960
J. Phys. Chem. 1996, 100, 960-966
Ab Initio Calculations of Hydrogen-Bonded Carboxylic Acid Cluster Systems: Dimer Evaporations Ruiqin Zhang† and Chava Lifshitz*,‡ Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew UniVersity of Jerusalem, Jerusalem 91904, Israel ReceiVed: July 6, 1995; In Final Form: October 6, 1995X
Ab initio calculations were performed on proton bound formic acid and acetic acid clusters, (RCOOH)nH+ at various levels of theory. Three types of competitive structures were deduced: Open-chain structures are favored energetically for lower members (n e 5) of the cluster series, chains terminated with a cyclic dimer unit at one end for intermediate n and chains terminated by cyclic dimer units at both ends are favored for high n (n g 6). The computational results corroborate previously reported experimental results from this laboratory, according to which there is a changeover from monomer evaporation from clusters of low n to dimer evaporation at n g 6 for R ) H. Fairly good agreement was obtained between calculated and experimental binding energies.
Introduction We have demonstrated experimentally recently1,2 that protonbound clusters of formic acid and acetic acid (RCOOH)nH+ (R ) H, CH3) evaporate neutral monomer units for n < 6 or 7 and dimers for n g 6 or 7, respectively. The attribute of dimer evaporation is shared by the clusters with the liquid phase.3 It reflects the special stability of carboxylic acid dimers in the gas phase in the cyclic two-hydrogen-bonded structure.4 Clusters are considered to bridge the gap between the gas phase and condensed phases. Dimer evaporation from carboxylic acid clusters is seen to occur already for n g 6. It was possible to prove1 that intact dimers are evaporated by reionization of the neutrals. Furthermore, thermochemical evidence was presented2 to show that the dimers are evaporated in the cyclic twohydrogen-bonded configuration. The two evaporation reactions
(RCOOH)nH+ f (RCOOH)n-1H+ + RCOOH
(low n) (1)
(RCOOH)nH+ f (RCOOH)n-2H+ + (RCOOH)2
(high n) (2)
were studied through metastable ion peak shape analysis in an MS/MS instrument of reverse geometry.1,2 The peak shapes were found to be pseudo-Gaussian, and the kinetic energy release distributions were Boltzmann-like. This led to the conclusion that the unimolecular fragmentations are evaporations in the true sense of the word; in other words they do not possess reverse activation energies or tight transition states. For cyclic dimers to evaporate via loose transition states would mean that they are present in a preformed cyclic dimer configuration in the cluster without necessitating rearrangements. The purpose of the research effort presented here was to demonstrate via ab initio calculations that this is indeed the case. A central byproduct of these calculations was the cluster binding energies † Permanent address: Institute of Optoelectronic Materials & Devices, Shandong University, Jinan, Shandong 250100, P. R. China. ‡ Archie and Marjorie Sherman Professor of Chemistry. * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, December 15, 1995.
0022-3654/96/20100-0960$12.00/0
Figure 1. Structures of formic acid species (a) neutral monomer, (b) proton-bound monomer, (c) proton-bound dimer 1, (d) dimer 2, and (e) dimer 3 (HF/6-31G*).
