubles from the space, with symmetry results in 23 990 CSF's. Several experiments were performed to test the adequacy of this procedure. In the first we added an additional active u orbital to the MCSCF space and generated 81 CSF's. All singles and doubles from this reference space resulted in 40996 CSF's. These additional configurations lowered the total energy of the lZ+ state by 10 mhartrees at the MCSCF levels and 1 mhartree at the MCSCF+I+2 level but had no appreciable effect on re or De. In the second we examined the necessity of including the 0 2s orbital to the MCSCF (CI) active space. The 0 2s orbital was added to the MCSCF active space (generating 81 CSF's) followed by all valence single and double substitutionsand resulted in 99 463 CSF's. We also constructed a CI function by allowing all valence single and double substitutions (including the 0 2s) from the 37 CSF MCSCF reference space. This resulted in 76 659 CSF's. The total CI energy dropped by 60 m H for each function while the computed De remained essentially the same at 145.9 and 144.7 kcal/mol, respectively. We conclude from these experiments that excitations from the 0 2s orbital are not important in determining the relative energy and re of the low-lying states of +ScO. Potential curves at the MCSCF+ 1 +2 (23 900 CSFs) level are presented in Figure 2 and the calculated re, De and w,(s are collected in Table 1. Electron Distribution. Included in Table I1 are the valence orbital populations6 predicted by the MCSCF function for various states of +ScO. Note that in the IZ+state there is very little Sc (6)Mulliken, R. S.J . Chem. Phys. 1955, 23, 1833. 1841,2338. 2743, 3428. For a critique see: Noell,J. 0.Inorg. Chem. 1982, 21, 11.
Structures of Products of the Sc+
+ H 2 0 Reaction
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5099
TABLE II: Valence MCSCF Orbital Populations at Equilibrium
sc+
0
state +ScO(X'Z+) +ScO()A) +SCOi)Zi)
4s 0.02 0.02 0.40
4p0 0.19 0.09 0.07
4px 0.05 0.04 0.04
4pu 0.05 0.04 0.04
3do 0.55 0.07 0.67
3dr, 0.43 0.16 0.19
3dry 0.43 0.16 0.19
+ScOH(X'P) +SCOH(~Z+)
0.03 0.48
0.10 0.08
0.03 0.03
0.03 0.03
0.10 0.61
0.12 0.16
0.12 0.16
H-+ScOH('A)
0.34
0.23
0.14
0.03
0.13
0.43
0.18
HZ*ScO('AI)
0.03
0.04
0.05
0.19
0.56
0.43
0.44
TABLE III: MCSCF Net Atomic Charges net atomic charge system state Sc 0 H(Sc) +sco (XIZ+) +1.28 -0.28 ()A) +1.42 -0.42 +sco ()E+) +1.40 -0.40 +sco +1.41 -0.77 (X2A) +ScOH (?2+) +1.45 -0.78 %OH +1.42 -0.75 -0.02 ('A) H-+ScOH €4 2 (s s) H,+ScO (IA,) +1.26 -0.34 +0.08
*
3db
2s 1.80 1.88 1.90
2pu 1.44 0.94 0.96
1.52 1.80 1.77
2p, 1.52 1.80 1.77
1.00
1.74 1.76
1.37 1.42
1.83 1.80
1.83 1.80
0.10
1.76
1.43
1.78
1.78
1.02
1.81
1.47
1.53
1.53
H2(S*S) 1.92
1.00
2p,
H(Sc)
H(O)
0.64 0.67 0.65
H(0)
?:
+0.36 +0.33 +0.35
@j!iJ) :
4s character and the Sc+ ion has lost electrons to neutral 0. The charge distribution may be rationalized by imagining the in situ Sc+ ion in the d7r,drY configuration interacting with the 0 atom in the 2pa227r,27ry configuration. Oxygen first donates charge to the empty 3da on Sc+ via the dative interaction of the doubly occupied 0 2p. As charge leaves 0 in the u system it returns in the 7r system.
