27 June 2002
Chemical Physics Letters 359 (2002) 500–506 www.elsevier.com/locate/cplett
A Gaussian-3 (G3) theoretical study of the interactions between alkali metal cations and polyhydroxyl ligands Seduraman Abirami a
a,b
, N.L. Ma
a,*
, N.K. Goh
b
Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricon, Singapore Science Park II, Singapore 117528, Singapore b National Institute of Education, Science and Technology Education, 1 Nanyang Walk, Singapore 637616, Singapore Received 22 March 2002; in final form 24 April 2002
Abstract Ab initio molecular orbital calculations at the G3(GCP) level were conducted for the alkali cation–alcohol complexes (Mþ –L, where Mþ ¼ Liþ , Naþ , and Kþ ; L ¼ methanol, ethylene glycol, propan-1,2-diol, propan-1,3-diol and propan-1,2,3-triol). In general, these cations maximize the number of Mþ O interactions with the ligands. The role of intramolecular hydrogen bonding, ligand polarizability, ligand deformations, number of Mþ O interactions and the Mþ O distances in governing Mþ –L affinities was discussed. The computationally less expensive G2(MP2,SVP)–FC/ ASC models were found to yield affinities in good agreement against the G3(GCP) benchmark, but the agreement deteriorates somewhat with increasing number of Mþ O interactions. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Alkali metal cations play important biological functions in living organisms [1]. The lightest alkali metal ion, Liþ , is used in the treatment of manicdepression psychosis and has effects on carbohydrate metabolism [2]. Phenomena such as glandular secretion, intestinal and tubular absorption of salt solutions, nervous activity, and bioelectric potentials are all intimately related to the movements of
*
Corresponding author. Fax: +65-6778-0522. E-mail address:
[email protected] (N.L. Ma).
sodium and potassium ion across cell membrane. The transport of the Naþ =Kþ also regulates enzyme activities, and these cations are active participants in nucleic acid metabolism [3–5]. Quantitative determination of the alkali cation affinities for small model organic ligand in the gas phase provides the intrinsic information necessary for better understanding of the interaction of these cations with larger biologically active molecules. The gas phase ligand affinities for the smaller alkali cations, Liþ and Naþ , have attracted considerable attention both experimentally and theoretically [6–16]; while studies on the larger potassium cation are relatively few.
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 0 7 4 3 - 1
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The structures of carbohydrates are believed to be important in biological events [17,18]. Due to the large size, exhaustive conformational studies on carbohydrates are very difficult. This difficulty can be partly overcome by selecting appropriate smaller molecules as models. Because of the presence of intramolecular OH O hydrogen bonds, polyhydroxyl alcohols have been used as simple models of carbohydrate [19,20]. In order to gain insight on the interactions that take place between alkali metal cations and sugars/ carbohydrates, in-depth understanding of cations– polyhydroxyl alcohol interaction is essential. Here, we employed the Gaussian-2 (G2) and Gaussian-3 (G3) protocols to model complexes between alkali cations and polyhydroxyl alcohol. G2 and G3 theories are the most widely ‘model chemistry’ protocols for obtaining the ionization energies, electron affinities and heats of formation, etc. for a range of simple organic and inorganic system [21– 23]. However, our group and others [13,14,24] showed that standard G2/G3 procedure may lead to erroneous energetics if inappropriate alkali cation core size is used. Furthermore, we have studied the effect of basis-set-superposition-error (BSSE) on the calculated alkali cation affinities [15]. Based on these studies, we recommended that accurate Liþ =Naþ and Kþ affinities can be obtained at the G2(MP2,SVP)-FC and G2(MP2, SVP)-ASC levels[15], respectively. Our previous benchmark study [15] was conducted on complexes in which the cations interact with the ligands in a mono-dentate fashion. It remained unclear whether the conclusion drawn there could be transferable to complexes with multidentate cation–ligand interactions. This issue is important, as the cations are likely to interact simultaneously with a few binding sites in biological systems. Furthermore, when the previous benchmark study was conducted [15], the ‘G3large’ basis set for potassium cation was not available. With the potassium G3large basis set published recently [23], we would like to benchmark our recommended G2(MP2,SVP)-ASC procedure for potassium cation against this higher G3 level of theory. All these factors motivated our present study of the three alkali cations (Mþ , where Mþ ¼ Liþ , Naþ , and Kþ ) with five alcohol
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ligands (L, where L ¼ methanol (meoh), ethylene glycol (ethgl), propan-1,2-diol (12diol), propan1,3-diol (13diol) and glycerol/propan-1,2,3-triol (123triol)).
