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Ab initio potential functions for the ionic states of OH
19 September 1997
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 276 (I 997) 171 - 176
Ab initio potential functions for the ionic states of OH A.V. Nemukhin *, B.L. Grigorenko Department of Chemistry Moscow State Unit:ersi~.', Moscow, 119899, Russia Received 26 June 1997; in final form 26 June 1997
Abstract
Potential curves of the OH molecule correlating to the four lowest energy dissociation limits O(3p) + H(2S), O(]D) + H(2S), O(IS) + H(2S), O-(2P) + H ÷ have been computed at the CI/CASSCF level with the AUG-cc-pVTZ basis sets with a special emphasis on the ion-pair states 3 2I-1 and C 2E +. A balanced treatment of the excited state potentials is achieved by using the state-averaging MO optimization procedure. The X ~E ÷ and ]II potentials of OH- have been also considered. After empirical correction of the errors at the dissociation limits, the computed functions are recommended for the future use in the diatomics-in-molecules studies of the structure and dynamics of oxygen/hydrogen containing molecular systems. © 1997 Elsevier Science B.V. Potential energy functions of OH correlating to the lowest dissociation limits, which include the neutral O(3p) + H(2S), O ( I D ) + H(2S), O ( I S ) + H(2S) as well as the ionic O - ( 2 p ) + H ÷ channels, are basically known from the results of ab initio quantum chemistry calculations which are nicely consistent with the reliable experimental spectral data. Several high quality calculations have been published not long ago, we mention here only the works which describe the potentials of the ground and excited states of OH for the extended regions of internuclear distances. The paper of Easson and Pryce [1] contains the results for the potential curves correlating to the lowest dissociation limits of the neutral atomic species, computed with the modest configuration interaction (CI) expansions. In 1982-1984 Van Dishoeck. Langhoff, Dalgarno et al. in the series of
* Corresponding author. Tel.: (095) 939-48-40; Fax: (095) 93902-83; e-mail: [email protected]
papers [2-5] presented the detailed picture of the OH potential curves for a variety of electronic states including the ion-pair ones computed with different CI wavefunctions and different basis sets. The CI calculations of Vivie, Marian and Peyerimhoff [6] gave a picture of 6 states of OH correlating to the neutral atomic dissociation limits. At last, in 1995 Varandas and Voronin [7] have constructed potential energy curves tor ten electronic states of OH correlating to the same three lowest dissociation limits of neutral species as well as to the ionic limit O - ( 2 p ) + H +, and provided their analytical representations. These functions should be excellent in the asymptotic regions and in the short-range regions for those potentials, parameters of which have been fitted by the experimental (RKR) data, namely for the X 2II, A2E - and B 2 E ÷ states. However, in order to adjust parameters of many excited state curves, including the ion-pair ones, the authors relied on the ab initio calculations of Ref. [2-5], and in this respect their representations do not go beyond the previous understanding. Therefore, it turns out that the present
0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 0 0 9 - 2 6 1 4 ( 9 7 ) 0 0 8 3 5 - X
A. V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 276 (1997) 171-176
172
knowledge about the ion-pair states of OH, i.e. the states correlating to the ionic dissociation limit O - ( 2 p ) + H +, stems only from the calculations of the single research group [2-5]. Our concern about the potential energy curves of the ion-pair states of OH is motivated by their planned use in the diatomics-in-molecules (DIM) studies of oxygen/hydrogen systems including, in particular, water clusters. The DIM theory [8] provides a representation of the energy of a polyatomic molecule in terms of contributions from diatomic fragments in the specific electronic states, and knowledge of diatomic potential energy functions corresponding not only to the ground states, but to the excited states as well is critically important for successful applications. The experience gained by carrying out the DIM calculations both in our previous applications [9,10] and as described in the literature [11,12] show that the ion-pair states contribute considerably to the interaction energy, especially for the intermolecular interactions. In particular, the most recent DIM studies of the hydrogen fluoride dimer, (HF) 2 [13], taught us that without the ion-pair states this theory can hardly be applied to the construction of reliable potential energy surfaces. Keeping in mind this particular application of the potential energy curves of the excited states of OH, although there are other areas of their utilization (see e.g. Refs. [5,7]) the analysis of the results of previous ab initio calculations [2-5] shows that we face some ambiguities when attempting to rely on the results for the ion-pair states of OH. From the computational point of view the energies of the excited states within each symmetry species come out as the higher roots of the CI Hamiltonian matrix, and the results depend on several factors, first of all: basis set, CI expansion principles, and molecular orbitals (MO)
used in the CI expansions. The discrepancies due to a different choice of the calculation scheme shown by the authors of Refs. [2,4] for the vertical excitation energies from the ground state are about 0.2-0.6 eV (1500-5000 cm -l ), if the internuclear distances R close to the ground state equilibrium R e = 0.97 A are considered, and for the smaller R they amount up to 10 eV. Such uncertainties will have dramatic consequences for the DIM predictions even for simple polyatomic systems like the single water molecule. The data given in Tables 1 and 2 provide an additional confirmation of the importance of calculation details in predicting relative energies of excited states for this particular system. In Tables 1 and 2, the cases I and II correspond to the versions when the sets of MO's for the CI expansions are chosen following the prescriptions of Refs. [2-5], namely, the orbitals optimized for the 12~- (case I) and 14]~- (case II) states are taken. Case III presents another approach which is actually advocated here, namely, the MO's are optimized by the multiconfigurational self-consistent field (MCSCF) procedure in an average for all states of interest, and then used in the large-scale CI expansions. Quantitatively, the differences between the results of the CI versions shown in Tables 1 and 2 which are less than 0.6 eV (which, however, accounts for about 5000 cm - I ) do not seem particularly dangerous. Nevertheless, the main reasons which have prompted us to report the new calculations are that even the shapes of the excited ion-pair states (the third CI root in the 21-1 symmetry block, and the fourth root in the 2A 1 ( 2 ~ + / 2 A ) symmetry block) in the short range regions are noticeably different from those obtained in the previous calculations [2-5].
