J . Phys. Chem. 1992, 96,2123-2129
2123
Ab Initio Muitireference Configuration Interaction and Coupled Cluster Studies of Potential Surfaces for Proton Transfer in (H3N-- -H- - -OH,)+ S. Roszak,*.t*lU. Kaldor,t D. A. Chapman,+ and Joyce J. Kaufmant Department of Chemistry, The Johns Hopkins University, Baltimore, Maryland 21218, and School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel (Received: September 16, 1991; In Final Form: October 25, 1991)
The multiple reference doubleexcitation configuration interaction method (MRD-CI) and the coupled cluster method (CCM) were applied for the studies of the ground-state and low-lying excited states for the proton-transfer system (H3N---H-- -OH2)+. The geometry optimization at the SCF level indicates the rapid change in geometry of subunits while the proton moves between N and 0 atoms. The significant difference was found between the structure of potential curves for the short N-O distances (2.707, 2.95, 3.2 A) and the long N-O distance (5.0 A). The complicated multireference structure of potential curves results from the strong interactions between them. The ground state is described by a single determinant wave function for short N-0 distances; however, for a distance of 5.0 A the multireference structure becomes significant for intermediate regions of the hydrogen bond. The correlation between the protonation potential surfaces for NH3 and H 2 0 and the structure of surfaces for the proton-transfer system of the complex can be recognized. The simple interpretation of the gross atomic population on the transferred proton indicates that the reaction proceeds as a “proton transfer” in the ground electronic state and a “hydrogen transfer” in low-lying excited states.
Introduction Proton-transfer reactions are important in chemical and biological processes,’ including photosynthesis2 and ~ i s i o n . ~Both of the mentioned processes often involve sufficient energy to proceed in excited states. The proton-transfer reaction has been extensively investigated by experimental4 and theoretical methods.s As the proton-transfer processes involve partial bond breaking and re-forming, a quantitatively accurate treatment of the processes require consideration of electron correlation effects in some regions even at a multideterminantal level. The few previous a b initio studies including electron correlation based on multideterminental configuration interaction wave function have shown discrepancies with Hartree-Fock studies.6 In addition previous theoretical investigations were focused on the ground-state processes in geometries relatively close to equilibrium. However, biological systems offer a variety of geometries where some of them are far from model cases with geometries from the gas phase. The proton-transfer reaction can also be seen as two consecutive elementary deprotonation/protonation processes represented by the general formula H+ + B = HB+. The ionization potential of H (13.6 eV) is higher than that of B for organic and most inorganic molecules, and the separated pair H+ B will be higher in energy than the separated pair H B+. The reaction path for this system involves, therefore, an avoided crossing, and its theoretical study requires multideterminant method^.^ The transfer of a proton between the nitrogen atom of NH3 and the oxygen atom of H 2 0 is a superposition of two protonation/deprotonation processes investigated previously by us by MRD-CI and MR-CCM: amm0nia7 and water! The deprotonation reaction starts with moving the proton out of the protonated molecule, but the ground-state potential curve changes its character, and the lowest potential surface leads to molecular cation and hydrogen. The corresponding excited w e continues the character of the ground state after the “avoiding” region, and this excited state leads to the proton and molecule. The superposition of protonation/deprotonation potential curves of water and ammonia would lead, at fairly large N-O separation, to the situation where the avoided crossing has to be taken into account. It would be manifested by the appearance of the multideterminantal character of the proton-transfer pathway.
+
+
‘The Johns Hookins University. *Tel Aviv UniGrsity. Visiting scientist, The Johns Hopkins University. Permanent address: Institute of Organic and Physical Chemistry (1-4), Wyb. Wyspinskiego 27, 50-370 Wroclaw, Poland.
Calculations have been performed within the multiplareference double-excitation configuration interaction method and coupled cluster method. The multireference CI method, by giving the wave function in terms of the most important configurations, allows better understanding of the nature of reaction. The multireference CI method is approximately size consistent by applying a correction to the full CI. The major advantage of the coupled cluster method is the ability to sum numerous perturbation terms to infinite order, thus accounting for large classes of virtual excitations, while being size consistent. The CC calculations may serve as a test for the size consistency. On the other hand, it is interesting to compare performance of both methods especially in cases when the wave function assumes multireference structure. MRD-CI calculations for the ground state and two low-lying excited singlets and two triplets has been performed for optimized geometries of (H,N- - -H- - -OH2)+ complex. Coupled cluster calculations have been carried out for the ground and the lowest excited singlet and triplet states.
