Theoretical Study of the Inter-ionic Hydrogen Bonding in the GZT Molecular System

Transcription

1 Journal of the Chinese Chemical Society, 2003, 50, Theoretical Study of the Inter-ionic Hydrogen Bonding in the GZT Molecular System Cheng Chen* ( ), Min-Hsien Liu ( ), Sou-Ro Cheng ( ) and Lung-Shing Wu ( ) Department of Applied Chemistry, Chung-Cheng Institute of Technology, Ta-Hsi, Taoyuan, Taiwan, R.O.C. Diguanidinium-5,5 -azotetrazolate (GZT) is an ionic type high energy compound, which is combined with two guanidinium cations (C(NH 2 ) 3 + or defined as G + ) and one 5,5 -azotetrazolate-2-anion (ZT 2- ). The structure of ZT 2- is made up of two N 4 C tetrazole type five-member rings connected by an azo type (-N=N-) linkage. The multi-nitrogen structure of the compound makes the ZT 2- anion in the GZT molecular system a major high-energy source with the properties of an electron donor. In addition to this, the C(NH 2 ) 3 + cation containing H atoms within its NH 2 groups behaves like a good charge acceptor not only for the formation of hydrogen bonds but also in regard to the stabilization effect within the whole molecular system. There are four strong inter-ionic hydrogen bonds in this GZT molecular system combining with the ZT 2- anion and the two C(NH 2 ) 3 + (or G + ) cations. It is impossible to calculate hydrogen bond energy between its ions by a conventional energy difference method because it is difficult to distinguish whether such an energy difference happens simply because of inter-ionic Coulomb attraction or because of the pure energy of the hydrogen bond. With our newly developed hydrogen bonding localization analysis methods, we have successfully calculated the localized hydrogen bond orders and energies of the inter-ionic hydrogen bonds in the GZT molecular system. When the localized hydrogen bond energy, the bond order, the shortening of the hydrogen bond distance, the elongation of the bond length, and the red shift of stretching frequency of the closely related NH bond are compared in order to determine the hydrogen bonding strength, all the evidence taken together, proves that the four hydrogen bonds in the GZT inter-ionic molecular system are stronger than most hydrogen bonds existing in all the inter-molecular and intra-molecular hydrogen-bonding problems we have ever considered previously. Keywords: Diguanidinium-5,5 -azotetrazolate (GZT); Inter-ionic hydrogen bonds; The DFT methods of B3LYP; Localiztion analysis of hydrogen bonds. 1. INTRODUCTION In the last few years, we became interested in the investigation of unknown high-energy compounds and their product of decomposition, N 2. We believed they might possibly be environmentally friendly. We then published our paper on the Theoretical Study of the High-energy Molecules or Clusters Constructed with Pure Nitrogen Atoms, N n (n=8to32). 1-7 However, these theoretically predicted substances, so-called stable pure nitrogen molecular clusters, have still not been found. In the past decade, several important stable nitrogenrich compounds have been invented for gas-generating mixtures They have been used in rocket and tubular weapon drive systems, as well as in inflatable air bags and rescue systems. In a similar fashion to the non-toxic behavior of the above theoretically predicted N n and the gas it produces by decomposition, N 2, most of these nitrogen-rich gases and the derived gases of combustion are lacking in toxicity. One of the most important molecules in gases we are going to study in this investigation is diguanidinium-5,5 -azotetrazolate (GZT) As mentioned in Ref. 1, GZT is a stable solid with the structure of empirical formula C 4 H 12 N 16 and with a high nitrogen content, namely 78.7% for a molecular weight of At room temperature, it is insoluble in most organic solvents. Its solubility in water is also quite moderate. Thanks to its high thermal stability, the relative melting point is within the range of 238 to 239 C. Because of the specialized stability of GZT, the structure of the composite inter-ionic molecular system of the two guanidinium cations, C(NH 2 ) 3 + (G + ) and one 5,5 -azotetra- Special Issue for the Second Worldwide Chinese Theoretical and Computational Chemistry Conference