Table I Total energies E~ (au) correlating to three different dissociation limits and energy differences E 0 (eV) for the 21-[ states of OH at R = 0.97 A computed with the same basis set (AUG-cc-pVTZ), the same CI expansions but with different choices of MO (Cases I-III) for this CI expansion Case
E I[O(3p) + H( 2S~
E2[O( ID) + H( 2S~
E3[O- (2P) + H +]
El 2
E23
I H 111
-75.624321 -75.625591 -75.633065
-75.197879 -75.185194 -75.198748
-75.141251 -75.131600 -75.142585
11.60 11.98 11.82
1.54 1.46 1.53
A.V. Nemukhin, B.L. Grigorenko/ Chemical Physics Letters 276 (1997) 171-176
173
Table 2 Total energies E i (au) correlating to three different dissociation limits and energy differences Eq (eV) for the 2~+ states of OH at R = i.01 A computed with the same basis set (AUG-cc-pVTZ), the same CI expansions but with different choices of MO (Cases l-III) for this CI expansion. (The 2nd root in this symmetry block corresponds to the 2A state not shown hem.) Case
E I[O(ID) + H( 2 S)]
E3[O(IS) + H( 2 S)]
E4[O-(2P) + H+]
E, 3
E34
I H III
-75.468581 -75.470246 -75.484913
-75.236986 -75.238646 -75.232592
-75.074434 -75.078956 -75.088417
6.30 6.30 6.87
4.42 4.35 3.92
Fig. 1 shows the picture of the OH potentials of the 21-I symmetry type recomputed in this work in the manner close to that described in Refs. [2-5]. More specific, the [Ss5p2d/4slp] Gaussian basis set of Ref. [2] was taken, the MO's were obtained as the Hartree-Fock solutions for the lowest 4 2 - state, and the CI wavefunctions of the multireference single and double excitation type contained 7026 configurations. As it can be seen in Fig. 1 of this Letter, as well as in Refs. [2-5], the ion-pair 3 2II potential undergoes strong avoided crossings with the neighbouring energy curves for the R values between 1 and 2.5 A. The strong avoided crossings and sharp changes in the shape of the curve are also observed
for the ion-pair C 2E+ potential as given in Refs. [2-51. Fig. 2 shows the total view of the potential curves of OH calculated in this work when using an approximation which should be considered as more advantageous than that of Ref. [2-5]. We see that the shape of the ion-pair potentials is different from the previous picture, namely, the avoided crossing behaviour is not as sharp, as in Refs. [2-5]. Quantitative differences in the region around the ground state equilibrium point are also obvious.
0,00 -0.05
0,05
O'(2p) + H +
-0,10
0,00
I
O_(2+ p)H+
-0,15
-0.05
-0.20
-0,10
3 2n
-0,25
-0.15
~.___ B 2x*
t0 -0,30
>~
= -0,20 o~ E> -0,25
2
:=
)
~ -0,35 C UJ -0,40
LU -0,30 -0,45 O(3p) + H(2S)
-0,35
O(1S)+
Z2r~
H(2S)
O(1D)+ H(2s)
~J~A2E%
O(3p) + H( 2s )
-0,50 !
-0,40
-0,55
-0,45
-0,60
-0,50 I
1
,
i
I
2
3
,
I
4
,
I
5
R,A Fig. 1. The potential functions for the 2II states of OH computed with the CI procedure similar to those used in Refs. [2-5]. The zero of energy is set at - 75.0 an.
-0,65
I
I
i
I
I
1
2
3
4
5
R,A Fig. 2. The potential curves of the 2II and 22+ states of OH calculated with the state-averaged CASSCF orbital selection for the CI wavefunctions. The zero of energy is set at - 75.0 au.