Methodology Multiple Reference S i and Double-Excitation configuration Interaction Method (MRDCI). The configuration interaction treatment is of the standard multiple reference singlets and doublets configuration interaction methods (MRD-CI) developed by Buenker et al.9310 The computations are carried out employing the table CI algorithm.” The number of symmetry-adapted functions (SAFs) generated by single and double excitations for (1) Proton-Transfer Reactions; Caldin, E., Gold, V.,Eds.; Chapman and Hail: London. 1975. -- -(2) Sauer, K. Acc. Chem. Res. 1918, 11, 257. ( 3 ) Honig, B.; Ebrey, T.; Callender, R. H.; Dinur, U.; Ottolenghi, M.Prm. Natl. Acad. Sci. U.S.A. 1919, 76. 2503. (4) Bohme, D. In Ionic Processes in the Gas Phase; Almester Ferreing, M. A., Ed.; Reidel: Dordrecht, Holland, 1984; p 11 1. ( 5 ) Scheiner, S. Acc. Chem. Res. 1985, 18, 174. ( 6 ) Scheiner, S.; Harding, L. B. J . Phys. Chem. 1983,87, 1145. ( 7 ) Kaldor, U.; Roszak, S.; Hariharan, P. C.; Kaufman, J. J. J . Chem. Phys. 1989, 90, 6395. ( 8 ) Roszak, S.; Kaldor, U.; Chapman, D. A.; Kaufman, J. J., in prepara-
tion. (9) Buenker, R. J.; Peyerimhoff, S. D. In New Horizons of Quantum Chemistry; Lowdin, P.-O., Pullman, B., Eds.; Reidel: Dordrecht, 1983; p 183. (IO) Buenker, R. J.; Peyerimhoff, S. D.; Butcher, W. Mol. Phys. 1983,35, 771. (1 1 ) (a) Buenker, R. J. In Studies in Physical and Theoretical Chemistry; Current Aspects of Quantum Chemistry, 1981; Carbo, R., Ed.; Elsevier Scientific: Amsterdam, 1982; Vol. 21, p 17. (b) Buenker, R. J. In Proceedings of Workshop on Quantum Chemistry and Molecular Physics; Wollongong: Australia, 1980. (c) Buenker, R.J.; Philip, R. A. J . Mol. Struct. (Themhem) 1985, 123, 291.
0022-3654192 12096-2 123%03.00/0 , 0 1992 American Chemical Society I
,
~~
2124
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992
a given electronic state was reduced by employing an energy selection criterion12with an assumed threshold T. The eigenvalues of diagonalizing the matrix corresponding to T together with the summed perturbative energy lowerings of the nonselected configurations in the total MRD-CI space have then been employedi3 to determine an extrapolated zero-threshold value (EEX,MRD-CI). The energy corresponding to the full CI treatment has been estimated via the relation EFCI= EEX.MRD-CI + (EEx,MRD-CI - Eref)(1 - Cci2) (1)
which is a generalizationi4 of the correction formula suggested by Langhoff and Davidson,ls where Erefis the reference secular equation energy. The Davidson formula was shown by Paldusi6 to be a good correction for the lack of size extensivity of the energy with single and double excitations. In a recent article'jb Buenker and co-workers have shown that there is excellent agreement of the MRD-CI method (as described above) with a large series of full CI benchmark calculatins (a root-mean-square deviation of only 0.94 kcal/mol relative to the full CI values). Multireference Coupled Cluster Method (MR-CCM). The exp(S) or coupled cluster m e t h ~ d * ~(CCM) - ~ I has been used widely in recent years for ab initio electronic structure calculations in closed-shell, nondegenerate systems, with highly satisfactory results.22 Physically it amounts to the inclusion of certain types of excitations to all orders. The method used here follows Lindgren's2j choice of a normal-ordered wave operator: Q = (exp(S)) = 1
+ S + Y2(S2)+ ...
(2)
S is the excitation operator describing connected single, double, etc., excitations:
where si,si,, etc., are excitation amplitudes, and the braces denote normal order with respect to a reference (core) determinant. The summation is carried over with respect to a reference (core) determinant. The summation is carried over connected terms only. The equations determining the excitation amplitudes for a complete model space may be derived from [SJfol = (QVQ - QVefdconn
v,,
(4)
= VQ
(5) where Hoand Vdescribe the usual partitioning of the Hamiltonian: H=Ho+V
(6)
The effective Hamiltonian, given by Herr = ~ ( H +O Veff)P
(7)
(12) Buenker, R. J.; Peyerimhoff, S. D. Theor. Chim. Acta 1974,35, 33. (13) (a) Buenker, R. J.; Peyerimhoff, S.D. Theor. Chim. Acta 1975,39, 217. (b) Knowles, D. B.; Alvarez-Collado, J. R.; Hirsch, G.; Buenker, R. G. J . Chem. Phys. 1990, 92, 585. (14) Peyerimhoff, S. D.; Buenker, R. J. Chem. Phys. 1979, 42, 167. (15) (a) Davidson, E. R. The World of Quantum Chemistry; Daudel, R., Pullman, B., Eds.; Reidel: Dordrecht, 1979; p 17. (b) Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8, 61. (16) Paldus, J.; Wormer, P. E.; Visser, F.; van der Avoird, A. Proceedings
of the 5th Seminar on Computational Methods in Quantum Chemistry; Groningen, Netherlands, Sept 1983; p 13. (17) Hubbard, J. Proc. R. SOC.(London) 1957, A240, 539; 1958, A243, 336. (18) (a) Coester, F. Nucl. Phys. 1958, 7, 421. (b) Coester, F.; Kummel, H. Nucl. Phys. 1960,17,477. (c) Kummel, H.; Luhrmann, K. H.; Zabolitzky, J. G. Phys. Rep. 1978, 61, 1. (19) Cizek, J. J. Chem. Phys. 1966,45,4256; Adu. Chem. Phys. 1969,14, 35. (20) Paldus, J.; Cizek, J.; Shavitt, I. Phys. Reu. 1972, A5, 50. (b) Paldus, J. J. Chem. Phys. 1977, 67, 303. (21) (a) Haque, M. A.; Mukherjee, D. J. Chem. Phys. 1984,80, 5058. (b) Haque, M. A.; Mukherjee, D. Pramana 1984, 23, 651. (22) Bartlett, R. J. J. Phys. Chem. 1989, 93, 1697. (23) (a) Lindgren, I. I n t . J. Quantum Chem. Symp. 1978, 12, 33. (b) Lindgren, I.; Morrison, J. Atomic Many-Body Theory;Springer: Berlin. 1982.
