Indian J. Phys. 81(9) 901-913(2007)
jut
Structure, energy and IR spectra of K-wNH
3cluster: A theoretical study
A K Pathak1, T Mukherjce1 and D K Maity2*
'Radiation and Photochemistry Division, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400 085, India
^Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre Mumbai-400 085, India
E mail dkmaity@barc gov in
Abstract : We report microscopic structure and properties of small size clusters of ammonia and K atom of the type K-nNH3 (n < 6) Structure of different minimum energy configurations for each size cluster has been predicted following Newton-Raphson procedure with a variety of initial guess structures A density functional having 50% HF exchange and 50% Slater exchange with additional correlation effects from LYP functional, namely, BHHLYP has been applied with Gaussian triple split valence basis set (6-311G) with polarization (2d,2p) and diffusion function on each atom for all the calculations It is observed that N of NM3 is oriented towards K atom of each cluster In all the structures, K atom remains as mono positive ion and the ejected electron is delocalized over the whole cluster IR spectra are calculated based on Hessian calculations on the optimized structures A large shift (<4i>= +100 cm"1) of IR band corresponding to the inversion of ammonia is predicted in all the clusters On interaction with K atom, IM-H stretching band of NH3 becomes much stronger than the inversion band As a number of stable minimum energy structures are predicted for higher clusters, weighted average IR spectra is generated based on statistical population of stable minimum energy structures at 150 K Weighted average solvation energy and vertical ionization potential (VIP) of the solvated clusters are also presented Calculations are carried out to find out a few low lying excited states for all the clusters, K(NH3)n(n =1-6) at the CIS/6- 311++G(2d,2p) level Visualization of appropriate MOs suggests that the strong optical absorption is mostly due to HOMO -> LUMO electronic transition The optical absorption profiles of a few selected K(NH3)n clusters are also reported
Keywords : K(NH3)n, cluster, electronic structure calculation, density functional theory, I R spectra, microsolvation, vertical ionization potential, excited states
PACS Nos. : 31 15 ae, 31 15 bw, 31 15 eg, 33 20 Ea, 33 20 kf, 36 40 Mr
1. Introduction
In recent years, hydrogen bonded cluster of polar solvent molecules encapsulating a solute atom, small molecule or ion have been a subject of intense investigations for experimental as well as theoretical researchers. When a solute is added into a solvent pool, preexisting hydrogen bonded solvent network breaks up to accommodate the solute and a new hydrogen bonded network forms surrounding the solute. A delicate
•Corresponding Author © 2007 IACS
902 A KPathak, TMukher/'ee andDKMaity balance between solvent-solute and solvent-solvent interactions determines the structure of the solvent clusters trapping a solute. A number of experiments, theory and simulation studies have been devoted to understand the structural, dynamic and spectroscopic aspects of solvation at molecular level for most common hydrogen bonded solvent, namely, water [1-20]. Ammonia is also an important solvent that can form hydrogen bonded network. The clusters of alkali metal atom and polar solvent molecules have been studied at length, often from the interests related to solvated electron. However, the detailed mechanism on the formation of solvated electron in this medium with alkali metal atom is not yet fully understood. Thus, solvated electron in polar solvents has been a subject of continued research. In this respect, a lot of research has been carried out to understand the structure and properties of singly negatively charged clusters of water and ammonia [21,22]. Hydrogen bonded water clusters with alkali metal atom residing in the cluster cavity (M-nH20) have also been studied to a great extent [23-28].
Solvated electrons can form rather readily with the alkali metals because of the relatively low energy requirement for ionization. The most familiar case occurs in the solvation of alkali metal atoms in bulk ammonia, where optical transitions involving these electrons are responsible for the strong colors of the resulting solutions. One also expects the formation of solvated electron in finite size clusters. A number of theoretical and experimental efforts have been put to gather knowledge on ammonia clusters in presence of Li, Na and Cs alkali metal atoms [26-34]. To the best of our knowledge, no report is available on ammonia clusters in presence K atom. We present structure, energy parameters, IR and optical absorption spectra of ammonia clusters in presence of a potassium metal atom (K-nNH3, n = 1-6) based on first principle electronic structure theory. Studies on these size selected clusters play a critical role to follow the evolution of molecular level properties with the size of the cluster in gas phase and to bridge the gap between the properties of single ammonia cluster (K-NH3) to the bulk solution of K metal in ammonia solvent. We also report the variation of calculated properties with size (n) of the clusters, K-A?NH3. AS a number of minimum energy structures are predicted for higher cluster, weighted average properties of the clusters are calculated based on the statistical population of different minimum energy structures at 298 K.