2 766 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Chen et al. zolate anion, N 4 C-N=N-CN 4 2- (ZT 2- ), deserves theoretical study. The structure of the ZT 2- anion is made up of two N 4 C tetrazole type five-member rings connected by an azo type (-N=N-) linkage. The anion ZT 2-, with ten nitrogen atoms and two carbon atoms in the ion, is the nitrogen rich high-energy center of GZT. Two G + ions with six NH 2 proton donor or electron acceptor functional groups possibly interact with ZT 2- and by doing so stabilize the whole GZT system. Working with this assumption, it is suggested that quantum mechanical methods be used in structurally studying the overall microscopic construction of this molecular system. 2. CALCULATION 2.1 Self-consistent field calculation Various ab initio and density function theory (DFT) calculation methods have been tested for this work. It is found that the results for DFT are better when using a B3LYP type calculation rather than an ab initio type Hartree- Fock or Moller-Plesset perturbation calculation. Such calculations cost substantially less than traditional correlation techniques. By the use of the B3LYP treatment, we have solved the problems of the intra-molecular and inter-molecular hydrogen-bonding in the last few years Within the limits of computational time and memory space for the GZT molecular system, 6-31G(d), 6-31G(d,p), 6-31+G(d), 6-31+G(d,p) and G(d,p) basis functions with B3LYP calculation selected from the Gaussian 98 program package 22 were chosen in order to undertake a comparable self consistent calculation in this paper. Among the above five basis functions, three of them incorporating diffuse functions with + sign may be considered to be much more suitable than the first two type of basis functions for the system of hydrogen bonding problems We used the G + and ZT 2- ionic SCF calculations to start each set calculation. After this, the SCF procedures were also applied to the combined system of the GZT molecule. In order to prove they are local minima, the optimization and frequency calculations are included in this work. 2.2 Hydrogen bonding analysis Conventionally, it was thought that, for a simple problem of inter-molecular hydrogen-bonding, the hydrogen bond energy might be easily calculated by the energy difference method of the separated sub-systems (or molecules) and the overall combined system. However, in the case of interionic combined systems, such as GZT, the story is quite different. It is because the large Columb attraction energy between the positive and negative ions, much greater than the energy of each of the hydrogen bonds between the related ions, creates such energy differences. Accordingly, the use of localization type analysis methods is the only way to identify the hydrogen bonds in the inter-ionic system. The semi-empirical type localized analysis method of hydrogen bonds, introduced and developed by us several years ago, 26 has successfully solved various kinds of problems in intra-molecular and inter-molecular hydrogen bonding In addition to the direct selection of d N H, the local hydrogen bond distance, and the local Coulomb attraction energy (-E N H ) calculation from the optimized result of the DFT type SCF calculation, we also applied the local analysis methods of Ref. 26 to calculate the localized hydrogen bond energy, (BE) N H using the energy-breaking procedure, and the localized hydrogen bond order, P N H by the use of semiempirical population analysis. It is normally thought that the strength of the hydrogen bond depends on the shortening of d N H and the increment of -E N H, (BE) N H and P N H. Furthermore, two important indirect parameters of the localized H-bond are also selected herein for comparison. The calculated bond distances, d NH and the calculated vibration frequency, NH for the closely related NH bond sharing the H of the hydrogen bond, are also selected as indirect parameters for comparison. The elongation of d NH, the red shift of NH and the related ir intensity are also closely related to the strength of the localized hydrogen bond. We will take an example from one of our problems of the inter-molecular hydrogen bonding appearing in the special polarization effect cases. 27 The strength determined by -E N H is significantly different from that determined by the other parameters. In that calculation, the strength determined by -E N H and the special increment of atomic charge and ir intensity, etc. were defined as the electrostatic type strength, while the strength determined by the remaining parameters was defined as the covalent type strength or simply the ordinary hydrogen bonding strength. 3. RESULTS AND DISCUSSION 3.1 Geometrical optimization The optimization procedures of ZT 2-,G + and GZT combined molecular systems were performed in the following steps and by the various DFT basis functions selected from the Gaussian 98 package. All calculations started with ZT 2- and G +. We found that the local minima with the lowest energies for these two ions and their multiplicity are both in the singlet states. The calculated bond distances and angles are