Roszak et al. may be separated into core and valence parts: Heff = + Kh! (8) where the first term on the right-hand side consist of diagrams without any external lines. The eigenvalues of ?I will $ then give directly the transition energies from the core, with correlation effects included for both core and valence electrons. The physical meaning of these energies depends on the nature of the model space. Thus, electron affinities may be calculated by constructing a model space with valence particles only,2"b ionization potentials are given using valence holes,24Eand both types are included for the purpose of getting excitations out of a closed-shell system.24d*e The S operator for an open-shell system may be partitioned according to the number of valence orbitals involved: S = S(0) S(i) S(2) ... (9) Haque and Mukherjee21 have shown that partial decoupling of the equations is then possible, as the equations for S(")involve only S(") elements with m I n. A similar decoupling holds when both valence holes and particles are present, and (9) is replaced by S = S(0,O)+ S(0,I) + S(l,l)+ ,,, (10) where the two superscripts give the numbers of valence holes and particles, respectively. This decoupling is helpful in reducing the computational effort.
+
+
+
-
Computational Details The basis used included the Huzinaga-Dunning2S (9s5p) [4s2p] set for N and 0 and (4s) [2s] for H. The basis set was also supplemented by one set of polarization functions of Pople et The geometry optimization of (H3N-- -H- - -OH2)+ was performed for four N - 0 separations (2.707, 2.95, 3.2, 5.0 A) and different R(N-H+) distances for every N-0 arrangement employing the GAUSSIAN 88 program pa~kage.~' Subsequent MRD-CI and CCM calculations were performed for these geometries. Single and double excitations from the most important 12 reference configurations were considered in the MRD-CI calculations for the singlet states, about 800 000 symmetry-adapted functions (SAFs) in all. Explicitly included were all configurations predicted by perturbation theory to have c2 1 0.005 and a configuration selection threshold of 20 pH was employed, leading to about 10000 SAFs. The exact number depends on R(N-0) and R(N-H+). For the triplet, there were 1600000 SAFs obtained by single and double excitations from the 13 most important reference configurations of which approximately 10000satisfied the same criterion as above. The estimate of the full CI energy was done by extrapolating and adding the Davidson correction, as described in the previous section. The open-shell multireference coupled cluster (MR-CCM) package, written originally for the Tel Aviv University CYBER 180/990, was adapted at the Johns Hopkins University to the SDSC CRAY YMP and vectorized. The integral, SCF, and transformation routines already in use at the Johns Hopkins University for MRD-CI calculation^^^^^^ were interfaced with the
-
(24) (a) Haque, A.; Kaldor, U. Chem. Phys. Lett. 1985, 117, 347. (b) Haque, A.; Kaldor, U. Chem. Phys. Lett. 1985, 120, 261. (c) Haque, A,; Kaldor, U. Int. J. Quantum Chem. 1986, 29, 425. (d) Kaldor, U.; Haque, A. Chem. Phys. Lett. 1986.128.45. (e) Kaldor, U. Int. J. Quantum Chem. 1986, S20, 445. (25) Huzinaga, S.J. Chem. Phys. 1965.42, 1923. Dunning Jr., T. H. J. Chem. Phys. 1971, 55, 3958. (26) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217. (27) GAUSSIAN 88, Frish, M. J.; Head-Gordon, M.; Schlegel, H. B.; Ra-
ghavachari, K.; Binkley, J. S.;Gonzalez, C.; Defreez, D. J.; Fox, D. J.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R.; Kahn, L. R.; Stewart, P.; Fluder, E. F.; Topiol, S.;Pople, J. A,; Gaussian Inc.: Pittsburgh, PA, 1988. (28) (a) Saunders, V. R.; Guest, H. F. ATMOL 3 Program System; Computational Science Group: SERC Daresbury Laboratory. (b) Saunders, V. R.; van Hemert, M.; Hariharan, P. C. ATMOL 3 Program System adapted to the CRAY XMP;The Johns Hopkins University, 1985. (c) Saunders, V. R. AtmolS. 1990.
Proton Transfer in (H3N-- -H- - -OHz)+
The Journal of Physical Chemistry, Vol. 96, No. 5, 1992 2125 "
H
:
X
I
n
R (N-H') +HI
-04
1
-0.6-
N I-fO
:
Figure 1. Geometry of (H,N- - -H- - -OH2)' system. The C, rotation axis of NH, coincides with the N - 0 axis along which the proton moves.
-0.8
"
0 (IV)
I.
N H'O 0%
-.
n
NH
0.9
LXOH'
lhsl
-
----OlJV)
1.3
1.1
-
NY
::4:
-
I'
I .5
I .9
1.7
2. I
[A] Figure 4. Variation of SCF orbital energies in (H,N- - -H- - -OH2)+ system for R(N-0) = 2.707 A. R(N-H')
E
1300
L---,-l 13
1 1
09
,
-12
1
1040
15
17
R M-ti')
0.4
21
I 9
id1
Figure 2. Variation of SCF optimized angles for the proton transfer in (H3N-- -H- -OH2)+for R(N-O) = 2.707 A.
-
I
09
I
I
I5
I
I
I
21
,
I
27
R (N-H+)[AI
ObI I
I
33
39
-
1
I
43
-
Figure 5. Variation of SCF orbital energies in (H,N- -H- -OH2)+ system for R(N-0) = 5.0 A.
1200i
, ,
0911
1
15
I
, , I9
I
23
I
, 21
R NH')
I
I
I
I
31
35
I
, , 11040 39
43
IAl
Figure 3. Variation of SCF optimized angles for the proton transfer in (H,N- -H- -OH2)+for R(N-O) = 2.707 A.
