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Theoretical studies on the stability of the H3O radical based on ab initio UHF-CI calculations
._
Chemical Physics.25 (1977) 207-213 0 North-Holland Publishii~ Company
THEORETICAL BASED
STUDIES
ON AB INITIO
ON.THE
UHF43
STABILITY
OF THE H,O RADICAL
CALCULATIONS
Ketstin SE. NIBLAEUS Dkpartment ofNuclear Chemistry. The Royal Institute of Technology, S-100 44 Stockholm 70, Sweden
and
Bjijrn 0. ROOS and Per E.M. SIEGBAHN Institute of Theoretical Physics, Universityof Stockholm, S-I I3 46 Stockholm, Sweden
Received 17 May 1977
An UHFCI investigation of parts of the energy surface for the HsO radical is reported. Several types of basis sets have beenused and the Ci expansion included all singly and doubly replaced configurations using an UHF determinant as the reference state. HaO, constrained to Cxv symmetry is in the best approximation found to be 20.5 kcal/mol less stable than Hz0 + H. A.smaU local barrier of 4.6 kcai/mol for dissociation is found on the UHF level of approximation. Correlation effects lower this barrier to 3.4 kcaljmol making the existence of a quasiiound state with a measurable lifetime improbable. The height of the barrier was found to be very sensitive to the detailed form of the diffuse singly occupied orbital.
1. Introduction An increasing interest in the possible existencd of the H30 radical has emerged in recent years. The first indication that the H30 radical might exist was presented in 1963 by Bern&in [l] based on an analysis of thermodynamical relationships. Indirect evidence for the existence of H30 has also been presented by Sworski [2]. Since then several attempts have been made, experimental as well as theoretical, to verify the existence.of the H30 radical. Melton and. Joy [3] presented the first experimen-
tal evidence for the stability of H,O in gas phase. Their investigations were performed by means of mass spectrometry. :Martin and Swift [4], in 1971, claimed to have identified the HjO radical from ESR spectra of irradiated ice, cont‘aining cerium ions. This result has however been rejected by several others..Thus there are three diffeient reports [S-7] suggesting that the spectrum should be assigned to methyl radicals, which are likely to be,produced by photooxidation of-organic
impurities. Kongshaug et al. [S], also in 1971, suggested the ejiistence of H30 in liquid phase based on results obtained by means of y-radiolysis of water. He stated that the reaction of hydrated electrons with hydronium ions does not yield hydrogen atoms as had earlier been assumed. Instead he postulated the formation of hydrated H30 radicals: eaq f H30iq + H,O,
.
By photolysis of aqueous solutions at 77 K Claxton et al. [9], in 1972, obtained
species which could be
described
H30 radicals HzO-H.
ti highly distorted
However, they found rio evidence for the existence of
a symmetrical radical. The integral cross section for the collision of atoms and molecules in the system H + Hz0 was measured as a function of the relative velocity at thermal energies by Bassi et al. [lo] in 1974. Their results did not indicate the existence of bound states. However, in their conclusion they point out the possibility that bound states might be found in a region of lower velo-
Niblaeus et aL/UHF-Clstudies
on the stability ofthe HsO radical
cities than they have investigated. The first theoretical study of H30 was performed by Bishop [II] in 1967. He reported a single centre expanded molecular wavefunction and concluded that the system was thermodynamically unstable with respect to HZ0 + H. Melton and Joy [3], however, stated H30 to be stable using similar methods. In 1971, Gangi and Bader [12] also claimed to have confirmed the existence of the radical by an extensive RHF investigation of the H30 potential surface. They predict symmetrical Ha0 to be about 14 kcalj mol less stable than HZ0 + H, but found a local barrier to dissociation of about 7 kcal/mol, and-therefore suggested the possibility of a low temperature isolation of H,O. The radical was predicted to have a pyramidal equilibrium geometry with a low inversion barrier of approximately 2 kcal/mol. Also in 1971 Iathan et al. [13] performed SCF calculations using smaller basis sets than Gangi and Bader. Their results did not lead to a bound H,O species. The lowest energy was found for a weak hydrogen bonded complex between a hydroxyl radical and a hydrogen molecule with HZ pointing approximately towards the doubly occupied lone pair orbital of OH. However, they pointed out that due to the insufficiency of the basis set this structure is presumably not close to the lowest point of the real potential surface. They instead suggested the most stable form to be a van der Waals complex between Hz0 and H. Semi-empirical calculations were performed by Efskirrd [143 in 1972. He used the INDO method and the results obtained indicated the existence of the H30 radical. The corresponding geometry was found to be planar. Thus the theoretical as well as the experimental studies show different results as to the Ijossible existence of the H30 radical. Since all theoretical investigations have been performed in the Hartree-Fock approximation and reaction barriers are known to be sensitive to the inclusion of correlation effects the results so far cannot be regarded as conclusive, and a CI study of H,O is therefore motivated_ In’the present communication we report the results of such an investigation.
2. Details of the calculations
208.
KSE.
.-
-_.
