JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 21
1 JUNE 1999
A quantum chemical study of negatively charged methanol clusters
László Turia)
Department of Physical Chemistry, Eötvös Loránd University, Budapest 112, P.O. Box 32,
Hungary, H-1518
~Received 2 November 1998; accepted 5 March 1999!
We performed high-level quantum chemical density functional theory calculations on negatively
charged methanol clusters containing up to six monomers. The calculations suggest that there exist
stable methanol cluster anions and that these anions are more stable than similar cluster anions of
water. Linear hydrogen bonded methanol chains are observed to bind the excess electron on dipole
bound states. The orientation and the size of the excess electron were characterized by the position
of the center of mass and the radius of gyration of the highest occupied molecular orbital ~HOMO!.
The electron occupies a large diffuse orbital concentrated outside the molecular frame in the
molecular dipole direction. The tendencies of the dipole moments, the vertical electron detachment
energies, and the size of the HOMOs all fit in the same cooperative trend, suggesting stronger
interactions in larger anions. We also located stable cluster anions which can serve as model systems
for the solvated electron in liquid methanol. Multiple O–H¯e 2 interactions with dominantly
bond-oriented arrangement toward the solvated electron are probably strongly favored in the liquid
phase for energetic reasons. Although the size of the excess electron is still significantly larger than
expected from quantum molecular dynamics simulations, the general decreasing trend of the radius
of gyration with increasing cluster size is reassuring. Similarly to the O–H¯e 2 interactions, we
located C–H¯e 2 interactions between appropriately oriented methyl hydrogens and the excess
electron in a large anion of six methanol molecules. We propose the interactions of both the
hydroxyl hydrogens and the methyl hydrogens with the excess electron to be considered hydrogen
bonds. © 1999 American Institute of Physics. @S0021-9606~99!30221-X#
I. INTRODUCTION
The existence of the solvated electron as an individual
species has been the focus of many experimentalists and
theoreticians since the original observation of Weyl in 1864
and since the postulation of the species.1,2 More recently, a
long series of experimental studies has been devoted to the
investigations of the structural and dynamical properties of
excess electrons in various solvents.3–12 Quantitative theoretical investigations into the solvated electron problem became
feasible after the development of powerful computers and
efficient numerical program packages to solve the Schrödinger equation for the given problem. Among the theoretical methods, recently developed quantum-classical molecular dynamics techniques13–15 were successfully employed for
the detailed characterization of various features of an excess
electron in water and methanol baths.16–22 Besides the molecular dynamics approach, traditional quantum chemical
methods provide additional insight into the energetics and
the structure of smaller negatively charged molecular clusters. Although these clusters can be strikingly different from
the solvated electron system in real liquids, it is important to
recognize that the implications of the results of the quantum
chemical approach can be very useful for predicting and understanding the properties of larger systems.
Since the early ’70s, a number of molecular orbital studies have appeared in the literature ~mostly on water cluster
anions!, several of them based upon the implicit assumption
a!
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of the cavity model of the solvated electron.23–25 Although
there have been interesting alternative reasonings and
calculations,26–28 the cavity model became, and still is,
widely accepted for the description of the solvated electron
in polar solvents. More recently, high-level quantum chemical calculations were performed on negatively charged water
clusters, including large basis set ab initio calculations employing the second-order Moeller–Plesset perturbation
theory ~MP2! and the density functional theory ~DFT!.29–31 It
appeared that, while the negatively charged water trimer
forms a dipole-bound anion,29 the HOMO electron density of
a specially oriented hexamer anion seems to localize in a
well-defined spatial region surrounded by the solvent
molecules.30,31 Since the hexamer calculations did not implicitly evoke the cavity model ~for example, by placing extra functions into the inferred cavity!, the localization of the
HOMO electron density is in gratifying accord with the cavity model. As a further interesting aspect, it was found both
theoretically30,31 and experimentally32 that the dangling hydrogens point toward the localized electron, thus forming
O–H¯e 2 hydrogen-bonding interactions. Ab initio calculations on anion clusters of other polar solvents are rare in the
literature. Recent experimental7,8 and theoretical20–22 interest
toward electron solvation in methanol and recent studies on
small water cluster anions,29–31 however, render it essential
to investigate the closely related system, the negatively
charged methanol clusters.