3 Theoretical Study of H-Bonding in GZT System J. Chin. Chem. Soc., Vol. 50, No. 3B, listed in Fig. 1. The structure of ZT 2- with C 2h symmetry in this figure is quite similar to the structure which resulted experimentally as recently reported by Hammerl et al. 27 As for the combined GZT molecular system, we, in order to proceed with the geometrical adjustment type SCF calculation, started our input structure data by setting one of the carbon atoms in G + with a near-planar D 3 structure above the five-member ring center in ZT 2-, and the other carbon atoms below the other five-member ring center in the same anion, ZT After a time-consuming but adjustable optimization procedure, GZT with a near-planar type structure with C i symmetry, as shown in Fig. 2, was obtained. Through the identification of positive vibration frequencies, all outputs are proved to be the stable local minima by all different basis functions. To make the procedure simple to follow, we have selected only three basis functions with the most important geometrical data among the five basis functions to reflect the complications in Figs. 1 and 2. These selected basis functions are B3LYP/6-31++G(d,p), B3LYP/6-31+G(d,p) and B3LYP/6-31G(d,p). All optimized geometrical results of the first two basis functions are completely identical, and some interest- Fig. 1. The bond distance and bond angles of G + ion and ZT 2- ion molecular structure (Distance in Å). a Result by B3LYP/6-31++G(d,p) and B3LYP/6-31+G(d,p); b Result by B3LYP/6-31G(d,p); c Observed various of recent paper: (Hammerl, A. et al. Z. Naturforsch, Teil, B. 56, 851, 2001). Fig. 2. The bond distance and bond angles of GZT molecular structure with Ci group (Distance in Å). a Result by B3LYP/6-31++G(d,p) and B3LYP/ 6-31+G(d,p); b Result by B3LYP/6-31G(d,p).

4 768 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Chen et al. ing results can be noticed immediately in the following examples: (1) Four relatively strong hydrogen bonds between ZT 2- and two G + ions are created between H 30 and N 1,H 20 and N 2, H 17 and N 6, and H 27 and N 8. Thanks to the center symmetry in C i group, H 30 N 1 and H 20 N 2 are equivalent, and so are H 17 N 6 and H 27 N 8. e.g., for the hydrogen bond H 17 N 6,d N H = Å is shorter or stronger than the related d N H = Å of the hydrogen bond H 20 N 2 in the cases of B3LYP/6-31++G(d,p) and B3LYP/6-31+G(d,p) methods. But, in the case of B3LYP/6-31G(d,p) result, the d N H s are in the same order. (2) In the G + part of GZT, the elongation of N 14 17,being larger than the related one of N 15 20, is additional indirect supporting evidence for the above-mentioned order of hydrogen bonding strength. (3) The bond angle of N 8 H 27 N 24 is equal to for the stronger hydrogen bond and close to being a linear structure and is significantly larger than that of N 1 H 30 N 25 which is equal to for this weaker hydrogen bond. (4) The bond angles in the five-member ring of ZT 2- in GZT system are very close to the related ZT 2- ionic structure of Fig. 1, but the bond distances in various parts of ZT 2-, except d N1N2 in the GZT system, are closer to each other than the related distances in the ionic structure of Fig. 1, which indicates that the aromatic resonance effect in the combined molecular system is stronger than this as shown in the ionic system, and consequently that the combined system will be more stable than the related isolated ions. 3.2 Energy and equilibrium constant K dis By the the use of the above-mentioned five basis functions, all the SCF procedures of the ions and the combined molecule are successfully completed. In addition to their optimized energies (E SCF ), the H(0 K) the energy of 0 K, the enthalpy, H(298 K), and the Gibbs energy, G(298 K), at 25 C are also calculated by the zero energy, thermal energy and entropy types of modification, as listed in Table 1 for comparison. For verifying the stability of the GZT molecular system, we used the energy values of Table 1 to calculate the energy difference for the GZT = 2G + +ZT 2- ionic dissociation reaction, and then applied the calculated G at the standard state under 25 C to predict the equilibrium constant K dis of this reaction by Eq. 1. G =-RTlnK dis (1) In the energy difference calculation, due to the different sizes of basis functions between the combined system and ions, it is better to use the counterpoise (CP) type correction 28 method to correct the basis function superposition errors (BSSE) of ions. These values, corrected by the DFT method for this reaction, are not very large, if compared with those in Table 2. Especially in the case of diffuse bases, they are all less than 10 kj/mol as shown in the footnote in Table 2, being less than 1% of all energy differences. The energy differences shown in the table are larger than 1000 kj/mol and most of the energies are created by inter-ionic attraction, which is much larger than the numerical order of hydrogen bond energy. The Table 1. Energies (in au) of GZT and Its Ions Energy particle E SCF H(0 K) H(289 K) G(298 K) GZT molecule a b c d e ZT 2- anion G + cation a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d).

