ARTICLE pubs.acs.org/JPCA
Exploring a Reaction Mechanism for Acetato Ligand Replacement in Paddlewheel Tetrakisacetatodirhodium (II,II) Complex by Ammonia: Computational Density Functional Theory Study Zdenek Futera,† Tomas Koval,† Jerzy Leszczynski,‡ Jiande Gu,§ Mariusz Mitoraj,|| Monika Srebro,|| and Jaroslav V. Burda†,* †
)
Department of Chemical Physics and Optics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic ‡ Department of Chemistry and Biochemistry, Jackson State University, 1325 J.R. Lynch Street, Jackson, Mississippi 39217-0510, United States § Center for Drug Discovery & Design and State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 294 Taiyuan Road, Shanghai 200031, P. R. China Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, R. Ingardena 3, 30-060 Cracow, Poland ABSTRACT: This study focuses on the first step of interaction between DNA and the paddle-wheel dirhodium complex. The ammonia molecule was used to model the oligonucleotide sequence. The reaction was considered in neutral and acidic conditions, in gas phase, and in solvent, using the COSMO model. Molecular structures of the complexes were optimized in both models at the B3PW91/6-31G(d) level. The B3LYP functional and aug-cc-pvdz basis set were employed for single-point energy determination and electron distribution analyses. It was shown that in neutral solution the replacement of axial aqua ligand is mildly exoergic. The reaction is characterized by a relatively low activation barrier (10-12 kcal/mol), and, according to Eyring transition state theory, it proceeds very quickly. The breaking of the Rh-O(ac) bond in neutral solution is mildly endoergic (less than 1 kcal/mol) with an activation barrier of about 21 kcal/mol. However, this process can occur much more spontaneously (ΔG of -14 kcal/mol) when the dirhodium complex is protonated at the acetyl oxygen in remote position.
’ INTRODUCTION The discovery of cisplatin anticancer activity1 has triggered a massive search for similar properties of other transition metal complexes. The driving force of this research is the fact that cisplatin suffers many serious drawbacks. Especially, because of cisplatin's very high toxicity, it is worth studying other substances in parallel to the development of cisplatin analogues. Promising results in anticancer activity were obtained for metallocene complexes of Ti or Mo (see, e.g., the review of Kuo et al.,2 who summarized some basic properties and activities of these compounds). Recently, several new studies on metallocene activity have appeared,3-7 including the computational study of Sponer et al.8 Phase II of clinical trials for some modified titanocenes has been recently announced. In addition, the activity of Ru(III) complexes has been thoroughly studied.9-12 Phase I of clinical trials has been passed by the NAMI-A complex (trans-Cl4(Me2SO)(Im)Ru(III) (Im = imidazole)). The half-sandwich Ru(II) complexes have been recognized as very potent anticancer agents.13-16 Several computational studies of these complexes can be found in the literature.17-20 Dirhodium(II,II) complexes represent another class of metallodrugs with some activity against cancer cells. Their antitumor r 2011 American Chemical Society
properties were recognized already in the 1990s, as it was demonstrated in several studies.21-24 A comprehensive review on rhodium complexes related to anticancer treatment was published by Katsaros.25 He reported not only Rh(II)-based agents, but also some other rhodium structures. The paper combines discussion on the length of carboxyl ligands of the paddle-wheel Rh(II) complexes with experimental results on the rhodium-amino acid adducts in proteins and peptides. Dunbar et al.26 performed NMR characterization and a mass spectroscopy study27 on binding properties of the metal adducts with diguanine and d(GpG) sequences. In this work, kinetic aspects of the metal addition were also examined. The obtained results were compared with the behavior of platinum complexes (cisplatin and carboplatin). The authors also suggested a probable molecular mechanism for the adduct formation between DNA bases and tetracarboxylate Rh 2(μ-O2CR)4 complexes. Measurements of variable oligomeric sequences, Received: May 23, 2010 Revised: December 7, 2010 Published: January 13, 2011 784
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where two adenine, adenine-guanine, and two guanine bases interact with a dirhodium complex, led to a conclusion that comparable rates for the replacement of the acetyl group were observed in the case of coordination of the same bases (AA and GG). Slightly slower reaction rates were found for the formation of mixed AG and GA adducts. The affinity of paddle-wheel dirhodium complexes with Trp 214 in human albumin was explored in studies.28,29 Recently, reactivity with a dirhodium complex with two bridging aspartate side chains in natural peptide sequences was also explored by Sambasivan et al.30 Recently, an interesting computational study on the dependence of chemical shift on various axial (in the Rh-Rh axis) or equatorial (in positions perpendicular to the Rh-Rh axis) imidazole ligands in dirhodium paddle-wheel complexes was published.31 Another study investigated the strength of Rh-Rh binding interaction under the influence of various axial ligands.32 In this work, the authors effectively combine experimental measurements and computational tools. Influence of the dirhodium complex on the activity of RNA polymerase was also explored.33 Interactions of the paddle-wheel dirhodium complex with amino acids were experimentally examined using electronic circular dichroism spectroscopy (ECD) by Szilvagyi et al.,34 who observed various chelate structures. In our previous study, the energy profiles of the acetyl ligand(s) replacement with purine DNA base(s) were explored. It was found that guanine is the thermodynamically preferred nucleobase for coordination to the paddle-wheel dirhodium complex.35 Recently, a study appeared that revealed the details of bischelate adenine-cytosine cross-links in oligomer DNA sequences.36 In the present contribution we focus on a possible molecular mechanism for the replacement of the initial stage of the reaction that involves substitution of either equatorial Rh-O(ac) or axial Rh-O(aq) bond by nitrogen (N7 of the purine base or N4 of cytosine). Since a nucleobase represents a relatively large molecule, we first developed a simpler, computationally feasible model with the ammonia molecule.