to be compared with the experimental values based on finite heat bath theory1,2 and on high-pressure mass spectrometry.5 Proton-bound clusters are known to form hydrogen-bonded networks. Some of these are characterized by solvation shells surrounding a central core ion6 while others are chainlike. A number of theoretical calculations of proton-bound clusters has been carried out in the past. A partial listing of these follows. Several of the studies were concerned with (H2O)nH+ systems7 and involved high-level ab initio calculations including electron correlation. Ab initio calculations were also performed in studies of (HCH)n(NH3)mH+,8 (N2H4)nH+,9 CH3O2+,10 (H2COH-OCX2)+ (X ) H, F, Cl),11 (CH3-CHO-H-OCH-CH3)+.12 Semiempirical quantum chemical calculations were carried out as well for proton-bound clusters, among them, the PM3 method was used to study (CH3COCH3)m(H2O)H+, (CH3COCH3)n(H2CO)nH+, and (CH3CHO)nH+,13 as well as © 1996 American Chemical Society
Hydrogen-Bonded Carboxylic Acid Cluster System
J. Phys. Chem., Vol. 100, No. 3, 1996 961
TABLE 1: Deviations of Representative Bond Angles and Bond Lengths for the Proton-Bound Formic Acid Dimer 3 (Open-Chainlike Structure) for 4-31G# and 4-31G from those for 4-31G* in Both the HF and MP2 Calculations (Data in Parentheses from HF or MP2/4-31G* Calculations) method bond angle (deg)
basis set *
HF
4-31G 4-31G# 4-31G 4-31G* 4-31G# 4-31G
MP2
method bond length (Å)
HF MP2
∠C3-O2-H1
∠H5-O4-C3
∠O6-O4-C3
∠C7-O6-O4
∠H9-O8-C7
(113.957) -0.822 +6.180 (112.019) -0.527 +4.336
(127.649) -1.907 +8.484 (120.588) -2.014 +6.674
(133.532) -1.804 +6.013 (123.509) -2.412 +5.525
(104.925) -1.263 +14.922 (107.947) -0.066 +9.425
(114.300) -0.777 +5.801 (111.623) -0.447 +4.086
basis set
O2-H1
H5-O4
O6-O4
H9-O8
4-31G* 4-31G# 4-31G 4-31G* 4-31G# 4-31G
(0.9533) +0.0004 +0.0016 (0.9798) +0.0008 +0.0036
(1.5291) +0.0156 -0.1447 (1.3868) +0.0040 -0.0390
(2.5202) +0.0126 -0.0903 (2.4742) +0.0060 -0.0096
(0.9619) +0.0015 +0.0010 (0.9877) +0.0013 +0.0041
Figure 2. Chain structures of proton-bound formic acid clusters: (HF/ 4-31G#) (a) monomer, (b) dimer 1, (c) trimer, (d) tetramer, and (e) neutral monomer.
Figure 3. Chain structures of proton-bound formic acid clusters: (HF/ 4-31G#) (a) pentamer and (b) hexamer.
(H2O)21H+.14 An AM1 method was applied to the systems (RCOOH)n(H2O)H+ (R ) H, CH3) and hydrogen-bonded cyclic structures15,16 were deduced. No theoretical work has addressed as yet dimer evaporations from proton bound clusters. The ab initio method is a most efficient tool connecting quantum theory to experiments and providing a reliable theoretical framework.17,18 However, results for hydrogen-bonded systems are sensitive to the basis set and method employed.19,20 Selection of a reliable basis set is of central importance. In general, the basis set size, inclusion of polarization functions, and diffuse functions have to be taken into account. High-level basis sets are normally recommended. However, these are not practical in the presently considered large systems, where the changeover from monomer loss to dimer loss is brought about
at a cluster size of n ) 6 for formic acid and n ) 7 for acetic acid. The smaller proton-bound clusters were calculated by us at a relatively high level of theory. A more economic scheme HF/4-31G# for geometry optimizations was applied to all the clusters investigated. In this scheme polarization functions were applied to the negatively charged oxygen atoms but not to the positively charged carbon and hydrogen atoms. This treatment enables one to save much CPU time, disk space, and memory, particularly when proton-bound acetic acid clusters are calculated, for which half of the polarization functions can be cut. To get energetics, higher level single point calculations with the optimized geometries, Viz., HF/6-31+G*//HF/4-31G#, were performed.
962 J. Phys. Chem., Vol. 100, No. 3, 1996
Zhang and Lifshitz
TABLE 2: Some Overlap Populations from HF/6-31+G*// HF/4-31G# for Chainlike Structures of Proton-Bound Formic Acid Clusters (Atom Numbers from Figures 2 and 3) n bond
1
2
3
4
5
6
C1-O2 C1-O3 C1-H4 O2-H5 O3-H6 O7-H6 O7-C8 C8-O9 O9-H10 C8-H11 O3-H10
0.342 0.370 0.405 0.216 0.217
0.358 0.336 0.443 0.218 0.053 0.140 0.353 0.336 0.156 0.419 0.044
0.297 0.390 0.441 0.210 0.078 0.083 0.336 0.334 0.102 0.420
0.288 0.398 0.441 0.209 0.070 0.091 0.325 0.339 0.077 0.422
0.254 0.436 0.441 0.206 0.037 0.133 0.261 0.391 0.087 0.451
0.262 0.436 0.441 0.206 0.036 0.133 0.260 0.393 0.083 0.451
neutral monomer 0.181 0.502 0.442 0.204
Figure 4. Dimer-terminated chain structures of proton-bound formic acid clusters: (HF/4-31G#) (a) dimer, (b) trimer, (c) tetramer, and (d) neutral dimer.