174
A.V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 276 (1997) 171-176
The potential curves shown in Fig. 2 have been computed by using the following strategy within the GAMESS program suits [14]. The correlation consistent polarized valence basis sets augmented with diffuse functions (AUG-cc-pVTZ) have been used to describe the orbitals. The MO's for CI expansions have been obtained with the MCSCF method, namely, by the complete active space SCF, CASSCF method (the full optimized reaction space, FORS, option in GAMESS) for each symmetry block ( 2A 1.2, 2BI. 2) of the C2v subgroup by distributing properly 7 valence electrons over the orbitals 2tr, 3tr, 4tr, l'rr. In the course of MO and configuration expansion coefficient optimizations the density matrices have been averaged with the equal weights for all the requested CI roots, namely, 3 for the 2B 1 (21-I) states, and 4 for the 2A I ( 2 ~ + / 2A) states. These sets of MO's have been introduced into the CI expansions of the multireference CI type, namely, the second order CI (SOCI) option in the GAMESS programs, taking the FORS configurations as the reference ones. The actual numbers of configuration functions in CI are 117408 for the 2B I (2I-I) symmetry block and 118003 for the 2A I block. Such a procedure should provide a balanced treatment for the excited state potential functions. The energies of the X 21I and A2E + states which are the lowest in their symmetry blocks have also been re-computed with the MCSCF optimization for the lowest roots. However, these calculations have been performed only in order to estimate an accuracy level of this approach, because it is known since long ago that the orbitals optimized by the MCSCF procedure for the ground states are bad for calculations of excited states within this symmetry block [15], and on the other hand, the better quality ab initio results for these lowest energy potentials are nicely described in the literature [16,17]. Complete tables of computed energies for the X 21"I, 2 2II, 3 211, A2~,+, B 2X+, C 2X+, 2A states of OH covering the region of R between 0.85 and 5 A may be obtained from the authors upon request. Fig. 2 illustrates the general view of the potentials with the main distinction from the previous [2-5,7] pictures for the ion-pair 3 21I and C 2X+ states in the region 1 < R < 2.5 A. The accuracy of these calculations may be estimated by comparing theoretical and experimental molecular constants. The ex-
perimental equilibrium internuclear distances [18] for the X 21-[ (0.97 A), A2~+(1.01 A), B 2E+(1.85 A) and C 2~+ (2.05 A) states are nicely reproduced. For the dissociation energies De estimated here as energy differences between "dissociation limit" at R = 100 A and corresponding equilibrium points we obtain: 4.48 eV for X 2II (experimental value is 4.63 [18]), 2.38 eV for A2~ + (exp. cited in Ref. [2] is 2.53 eV), 0.11 eV for B 2X+ (exp. cited in Ref. [2] is 0.17 eV). Therefore, the errors of less than 0.15 eV are typical for this approach. For the ion-pair states we predict the following dissociation energies: 5.92 eV for 3 21-1, and 5.79 eV for C 2E+. The errors in the excitation energies are partly due to the inaccuracies in relative positions of atomic dissociation limits. For instance, the calculated difference of the O(ID) + H(2S) and O(3p) + H(2S) energies, 2.03 eV, deviates from the experimental O(ID) -- O(3p) value 1.97 eV [19] by 0.06 eV. If we correct our computed dissociation limits by the experimental data [19], then the adiabatic excitation energies from the X 2II ground state are in a good agreement with the spectroscopic estimates [18]: 4.06 eV for A2E + (exp. 4.05), 8.56 eV for B 2~+ (exp. 8.65), 10.82 eV for C 2~+ (exp. 11.09). Therefore, these computed excited state potentials may be recommended for future applications. Another point of our concern in respect of the DIM perspectives is the III potential curve of the hydroxide ion OH-. The ground state X 12~+ potential function is known very accurately from high quality ab initio calculations [16]. The excited IlI potential for the short R values refers to the state of OH- which is unstable with respect to the electron detachment OH + e. The long range segment of this potential was estimated in the work of Tellinghuisen and Ewig and it was concluded that at large R this curve was repulsive [20]. Totally repulsive shape for this potential function is also given in Ref. [11] following the results of a semi-qualitative treatment. Fig. 3 shows the behaviour of the ground state potentials of OH (X 2II), OH- (X 1~+) and that of the ~II potential of OH- computed in the same fashion as described above for the lowest energy potentials of OH, namely, with the help of the large-scale SOCI procedure after the CASSCF orbital optimization. However, in this series of calculations one more diffuse function (hydrogen centered
A. V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 2 76 (I 997) 171-176
O(3p) + H(2S)
ln~O-(2P)+H(2S)
-0,50
-0,55
e-
/
-0,60
-0,65
.0,7~
X xl~
I 1
l
+
I 2
,
I 3
i
I 4
L
I 5
,
R,A Fig. 3. The computed potential curves of the tII and J~7+ states of OH- with the reference to the ground state OH potential. The zero of energy is set at - 75.0 au.