Scheme 1
on deformation energies: ΔEStab ¼ - ðEcomplex -
X
Efragment Þ -
X
Edeform
ð1Þ
Binding energies were calculated according to an analogous formula without the deformation energy corrections. The partitioning of the complex for the calculation of the fragment energies (Efragment) was carried out according to the examined bond(s). For the estimation of the binding energy of the acetate coordination, a simultaneous cleavage of both Rh-O bonds was considered. The Hessian matrices were determined for all the optimized structures, and frequency analysis confirmed the character of local minima in the case of all reactants and products. For the structures of transition states, one negative vibration coordinate of antisymmetric stretching mode was confirmed. On the basis of frequency analysis and canonical ensemble formulas, Gibbs free energies were determined. Rate constants were estimated according to a formula based on the Eyring transition state theory(TST):
’ COMPUTATIONAL DETAILS A simplified model of the reaction for the substitution of the Rh-O bond from the acetyl or aqua ligand in tetrakisacetatodiaqua-dirhodium(II,II) complexes by ammonia was investigated here. Stereochemical formulas of the considered reactions are in Scheme 1. All the calculations were performed at the density functional theory (DFT) level. For geometry optimizations, the B3PW91 functional and 6-31G(d) basis set were employed. The rhodium atoms were described by Stuttgart MWB-28 effective core potentials and by the original valence pseudoorbital37 extended with a set of f-polarization functions (exponent Rf = 1.471). The single-point (SP) energy decomposition and electron density analysis were carried out with the B3LYP functional and aug-cc-pvdz basis set for H, C, N, and O atoms.38 The Rh valence space was augmented by a set of diffuse functions (exponents Rs = 0.007, Rp = 0.01, and Rd = 0.02) and a set of 2fg polarization functions (Rf = 1.936, 0.532 and Rg = 1.19). Since we are interested in reactions relevant for “bioprocesses”, the gas phase results were further refined by examination of the solvent effects within the polarizable continuum model (in the COSMO version with Klamt radii39). Stabilization energies were determined in the framework of the basis set superposition error (BSSE)40 including corrections
kTST ðTÞ ¼
kT expðΔGa =kTÞ hc 3
where ΔGa is the activation Gibbs energy. In addition to the canonical (KS-)MO analysis, partial charges obtained in natural population analysis (NPA) and critical points from Bader’s atoms-in-molecules (AIM)41 were determined for detailed insight into binding phenomena. For evaluation of the electronic structures, the Gaussian 03 C2 program package was used; the NPA charges were determined using the program NBO v.5.0 from Wisconsin University, 42 and AIM results were obtained with the Keith AIMAll program.43 The ADF program was employed for the energy decomposition according to the extended transition state (ETS) method combined with the natural orbitals for chemical valence (NOCV) theory.44 Structures. The gas phase and Polarizable Continuum Model (PCM) approaches were applied to the calculations of processes that mimic the replacement of the Rh-O dative bond of either acetato or aqua ligands from the paddle-wheel dirhodium(II,II) complex by coordination of an ammonia molecule to the Rh-N bond. All the complexes optimized within the PCM approach are displayed in Figure 1. In this figure, character R represents reactant and P represents product. If there is no numeric specification, 785
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Figure 1. PCM optimized structures of all considered dirhodium complexes. (a) Neutral reactant R. (b) Reactant complex protonated in proximate oxygen R1 (forming proton transferred structure). (c) Reactant complex protonated in the remote oxygen position R2. (d-f) Transition structures for breaking one of the RhO(ac) bonds: (d) TSa, (e) TS1a, and (f) TS2a. (g-i) Transition structures for aqua ligand replacement: (g) TSw, (h) TS1w, and (i) TS2w. (j-l) Products with one monodentate acetyl ligand: (j) Pa, (k) P1a, and (l) P2a. (m-o) Product complexes with axial ammonia ligands (m) Pw, (n) P1w, and (o) P2w.