From this consideration in the present study, we examine
the negatively charged (CH3OH) 2
n complexes with n52, 3,
4, and 6. The main questions we ask are the following. Do
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© 1999 American Institute of Physics
J. Chem. Phys., Vol. 110, No. 21, 1 June 1999
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stable methanol cluster anions exist? If yes, which complexes are stable, and how is their stability reflected in the
vertical electron detachment energies? What is the electron
distribution in the investigated structures? Is the excess electron located in a cavity-like region or more like on a diffuse
orbital? If stable structures exist, what interactions play a
role in the stabilization? How important are the hydrogens
not participating in conventional O–H¯O type hydrogen
bonds ~dangling hydrogens!? An important question also
arises concerning the role of the methyl group. In the last few
years, a series of experimental33–35 and theoretical
investigations36–38 illustrated the role C–H¯O hydrogen
bonds may play in contributing to the stabilization of larger
molecular clusters, crystals. As an analogy to the O–H¯e 2
interactions found in negatively charged water clusters,30,31
and ~as we shall see! in methanol cluster anions, we consider
the possibility of the formation of C–H¯e 2 interactions
between the methyl hydrogens and the excess negative
charge. The present investigation may also take us closer to
answering the long-standing issue dating back to the electron
spin resonance ~ESR! measurements of Kevan et al. concerning the orientation of the methanol molecules around the
solvated electron.11,12 Are the methanol molecules dominantly O–H bond directed or dipole oriented toward the solvated electron?
II. METHODS
We performed high-level ab initio calculations using the
density functional theory ~DFT! employing the B3-LYP
functional.39 The negatively charged clusters were completely optimized in all degrees of freedom at the
B3-LYP/6-3111G(d, p) level ~basis set 1!. Further calculations were carried out on the optimized structures with the
6-3111G(d,p) basis augmented with one extra set of diffuse functions on the hydrogens for all considered species
~basis set 2! and with one set of diffuse functions on all
atoms for all dimers and trimers ~basis set 3!.40 The vertical
electron detachment energy is calculated as the difference
between the energy of the negatively charged cluster and the
energy of the corresponding neutral structure in the geometry
of the charged species. The calculations were performed using the GAUSSIAN94 program package.41
III. RESULTS AND DISCUSSION
A. Dipole bound anions: Dimer, trimer, and tetramer
anions
Figure 1 shows the molecular structures considered in
the present work. The corresponding total energies and vertical electron detachment energies ~VDE! are collected in
Table I. Although almost all the hydrogen-bonded dimer,
trimer, and tetramer structures studied in the present work
~I–IV! were found to be unstable in terms of the vertical
detachment energy with the original 6-3111G(d, p) basis
set, addition of extra diffuse functions completely reverses
the tendency: all examined structures bind the excess electron with positive VDEs. Let us first examine the open chain
structures. The dimer binds the electron by 59 meV, the trimer by 154 meV, while the tetramer VDE is even larger, 235
FIG. 1. Schematic representation of the methanol anions considered in the
present work.
meV calculated with basis 2. The results are not significantly
different, although a little higher ~75 and 162 meV for the
dimer and trimer anions, respectively!, with the largest set
adding diffuse functions on the heavy atoms as well. These
molecular cluster anions are representative examples of the
dipole bound anions.