TABLE 3: Overlap Population of the Dimer Units in Dimer-Terminated Chain Structures of Proton-Bound Formic Acid Clusters from HF/6-31+G*//HF/4-31G# (Atom Numbers are from Figures 4 and 5) n bond
2
3
4
5
6
neutral dimer
H1-O2 O2-C3 C3-O4 O4-H5 H5-O6 O6-C7 C7-O8 O8-H1 C3-H9 C7-H10 O8-H11
0.158 0.335 0.352 0.110 0.068 0.497 0.134 0.018 0.372 0.424 0.179
0.126 0.327 0.353 0.094 0.077 0.480 0.135 0.037 0.421 0.433 0.081
0.155 0.192 0.482 0.052 0.131 0.323 0.350 0.026 0.440 0.445 0.063
0.153 0.198 0.478 0.048 0.136 0.301 0.370 0.031 0.442 0.447 0.042
0.153 0.199 0.477 0.048 0.136 0.300 0.371 0.031 0.442 0.447 0.041
0.148 0.235 0.455 0.038 0.148 0.235 0.455 0.038 0.444 0.444 ---
Figure 5. Dimer-terminated chain structures of proton-bound formic acid clusters: (HF/4-31G#) (a) pentamer and (b) hexamer.
Computational Details All calculations were carried out by using the Gaussian 92 package21 on Silicon Graphics Indy R4400 and Challenge R4400 work stations at The Hebrew University of Jerusalem. The geometrical structures, total energies, and binding energies of the proton-bound dimer of formic acid were investigated at various levels of theory: HF/4-31G#, HF/4-31G*, HF/6-31G*, HF/6-31G**, HF/6-31+G*, HF/6-31+G*//HF/4-31G#, MP2/431G*, MP2/6-31G* and MP4/6-31G*//MP2/6-31G*. The conclusion from these comparative calculations was that the HF/ 4-31G# level, which applies polarization functions to the oxygen atoms, which are negatively charged, but not to the carbon and hydrogen atoms of the clusters, reproduces quite well the structural details (angles and bond lengths) and relative energies between competitive isomers deduced by higher levels of theory. Table 1 lists the deviations of some sensitive bond angles and
bond lengths for a representative structure, an isomer of the proton-bound formic acid dimer, dimer-3 whose structure is not cyclic and rigid (see Figure 1e), as corroborative evidence concerning the reliability of the HF/4-31G# model. The relative energies for the competitive isomers of the proton-bound dimer (see Figure 1), which are very basis set sensitive according to our results, did not change their order when higher level Hartree-Fock calculations, such as HF/431G*, 6-31G*, 6-31G**, and 6-31+G* were performed. The PM3 semiempirical method was used for initial geometry optimizations. All structures were optimized at the HF/4-31G# level. The formic acid trimer and tetramer structures were also optimized at the HF/6-31G* level. Relative energies of competitive structures were obtained from HF/6-31+G*//HF/
Hydrogen-Bonded Carboxylic Acid Cluster System
J. Phys. Chem., Vol. 100, No. 3, 1996 963
Figure 6. Energy and enthalpy differences between the dimerterminated chain and open-chain structures for proton-bound formic acid clusters. (3) HF/4-31G#; (0 K energy difference) (O) HF/6-31+G*/ /HF/4-31G#; (0 K energy difference) (b) HF/6-31+G*//HF/4-31G# (298.15 K enthalpy difference).
Figure 8. Dimer-chain-dimer structures of proton bound formic acid clusters: (HF/4-31G#) (a) tetramer, (b) pentamer; (c) hexamer.