s-type AO with the exponent 0.0001) was added to the AUG-cc-pVTZ basis set. Only in this case the true CASSCF solutions in the vicinity of the crossing point near 1.75 A of the X 2II potential of OH and the I II potential of O H - could be obtained. To the shorter distances, the free electron occupies the MO composed almost exclusively of this diffuse function. We mention that the parameters of the computed ground state X I E + potential O H - are of the same good accuracy as for the neutral molecule. Namely, the dissociation energy De is 4.84 eV compared to experimental [18] 4.98 eV, and if we correct the relative position of the dissociation limits O(3p) + H(2S) and O - ( 2 p ) + H by taking into account the difference between experimental 1.465 eV [21] and computed with this approach (1.02 eV) electron affinity of O(3p), then the theoretical electron affinity of OH completely coincides with the experimental value 1.83 eV [22]. The picture in Fig. 3 illustrates the situation on calculations of the autoionizing states with the customary quantum chemistry tools, seen also for instance, in the large-scale CI treatment of H F - [23].
175
Clearly, upon saturating the basis set with a proper amount of diffuse functions and providing a proper treatment of correlation, the energy of OH- (l I I) will tend toward the energy of the neutral molecule OH (X 2II) at distances to the left from the intersection point. The behaviour at large distances can be reproduced without substantial difficulties with the CI method. We believe that the present calculations give a reliable picture of the t II potential of OH- in that region as well as the position of the intersection point 1.75 A. In conclusion, we should notice that the results of these calculations do not pretend on the high accuracy of modem ab initio treatments of simple systems, composed of oxygen and hydrogen, like for instance, in Refs. [24,25], however, they should provide a more balanced description of the ion-pair potential functions of OH and of the O H - anion potentials than used before in attempts to apply the DIM theory for studies of structure and dynamics of oxygen/hydrogen systems. We hope that these excited state potentials may be helpful in other applications as well.
Acknowledgements This work was supported in part by the Russian Basic Research Foundation under Grant 96-03-32284. The authors are grateful to Dr. V.I. Pupyshev for helpful discussions.
References [1] I. Easson, M.H.L. Pryce, Can. J. Phys. 51 (1973) 518. [2] S.R. Langhoff, E.F. van Dishoeck, R. Wetmore, A. Dalgarno, J. Chem. Phys. 77 (1982) 1379. [3] E.F. van Dishoeck, R.S. Langhoff, A. Dalgarno, J. Chem. Phys. 78 (1983) 4552. [4] E.F. van Dishoeck, A. Dalgarno, J. Chem. Phys. 79 (1983) 873. [5] E.F. van Dishoeck, M.C. van Hemert, A.C. Allison, A. Dalgarno, J. Chem. Phys. 81 (1984) 5709. [6] R. Vivie, C.M. Marian, S.D. Peyerimhoff, Mol. Phys. 63 (1988) 3. [7] A.J.C. Varandas, A.I. Voronin, Chem. Phys. 194 (1995) 91. [8] J. Tully. in: Modern Theoretical Chemistry, Semiempirical Methods of Electronic Structure Calculations, Vol. 7A, ed. G.A. Segal (Plenum Press, New York, 1977). ch. 6.
176
A. V. Nemukhin, B.L. Grigorenko / Chemical Physics Letters 276 (1997) 171-176
[9] A.V. Nemukhin, N.F. Stepanov, Int. J. Quantum Chem. 15 (1979) 49. [10] B.L. Grigorenko, A.V. Nemukhin, V.A. Apkarian, J. Chem. Phys. 104 (1996) 5510. [11] R. Polak, I. Paidarova, P.J. Kuntz, J. Chem. Phys. 82 (1985) 2352. [12] I. Last, T.F. George, M.E. Fajardo, V.A. Apkarian, J. Chem. Phys. 87 (1987) 5917. [13] B.L. Grigorenko, V.A. Apkarian, A.V. Nemukhin, in preparation. [14] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elhert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Compnt. Chem. 14 (1993) 1347. [15] J. Almlof, A.V. Nemukhin, A. Heiberg, Int. J. Quantum Chem. 20 (1981) 655. [16] H.-J. Werner, P. Rosmus, E.-A. Reinsch, J. Chem. Phys. 79 (1983) 905.
