An Ab Initio Study of Complexes With N-H-N Hydr.gen Bonds
by
Barry C. Husowitz
Submitted in Partial Fulfillment of the Requirements
For the Degree of
Master of Science
in the
Chemistry
Program
YOUNGSTOWN STATE UNIVERSITY
August, 2002
An Ab Initio Study of Complexes With N-H-N Hydrogen Bonds
Barry C. Husowitz
I hereby release this thesis to the public. I understand this thesis will be made available
from the OhioLINK ETD Center and the Maag Library Circulation Desk for public
access. I also authorize the University or other individuals to make copies of this thesis
as needed for scholarly research.
0..2.
Signature:
Approvals:
-
~c.~
:Bal1)lC usowitz, stUdel1t
Dr. Howard Mettee, Committee Member
Dr. Timothy Wagner, Committee Member
~/ollo;)..
I i
Date
Date
Date
~c.~~c.~
11
ABSTRACT
Ab initio MP2/6-31+G(d,p) calculations have been perlonned on a series of hydrogen 
bonded complexes stabilized by N-H-N hydrogen bonds. These complexes have 2,5- and
3,4-disubstituted pyrroles as proton donors (with substituents H, F, and Be+
1
), and
nitrogen bases including HCN, LiCN, NaCN, SCN-, OCN-, NH
3
, and N(CH
3
)3 as proton
acceptors. Correlations have been established among the structures, binding energies,
proton-stretching frequencies, and intensities of the proton-stretching bands of these
complexes. The great majority of complexes are stabilized by traditional N-H...N
hydrogen bonds, with proton-shared and ion-pair hydrogen bonds occurring only in
charged complexes.
iii
ACKNO~DGEMENTS
I would like to thank my advisor, Dr. Janet E. Del Bene, for her guidance on this
project. I am proud to have studied under her. I am grateful for the knowledge she has
imparted to me. This knowledge will benefit me for years to come. I am also grateful for
the time she has dedicated, and for her patience and understanding. Secondly, I would
like to thank the National Science Foundation (NSF) for financial support of this
research, and the Ohio Supercomputer Center. Finally, I would like to thank my family
and friends for believing in me, and for their constant encouragement throughout my life.
This has made it possible for me to make it this far. I would especially like to thank my
brother for his encouraging words and constant support.
IV
TABLE OF CONTENTS
PAGE
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . ..... iii
TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI
LIST OF TABLES vii
I. INTRODUCTION. 1
Aims of Study
II. METHODS... . 7
Basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Minimal Basis Set
Double Zeta and Triple Zeta Basis Sets
Double-split and Triple-split Valence Basis sets
Augmented Basis
Wavefunction Models . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Single Determinant Wavefunction
Hartree-Fock Method
Full Configuration Interactions (Full CI)
Configuration Interaction Singles and Doubles (CISD)
Coupled Clusters (CC)
M¢ller-Plesset Perturbation Theory (MPn)
Level of Theory for Studies of Hydrogen-Bonded Complexes 18
Geometry Optimization 18
Monomers
Complexes
Calculation of Harmonic Vibrational Spectra. . . . . . . . . . . . . . 20
'Reaction Energies 21
Electronic Binding Energies of Hydrogen-Bonded Complexes
Binding Enthalpies of Hydrogen-Bonded Complexes
Electronic Proton Affinities
III. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . ..... 22
Pyrrole and Disubstituted Pyrroles
Nitrogen Bases: HCN, LiCN, NaCN, SCN-, OCN-, NH
3
and N(CH
3
)3
Complexes of Pyrrole with HCN and its Derivatives
Complexes of 3,4-difluoropyrrole with HCN and its Derivatives
Complexes of 2,5-difluoropyrrole with HCN and its Derivatives
Complexes of 3,4-diberylliumpyrrole+
2
with HCN and its Derivatives
Complexes of Pyrrole and Disubstituted Pyrroles with NH
3
and N(CH
3
)3
IV. CONCLUSIONS....................... ..... 43
v
V. REFERENCES................. 45
VI. APPENDICES
Z-matrices for optimized monomers reported in Tables 1 and 2
Z-matrices for optimized complexes reported in Tables 5 and 6
Binding enthalpies(~Ho)for complexes in Tables 5 and 6
VI
LIST OF FIGURES
FIGURE
1.