5 Theoretical Study of H-Bonding in GZT System J. Chin. Chem. Soc., Vol. 50, No. 3B, Table 2. The Reaction Energies of GZT = 2G + +ZT 2- (in kj/mol) Energy correction ÄE scf ÄH(0 K) ÄH(289 K) ÄG(298 K) Ksp(298 K) Without bsse correction a b c d e With CP type* correction a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d). 1au=2625.5kJ/mol. * These energies of ions are corrected with CP type correction, theäe bsse s of (a), (b), (c), (d) and (e) basis are -7.7, -7.1, -9.7, -41.1, and kj/mol. endothermic reaction with a strong reaction energy (> 1000 kj/mol) and especially small K dis value (in the order of ) results in great stability and makes GZT very difficult to dissociate as shown in Refs. 8 to Charge distribution analysis Several well-known quantum chemists have pointed out that the effects of the diffuse and polarization functions of first-row elements with lone pairs are complementary to each other. In the case of hydrogen bonding or other molecular interactions, the energies of the processes involved come from changing the number of lone pairs. Therefore, it is best to consider the role of diffuse basis functions in the SCF calculation. The geometrical and energy results in the former sections of this work are shown in Figs. 1 and 2 and Tables 1 and 2. There are no significant deviations between the results of different calculations obtained by various basis functions. However, after we list the charges of ions in Fig. 3 and of the combined GZT molecule in Fig. 4, the story is quite different. The charge shifts of different methods using different basis functions have significantly large variations among them. In Fig. 4, the atomic charge densities are listed in the upper lefthand part of the figure, and the increment of charge densities between molecules and related ions are listed in the lower right of the same figure as a comparison. Based on the listed values in these figures, it is easily found that the variation in charge and charge shift is significantly noticeable if the diffuse basis is involved in such calculations. Especially in the case of B3LYP/6-31++G(d,p) with a diffuse base of both hydrogen and heavy atoms, its calculated charge densities are quite different from the related values derived by other methods. In particular, at the various terminals of the hydrogen bonds, the variation in charges is extremely large and creates a large local electrostatic attraction in a very peculiar way. E.g., for the hydrogen bond H 20 -N 2 (or H 30 -N 1 ), the positive charge density of H 20 (or H 30 ) increases from to of G + ion in the combined GZT molecule with a positive charge increment at Meanwhile, the negative charges density of N 2 (or N 1 ) increases from to of ZT 2- ion in GZT with a negative charge change at In the case of charge variations of H 17 -N 6 (or H 27 - N 8 ), although the B3LYP/6-31++G(d,p) calculation ends up with the greatest variation between various methods, the charge increment of H 17 (or H 27 ) is only and on the other hand the negative charge density of N 6 (or N 8 )decreases its negative charge from to This particular change of atomic charges in different positions in GZT for different methods with a diffused basis may largely Fig. 3. The charge distribution in G + and ZT 2- ion molecule.