The present work is an UHF-CI study of some essential parts of the potential surface of the H,O radical. The systems H2d and H30 have been investigated together with points along the mlniium energy path for the reaction HZ0 + H+.H,O. All calculations have been performed with the direct CI method as implemented in the program system MOLECULE [15]. Three different types of contracted gaussian basis sets were used tdconstruct the oneparticle basis orbitals. The smallest one (I) consists of 9s-type and Sp-type primitive functions for oxygen and S-type functions for each hydrogen [16], contracted to a double zeta basis. The hydrogen basis functions were multiplied with a s&ding factor of 1.25. To better describe the diffuse nature of the singly occupied orbital s-and p-type functions with exponents 0.08 and 0.06, respectively, on the oxygen atom, were added to the original basis set. The second basis set (II) included bond functions (bf), i.e. auxiliary functions of s and p type placed along the three bonds in H,O. These functions were incorporated in order to stimulate d-type polarization functions on oxygen. The advantage of bond functions is the saving of computational time which can be achieved compared to calculations using d-type functions. Aspects concerning the use of bond functions are developed in more detail below. Thus basis set II can be designated as (O/10,6), (H/S), (bf/l,l) contracted to (O/5,3),
K.S.E. Nibkxus et aL/UHF-Clstudies on the stability of the H30 radical
209
Table 1 GaussIanbasis sets for qxygen and hydrogen: I
(O/10,6), (H/S)+ tO/5,3), (H/2); II (O/10,6), (H/5), (bf,‘l,l)+ (O/5,3), (H/2), W/1,1% HI (O/11,5,1), @I/5.1)-L(O/6,2,1,, (H/2,1, Center
Type
Number df contracted gaussianfunctions
Coefficient
Exponent
0
S
1
0.00118 0.00897 0.04287 0.14389 0.35555 0.46137 0.14017 1.0 1.0 1.0 1.0 0.01541 0.09774 0.31066 0.49376 1.0 1.0 1.0 0.00612 0.04575 0.20572 0.50822 1.0 1.0
7816.54 1175.82 273.188 81.1696 27.1836 9.53223 3.41364 0.93978 0.28461 0.08 0.03 35.1832 7.90403 2.30512 0.71706 0.21373 0.06 1.0 42.05550 6.322450 1.43350 0.401430 0.126636 0.7
2 3 4 5 a) 6 h) 1
H
d s
2 3 c) 1 b) 1
P
2 1 b)
a) In basis set III the exponent was 0.09.
b) Occurs only in basis set IIt.
had earlier found to be optimal for H2. The exponents and the coefficients of the contracted gaussian basis sets for oxygen and hydrogenhave been collected in table 1. The exponents and the position of the bond functions were optimized in SCF calculations on the water molecule. The energy was found to be very insensitive to the exact location of the bond functions. Therefore the distance between the oxygen atoq and all bond functions was kept.constant at the optimized value of 0.546 A throughout the following calculations on HZ0 and H30. With this distance fmed the exponents of the bond functions were optimized to cs = 1.50 and S, = 0.66. The lowest energy for the water molecule obtained with basis set II was -76.046793 au. The corresponding energy obtained from calculatiqns using d-type polarization
functions (basis set III) was
-76.044285 au. The timing for integral evaluation was reduced by a factor of two when bond functions
c) Occurs only in basis set I and II.
were used instead of d-type polarization functions. The calculations on H30 were first performed on the UHF 1eveIof approximation. With this wavefunction as the reference state, CI calculations were then performed, including all singly and doubly replaced configurations in the CI expansion except replacements from the oxygen 1s orbital. The number of configurations (Slater determinants) for planar H30 (Ch symmetry) was 1497 with basis set I and 5086 with basis set II. For non-planar H30 (C, symmetry) the corresponding numbers were 2654 and 9289, respectively, and with basis set III 10074.
3. Results and discussion The investigation was performed in three different steps. The geometry of H20 was first optimized. Secondly, the geometry of symmetrically constrained
K.S.E. Nib&us et aL/UHF-Clstudies on the stabiliry of the H30 radical
210 Table
2
O#mal
Hz0
geometry of
Basis set
I
II
SCF
0 (HOH) (degrees)
E(au)
0.986
112.0
-76.010239
CI
SCF
CI
0.960
(A)
&O-H)
III
112.2 -76.139160
CI
SCF
0.965
0.944 106.3 -76.046793
Exp.
0.948
104.6 -16.228899
105.3 -76.046823
0.963 103.1 -16.241967
0.957 104.5 -16.431
a)
a) Ref. (181.
H, 0 (C&
was
determined, and in the last step the H + H30 was investigated.
3.2. The H30 radical
reaction path of H2D+ 3.1. llte
Hz0 molecule
‘Ihe calculations on H,O were made in order to obtain a starting point for the subsequent studies of the reaction path, but also to allow a study of the accuracy of the wavefunctions. A search for the equiIibrium geometry of Hz0 was made by varying the bond distance, keeping the bond angle fixed, and vice versa. These calculations were performed using all three basis sets. Thegeometrical parameters were obtained by parabolic interpolation and are given in table 2. We can draw two main conclusions from these results. First, the well known fact that accurate geometry predictions on the CI level cannot be made without the inclusion of polarizing functions. Second, very similar results are obtained with basis sets II and III, showing the adequacy of the bond functions in these types of calculations. The calculated geometry with basis set III is also close to the results obtained by Diercksen et al. [17] using a larger basis set.
A series of calculations were made in order to determine the minimum energy for the symmetrical H30 radical, i.e. the equilibrium. geometry the radical would have if it did exist. The bond distance was first optimized in the planar form. Keeping this distance fixed the pyramidal angle was then determined. These calculations were Performed both at the UHF and the CI level, except with basis set III where the geometry optimization was only performed on the UHF level. The geometry obtained on this level was then used in the CI calculations. The results from these calculations are presented in table 3. Comparing the results at the UHF level we note that the calculated barrier to inversion is much higher with basis set II than with basis set III. The latter result is probably more reliable since the positioning of the bond functions in basis set II is likely to artificially favour a tetrahedral structure. The lack of the most diffuse s-type function on oxygen is another argument against the reliability of the results obtained with basis set II. The geometry and barrier obtained from the UHF calculations with basis set III is also very close to
Table 3 Optimized values of bond distance and bond angle for HsO (D3h and Csv symmetry) Basis set
R(O-H) (A) 0 (HOH) (degrees) inversion barrier (kcal/mol) E pyramidal (au) aE a) &A/mol)
a) Energy
I
II
III
UHF
ci
UHF.