2. Theoretical methods Ab initio molecular orbital calculations were carried out using GA U S S I A N 98 [25] package of programs. The alkali metal cation (Mþ ) affinity of a ligand (L) at 0 K (DH0 ) is calculated using the following equation þ þ DH0 ¼ ½EM þ EL ½EM–L ; þ EM ,
þ EM–L
ð1Þ
where the EL , and is the electronic energy calculated by variants of G2/G3 protocol for the alkali cation, the free ligand and the cation–ligand complex, respectively. As details of these procedures can be found in the original references [21,22], we will only highlight a few issues here. All Gaussian procedures are based on geometries of species obtained at the MP2(full)/6-31G(d) level of theory, but differ at the level at which energetics are calculated. The G2(MP2,SVP) protocol is a variant of the standard G2(MP2) procedure, in which the resource demanding QCISD(T) single point is carried out with a smaller double-zeta split-valence polarization (SVP) 6-31G(d) basis [26]. Our procedure, G2(MP2,SVP)-FC [15,24], is in fact, identical to the standard G2(MP2,SVP). The ‘FC’ in our notation highlights that the default Gaussian94 frozen core size for Liþ and Naþ is employed. For potassium cation, the G2(MP2,SVP)-ASC level is recommended [15]. The ‘ASC’ notation indicated that all the post-Hartree–Fock single point energies are calculated with a smaller than default core size in Gaussian94. In other words, only the 1s and 2s2p electrons are in the core for Kþ in the ASC model. In this work, the benchmark affinities of these Mþ –L complexes were calculated at the geometrycorrected-counterpoise Gaussian-3 (G3(GCP)) level [15], in which the geometry corrected counterpoise (GCP) procedure was employed to correct the standard G3 affinity [21,23]. The GCP corrected enthalpy is different from the standard
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counterpoise (CP) corrected enthalpy by Edef , given by Eq. (2) Edef ¼ Eðligand in the complexÞ Eðligand
in the uncomplexed formÞ ;
ð2Þ
calculated at MP2/G3large//MP2(full)/6-31G(d) level of theory. Hence, the raw attractive interaction energy between the cation and the ligand is thus given by Estabilization as Estabilization ¼ DH0 þ Edef :
ð3Þ
3. Results and discussions 3.1. Geometries of the free alcohol ligands The optimized structures of the five alcohols (meoh, ethgl, 12diol, 13diol, and 123triol) are summarized in Fig. 1. Gas phase geometry for meoh has been reported [27], and our optimized geometry for this species is in good agreement with the experimental structure. Comprehensive conformational studies for ethgl, 12diol, 13diol and 123triol have been reported [20,28,29]. Hence, we did not carry out further conformation search but only make use of these previous findings. All the polyhydroxyl alcohols (ethgl, 12diol, 13diol and 123triol) exhibit intramolecular hydrogen bonds. Both ethgl and 12diol are stabilized by a five-membered hydrogen bond ring moiety, with OH O distance of approximately 2.2 . Interestingly, the OH O distance in 13diol is A . significantly shorter at approximately 0.2 A However, even with this shorter hydrogen bond, the 13diol is less stable than the 12diol by 18 kJ mol1 at the G3 level. We attribute this instability to the larger permanent molecular dipole estimated for 13diol ( 3.6 Debye) as compared to that of 12diol ( 2.5 Debye). 3.2. Effect of metal cation complexation on the geometries of the alcohol ligands The MP2(full)/6-31G(d) optimized structure of the Mþ –L complexes are shown in Fig. 2. For all Mþ , the most stable cation–ligand complex with
Fig. 1. Optimized geometries of the ligands, at MP2(full)/ 6-31G(d) level. The dotted lines represent the intramolecular , given in italics). hydrogen bond (distance in A
the three diols (ethylene glycol, propan-1,2-diol and propan-1,3-diol) and glycerol are bi- and tridentate, respectively. In order to understand the effect of multidentate Mþ binding on geometries and affinities of the ligand, we also obtained the less stable mono-dentate Mþ –L complexes for comparison. All these Mþ –L complexes exhibit no symmetry except for the bi-dentate complexes of Mþ -ethgl ðC2 Þ and Mþ -13diol ðCs Þ, with a typical for Liþ , Mþ O distances of 1.9, 2.2 and 2.5 A þ þ Na , and K complexes, respectively. We note here that the structure obtained here for Naþ =Kþ ethgl is in good qualitative agreement with that reported previously [9,30].