[17] C.W. Bauschlicher, S.R. Langhoff, J. Chem. Phys. 87 0987) 4665. [18] K.P. Hubcr and G. Herzberg, Molecular Spectra and Molecular Structure, Voi. 4. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). [19] A.A. Radzig and B.M. Smirnov, Handbook on Atomic and Molecular Physics (Atomizdat, Moscow, 1980). [20] J. TeUinghuisen, C.S. Ewig, Chem. Phys. Lett. 165 (1990) 355. [21] H. Hotop, W.C. Lineberger, J. Phys. Chem. Ref. Data 4 (1975) 539. [22] P.A. Schulz, R.A. Mead, P.L. Jones, W.C. Lineherger, J. Chem. Phys. 77 (1982) 1153. [23] M. Bet~ndorff, RJ. Buenker, S.D. Peyerimhoff, Mol. Phys. 50 (1983) 1363. [24] P.E.M. Siegbahn, J. Compnt. Chem. 17 (1996) 1099. [25] H. Partridge, D.W. Schwenke, J. Chem. Phys. 106 (1997) 4618.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 276 (I 997) 171 - 176
Ab initio potential functions for the ionic states of OH A.V. Nemukhin *, B.L. Grigorenko Department of Chemistry Moscow State Unit:ersi~.', Moscow, 119899, Russia Received 26 June 1997; in final form 26 June 1997
Abstract
Potential curves of the OH molecule correlating to the four lowest energy dissociation limits O(3p) + H(2S), O(]D) + H(2S), O(IS) + H(2S), O-(2P) + H ÷ have been computed at the CI/CASSCF level with the AUG-cc-pVTZ basis sets with a special emphasis on the ion-pair states 3 2I-1 and C 2E +. A balanced treatment of the excited state potentials is achieved by using the state-averaging MO optimization procedure. The X ~E ÷ and ]II potentials of OH- have been also considered. After empirical correction of the errors at the dissociation limits, the computed functions are recommended for the future use in the diatomics-in-molecules studies of the structure and dynamics of oxygen/hydrogen containing molecular systems. © 1997 Elsevier Science B.V. Potential energy functions of OH correlating to the lowest dissociation limits, which include the neutral O(3p) + H(2S), O ( I D ) + H(2S), O ( I S ) + H(2S) as well as the ionic O - ( 2 p ) + H ÷ channels, are basically known from the results of ab initio quantum chemistry calculations which are nicely consistent with the reliable experimental spectral data. Several high quality calculations have been published not long ago, we mention here only the works which describe the potentials of the ground and excited states of OH for the extended regions of internuclear distances. The paper of Easson and Pryce [1] contains the results for the potential curves correlating to the lowest dissociation limits of the neutral atomic species, computed with the modest configuration interaction (CI) expansions. In 1982-1984 Van Dishoeck. Langhoff, Dalgarno et al. in the series of
* Corresponding author. Tel.: (095) 939-48-40; Fax: (095) 93902-83; e-mail: [email protected]
papers [2-5] presented the detailed picture of the OH potential curves for a variety of electronic states including the ion-pair ones computed with different CI wavefunctions and different basis sets. The CI calculations of Vivie, Marian and Peyerimhoff [6] gave a picture of 6 states of OH correlating to the neutral atomic dissociation limits. At last, in 1995 Varandas and Voronin [7] have constructed potential energy curves tor ten electronic states of OH correlating to the same three lowest dissociation limits of neutral species as well as to the ionic limit O - ( 2 p ) + H +, and provided their analytical representations. These functions should be excellent in the asymptotic regions and in the short-range regions for those potentials, parameters of which have been fitted by the experimental (RKR) data, namely for the X 2II, A2E - and B 2 E ÷ states. However, in order to adjust parameters of many excited state curves, including the ion-pair ones, the authors relied on the ab initio calculations of Ref. [2-5], and in this respect their representations do not go beyond the previous understanding. Therefore, it turns out that the present
0009-2614/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. Pll S 0 0 0 9 - 2 6 1 4 ( 9 7 ) 0 0 8 3 5 - X
A. V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 276 (1997) 171-176
172
knowledge about the ion-pair states of OH, i.e. the states correlating to the ionic dissociation limit O - ( 2 p ) + H +, stems only from the calculations of the single research group [2-5]. Our concern about the potential energy curves of the ion-pair states of OH is motivated by their planned use in the diatomics-in-molecules (DIM) studies of oxygen/hydrogen systems including, in particular, water clusters. The DIM theory [8] provides a representation of the energy of a polyatomic molecule in terms of contributions from diatomic fragments in the specific electronic states, and knowledge of diatomic potential energy functions corresponding not only to the ground states, but to the excited states as well is critically important for successful applications. The experience gained by carrying out the DIM calculations both in our previous applications [9,10] and as described in the literature [11,12] show that the ion-pair states contribute considerably to the interaction energy, especially for the intermolecular interactions. In particular, the most recent DIM studies of the hydrogen fluoride dimer, (HF) 2 [13], taught us that without the ion-pair states this theory can hardly be applied to the construction of reliable potential energy surfaces. Keeping in mind this particular application of the potential energy curves of the excited states of OH, although there are other areas of their utilization (see e.g. Refs. [5,7]) the analysis of the results of previous ab initio calculations [2-5] shows that we face some ambiguities when attempting to rely on the results for the ion-pair states of OH. From the computational point of view the energies of the excited states within each symmetry species come out as the higher roots of the CI Hamiltonian matrix, and the results depend on several factors, first of all: basis set, CI expansion principles, and molecular orbitals (MO)