To assess the reliability of our single-point calculations
with basis set 2 on the structures optimized with basis set 1,
we performed a complete geometry optimization for the neutral dimer and for the dimer anion with basis set 2. We found
that the adiabatic electron affinity of the neutral methanol
dimer, although a very small quantity, is negative ~232
meV!. Correspondingly, the vertical electron detachment energy becomes slightly larger in absolute value by the relaxation energy of the neutral dimer giving 54 meV. This value
is in very good agreement with the corresponding single-
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László Turi
TABLE I. Total energies and vertical electron detachment energies for various methanol cluster anions. Total
energy in hartrees, VDE in meV.
Basis 1
Total energy
a
Basis 2
Basis 3
VDE
Total energy
a
VDE
Total energya
VDE
Dimer
I
2231.464 700
2358.3
2231.480 041
58.8
2231.480 781
74.6
Trimers
II
III
2347.216 944
2347.215 482
2189.8
2399.4
2347.229 580
2347.230 962
153.5
21.2
2347.230 139
2347.231 667
161.9
32.5
Tetramers
IV
V
2462.968 622
2462.964 970
256.7
300.0
2462.979 365
2462.968 044
234.7
382.6
¯
¯
¯
¯
Hexamer
VI
2694.460 543
16.7
2694.466 706
183.0
¯
¯
a
Total energy of the anionic species.
point calculations for the 6-3111G(d, p) optimized structures employing extra diffuse functions on the hydrogens
~see Table I!.
Before going into specific examination regarding the geometry of the dimeric species, a word of caution is necessary
at this point. It is widely realized that the hydrogen-bonded
structures usually have a very flat potential surface, the structures being floppy with respect to the intermolecular vibrations. The original 6-3111G(d, p) optimized anion structure, thus, may happen to differ dramatically from that
calculated with the more flexible set ~basis 2! applied in the
single-point calculations. Fortunately this is not the case,
since the basic geometric features of the dimer anions are in
good agreement when optimized with both basis sets ~basis
sets 1 and 2!. Consequently, we think, the approach followed
in the present study employing single-point calculations with
larger basis sets on the structures optimized with a smaller
set seems to be reliable enough for our purposes.
Returning to the structural analysis, we observed that the
hydrogen-bonding arrangement of the optimized methanol
dimer anion changes significantly relative to the neutral
dimer. In particular, the trans-linear hydrogen-bonding preference of the neutral dimer turns to cis-linear hydrogenbonded orientation in the anion. As one of the consequences,
for example, the methyl groups get significantly closer to
each other in the anion. Similarities of these results to those
for the water dimer anion42 are apparent. The neutral methanol dimer with its relatively large dipole moment ~2.99 D
with basis 2! is an ideal candidate to bind an excess negative
charge. The excess electron is located on a large diffuse orbital in the dipole moment direction ~Fig. 2!. Although it is
generally of limited use, Mulliken population analysis is instructive in this case, indicating significant increase of the
negative charge on the free OH hydrogen and the methyl
protons of the same molecule. The increased charge density
around the methyl group of the OH terminal molecule may
play an important role in the preference of the dimer anion
toward the cis-linear hydrogen-bonding orientation. Nevertheless, the center of mass of the highest occupied molecular
orbital ~occupied by the excess electron! is located well outside the molecular frame. The distance of the center of mass
of the electron to the nonhydrogen-bonding hydroxyl hydrogen is 2.15 Å, while the electron and the closest methyl
proton are 1.87 Å apart. The corresponding H–O¯e 2 and
C–O¯e 2 angles ~49.7 and 59.9 degrees, respectively!, are
indicative of the approximate dipole orientation of the excess
charge. The size of the HOMO characterized by its radius of
gyration, ^ w u r 2 u w & 1/2, is quite large, approximately 6.3 Å.
Consequently, the HOMO basically buries the dimer itself.