axial water ligand is replaced by ammonia, and “a” is for acetato coordination in one of the equatorial positions. This reaction simulates the first interaction step in the nucleobase (guanine or adenine) substitution process, assuming that the N7 coordination
neutral complexes are regarded, number 1 labels protonated complexes with the proton located in the proximity of ammonia, and label 2 designates protonation on the O10 atom of the Rh2 complex. Additional character “w” is used for reaction where the 786
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Table 1. Rhodium Coordination Distances and O-H Distance within the Reaction Course (in Å) Rh-Rh0
H2O/NH3 gp
PCM
gp
PCM
gp
PCM
PCM
gp
PCM
gp
PCM
Rh-O(aq)
Rh0 -O0 (aq)
Rh-O1
Rh0 -O10
Rh-N
R
2.394
2.279
2.387
2.066
2.046
3.748
TSw
2.382
3.250
2.272
2.044
2.042
3.711
Pw
2.403
3.424
2.418
2.060
2.048
2.221
R
2.395
2.299
2.384
2.063
2.051
3.785
TSw
2.384
3.324
2.330
2.043
2.041
3.696
Pw
2.415
3.929
2.407
2.060
2.061
2.225
R1
2.379
1.627
2.506
2.258
2.081
2.050
3.539
Ts1w P1w
2.394 2.409
0.982 1.025
3.229 3.324
2.245 2.325
2.103 2.138
2.123 2.099
2.670 2.237
R1
2.389
1.850
2.387
2.304
2.072
2.048
3.817
Ts1w
2.397
0.984
3.524
2.235
2.088
2.124
2.587
P1w
2.409
1.146
3.841
2.363
2.100
2.062
2.239
R2
2.408
0.974
2.206
2.351
2.114
2.159
3.884
Ts2w
2.403
0.974
2.610
2.288
2.122
2.149
3.043
P2w
2.419
0.974
3.784
2.384
2.119
2.159
2.189
R2 Ts2w
2.408 2.403
0.979 1.001
2.237 2.290
2.329 2.288
2.090 2.084
2.144 2.152
3.944 4.586
P2w
2.421
0.978
3.844
2.376
2.090
2.147
2.192
Rh-Rh0
O1-H
Rh-O(aq)
Rh0 -O0 (aq)
Rh-O1
Rh0 -O10
Rh-N
acetato/NH3 gp
O1-H
R
2.394
2.279
2.387
2.066
2.046
3.748
TSa
2.447
3.649
2.282
2.826
2.028
2.246
Pa
2.437
2.384
2.336
3.844
2.035
2.039
R
2.395
2.299
2.387
2.063
2.051
3.785
TSa Pa
2.451 2.448
3.805 2.350
2.254 2.341
2.805 3.894
2.025 2.050
2.234 2.041
R1
2.379
1.627
2.506
2.258
2.081
2.050
3.539
TS1a
2.445
0.999
3.706
2.248
2.762
2.083
2.293
P1a
2.438
0.972
2.320
2.325
4.124
2.101
2.061
R1
2.389
1.850
2.387
2.304
2.072
2.048
3.817
TS1a
2.451
1.024
4.452
2.246
2.772
2.063
2.277
P1a
2.446
0.975
2.313
2.337
4.024
2.084
2.049
R2 TS2a
2.408 2.436
0.974 0.974
2.206 3.726
2.351 2.308
2.114 2.934
2.159 2.141
3.884 2.232
P2a
2.436
0.979
2.284
2.414
4.096
2.206
2.055
R2
2.408
0.979
2.237
2.329
2.090
2.144
3.944
TS2a
2.442
0.977
3.812
2.265
2.536
2.112
2.263
P2a
2.441
0.994
2.295
2.328
4.038
2.177
2.045
occurs first, since Rh is a soft atom according to HSAB Pearson principle.45,46 The influence of pH of the surrounding environment was considered by protonation of one of the acetato ligands from the dirhodium complex. The important coordination parameters of the optimized structures in individual reaction states are compiled in Table 1. An interesting feature of the Rh-Rh bond is the very small influence of the solvent on its characteristics, since practically no change in the distance was observed after reoptimization of the gas-phase geometry in the PCM model. When acetate oxygen is protonated in proximate position to the attacking ammonia, a proton transfer (PT) occurs (cf. Figure 1b) in accord with the acidic behavior of acetate ligand and the basic character of ammonia. In this case, axial aqua ligand cannot play the role of H-donor in the interaction with ammonia like in the neutral reactant complex. On the contrary, it has to accept H-bonding from NH4þ. Hence,
Scheme 2
O(aq) has to partially redistribute electron density in favor of accepting the H-bond from ammonium at the expense of the dative Rh-O bond. This results in mild shortening (and strengthening) of the Rh-Rh bond. Such an effect is more pronounced in the gas phase model where no electrostatic screening is present. If the acetyl oxygen on the remote site is protonated, 787
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Table 2. Thermodynamic Characteristics (in [kcal/mol], at T = 298K, p = 101.325 kPa) and Rate Constants ka ΔER neutral complex
GP PCM
þ
H on proximate O1 Hþ on remote O10
-5.2 -2.1
10.2
9.4
7.8 105
10.0
2.8 10
2.8 103 1.9 103
5 -6
6.6
7.8
25.7
25.3
1.8 10
22.1
22.1
36.8
38.8
2.1 10-16
3.2Eþ00
GP PCM
-3.6 -4.6
-3.6 -5.2
-1.3 -5.3
17.5 21.6
17.6 21.0
7.8 10-1 2.4 10-3
8.7 10-2 3.1 10-7
kRfP [M-1 3 s-1]
kPfR [s-1]
(b) Substitution of One of the O(acet) by Ammonia ΔHR ΔGR ΔEA ΔGA
1.0Eþ00
2.4
3.3
3.2
18.9
19.3
4.1 10-2
9.0Eþ00
PCM GP
-0.4 2.0
-2.1 2.2
0.5 2.8
21.0 21.7
19.1 22.2
5.9 10-2 3.3 10-4
1.4 10-1 3.9 10-2
PCM
10.5
10.7
9.7
28.3
29.5
1.4 10-9
1.9 10-2
Hþ on proximate O1
remote a
-3.0
12.3
6.8
GP
GP O10
-3.8
-3.3
kPfR [s-1]
21.5
GP
neutral complex
H on
-4.0
kRfP [M-1 3 s-1]
PCM
ΔER
þ
(a) Substitution of Axial Aqua-Ligand by Ammonia ΔHR ΔGR ΔEA ΔGA
PCM
-11.3 -9.3
-10.2 -10.3
-9.4 -14.5
12.6 13.1
14.4
1.8 10
2.4 10-5
9.4
7.3 10
1.7 10-5
2 5
ΔE is electronic energy, ΔH is enthalpy, and ΔG is Gibbs free energy. Subscript R means reaction energy, and A means activation energy. k is the rate constant for the corresponding forward (RfP) and backward (PfR) reaction.