While the total charge on the Sc+ ion in the 'I: state is similar to that in the IZ+ state (+1.40 vs +1.28) the distribution of electrons is very different. In particular, in the 'E+ state there is a large 4s component and a significantly reduced 3d7r occupation. We can rationalize this by noting that the 'I:+ may be formed from the 'E+ by triplet coupling the a-bonding electrons. This localizes one electron in a orbitals on Sc and the other in a 2pa on 0. As a result of this transfer the oxygen atom becomes more positive and attracts electrons into the 2pr orbitals, considerably reducing the Sc 3d7r occupation. The choice Sc has to make is the relative amount of 4s and 3da character to allot to its unpaired electron. If the in situ character of Sc was Sc2+we would expect the unpaired electron to be primarily 3 d ~ The .~ observed 40% 4s, 60% 3da reflects the intermediacy of the Sc charge (greater than +1 but less than +2). The electron distribution in the 'A can be understood by noting that the 'A is formed from the 'E+ by exciting the unpaired a electron to a d orbital, precluding any 4s character. The electron distribution in the I F and 'Z+states is so different that it is easily seen at the total density level. Figure 3 shows the total electron density contoured in a plane containing both nuclei for these two states. +%OH. The hydroxide can be formed by adding a H atom to +ScO. Both the 'A and 'E+ states have an unpaired 2p electron on oxygen and singlet coupling the H 1s to the oxygen electron
e -
J
B -
w
lam
sm 2
5m
axis
,OW
ZOXb
Figure 3. MCSCF total density contours (TDC's) and difference density contours (DDC's) for the lE+,)A, and 'E+ states of +ScO. The DDC's are molecular differences where the indicated triplet state is subtracted from the ground 'E+state. The triplets are at the equilibrium geometry. The contour level ranges are from 0.0025e to 1.28e (TDC's) and -0.04e to +O.O4e (DDC's).Each level differs by a factor of 2. No zero contour is displayed and negative contours are indicated by a dashed line.
results in the linear 2A and 2E+states of +ScOH. The two states have the Lewis structure
("r
d 8 or d,
+ 14
FH
in which the unpaired electron is localized on Sc in either a d6 (2A)or u orbital of mixed du and 4s character (*2+).MCSCF
TABLE IV: +%OH Luillbrium Enemies (au). huilibrium Bond Lengths (au). and Dissociation Energies (kcal/mol) enerw MCSCF MCSCF+I+2 state MCSCF MCSCF+1+2 r,(Sc-O) D,(Sc-O) r,(O-H) D,(*H) r,(Sc-O) D,(Sc-O) r,(O-H) 'A -835.15522 -835.22690 3.509 101.8 57.4 (136.7)" 3.505 108.0 1.848 1.821 2E+ -835.135 83 -835.19948 3.505 89.7 1.829 45.3 (140.2jb 3.481 90.8 1.836 I .
'Values in parentheses are for separation to ScO+()A) + H. *Values in parentheses are for separation to ScO+('E+)
+ H.
De@-H) 59.6 (139.2)' 42.4 ( I 59.0)*
Tilson and Harrison
5100 The Journal of Physical Chemistry. Vol. 95, No. 13, 1991 'ScOH '2'
-"
200
1
1
IOD
,
x
'SCO
I
Znxls
lz*
,
-
150
h
P .,A .. 3 :m
2
c
100
P
e,
so
0
'SCOH('A)
Figure 5. MCSCF+1+2 relative energies (kcal/mol) (numbers in parentheses are experimental values).
I rm
tm
z axb
1
t
am
nm
-,
1 axb
Figure 4. MCSCF total density contours (TDC's) and difference density contours (DDC's) for the 22+state of + W Hgeometry and the '2+and ?Zt states of +ScO geometry. The DDC's are molecular differences where the +ScO states are subtracted from the %OH density. The 'ScO states are at the %OH (Sc-0) geometry. The contour level ranges are from 0.0025e to 1.28e (TDC's) and -0.04e to +0.04e (DDC's). Each level differs by a factor of 2. No zero contour is displayed and negative contours are indicated by a dashed line.