6 770 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Chen et al. change the order of the electrostatic bonding strength 22 between the two types of hydrogen bonds in the GZT system. For all methods of calculation with different basis functions, we have evaluated their total charge shifts and have listed them together in Table 3 for comparison. By comparing the total charge of both anion and cation parts of the combined GZT molecule ( 2- ZT and + G ) as well as their charge shift, that is, 2- ZT =( 2- ZT )-(-2)=( 2- ZT )+2and + G = ( + G ) - 1, we might see some significant differences among them. For the methods witho ut a diffuse basis function, the large positive 2- ZT and large negative + G, both in the B3LYP/6-31G(d,p) and B3LYP/6-31G(d) methods, overemphasize the charge shift in the inter-ionic combination. Whenever the diffuse basis function is added into the system of computation, the charge shift behavior decreases significantly. In the case of B3LYP/6-31++G(d,p) with a diffuse basis function for both hydrogen and heavy atoms, the shift moves in the reverse direction from the remaining basis function methods, which are ZT = and + G = From this result, it is clearly shown that the charge distribution and the shift of charge in the inter-ionic combined system are closely related to the basis function which we selected for our calculation. 3.4 Localized hydrogen bonding analysis As shown in the optimized structure of GZT in Fig. 2 and as indicated in section 3.1, two pairs of four hydrogen bonding connections exist between ZT 2- and two G +. When the distances of inter-ionic connection (d N H s) are compared with the problems of hydrogen bonding, 15-21,27 it can be easily seen that both of these two pairs of d N H s are within the range of the category of strong hydrogen bonds. However, because it is impossible to solve the problems of inter-ionic hydrogen bonding by using the energy difference method, the localized analysis procedures are hereby selected in this theoretical study. The localized Coulomb attraction (-E N H ) was calculated by d N H and the related atomic charges, as shown in Fig. 4. By using the Localized Energy-breaking Procedure and the Semi-empirical Type Population Analysis of our previous papers, 27 we calculated the localized bond energies Fig. 4. The charge distribution and change of charge in GZT molecular structure.

7 Theoretical Study of H-Bonding in GZT System J. Chin. Chem. Soc., Vol. 50, No. 3B, Table 3. Charge Shift in Various Methods 2- Charge methods ñ ZT ñ G + ñ ZT 2- ñ G + 2 ñ G + B3LYP/6-31++G(d,p) B3LYP/6-31+G(d,p) B3LYP/6-31+G(d) B3LYP/6-31G(d,p) B3LYP/6-31G(d) ((BE) N H ) and localized bond orders (P N H ), and listed all d N H, (BE) N H,P N H,-E N H and related hydrogen bond angle ( N HN ) together in Table 4 for comparison. To achieve additional verification, the bond distance of HN with the shared H of hydrogen bond (d HN ) and its elongation related to the structure of G + ion ( d HN =d HN(GZT) -d HN(G+) ) shown by various basis functions are also listed in the same table. The shortness of d N H and the elongation effect of d HN demonstrate that the N 6 H 17 (or N 8 H 27 ) hydrogen bond is stronger than the hydrogen bond of N 2 H 20 (or N 1 H 30 ), when compared. The bond angle ( N HN ) of the stronger bond is closer to being a linear structure (180 ) than the related angle of the weaker bond. By localized analysis methods proposed by us, all (BE) N H s and P N H s are calculated as being in the same order of bonding strength as mentioned above, and if we compare these bond energies and orders with the cases of the O-H type of hydrogen bonding in our former research, both the values of (BE) N H s and P N H s for the N 6 H 17 (or N 8 H 27 ) hydrogen bond are obviously larger and exceed the upper limit of our formerly assigned range of strong hydrogen bonds. 