CI
UHF
1.035 110.6
1.077 111.0
1.016 103.2
1.053 101.8
0.989 109.5
1.5 -76.437616 45.56
1.1 -76.581197 36.40
7.5 -76.470927 47.63
6.3 -76.668936 37.65
2.8 -76.499800 29.49
difference for the reaction H30 + Ha0 + H.
CI
Gangi and Bader [ 121 RHF
0.984 111.8 4.5 -76.115324 20.52
2.0 -76.49571 28.16 _
RSE.
Nibkaeuset &/UHF-Clstudies on the stability of the H30 radical
the RHF results of Gangi and Bader 1121. Spin-polarization, as expected in this case, is of minor importance. The correlation effect with basis set III, is to increase the barrier height. This is in accordance with results reported for H,Oc, where a more extended basis set was used [17]. The singly occupied orbital which is of Rydberg character should have a very small effect on the angular dependence of the correIation enemy. As this orbital can be described qualitatively as a linear combination of an pxygen 3s.orbital with hydrogen Is-orbitals it can, however, be expected to favour a more tetrahedral arrangement. The barrier obtained for H,O is therefore found to be slightly larger than the corresponding barrier in H,O’, for which a value of 2.1 kcal/mol was reported [17]. Summarizing these results, H30 is found to be non-planar with a small inversion barrier which, like in H,O+, is increased slightly by including correlation effects. In the last row of table 3 we report the calculated energy difference AE between H,O and H20 f H. These results are conclusive on two points. H,O is not thermodynamically stable with respect to dissociation. The AE is, however, lowered by inclusion of correlation, an effect earlier assumed by Gangi and Bader [12] based on a comparison of atomic correlation energies. The total correlation effect on AE, which would have been obtained with an infinite basis set and complete CI, can be estimated by assuming that the computed effect is proportional to the fraction obtained of the total valence correlation energy. Since we compute approximately 75% of the valence correlation energy and our computed energy lowering is 9 kcal/ mol, the estimated total correlation effect would be around 12 kcal/mol. With the UHF value from basis set III of 29 kcaljmol this leads to an estimatedAl_? value of around 17 kcal/mol from the calculated20.5 kcal/$ol. We note that the AE values obtained; with basis set II are much higher than with basis set III. This is due to the lack of the most diffuse s-type function on oxygen in basis set II. The other diffuse s-type function completely fails to describe the 3s character of the diffuse orbital, which is very sensitive to the precise value of the orbital exponent. The correlation effect is on the other hand the same with all three basis sets and is thus, as expected, rather unsensitive to the exact shape of the diffuse Rydberg type orbital. Since H30 is definitely predicted to have a higher
211
energy than the separated system H20 + H, the possibility to observe H,O will depend on the existence of a barrier for dissociation, leading to a metastable radical. This possibility is investigated in the next section. 3.3. The minimum energy path for the reactionHz0 +H+H30 The minimum energy path for the formation of a H30 radical was investigated using all three basis sets. For a system with four atoms there are six degrees of freedom. Since the hydrogen atom obviously is going to bisect the HOH angle in water, the minimum energy path will be described by a simultaneous variation in four coordinates. The choice of coordinates, as shown h-rfig. 1, are the r(OHI) distance and the 0 (HOH) angle in water, the distance R[OH$ and the angle rp between the H20 plane and the approaching hydrogen atom. A simultaneous optimization of four degrees of freedom would require too much computing effort, and only one independent reaction coordinate, the R distance, is therefore used. The remaining three degrees of freedom were related to the reaction coordinate through analytical expressions. The parameters appearing in the analytical forms were obtained by optimizing ali geometry parameters at three different values of R, namely, besides the equilibrium structure of Hz0 and the dissociation limit, also at two intermediate distances with R = 2.20 and 2.50 au, respectively. These geometry optimizations were done on the UHF level. Thus the same reaction pathway was used for the UHF and the UHF-C1 calculations. With basis set III several points were caiculated, with a concentration in the interesting region of the minimum energy path and the results are presented in table 4. The reaction path as obtained from the UHF calculations is also illustrated in fig. 2. The
Fig. 1. Geometricalstructure of Hz0 + H used in the investigation of the minimum energypath.
212
KSE.
i%TbIaeus et al.f UHF-U studies on the stabiIity of the H30 radical
Table 4 Calculated points aIong the minimum energy pathforthe r&&n
Hz0 + H in kcal/mol a) ti(UH$J)
aE(cI)d’:
(au)
e (degree)
+
(au)
(degxej
(kcal/inol)
(kcil/moI)~
1.700
1.875
110.1
54.6
34.136
26.920
1.869. 2.050 2.200 2.350 2.500
LS69 1.860 1.838 1.821 1.805
109.5 108.8 108.3 107.8
54.6 54.6 54.7 55.3
29.493 31.814 33.948 33.007
20.519. 21.084 23.029 23.469
107.2
57.7
29.681
21.900
R-
.r
a) Energy zero point is taken at Longdistance. b) E(Hz0) + E(H) = -76.546823 au. c) E(Hz0) + E(H) = -76.747967 au.
most striking feature of the curves in fig. 2 is the small, but marked, barrier of4.6 kcal/mol, with a maximum at R = 2.24 au obtained with basis set III, and the total absence of the barrier with basis sets I and II. The appearance of the barrier has been found to depend critically on the inclusion of the most diffuse s-type function on oxygen. Usually the origin of barriers of this type is a change of electronic structure along the reaction path, which gives rise to an avoided crossing between two potential curves. In this case this change of structure occurs in the singly occupied orbiAE
50-
40-
30-
20-
loO-
1.0
1.5
2.0
Fig. 2. The minimum (UHF) energy path for the reaction. Hz0 f H in kcal/mol. Distances in angstrBms. Energy zero point is taken at long distance.
