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Computational study of amine basicities in the gas phase

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Computational study of amine basicities in the gas phase
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Caskey, Doug
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43 leaves : illustrations ; 28 cm

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Subjects / Keywords:
Amine oxidase ( lcsh )
Methylamines ( lcsh )
Acids -- Basicity ( lcsh )
Acids -- Basicity ( fast )
Amine oxidase ( fast )
Methylamines ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Bibliography:
Includes bibliographical references (leaves 42-43).
General Note:
Department of Chemistry
Statement of Responsibility:
by Doug Caskey.

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University of Colorado Denver
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Full Text
COMPUTATIONAL STUDY OF AMINE BASICITIES IN THE GAS PHASE
AND PROTIC SOLUTION
by
Doug Caskey
B.S., University of Missouri, 1995
A thesis submitted to the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Chemistry
2001


This thesis for the Master of Science
degree by
Douglas Caskey
has been approved
by
Date
11


Caskey, Douglas (M.S., Chemistry)
A Computational Study of Amine Basicities in the Gas Phase and Protic Solution
Thesis directed by Professor Robert Damrauer
ABSTRACT
The irregular order in basicities of a series of methylamines in aqueous solution is
studied by means of a quantum mechanical/molecular mecanical method. Hartree-
Fock and the effective fragment potential methods not only reproduce the anomalous
order in basicities in qualitative agreement with well-established experimental results
but reveal interesting structural effects with only a handful of water molecules.
Structural and energy effects are used to untangle some of the molecular details
responsible for the basicity order of methylamines in aqueous solution.
This abstract accurately represents the content of the candidate's thesis. I recommend
its publication. /
Signed|
Robert Damrauer
in
t


DEDICATION
I dedicate this thesis to my wife who has allowed me to neglect fixing the window
screens for the last six months while I write this paper.


ACKNOWLEDGEMENT
I would like to thank Dr. Damrauer, who allowed me to get in over my head but was
also willing to help me when things went tragically wrong.


CONTENTS
Figures..................................................................... vii
Tables..................................................................... viii
Chapter
1. Introduction.............................................................1
2. Computational Methods.................................................... 6
2.1 Effective Fragment Potential Method..................................... 6
2.2 Computational Details..................................................7
3. Results and Discussion...................................................10
3.1 Structural Analysis: Neutral Species....................................10
3.2 Structural Analysis: Protonated Species................................ 22
3.3 Trends in Energy.......................................................25
4. Conclusions..............................................................40
Bibliography................................................................42
vi


FIGURES
Figure
3.1.1 Trimethylamine..................................................13
3.1.2 Typical Trimethylamine Structure................................14
3.1.3 Ammonia with Six Water Fragments................................15
3.1.4 Ammonia with Fourteen Water Fragments...........................16
3.1.5 Methylamine with One Water Fragment.............................19
3.1.6 Dimethylamine with Two Water Fragments..........................20
3.1.7 Methylamine with Four Water Fragments...........................21
3.1.8 Typical Three Dimensional Water Clusters for n > 6; Ammonia with 10 Water
Fragments.............................................................23
3.1.9. Typical Three Dimensional Water Clusters for n > 6 for Neutral Species;
Trimethylamine with Six Water Fragments...............................24
3.2.10 Typical Ammonium Ion with Four Water Fragments.................26
3.2.11 Methylammonium with Four Water Fragments.......................27
3.2.12 Methylammonium with Fourteen Water Fragments...................29
3.3.13 Trimethylammonium with Fourteen Water Fragments................30
3.3.14 Amine Relative Energy Vs. # of Fragments.......................34
3.3.15 Cation Relative Energy Vs. # of Fragments......................35
3.3.16 Delta H of Protonation Vs. Water #.............................38
vn


TABLES
Table
1. Internal Geometry of Neutral Species......................................11
2. H-Bonding of Neutral Species with Water................................... 17
3. H-Bonding of Protonated Species with Water................................28
4a. Relative Energy and AH data obtained at EFP/6-31 ++G(d,p)................31
4b. Relative Energy and AH data obtained at EFP/6-31 ++G(d,p)................32
viii