used in the CI expansions. The discrepancies due to a different choice of the calculation scheme shown by the authors of Refs. [2,4] for the vertical excitation energies from the ground state are about 0.2-0.6 eV (1500-5000 cm -l ), if the internuclear distances R close to the ground state equilibrium R e = 0.97 A are considered, and for the smaller R they amount up to 10 eV. Such uncertainties will have dramatic consequences for the DIM predictions even for simple polyatomic systems like the single water molecule. The data given in Tables 1 and 2 provide an additional confirmation of the importance of calculation details in predicting relative energies of excited states for this particular system. In Tables 1 and 2, the cases I and II correspond to the versions when the sets of MO's for the CI expansions are chosen following the prescriptions of Refs. [2-5], namely, the orbitals optimized for the 12~- (case I) and 14]~- (case II) states are taken. Case III presents another approach which is actually advocated here, namely, the MO's are optimized by the multiconfigurational self-consistent field (MCSCF) procedure in an average for all states of interest, and then used in the large-scale CI expansions. Quantitatively, the differences between the results of the CI versions shown in Tables 1 and 2 which are less than 0.6 eV (which, however, accounts for about 5000 cm - I ) do not seem particularly dangerous. Nevertheless, the main reasons which have prompted us to report the new calculations are that even the shapes of the excited ion-pair states (the third CI root in the 21-1 symmetry block, and the fourth root in the 2A 1 ( 2 ~ + / 2 A ) symmetry block) in the short range regions are noticeably different from those obtained in the previous calculations [2-5].
Table I Total energies E~ (au) correlating to three different dissociation limits and energy differences E 0 (eV) for the 21-[ states of OH at R = 0.97 A computed with the same basis set (AUG-cc-pVTZ), the same CI expansions but with different choices of MO (Cases I-III) for this CI expansion Case
E I[O(3p) + H( 2S~
E2[O( ID) + H( 2S~
E3[O- (2P) + H +]
El 2
E23
I H 111
-75.624321 -75.625591 -75.633065
-75.197879 -75.185194 -75.198748
-75.141251 -75.131600 -75.142585
11.60 11.98 11.82
1.54 1.46 1.53
A.V. Nemukhin, B.L. Grigorenko/ Chemical Physics Letters 276 (1997) 171-176
173
Table 2 Total energies E i (au) correlating to three different dissociation limits and energy differences Eq (eV) for the 2~+ states of OH at R = i.01 A computed with the same basis set (AUG-cc-pVTZ), the same CI expansions but with different choices of MO (Cases l-III) for this CI expansion. (The 2nd root in this symmetry block corresponds to the 2A state not shown hem.) Case
E I[O(ID) + H( 2 S)]
E3[O(IS) + H( 2 S)]
E4[O-(2P) + H+]
E, 3
E34
I H III
-75.468581 -75.470246 -75.484913
-75.236986 -75.238646 -75.232592
-75.074434 -75.078956 -75.088417
6.30 6.30 6.87
4.42 4.35 3.92
Fig. 1 shows the picture of the OH potentials of the 21-I symmetry type recomputed in this work in the manner close to that described in Refs. [2-5]. More specific, the [Ss5p2d/4slp] Gaussian basis set of Ref. [2] was taken, the MO's were obtained as the Hartree-Fock solutions for the lowest 4 2 - state, and the CI wavefunctions of the multireference single and double excitation type contained 7026 configurations. As it can be seen in Fig. 1 of this Letter, as well as in Refs. [2-5], the ion-pair 3 2II potential undergoes strong avoided crossings with the neighbouring energy curves for the R values between 1 and 2.5 A. The strong avoided crossings and sharp changes in the shape of the curve are also observed
for the ion-pair C 2E+ potential as given in Refs. [2-51. Fig. 2 shows the total view of the potential curves of OH calculated in this work when using an approximation which should be considered as more advantageous than that of Ref. [2-5]. We see that the shape of the ion-pair potentials is different from the previous picture, namely, the avoided crossing behaviour is not as sharp, as in Refs. [2-5]. Quantitative differences in the region around the ground state equilibrium point are also obvious.
0,00 -0.05
0,05
O'(2p) + H +
-0,10
0,00
I
O_(2+ p)H+
-0,15
-0.05
-0.20
-0,10
3 2n
-0,25
-0.15
~.___ B 2x*
t0 -0,30
>~
= -0,20 o~ E> -0,25
2
:=
)
~ -0,35 C UJ -0,40
LU -0,30 -0,45 O(3p) + H(2S)
-0,35
O(1S)+
Z2r~
H(2S)
O(1D)+ H(2s)
~J~A2E%
O(3p) + H( 2s )
-0,50 !