* R
tal. When the hydrogen atom approaches the water molecule the odd electron is originally located on hydrogen and the curve is repulsive. In the region of tlie barrier the singly occupied orbital changes nature and becomes delocalized with a dominant Character as a Rydberg type 3s-orbital. With this change in the electronic structure the interaction for a while becomes attractive. An immediate conclusion is that basis sets which h&de functions which can describe diffuse Rydberg type orbitals are necessary for a correct description of reactions of this type. An indication of the sensitivity of the barrier height to the basis set can be obtained by comparing the basis set III results with those of Gangl and Bader [12]. They used the RH!T method arid a primitive basis set of(O/l1,5,2), (H/4,1) contracted to {O/6,3,2), (H/2,1) and obtained a barrier of 6.6 kcal/mol. The discrepancy of 2.0 kcal/mol between their result and the present UHF result has basically two origins. Half of the effect is due to the inclusion of spin-polarization in the UHJ? approximation. Most of the remaining difference comes from the less extensive geometry optimization performed in .[12]. Thus the pure basis set effect to the difference in the results is small, whjch can be taken as a sign of enough flexibility. The next question is in what direction and how much the change in correlation energy affects the barrier height. The UHF-C1 results as plotted in fig. 3 show that the barrier with basis set INstill remains but is lowered to 3.4 kcal/mol and the maximum is shifted out-by 0.07 au to 2.31 au. There is still no barrier with basis sets I and-II. If.we am assuine that the obtained fraction of the correlation effect on the barrier is.proportional to th&alculaied fraction df the
K.S.E. Niblaeus et aL/UHF-CI studies on the stability of the H30 radical
213
origin of the barrier is a curve crossing between a repulsive state with the single electron at the hydrogen atom and a delocalized attractive Rydberg state, where the electron is shared between the oxygen and the hydrogen atoms. A knowledge of the Rydberg or valence states of a closed shell molecule should therefore allow a prediction of the possibility for the molecule to bind a hydrogen atom. Low lying states should favour stable complexes. A molecule like H3S for example would with these arguments be more likely to be observable than H30.
References
0’
w
1.0
15
2.0
R
Fig. 3. The minimum (UHF-CD energy path for the reaction Hz0 + H in kcal/mol. Distances ln angstrtims. Energy zero point ls taken at long distance.
valence correlation energy, we can estimate that the true barrier height would be around 3.0 kcal/mol. In order to estimate the position of a possible quasibound state, a 6th degree polynomial was fitted to the points around the local minimum. The vibrational problem was then solved using a 10 term expansion in Hermite polynomials. For the single dissociation degree of freedom the resulting zero point energy, which is very close to the harmonic result, is 4.0 kcaI/mol and thus above the predicted barrier. The present calculations therefore indicate that the existence of a metastable H30 in the gas phase with a measurable lifetime is improbable.
4. Conchrsions The present calculations yield a thermodynamically unstable H,O by an estimated 17 kcaljmol (from the calculated 20.5 kcal/mol). There is however a local minimum with an estimated barrier to dissociation of 3.0 kcal/mol (from the calculated 3.4 kcal/mol). Since the estimated zero point energy for the dissociative degree of freedom is 4.0 kcal/mol, it is not probable that H3,0 could be observed even at low temperatures. The
[ 11H.J.Bernstein, J. Am. Chem. Sot. 85 (1963) 484. [2] T.J. Sworski, J. Am. Chem. Sot. 86 (1964) 5034; 77 (1955) 4689; 76 (1953) 4687. [3] C.E. Melton and H.W. Joy, I. Chem. Phys. 46 (1967) 4275; 48 (1968) 5286. [4] T.W. Martinand L.L. Swift, I. Am. Chem. Sot. 93 (1971) 2788. (51 E. Melamud, D. Gem, S. Schlick and B.L. Silver, Chem. Phys. Letters 15 (1972) 590. [6] S. Noda, H. Yoshida and L. Kevan, Chem. Phys. Letters 19 (1973) 240. [7] J.A. Wargon and F. Williams,Chem. Phys. Letters 13 (1972) 579. [8] M. Kongshaug, H.B. Steen and B. Cercek, Nature Phys. .Sci. 234 (1971) 97. [9] T.A. Claxton, IS. Glnns, M.J. Godfrey, K.V.S. Rao and M.C.R. Symons, J. Chem. Sot. Faraday Trans. II 69 (1973) 217. [lo] D. Bassi, M. De Paz, A. Pesce and F. Tommasini, Chem. Phys. Letters 26 (1974) 422. [II] D.M. Bishop, J. Chem. Phys. 45 (1966) 2474; 48 (1968) 5285. [12] R.A. Cangi and R.F.W. Bader, Chem. Phys. Letters 11 (1971) 216. 1131 W.A. Lathan, W.J. Hehre, L.A. Curtiss and J.A. Pople, J. Am. Chem. Sot. 93 (1971) 63771 [14] L. Efskind, Acta Chem. Sand. 26 (1972) 4147. [ 151 J. Almlof, USIP Report 74-29, Institute of Physics, University of Stockholm, Sweden, December 1974 (for the hue&xl part); B. Roos, Chem. Phys. Letters 15 (1972) 153; P. Siegbahn, Proceedings from the SRC Atlas Symposium No. 4 (April 1974); B. ROOSand P. Siegbahn, in: Methods in modern theoretical chemistry, Vol. 2, Ab initio methods, ed. H.F. Schaefer III (Plenum Press, New York, 1977). [16] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [ 171 G. Diercksen, W. Kraemer and B. Roos, Theoret. Chii. Acta 36 (1975) 249. [IS] W. Meyer, Intern. J. Quantum Chem. 5 (1971) 341.