Figure 2. Reaction energy profile (ΔG) for (a) replacement of an axial aqua ligand by ammonia and (b) replacement of one of the acetate coordinations in equatorial position.
then (contrary to the previous situation) the weakening of the intermetallic bond becomes more pronounced as a result of the less negative charge on O10 oxygen caused by the H atom linked to it (cf. discussion on electron densities below). A small, but notable elongation of the Rh-Rh distance in all the product states indicates weakening of this bond in the complexes with ammonia ligand. This clearly demonstrates the stronger donation from the softer nitrogen atom. Similarly to shortening of the Rh-Rh bond in the R1 complex, the product structure P1w exhibits proton transfer leading to H3Oþ cation and follows the same rule, leading to only small elongation of the Rh-Rh bond in the gas phase, and even shortening of this bond (in comparison with neutral structure) in acidic solution. Comparing the corresponding Rh-O1 (in proximal) and Rh0 -O10 distances (in remote position to ammonia; the notation is displayed in Scheme 2), a visibly longer Rh-O1(-H) coordination in both of the protonated reactants can be noticed. Also, the axial Rh-O(aq) bond is visibly longer (by more than 0.1 Å) in both gas phase and PCM calculations (with the exception of the proton transferred R1 structure).
An interesting feature arises from a comparison of the substitution reaction in axial and equatorial positions. In the case of axial replacement, it can be noticed that in the TS structures the intermetallic bond is systematically shorter than in the reactant or product (strengthening the Rh-Rh interaction). This is due to weaker donation from axial ligands (none of replacing ligands is exactly in the axial position in the TS structures). However, replacement of one of the equatorial Rh-O(acetyl) bonds causes elongation of the intermetallic Rh-Rh distance in TS structures. The TS structure represents a perturbed complex where ammonia is partially coordinated in the axial position (with bond angle Rh-Rh-N about 150-160°), and water is transferred to the first solvation shell forming H-bond with one of the neighboring O(ac) atoms. The TSa structure resembles the characteristics of the activation barrier species for the process where the ammine-ligand is relocated from axial to equatorial position (with water molecules already transferred to solvent). Energy and Thermodynamics. Evaluation the reaction energies (ΔER, and ΔGR) indicates that ammonium can relatively 788
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Table 5. Electron Density in BCPs ( 10-2)
Table 3. Binding Energies at the B3LYP/aug-cc-pvdz Level in Gas Phase and COSMO Approaches system
H2O/NH3
Rh-Rh0 Rh-O(aq) Rh-O0 (aq) Rh-NH3 Rh-O1 Rh0 -O10
acetato/NH3
Rh-acet Rh-OH2 Rh-NH3 Rh-acet Rh-OH2 Rh-NH3 gas phase R TS
176.4 191.1
17.0 3.3
11.5 0.4
176.4 150.2
P R1
17.0 7.4
11.5 18.0
179.3
8.0
18.9
143.5
7.4
47.0
262.4
17.8
43.9
262.4
17.8
43.9
R
9.97
4.23
8.60
8.85
TSw
9.75
5.68
9.08
9.20
Pw
9.65
3.93
R1
10.05
3.47
8.85
4.36
6.84
7.56
8.39
R2
9.82
5.84
4.71
8.97
9.15
TS2w P2w
9.91 9.58
5.07
5.13 4.31
7.68 8.61
6.17 8.93
6.4
16.4
39.3
17.5
17.9
20.7
29.9
12.5
40.6
R2
42.9
25.8
14.9
42.9
25.8
14.9
TS2
39.9
4.8
1.4
25.5
7.3
26.2
P2
44.8
7.1
28.9
25.7
14.1
47.3
R
115.0
39.5
33.2
115.0
39.5
33.2
TS1a
8.79
TS
124.4
27.5
24.5
79.2
26.4
37.2
P
114.2
26.6
41.3
77.6
28.8
67.2
P1a R2
9.09 9.82
R1
124.1
35.9
34.3
124.1
35.9
34.3
TS2a
9.07
TS1
64.7
26.5
34.1
62.8
38.4
40.5
P2a
9.20
P1
141.79
48.2
41.9
50.7
31.2
66.6
R2
67.1
44.6
35.9
67.1
44.6
35.9
TS2 P2
84.5 67.2
49.0 27.2
37.7 45.7
53.2 42.2
31.5 32.1
43.3 68.7
O10
-1.141
0.927 0.875 -1.017
-0.972 -0.710 -0.693
-1.170
0.813 0.990 -1.023
-0.953 -0.703 -0.687
Pw R1
-1.082 0.920 0.841 -1.010 -0.947 0.466 0.884 0.922 -0.983
-0.984 -0.708 -0.694 -0.967 -0.731 -0.677