functions which correlate the three bonds and allow all spin couplings, consist of 76 C S F s in C, symmetry for each molecular state. We optimized the ScO and OH bond lengths as well as the Sc-0-H angle at the MCSCF and MCSCF+1+2 levels. Both electronic states are linear and the total energy, bond lengths, and various dissociation energies are collected in Table IV. The electron populations in the valence orbitals and the charges on each atom are collected in Tables I1 and 111. The zA state of +ScOH is calculated to be 17.2 kcal/mol lower than the zZ+ state which is very similar to the corresponding 3A-3t;+ separation of 19.9 kcal/mol for +ScO (both calculated at the MCSCF+I +2 level of theory). As we see from Table 11, the H atom has little effect on the charge distribution on Sc and in particular on the character of the unpaired electron. Figure 4 shows the electron density in the W state of +%OH minus the density in the 3Z+and 'Z+states of +ScO. The +%OH (2Z+) - +ScO('E+)difference density illustrates the negligible effect bonding of H to 0 has on the character of the Sc nonbonding electron. The difference density is very similar to that of +ScO('Z+)-+ScO('Z+) (Figure 3) and results from a similar mixing of du and 4s orbitals. The +ScOH(22+)-+ScO(3Z+)density shows little difference in the scandium structure, in situ, and indicates that slightly more Sc-0 u density is present in the hydroxide. The relative energies of +ScOand +ScOH are shown in Figure 5 . Experimental values (corrected for zero-point energy) are shown in parentheses. Our calculated bond energy for free OH is 97.6 kcal/mol, approximately 10% lower than the experimental De of 106.8 kcal/moL7 We have two options for the OH bond (7) CRC Handbook of Chemistry and Physics, 63rd ed.;Weast, R. C., Ed.;CRC Press: Boca Raton, FL, 1982.
-
34
Sc+('D)+&O --.--*Products 214.7
117.1 Sc'(3D)+OH+H.
s; ('D)+o+H,
101.1 H:ScO.( t')+H.
68.7 'ScO ('Z*)+ZH.
Figure 6. MCSCF+l+2 relative energies for the reaction Sct
+ H20.
strength in +SCOH(~A).First, we may break the OH bond along the A potential curve +SCOH(~A) +SCO(~A) H(%)
-
+
which requires 139.2 kcal/mol, significantly larger than the free OH value. This enhanced OH bond strength obtains because the Sc-0 and 0-H bonds are strongly coupled in %cOH(~A). When H bonds to the unpaired 2pu electron in +SCO(~A)the 0 2s and 2pu hybridize, simultaneously strengthening the OH bond and forming a dative bond in the empty u space of Sc using the companion to the 0-H bond hybrid. This symbiosis also manifests itself in a stronger than expected Sc-0 bond strength in +ScOH. From Figure 5 we see that the Sc-0 bond strength in %OH is 108 kcal/mol, intermediate between the strength of a +SCO(~A) double bond (66.4 kcal/mol) and the +Sd3('Z+) triple bond (146.0 kcal/mol). Our computed + W H bond strength (108 kcal/mol) is significantly higher than that reported3 by Michl et al. (87.8 kcal/mol). The second option for the OH bond strength is the thermodynamically lowest path +SCOH(~A) +SCO(IZ+)+ ~ ( 2 s )
-
Structures of Products of the Sc+
TABLE V Ha%
+ H 2 0 Reaction
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5101
and H-+ScOH Equilibrium Energies (au), Bond Lengths (au), and Angles (deg) A1
'A
H
H
I ,,,,,sc+=o
enerw re(H ~ H rAH2-W r.(SC-O)a
MCSCF
MCSCF+1+2
-835.1 1153 1.4603 5.2020 3.1
-8 35 39614 1.4422 5.1164 3.1
'\
'3-L-NH
H
energy re(H-Sc) re(Sc-0) rS0-H)
B
a
MCSCF
MCSCF+I+2
-835.12224 3.5320 3.4414 1.8486 117.4 162.1
-835.80464 3.4985 3.4335 1.8402 112.6 161.0
'Constraint. Minimum occurs between 3.2 and 3.0 au. which requires 59.6 kcal/mol. This is much lower than the free O H bond strength, reflecting the differentially stronger ScO bond in +ScO(l2+) compared to +SCOH(~A). H-+ScO. If we bond to the unpaired electron on Sc in the 3A or 3Z+ states of +ScO we form H-+ScO(*P). The Sc-H bond strength, relative to the 3A state of +ScO, is calculated to be 47.2 kcal/mol (MCSCF+l+2 level), a typical9 Sc-H bond strength. +ScOH2. There are three isomers with this empirical formula: the two electrostatic complexes Sc+--OH2 (triplet) and H2-.+Sc0 (singlet) and the insertion product H-+Sc-OH (singlet) The electrostatic complex involving intact H 2 0 was studied by Bauschlicher et ale8 The Sc+-OH2 complex is bound, relative to the ground-state products, by 36.2 kcal/mol with a Sc+ to OH2 distance of 4.296 au. The H 2 0 was constrained to the S C F geometry. We will focus on the two remaining isomers. Consider first the electrostatic complex involving intact H2. It is easily seen that this will be an exothermic product of the reaction of Sc+with H20. It requires 219 kcal/mol to dissociate H 2 0 into its atoms' and we regain 103 kcal/mol when H2is formed' and 159 f 7 kcal/mol when +ScO('Z+) is f0rmed.l AE for the reaction S C + ( ~ D+) H20('AI) +ScO('Z+) + H 2 ( l P g )