-
-
open-shell MR-CCM package, and the same transformed integrals served as input in both methods. The MR-CCM scheme as implemented by requires a closed-shell reference configuration, from which the states of interest can be obtained by adding and/or subtracting electrons. The selection of the reference states depends mainly on the orbital energy spectrum and on the states under investigation.
Results and Discussion Geometry Optimization. Delpuech et have carried out a full geometry optimization of the (H3N- -H- - -OHz)+cationic system in the DZP basis at the S C F level. This geometry was used to study proton-transfer potentials: in the way that the proton was translated along the N-O axis and the rest of atoms were held fixed in the same geometry as for the optimized structure. This "rigid molecule approximation" works well for N-H and 0-H bonds since these bonds are almost the same in separated molecules, protonated forms, and the equilibrium structure. However, the bond angles change significantly between the molecule and its protonated form. The experimental HNH angle is 106.7' in NH331and 109.27' in NH4+;the angle HOH in water is 1 0 4 . 5 O
-
(29) (a) Buenker, R. J . MRD-CI Program System; Lehrstuhl Fur Theoretische Chemie, Gesamthochschule Wuppertal. (b) Buenker, R. J.; Hariharan, P. C. MRD-CI Program System adapted to the CRAY XMP. The Johns Hopkins University, 1985. (c) Roszak, S. MRD-CI Program System adapted to the CRAY YMP. The Johns Hopkins University, 1989. (30) Delpuech, J. J.; Serratrice, G.; Strich, A.; Veillard, A. Mol. Phys. 1975, 29, 849. (31) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
and 112.5O in the OH3+cation.32 Thus in this study the optimization of three angles, HNH, HOH, and the angle between bisection line of the HOH molecule and the N - 0 bond (Figure l), has been performed. The C, symmetry was kept unchanged for every optimized point, and the bond distances R(N-H) = 1.007 A and R(O-H) = 0.95 A (which are optimized values of ref 30) are fmed also. The optimization was performed for four different R(N-O) distances 2.707, 2.95, 3.2, and 5.0 A. Figures 2 and 3 present changes of angles for two extreme N-O cases (2.707 and 5.0 A). In both cases the behavior of angles is qualitatively the same. When the proton is bonded to NH3{R(N-H+) == 1.1 A], H 2 0 lies in plane perpendicular to the C, plane. The complex keeps this geometry while moving the proton toward oxygen, but at the critical point (R(N-H+) = 1.3 for R(N-O) = 2.707 A and R(N-H+) = 2.3 for R(N-0) = 5.0 A1 the angle a(XOH+) (Figure 1) starts to decrease rapidly while H 2 0forming new 0-H+ bond adjusts its geometry to that of OH3+. The angle HNH changes from tetrahedral (NH,+) to the experimental value in NH3. The angle HOH follows the change from the value in water to the value in OH3+. For all four N - 0 distances geometries for N-H+ were optimized a t 0.2-A intervals. MRD-Cl calculatiolra Multireference configuration interaction calculations were performed for the ground state and for lowest singlet and triplet states. The variation of orbital energies are presented on Figure 4 and Figure 5 for the R(N-0) distances 2.707 and 5.0 A, respectively. In both cases orbital pictures are complicated by crossings between a' and a" symmetries and with avoided crossings for a' symmetry curves. In both cases the two LUMO are weakly localized and the first LUMO can be recognized as (N-H+-0) while the second as (H3NOH2)with populations of particular atoms depending on the position of the proton. The structure of occupied orbital space is different for different R(N-0) distances. In case of A(N-0) = 2.707 A two HOMO orbitals interact strongly, and there is a curve switching around R(N-O) = 1.3 A. For distances closer to nitrogen the lone oxygen (32) Raffenetti, R. C.; Preston, H. J. T.; Kaufman, Joyce, J. Chem. Phys.
Lett. 1917, 46, 513.
2126 The Journal of Physical Chemistry, Vol. 96,No. 5, 1992 E
Roszak et al.
.I32.5
Ia.u.1 -1327
, w-_-
-1328
i
-1330
-
- _ -
-
- - - - -
-
1
1
09
-132.8
I I
13
17
I5
19
-1330
-1331
21
09
13
1 1
15
R(N-H+)[A]
Figure 6. MRD-CI potential energy curves for the ground state and two excited singlets (solid lines) and triplets (dotted lines) for R(N-0) = 2.707 A.
17
19
21
23
R(N-H?IAl
Figure 8. MRD-CI potential energy curves for the ground state and two excited singlets (solid lines) and triplets (dotted lines) for R(N-0) = 3.2
A.
E
-1324
[a.u.] -132 5 .132.6 -1327 -132.8 -132.9
-133.0
-1331
-133.0
1 1 09
1 1
13
15
17
19
21
R(NHW1
Figure 7. MRD-CI potential energy curves for the ground-state and excited singlet (solid line) and triplet (dotted line) states for R(N-0) = 2.95 A.