S. Abirami et al. / Chemical Physics Letters 359 (2002) 500–506
Fig. 2. Optimized geometries of the Mþ –L complexes, at MP2(full)/6-31G(d) level. The dotted lines represent the intra, given in italics); and molecular hydrogen bond (distance in A Mþ O interaction. Values related to the Naþ and Kþ complexes are enclosed in square brackets and parentheses, respectively. The structures of the less stable mono-dentate alkali cation–alcohol complexes of ethgl, 12diol and 13diol are displayed on the left-hand side of this figure.
The binding of Mþ has no major effect on the covalent framework of the ligand. For the oxygen atom(s) which the Mþ binds to, the OH bond(s) ), while the lengthens slightly (by less than 0.02 A CO bond increases by 0.02–0.04 A. As the Mþ –L interactions weaken with increasing ionic radii, the larger cations are expected to have even smaller perturbation on the structure of the ligands. The lengthening of CO bond upon cation complex-
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ation in the order of Liþ > Naþ > Kþ is inline with this expectation. While the covalent framework is virtually unperturbed upon cation complexation, the hydrogen bond network can undergo quite significant changes, depending on the type of Mþ –L interaction. For the multidentate complexes, in order to accommodate the Mþ , the intramolecular hydrogen bonds in the free ligand cannot be retained. From this, we conclude that the stability of the Mþ –L complexes in multidenate modes arises largely from the electrostatic interactions between the Mþ and the oxygen binding sites in the ligand. On the other hand, for the mono-dentate modes, the intramolecular OH O hydrogen compared to the free bond shortens by 0.2–0.3 A ligands. The shortening effect is most pronounced in Liþ , and is in the general order of Liþ > Naþ > Kþ . This shortening of intramolecular hydrogen bond is partly due to the increase in electrostatic interaction between the hydrogen (natural charge increases by 0.06 e) and oxygen (decreases of charge by 0.02 e) involved in the OH O hydrogen bond. However, the major contribution to this shortening arises from the decrease of electrostatic repulsion between the oxygens. Upon cation complexation, the distance between the oxygen pair in ethgl, 12diol and 13diol . When Mþ interacts with an decreases by 0.2 A oxygen binding site, the electron density of this site will be polarized towards the metal cation. Thus reducing the unfavorable oxygen–oxygen lone pair repulsion, shortening the O O distance, and indirectly leading to shortening of the intramolecular OH O bond. Hence, as opposed to the multidentate complexes, these mono-dentate Mþ –L complexes appear to be stabilized by the combined effect of electrostatic interactions and intramolecular hydrogen bonding. 3.3. Alkali cation affinities of alcohol ligands The alkali cation affinities are calculated at the benchmark G3(GCP) level, and the recommended G2 levels previously [15] (Table 1). The discussions below are based on the energetics obtained at the
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Table 1 Theoretical affinities ðDH0 Þ, deformation energies ðEdef Þ and stabilization energies ðEstabilization Þ for various Mþ –L complexes (in kJ mol1 at 0 K) Species
DH0 a
DH0 b
Edef c
Estabilization d
Liþ -meoh Liþ -ethgle Liþ -ethgl Liþ -12diole Liþ -12diol Liþ -13diole Liþ -13diol Liþ -123triol Naþ -meoh Naþ -ethgle Naþ -ethgl Naþ -12diole Naþ -12diol Naþ -13diole Naþ -13diol Naþ -123triol Kþ -meoh Kþ -ethgle Kþ -ethgl Kþ -12diole Kþ -12diol Kþ -13diole Kþ -13diol Kþ -123triol
147.2 165.7 227.1 172.5 230.2 190.4 248.6 264.5 101.4 115.6 157.5 121.3 158.2 135.7 168.0 184.3 76.4 88.0 117.4 92.1 117.2 105.5 121.7 134.6
147.8 166.2 229.7 174.0 233.0 190.5 251.7 269.0 98.8 112.7 153.7 118.4 154.7 132.4 163.9 178.7 75.7 87.1 118.5 91.6 118.5 104.5 123.2 136.6