2. Theoretical method
Full geometry optimization of ammoniated clusters has been carried out without any symmetry restriction to locate minimum energy structures applying a nonlocal hybrid density functional, namely, Becked half-and-half (BHH) exchange and Lee-Yang-Parr (LYP) correlation functional (BHHLYP) [35]. Split valence basis set with diffusion and double polarization functions on all the atoms, 6-311++G(2d,2p) has been used through out the calculation. The maximum number of Cartesian Gaussian basis functions taken
Structure, energy and IR spectra ofK-nNH3 cluster: A theoretical study 903 was 405. Newton Raphson based algorithm has been applied to look for the minimum energy structures for each /<(NH3)„ cluster. The major concern in this algorithm is to guess a good starting geometry of the cluster, which might converge during the calculation to a local or the global minimum. In the present calculation, several possible starting geometries are generated based on different possible three-dimensional structures. However, it is worth mentioning that this algorithm does not guarantee to locate the global minimum energy structure especially for the higher clusters. Hessian calculations have been performed to check the nature of the optimized structures, to calculate thermodynamic parameters and to generate IR spectrum of the clusters. In a number of cases, first hand optimized minimum energy structures of these open shell systems have yielded one or more normal modes having imaginary frequency. In these cases, the structures have been reoptimized focusing attention on these normal modes till the structures generate no imaginary frequency. Population of the minimum energy configurations of each size clusters has been calculated based on free energy change (AG) at 298 K following Boltzman distribution. All electronic structure calculations have been carried out adopting GAMESS program system on a LINUX cluster platform [36].
MOLDEN program system has been used for visualization of molecular geometry, normal modes and IR spectra [37].
3. Results and Discussion A. Structure :
Only one stable minimum energy structure is obtained through full geometry optimizations of small size (n = 1-3) K-nNH3 clusters. It is to be noted that the geometries of clusters having different orientations of N atoms from NH3 molecule with respect to K atom are considered as the initial guess structures in the present study and only the most stable minimum energy structure is taken from different optimized configurations with small difference in dangling hydrogen orientations. All the stable configurations that are found for each size K(NH3)„ cluster are displayed in Figure 1. The minimum energy structure of mono-ammoniated potassium cluster, K(NH3) is shown in Figure 1-1. It is clearly seen that N atom of NH3 is directed towards the K atom and it is -2.8 A apart from the metal atom. It is worth to mention that two initial guess structures are considered for geometry optimization. In one case, the N atom of NH3 is directed towards K atom and in the other case H atoms of NH3 face towards the metal atom.
Full geometry optimization generates exactly the same structure as shown in Figure M. Thus for the larger clusters, the initial thought structure is made where the N atom of NH3 is oriented towards K atom. Only one minimum energy structure is predicted for di-ammoniated cluster, K(NH3)2 with ZNKN of 180° and the optimized structure is displayed in Figure 1-11. Several initial guess structures are considered for the tri-ammoniated clusters, K(NH3)3 based on the minimum energy structure of K(NH3)2. But only one stable minimum energy structure displayed in Figure "1 -III is predicted
904 AKPathak, TMukherjeeandDKMaity
o--4 fr-°-< r > ,-6.