pair has the highest energy, but when the proton is moving toward oxygen it becomes the second highest by switching the order with (0-H+-N) molecular orbital. In the case of R(N-O) = 5.0 A, three different regions may be selected. Orbital energies in regions around N and 0 correspond to the orbital pictures of separated fragments. The orbital energy of (NH+) is fourth in the N region, and (OH+) is fourth in the 0 region, behind HOMOs corresponding to neutral fragments. At the intermediate distances (2.1-3.4 A) the (NH+O) molecular orbital is the highest. For the case of R(N-O) = 2.707 A the ground-state 'A' curve is purely single determinantal. The curve has one minimum at R(N-H) = 1.07 A (Figure 5). Excited states have more complex structure. The potential surfaces for N-H+ close to nitrogen in case of the lowest excited singlet and triplet correspond to the transition of an electron from the lone pair of oxygen to delocalized (H,NOH2) MOs (Table I). At R(N-H+) = 1.5 A, surfaces change character and correspond to excitations from (NH+-O) to the two lowest LUMOs. In this region two lowest excited states (of the same spin symmetry) interact strongly, which leads to wave functions constructed from the same configurations (Table I). Both curves (singlet and triplet) have two minima. The behavior of potential surfaces for longer distances R(N-0) = 2.95 A (Figure 6) and R ( N - 0 ) = 3.2 A (Figure 7) closely resemble that at 2.707 A as far as reference structure of wave function is concerned. However, the ground-state curves in both cases have two minima. The structure of potential surfaces at R(N-0) = 5.0 A, as could be expected from the inspection of the orbital energy picture, is significantly different than that for shorter distances. The ground-state wave function is single determinantal in regions where the proton is bounded to N or 0 atoms. For intermediate N-H+ distances configurations related to the transition of one or two electrons between HOMO and LUMO are significant. The triplet LUMO(N-H+-O) state is related to the HOMO(N-H+-O) transition. The first excited singlet through all H+ pathway corresponds to a one-electron HOMO-LUMO transition, even when HOMOs change their character significantly. The excited
-
-133 I
0.9
15
21
21
33
39
4.3
R(N-H+) [A]
Figure 9. MRD-CI potential curves for the ground state and excited singlet (solid line) and triplet (dotted line) states for R(N-0) = 5.0 A.
singlet interacts with the ground state in the intermediate area (R(N-H+) = 2.5 A} and is completely different in regions around atoms (Table 11). The gap between ground state and excited singlet has been reduced substantially when lengthening the R(N-O) distance to 5.0 A. The same configurations are present in both states, indicating the significant interactions. This situation is similar to deprotonation of a single molecule in an "avoiding" region. The second excited states (singlet and triplet) were calculated to resolve a problem of interactions with lower states. Only one strong interaction has been found at excited singlets for N-H+ of 2.5 A and N - 0 5.0A (Figure 9). These interactions are confirmed by the structure of the wave function (Table 11). Excited triplet states do not interact directly at any point. Coupled Cluster Calculations. The major advantage of the coupled cluster method (CCM) is the ability to sum numerous perturbation terms to infinite order, thus accounting for large classes of virtual excitations, while being size consistent. The coupled cluster method serves as a test for the performance of the Davidson correction. The MRD-CI method with the approximate correction to full CI is approximately size consistent, while the coupled cluster method is rigorously size consistent. The different MRD-CI and CCM calculations for the ground state carried out at the same geometry gave very close agreement, differing by only a few milihartrees (Table 111). Results are comparable for both short (2.702 A) and long (5.0 A) N-O distances. The results are very encouraging and shows the good performance of Davidson correction in the case studied. The lowest excited states were calculated as one-electron excitations from the ground state, which served as a reference. Excited singlet and triplet states calculated in CCM are close to MRD-CI values; however, differences are slightly bigger (0.04 hartree in the worst case). This is the magnitude of the errors inherent in the two methods, coming in MRD-CI from the extrapolation to full CISD and from the estimate of higher excitations by the Davidson correction, and in MR-CCM the neglect of connected triple and higher excitations (disconnected excitations, which are products of single and double excitations, are taken into account).
- -
The Journal of Physical Chemistry, Vol. 96,No. 5, 1992 2127
Proton Transfer in (H3N- -H- -OHz)+
TABLE I: MRD-CI Squares of Coefficient for Important Configurations for Ground, Two Excited Singlets States, and Two Triplet States for
(HIN- - -H- - -OH2)' at R(N-0) = 2.707 k
A
R(N-H'), configuration
state
SCF
1.07 0.918 0.918 0.090 0.812 0.000 0.000 0.907 0.000 0.000 0.287 0.600 0.902 0.080 0.822 0.000 0.000 0.915 0.000 0.000 0.139 0.751 0.890
--
Df
O(lp)'
(NH'O)' (NH'O)'
(NH'O')' (HINOH,*)' (N'O*)' (H3NOH2*)'
O(1p)l O(lp)' (NH'O)' (NH'O)'
(NH'O*)' (H3NOH2*)' (NH'O*)' (H3NOHZ*)'
O(1p)'
+
--. D? -cciz
+
O(1p)l
O(lp)' (NH'O)' (NH'O)'
n z i
-
(NH'O*)' (H3NOH2*)' (NH'O*)' (H3NOH2*)'
+
O(1p)' O(lp)' (NH'O)' (NH'O)'
+
D?
(NH'O*)' (HJNOH2*)' (NH'OI)' (H,NOH2*)'
--
1.3 0.916 0.916 0.008 0.314 0.580 0.000 0.908 0.877 0.000 0.007 0.001 0.886 0.005 0.366 0.534 0.000 0.912 0.876 0.000 0.004 0.001 0.881
1.5 0.915 0.917 0.162 0.012 0.681 0.037 0.894 0.661 0.016 0.109 0.109 0.899 0.122 0.010 0.701 0.020 0.906 0.722 0.033 0.091 0.045 0.904
1.7 0.918 0.918 0.000 0.000 0.614 0.281 0.902 0.000 0.000 0.268 0.621 0.896 0.000 0.000 0.488 0.406 0.910 0.000 0.000 0.380 0.498 0.904
1.8 0.919 0.920 0.000 0.000 0.632 0.266 0.906 0.000 0.000 0.259 0.639 0.902 0.000 0.000 0.504 0.398 0.913 0.000 0.000 0.385 0.520 0.909
Cc; is the sum of included reference configurations. (yc
1
CU.1
nf
1
.