3.6 12.4 27.9 16.2 31.6 11.9 31.9 66.2 2.1 8.3 22.5 7.5 26.1 7.3 29.3 59.9 1.3 6.2 21.3 6.2 25.0 5.0 27.7 59.4
150.8 178.1 255.1 188.7 261.8 202.3 280.5 330.7 103.5 123.9 179.9 128.8 184.3 143.1 197.3 244.2 77.7 94.2 138.8 98.3 142.2 110.5 149.2 194.0
(73.9) (85.1) (115.4) (89.4) (115.2) (102.4) (119.7) (132.2)
Theoretical affinities calculated at the G3(GCP) level for Liþ , Naþ and Kþ containing complexes. Theoretical affinities calculated at the G2(MP2,SVP)-FC level for Liþ and Naþ containing complexes. For Kþ containing complexes, affinities reported at the G2(MP2,SVP)-ASC level; the GCP corrected G2(MP2,SVP)-ASC affinities are included in bracket. c Deformation energies, Eq. (2), calculated at the MP2(full)/G3large. d Stabilization energies, calculated from Eq. (3), using G3(GCP) affinity. e The metal cation interacts with the ligand in a mono-dentate fashion. a
b
G3(GCP) level, and similar conclusions can also be drawn at the G2 levels. For a given cation Mþ , its ligand affinity increases with increasing molecular weight of the ligand. In other words, the Mþ binding affinities are in the order of ethgl < 12diol < 13diol 123triol: As these alkali cation–ligand interactions are largely electrostatic [31,32], both the number of Mþ O (dentate) and the Mþ O distance(s) play important roles in determining the raw interaction energies ðEstabilization Þ in these complexes. We would like to investigate how the number of Mþ O interactions affects the cation–ligand affinity. For ease of discussion, we have taken the average energetics obtained for the four mono-
dentate complexes (of meoh, ethgl, 12diol and 13diol), and three bi-dentate complexes (of ethgl, 12diol and 13diol) as representative of the monoand bi-dentate interactions, respectively. Using Kþ as an example, the ratio of DH0 for the tri-, bi- and mono-dentate modes of binding is 1.5:1.3:1.0. At the same time, the ratio for Estabilization is 2.0:1.5:1.0. In other words, the affinities and the raw interaction energies of a tri-dentate interaction are not three times that of a mono-dentate interaction; nor bi-dentate binding twice as stabilizing as monodentate binding. The smaller than ‘ideal’ Estabilization for multidentate modes can be partly attributed to the longer Mþ O distances in these complexes: when the Mþ interacts with more than one binding site, the cation cannot achieve optimal binding with each
S. Abirami et al. / Chemical Physics Letters 359 (2002) 500–506
of the individual site. The much smaller than expected DH0 is partly due to the Estabilization factor. A more significant factor is the effect of ligand deformation. From Table 1, it is clear that Edef is much larger for the tridentate than the bi- and mono-dentate modes, by at least 30 and 50 kJ mol1 , respectively. Hence, even though Estabilization is estimated to be at least 30 kJ mol1 larger for Mþ -123triol than Mþ -13diol, the effect arises from the decrease in Edef in bi-dentate mode is significant as the Mþ affinity for glycerol and propan1,3-diol is found to be comparable. For a given ligand L, its Liþ : Naþ : Kþ affinity is approximately in the ratio of 2.0:1.3:1.0, in agreement with the expected decrease of Mþ affinities with increasing ionic radii. We note that the difference in the Mþ affinity for 12diol and 13diol in the mono-dentate mode displayed an interesting trend: the Mþ affinity of the 12diol is consistently around 18 kJ mol1 smaller than that for 13diol. As this difference is independent on the nature of Mþ , it must be related to some differences in property between the 12diol and 13diol ligands. We attribute this difference to the stronger hydrogen bond (reflected in the shorter OH O distance) present in the 13diol: the intramolecular hydrogen bond in Mþ -13diol is consistently about shorter than that found in Mþ -12diol 0.2 A (Fig. 2). 