Chemical Physics.25 (1977) 207-213 0 North-Holland Publishii~ Company
THEORETICAL BASED
STUDIES
ON AB INITIO
ON.THE
UHF43
STABILITY
OF THE H,O RADICAL
CALCULATIONS
Ketstin SE. NIBLAEUS Dkpartment ofNuclear Chemistry. The Royal Institute of Technology, S-100 44 Stockholm 70, Sweden
and
Bjijrn 0. ROOS and Per E.M. SIEGBAHN Institute of Theoretical Physics, Universityof Stockholm, S-I I3 46 Stockholm, Sweden
Received 17 May 1977
An UHFCI investigation of parts of the energy surface for the HsO radical is reported. Several types of basis sets have beenused and the Ci expansion included all singly and doubly replaced configurations using an UHF determinant as the reference state. HaO, constrained to Cxv symmetry is in the best approximation found to be 20.5 kcal/mol less stable than Hz0 + H. A.smaU local barrier of 4.6 kcai/mol for dissociation is found on the UHF level of approximation. Correlation effects lower this barrier to 3.4 kcaljmol making the existence of a quasiiound state with a measurable lifetime improbable. The height of the barrier was found to be very sensitive to the detailed form of the diffuse singly occupied orbital.
1. Introduction An increasing interest in the possible existencd of the H30 radical has emerged in recent years. The first indication that the H30 radical might exist was presented in 1963 by Bern&in [l] based on an analysis of thermodynamical relationships. Indirect evidence for the existence of H30 has also been presented by Sworski [2]. Since then several attempts have been made, experimental as well as theoretical, to verify the existence.of the H30 radical. Melton and. Joy [3] presented the first experimen-
tal evidence for the stability of H,O in gas phase. Their investigations were performed by means of mass spectrometry. :Martin and Swift [4], in 1971, claimed to have identified the HjO radical from ESR spectra of irradiated ice, cont‘aining cerium ions. This result has however been rejected by several others..Thus there are three diffeient reports [S-7] suggesting that the spectrum should be assigned to methyl radicals, which are likely to be,produced by photooxidation of-organic
impurities. Kongshaug et al. [S], also in 1971, suggested the ejiistence of H30 in liquid phase based on results obtained by means of y-radiolysis of water. He stated that the reaction of hydrated electrons with hydronium ions does not yield hydrogen atoms as had earlier been assumed. Instead he postulated the formation of hydrated H30 radicals: eaq f H30iq + H,O,
.
By photolysis of aqueous solutions at 77 K Claxton et al. [9], in 1972, obtained
species which could be
described
H30 radicals HzO-H.
ti highly distorted
However, they found rio evidence for the existence of
a symmetrical radical. The integral cross section for the collision of atoms and molecules in the system H + Hz0 was measured as a function of the relative velocity at thermal energies by Bassi et al. [lo] in 1974. Their results did not indicate the existence of bound states. However, in their conclusion they point out the possibility that bound states might be found in a region of lower velo-
Niblaeus et aL/UHF-Clstudies
on the stability ofthe HsO radical
cities than they have investigated. The first theoretical study of H30 was performed by Bishop [II] in 1967. He reported a single centre expanded molecular wavefunction and concluded that the system was thermodynamically unstable with respect to HZ0 + H. Melton and Joy [3], however, stated H30 to be stable using similar methods. In 1971, Gangi and Bader [12] also claimed to have confirmed the existence of the radical by an extensive RHF investigation of the H30 potential surface. They predict symmetrical Ha0 to be about 14 kcalj mol less stable than HZ0 + H, but found a local barrier to dissociation of about 7 kcal/mol, and-therefore suggested the possibility of a low temperature isolation of H,O. The radical was predicted to have a pyramidal equilibrium geometry with a low inversion barrier of approximately 2 kcal/mol. Also in 1971 Iathan et al. [13] performed SCF calculations using smaller basis sets than Gangi and Bader. Their results did not lead to a bound H,O species. The lowest energy was found for a weak hydrogen bonded complex between a hydroxyl radical and a hydrogen molecule with HZ pointing approximately towards the doubly occupied lone pair orbital of OH. However, they pointed out that due to the insufficiency of the basis set this structure is presumably not close to the lowest point of the real potential surface. They instead suggested the most stable form to be a van der Waals complex between Hz0 and H. Semi-empirical calculations were performed by Efskirrd [143 in 1972. He used the INDO method and the results obtained indicated the existence of the H30 radical. The corresponding geometry was found to be planar. Thus the theoretical as well as the experimental studies show different results as to the Ijossible existence of the H30 radical. Since all theoretical investigations have been performed in the Hartree-Fock approximation and reaction barriers are known to be sensitive to the inclusion of correlation effects the results so far cannot be regarded as conclusive, and a CI study of H,O is therefore motivated_ In’the present communication we report the results of such an investigation.
2. Details of the calculations
208.
KSE.
.-
-_.