1. Introduction
It has been well established that a reaction medium can drastically affect acidity
and basicity: the relative acid strength in a series of simple alcohols or amines can be
made irregular or even reversed by solvent effects.! "6 While basicity increases with
methyl substitution in the series of methylamines in the gas phase,2'!0 (CHa^N >
(CH3)2NH > CH3NH2 > NH3, the order found in aqueous solution is: (CHa)2NH >
CH3NH2 > (CH3)3N > NH3.2>5,11 The order in solution with respect to the change in
enthalpy of protonation is: CH3NH2 > NH3 > (CH3)2NH > (CH3)3N.2>5>12 The
different order as a result of subtraction of entropy effects is indicative of just how
small, much smaller than in the gas phase, the differences between the free energy
and enthalpy are for protonation for the series. The apparent stabilizing effect of the
alkyl groups on the conjugate acids observed in the gas phase has been explained by
induction,8,11-13 but work showing that alkyl groups enhance acidity as well as
basicity should exclude this as a major source of stabilization.^, 14,15 Polarizability
effects are a more reasonable suspect, where stability increases as polarizability
increases, which increases as alkyl size increases.^, 14,15 Polarizability can
therefore be used to explain differences in both gas phase acidities and basicities
resulting from varying alkyl substitutions. The basicity order in aqueous solution
appears to arise from the sum of intrinsic effects and interactions with the
1


solvent. 1 >2,5,10,12 As hydrogen atoms on nitrogen are replaced by methyl groups
the degree of hydration decreases.! >2,5,10,12 These solvent effects oppose and
almost completely neutralize the polarizability effects of alkyl substitution, giving
rise to the observed basicity order.2>5,10,12
Recently there have been computational studies which have reproduced the
experimental solution basicity order. Almost all of these studies have employed
continuum models of varying complexity in order to model the solvent. One such
study by Silla et. al.^ demonstrates the importance of the basis set in reproducing the
experimental solution basicity order with a continuum model of the solvent. The
authors show that the correct basicity order is only obtained when diffuse and
polarization functions are included in the basis set. They conclude that their data
indicate that with a sufficient basis set specific interactions such as H-bonding can be
accounted for simply by an electrostatic term for the solvent. 13,16 That is since H-
bonding is primarily an electrostatic interaction the irregularities observed in the
order can be accounted for electrostatically. In this study the solvent was represented
as a bulk medium by estimating the electrostatic and non-electrostatic perturbations
of the solvent on the gas phase behavior of the system. It should be noted that as with
all continuum solvent models, the behavior of the model is ultimately governed by the
solvents dielectric constant and the shape of the cavity that encloses the solute. 17-19
2


While models of the solvent as a continuum have reproduced the experimental
relative basicities of these amines, the source of this irregular ordering is still
somewhat ambiguous because of the inability of continuum models to reveal details
about solute-solvent and solvent-solvent interactions, such as hydrogen bonding.
There are currently several methods of studying the solvation of small molecules.
Solute-solvent and solvent-solvent interactions can be investigated through full
Hartree Fock calculations of both the solute and solvent. Although this method is
very costly, it is also very reliable. Less reliable and less expensive molecular
mechanics methods have also been used. One method that has been shown to
produce results consistent with Hartree Fock levels of theory at a cost comparable to
models using empirical potentials is the effective fragment potential (EFP)
method. 15,20-22 This method is not only a cost effective alternative to Hartree-Fock
methods for treating small water clusters but is quite capable of probing the solute-
solvent and solvent-solvent interactions which are fundamental to understanding the
physical basis of solvation. The model describes the system by treating solute
molecules with a full Hartree Fock treatment, while introducing solvent molecules
individually through potentials added as one-electron terms directly into the
Hamiltonian of the solute: H = Har + V. Har is the Hamiltonian of the solute and V,
the potential due to the solvent molecule, is a perturbation on the solute
Hamiltonian. 15,20-22
3


Damrauer has recently used this method in the disclosure of structural details
responsible for the reversal of acid strength of the series of alcohols, (Cfy^COH >
(CH3)2CHOH > CH3CH2OH > CH3OH in the gas phase to CH3OH > CH3CH2OH >
(CH3)2CHOH > (CH3)3COH in aqueous solution. 15 Reproduction of the inversion of
the acidity order was accomplished by adding just a handful of water molecules to the
alcohols and alkoxides with both the EFP method and full Hartree-Fock treatments of
the clusters While the EFP method showed the inversion resulting from differences
in the alcohols, full Hartree-Fock treatments revealed the inversion results from
differences in the alkoxides. Although energy data obtained with the EFP was
inconsistent with Hartree-Fock data, the most conspicuous aspect of this study was
the characterization of interactions of the solvent molecules with the alcohols and
alkoxides. Structural data gathered with the EFP method was very consistent with
that obtained through full Hartree-Fock treatments. Some of the observed differences
in structures revealed interactions which were likely responsible for the acidity
reversal. Light was also shed on how the solvent molecules contribute to the bulk
solvent.
This thesis reports results of a study in which the EFP method was used to
investigate the molecular details involved in solvation of ammonia, methylamine,
dimethylamine, trimethylamine, and their corresponding ammonium ions. It is the
goal of the work contained herein not only to reproduce the relative orders of basicity
of these amines in both the gas phase and aqueous solution but to explain the
4


anomalous order found in solution using the structural information obtained from
the EFP method. It is of primary interest to characterize structural differences in the
solutes as they are solvated and their interactions with solvent molecules as well as
solvent-solvent interactions. This study also serves as an evaluation of the ability of
the EFP method to reproduce characteristics of both water clusters and bulk water.
5