-
is at least 36 kcal/mol exothermic. Detailed calculation at the MCSCF and GVB+ 1+2 level result in the energies collected in Tables V and VI. Our explicitly calculated AE for the above reaction is 32.6 kcal/moLat the GVB+l+2 level. The electrostatic complex is bound by an additional 2.5 kcal/mol, making our calculated AE = -35.1 kcal/mol for the reaction Sc+('D) H20(IAI) H~.**+SCO('AI)
+
-
The insertion product may be formed from either the 2A or 2Z+ states of %OH by coupling the second H atom to the unpaired electron on Sc. The resulting molecule has four formal electron pairs (a Sc-H, 0-H, and two Sc-0 bonding pairs) and an MCSCF function which correlates each (in the left-right GVB sense) and includes all spin couplings consists of 150 CSF's. The bond lengths and bond angles for the planar structure were optimized and the results are shown in Table V. Also listed is the optimal geometry and associated energy obtained from a CI wave function which includes all single and double excitation relative to an eight configuration (four pair) GVB function (which generates 112088 C S F s of 'A symmetry). The single-particle bases for this CI were the natural orbitals from the MCSCF function. This calculation places the insertion product -5 kcal/mol lower than the electrostatic complex. The errors in these calculations increase in the order SC+...OH~ < H~**.+SCO < H-+Sc-OH (8) (a) Rosi, M.; Bauschlicher, Jr. C. W.J . Chem. Phys. 1990,92, 1876. (b) Rosi, M.; Bauschlicher, Jr. C. W. J . Chem. Phys. 1989, 90, 7264. (9) Alvarado-Swaisgood,A. E.; Harrison, J. F. J . Phys. Chem. 1985.89,
5198.
TABLE V1: Dissociation Energies (Dekcal/mol) H'ScOH HtScOH H'ScOH HZtScO HZtScO ?%OH2
--
Sc+('D) + H20(IAI) H(2S) ?SCOH(~A) H(2S) H+SCO(~Z+)
-------
+ + Sct('D) + H20('A,) H2(12:) + +ScO(lZ+) Sc+('D)
DJMCSCF)
D,(CI)
31.4 42.5 136.7
40.1 50.5 141.2
28.5 3.10
+ H20(IAI)'
35.1 2.50 36.2
+SCOH(~A) +ScO('A) + H@) + s ~ o H ( ~ A )+sc0(32+) ~ ( 2 s ) +SCOH(~A) Sc+('D) OH(Zll) +SCOH(~A) +Sc0(lZt) H(*S)
+ + + +s~oH(*z+) +sc0(32+)+ ~(2s) +SCOH(~Z+) +ScO('A) + H@) +SCOH(~Z+) Sc+('D) + OH(*II) + S C O H ( ~ ~ ' ) +ScO('Z+) + H(%) HtScO(*Zt) +ScO('A) + H(%) H+s~o(~z+)+ S ~ O ( ~ Z++ )~ ( 2 s )
136.8 152.4 101.8 57.4
139.1 159.1 108.0 59.6
140.2 124.6 89.7 45.3
141.8 121.9 90.8 42.4
42.6 58.2
47.2 67.1
@Reference8. and improved calculations should favor the insertion product, suggesting that it is the global ground state. The charges on the various atoms predicted by the MCSCF function are shown in Table 111. Comparing the atomic charges in the insertion product with the charge on the +%OH fragment shows that, overall, the additional H atom bonded to Sc has little effect on the global charge distribution. Comparing the orbital populations shows the total d population on Sc is 0.93 in +ScOH(*Z+)and 0.77 in H-+ScOH. The Sc-H bond length is 3.50 au and the bond energy is calculated to be 50 kcal/mol H-+SC-OH ~ ( 2 s ) +SC-OH(~A) AE = 50.5 kcal/ mol
-
+
which is remarkably similar to the 3.52 au and 50.7 kcal/mol calculated by Alvarado-Swaisgood and Harrison9 for +SCH(~A). The computed AE for removing the 0-H hydrogen H-+%-OH H-+Sc-O H AE = 141 kcal/mol
-
+
is 141 kcal/mol, virtually the same as that computed for +SCOH(~A) +SCO(~A)+ H(2S) AE = 139 kcal/mol
+
Comparison with the Sc+ NH3 System. It is interesting to compare these results with those reported recently for the Sc++ NH3 system.'O The ground state of +ScN is of 2Z+symmetry and has a calculated bond energy ( D e ) of 63.1 kcal/mol. The molecule has two K bonds and no u bond. Its Lewis structure is
I".f-
'Sc-N
Po
Ln (IO) Mavridis, A.; Kunze, K.;Harrison, J. F.: Allison, J. In Bonding Energetics in Organometallic Compounds; Marks, T. J., Ed.; ACS Symposium Series 428; American Chemical Society: Washington, DC, 1990; Chapter 18.