-0,40
-0,55
-0,45
-0,60
-0,50 I
1
,
i
I
2
3
,
I
4
,
I
5
R,A Fig. 1. The potential functions for the 2II states of OH computed with the CI procedure similar to those used in Refs. [2-5]. The zero of energy is set at - 75.0 an.
-0,65
I
I
i
I
I
1
2
3
4
5
R,A Fig. 2. The potential curves of the 2II and 22+ states of OH calculated with the state-averaged CASSCF orbital selection for the CI wavefunctions. The zero of energy is set at - 75.0 au.
174
A.V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 276 (1997) 171-176
The potential curves shown in Fig. 2 have been computed by using the following strategy within the GAMESS program suits [14]. The correlation consistent polarized valence basis sets augmented with diffuse functions (AUG-cc-pVTZ) have been used to describe the orbitals. The MO's for CI expansions have been obtained with the MCSCF method, namely, by the complete active space SCF, CASSCF method (the full optimized reaction space, FORS, option in GAMESS) for each symmetry block ( 2A 1.2, 2BI. 2) of the C2v subgroup by distributing properly 7 valence electrons over the orbitals 2tr, 3tr, 4tr, l'rr. In the course of MO and configuration expansion coefficient optimizations the density matrices have been averaged with the equal weights for all the requested CI roots, namely, 3 for the 2B 1 (21-I) states, and 4 for the 2A I ( 2 ~ + / 2A) states. These sets of MO's have been introduced into the CI expansions of the multireference CI type, namely, the second order CI (SOCI) option in the GAMESS programs, taking the FORS configurations as the reference ones. The actual numbers of configuration functions in CI are 117408 for the 2B I (2I-I) symmetry block and 118003 for the 2A I block. Such a procedure should provide a balanced treatment for the excited state potential functions. The energies of the X 21I and A2E + states which are the lowest in their symmetry blocks have also been re-computed with the MCSCF optimization for the lowest roots. However, these calculations have been performed only in order to estimate an accuracy level of this approach, because it is known since long ago that the orbitals optimized by the MCSCF procedure for the ground states are bad for calculations of excited states within this symmetry block [15], and on the other hand, the better quality ab initio results for these lowest energy potentials are nicely described in the literature [16,17]. Complete tables of computed energies for the X 21"I, 2 2II, 3 211, A2~,+, B 2X+, C 2X+, 2A states of OH covering the region of R between 0.85 and 5 A may be obtained from the authors upon request. Fig. 2 illustrates the general view of the potentials with the main distinction from the previous [2-5,7] pictures for the ion-pair 3 21I and C 2X+ states in the region 1 < R < 2.5 A. The accuracy of these calculations may be estimated by comparing theoretical and experimental molecular constants. The ex-
perimental equilibrium internuclear distances [18] for the X 21-[ (0.97 A), A2~+(1.01 A), B 2E+(1.85 A) and C 2~+ (2.05 A) states are nicely reproduced. For the dissociation energies De estimated here as energy differences between "dissociation limit" at R = 100 A and corresponding equilibrium points we obtain: 4.48 eV for X 2II (experimental value is 4.63 [18]), 2.38 eV for A2~ + (exp. cited in Ref. [2] is 2.53 eV), 0.11 eV for B 2X+ (exp. cited in Ref. [2] is 0.17 eV). Therefore, the errors of less than 0.15 eV are typical for this approach. For the ion-pair states we predict the following dissociation energies: 5.92 eV for 3 21-1, and 5.79 eV for C 2E+. The errors in the excitation energies are partly due to the inaccuracies in relative positions of atomic dissociation limits. For instance, the calculated difference of the O(ID) + H(2S) and O(3p) + H(2S) energies, 2.03 eV, deviates from the experimental O(ID) -- O(3p) value 1.97 eV [19] by 0.06 eV. If we correct our computed dissociation limits by the experimental data [19], then the adiabatic excitation energies from the X 2II ground state are in a good agreement with the spectroscopic estimates [18]: 4.06 eV for A2E + (exp. 4.05), 8.56 eV for B 2~+ (exp. 8.65), 10.82 eV for C 2~+ (exp. 11.09). Therefore, these computed excited state potentials may be recommended for future applications. Another point of our concern in respect of the DIM perspectives is the III potential curve of the hydroxide ion OH-. The ground state X 12~+ potential function is known very accurately from high quality ab initio calculations [16]. The excited IlI potential for the short R values refers to the state of OH- which is unstable with respect to the electron detachment OH + e. The long range segment of this potential was estimated in the work of Tellinghuisen and Ewig and it was concluded that at large R this curve was repulsive [20]. Totally repulsive shape for this potential function is also given in Ref. [11] following the results of a semi-qualitative treatment. Fig. 3 shows the behaviour of the ground state potentials of OH (X 2II), OH- (X 1~+) and that of the ~II potential of OH- computed in the same fashion as described above for the lowest energy potentials of OH, namely, with the help of the large-scale SOCI procedure after the CASSCF orbital optimization. However, in this series of calculations one more diffuse function (hydrogen centered
A. V. Nemukhin, B.L Grigorenko / Chemical Physics Letters 2 76 (I 997) 171-176
O(3p) + H(2S)
ln~O-(2P)+H(2S)
-0,50
-0,55
e-
/
-0,60
-0,65
.0,7~
X xl~
I 1
l
+
I 2
,
I 3
i
I 4
L
I 5
,
R,A Fig. 3. The computed potential curves of the tII and J~7+ states of OH- with the reference to the ground state OH potential. The zero of energy is set at - 75.0 au.