Figure 7. Energy and enthalpy differences between dimer-terminated and open-chain structures for proton-bound acetic acid clusters. (3) HF/4-31G# (0 K energy difference) (O) HF/6-31+G*//HF/4-31G# (0 K energy difference); (b) HF/6-31+G*//HF/4-31G# (298.15 K enthalpy difference).
4-31G# calculations, and all the global minima found by HF/ 4-31-G# were identified to be of the lowest energies. Vaporization energies (or binding energies) were calculated from the total energies, ET, using the following equations:
∆En,n-1 ) ET((RCOOH)n-1H+) + ET(RCOOH) ET((RCOOH)nH+) (3) for monomer evaporation (R ) H, CH3) and
Figure 9. Energy difference between dimer-chain-dimer and dimerchain structures (HF/6-31+G*//HF/4-31G#).
for ∆Hn,n-2):
∆Hn,n-1 ) ∆En,n-1 + ∆ZPE + ∆Et298 + ∆Er298 +
+
∆En,n-2 ) ET((RCOOH)n-2H ) + ET((RCOOH)2) +
∆Ev298 + ∆PV (5)
ET((RCOOH)nH ) (4) for dimer evaporation. The vaporization energies were converted into enthalpies of reaction8 via eq 5 (and its analogue
The zero-point vibrational energies (ZPEs) and the translational (∆Et298), rotational (∆Er298), vibrational (∆Ev298), and pressure volume work (∆PV) terms were obtained from thermochemical
964 J. Phys. Chem., Vol. 100, No. 3, 1996
Figure 10. Binding energies ()vaporization energies) for monomer (M) loss from proton-bound formic acid clusters (HCOOH)nH+ f (HCOOH)n-1H+ + HCOOH, n )2, 3, 4 at different levels of theory: (+) MP2/6-31G*; (]) MP2/4-31G*; (3) HF/6-31G**; (bold +) HF/6-31+G*; (‚-‚) HF/6-31G*; (+ - - - - +) HF/6-31+G*//HF/431G#; (O - - - O) HF/4-31G*; (0‚‚‚0) HF/4-31G#.
Figure 11. Binding energies and enthalpies for monomer (M) loss from proton-bound acetic acid clusters (CH3COOH)nH+ f (CH3COOH)n-1H+ + CH3COOH, n ) 2-5. (0) HPMS experimental results at 298.15 K from ref 5; (3) HF/6-31+G*//HF/4-31G#; (b) HF/ 6-31+G*//HF/4-31G# with zero-point energy correction; (1) evaporation enthalpy at 298.15 K calculated at the HF/6-31G*//HF/4-31G# level (see text).
calculations of Gaussian 92. The ZPEs were corrected by a factor of 0.91. The temperature dependence of the vibrational correction was determined from computed frequencies without a correction factor. Results and Discussion Structures of Proton Bound Formic and Acetic Acid Clusters: Chainlike Structures. We have attempted a nearly exhaustive structure search. Alternative structures were tested including cyclic ones in which the proton, protonated formic acid, or protonated acetic acid form the core ion. The calculations led however to chainlike structures in which the extra proton occupies a near-central position along the chain.
Zhang and Lifshitz
Figure 12. Binding energies for monomer loss from (HCOOH)nH+: (O) experimental data from ref 1; (0) experimental data from ref 2; (b) calculated data with zero-point energy corrections at the HF/631G*//HF/4-31G# level (open chain n-mer leading to open chain (n 1)-mer).