TS1w -1.191 0.593 0.860 0.959 -1.013
-0.962 -0.695 -0.602
P1w
-1.093 0.555 0.912 0.853 -0.882
-0.982 -0.747 -0.651
R2
-1.124 0.587 0.937 0.880 -1.016
-0.980 -0.589 -0.694
TS2w -1.166 0.612 0.913 0.909 -0.981
-0.984 -0.587 -0.711
-1.085 0.586 0.927 0.837 -1.014
-0.988 -0.591 -0.694
P2w
N
Hþ
Rh
(b) Acetyl/NH3 Rh0 O(H2O) O0 (H2O)
O1
O10
R
-1.141
0.927 0.875 -1.017
-0.972 -0.710 -0.693
TSa
-1.139
0.854 0.974 -1.020
-0.952 -0.763 -0.737
Pa
-0.983
0.822 0.912 -0.969
-0.968 -0.773 -0.762
R1
-0.947 0.466 0.884 0.922 -0.983
-0.967 -0.731 -0.677
TS1a -1.137 0.545 0.881 0.967 -0.989 P1a -0.972 0.553 0.837 0.902 -0.968
-0.955 -0.729 -0.635 -0.969 -0.697 -0.632
-1.124 0.587 0.937 0.880 -1.016
-0.980 -0.589 -0.694
TS2a -1.145 0.591 0.921 0.925 -1.011
-0.974 -0.622 -0.716
-0.975 0.572 0.842 0.897 -0.970
-0.984 -0.622 -0.741
R2 P2a
R
9.97
TSa
8.70
5.07
Pa
9.04
4.44
R1
10.05
4.05 4.79 5.84 4.99
4.23
8.60
5.45
7.51
4.52
10.85
4.87
2.08
6.84
4.60 4.71
10.55
5.42
7.07
4.71
10.75
9.66 8.87
8.34
5.56
8.85
8.89
2.00
8.33
8.97
7.57 9.15
2.97
6.82 5.85
of the aqua ligand in the tetrakisacetato-diaqua-dirhodium complex (see section on binding energy). Also, the value of reaction Gibbs free energy (about -3 kcal/mol) points to a mildly spontaneous process. In an acidic environment, when ammonia is on the same side as the protonated acetate ligand, the reaction exhibits relatively high endoergic character due to proton transfer and the formation of a stable NH4þ-Rh2 complex of the reactant R1. Nevertheless, analogous replacement on the opposite site of the dirhodium complex leads to an even more exoergic reaction ((ΔGR = -5.3 kcal/mol). It can be expected that in both neutral and acidic conditions the aqua ligand is replaced by ammonia more or less spontaneously. When competitive reaction is considered, breaking one of the Rh-O(ac) coordinations and placing NH3 ligand into the equatorial position, the reaction Gibbs energy is close to zero in a neutral environment (þ3.2 kcal/mol in gas phase and 0.5 kcal/mol in solution). However, in acidic solution, when protonation occurs on the oxygen atom in a remote position relative to the attacking ammonia, a spontaneous reaction is predicted (-14.5 kcal/mol in a water environment). Notice the spontaneous reaction course of the same (R2) reactant complex is also predicted for aqua replacement. This conclusion is surprising when one realizes how strong the Rh-O(ac) coordination is. When transition state (TS) structures are considered for both reactions, it can be concluded that the water-replacement process under neutral conditions can occur relatively easily: it is connected with a low activation barrier of about 10 kcal/mol. The other reaction of breaking the Rh-O(ac) bond is characterized by the much higher TSa energy of 19 kcal/mol. When protonation in proximal position to ammonia is considered in acidic solution, the water releasing process upholds a high (TS1w) reaction barrier of about 25 and 39 kcal/mol in gas phase and PCM, respectively. Similarly, the process of breaking of equtorial Rh-O(ac) coordination has to pass through TS1a, which lies 22 and 29 kcal/mol above the energy level of reactant R1. Reaction of the R2 complex is associated with substantially lower TS2w
Table 4. NPA Partial Charges of Selected Atoms from PCM Calculations (in e)
R
7.74
Rh-Rh0 Rh-O(aq) Rh-O0 (aq) Rh-NH3 Rh-O1 Rh0 -O10
COSMO
TSw
9.11
5.73
20.5
O1
8.89
9.81
45.9
(a) H2O/NH3 Rh0 O(H2O) O0 (H2O)
8.58
8.34
9.82
55.9
Rh
4.87
8.67
P1w
P1
Hþ
4.05
7.04
TS1w
TS1
N
5.07
easily replace the aqua ligand in the neutral complex (cf. Table 2 and Figure 2). This is in accord with the very low binding energy 789
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Figure 3. Topology graph of the neutral reactant complex with bond and ring critical points obtained from AIM analysis on the B3LYP/aug-cc-pvdz electron density.