s-type AO with the exponent 0.0001) was added to the AUG-cc-pVTZ basis set. Only in this case the true CASSCF solutions in the vicinity of the crossing point near 1.75 A of the X 2II potential of OH and the I II potential of O H - could be obtained. To the shorter distances, the free electron occupies the MO composed almost exclusively of this diffuse function. We mention that the parameters of the computed ground state X I E + potential O H - are of the same good accuracy as for the neutral molecule. Namely, the dissociation energy De is 4.84 eV compared to experimental [18] 4.98 eV, and if we correct the relative position of the dissociation limits O(3p) + H(2S) and O - ( 2 p ) + H by taking into account the difference between experimental 1.465 eV [21] and computed with this approach (1.02 eV) electron affinity of O(3p), then the theoretical electron affinity of OH completely coincides with the experimental value 1.83 eV [22]. The picture in Fig. 3 illustrates the situation on calculations of the autoionizing states with the customary quantum chemistry tools, seen also for instance, in the large-scale CI treatment of H F - [23].
175
Clearly, upon saturating the basis set with a proper amount of diffuse functions and providing a proper treatment of correlation, the energy of OH- (l I I) will tend toward the energy of the neutral molecule OH (X 2II) at distances to the left from the intersection point. The behaviour at large distances can be reproduced without substantial difficulties with the CI method. We believe that the present calculations give a reliable picture of the t II potential of OH- in that region as well as the position of the intersection point 1.75 A. In conclusion, we should notice that the results of these calculations do not pretend on the high accuracy of modem ab initio treatments of simple systems, composed of oxygen and hydrogen, like for instance, in Refs. [24,25], however, they should provide a more balanced description of the ion-pair potential functions of OH and of the O H - anion potentials than used before in attempts to apply the DIM theory for studies of structure and dynamics of oxygen/hydrogen systems. We hope that these excited state potentials may be helpful in other applications as well.
Acknowledgements This work was supported in part by the Russian Basic Research Foundation under Grant 96-03-32284. The authors are grateful to Dr. V.I. Pupyshev for helpful discussions.
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[9] A.V. Nemukhin, N.F. Stepanov, Int. J. Quantum Chem. 15 (1979) 49. [10] B.L. Grigorenko, A.V. Nemukhin, V.A. Apkarian, J. Chem. Phys. 104 (1996) 5510. [11] R. Polak, I. Paidarova, P.J. Kuntz, J. Chem. Phys. 82 (1985) 2352. [12] I. Last, T.F. George, M.E. Fajardo, V.A. Apkarian, J. Chem. Phys. 87 (1987) 5917. [13] B.L. Grigorenko, V.A. Apkarian, A.V. Nemukhin, in preparation. [14] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elhert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S.J. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. Compnt. Chem. 14 (1993) 1347. [15] J. Almlof, A.V. Nemukhin, A. Heiberg, Int. J. Quantum Chem. 20 (1981) 655. [16] H.-J. Werner, P. Rosmus, E.-A. Reinsch, J. Chem. Phys. 79 (1983) 905.
[17] C.W. Bauschlicher, S.R. Langhoff, J. Chem. Phys. 87 0987) 4665. [18] K.P. Hubcr and G. Herzberg, Molecular Spectra and Molecular Structure, Voi. 4. Constants of Diatomic Molecules (Van Nostrand Reinhold, New York, 1979). [19] A.A. Radzig and B.M. Smirnov, Handbook on Atomic and Molecular Physics (Atomizdat, Moscow, 1980). [20] J. TeUinghuisen, C.S. Ewig, Chem. Phys. Lett. 165 (1990) 355. [21] H. Hotop, W.C. Lineberger, J. Phys. Chem. Ref. Data 4 (1975) 539. [22] P.A. Schulz, R.A. Mead, P.L. Jones, W.C. Lineherger, J. Chem. Phys. 77 (1982) 1153. [23] M. Bet~ndorff, RJ. Buenker, S.D. Peyerimhoff, Mol. Phys. 50 (1983) 1363. [24] P.E.M. Siegbahn, J. Compnt. Chem. 17 (1996) 1099. [25] H. Partridge, D.W. Schwenke, J. Chem. Phys. 106 (1997) 4618.