5102 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 When a H atom bonds to the N atom, its 2s and 2pu orbitals hybridize, one component reaching out to bond the H atom while the companion component forms a dative bond in the empty valence u space of Sc.
1, The resulting %NH bond is calculated to be 106 kcal/mol, some 43 kcal/mol stronger than the Sc-N bond in +ScN. The ground state of +ScO('Z+) has a triple bond
with no unpaired electron in 0. However, the 3A state is a A,* state, similar to +ScN, except that it has been formed formally from a dative interaction in the A system
where we show both A bonds as being equivalent, of course. When a H atom approaches the 0, it will also hybridize its 2s and 2pu orbitals forming a covalent bond to H and a second dative bond (in the u system) to Sc. .+SEOH
OR
.+Sc=OH
6 J
The Sc-0 bond strength in this molecule is calculated to be 109 kcal/mol, 43 kcal/mol more than in +SCO(~A)and essentially the same as the Sc-N bond strength in +ScNH. It is interesting that the u dative interaction has stabilized both the Sc-0 and Sc-N bonds to the same extent, 43 kcal/mol. This suggests that the M-L bond energies in the pairs
Tilson and Harrison TABLE VII: Total Frameat Enemies - (ad fragment V,,,i,(MCSCF) Sc+('D(4s13d')) -759.52848 S~+('B~(3dd3d8~)) -159.485 16 S~~+(~D(3dl)) -159.081 87 -14.822 54 O(W -0.499 28 H('S) OH(211) -75.464 83 HzWIAI) -76.14408 HZ(IZ:(~~/~P)) -1.148 13
V,,,i,(MCSCF+ 1+2) -759.52906 -159.485 16 -14.871 00 -15.525 13 -76.21 1 73 -1.166 52
bond strength of 107 kcal/mol. Since the Sc-H bond energy is similar in both systems (46 kcal/mol in H-+ScNH2 and 47 kcal/mol in H-+Sc-OH), the insertion product in H-+Sc-NH2 lies -24 kcal/mol above the electrostatic complex while in H-+ScOH it lies at least 3 kcal/mol below the Sc+-.H20 complex. Conclusions The electronic and geometric structure of all possible products of the reaction of Sc+ with H 2 0 have been studied. We find the following: 1. The ground state of +ScO is of IZ+symmetry. Our computed Do of 144.4 kcal/mol compares favorably with the experimental value of 159 f 7 kcal/mol. 2. A major factor contributing to the strength of the ScO bond is the dative bond formed between the 2pu electron pair on 0 and the empty u valence orbitals on Sc. This suggests that the ground while +VOwill state of +Ti0 will be of 2A symmetry ('+Ti*) be a 3Z-(:+V=O) (as observed)." When the metal valence u orbitals are not empty the u dative structure will compete with a structure having a singlet-coupled oxygen-metal u bond and a dative bond in the A system. In +CrO for example, the u dative structure
-U is of 4Z- symmetry, while the electron pair structure
u
singlet-coupled oxygen-metal
dx
and 6
n e'
o-:
"J
-LJ
6 . 1
+V=OH (42-)
+ V g N H (32')
and
s*
3
will be similar. Indeed, Armentrout et al." have determined Do for the +V-L pairs and finds 100 kcal/mol for +V-OH and 102 kcal/mol for +V-NH. Since these two bond strengths are similar, the unpaired u electron in +VOH must not interfere with the u dative bond. It would be very interesting to know the detailed atomic orbital composition of this electron. Finally, the +Ti-L bond strengths were previously found to be essentially the same with +TiOH Do = 113 kcal/mol and +TiNH Do = 111 kcal/ m01.3~2 Another consequence of the strong Sc-OH bond is that the calculated global minimum in the Sc+ + H 2 0system is the insertion product H-+Sc-OH while the calculated global minimum in the Sc+ + NH3 system is the electrostatic complex +Sc...NH3. This situation obtains because the +ScNH2 bond strength is calculated to be 78 kcal/mol substantially smaller than the +ScOH ( I 1) Armentrout, P. B. In Bonding Energetics in Organometallic Comp o ~ ? ~Marks,,T. ; J., Ed.; ACS Symposium Series 428; American Chemical Society: Washington, DC. 1990 Chanter 2. (la ClemmecD. E.; Sunderlin, L. S.;Armentrout, P. B. J . Phys. Chem. 1990, 94, 3008.