The present work is an UHF-CI study of some essential parts of the potential surface of the H,O radical. The systems H2d and H30 have been investigated together with points along the mlniium energy path for the reaction HZ0 + H+.H,O. All calculations have been performed with the direct CI method as implemented in the program system MOLECULE [15]. Three different types of contracted gaussian basis sets were used tdconstruct the oneparticle basis orbitals. The smallest one (I) consists of 9s-type and Sp-type primitive functions for oxygen and S-type functions for each hydrogen [16], contracted to a double zeta basis. The hydrogen basis functions were multiplied with a s&ding factor of 1.25. To better describe the diffuse nature of the singly occupied orbital s-and p-type functions with exponents 0.08 and 0.06, respectively, on the oxygen atom, were added to the original basis set. The second basis set (II) included bond functions (bf), i.e. auxiliary functions of s and p type placed along the three bonds in H,O. These functions were incorporated in order to stimulate d-type polarization functions on oxygen. The advantage of bond functions is the saving of computational time which can be achieved compared to calculations using d-type functions. Aspects concerning the use of bond functions are developed in more detail below. Thus basis set II can be designated as (O/10,6), (H/S), (bf/l,l) contracted to (O/5,3),
K.S.E. Nibkxus et aL/UHF-Clstudies on the stability of the H30 radical
209
Table 1 GaussIanbasis sets for qxygen and hydrogen: I
(O/10,6), (H/S)+ tO/5,3), (H/2); II (O/10,6), (H/5), (bf,‘l,l)+ (O/5,3), (H/2), W/1,1% HI (O/11,5,1), @I/5.1)-L(O/6,2,1,, (H/2,1, Center
Type
Number df contracted gaussianfunctions
Coefficient
Exponent
0
S
1
0.00118 0.00897 0.04287 0.14389 0.35555 0.46137 0.14017 1.0 1.0 1.0 1.0 0.01541 0.09774 0.31066 0.49376 1.0 1.0 1.0 0.00612 0.04575 0.20572 0.50822 1.0 1.0
7816.54 1175.82 273.188 81.1696 27.1836 9.53223 3.41364 0.93978 0.28461 0.08 0.03 35.1832 7.90403 2.30512 0.71706 0.21373 0.06 1.0 42.05550 6.322450 1.43350 0.401430 0.126636 0.7
2 3 4 5 a) 6 h) 1
H
d s
2 3 c) 1 b) 1
P
2 1 b)
a) In basis set III the exponent was 0.09.
b) Occurs only in basis set IIt.
had earlier found to be optimal for H2. The exponents and the coefficients of the contracted gaussian basis sets for oxygen and hydrogenhave been collected in table 1. The exponents and the position of the bond functions were optimized in SCF calculations on the water molecule. The energy was found to be very insensitive to the exact location of the bond functions. Therefore the distance between the oxygen atoq and all bond functions was kept.constant at the optimized value of 0.546 A throughout the following calculations on HZ0 and H30. With this distance fmed the exponents of the bond functions were optimized to cs = 1.50 and S, = 0.66. The lowest energy for the water molecule obtained with basis set II was -76.046793 au. The corresponding energy obtained from calculatiqns using d-type polarization
functions (basis set III) was
-76.044285 au. The timing for integral evaluation was reduced by a factor of two when bond functions
c) Occurs only in basis set I and II.
were used instead of d-type polarization functions. The calculations on H30 were first performed on the UHF 1eveIof approximation. With this wavefunction as the reference state, CI calculations were then performed, including all singly and doubly replaced configurations in the CI expansion except replacements from the oxygen 1s orbital. The number of configurations (Slater determinants) for planar H30 (Ch symmetry) was 1497 with basis set I and 5086 with basis set II. For non-planar H30 (C, symmetry) the corresponding numbers were 2654 and 9289, respectively, and with basis set III 10074.
3. Results and discussion The investigation was performed in three different steps. The geometry of H20 was first optimized. Secondly, the geometry of symmetrically constrained
K.S.E. Nib&us et aL/UHF-Clstudies on the stabiliry of the H30 radical
210 Table
2
O#mal
Hz0
geometry of
Basis set
I
II
SCF
0 (HOH) (degrees)
E(au)
0.986
112.0
-76.010239
CI
SCF
CI
0.960
(A)
&O-H)
III
112.2 -76.139160
CI
SCF
0.965
0.944 106.3 -76.046793
Exp.
0.948
104.6 -16.228899
105.3 -76.046823
0.963 103.1 -16.241967
0.957 104.5 -16.431
a)
a) Ref. (181.
H, 0 (C&
was
determined, and in the last step the H + H30 was investigated.
3.2. The H30 radical
reaction path of H2D+ 3.1. llte
Hz0 molecule
‘Ihe calculations on H,O were made in order to obtain a starting point for the subsequent studies of the reaction path, but also to allow a study of the accuracy of the wavefunctions. A search for the equiIibrium geometry of Hz0 was made by varying the bond distance, keeping the bond angle fixed, and vice versa. These calculations were performed using all three basis sets. Thegeometrical parameters were obtained by parabolic interpolation and are given in table 2. We can draw two main conclusions from these results. First, the well known fact that accurate geometry predictions on the CI level cannot be made without the inclusion of polarizing functions. Second, very similar results are obtained with basis sets II and III, showing the adequacy of the bond functions in these types of calculations. The calculated geometry with basis set III is also close to the results obtained by Diercksen et al. [17] using a larger basis set.
A series of calculations were made in order to determine the minimum energy for the symmetrical H30 radical, i.e. the equilibrium. geometry the radical would have if it did exist. The bond distance was first optimized in the planar form. Keeping this distance fixed the pyramidal angle was then determined. These calculations were Performed both at the UHF and the CI level, except with basis set III where the geometry optimization was only performed on the UHF level. The geometry obtained on this level was then used in the CI calculations. The results from these calculations are presented in table 3. Comparing the results at the UHF level we note that the calculated barrier to inversion is much higher with basis set II than with basis set III. The latter result is probably more reliable since the positioning of the bond functions in basis set II is likely to artificially favour a tetrahedral structure. The lack of the most diffuse s-type function on oxygen is another argument against the reliability of the results obtained with basis set II. The geometry and barrier obtained from the UHF calculations with basis set III is also very close to
Table 3 Optimized values of bond distance and bond angle for HsO (D3h and Csv symmetry) Basis set
R(O-H) (A) 0 (HOH) (degrees) inversion barrier (kcal/mol) E pyramidal (au) aE a) &A/mol)
a) Energy
I
II
III
UHF
ci
UHF.