16,27 Regarding the cases of N 2 H 20 (or N 1 H 30 ), P N H s are also within the range of strong bonds, but (BE) N H s are a little under or close to the lower limit of the range. The result of analysis clearly indicates that the inter-ionic connection between ions in the GZT system is a simple connection of two pairs of strong hydrogen bonds. However, an unusual result of the -E N H calculation appears as specified in the last column of Table 4. The first three basis function calculation methods with a diffuse basis function give a completely reversed order of bonding strength in this special result. This unusual order of strength has also appeared in our recent research. 22 of inter-molecular hydrogen bonding. In our former investigations and in section 3.3 of this paper, we have defined this bonding strength as an electrostatic type strength. Especially for the inter-molecular or inter-ionic problems, the order of this strength usually contradicts the order of the ordinary covalent type of hydrogen bonding strength. 22 We will discuss this subject in detail in the conclusion. 3.5 Analysis of the characteristic vibration of NH stretching For localized hydrogen bond analysis, in addition to the parameters shown in Table 4, the information of NH stretching type vibration is also very important. When the H atom of a NH bond is the shared atom of a strong hydrogen bond, both the frequency and ir intensity of the related NH stretching will have prominent changes caused by hydrogen bond formation. 22 Therefore, all calculated results related to the NH stretching vibration of G + and GZT should be analyzed in detail. In order to set the reference values for the following analysis, we have listed the results of G + in Table 5. All the fre- Table 4. Result of Localized Hydrogen Bonding Analysis (energy in kj/mol) Analysis H-bonds d N-H (A) N-HN (deg.) d HN d HN (BE) N-H P N-H -E N-H N 6 H 17 or N 8 H a b c d e N 1 H 30 or N 2 H a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d).

8 772 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Chen et al. Table 5. The Characteristic NH Stretching Vibrations of G + Ion with D 3 Group ( NH in cm -1 and IR Intensity, I in km/mol) 19 and and 24 Order analysis E A 1 A 2 E NH 3448 a b c d e I (Intensity) a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d). quencies, modified scalar factor of and ir intensities of NH stretching, are listed in the table as the standard data of the NH bond without any hydrogen bonding effect involved. From among 90 normal modes of vibration in the combined GZT system, 12 modes are seen as the characteristic frequencies of NH stretching ( NH ). In these 12 modes, the coordinates of both the related N atom and the remaining heavy atoms are negligibly smaller than the related hydrogen coordinates. Thus, these vibration modes can be assigned very simply to their related hydrogen coordinates. The Cartesian coordinates of hydrogen differ according to the varying orientation of this atom. In order to achieve a relatively reliable comparison, we have calculated the absolute vibration coordinate (AVC) by Eq. (2). This coordinate is invariant with respect to the coordinate s transformation. With an inversion center in the GZT system, AVC=(x H 2 +y H 2 +z H 2 ) 1/2 (2) each NH stretching should be linear, combining with its inversion image by means of an in-the-phase manner for A g motion or an out-of-phase manner for A u motion. The corresponding linear combination coefficients in the first case are (0.5) 1/2 = for both NHs, and and in the second case. If the calculated AVC equals approximately 0.70, a little less than 0.707, we can observe that such vibration is created by its related NH bond and inverted counterpart. In G +, six NHs are equivalent. But in the GZT system, due to the strong hydrogen effect and the large geometrical distortion, most NH vibrations become mixed together and the AVC value is near to This is except for N 16 H 21,N 16 H 22, N 26 H 31 and N 26 H 32, which mix together with the coefficients near to 0.5 or These four motions become equivalently mixed together because they are far from the regions of hydrogen bonds and no significant distortion effect influences their motions. Consequently, the related Hs AVC values of the above four NHs are 0.49 or 0.50, being the same as our calculations. In the final stages, the AVC values of the hydrogen bonds in the 12 modes have been calculated, and so all