m
o ^ >V^-Tt
4 K.
X /
IV-A IV-B V-A
H^ --4
t<
V-B V-C VI-A
& JL -^
VI-B Vl-C
Figure 1. The fully optimized structures calculated at BHHLYP/6-311++G(2d,2p) level of theory for (I) K(NH3), (II) K(NH3)2, (III) K(NH3)3) (IV) K(NH3)4, (V) K(NH3)5> and (VI) K(NH3)6 clusters Marked alphabets in upper case are used to refer different minimum energy conformers for each ammoniated cluster size arranged in order of stability showing *A' as the most stable one K atoms are shown by the largest spheres, the smallest spheres refer to H atoms and the rest corresponds to N atoms in each structure shown in the figure In each case, the distance between the K and N atoms of ammonia molecule is 2 8-3 0 A
Structure, energy and IR spectra of K-nNH3 cluster: A theoretical study 905 having ZNKN = 120°. In all these cases N and K atoms are in same plane. Two minimum energy structures shown in Figure 1 as IVA and IVB are obtained for K(NH3)4
cluster. Structure IVA is a distorted tetrahedral with four N atoms in the corners keeping K atom at the center and more stable than structure IVB having square planar arrangement with four N atoms at the corners by 1.09 kcal/mol. Based on these minimum energy structures, initial guess structures for K(NH3)5 and K(NH3)6 are modeled. In each case, three stable minimum energy structures are found and displayed in Figure 1-(VA-VC) and Figure I-(VIA-VIC) for K(NH3)5 and K(NH3)6 clusters respectively. The most stable conformer of K(NH3)5 cluster is displayed in Figure 1-VA having distorted trigonal bipyramidal arrangement with five N atoms around K atom. The planar arrangement of five N atoms around K atom as shown in Figure 1-VC is the least stable structure. The solvent ammonia molecules are bound by weak intermolecular hydrogen bonding. In structure 1-VB, three NH3 molecules are in a plane and approach to K from one side and remaining two NH3 molecules approach to the metal atom from the other side. The minimum energy structures shown in Figures 1-VB and 1-VC are less stable than the most stable structure VA by 0.89 and 3.20 kcal/mol. The most stable minimum energy structure of K(NH3)6 cluster is displayed in Figure 1-VIA having distorted octahedral arrangement with six N atoms around the central K atom. Figure 1-VIB shows pentagonal pyramidal arrangement of N atoms around K atom. The least stable structure of hexa ammoniated potassium cluster is shown in Figure 1-VIC which has a planar arrangement of six NH3 molecules around K atom. The solvent NH3 molecules are connected by six weak intermolecular hydrogen bonds. This structure is less stable than the most stable one by 4.07 kcal/mol.
In all the clusters, K(NH3)n (n = 1-6) the K-N distance varies from 2.8-3.0 A.
The energy of K..NH3 interaction is calculated to vary from 5-6 kcal/mol and the energy due to hydrogen bonding between two NH3 molecules is - 1 kcal/mol. Thus, the ammoniated cluster is dominantly stabilized by the solute-solvent interaction rather than solvent-solvent interaction. The solvent-solvent interaction energy plays significant role in the larger size clusters though.
B. Solvation energy :
The solvation energy of K-(NH3)„ clusters can be expressed as
E = ^K(NH3)/? "" (rt^NHg + EK) .
where ^KCNH,),, , ^ N H3 and EK refer to the total energy of the optimized cluster, K(NH3)n, the energy of a single NH3 molecule at equilibrium geometrical and the energy of K atom, respectively. Thus, calculated E80'* essentially refers to the total interaction energy of the solute with n solvent NH3 units around it in the ammoniated cluster of size n. The calculated solvation energy of the K(NH3)„ (n = 1-6) clusters are supplied in Table 1. The plot showing the linear variation of solvation energy (E80^) of the most stable conformer of each size with the number of ammonia molecules (n) for K(NH3Jn
906 A KPathak, TMukherjee andD KMaity
Table 1. Calculated molecular properties of K(NH3)„ clusters (n « 1-6) at BHHLYP/6-311++G(2d,2p) level of theory.
Species AE
(kcal/mol)a
Solvation energy,
psolv (kcal/mol)
Vertical ionization
potential VIP (eV)
Weighted average solvation
energy, Ew solv (kcal/mol)
Weight average
vertical ionization
potential V I P . (eV)
Atomic spin population
over K
absorption maxima, (nm)
K(NH3) K(NH3)2
K(NH3)3
K(NH3)4
A B K(NH3)5
A B C K(NH3)6
A B C
0 0 0
0 1.09
0 0.89 3.20
0 0.36 4.07
6.21 12.41 19.22
26.22 25.13
31.92 31.03 28.72
36.63 36.27 32.56
3.75 3.28 2.94
2.74 2.77
2.63 2.71 2.75
2.70 2.62 2.60
6.21 12.41 19.22 25.52
28.74
3.75 3.28 2.94 2.76
2.75
32.6 2.60
= relative energy [energy of any structure - energy of structure A in K(NH3)„].