CI
UHF
1.035 110.6
1.077 111.0
1.016 103.2
1.053 101.8
0.989 109.5
1.5 -76.437616 45.56
1.1 -76.581197 36.40
7.5 -76.470927 47.63
6.3 -76.668936 37.65
2.8 -76.499800 29.49
difference for the reaction H30 + Ha0 + H.
CI
Gangi and Bader [ 121 RHF
0.984 111.8 4.5 -76.115324 20.52
2.0 -76.49571 28.16 _
RSE.
Nibkaeuset &/UHF-Clstudies on the stability of the H30 radical
the RHF results of Gangi and Bader 1121. Spin-polarization, as expected in this case, is of minor importance. The correlation effect with basis set III, is to increase the barrier height. This is in accordance with results reported for H,Oc, where a more extended basis set was used [17]. The singly occupied orbital which is of Rydberg character should have a very small effect on the angular dependence of the correIation enemy. As this orbital can be described qualitatively as a linear combination of an pxygen 3s.orbital with hydrogen Is-orbitals it can, however, be expected to favour a more tetrahedral arrangement. The barrier obtained for H,O is therefore found to be slightly larger than the corresponding barrier in H,O’, for which a value of 2.1 kcal/mol was reported [17]. Summarizing these results, H30 is found to be non-planar with a small inversion barrier which, like in H,O+, is increased slightly by including correlation effects. In the last row of table 3 we report the calculated energy difference AE between H,O and H20 f H. These results are conclusive on two points. H,O is not thermodynamically stable with respect to dissociation. The AE is, however, lowered by inclusion of correlation, an effect earlier assumed by Gangi and Bader [12] based on a comparison of atomic correlation energies. The total correlation effect on AE, which would have been obtained with an infinite basis set and complete CI, can be estimated by assuming that the computed effect is proportional to the fraction obtained of the total valence correlation energy. Since we compute approximately 75% of the valence correlation energy and our computed energy lowering is 9 kcal/ mol, the estimated total correlation effect would be around 12 kcal/mol. With the UHF value from basis set III of 29 kcaljmol this leads to an estimatedAl_? value of around 17 kcal/mol from the calculated20.5 kcal/$ol. We note that the AE values obtained; with basis set II are much higher than with basis set III. This is due to the lack of the most diffuse s-type function on oxygen in basis set II. The other diffuse s-type function completely fails to describe the 3s character of the diffuse orbital, which is very sensitive to the precise value of the orbital exponent. The correlation effect is on the other hand the same with all three basis sets and is thus, as expected, rather unsensitive to the exact shape of the diffuse Rydberg type orbital. Since H30 is definitely predicted to have a higher
211
energy than the separated system H20 + H, the possibility to observe H,O will depend on the existence of a barrier for dissociation, leading to a metastable radical. This possibility is investigated in the next section. 3.3. The minimum energy path for the reactionHz0 +H+H30 The minimum energy path for the formation of a H30 radical was investigated using all three basis sets. For a system with four atoms there are six degrees of freedom. Since the hydrogen atom obviously is going to bisect the HOH angle in water, the minimum energy path will be described by a simultaneous variation in four coordinates. The choice of coordinates, as shown h-rfig. 1, are the r(OHI) distance and the 0 (HOH) angle in water, the distance R[OH$ and the angle rp between the H20 plane and the approaching hydrogen atom. A simultaneous optimization of four degrees of freedom would require too much computing effort, and only one independent reaction coordinate, the R distance, is therefore used. The remaining three degrees of freedom were related to the reaction coordinate through analytical expressions. The parameters appearing in the analytical forms were obtained by optimizing ali geometry parameters at three different values of R, namely, besides the equilibrium structure of Hz0 and the dissociation limit, also at two intermediate distances with R = 2.20 and 2.50 au, respectively. These geometry optimizations were done on the UHF level. Thus the same reaction pathway was used for the UHF and the UHF-C1 calculations. With basis set III several points were caiculated, with a concentration in the interesting region of the minimum energy path and the results are presented in table 4. The reaction path as obtained from the UHF calculations is also illustrated in fig. 2. The
Fig. 1. Geometricalstructure of Hz0 + H used in the investigation of the minimum energypath.
212
KSE.
i%TbIaeus et al.f UHF-U studies on the stabiIity of the H30 radical
Table 4 Calculated points aIong the minimum energy pathforthe r&&n
Hz0 + H in kcal/mol a) ti(UH$J)
aE(cI)d’:
(au)
e (degree)
+
(au)
(degxej
(kcal/inol)
(kcil/moI)~
1.700
1.875
110.1
54.6
34.136
26.920
1.869. 2.050 2.200 2.350 2.500
LS69 1.860 1.838 1.821 1.805
109.5 108.8 108.3 107.8
54.6 54.6 54.7 55.3
29.493 31.814 33.948 33.007
20.519. 21.084 23.029 23.469
107.2
57.7
29.681
21.900
R-
.r
a) Energy zero point is taken at Longdistance. b) E(Hz0) + E(H) = -76.546823 au. c) E(Hz0) + E(H) = -76.747967 au.
most striking feature of the curves in fig. 2 is the small, but marked, barrier of4.6 kcal/mol, with a maximum at R = 2.24 au obtained with basis set III, and the total absence of the barrier with basis sets I and II. The appearance of the barrier has been found to depend critically on the inclusion of the most diffuse s-type function on oxygen. Usually the origin of barriers of this type is a change of electronic structure along the reaction path, which gives rise to an avoided crossing between two potential curves. In this case this change of structure occurs in the singly occupied orbiAE
50-
40-
30-
20-
loO-
1.0
1.5
2.0
Fig. 2. The minimum (UHF) energy path for the reaction. Hz0 f H in kcal/mol. Distances in angstrBms. Energy zero point is taken at long distance.