All levels of calculation predict similar global minimum energy structures for the unprotonated monomer, HCOOH, and for the protonated monomer (HCOOH)H+, which are illustrated in Figure 2e,a, respectively, and were created from the geometrical data of HF/4-31G#. The structure calculated for (HCOOH)H+ is the same as the EZ structure of ref 10. For the proton-bound dimer, (HCOOH)2H+, we found three competitive conformations of nearly equal energies. The planar protonated monomer HO-CH-OH+ may exist in the EZ, ZZ, or EE conformation,10 but the EZ conformation was found to be of lowest energy (Figure 2a and ref 10). However in the protonated dimer conformation in Figure 2b the structure is made up of a formic acid unit which is hydrogen bonded to an EE conformation of the protonated monomer. This is brought about by the formation of two hydrogen bonds between the CdO group of HCOOH and HO-CH-OH+ in a cyclic structure. Dimers which possess the EE conformation are slightly more stable (3 kJ/mol) than the dimer with the EZ conformation. (Energies calculated at the MP4/6-31G*//MP2/ 6-31G* level). The structures derived for the protonated trimer and tetramer are included in Figure 2 and those for the protonated pentamer and hexamer are presented in Figure 3. There exist many alternative conformations of the open chainlike structures including many different positions of the proton along the chain. The structures finally derived at the HF/4-31G# level are the ones presented in Figures 2 and 3. The structures of proton bound acetic acid clusters were calculated up to n ) 5. They can be deduced by replacing H by CH3 in Figures 2 and 3. Competitive structures were checked at the HF/6-31+G*//HF/ 4-31G# level to make sure that global minima have indeed been located. Further checks were carried out by calculating the frequencies for all the structures up to n ) 5 of (HCOOH)nH+ and n ) 4 of (CH3COOH)nH+ with HF/4-31G# and finding that they were all real. The atomic net charges from Mulliken population analysis are included in Figures 2 and 3 to show the position of the extra proton, bond properties, and the dispersion of the effect of protonation. The net charges approach the ones on the neutral with increasing cluster size. The Mulliken overlap populations which indicate the bondings between some of the atoms are
Hydrogen-Bonded Carboxylic Acid Cluster System
Figure 13. Calculated binding energies (HF/6-31+G*//HF/4-31G#) for monomer and dimer losses from (HCOOH)nH+. Dimer-terminated chains Dn+ evaporating monomers M and forming dimer-terminated chains Dn-1+ (O); dimer-terminated chains Dn+ evaporating dimers D and forming open-chain. cluster Cn-2+ (4); open-chain clusters Cn+ evaporating monomers (b); structures terminated at both ends by dimer units evaporating dimers (2).
listed in Table 2 for proton-bound formic acid clusters to show the bond properties and the dispersion of the protonation effect. The overlap populations between atoms in single formic acid units deviate from those in the neutral but tend to the neutral values with increasing cluster size. The bonding in formic acid units other than the ones on which the proton is located is similar to that in free neutral formic acid. The bonding between two units tends to reflect the balance between covalent and iondipole interactions. All of the attributes show a decreasing protonation effect on every part of the cluster with increasing cluster size due to dispersion of the protonation effect. The structures displayed in Figures 2 and 3 demonstrate that the different formic acid units have similar shapes save for the case of n ) 2 and the proton prefers to be located in the middle or near the middle of the chains. Dimer-Terminated Chain Structures. Two neutral carboxylic acids form a ring-closed two-hydrogen-bonded dimer of high stability.4 Its calculated structure and net charges are presented in Figure 4d, while its overlap populations are listed in Table 3. To form the dimeric structure, the net charges are redistrib-
J. Phys. Chem., Vol. 100, No. 3, 1996 965 uted and quite different from those on the monomer (Figure 2). This redistribution leads to a stronger ion-dipole bonding. This occurs in a symmetrical way and leads to structural stability. Chainlike proton-bound clusters terminated at one of their ends by the ring-closed dimer are stable (see Figures 4 and 5). At the HF/4-31G# level they become more stable than the openended chain structures at n ) 5 for formic acid and at n ) 4 for acetic acid. The crossover from open ended most stable structures to dimer terminated ones occurs at higher n for higher levels of theory, e.g., HF/6-31+G*//HF/4-31G#. The crossover occurs at n ) 6 for formic acid and at n ) 5 for acetic acid when the sums of the Hartree-Fock energies for HF/6-31+G*/ /HF/4-31G# and thermal energies for HF/4-31G# are compared. It is possible that the true limiting n value has not been reached, particularly for acetic acid clusters due to limitations of the level of theory used. The differences between the total energies of open-ended chain clusters and dimer terminated ones are presented for proton-bound formic and