2. Computational Methods
2.1 Effective Fragment Potential Method
A brief conceptual description of the EFP method may be helpful in interpreting
these results. The model treats the system of interest by dividing it into an active
region (AR), described using a full ab initio treatment, and a spectator region (SR),
for the surrounding solvent molecules: Htot = HAr + Hsr. ^>20-23 in this study the
AR consists of the solute: ammonia, methylamine, dimethylamine, trimethylamine, or
their corresponding ammonium ions. The SR consists of water molecules that have
been described by the EFP. The effective fragment potential describing the solvent
molecules is composed of three one-electron terms. Each represents a particular
component of the total interaction: coulombic interactions between solvent molecules
and/or with the ab initio solute, solvent-solvent and solute-solvent induction or
polarization interactions. The water fragments are treated as rigid bodies where
experimentally determined coordinates (roH = 0.944 A and their geometry. The position of each water molecule relative to the others and the
solute is not predefined but can be optimized. The EFP method, which has been
incorporated into the GAMESS suite of programs, uses analytic gradients for the
entire (ab initio + fragments) system. Numerical Hessians can be obtained from finite
double differences of the analytical derivatives and can be used to verify the
6


authenticity of minimum energy structures by checking for a positive definite
Hessian, or no negative eigenvalues. Zero negative vibrations is indicative of a
minimum and one negative vibration indicates the structure is a saddle point. Thus,
geometric, energetic, and reaction path information can be obtained for minimum
energy structures. 15,20-23
2.2 Computational Details
The potential energy surfaces of ammonia, methylamine, dimethylamine,
trimethylamine and the corresponding ammonium ions have been explored so that
structural details of the interaction of the amine/ammonium ion and solvent may be
gathered. Differences in these structures/energies may help explain the anomalous
basicity order in protic solution. The amines and ammonium ions were treated at the
restricted Hartree-Fock level of theory with the 6-31++G(d,p) basis set, while the
water molecules were represented using the EFP method previously described.
Protonation of all the amines, [H+(H20)m + B(H20)n -> BH+(n+m)H20], involves a
proton, in both the gas phase and solution, therefore the proton may be neglected
without altering the basicity order. Neglect of the proton will make AH and AG for
the process of protonation, shown above, more positive than the corresponding gas
phase process because for the expression: H+gas H+soiution, AH and AG are negative.
For each amine/ammonium water cluster represented in the equation above (where
the number of water molecules is m+n = 0, 1, 2, 4, 6, 10, 14), full geometry
optimizations (except internal water geometry) were performed for various initial
7


geometries. As the number of water molecules increases, the number of possibilities
for different starting geometries increases dramatically. This is to be expected for
two reasons: first, the potential energy surface for a molecule with N atoms is 3N-6
dimensional and second, the potential energy surfaces associated with water clusters
have often been found to be flat, containing small barriers separating many
neighboring minimal 5,20 vibrational frequencies were calculated by numerical
Hessians for each of the lowest energy structures and used to determine the zero-point
corrections to the energy and enthalpy. Internal vibrations of the water molecules are
not included in the Hessian matrix; therefore, these vibrations are also not included in
the zero point energy correction or enthalpy. Enthalpies are reported at 0 K. These
data have not been corrected for temperature effects since the normal rigid rotor-
harmonic oscillator approximation is unreliable for such a flat potential energy
surface. 15 it may be helpful to note that except for ammonia and trimethylamine, the
solution basicities are all nearly the same ( 0.5 kcal/mol) and that these results are
reported in terms of AH. Also, high level electron correlations were not performed in
this study (in the active region the more significant electron-electron interactions
were replaced by average interactions). Thus the reported energies should be slightly
higher than the real energy. It has been shown previously that comparison for larger
water clusters of lowest energy structures, averaged energies, or Boltzmann averaged
energies all capture the same relative differences in energy between species at this
basis set level. The probability of a found minimum being a global minimum
8


decreases as the number of water fragments increases thus necessitating the large
number of calculations performed here. All computations were carried out using the
GAMESS suite of programs.24 MacMolPlot has been used to visualize the molecular
structures.25
9