barriers of 18 and 21 kcal/mol (in gas phase and PCM, respectively) for the deaquation process, and 14 and 9 kcal/mol in the case of the first deacetylation step (TS2a). The ligand binding energies are summarized in Table 3 for the aqua, ammino, and acetato ligands in all the stationary points. The most remarkable feature is related to the substantially stronger rhodium-ammonia bond in products when coordinated in equatorial position (by ca. 20 kcal/mol), in comparison with the axial Rh-N bond. Also, the coordinations of aqua and amine ligands in both axial and equatorial positions are highly influenced by solvent effects. Solvation almost doubles the binding energies of water and ammonia ligands in both the axial and equatorial positions. For instance, NH3 binding energies in neutral reactants are 12 versus 33.2 kcal/mol (in gas phase and COSMO, respectively) or in neutral Pw products, -19 versus 41 kcal/mol. The only remarkable exception occurs in the R1 complex, where strong electrostatic enhancement of the O 3 3 3 H-NH3 H-bonding is reduced in the solvent model. Generally, this increase compensates for a weaker donation from the acetato groups. Since the coordination of acetato ligands is strongly enhanced by electrostatic contributions between negatively charged acetyl anions and the 2þ charged dirhodium kernel, it is visibly reduced (screened) in water solution. In this way, the extent of individual dative bonds is changed in favor of neutral ligands: ammonia and water. In protonated complexes, some reduction of the binding energies of the acetato ligand can be noticed in comparison with neutral complexes since some valence electron density of the acetyl oxygen is involved in the O-H binding. In gas phase, the reduction is much more pronounced. However, in R2fP2 reactions, protonation makes the
acetato ligand neutral, in contrast to the R1fP1w reaction where the proton is transferred to the NH3 ligand. Therefore no reduction of binding energies occurs when passing to the COSMO model. Actually, higher values of about 20 kcal/mol can be noticed in accord with the similar increase of the binding energies of NH3 and aqua ligands discussed above. The larger binding energies of the acetato ligand in the R1 complex (especially in gas phase) are caused by the formation of an ionpair structure, as mentioned above. The binding energies of replacing ligands (water and ammonia) in TS structures clearly indicate the type of reaction mechanism. In nearly all cases, the binding energies of both water and ammonia molecules are very small in both gas or liquid phase. They are often smaller than the H-bonding energies of ammonia in reactant complexes or water in product complexes. This means that in TS neither water nor ammonia is actually coordinated with the dirhodium kernel by a dative bond. Therefore, the explored reactions occur by a dissociative mechanism. Rate Constants. The rate constants can be determined from the known activation barriers based on the Eyring TST. The calculated values are collected in the last two columns in Table 2. In the upper part of the table, one can see that replacement of the axial aqua ligand is a very fast process under neutral conditions (kRfP = 105 [M-1 3 s-1]). On the contrary, in acidic solution only, slow reaction can be expected. In the second part of Table 2, the energetics and rate constants of the substitution of the acetato coordination are summarized. In accord with the high binding energy of acetato ligands, this reaction is relatively slow in neutral environment. Comparing both reaction branches, it is apparent that deaquation is by 7 orders of 790
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Figure 4. Frontier orbitals of the neutral reactant obtained from BLYP/TZ2P calculations: (a) MO77: σ* orbital with antibonding character of Rh-Rh and with bonding character of Rh-O(aq) (to the axial aqua ligand) (σ*Lþ). (b) HOMO with π* character of the Rh-Rh kernel. (c) LUMO: σ* orbital has antibonding character not only for the Rh-Rh kernel but also for the Rh-O dative bond of axial aqua ligands (σ*L-).
Table 6. Eigenvalues of Valence MOs (in a.u.) Determined at the B3LYP/aug-cc-pvdz Level for Neutral Reactions R MO
char
Pw en.
char
Pa en.
char
TSw en.
char
TSa en.
char
97
De1b
-0.032
De1b
-0.027
De1b
-0.025
De1 b
-0.040
De1b
96
De1a
-0.044
De1a
-0.042
De1a
-0.037
De1 a
-0.055
De1 a
95
Si a
-0.058
Si a
-0.048
Si a
-0.059
Si a
-0.085
Si a
en. -0.040 0.051 -0.089
94
Pi a
-0.211
Pi a
-0.206
Pi a
-0.208
De2a
-0.225
Pi a
-0.199
93
Pi a
-0.212
Pi a
-0.207
Pi a
-0.208
Pi a
-0.225
Pi a
-0.215
92
De2a
-0.214
De2a
-0.210
De2a
-0.214
Pi a
-0.226
De2a
-0.222
91
Si b
-0.251
Si b
-0.236
Si b
-0.244
De2b
-0.268
De2 b
-0.253
90 89
De2 b Pi b
-0.255 -0.268
De2 b Pi b
-0.251 -0.262
De2 b Pi b
-0.246 -0.258
NH3 Pi b
-0.276 -0.282
Si b PiþO=C
-0.261 -0.263
88
Pi b
-0.270
Pi b
-0.263
PiþO=C
-0.263
Pi b
-0.284
Pi b
-0.269
87
NH3
-0.293
NH3
-0.302
PiþO=C
-0.270
Si b
-0.286
O=CþPi
-0.281
86
LigO
-0.304
LigO
-0.309
LigO
-0.293
LigO
-0.313
LigO
-0.302
magnitude faster. Nevertheless, in acidic solutions when remote acetato oxygen is protonated, the reaction can run with a
rate constant similar to that of the deaquation of the axial position. 791
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Table 7. Energy Decomposition for Interaction of the Ammonia Ligand with the Dirhodium Complex in the Gas Phase (in kcal/mol).a ΔEtotal
a
ΔEorb
ΔEelstat
ΔEPauli
R
-14.04
-19.69
-24.70
30.34
TSw
-20.57
-39.02
-80.30
98.75 132.20
Pw
-48.98
-66.16
-115.01
TSa
-1.42
-2.91
-2.86
4.36
Pa R1
-20.41 -91.02
-29.90 -197.35
-65.12 -105.35
74.60 211.67
TS1w
-18.89
-21.47
-39.94
42.53
P1w
-17.83
-27.97
-61.84
71.97
TS1a
-17.26
-28.94
-63.23
74.91
Pa
-42.75
-53.29
-102.02
112.56
R2
30.23
-17.13
-21.83
-25.53
TS2w
-0.74
-1.89
-2.32
3.47
P2w TS2a
-31.54 -24.08
-41.78 -35.83
-79.87 -73.24
90.10 84.99
P2a
-48.17
-59.21
-107.84
118.88
ΔEtotal = ΔEorb þ ΔEelstat þ ΔEPauli.