* R
tal. When the hydrogen atom approaches the water molecule the odd electron is originally located on hydrogen and the curve is repulsive. In the region of tlie barrier the singly occupied orbital changes nature and becomes delocalized with a dominant Character as a Rydberg type 3s-orbital. With this change in the electronic structure the interaction for a while becomes attractive. An immediate conclusion is that basis sets which h&de functions which can describe diffuse Rydberg type orbitals are necessary for a correct description of reactions of this type. An indication of the sensitivity of the barrier height to the basis set can be obtained by comparing the basis set III results with those of Gangl and Bader [12]. They used the RH!T method arid a primitive basis set of(O/l1,5,2), (H/4,1) contracted to {O/6,3,2), (H/2,1) and obtained a barrier of 6.6 kcal/mol. The discrepancy of 2.0 kcal/mol between their result and the present UHF result has basically two origins. Half of the effect is due to the inclusion of spin-polarization in the UHJ? approximation. Most of the remaining difference comes from the less extensive geometry optimization performed in .[12]. Thus the pure basis set effect to the difference in the results is small, whjch can be taken as a sign of enough flexibility. The next question is in what direction and how much the change in correlation energy affects the barrier height. The UHF-C1 results as plotted in fig. 3 show that the barrier with basis set INstill remains but is lowered to 3.4 kcal/mol and the maximum is shifted out-by 0.07 au to 2.31 au. There is still no barrier with basis sets I and-II. If.we am assuine that the obtained fraction of the correlation effect on the barrier is.proportional to th&alculaied fraction df the
K.S.E. Niblaeus et aL/UHF-CI studies on the stability of the H30 radical
213
origin of the barrier is a curve crossing between a repulsive state with the single electron at the hydrogen atom and a delocalized attractive Rydberg state, where the electron is shared between the oxygen and the hydrogen atoms. A knowledge of the Rydberg or valence states of a closed shell molecule should therefore allow a prediction of the possibility for the molecule to bind a hydrogen atom. Low lying states should favour stable complexes. A molecule like H3S for example would with these arguments be more likely to be observable than H30.
References
0’
w
1.0
15
2.0
R
Fig. 3. The minimum (UHF-CD energy path for the reaction Hz0 + H in kcal/mol. Distances ln angstrtims. Energy zero point ls taken at long distance.
valence correlation energy, we can estimate that the true barrier height would be around 3.0 kcal/mol. In order to estimate the position of a possible quasibound state, a 6th degree polynomial was fitted to the points around the local minimum. The vibrational problem was then solved using a 10 term expansion in Hermite polynomials. For the single dissociation degree of freedom the resulting zero point energy, which is very close to the harmonic result, is 4.0 kcaI/mol and thus above the predicted barrier. The present calculations therefore indicate that the existence of a metastable H30 in the gas phase with a measurable lifetime is improbable.
4. Conchrsions The present calculations yield a thermodynamically unstable H,O by an estimated 17 kcaljmol (from the calculated 20.5 kcal/mol). There is however a local minimum with an estimated barrier to dissociation of 3.0 kcal/mol (from the calculated 3.4 kcal/mol). Since the estimated zero point energy for the dissociative degree of freedom is 4.0 kcal/mol, it is not probable that H3,0 could be observed even at low temperatures. The
[ 11H.J.Bernstein, J. Am. Chem. Sot. 85 (1963) 484. [2] T.J. Sworski, J. Am. Chem. Sot. 86 (1964) 5034; 77 (1955) 4689; 76 (1953) 4687. [3] C.E. Melton and H.W. Joy, I. Chem. Phys. 46 (1967) 4275; 48 (1968) 5286. [4] T.W. Martinand L.L. Swift, I. Am. Chem. Sot. 93 (1971) 2788. (51 E. Melamud, D. Gem, S. Schlick and B.L. Silver, Chem. Phys. Letters 15 (1972) 590. [6] S. Noda, H. Yoshida and L. Kevan, Chem. Phys. Letters 19 (1973) 240. [7] J.A. Wargon and F. Williams,Chem. Phys. Letters 13 (1972) 579. [8] M. Kongshaug, H.B. Steen and B. Cercek, Nature Phys. .Sci. 234 (1971) 97. [9] T.A. Claxton, IS. Glnns, M.J. Godfrey, K.V.S. Rao and M.C.R. Symons, J. Chem. Sot. Faraday Trans. II 69 (1973) 217. [lo] D. Bassi, M. De Paz, A. Pesce and F. Tommasini, Chem. Phys. Letters 26 (1974) 422. [II] D.M. Bishop, J. Chem. Phys. 45 (1966) 2474; 48 (1968) 5285. [12] R.A. Cangi and R.F.W. Bader, Chem. Phys. Letters 11 (1971) 216. 1131 W.A. Lathan, W.J. Hehre, L.A. Curtiss and J.A. Pople, J. Am. Chem. Sot. 93 (1971) 63771 [14] L. Efskind, Acta Chem. Sand. 26 (1972) 4147. [ 151 J. Almlof, USIP Report 74-29, Institute of Physics, University of Stockholm, Sweden, December 1974 (for the hue&xl part); B. Roos, Chem. Phys. Letters 15 (1972) 153; P. Siegbahn, Proceedings from the SRC Atlas Symposium No. 4 (April 1974); B. ROOSand P. Siegbahn, in: Methods in modern theoretical chemistry, Vol. 2, Ab initio methods, ed. H.F. Schaefer III (Plenum Press, New York, 1977). [16] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [ 171 G. Diercksen, W. Kraemer and B. Roos, Theoret. Chii. Acta 36 (1975) 249. [IS] W. Meyer, Intern. J. Quantum Chem. 5 (1971) 341.