3. Results and Discusssion
3.1 Structural Analysis: Neutral Species
Optimized structures obtained with the EFP method to describe water fragments
for n = 0, 1, 2, 4, 6, 10, and 14 fragments using the 6-31++G(d,p) basis set for the
amine were examined for interesting structural characteristics within the amines
(internal geometry), interactions between the amines and water, and finally
organization of the water network as the number of water molecules increase. The
internal structures of the amines appear to be largely independent of the number of
water fragments and the number of methyl substituents (Table 3.1.1). The C-H, N-H,
and C-H bond distances are nearly constant and are in agreement with literature
values.26 What does not appear to be independent of the number of water fragments
are internal angles, < S1NS2 (where Si,2 are any substituent on nitrogen), that decrease
slightly when water is added (Table 3.1.1). This observation could possibly be
explained with a steric argument, where the methyl groups are pushed closer to each
other by the network of water. While the water cluster obtains a lower energy when
water H-bonds to itself or to a hydrogen on the amine nitrogen, little would be
expected to be gained by water associating with the methyl groups. Interaction
between water and the methyl groups is minimized by pushing the methyl groups
closer to each other.
10


Table 1. Internal Geometry of Neutral Species
Species Internal Geometry
nh3 nH20 (n) N-H (A) 0 14 3-1.00(1.01) 2-1.00 1-1.01 3-108.8 (106.7) 2-106.7 1-106.4
Species Internal Geometry
CH3NH2 nH20 (n) N-H(A) C-N (A) C-H (A) 0 2-1.00(1.01) 1-1.45(1.47) 2-1.08(1.10) 2-111.7(110.3) 1-107.9(107.1)
1-1.09
14 2-1.00 1-1.46 2-1.08 1-110.6 1-107.6
1-1.09 1-110.5
Species Internal Geometry
(CH3)2NH
nH20(n) N-H(A) C-N (A) C-H (A) 0 1-1.00(1.00) 2-1.45(1.46) 4-1.09(1.10) 2-110.3(107.0) 113.8 (111.8)
2-1.08
14 1-1.00 2-1.46 4-1.09 2-108.7 1-112.5
2-1.08
Species Internal Geometry
(CH3)3N
nH20 (n) C-N (A) C-H (A) 0 3-1.45(1.46) 6-1.08(1.10) 3-112.0(110.9)
3-1.09
14 3-1.45 6-1.08 2-111.1
________________________________________3-1.09________________1-111,2_______________
Note: Parenthetical values are literature values obtained by electron diffraction of the
species in the gas phase.26
11


Another interesting feature found concerning the internal geometry of the
substituted amines is a staggered conformation of each methyl group with respect to
the other two N-substituent bonds (Fig. 3.1.1) with the methyl group tilted slightly
toward the unshared electrons. This can be explained by the short length of the C-N
bond (1.47 A) which should give rise to an increased van der Waals repulsive
interaction between the nitrogen lone pair and electron density on the hydrogens of
the methyl groups. This conformation appears to be unaffected by the presence of
water fragments, which is supported by spectroscopic data.27
The interaction of the amine with the surrounding water consists of one or two
hydrogen atoms from water fragments within hydrogen bonding (H-bonding) distance
from the nitrogen with each water donating one hydrogen (Fig. 3.1.2). It is not
surprising to see that as water molecules are added, the number of Fl-bonds between
the amine and water increases slowly with most of the water being added to the
extended water network (Fig. 3.1.3 and 3.1.4; Table 3.1.2). In fact, the only amine
water cluster containing more than 1 N-H20 H-bond is the NH3(H20)i4 species
which contains two with fourteen water fragments. There are also NH-OH2 bonds.
When fourteen water fragments are present these range in number from zero for
trimethylamine to three for ammonia. Each NFF -OH2 corresponds to each and every
acidic amine hydrogen H-bonding to the oxygen of only one water fragment. Thus,
the number of direct H-bonds between the amine and the water network increases in a
fairly regular way as methyl substitution decreases.
12


Figure 3.1.1. Trimethylamine: Each methyl group is staggered with respect to the
other N-C bonds.
13


Figure 3.1.2. Typical Trimethylamine Structure: trimethylamine with 14 water
fragments.
14


Figure 3.1.3 Ammonia with Six Water Fragments.
15


Figure 3.1.4
Ammonia with Fourteen Water Fragments.
16


Table 2. H-Bonding of Neutral Species with Water
Species nh3 nH20 (n) Type and Length of H-bond
N-H20 (A) nh-oh2 (A) total
1 2.05 1
2 2.02 2.41 2
4 1.94 2.10 2
6 1.97 2.28 2
10 1.87 2.14, 2.32 3
14 1.96, 2.20 2.77,2.22, 2.12 5
Species Type and Length of H-bond
CH3NH2
nH20 (n) N-H20 (A) nh-oh2 (A) total
1 2.04 1
2 2.00 2.45 2
4 1.93 2.12 2
6 1.91 2.21 2
10 1.95 2.38, 2.64 3
14 1.92 2.33,2.25 3
Species Type and Length of H-bond
(CH3)2NH
nH20 (n) N-H20 (A) NH-OH2 (A) total
1 2.03 1
2 2.00 2.44 2
4 1.94 2.12 2
6 1.99 2.29 2
10 1.92 2.18 2
14 1.86 2.18 2
Species Type and Length of H-bond
(CH3)3N
nH20 (n) N- H20 (A) total
1 2.04 1
2 .99 1
4 2.01 1
6 .95 1
10 .94 1
14 1.97 1
17