0
j
p
08
10.2
10.0
0.5
-
/
\
-
0.45
l
0.9
1.1
~
l
1.3
'
l
1.5
'
1.7
l
'
1.9
l
'
0.6 0.6
0.4
l
0.0
2.1
1.3
1.1
NKH?[AI
Figure 10. Gross atomic population for hydrogen transferred between N and 0 atoms, calculated for the ground state (SCF and MRD-CI wave function) and for excited singlet and triplet for R(N-O) = 2.707 A.
The coupled cluster method has not converged for the excited singlet for one point {R(N-H) = 2.9 A, R(N-0) = 5.0 A). The MRD-CI for this point indicate that the state has important contributions of other configurations in addition to one representing HOMO-LUMO one-electron transition. The single determinant ground state serving as a reference is not sufficient to describe this point properly. Cross Atomic Populations from MRD-CI Wave Function. The formation of the hydrogen bond is related to the proton transfer between two heavy atoms. The moving of proton generates changes in an electronic cloud. To some extent, the measure of these effects can be the Mulliken gross atomic population (GAP). Despite the arbitrariness of any electron population33and known cases of artifacts, GAP is a useful tool to study the composition of electron density. In a classical way the question arises, what is transferred, proton or hydrogen? The answer is especially interesting when electronic excited states are considered. The Mulliken grass atomic population has been studied for two extreme cases of N-O distances, the short N-0 distance being 2.107 A and the long distance 5.0 A. The GAP for the short N-O distance is presented in Figure 10. The population for H+ transferred in the ground state is significantly lower than that in the excited state. Figure 1 1 presents atomic populations summed for OH2 and OH3+for each investigated state. The corresponding populations for long N-O (33) Roszak, S.;Sokalski, W. A.; Kaufman,Joyce J. J . Compur. Chem., submitted.
1.5
1.7
1.9
2.1
RKH?[AI
Figure 11. Gross atomic population summed for OH2 (lower lines) and OH3' (upper lines) for the ground state (solid line), excited singlet (dotted line), and excited triplet (semidotted line) for R(N-O) = 2.707
A.
7
1.0
1.4
I-
-j
1
0.8
0.2
1
I
1
I
0.0
1.75
2.6
3.45
t 4.3
WNH+)IAI
Figure 12. Gross atomic population for hydrogen transferred between N and 0 atoms, calculated for the ground state (SCFand MRD-CI wave function) and for excited singlet and triplet for R(N-O) = 5.0 A.
distance are presented in Figures 12 (H+ GAP) and 13 (OH2and OH,+ summed populations). In both cases two regions can be selected, the region of NH4+ and the region of OH3+. Borders between regions are about 1.5 and 2.6 A for the N-H+ bond for the short and long cases, respectively. The gap between ground and excited states is even bigger for the long N-O distance-i The ground-state population of OH2 is approximately constant when H+ is in the NH4+ zone, and population drops when H+ moves to OH3+zone. The molecule uses part of the electrons to form
Roszak et al.
2128 The Journal of Physical Chemistry, Vol. 96, No. 5, 1992
TABLE II: MRD-CI Squares of Coefficients for Important Configurationsfor Ground, Two Excited Singlet States, and Two Triplet States for (H3N- -H- - -OH2)+at R(N-0) = 5.0 8, R(N-Ht), 8, state configuration 1.1 1.5 I 1.9 2.1 2.5 2.9 3.4 4.1 0.913 0.888 0.859 0.804 0.857 0.904 'A' 0.904 0.909 SCF 0.000 0.000 0.000 0.000 0.000 0.000 0.01 1 0.000 (NHtO*)' (NH')' 0.000 0.000 0.000 0.05 1 0.000 0.026 0.001 (NH+0*)2 0.000 (NH'), 0.914 0.912 0.907 0.907 0.913 0.9 12 0.910 0.914 Diz 0.000 0.000 0.000 0.000 0.092 0.029 0.001 'A'(I1) SCF 0.000 0.000 0.000 0.007 0.000 0.001 0.000 (NH+)2 (NH+O*)2 0.001 0.070 0.000 0.000 0.000 0.878 0.000 0.005 0.762 0.878 (NH'O*)' (NH')' 0.882 0.878 0.883 0.000 0.872 0.034 (NH'O')' 0.882 0.000 (O(1p))' 0.898 0.898 0.896 0.895 0.896 0.894 0.888 0.905 Diz 0.000 0.000 0.000 0.031 0.001 0.016 'A'(II1) 0.000 0.000 SCF 0.000 0.000 0.000 0.000 0.000 0.000 0.129 0.002 (NH+O*)2 (NHt)2 0.000 0.000 0.000 0.000 0.680 0.027 (NHtO*)l 0.000 0.006 (NH')' 0.750 0.880 0.885 0.880 0.000 0.000 0.000 (NH:)' 0.000 (OH,)' 0.000 0.000 0.885 (NH'O*)' 0.000 0.000 0.008 0.000 (NH,)' 0.801 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.867 (N(lp))' (HJOH;)' 0.883 0.891 0.91 1 0.889 0.888 0.914 0.886 0.882 D? 0.000 0.000 0.000 0.884 0.881 0.871 0.885 3A' 0.000 ( O ( ~ P ) ) ' (NH:*) 0.000 0.000 0.000 0.000 0.304 0.890 0.887 0.881 (N(1p))' (NHtO*)' 0.897 0.899 0.874 0.900 0.898 0.914 0.906 0.898 ES2 0.000 0.000 0.000 0.883 0.879 0.885 0.888 ~ A ~ I I ) (OH,)' (NH:*)' 0.000 0.000 0.000 0.889 0.000 0.000 0.883 0.882 0.000 (NH+O*)' (NHI)' 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.868 (N(;p))' (OH,*)' 0.891 0.900 0.892 0.831 0.887 0.890 0.887 0.875 D,
-
---
---
---
TABLE 111: Coupled Cluster and MRD-CI Results for the Selected Points of the Ground State, the First Excited Singlet, and the First Triplet Curves for N-O Distances of 2.707 and 5.0 8, for the (H3N- -H- -OH2)+System (Energy Results in hartrees) R(N-0) = 2.707 8, R(N-0) = 5.0 8, R(N-H), A cc MRD-CI R(N-H), A cc MRD-CI
-
-
0.9 1.07 1.3 1.5 1.7 1.9
-1 33.029 80 -133.04943 -133.031 56 -133.019 59 - 133.01 3 03 -1 32.956 94