Examination of the trimer anions points to other interesting aspects of the problem. We added an excess electron to
two different neutral trimers. The first neutral structure, II, is
an open chain, while the other one ~III! is cyclic, with all
methyl groups pointing to the same direction relative to the
plane of the three oxygen atoms ~the second-most stable configuration of the neutral trimer hypersurface!. Although in
geometry optimization a neutral trimer chain would collapse
to a cyclic structure, the anion has a true local minimum in
the chain arrangement. We suggest, consequently, that unlike
the neutral trimer species having only two stable cyclic
configurations,43 the trimer anion possesses ~at least! one cyclic and one chain minima on the potential energy surface.
FIG. 2. Contour surface of 0.015 of the HOMO of the methanol dimer anion
~I!. Similar surfaces are obtained for the trimer and tetramer anions ~II and
IV!.
J. Chem. Phys., Vol. 110, No. 21, 1 June 1999
FIG. 3. Contour surface of 0.010 of the HOMO of the cyclic methanol
trimer anion ~III!.
Of the two minima, the open chain anion with only two
hydrogen bonds becomes very similar in stability to the cyclic anion having three hydrogen bonds. Thus, the VDE of
the chain trimer anion should be larger by about the energy
of a hydrogen bond than that of the cyclic trimer ~154 vs 21
meV, and 162 vs 33 meV with basis sets 2 and 3, respectively, the difference being about 3 kcal/mol!. In both species, the excess electron is found on a similar diffuse orbital,
as we have seen for the dimer anion ~see Fig. 2!. In the chain
trimer, II, however, the electron can be more effectively attached to the field of the molecular dipole moment. Inspection of the dipole moments supports this conclusion. The
substantially larger dipole moment of the neutral chain trimer in the geometry of the anion is more likely to provide
the energetically more favorable possibility for forming a
dipole bound anion. Nevertheless, due to the significantly
larger dipole moment of the neutral, cyclic methanol trimer
~2.79 D with basis 1! as compared to the similar water trimer, III is also able to bind the excess electron ~Fig. 3! on a
dipole bound state. This is not the case for the cyclic water
trimer.29
As a more general observation regarding the dipole moments, we found that for the dimer and the cyclic trimer
anions ~these structures have corresponding neutral minima!
the dipole moment of the neutral species in the anion’s geometry is enhanced relative to the optimized neutral species.
This indicates that while the formation of a dipole bound
anion requires sufficiently large dipole moment of the neutral
molecule, the formation of the dipole bound anion induces
such structural changes in the molecule which, in turn, increase the dipole moment. We would also like to point out
that in the cyclic trimer anion ~III! the diffuse HOMO is
concentrated on the methyl side of the molecule ~Fig. 3!.
This aspect will be important to rationalize the properties of
László Turi
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a larger negatively charged methanol cluster, VI.
We have seen previously that the VDE increases substantially going from the dimer to the chain trimer. The tendency also continues for the chain tetramer anion ~IV!, the
VDE becoming significantly larger ~235 meV with basis 2!
than for the dimer or the trimers. The observed cooperative
behavior is clearly manifest in the decreasing radius of gyration of the HOMO. The radius of gyration of the excess
electron ~HOMO! changes from 6.3 Å ~dimer!, through 6.2
Å ~trimer!, to 5.9 Å ~tetramer!. The increasing kinetic energy
of the HOMO, due to the smaller spatial extent of the electron, must therefore be balanced by the decreasing potential
energy leading to the overall increase in the stability of the
larger aggregates. The relative position of the center of mass
of the electron to the molecular frame reflects the observed
tendency of the stability of the dipole bound methanol anions
by a gradual shift toward the hydroxyl hydrogen, decreasing
the electron-hydrogen distance ~2.15, 1.84, and 1.70 Å for
the dimer, trimer, and tetramer, respectively!. The stronger
electron–molecule interaction in IV ~indicated by the increased vertical detachment energy and the shrunken electronic distribution! is in perfect accordance with the increasing dipole moments ~for example, 6.14 D in the trimer, 8.49
D in the tetramer with basis 2 for the neutral chain in the
optimized anion’s geometry!. From the viewpoint of the
structure, the large dipole moment is the result of a particular, optimal arrangement of the hydrogen-bonded monomers.