The N-HbO H-bonds range in length from 1.86-2.19 A and the NHOH2 bonds
range in length from 2.09-2.76 A (Table 3.1.2).
Organization of the water clusters agrees well with the existing literature on water
clusters.28-30 Optimizations with only one water fragment result in a hydrogen from
water in H-bonding proximity ( 2.8 A) of the nitrogen with the water oxygen
directed away from the nitrogen. The second water hydrogen is either in a staggered
or eclipsed geometry with respect to the nitrogen substituent such that a mirror plane
of reflection is present for the complex (Fig. 3.1.5). Structures obtained for all four
amines with n 2 and 4 fragments are cyclic and look strikingly similar to global
minima structures of the water trimer and pentamer with the amine nitrogen taking
the place of the water oxygen and an amine hydrogen taking the place of a water
hydrogen (Fig. 3.1.6 and 3.1.7).30 There are sixteen other minimum energy
structures reported for the water pentamer, many of which are analogous in structure
to higher energy structures found for n = 4.30 has a]s0 been reported that for the
water heptamer and larger clusters, there is a tendency toward three dimensional
water structures which is also seen in this current work.30 The most notable feature
of the larger water clusters (n > 6) is the number of H-bonds that the water molecules
make. While in the cyclic structures only one H atom from each water is an H-bond
donor, the three dimensional clusters contain some water molecules in which both
hydrogen atoms are H-bond donors
18


Figure 3.1.5 Methylamine with One Water Fragment.
19


Figure 3.1.6 Dimethylamine with Two Water Fragments
20


Figure 3.1.7 Methylamine with Four Water Fragments.


(Fig. 3.1.8 and 3.1.9). As the structures grow in size and complexity, it becomes
apparent that there is competition between maximizing the number of H-bonds and
minimizing the geometric strain of the water network. The quasi cyclic water ring
structure grows with the addition of water until the energy reduction associated with
ring strain becomes less than the reduction associated with forming a new ring system
allowing for water molecules to participate in more than two H-bonds.
All of the amine water clusters appear to be differentially hydrated, where the
more polar portion of the solute is hydrated more than the aliphatic portion. This
feature is most obvious with trimethylamine and least with ammonia. This same
trend was observed recently in a series of aliphatic alcohols, where the feature was
explained in steric terms. ^ The extended water structure minimized interaction with
the aliphatic regions of the solute because nothing was gained energetically by the
cluster if water arranged around the aliphatic portion of the solute. Conversely, the
clusters energy was reduced through increased H-bonding by adding water to itself
or to the amine nitrogen or to the hydrogen on the nitrogen. This appears to be the
case with the amines as well, where the water fragments orient themselves away from
the methyl groups as much as possible. It is interesting to note that this feature seems
more pronounced with the more substituted amines (Fig. 3.1.8 and 3.1.9).
3.2 Structural Analysis: Protonated Species
Examination of the ammonium ion structures reveals some stark differences
compared to the neutral species. All of the neutral species with two or four water
22


Figure 3.1.8 Typical Three Dimensional Water Clusters for n > 6; Ammonia with 10
Water Fragments.
23


I,
111
I
I
Figure 3.1.9 Typical Three Dimensional Water Clusters for n > 6 for Neutral
Species; Trimethylamine with Six Water Fragments.
24


fragments optimize to form a ring structure, while the ammonium ion forms one
direct water H-bond through each hydrogen on the nitrogen atom for a total of four
H-bonds. In the same manner methylammonium forms two direct H-bonds when n =
2 and three when n = 4, through the hydrogens on the nitrogen atom.
Dimethylammonium makes two H-bonds with the first two water fragments before
extending the water network while trimethylammonium forms only one. All four
species make exactly one direct H-bond per hydrogen on the nitrogen before
extending the water network in three dimensions (Fig. 3.2.10 and 3.2.11, Table 3.3.3).
The larger n value structures, as was seen in the neutral species, show little bonding
of waters in the hydrophobic regions, but this feature does seem to be less
pronounced (Fig. 3.2.12 ad 3.3.13). This maybe because of polarizability effects
created by the positive charge on the molecule. If electron density in the methyl
groups is polarized toward the positive charge then this could make the opposite sides
of the methyl groups less repulsive electronically.
3.3 Trends in Energy
Table 3.3.4 presents the relative ZPC energies (see Computational Methods for
explanation) of both the neutral and protonated species with n water fragments.
These data are the lowest relative energy values found for each n (see Computational
Methods for details) where n = 0, 1, 2, 4, 6, 10, 14 water fragments. Also presented
in Table 3.3.4 are the AH of protonation values obtained from the lowest energy
species.
25