Ground State -1 33.026 06 0.9 -133.046 52 1.1 -133.027 63 1.9 -133.01568 2.9 -133.008 47 3.5 4.1 -132.953 37
-133.007 22 -133.021 96 -1 32.883 62 -132.811 21 -132.858 15 -1 32.952 70
-133.005 85 -133.02021 -132.88087 -132.813 29 -132.85476 -132.95039
0.9 1.07 1.3 1.5 1.7 1.9
-132.62509 -132.640 10 -132.65463 -132.61770 -132.637 36 -132.605 96
Excited Singlet -132.654 50 0.9 1.1 -132.66500 -132.631 31 1.9 -132.614 13 2.9 3.5 -132.63012 -132.600 10 4.1
-132.63053 -132.658 76 -132.716 10 not converged -132.769 17 -132.676 23
-132.621 56 -132.65026 -1 32.709 69 -132.753 78 -132.761 27 -132.671 64
0.9 1.07 1.3 1.5 1.7 1.9
-132.64056 -132.659 79 -132.68391 -132.657 07 - 132.660 86 -132.619 46
-1 32.679 18 -132.700 14 -132.655 98 -1 32.663 98 -132.666 31 -1 32.620 25
-132.63078 -132.65922 -132.71644 -132.780 34 -132.767 60 -132.67660
-132.614 85 -132.648 38 -132.70942 -132.78227 -132.761 33 -132.665 02
First Triplet 0.9 1.1 1.9 2.9 3.5 4.1
a new 0-H+ bond. At the same time the GAP of OH3+becomes about 10 electrons, indicating that the new bond does not use any electrons from the N H 3 part. These behaviors indicate that transferred proton shares electrons with NH3 while it is in NH4+ zone and with OHz when is in OH3+zone. The border region is thin. The transfer of proton in excited states has a different nature. While the electronic population on proton is about one electron, OHz does not use its own electrons to form a bond. The electron density which contributes to hydrogen is donated by both sides of complex and hydrogen is moving in a delocalized system. /
Conclusions The potential surfaces study performed for proton transfer in (H3N-- -Ht- - -OHz) complex allows the interpretation of this well-known reaction from different points of view. The geometry optimization indicates the rapid switch from protonated to deprotonated form (and vice versa) depending on the proton position. While transferring proton from NH4+ to HzO the protonated water rapidly adjust its geometry to optimal OH3+ geometry.
9.0
I
0.9
1.75
-
/ I
1
2.6
3.45
4.3
R(KH3lA1
Figure 13. Gross atomic population summed for OH, (lower lines) and OH,+ (upper lines) for the ground state (solid line), excited singlet (dotted line), and excited triplet (semidotted line) for R(N-0) = 5.0 A.
The moving proton between N and 0 can be seen as a protonation of NH3 and OHz. While protonation of N H 3 change the geometry slightly, the protonation of OHz changes the ge-
J . Phys. Chem. 1992, 96, 2129-2141
ometry drastically. The proton approaches oxygen in the C2, symmetry, while the optimal geometry of OH3+is C3". From the study of geometry variation along the R(N-0) bond the conclusion can be drawn that the proton always belongs to the one subunit or the other, the areas of "sharing" proton are very narrow. Orbital pictures for extreme cases (2.707 and 5.0 A) are significantly different, which may affect the structure of potential surfaces. The correlation between orbital pictures of separated systems and the complex is obvious for the long N - 0 distance. However an intermediate region is recognized also. The orbital pictures are more complicated for shorter distances (2.7-3.2 A). In the case of R(N-0) from 2.707 to 3.2 A the ground state is purely one-determinantal. The gap between ground and excited states is too large to allow interactions. In the case of long distances (5.0 A) the function for the ground state is contaminated by configurations characteristic for the "avoided" region. The gap between ground and excited states is much smaller than for shorter distances, and the interactions are much bigger. The curve in regions around atoms N or 0 resembles the situation in separate molecules. Energy potential curves calculated by coupled cluster method agree well with those from MRD-CI calculations. However, the
2129
multireference character of the wave function a t N-H+ distance of 2.9 A (for N - 0 distance 5.0 A) is manifested by lack of convergence for the excited singlet state, while starting from a single determinantal ground-state function. Mulliken gross atomic population indicates that the reaction proceeds as a proton transfer, while at excited states the proton carries more electron density. Similarly to the geometry optimization, in the ground state the proton belongs to OH2or NH3 and not to a "common" zone. This picture supports the concept of proton transfer as a tuneling between two structures. Electrons in excited states are much more delocalized, and the proton carries an electron acquired partially from ammonia and partially from water. Electrostatic properties of the excited-state systems are completely different from that of the ground state. Acknowledgment. This research was supported by ONR, Power Programs Branch, under Contract NOOO 14-80-C-OOO3 and Grant "14-89-5-1613, U.K. was partly supported by the US-Israel Binational Science Foundation. The calculations were carried out at the NSF San Diego Supercomputer Center on the CRAY YMP. We thank SDSC for the grant of computer time. Registry No. H20, 7732-18-5; NH4, 14798-03-9.