the normal modes can be easily assigned according to the AVC values. The 8 modes with the largest NH s are related to Hs, which are not related to any hydrogen bond, and all scalar factor modified NH, ir intensity(i), the related hydrogen, and its calculated AVC values are listed together in Table 6. In order to compare the results of Tables 5 and 6, all the numerical orders of NH and I are both in the same order for NHs without relating to any hydrogen bond. Four most important normal modes (79 to 82) are close to the motions of H 17,H 27,H 20 and H 30. They are closely related to the two strong hydrogen bonds mentioned in the last section. As the results in Table 7 show, all the NH s are significantly smaller than the related NH of G +, and all the ir intensities are much larger than the related I of the corresponding G + shown in Table 5. In order to make an easier comparison, we have calculated the largest red shift ( NH ) max by the difference of largest NH of the related value of G + minus NH, the smallest red shift ( NH ) min by the difference of the smallest NH of the related value of G + minus NH, and the least increment of ir intensity ( I) min with the difference calculated by I of the A u modes minus the related largest I of G + in Table 5. Ordinarily, both the red shift of ir frequencies and the increment of ir intensity are closely related to the corresponding strength of the hydrogen bond. The range of the red shift is within the 79 th and 80 th modes, of which the related H 17 and H 27 are from 704 to 954 cm -1. But, for the range of the red shift within the 81 st and 82 nd modes, the related H 20 and H 30 are from 393 to 628 cm -1. The range of the first set is significantly larger than that of the second set without any overlap, consistently supporting the predicted result that N 6 H 17 (or N 8 H 27 ) is stronger than N 1 H 30 (or N 2 H 20 ). The ir intensity problems happen only in the A u modes of 79 th and 81 st stretching vibrations with allowed ir transitions of A u modes. However, if we compare the related relative quantities of ( I) min s between the two sets in Table 7, the story will be quite different. Whenever using a calculation method with the diffuse basis function, the result of the hydrogen bonding strength prediction is similar to that as predicted by -E N H of Table 4. Or, with this electrostatics type strength prediction, N 1 H 30 (or N 2 H 20 ) is stronger than N 6 H 17 (or N 8 H 27 ), which completely contradicts the aforementioned prediction of the covalent type hydrogen bonding strength methods.

9 Theoretical Study of H-Bonding in GZT System J. Chin. Chem. Soc., Vol. 50, No. 3B, Table 6. Comparison of the Characteristic NH Stretching Vibrations of GZT with C i which Related to Hydrogen Atoms of no Hydrogen Bonds ( NH in cm -1 and IR Intensity, I in km/mol) Order analysis A u A g A u A g A u A g A g A u NH NH 3470 a b c d e I (IR) H s** H 21 H 22 H 21 H 22 H 19 H 19 H 18 H 18 H 21 H 22 H 21 H 22 H 21 H 22 H 21 H 22 H 19 H 19 H 18 H 18 H 21 H 22 H 21 H 22 H 21 H 22 H 21 H 22 H 19 H 19 H 18 H 18 H 21 H 22 H 21 H 22 H 21 H 22 H 21 H 22 H 19 H 19 H 18 H 18 H 21 H 22 H 21 H 22 H 21 H 22 H 21 H 22 H 19 H 19 H 18 H 18 H 21 H 22 H 21 H 22 AVC* a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d). * AVC is the absolute vibration coordinate of the related hydrogen atom. ** H 28,H 29,H 31 and H 32 have the same AVC as H 18,H 19,H 21 and H CONCLUSION Based on the result and analysis of the above theoretical calculations and interpretations, we can conclude as follows: (1) As theoretically predicted, the ionic dissociation energy of the GZT molecular system (GZT = 2G + +ZT 2- )approximately equals or is higher than 1000 kj/mol, and K dis of Eq. (1) of this reaction is in the order of The result proves that the stable behaviors that are mentioned are quite reasonable in the cases without any polar solvent in this system. (2) Four strong hydrogen bonds exist between the two G + and ZT 2- ions, including the pairs N 6 H 17,N 8 H 27,N 1 H 30, and N 2 H 20. The first pair of hydrogen bonds is stronger than the second pair in the local bond energy (BE) N H and local