Figure 3.2.10 Typical Ammonium Ion with Four Water Fragments; ammonium with
each ammonium hydrogen H-bonded to a water fragment.
26


Figure 3.2.11 Methylammonium with Four Water Fragments.
27


Table 3. H-Bonding of Protonated Species with Water
Species Type and Length of H-bond
NH4
nH20 (n) NH-OH2 (A) total
1 1.76 1
2 2@1.85 2
4 4@1.91 4
6 1.92, 1.98, 1.84, 1.86 4
10 1.87, 2.11, 1.79, 1.74 4
14 1.87, 1.76,2.10, 1.99 4
Species Type and Length of H-bond
CH3NH3
nH20 (n) NH-OH2 (A) total
1 1.82 1
2 1.86, 1.87 2
4 1.97, 2.08, 1.82 3
6 1.96, 1.82, 1.81 3
10 1.73, 1.91, 1.85 3
14 1.85, 1.96, 1.79 3
Species Type and Length of H-bond
(CH3)2NH2
nH20 (n) NH-OH2 (A) total
1 1.87 1
2 2@1.91 2
4 1.90, 1.74 2
6 1.97, 1.90 2
10 1.73, 1.80 2
14 2.43,2.12, 1.85 3
Species Type and Length of H-bond
(CH3)3NH
nH20 (n) NH-OH2 (A) total
1 1.90 1
2 1.80 1
4 1.89 1
6 1.86 1
10 1.85 1
14 1.97 1


Figure 3.2.12 Methylammonium with Fourteen Water Fragments.
29


Figure 3.3.13 Trimethylammonium with Fourteen Water Fragments.
30


Table 3.3.4 Relative energy and AH data obtained at EFP/6-31++G(d,p).
species relative ZPC enerev /kcal/mol)
nh3 nH,0 (n) ammonia ammonium AH (kcal/mol)
0 0.0 (-56.16441) 0.0 (-56.49305) -206.2
1 -3.9 -17.8 -220.1
2 -8.5 -33.2 -230.9
4 -20.8 -57.8 -243.2
6 -32.2 -73.1 -247.2
10 -57.6 -104.3 -252.9
14 -81.5 -136.6 -261.3
species relative ZPC enerev (kcal/mol)
CH3NH2 H20 (n) methylamine methylammonium AH (kcal/mol)
0 0.0 (-95.15810) 0.0 (-95.50491) -217.6
1 -4.3 -16.0 -229.3
2 -9.1 -30.1 -238.7
4 -21.5 -48.0 -244.2
6 -34.4 -66.9 -250.1
10 -59.4 -98.6 -256.8
14 -83.9 -127.8 -261.5
Energies are relative to parenthetical values which are zero point corrected and listed
in Hartrees.
31


Table 3.3.5 Relative energy and AH data obtained at EFP/6-31++G(d,p).
species (CH3)2NH H,0 (n) relative ZPC enerev ('kcal/moll dimethylamine dimethylammonium AH (kcal/mol)
0 0.0 (-134.15695) 0.0 (-134.51563) -225.1
1 -4.2 -15.0 -235.8
2 -9.3 -28.2 -243.9
4 -21.9 -46.1 -249.3
6 -33.9 -61.0 -252.2
10 -61.0 -92.2 -256.3
14 -83.9 -118.7 -259.9
species relative ZPC enerev ('kcal/mol')
(CH3),N
nH,0 (n) trimethylamine trimethylammonium AH (kcal/mol)
0 0.0 (-173.15813)1 0.0 (-173.52447) -229.9
1 -4.1 -14.2 -239.9
2 -8.8 -23.5 -244.6
4 -21.0 -38.9 -247.8
6 -33.2 -55.6 -252.3
10 -60.0 -85.7 -255.6
14 -85.5 -112.1 -256.5
Energies are relative to parenthetical values which are zero point corrected and listed
in Hartrees.
32