Energetics and Electronic Structure of Chromium Hexacarbonyl Kathryn L. Kunzet and Ernest R. Davidson* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: October 31, 1991)
We investigate the molecular orbital self-consistent-field model of bonding in Cr(CO),. The energetics and electron density are examined using a large range of tools. The change in density compared to a promoted 3dt22 'A,, chromium atom and six CO molecules is primarily charge transfer from the tlg orbitals of chromium to the empty 2r*t2, orbital of the (CO), cage. This mixing is counterintuitive, as the largest increase in electron density is in the oxygen p r orbitals. The restricted Hartree-Fock energy is actually repulsive compared to that of ground-state fragments by 111 kcal/mol. This energy change cage formation energy, -272 kcal/mol consists of +266 kcal/mol of fragment promotion energy, +67 kcal/mol of (CO), and finally -329 kcal/mol of orbital of electrostatic attraction, +359 kcal/mol of overlap repulsion between Cr and (CO),, relaxation energy. Most of the relaxation energy is associated with the t2, HOMO-LUMO charge transfer. The u electrons contribute to the bond energy primarily through electrostatic penetration, leading to a large electrostatic attraction between and not through mixing of CO u orbitals with Cr empty valence orbitals. Cr and (CO),,
Introduction The nature of the bonding in low-oxidation-state transitionmetal carbonyl complexes is of considerable importance due to their high catalytic activity, their use as precursors in organometallic chemistry, and their use as models for the chemisorption bond between CO and metal surfaces.'-3 Theoretical studies of the metal-ligand coordinate bond in the metal carbonyls, especially Cr(CO),, Fe(CO)5, and Ni(C0)4, are numerous,"-34 as are qualitative papers "explaining" the b ~ n d i n g . ~ ~ - ~ ~ The main experimental facts about these complexes addressed by qualitative models have been (a) the obedience of the "18electron rule",' (b) the octahedral, trigonal bipyamidal, and tetrahedral shapes of the complexes,' (c) the linear MCO bond with C next to M,"3,4 (d) the relatively constant metal-CO average bond en erg^,^^-$^ (e) the relatively short metal-carbon bond length,', (f) the slight lengthening of the CO bond,43344(g) the decreases in the CO stretching frequency,5842 (h) the decrease (i) the high in the 1s carbon and oxygen ionization potential~,6~*~ d-d transition energy,6446 and (j) the singlet spin ground state.' The very high ligand field transition (d-d) energiesu correspond to a field strength Dq/B in excess of 5 . This very high apparent field defies an interpretation in terms of an electrostatic model of fragment charges and multipoles as in ligand field theory.,' 'Deceased, March 28, 1991.
For Cr(CO),, this large value of Dq/B suggests that the d6 electrons of the metal can be adequately represented by a single (1) Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; Wiley Interscience: New York, 1988. (2) Mingos, D. M. P. Comprehensive Organomeiallic Chemistry; Wilkinson, G . , Stone, F. G. A., Abel, E. W., Eds.; Pergamon Press: New York, 1982; Vol. 3, p 1. (3) (a) Muetterties, E. Science 1976, 194, 1150. (b) Muetterties, E. Science 1977, 196, 839. (4) Arratia-Perez, R.; Yang, C. Y. J . Chem. Phys. 1985, 83, 4005. (5) (a) Baerends, E. J.; Rozendaal, A. Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A., Ed.; D. Reidel: Dordrecht, 1986; p 159. (b) Chornay, D. J.; Coplan, M. A.; Tossell, J. A.; Moore, J. H.; Baerends, E. J.; Rozendaal, A. Inorg. Chem. 1985, 24, 877. (c) Heijser, W.; Baerends, E. J.; Ros, P. J . Mol. Struct. 1980, 63, 109. (6) Barandiaran, Z.; Seijo, L.; Huzinaga, S.; Klobukowski, M. Int. J . Quantum Chem. 1986, 29, 1047. (7) (a) Bauschlicher, C. W.; Bagus, P. S.J. Chem. Phys. 1984,81,5889. (b) Bauschlicher, C. W.; Pettersson, L. G. M.; Siegbahn, P. E. M. J . Chem. Phys. 1987,87, 2129. (c) Bauschlicher, C. W.; Langhoff, S.R.; Barnes, L. A. Chem. Phys. 1989,129,431. (d) Bauschlicher,C. W. J. Chem. Phys. 1986, 84, 260. (e) Bauschlicher, C. W.; Bagus, P. S.;Nelin, C. J.; Roos, B. 0. Chem. Phys. 1986,85, 354. (f) Barnes, L. A.; Rcsi, M.; Bauschlicher, C. W. J. Chem. Phys. 1991, 94, 2031. (g) Barnes, L. A.; Rosi, M.; Bauschlicher, C. W. J . Chem. Phys. 1990,93,609. (h) Barnes, L. A,; Bauschlicher, C. W. J . Chem. Phys. 1989,91,314. (i) Blomberg, M. R.A,; Brandemark, U. B.; Siegbahn, P. E. M.; Wennerberg, J.; Bauschlicher, C. W. J . Am. Chem. Soc. 1988, 110, 6650.
0022-3654/92/2096-2129%03.00/0 0 1992 American Chemical Society