3.4. Comparison between G2 and G3 alkali cation affinities of alcohol ligands The G2(MP2,SVP)-FC and G2(MP2,SVP)ASC affinities for Liþ =Naþ and Kþ are compared against the benchmark G3(GCP) affinities (Table 1). While the resources required for the standard G3 calculation is similar to that at these two G2 levels, the GCP correction required three additional MP2 single points calculations with the G3large basis sets. Thus, it is of interest to evaluate the performance of the two computationally less expensive G2 protocols. The only experimental affinities available for comparison are that of Liþ -meoh [33] and Naþ meoh [34], and both values are in good agreement with the G3(GCP) estimates (within 7 kJ mol1 ). It is pleasing to find that our recommended G2
505
protocols [15] yields affinities very close to the G3(GCP) benchmark level. For Liþ , Naþ , and Kþ , the mean-absolute-deviation (MAD) is 2, 4, and 1 kJ mol1 , respectively. Interestingly, while the G2 Liþ affinities tend to be larger than that at G3, the reverse is found for Naþ affinities. Moreover, the difference between G2 and G3(GCP) affinities appears to be dependent on the number of Mþ O interaction(s). Using Liþ as an example, compared to the G3(GCP) benchmarks, the G2 affinities for the mono-dentate modes are less than 1 kJ mol1 larger. This difference increased to about 3 kJ mol1 for bi-dentate modes, and 5 kJ mol1 for tri-dentate binding in the Liþ -123triol complex. Similar trend is observed in the Naþ and Kþ complexes. It is presently not clear about the origin of this difference but BSSE is not likely to be involved as GCP correction would bring the G2 affinities for Naþ complexes lower, and hence, even further away from the benchmark G3(GCP) affinities. The performance of G2(MP2,SVP)-ASC for obtaining Kþ affinities is particularly good. The largest difference of 2 kJ mol1 , found in Kþ 123triol, amounts to less than 3% of the calculated affinity of this species. Finally, we wish to note that applying the GCP corrections to G2(MP2,SVP) (Table 1) will bring the calculated affinities further away from the G3(GCP) values. Thus, it appears that in order to yield good agreement against the G3(GCP) benchmark, no BSSE correction would be necessary for the G2(MP2,SVP)-ASC calculation.
4. Conclusions For the first time, geometry-corrected-counterpoise Gaussian-3 (G3(GCP)) calculations have been conducted for ligands that is capable for forming multiple Mþ O bonds. For these ligands, the multidentate complexes are always more stable than the corresponding mono-dentate complexes. Several factors (ligand polarizability, ligand deformations, number of Mþ O interactions(dentate), the Mþ O distances and
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intramolecular hydrogen bond) in governing the alkali cation–polyhydroxyl alcohol affinities were identified. Based on the shortening of intramolecular OH O hydrogen bond distances, we concluded that the stability of the mono-dentate alkali cation complex with ethylene glycol, propan-1,2diol and propan-1,3-diol arise partly from the strengthening of intramolecular hydrogen bonds upon metal cation complexation. Using the G3(GCP) affinities as benchmarks, the performance of the G2(MP2,SVP)-FC and G2(MP2,SVP)-ASC protocol, for Liþ =Naþ and Kþ complexes, respectively, were compared. These computationally less expensive G2 protocols are in good agreement with the G3(GCP) benchmarks, with MAD of 2, 4, and 1 kJ mol1 for Liþ , Naþ and Kþ complexes, respectively. This confirms our previous conclusion that these G2 protocols are in fact sufficiently accurate for obtaining the alkali cation–ligand interactions energies in the gas phase.
Acknowledgements We like to thank Prof. C.W. Tsang for his comments on this work. The generous allocation of supercomputer time and the award of a postgraduate studentship from the Institute of High Performance Computing to SA are gratefully acknowledged.
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