hydrogen bond order P N H calculation. (3) This prediction may be shown through the shortness of d N H, the elongation of d H N, the red shift of NH and the linear type bond angle ( N HN ). Since this bonding strength is determined by the type bond order and the overlap between the orbitals of the different atoms is close to the linearity of N HN, we define this bonding strength as the covalent type of strength. (4) On the other hand, based on the prediction of ( I) min,-e N H and the special increment of the charge density of the hydrogen atom, the bonding strength will be in favor of the pairs of N 1 H 30 and N 2 H 20, rather than N 6 H 17 and N 8 H 27. We define this kind of strength as the electrostatic type of strength. This problem also appears in another of our recent papers on The Problem of Inter-molecular Hydrogen Bonding. 22 In the case of inter-ionic or inter-molecular interactions with more than one hydrogen bond, the competitive effect of the various hydrogen bonds usually aims to preserve the equilibrium and stability of the combined system. These two types of bonding strength may appear together in this system. Most evidence shows that the N 1 H 30,N 2 H 20 pair is weaker than the other pair in its hydrogen bond. But, in the case of the SCF calculation including the diffused type of basis, the compensation effect will cause the electrostatic type strength to increase in this weak pair and influence the balance and stability behavior of an overall stable system. (5) This is the first time we have tried to use localization analysis methods to solve the inter-ionic problem. Fortunately, the successful result of this work has the value of indicating that our developed methods might reliably and usefully solve most of the hydrogen bonding problems, includ-

10 774 J. Chin. Chem. Soc., Vol. 50, No. 3B, 2003 Chen et al. Table 7. Comparison of the Characteristic NH Stretching Vibrations of GZT with C i which Related to Hydrogen Atoms of Hydrogen Bonds ( NH in cm -1 and IR Intensity, I in km/mol) Order Mode NH I related H s AVC** ( NH ) max ( NH ) min ( I) min 79* A u 2628 a 3710 H 17 and H b 3711 H 17 and H c 2996 H 17 and H d 3349 H 17 and H e 2663 H 17 and H A g H 17 and H H 17 and H H 17 and H H 17 and H H 17 and H A u H 20 and H H 20 and H H 20 and H H 20 and H H 20 and H A g H 20 and H H 20 and H H 20 and H H 20 and H H 20 and H *From79to90allthelasttwelvenormalmodesarerelatedtotheNHstretchingvibration,inwhich79to82are related to the four hydrogen bonds. ** AVC is the absolute vibration coordinate of the related hydrogen atom. a B3LYP/6-31++G(d,p); b B3LYP/6-31+G(d,p); c B3LYP/6-31+G(d); d B3LYP/6-31G(d,p); e B3LYP/6-31G(d). ( NH ) max,( NH ) min and ( I) min are the maximum and minimum red shifts, and the smallest ir intensity increment which is related to the NH s and I s of corresponding G + ion. ing the inter-ionic cases. ACKNOWLEDGMENTS The authors would like to thank the National Science Council of the Republic of China for financial supporting the work as described in this manuscript under Contract No. (NSC M ). The calculation facility was provided by the National Center for High-performance Computing. Received September 5, REFERENCES 1. Chen, C.; Lu, L. H.; Yang, Y. W. J. Mol. Struct. (Theochem) 1992, 253,1. 2. Chen, C.; Sun, K. C. J. Mol. Struct. (Theochem) 1995, 340, Chen, C.; Sun, K. C. J. Mol. Struct. (Theochem) 1996, 362, Chen, C.; Sun, K. C. Int. J. Quant. Chem. 1996, 60(7), Chen, C.; Sun, K. C.; Shyu, S. F. J. Mol. Struct. (Theochem) 1999, 459, Chen, C.; Shyu, S. F. Int. J. Quant. Chem. 1999, 73, Chen, C.; Sun, K. C.; Shyu, S. F. J. Mol. Struct. (Theochem) 2000, 459, Bucerius, K. M. Germany Patent DE , Bucerius, K. M. US Patent , Peng, P. L.; Wong, C. W. J. Exp. Propel. R. O.C. 1997, 13(1), Bucerius, K. M. Germany Patent DE , Bucerius, K. M. US Patent , Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, Becke, A. D. J. Chem. Phys. 1993, 98, Chen, C.; Shyu, S. F. J. Mol. Struct. (Theochem) 2001, 536, Chen, C.; Hsu, F. S. J. Mol. Struct. (Theochem) 2000, 506, Chen, C.; Shyu, S. F. J. Mol. Struct. (Theochem) 2000, 503,

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