acetic acid clusters in Figures 6 and 7, respectively, at the HF/4-31G#, HF/6-31+G*/ /HF/4-31G# including thermal energy terms at 298.15 K. Chain structures terminated at both ends by dimer units become the global minima at slightly higher n values than those with a single dimer unit. The differences in energy between those with two dimer units or one dimer unit are rather small above a certain n value, and the two species probably coexist under experimental conditions. Both types of species of size n may be formed experimentally through recombination of openchain proton-bound clusters with neutral dimers and/or by isomerization of an open-chain cluster of size n. Calculated structures for chains doubly terminated by dimer units are presented in Figure 8 for (HCOOH)nH+ (n ) 4-6). The differences between the total energies of the chain structures terminated by a single dimer unit and the dimer-chain-dimer structures, for proton-bound formic acid clusters, are presented in Figure 9. We have tried to carry out a fairly exhaustive study of possible alterative structures and believe that the open chains and the chains singly terminated or doubly terminated by dimer units are the global minima for the proton-bound carboxylic acids studied. Future, higher level calculations may be carried out to verify this. Evaporation Energies and Enthalpies. We believe that monomer evaporation takes place from open-chain structures and from structures having a dimer unit at one end only and that dimer evaporation takes place from singly as well as doubly dimer-terminated chains. We have calculated the evaporation energies accordingly. Furthermore, comparisons with high pressure mass spectrometry (HPMS) experimental results requires calculations of ∆H values at 298.15 K in addition to 0 K values. The binding energies were first calculated for the lower members of the proton bound formic acid clusters, (HCOOH)nH+ (n ) 2-4) at several levels of theory (Figure 10). Inclusion of electron correlation at the MP2 level increases the dimer binding energy, compared to SCF Hartree-Fock (Figure 10). Good agreement between calculated binding energies based on HF/ 4-31G# and HF/6-31+G*//HF/4-31G# and some other relatively higher levels (HF/4-31G*, 6-31G*, 6-31+G*, and 6-31G**) was reached. There is some discussion in the literature as to the optimum level of calculation of binding energies for hydrogenbonded systems.8 Comparison with experimental results is usually advisable. The most accurate experimental results for cluster binding energies are usually derived from HPMS. Such data are available for low members of proton-bound acetic acid clusters.5 A comparison between experimental and calculated
966 J. Phys. Chem., Vol. 100, No. 3, 1996 binding energies and enthalpies for (CH3COOH)nH+ (n ) 2-5) is presented in Figure 11. The SCF Hartree-Fock calculated values are seen to be in quite good agreement with experiment but the 298.15 K enthalpies which are to be compared with the experimental data are consistently ∼0.1 eV too low. There are to the best of our knowledge, no experimental HPMS data for proton-bound formic acid clusters. We have determined experimentally1,2 kinetic energy release distributions (KERDs) for monomer and dimer evaporations. Binding energies were deduced from the KERDs, by applying finite heat bath theory.22 We have published two sets of binding energies for the formic acid clusters1,2 which are compared with the calculated values in Figure 12. The computed results are in better agreement with the older (and lower binding energy) experimental data1 than with the new ones.2 We noted earlier2 that the recent binding energies deduced for formic acid clusters with n ) 6-8 might be too high in comparison with acetic acid clusters of the same sizes. On the other hand the comparison of the calculated binding enthalpies with the HPMS data for acetic acid clusters (Figure 11) demonstrated that the calculated values which we get at the present level of theory might be ∼0.1 eV too low. It is thus plausible that the correct formic acid data are intermediate between the two sets of experiments of Figure 12. Calculations show that dimer evaporation is energetically favored over monomer evaporation for dimer terminated pentamers as well as hexamers. However, the monomer binding energy of the open-chain pentamer is lower than the dimer binding energy of the dimer-terminated pentamer, while the monomer binding energy of the open-chain hexamer is higher than the dimer binding energy of the dimer-terminated hexamer. In other words, both the relative stability of dimer terminated chains (Figures 6 and 9) and the relative monomer and dimer binding energies (Figure 13) favor monomer evaporations for n < 6 and dimer evaporations for n g 6, as was observed experimentally for formic acid clusters.1,2 Acknowledgment. We are grateful for helpful discussions with Prof. L. Radom, Dr. J. Martin, Dr. Y. Ling, Dr. W. Y. Feng, and Dr. V. Aviyente. R.Z. is very grateful to Dr. D. Danovich for assistance provided using the Gaussian 92 program. This research has been supported by a grant from the Israel Science Foundation.