One has to recognize in this context, however, that due to the
existence of diastereomeric methanol chains, the aboveobserved hydrogen-bonding patterns with their particular local hydrogen-bonding configurations may not be the only
possibilities to form stable dipole bound anions.
B. Alternative tetramer and hexamer anions
Our goal in this section is to find and examine further
alternative methanol cluster anions which possibly can serve
as simplified model systems for the solvated electron in
methanol. To do this, following similar lines as in the previous section, we chose a negatively charged methanol tetramer ~V! and a hexamer ~VI!.
Tetramer V differs basically from the chain tetramer anion ~IV! inspected above. V represents a model system of
methanol clusters with more than one electron–molecule interactions. This type of system can be considered to model
the hypothetical arrangement of the solvent molecules
around a localized solvated electron in a solvent cavity. In V,
we place two dimers in a special orientation facing the same
excess electron with their free ~nonhydrogen-bonding! hydroxyl groups. Not surprisingly, after completely optimizing
the structure, the VDE points to the existence of a stable
species. The two free hydroxyl hydrogens not participating
in conventional hydrogen bonds turn toward the center of
mass of the electron favoring OH bond-oriented arrangement. The above observed orientation strongly resembles
that found in a water hexamer anion by Kim et al.31 Based
on the structural and energetic similarities to the water anion
case, we propose that the O–H¯e 2 interactions of V be
considered hydrogen bonds. The approximately 400 meV
vertical detachment energy turns out to be significantly
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J. Chem. Phys., Vol. 110, No. 21, 1 June 1999
larger than the VDE of the dipole bound tetramer anion, IV.
More interestingly, this VDE is more than six times larger
than the corresponding value for the dipole bound methanol
dimer anion. One may thus conclude that multiple
O–H¯e 2 interactions are strongly favored energetically in
negatively charged methanol clusters. The species is also observed to be stable relative to two noninteracting neutral
dimers and a free electron by about 4.0 kcal/mol. The 4.0
kcal/mol interaction energy for two O–H¯e 2 interactions
of V indicates a roughly 2 kcal/mol/interaction stabilization
energy.
The radius of the electron also shrinks more than 1 Å to
just under 5.0 Å in V compared to the dimer, I, or tetramer,
IV. This suggests that the size of the HOMO and the stability
of the anion clusters are correlated; stronger binding of the
excess electron manifests itself in more compact HOMO
electronic distribution. Although the HOMO of V is still significantly larger than the radius of gyration of the groundstate solvated electron in methanol ~2.5 Å! calculated
from mixed quantum-classical molecular dynamics
simulations,21,22 the tendency is encouraging. Addition of
further methanol molecules interacting with the excess electron with their free OH groups may be expected to further
decrease the size of the electron. The molecular clusters considered in the present work and, in general, those affordable
in quantum chemical calculations are by no means sufficient
to model the real interactions in the liquid phase. On the
other hand, it should be kept in mind that in mixed quantumclassical simulations the methanol molecules are treated
completely classically. Thus, for the excess charge there are
no available orbitals on the solvent molecules. This effect
may artifactually decrease the size of the electron in the
mixed quantum-classical treatment.
It is noteworthy that the original diffuse functions of
larger coefficients of basis 1 are seemingly sufficient to capture the basic features of the HOMO for V ~e.g., the VDE,
see Table I!, whereas this is not the case for the other anions
where application of extra functions of smaller coefficients
~see basis sets 2 and 3! is necessary. The fact that the VDE of
V is reasonably well predicted with the otherwise inferior
basis set 1 is evidently the consequence of the sizable decrease of the radius of gyration of the HOMO.
What is the situation with the C–H bonds? Can they
participate in stabilizing the excess electron? Can they form
C–H¯e 2 interactions in analogy to the C–H¯X (X5O,
N,...,) interactions?33,34 To address this question, we analyzed the structure and energetics of hexamer VI ~see Fig. 1!.