Several trends surface in Table 3.3.4. First, the relative energies of all of the species
decrease as the number of water fragments increase. The heats of hydration of the
neutral amines become more exothermic with increasing alkyl size with the exception
of the mono- and di- substituted amines which decrease in energy the same amount
with 14 water fragments. The heats of hydration become less exothermic with
increasing methyl substitution for the cations. Secondly, the decrease in the relative
energies of the neutral species is smaller per added water fragment than with the
ammonium ions. Both of these trends were also seen by
Damrauer in the alcohol study where the alcohols decreased less in energy per added
water than the alkoxides.^ The third trend found was that the relative energies of the
neutral species decrease not only linearly but in very similar ways to each other (Fig.
3.3.14) . R values (measure of deviation of data from a best fit line: SSregression /
SStotai) obtained from plots of relative energy versus the number of water fragments
are all greater than 0.995 and slopes of best fit lines range from -5.71 to -5.95
kcal/fragment. Although these plots are nearly linear, addition of the first few water
fragments results in a decrease in energy of only about 4.5 kcal/mol per fragment for
all four amines while further water addition results in reductions in energy of about
6.2 kcal/mol per fragment. On the other hand plots of relative energy versus the
number of water fragments for the cations have two very different linear regions (Fig.
3.3.15) . The first is steeper with nearly the same slope for all four cations, ranging
33


Rel. Energy (kcal/mol)
Figure 3.3.14 Amine Relative Energy Vs. # of Fragments


Rel. Energy (kcal/mol)
Figure 3.3.15 Cation Relative Energy Vs. # of Fragments


from -15.0 (kcal x fragment)/mol for trimethylammonium to -14.2 (kcal x
ffagment)/mol, but are of varying lengths. The length of the steep region depends on
the amount of methyl substitution. For example this region extends to x =4 for
ammonia, and x = 1 for trimethylamine. The second, more shallow, region has nearly
the same slope for all of the cations, ranging from -7.9- -7.5 (kcal x ffagment)/mol.
The only feature that is really different among the plots of the cation relative energy
versus number of water fragments is the length of the two regions. The fact that plots
for the neutral species are nearly identical implies that the EFP method is that changes
in the relative order of basicity on going from the gas phase to aqueous solution must
arise from differences in the protonated species. Specifically, these differences in
basicity must come from the varying lengths of the two linear regions. Thus the
ability of water to solvate the cations varies more with methyl substitution than with
the neutral amines.
Comparison of energetic and structural characteristics for the amines and
ammonium species reveal some particularly interesting features. The shallow portion
of the plots of relative energy versus number of water fragments for the cations
corresponds to where water no longer adds to the cation but begins to add to other
water fragments. Thus, ammonium forms four H-bonds with four water molecules
before water begins to add to itself, methylammonium should be expected to form
three H-bonds (no methylammonium with three water fragment jobs were run),
dimethylammonium forms two and trimethylammonium forms one before water adds
36


to itself. So the EFP method indicates that a greater reduction in energy is obtained
by direct H-bonding of the water to the cation than by water H-bonding to more
water. It also becomes apparent that because all of the cations see about the same
energy reduction per added water in both regions of the plots that differences in
stability of the ions primarily arise from the number of H-bonds made directly to the
cation. This makes sense because the interaction between the cation and water is an
ion-dipole interaction, typical energy is about 15 kJ/mol with a 1/r2 dependence,
while water interacting with other water molecules is a dipole-dipole interaction,
typically about 2 kJ/mol with a 1/r3 dependence.31 This can be used to explain why
there is no large break in the relative energy plots for the neutral amines even though
the number of direct H-bonds between the solute and water network varies much like
that seen with the cations. Since the amine interaction with water is a dipole-dipole
interaction, energy associated with amine-water H-bonding should be closer in energy
to that of water-water H-bonding than the ammonium ions H-bonding with water.
While most of the direct interactions between the cation and the water network can be
accounted for with only four water molecules it would be naive to conclude that only
four water molecules, as in the case of ammonium, are involved in binding the ion in
solution. Considering the number of water molecules associated through an extended
network by H-bonds, it is clear that more water molecules are bound to these ions.
This is evidenced by the fact that inclusion of the amine data does not produce the
correct order of basicities in solution with four water fragments. In fact with four
37


delta H (kcal/mol)
Figure 3.3.16 Delta H of protonation vs. Water #
Water #


water fragments, the order more resembles the order in the gas phase (Fig. 3.3.16).
AH of protonation was found for each n value by subtracting AH of hydration for the
neutral species from AH of hydration for the corresponding cation (see Computational
Methods for details) (Fig. 3.3.16). While the gas phase order is in agreement with
existing literature, and the order at n = 14 is the same as that found in aqueous
solution, these data have to be considered cautiously.2>5,12 First, the precipitous
drop in energy for ammonia from n = 10 to /? = 14 appears suspect. Second,
trimethylamine at n 4 appears to be an outlier. These points could be the result of
not searching the potential energy surfaces at these points thoroughly. These energies
should not be expected to be reliable considering the previously mentioned alcohol
study where EFP energy data proved to be unreliable. 15 Therefore any interpretation
of these energies should be done with caution. Since structural data was consistent
with higher level calculations in the alcohol study it would definitely be of interest to
compare the amine/ammonium structural data to higher level calculations. Further
studies should include full Hartree Fock treatments of these clusters for comparison.
It may also be of interest to include higher-level electron correlation.
39