Table 8. Energy Decomposition for Interaction of Acetate Acid with the Dirhodium Complex in the Gas Phase (in kcal/mol).a
R
a
ΔEtotal
ΔEorb
ΔEelstat
ΔEPauli
-181.29
-109.88
-234.65
163.24 125.20
TSa
-150.15
-88.60
-186.75
Pa
-147.12
-75.60
-167.42
95.90
R1
-260.35
-119.32
-315.99
174.96
TS1a
-39.21
-68.29
-93.81
122.89
Pa R2
-32.43 -44.16
-39.73 -60.99
-58.11 -98.07
65.40 114.90
TS2a
-27.69
-43.67
-74.94
90.92
P2a
-25.74
-29.98
-49.78
54.02
Figure 5. The contours of deformation density contributions from selected NOCV pairs together with the corresponding energies for the reactants R, R1, and R2.
changes in the distributions of electron density occurring during the explored reactions can be compared with the electron distribution in isolated tetrakisacetatodiaquadirhodium complex, where δ(Rh) = 0.89 e.35 Interesting conclusions follow from the observation of the polarization of the Rh-Rh bond. In the neutral reactant complex, the more positive kernel atom is Rh (in comparison with Rh0 ). It is due to weaker donation of the equatorial O1 atom interacting with NH3. In acidic solution, the position of the proton is an important factor that (re)polarizes the intermetallic bond of the reactants. In products with ammonia located in the axial position (P1w, P2w), the polarization of the metallic bond is the same. The axial NH3 ligand donation is only slightly stronger than the donation of an aqua ligand (compare also the corresponding binding energies in Table 3), and some electron density of NH3 (and neighboring equatorial acetyl oxygen) is associated with H-bonding of the released water molecule. The Rh-Rh polarization in products with ammonia in equatorial position is inversed because of strong donation (binding energies are higher by 20 kcal/mol than those for the axial position), which reduces the positive charge of the interacting Rh atom. Another insight into the investigated phenomena can be obtained from partial charge of the nitrogen atom. The highest (the least negative) nitrogen charge is revealed in product states (with the exception of the ammonium cation in the R1 complex) where equatorial Rh-N coordination is established. Comparing δ(N) in products for equatorial (Pa) and axial (Pw) reactions, the higher binding energy (67.2 vs 41.3 kcal/mol in the PCM case) correlates with higher partial charge of nitrogen in the case of ammonia coordinated in the equatorial position (-0.983)
ΔEtotal = ΔEorb þ ΔEelstat þ ΔEPauli.
Analyses of Electron Distributions. All the binding and structural relations follow from electron distribution of the considered species. We have performed molecular orbital (MO) analyses, NPAs, and AIM analyses. The NPA partial charges δ for the most important atoms involved in the replacement reactions are displayed in Table 4. Comparing δ(Rh) of the reactants and products, it can be seen that higher charge roughly correlates with weaker donation. Since there are several simultaneous effects that influence donation to a metal kernel, it is difficult to extract a contribution of each individual ligand. Nevertheless, some general trends can be noticed. For instance, a lower charge on the interacting Rh atom, after replacement of Rh-O coordination by a Rh-N one, is revealed. This effect is due to the higher dative capability of nitrogen atom. However, even this simple conclusion has an exception for the R1/P1w pair for replacement of the axial aqua ligand. In this case, the explanation dwells in the fact that the proton (actually transferred to the ammonium cation) induces higher negative partial charge on the oxygen O1. In the P1a complex, the proton is already bounded to the partially released acetyl ligand, and the closest vicinity of the Rh atom is similar to the binding conditions in a neutral complex. All the 792
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The Journal of Physical Chemistry A versus the axial position (-1.082). The difference in partial charges δ(N) in these two products is close to 0.1 e. Higher partial charge of O(H2O) than that of O0 (H2O) in a reactant complex is not directly connected with weaker donation. This is due to the fact that the aqua ligand, which interacts with ammonia, also donates its proton in H-bonding to NH3. This leads to releasing some electron density from the O-H bond back to oxygen. In this case, the strength of the Rh-O(aq) bond can be correctly determined through the AIM bond critical points (BCPs) summarized in Table 5. From the data displayed in Table 5, a clear correlation with the previously discussed Rh-Rh bond lengths can be seen. An illustrative plot of the AIMAll analysis of CPs is displayed in Figure 3. From the MO analysis of the 4þ charged Rh2 kernel follows that, in valence space, all five bonding orbitals σ, πx πy, δxy, and δx2-y2 (formed by the combination of the 4d-AOs of Rh) are occupied together with two lower-lying antibonding orbitals δxy* and δx2-y2* leaving πx*, πy*, and σ* MOs vacant. However, when this kernel interacts with small organic acids forming paddlewheel complexes, the δx2-y2 orbitals of two Rh atoms are involved in binding of the equatorial ligands, which donate electrons to the δx2-y2 orbitals of the core metals. Therefore, the electron configuration of the dinuclear core Rh24þ can only be σ2πx2πy2δxy2 δ*xy2 π*x2π*y2σ*0. Two Rh atoms in this paddlewheel complex are bonded through a single σ bond. Moreover, under the influence of the axial ligands (waters at the axial position), this single bond is further weakened. Examination of the lowest unoccupied MO (LUMO) reveals that it contains an antibonding feature between the two Rh’s as well as antibonding characteristics between water and Rh. The σ* orbital of Rh24þ splits into σ*Lþ and σ*L- by interacting with the group orbital formed by the lone pairs