Zhang and Lifshitz References and Notes (1) Feng, W. Y.; Lifshitz, C. J. Phys. Chem. 1994, 98, 6075. (2) Lifshtiz, C.; Feng. W. Y. Int. J. Mass Spectrom. Ion Processes, in press. (3) Faubel, M.; Kisters, Th. Nature 1989, 339, 527. (4) Chao, J.; Zwolinski, B. J. J. Phys. Chem. Ref. Data 1978, 7, 363. (5) Meot-Ner (Mautner), M. J. Am. Chem. Soc. 1992, 114, 3312. (6) Lifshitz, C.; Louage, F. J. Phys. Chem. 1989, 93, 5633. (7) Lee, E. P. F.; Dyke, J. M. Mol. Phys. 1991, 73, 375. Deakyne, C. A.; Meot-Ner (Mautner), M.; Campbell, C. L.; Hughes, M. G.; Murphy, S. P. J. Chem. Phys. 1986, 84, 4958. Edison, A. S.; Markley, J. L.; Weinhold, F. J. Phys. Chem. 1995, 99, 8013. (8) Deakyne, C. A.; Knuth, D. M.; Speller, C. V.; Meot-Ner (Mautner), M.; Sieck, L. W. J. Mol. Struct. (THEOCHEM) 1994, 307, 217. (9) Feng, W. Y.; Aviyente, V; Varnali, T.; Lifshitz, C. J. Phys. Chem. 1995, 99, 1776. (10) Cheung, Y.-S.; Li, W.-K. Chem. Phys. Lett. 1994, 223, 383. (11) Chu, C. H.; Ho, J. J. J. Am. Chem. Soc. 1995, 117, 1076. (12) Chu, C. H.; Ho, J. J. J. Phys. Chem. 1995, 99, 1151. (13) Aviyente, V.; Varnali, T. J. Mol. Struct. (THEOCHEM) 1992, 227, 285; 1993, 299, 191. (14) Jurema, M. W.; Kirschner, K. N.; Shields, G. C. J. Comput. Chem. 1993, 14, 1326. (15) Teshima, S.; Kaneko, T.; Yokoyama, Y.; Tsuchiya, M. 12th Int. Mass Spectrom. Conf. Amsterdam, 1991. (16) Tsuchiya, M.; Teshima, S.; Kaneko, T.; Harano, T. J. Chem. Soc. Jpn. 1993, 6, 687. (17) Hehre, W. J.; Radom, L.; Schleyer, P.v.R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (18) Radom, L. Int. J. Mass Spectrom. Ion Processes 1992, 118/119, 339. (19) Del Bene, J. E. J. Comput. Chem. 1985, 6, 296; 1987, 7, 259; 1987, 8, 810; 1989, 10, 603; J. Comput. Phys. 1987, 86, 2110, and references therein. (20) Dannenberg, J. J. J. Phys. Chem. 1988, 92, 6869. Dannenberg, J. J.; Mezei, M. J. Phys. Chem. 1991, 95, 6396. Turi, L.; Dannenber, J. J.; Rama, J.; Ventura, O. N. J. Phys. Chem. 1992, 96, 3709. Turi, L.; Dannenberg, J. J. J. Phys. Chem. 1992, 96, 5819. Rama, J.; Ventura, O. N.; Turi, L.; Dannenberg, J. J. J. Am. Chem. Soc. 1993, 115, 5754. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT Revision F.4, Gaussian, Inc., Pittsburg, PA, 1993. (22) Klots, C. E. J. Chem. Phys. 1985, 83, 5854; Z. Phys. D 1987, 5, 83; J. Phys. Chem. 1988, 92, 5864; Z. Phys. D 1991, 20, 105; Z. Phys. D 1991, 21, 335; J. Chem. Phys. 1993, 98, 1110.
JP951843T