4. Conclusions
The EFP method has been used to examine the structural and energetic effects of
adding small numbers of water molecules to ammonia, methylamine, dimethylamine,
trimethylamine and their corresponding ammonium ions. The results were used to
attempt to understand the basicity order of these amines in aqueous solution.
Important features of the neutral amines interacting with water include the formation
of ring structures of water for clusters containing less than six water fragments.
These structures look strikingly similar to lowest energy structures of water clusters
with the N-H of the amine taking the appropriate place of a water molecule. After six
or more water fragments have been added, additional water molecules build in three
dimensions. Also, direct H-bonding of water to the amine increases with decreasing
methyl substitution. Comparison of energy data with structures reveal that energy
associated with direct H-bonding of the amine with water is of slightly less energy
than water H-bonding to water. The cation structures also contain direct H-bonding
of the water to the solute, with the number of H-bonds being equal to the number of
hydrogens on the nitrogen atom. As in the case of the amines, solute-water
interactions are established first with subsequent addition of water resulting in a three
dimensionally extended water network. Energy data for the EFP method indicate that
the irregular order of basicity in solution is a result of differences in stability of the
cations, which is directly related to the number of H-bonds made between water and
40


the cation. All of the cations get a reduction in energy of 14.2-15.0 kcal/mol with
direct addition of water, and they all see a reduction of 7.9-7.5 kcal/mol when water
adds to other water molecules in the network. The differences arise solely from the
number of H-bonds made between the cation and the water network. Energy data
also reproduces the correct order of basicities in the gas phase as well as in solution
when n 14. These energy data should be cautiously interpreted considering several
suspicious data points in this study and the previous alcohol study by Damrauer
where the EFP method was compared to full Hartree-Fock calculations when used as
a probe for studying small differences in acidity. 15 On the other hand, the structural
information revealed in this study indicate the nature of important interactions among
hydrating water fragments and the neutral amine and their corresponding ammonium
ions. It would be very interesting to compare structures obtained with the EFP
method to higher level calculations. Future studies might include investigation of
structural changes in these clusters caused by inserting them into a continuum cavity.
Full Hartree-Fock treatments should be performed or possibly moving just a few
water fragment into the active region. Electron correlation work may also be of use
in evaluating the structures otained with the EFP method.
41


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42


1) Aue, D. H.; Webb, H. M.; Bowers, M. T. J. Am. Chem. Soc 1976, 98, 854-6.
2) Aue, D. H.; Webb, H. M.; Bowers, M. T. J. Am. Chem. Soc 1976, 98, 318-29.
3) Baird, N. C. Can. J. Chem 1969, 47, 3535-8.
4) Brauman, J. I.; Blair, L. K. J. Amer. Chem. Soc 1970, 92, 5986-92.
5) Taft, R. W.; Wolf, J. F.; Beauchamp, J. L. J. Am. Chem. Soc 1978,100, 1240-9.
6) Arnett, E. M.; Small, L. E.; Mclver, R. J. Am. Chem. Soc 1974, 96, 5638-40.
7) Munson, M. S., B. J. Am. Chem. Soc. 1965, 87, 2332.
8) Brauman, J. I.; Blair, L. K. J. Amer. Chem. Soc 1971, 93, 3911-14.
9) Arnett, E. M.; Jones, F. M., Ill J. Amer. Chem. Soc 1972, 94, 4724-6.
10) Aue, D. FI.; Webb, H. M.; Bowers, M. T. J. Amer. Chem. Soc 1972, 94, 4726-8.
11) Brown, H. C. J. Am. Chem. Soc. 1945, 67, 1452-1455.
12) Drago, R. S. C.; Thomas, R.; Ferris, D. C. J. Am. Chem. Soc. 1989, 54, 1042-
1047.
13) Tunon, I. S.; Silla, E.; Tomasi, J. J. Phys. Chem. 1992, 96, 9043-9048.
14) Brauman, J. I.; Blair, L. K. J. Amer. Chem. Soc 1968, 90, 5636-7.
15) Damrauer, R. J. Am. Chem. Soc 2000, 122, 6739-6745.
16) Pascual-Ahuir, J. L.; Andres, J.; Silla, E. Chem. Phys. Lett 1990,169, 297-300.
17) Leach, A. R. Molecular Modelling: Principles and Applications', 1 ed.; Addison
Wesley Longman Limited: Essex, 1996.
43