of the waters in the axial position (see Figure 4). It is clear that the σ*Lþ orbital is occupied (MO77 in Figure 4a). MO coefficient analysis showed that the contribution of the metal core for this orbital (σ*Lþ) amounts to approximately 17%. In this way, the filled σ*Lþ partly reduces the Rh-Rh binding. It causes the following characteristics of the explored complexes (including TS structures): the highest occupied MO (HOMO) (and HOMO-1) has π* character, and in the LUMO orbital, both antibonding characters (σ*(Rh-Rh) and σ*(Rh-O)) are combined (σ*L-). At the DFT level, there are visible energy gaps between bonding and antibonding (dirhodium) orbitals (around 0.24 au) as well as between valence bonding orbitals of the Rh2 kernel and nonbonding orbitals of the oxygen atoms of the carboxyl groups (around 0.28 au). In Table 6, orbital energies of the highest valence orbitals of neutral complexes of both reaction pathways are collected. The HOMO and LUMO orbitals of the neutral reactant are depicted in Figure 4. From the HOMO and LUMO eigenvalues, the chemical potential can be estimated (μ ≈ -IP þ EA/2) but such estimation is too rough for a comparison with reaction ΔG. In order to compare various coordination strengths in reactants, TS, and products, another kind of bonding analysis was regarded. The ETS-NOCV method is a combined charge and energy decomposition scheme for bonding analysis, which is able to give more detailed insight to differences in coordination of individual ligands to the dirhodium kernel. In Table 7, the energy decomposition44,47 for interaction of dirhodium complex with ammonia is summarized, and in Table 8 the energy decomposition of the interaction of the dirhodium kernel with acetato ligand is collected. Both tables contain gas phase results. Comparing total
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energies with corresponding data from Table 3 (gas phase Rh-NH3 and Rh-acet), an excellent match was obtained. In the ΔEorb column, the energies of the coordination-covalent contributions can be observed, clearly showing that acetato ligand is quite similarly coordinated to the Rh2 kernel in both R and R1 reactants (in Table 8) as compared to R2. This clearly confirms the same coordination strength and also a similar polarization of dirhodium kernel in those complexes. This situation is depicted in Figure 5 where the orbital-interaction energy contributions from most important natural orbitals are displayed. From the Figure it is visible that while, in the first two R and R1 reactants, both Rh-O(acet) bonds are degenerated, in the case of R2 reactant, the two separated deformation density contributions can be seen. The electronic strength of the Rh-O1 coordination is about 25 kcal/mol, while the energy of the other Rh0 -O10 bond is only 16 kcal/mol. This clearly shows the consequence of the protonation of the O10 site.
’ CONCLUSIONS In the present study, it was shown that in neutral solution the replacement of an axial aqua ligand represents a mildly exoergic process characterized by a relatively low activation barrier. This means that, according to Eyring TST, it occurs very quickly. This can also be estimated from low binding energies of the axial ligand. In acidic solution, the replacement of aqua ligand is a little more demanding, especially in the gas phase, if the reaction occurs in proximal position. However, in a position remote to the replaced ammonia molecule, the reaction occurs spontaneously. The breaking of the Rh-O(ac) bond in neutral solution is slightly endoergic (ca. 1 kcal/mol), but it could occur if the dirhodium complex is protonated in acetyl oxygen in the remote position (reactant R2) since the protonated acetato ligand becomes more labile. The two forms of acidic reactants differ in positions of the attached proton. Due to the strong basicity of ammonia, the R1, TS1, and P1 conformers are substantially more stable in the gas phase (by 16, 8, and 6 kcal/mol) than the corresponding R2, TS2, and P2 forms. In solution, R1 is even more stable (by 28 kcal/mol) but the TS structures exhibit inverted energy order (by 7 kcal/mol), and products are practically equally stable. If one uses a more realistic model for the drug interaction with DNA, e.g., purine bases or even nucleotide(s), the energy ratio between conformers protonated at the remote and proximate oxygens would be smaller (especially in the nucleotide case). If this ratio is small enough (under 4 kcal/mol), then the probability for occurrence of the remote protonated form R2 (or its instant concentration) could be sufficient for leading the reaction through this pathway. It would increase the rate of Rh-O(ac) breaking, and finally the formation of dirhodium adduct with DNA genomic code. Finally we would like to mention one aspect of the higher laying TS structure in the reaction R1fP1, where one of the Rh-O(ac) bonds was broken and replaced by ammonia coordination. Here, the R1 and P1 complexes are additionally stabilized by proton transfer from the dirhodium complex to ammonia (in the case of R1) and water molecule (in P1). However, such transfer is impossible in the transition structure, which contains both molecules (water and ammonia) in neutral form. Due to electrostatic repulsion, neither NH4þ can coordinate to the Rh kernel nor H3Oþ can be H-bonded to ammonia. Therefore this reaction is partially kinetically disfavored, especially in the gas phase model. 793
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’ ACKNOWLEDGMENT The authors are grateful for support provided by the MSMT R Grant Projects MSM 0021620835, ME10149, and by GA C R C Grant Project P205/10/0228 (J.V.B.). Work in the USA was supported by the NSF CREST Grant No. HRD-0833178.
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