is of 411symmetry.14 We calculate that these two states are separated by only 7 kcal/mol and that the lower, the 411,has a calculated bond energy of 57 kcal/mol. This is significantly less than the triply bonded +ScO('Z+) but comparable to the doubly bonded +SCO(~A). 3. The ScO bond in +ScOH is 108 kcal/mol or 43 kcal/mol stronger than the bond in +SCO(~A).This is due, primarily, to the dative interaction with Sc of the 0 2s,2pu hybrid induced on 0 when bonded to H. This is in substantial disagreement with the recent3 experimental value of 88 kcal/mol. 4. We calculate three exothermic products of the reaction of Sc+ + H20: the ion-dipole complex Sc+--H20, the oxide-H2 complex H2-+Sc0, and the insertion product, H-+Sc-OH. The oxide product is a consequence of the very strong bond in +ScO( I F ) which is due, in large measure, to the 0 lone pair forming a dative bond to Sc. The oxide will not be nearly so exothermic with any other first-row transition element. The insertion product is calculated to be the global ground state, although by only 3 kcal/mol. The stability of this product is due, in large measure, to a dative bond between the 0 2s,2pu hybrid on O H and Sc. As (13) Dyke,J. M.; Gravenor, B. W. J.; Hastings. M. P.; Moms, A. J. Phys. Chem. 1985,89,4613. (14) Harrison, J. F. J . Phys. Chem. 1986, 90, 3313.
Structures of Products of the Sc+
+ H 2 0 Reaction
TABLE VIII: Mwocirtion Energies (kcrrl/mol)
- + --
OH(’II) O(’P) H(%) H2O(’AI) OH(’P) + H(’S) H20(IAI) O’P + 2H(%) H2(’2:(3~/3~)) 2H(’S) +
MCSCF MCSCF+1+2 (DelDo) (DelDo) exPtla 97.6192.2 401.4’ 89.1184.5 117.2 118’ 112.9 214.7 219.4’ 202.7 103.3’ 93.8181.7 105.4199.3
Reference 7.
this bond strength is decreased, the exothermicity of the insertion product will decrease.