VI consists of two cyclic trimers with their methyl groups
pointing to the same side of the plane of the oxygen atoms,
while these ‘‘dangling’’ methyls between the trimers orient
toward each other, practically, creating a cavity inside the
cluster. VI is clearly analogous to one of the possible water
hexamer anions studied recently,30,31 except that we replaced
the dangling hydrogens with methyl groups. The calculated
183 meV VDE indicates that the methyl groups stabilize the
free electron. The HOMO is a typical internal state similar to
that found for water hexamer anions. Although significant
electronic density is concentrated in this cavity, the radius of
gyration of the electron is relatively large, 7.0 Å, indicating
László Turi
FIG. 4. Contour surface of 0.013 of the HOMO of the methanol hexamer
anion ~VI!.
the more diffuse nature of the excess electron. As the most
striking structural feature, one C–H bond of each methyl
orients toward the center of mass of the HOMO surrounded
by the six methyl groups ~Fig. 4!. From an energetic point of
view, assuming the geometrical distortion of the trimers in
the hexamer anion to be negligible relative to the optimized
trimers, the 0.3 kcal/mol repulsion between the two neutral
trimers in the hexamer anion is compensated by about 4.3
kcal/mol C–H¯e 2 attraction. The resulting approximately
0.7 kcal/mol/interaction C–H¯e 2 stabilization energy is
somewhat weaker than that for the O–H¯e 2 bonds but
comparable to such C–H¯O interactions as those calculated, for example, in formic acid,44 acetic acid45 and
acetone.46 Based on the strong resemblance to the C–H¯X
(X5O, N, F,...,) hydrogen bonds, we attribute the directionality of the methyl hydrogens and the stability of the anion to
the presence of C–H¯e 2 interactions.
IV. CONCLUSIONS
In the present paper, we investigated the properties of
various methanol cluster anions. As the first important result,
similarly to water cluster anions, we found several stable
dipole bound anions of the (CH3OH) 2
n complexes up to n
54. Neutral molecules ~and molecular clusters! are postulated to bind an excess electron on a very diffuse, dipole
bound orbital if the dipole moment of the neutral parent is
larger than 2.5 D.42,47,48 This qualitative rule concerning the
stability of the dipole bound anions definitely applies for
methanol clusters. The size of the excess electron defined as
the radius of gyration of the highest occupied molecular orbital is between 5.8 and 7.0 Å, indicating that the excess
electron occupies a large, diffuse orbital. The gradually decreasing radius and the increasing VDE in larger clusters
indicate cooperative behavior. The properties of the inspected methanol cluster anions parallel those for the negatively charged water clusters, the water dimer,42 and trimer29
anions. As illustrated above in the example of the cyclic
methanol trimer anion, the larger dipole moment of the neutral methanol clusters relative to the water clusters is consistent with the larger electron detachment energy and with the
enhanced dipole bound character of the examined species.
However, it remains a challenging problem to comprehend in
J. Chem. Phys., Vol. 110, No. 21, 1 June 1999
quantitative detail why and how this negative charge-dipole
moment coupling takes place in methanol ~and in water!
clusters in quantum chemical terminology, an issue which
will be further investigated in the near future.