1.0 0.95 0.84
0.70 0.73
0.63 0.64 0.77
0.72 0.80 0.95
1155 1301 1959
2738 2416
3157 2631 2130
2307 2977 2077
\4E
Figure 2. Plot of calculated (a) solvation energy (E*0*) and (b) weighted average solvation energy (E™1*) in kcal/mol vs. number of ammonia molecules (n) in K(NH3)„ (n = 1 -6) cluster at BHHLYP/6-311 ++G(2d,2p) level of theory. The £ " * is plotted for the most stable structure of each size of cluster. To estimate EJ0*" the weight factor is calculated based on the statistical population of alt the minimum energy structures of each size cluster at 298 K.
Structure, energy and IR spectra ofK-nNH3 cluster: A theoretical study 907 clusters is displayed in Figure 2(a). The best-fitted linear plot having correlation coefficient greater than 0.99 is Eso,v = 0.34 + 6.22n, where Eso,v is expressed in teal/
mol and n is the number of solvent NH3 molecules. The weighted average solvation energy (E£0,v) values are also calculated and provided in Table 1. The plot for the variation of E*0,v vs. n is shown in Figure 2(b). The weight factor of a minimum energy structure within a particular size (n) of cluster is calculated based on the statistical population of the conformer at 298 K. The best-fitted linear plot having correlation coefficient greater than 0.99 is E*0]v = 2.06 + 5.35n, where E^olv is expressed in kcal/
mol and n is the cluster size.
C. Vertical ionization potential :
Vertical ionization potential (VIP) of the ammoniated clusters, K(NH3)n can be calculated based on the relation :
VIP = E[K(NH3)„] - ES[K+(NH3)„],
where E[K(NH3)n] is the energy of the optimized K(NH3)„ cluster and Es[K+(NH3)n] is the single point energy of the K(NH3)n obtained by removing one electron from the optimized K(NH3)n cluster. VIP is the energy required to remove an electron from the neutral clusters. The calculated VIP for different minimum energy structures of the ammoniated cluster, K(NH3)„(n = 1-6) are tabulated in Table 1. The weighted average VIP (VIPJ values are also calculated and listed in Table 1. The plot for the variation of VIPW vs. n is displayed in Figure 3 showing gradual decrease in energy with the size of the cluster (n).
40
35
I
>
3.0
2.5
1 2 3 4 5 6
n
Figure 3. Plot of calculated weighted average vertical ionization potential (VIP J in eV vs. number of ammonia molecules (n) in K(NH3)„ (n = 1-6) cluster at BHHLYP/6-311++G(2d.2p) level of theory. VIP* is calculated based on the population of minimum energy structures at 298 K for a particular size of ammoniated cluster.
908 AKPathak, TMukherjeeandDKMaity D. Spin distribution :
To see the effect of solvation on the distribution of the odd electron in potassium metal, Mulliken atomic spin (a-/?) population over the atoms is calculated in all the ammoniated clusters, K(NH3)„ (n = 1-6). The calculated atomic spin (a-/3) population over the K atom in all the clusters is listed in Table 1. It is clearly seen that the odd electron spin is localized for over K atom only, especially for the lower cluster. It is also noticed that the spin distribution of the odd electron changes significantly on successive addition of solvent NH3 molecules in K(NH3)n cluster. For mono ammoniated cluster, K(NH3) the atomic spin (a-/7) population over the K is 1.0. The atomic spin (a-/?) population over the K reduces with addition of successive ammonia molecule up to cluster size n = 5, and shows increase for K(NH3)6 cluster.