Acknowledgment. We are indebted to the Argonne National Laboratory Theoretical Chemistry Group for providing the QUEST-164 electronic structure codes used in this study. This work was supported in part by the National Science Foundation (Grant CHE85 19752). Appendix: General Computational Details 1. Basis Sets and Molecular Codes. The scandium basis set used in this study consists of the (14s,9p,5d) basis from WachtersI5 augmented with two diffuse p functions (Dunning)I6and a diffuse d function as recommended by Hay.” This set was contracted to (5s,4p,3d) following Raffenetti.I8 The oxygen basis was the (1 ls,7p) set from DuijneveldtI9 augmented with a single diffuse d (exp = 0.85) function and contracted to (4s,3p,l d) following Raffenetti.I8 Two basis sets were used for the hydrogen atom. The first consists of the Huzinaga20 (4s) augmented with a single p (exp = 1.00) function and contracted to (2s,lp). This was the set chosen for the +ScOH and H-+ScOH calculations. The second basis set consists of the above 4s basis augmented with a single s (exp = 0.03) function and 3 p (exp = 1.00,0.33,0.11) functions. This set was contracted to (3s,3p) and used in the H2-+Sc0 calculations. This basis was previously shown to adequately represent the polarizability of the H2 All ab initio calculations were done on a FPS-164 jointly supported by the Michigan State University Chemistry Department and the Office of the Provost by using the Argonne National Laboratory collection of QUEST-164 codes. The integrals were calculated by using the program ARGOS written by PitzecZ2the (IS) Wachters, A. J. H. J . Chem. Phys. 1970.52. 1033. (16) Dunning, Jr. T. H. Private communication. (17) Hay, P. J. J . Chem. Phys. 1977,66,4377. (18) Raffenetti. R. C. J . Chem. Phys. 1973, 58, 4452. (1 9) Duijneveldt, F. B. IBM Tcchnical Rcsearch Report No. RJ-945; IBM Research Laboratory, San Jose, CA, 1971. (20) Huzinaga, S. Approximate Atomic Functions 11. Research Report; Division of TheoreticalChemistry, Department of Chemistry,The University of Alberta, I97 I . (21) Rivera, M.; Harrison, J. F.; Alvarado-Swaisgood. A. J. Phys. Chem. 1990, 94, 6969. (22) The ARGOS integral program was developed by R. M. Pitzer (Ohio State University).
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5103 SCF and MCSCF calculations were done using GVB164 written by Bair2’ and the UEXP program and related utility codes written by S h e ~ a r d .The ~ ~ configuration interaction calculations were performed using the program UCI (and related utility codes) written by Lischka et All density and difference density contours were calculated with the MSUPLOT collection of codes written by Harrison, and all spectroscopic constants were determined by performing a Dunham analysis.26 2. Fragment Energies. Sc+. The ground-state5 (’D, 3dI4s’) and excited-state (SF, 3d2) energies were computed by using the SCF and SCF+1+2 (substitutions from only valence electrons) functions. The Sc2+(3d1)SCF energy was also determined. The total energies plus the energy for the mixed state Sc+(’B2, 3d6’3d7r1)are collected in Table VII. 0. The oxygen 2P state was analyzed with MCSCF and MCSCF+ 1+2 wave functions. The MCSCF function was constructed from the left-right correlation (GVB) of the doubly occupied 2 p Xorbital plus all valence spin couplings. This results in five CSF’s of 2B2symmetry. All valence single and double substitutions (of 2B2symmetry) from the MCSCF reference space results in the 408 CSF MCSCF+1+2. These energies are collected in Table VII. OH. The 211state of OH was examined by a 2B, 17-configuration MCSCF function. This was constructed from all spin couplings of a GVB(2/4) function (correlating the T bond and the doubly occupied 0 2prY orbital) and a 2729 C S F MCSCF+1+2 constructed from all valence single and double substitutions (of 2BIsymmetry) from the MCSCF reference space. The total energies are listed in Table VI1 while the dissociation energy (0,) and some spectroscopic constants are collected in Table VIII. H 2 0 . The energy and optimized geometry of H 2 0 was computed with a 37 CSF MCSCF function (constructed from all spin couplings of a GVB(2/4) function) and an 18410 CSF MCSCF+ 1+2 function derived from all valence single and double substitutions from the MCSCF reference space. The equilibrium energies are listed in Table VII, and the dissociation energies and spectroscopic constants are collected in Table VIII. H2 and H . The H(2S) energy was computed with a SCF function using the (2s,lp) basis. This energy is collected in Table I. The total energy of H2 using the (3s,3p) basis was determined with a 3 CSF MCSCF and 120 CSF MCSCF+1+2 constructed from all single and double excitations. The total energy and spectroscopic constants are listed in Tables I and 11, respectively. (23) The G V B I ~program ~ was written by R. Bair (Argonne National Laboratory). (24) A description of the UEXP program is given in: Shepard, R.; Simons, J.; Shavitt, I. J. Chem. Phys. 1982, 76, 543. (25) Lischka, H.; Shepard, R.; Brown, F. B.; Shavitt, I. Int. J . Quanrum Chem. Symp. 1981, 15, 91. (26) Dunham, J. L. Phys. Rev. 1932, 41, 721. (27) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Srrucrure; Van Nostrand Reinhold: New York, 1979.