We also located two stable methanol cluster anions with
more than one O–H¯e 2 or C–H¯e 2 interactions. These
structures can be regarded as models of small size for the
cavity-forming arrangement of the solvent molecules anticipated to be potentially important in the description of the
solvated electron. The estimated strength for the individual
O–H¯e 2 and C–H¯e 2 interactions were found to be
about 2 and 0.7 kcal/mol, respectively. The interaction energy and directionality of the appropriate bonds to the corresponding HOMOs may allow one to postulate the abovementioned interactions as weak hydrogen bonds to the
excess electron. It is interesting that while the O–H¯e 2
interactions are weaker than the O–H¯O hydrogen bonds,
the stabilization of the C–H¯e 2 bonds is comparable to the
hydrogen-bonding strength of several C–H¯O stabilized
species. Nonetheless, the magnitude of the VDEs suggests
that the strongly polar OH bonds are more likely to stabilize
the free electron in methanol than the methyl groups. Furthermore, the present study also predicts that multiple
O–H¯e 2 hydrogen bonds to an electron are more stable
than the corresponding individual O–H¯e 2 interactions. A
similar cooperative effect is observed for water hexamer anions, the electron density favoring clustered dangling hydrogen atoms.31 Nevertheless, the participation of the C–H¯e 2
interactions in stabilizing the solvated electron should not be
ruled out solely on the basis of the present simple arguments
formulated for very small clusters.
The two different interactions, namely the O–H¯e 2
and the C–H¯e 2 interactions, lead to different molecular
orientations toward the solvated electron as in V or VI. The
implications of the molecular directionality are important for
condensed phases as well. Molecular dynamics simulations
of a solvated electron in liquid methanol by Zhu and Cukier
predicted different molecule–electron orientations depending
on the specific form of the methanol–electron
pseudopotential.20 A small modification in the methyl–
electron terms of the exchange part of the pseudopotential
alters the OH bond directionality of the methanol molecules
to molecular dipole orientation toward the solvated electron.
The picture is further complicated by the application of a
three-site classical methanol model in the simulations which
prevents the possibility of the formation of ‘‘real’’
C–H¯e 2 hydrogen bonds. Thus, in the first step, the use of
an all-interaction site model would be necessary in the simulations to receive more reliable structural data of the solvated
electron system.
ACKNOWLEDGMENTS
The author gratefully acknowledges the financial support
of the National Research Fund of Hungary ~OTKA! ~research grants under Contract Nos. F019474 and W015439!.
1
W. Weyl, ‘‘Über die Bildung des Ammoniums und Cineger AmuroniumMaltalle.’’ Annalen der Physik und Chimie, 2 Folge, Vol. 123, pp. 350–
367, 1864.
László Turi
10369
C. A. Kraus, J. Am. Chem. Soc. 30, 1323 ~1908!.
J. H. Baxendale and P. Wardman, J. Chem. Soc., Faraday Trans. 1 69, 584
~1973!.
4
W. J. Chase and J. W. Hunt, J. Phys. Chem. 79, 2835 ~1975!.
5
A. Migus, Y. Gauduel, J. L. Martin, and A. Antonetti, Phys. Rev. Lett. 58,
1559 ~1987!.
6
Y. Gauduel, S. Pommeret, and A. Antonetti, J. Phys. Chem. 97, 134
~1993!.
7
C. Pépin, T. Goulet, D. Houde, and J. P. Jay-Gerin, J. Phys. Chem. 98,
7009 ~1994!.
8
P. K. Walhout, J. C. Alfano, Y. Kimura, C. Silva, P. Reid, and P. F.
Barbara, Chem. Phys. Lett. 232, 135 ~1995!.
9
M. U. Sander, U. Brummund, K. Luther, and J. Troe, J. Phys. Chem. 97,
8378 ~1993!.
10
L. D. A. Siebbeles, U. Emmerichs, A. Hummel, and H. J. Bakker, J.
Chem. Phys. 107, 9339 ~1997!.
11
L. Kevan, Radiat. Phys. Chem. 17, 413 ~1981!.
12
L. Kevan, Chem. Phys. Lett. 66, 578 ~1979!.
13
M. Sprik and M. L. Klein, J. Chem. Phys. 89, 1592 ~1988!.
14
J. C. Tully, J. Chem. Phys. 93, 1061 ~1990!.
15
F. A. Webster, P. J. Rossky, and R. A. Friesner, Comput. Phys. Commun.
63, 494 ~1991!.
16
J. Schnitker, K. Motakabbir, P. J. Rossky, and R. Friesner, Phys. Rev.
Lett. 60, 456 ~1988!.