E IR spectra :
As discussed in the previous sections, K(NH3)n clusters are stabilized by the interaction between metal K atom and N atoms from solvent NH3 molecule as well as inter ammonia H-bonding interaction. Due to these interactions, it is expected that IR bands due to stretching (N-H), bending and inversion modes of NH3 in the ammoniated clusters K(NH3)„ (n = 1-6) get affetcted compared to that of free ammonia molecule IR spectra for all the conformers of K(NH3)n cluster (n < 6) and free NH3 are calculated Lorentzian line shape has been applied with peak half-width of 20 cm"1 for all the IR spectra plots. Based on the literature data on the vibrational frequency of NH3 (vsym
= 3337 cm"1, yasym = 3444 cm*1, v^nd = 1627 cm'1 and Aversion = 950 cm"1) and the present calculated values (vsym = 3596 cm"1, vasym = 3720 cm"1, vbend = 1732 cm-1
and vim/ers»on = 1 0 6 1 cm~1) a t BHHLYP/6-311++G(2d,2p) level, the scaling factor is taken as 0.93 to account the anharmonic nature of vibration. The same scaling factor has been used for predicting IR spectrum in all these clusters. Calculated scaled frequencies for free NH3 molecule are 986, 1611, 3345 and 3460 cm"1, respectively for inversion (Aversion), bending (n,end), symmetrical stretching (vsym) and asymmetrical stretching (vasym) at BHHLYP/6-311++G(2d,2p) level of theory and the theoretical IR spectra is displayed in Figure 4-I. It is worth to mention that the peak in the N-H stretching region is due to asymmetric mode, and the symmetric mode is too weak to observe. Scaled IR spectra for mono ammoniated cluster, K(NH3) with a strong sharp peak in the N-H stretching region is shown in Figure 4-II. It is interesting to observe that all the normal modes of ammonia get red shifted Odv^nd = - 2 0 cm"1, Av^m = - 4 8 cm"1 and 4va8ym = - 5 9 cm"1) except the inversion mode which is blue shifted compare to the same (4vinversion = +100 cm"1) in K(NH3) cluster compared to free NH3
molecule. The major contribution to the peak in the N-H stretching region is from symmetric N-H stretching mode. The IR bands below 1000 cm"1 are due to Iterations of NH3 in this cluster. Scaled IR spectra for di-ammoniated cluster, K(NH3)2 with a strong sharp peak in the N-H stretching region is shown in Figure 4-III. It is clear from
Structure, energy and IR spectra of K-nNH3 cluster A theoretical study 909
Intensity
S£
(
NHj
-^ , A A A
1 0 0 0 2 5 5 5 3 0 0 0 4000
K(NH3)
U_J_ 1
Frequency (cm') I
1000 2000 3000 4000 Frequency (cm ')
V)
I
K ( N H3)2
ULJL A
1
cc
• * * - '
K ( N H3)3
Lft-^.
0 1000 2000 3000 4000 Frequency (cm ')
K ( N H3)4
-
A
1000 2000 3000 4000 Frequency (cm ])
K
K ( N H3)5
A "k-JL—J U
1000 2000 3000 Frequency (cm 1)
V
K ( N H3)6
4000 1000 2000 3000
Frequency (cm"1) VI
4000
LJ_
1000 2000 3000 Frequency (cm ')
VII
4000
Figure 4. Calculated scaled IR spectra at BHHLYP/6-311++G(2d,2p) level of theory for (I) free NH3 molecule, and for the ammoniated cluster, K(NH3)n (n = 1-3), (II) K(NH3). (Ill) K(NH3)2, (IV) K(NH3)3 Calculated scaled weighted average IR spectra at the same level of theory for the ammoniated cluster, K(NH3)„ (n = 4-6), (V) K(NH3)4, (VI) K(NH3)5, (VII) K(NH3)6 The scaling factor Is considered as 0 93 to account the anharmomc nature of vibrations The scaling factor is calculated based on expenmental and calculated IR band at the present level of theory The weight factor is calculated based on statistical population of individual structures at 298 K Lorentzian line shape has been considered with peak half-width of 20 cm- 1 for all the IR plots
910 A KPathak, T Mukherjee andDKMaity the figure that the inversion mode gets blue shifted (<4vmversion = +105 crrr1) compared to that in free ammonia molecule and the bending mode is not noticeable. The scaled IR spectra of K(NH3)3 cluster is displayed in Figure 4-IV and the nature is very similar to that of K(NH3)2 cluster. Weighted average scaled IR spectra is generated based on the statistical population of different minimum energy structures at 298 K for K(NH3)n clusters (n = 4-6). Weighted average scaled IR spectra of K(NH3)4 cluster with strong sharp peak in the N-H stretching region is displayed in Figure 4-V. Figure 4-V suggests that the inversion band does not have appreciable intensity to notice in this cluster, however, the bending mode reappears. Both the bending and inversion mode is seen in the weighted average scaled IR spectra of K(NH3)5 cluster shown in Figure 4-VI. The IR spectra of K(NH3)5 cluster consists of a strong peak at the N-H stretching region.
The features of the weighted average scaled IR spectra of K(NH3)6 cluster (see figure 4-VII) is very similar to that of K(NH3)5 cluster. In all the IR spectra of K(NH3)n cluster (n = 1-6) the bending and stretching bands are red shifted (Av = -ve) and inversion band is blue shifted (Av = +ve) compared to that of free ammonia molecule. It is also interesting to observe that the major contribution to the peak in the N-H stretching region is from symmetric mode in all the ammoniated clusters, K(NH3)n (n =1-6). But in case of for free NH3 molecule, the major contribution to the peak in the N-H stretching is due to the asymmetric mode.
E Excited state :
Calculations are carried out to find out 40 low lying electronic excited states for all the ammoniated clusters, K(NH3)n (n = 1-6) at the CIS/6-311++G(2d,2p) level of theory and the optical absorption maxima are listed in Table 1. Visualization of appropriate MOs shows that the strong absorption is due to the electronic transition from the highest occupied MO (HOMO) to the lowest unoccupied MO (LUMO) or to some higher unoccupied MO in all these clusters. The optical absorption profile of a few selected ammoniated clusters is shown in Figure 5. Table 1 shows that with the addition of solvent NH3 molecules, the optical absorption maxima (Anax) is largely red shifted (for n = 2-4) compared to the mono ammoniated cluster, K(NH3). Both red and blue shifting is observed for different minimum energy structures in penta and hexa ammoniated clusters. Figure 5a shows the optical absorption profile for the mono ammoniated cluster, K(NH3). The absorption profile of the energetically most stable structures of K(NH3)3 and K(NH3)6 clusters are displayed in Figures 5b and 5c, respectively. It is clearly seen from Figure 5 that the optical absorption profiles of the higher clusters are much broader than the mono-ammoniated cluster.
4. Conclusion
Structure, energy, vibrational and optical absorption spectra of ammoniated clusters,
Structure, energy and IR spectra ofK-nNH3 cluster A theoretical study
911
(ft c
0)
c
1000 2000 3000 Wavelength
4000 5000
Figure 5. Calculated optical absorption spectra at CIS/6-311++G(2d,2p) level of theory for the most stable structure of the ammoniated clusters (a) K(NH3), (b) K(NH3)3 and (c) K(NH3)6
K(NH3)n (n = 1-6) clusters are reported to study the micro-solvation of potassium atom in ammoniated environment. Becke's half and half hybrid exchange-correlation functional (BHHLYP) has been applied to study the present systems with a Pople triple split valence 6-311++G(2d,2p) basis function Various initial guess structures are taken for each size of cluster and full geometry optimizations are carried without imposing any symmetry restriction Several closely spaced minimum energy structures are predicted for larger size clusters (n > 3) based on quasi-Newton search. It is observed that the ammoniated potassium cluster is stabilized by different types of interactions namely potassium-nitrogen interaction and hydrogen bonded interaction in ammoniated network But structures having potassium-nitrogen interactions are more stable compared to those of hydrogen bonded structures. Solvation energy and vertical ionization potential are also calculated. As several closely spaced minimum energy structures are obtained for larger clusters {n > 3), weighted average energy parameters are also calculated based on the statistical population at 298 K. Linear variation of weighted average solvation energy with size of the cluster (n) is observed. In all the IR spectra of
K(NH3)n clusters, the bending and stretching bands are red shifted {Av = -ve) and inversion band is blue shifted {Av = +ve) compared to that of free ammonia molecule.
It is also interesting to observe that in the N-H stretching region the major contribution to the IR band is from symmetric mode in all K(NH3)n clusters. On the other hand, the major contribution to the IR band due to N-H stretching for free NH3 molecule is due to the asymmetric mode. Excited state calculations on these clusters are carried out and electronic transitions are assigned mostly to HOMO -» LOMO transition.
912 A KPathak, TMukherjee andDKMaity Acknowledgment
Sincere thanks are due to Computer Centre, BARC for providing ANUPAM parallel computing facility. AKP and DKM would like to thank Dr. S K Sarkar and Dr. S K Ghosh for their constant support and encouragement.
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Structure, energy and IR spectra of K-nNH3 cluster A theoretical study 913
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