17
T. H. Murhprey and P. J. Rossky, J. Chem. Phys. 99, 515 ~1993!.
18
B. J. Schwartz and P. J. Rossky, J. Chem. Phys. 101, 6902 ~1994!.
19
O. V. Preshdo and P. J. Rossky, J. Chem. Phys. 107, 5863 ~1997!.
20
J. Zhu and R. I. Cukier, J. Chem. Phys. 98, 5679 ~1993!.
21
L. Turi, A. Mosyak, and P. J. Rossky, J. Chem. Phys. 107, 1970 ~1997!.
22
A. Mosyak, P. J. Rossky, and L. Turi, Chem. Phys. Lett. 282, 239 ~1998!.
23
M. D. Newton, J. Phys. Chem. 79, 2795 ~1975!.
24
T. Clark and G. Illing, J. Am. Chem. Soc. 109, 1013 ~1987!.
25
H. Tachikawa, A. Lund, and M. Ogasawara, Can. J. Chem. 71, 118
~1993!.
26
H. F. Hameka, G. W. Robinson, and C. J. Marsden, J. Phys. Chem. 91,
3150 ~1987!.
27
T. R. Tuttle, Jr. and S. Golden, J. Phys. Chem. 95, 5725 ~1991!.
28
F. F. Muguet, H. Gelabert, and Y. Gauduel, J. Chim. Physique 93, 1808
~1996!.
29
D. M. A. Smith, J. Smets, Y. Elkadi, and L. Adamowicz, J. Chem. Phys.
107, 5788 ~1997!.
30
K. S. Kim, S. Lee, J. Kim, and J. Y. Lee, J. Am. Chem. Soc. 119, 9329
~1997!.
31
K. S. Kim, I. Park, S. Lee, K. Cho, J. Y. Lee, J. Kim, and J. D. Joannopoulos, Phys. Rev. Lett. 76, 956 ~1996!.
32
C. G. Bailey, J. Kim, and M. A. Johnson, J. Phys. Chem. 100, 16782
~1996!.
33
R. Taylor and O. Kennard, J. Am. Chem. Soc. 104, 5063 ~1982!.
34
G. R. Desiraju, Acc. Chem. Res. 24, 290 ~1991!.
35
S. W. Han and K. Kim, J. Phys. Chem. 100, 17124 ~1996!.
36
L. Turi and J. J. Dannenberg, J. Phys. Chem. 97, 7899 ~1993!.
37
L. Turi and J. J. Dannenberg, J. Phys. Chem. 100, 9638 ~1996!.
38
P. Jedlovszky and L. Turi, J. Phys. Chem. B 101, 5429 ~1997!.
39
A. D. Becke, J. Chem. Phys. 98, 5648 ~1993!.
40
The exponents of the diffuse functions are the following: oxygen: 0.02;
carbon: 0.015; hydrogen: 0.006.
41
M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson,
M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J.
B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E.
S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J.
Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A.
Pople, GAUSSIAN94, Revision B.2 ~Gaussian Inc., Pittsburgh, PA, 1995!.
42
Y. Boutellier, C. Desfrançois, H. Abdoul-Carime, and J. P. Schermann, J.
Chem. Phys. 105, 6420 ~1996!.
43
O. Mó, M. Yáñez, and J. Elguero, J. Chem. Phys. 107, 3592 ~1997!.
44
L. Turi, J. Phys. Chem. 100, 11285 ~1996!.
45
L. Turi and J. J. Dannenberg, J. Phys. Chem. 97, 12197 ~1993!.
46
L. Turi, Chem. Phys. Lett. 275, 35 ~1997!.
47
O. H. Crawford, Mol. Phys. 20, 585 ~1971!.
48
C. Desfrançois, H. Abdoul-Carime, N. Khelifa, and J. P. Schermann,
Phys. Rev. Lett. 73, 2436 ~1994!.
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