PAGE
Computed harmonic vibrational spectra of ClH:4-R-pyridine complexes 4
2. Na-N
b
and Na-H distances versus computed MP2/6-31+G(d,p) binding
energies of complexes with pyrrole as the proton donor to HCN and its
derivatives . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. 31
3. Harmonic vibrational spectra of complexes of pyrrole with HCN and its
derivatives 33
4. Na-N
b
distances and proton-stretching frequencies versus Na-H distances
in complexes of pyrrole and disubstituted pyrroles with NH
3
and
N(CH
3
h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
vii
LIST OF TABLES
TABLE
1.
PAGE
MP2/6-31+G(d,p) electronic energies, zero point vibrational energies,
Na-H distances, harmonic proton-stretching frequencies and band
intensities for pyrrole and disubstituted pyrroles. . . . . . . . . . " 23
2. MP2/6-31+G(d,p) electronic energies, zero-point vibrational energies,
and electronic proton affinities for the nitrogen bases . . . . . . . .. 24
3. MP2/6-31+G(d,p) electronic energies, zero-point vibrational energies,
and frequency data for complexes of pyrrole and substituted pyrroles
with HCN and its derivatives . . . . . . . . . . . . . . . . . . . " 25
4. MP2/6-31+G(d,p) electronic energies, zero-point vibrational energies,
and frequency data for complexes of pyrrole and disubstituted pyrroles
with NH
3
and N(CH
3
)3 . . . . . . . . . . . . . . . . . . . . . . 27
5. MP2/6-31+G(d,p) Na-N
b
and Na-H distances, electronic binding
energies, harmonic proton-stretching frequencies and band intensities
for complexes of pyrrole and substituted pyrroles with HCN and its
derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6. MP2/6-31+G(d,p) Na-N
b
and Na-H distances, electronic binding
energies, harmonic proton-stretching frequencies and band intensities
for complexes of pyrrole and substituted pyrroles with NH
3
and
N(CH
3
h 39
1
I. INTRODUCTION:
Hydrogen bonding is an important intermolecular interaction, which is ubiquitous
in chemical and biochemical systems. Hydrogen bonding influences the properties of
water in its various phases and of molecules in aqueous solution. The high boiling points
of many solvents are a consequence of hydrogen bonding, and hydrogen bond formation
influences products formed in reactions.! In biological systems such as DNA, the
formation of nucleic acid base pairs involves hydrogen bonding.
2
Hydrogen bonds
determine the structures of proteins
3
, and are a factor in enzymatic activity.4 It has been
postulated that low barrier hydrogen bonds can provide stabilization during enzyme
catalysis, which results in rate enhancement of the reaction.
4
In the most general case the hydrogen bond can be represented as
A-H---B
where A-H is the proton donor and B is the proton acceptor atom. In recent studies, three
types of hydrogen bonds have been characterized: traditional, ion-pair, and proton 
shared.
s
-
7
In a traditional hydrogen bond between two neutral molecules, the A-H
covalent bond of the proton donor remains intact in thecomplex~Ifproton transfer from
A to B occurs, an ion-pair hydrogen bond is formed. In this type of hydrogen bond a
covalent bond is now formed between Wand B, and what was previously the proton
acceptor is now the proton donor. Intermediate between traditional and ion-pair
hydrogen bonds is the proton-shared hydrogen bond. In this type of hydrogen bond the
A-B distance is shorter than in traditional and ion-pair hydrogen bonds, but the A-H and
B-H bond lengths are longer than the covalent A-H and B-W bonds in traditional and
ion-pair hydrogen bonds, respectively.
complex~complex~
2
The first ab initio theoretical studies of hydrogen-bonded complexes were
conducted in the late 1960's and the early 1970'S.8-12 In these studies a single
determinant Hartree-Fock wavefunction was used with a small basis set. Geometry
optimizations where carried out by freezing the monomer geometries and optimizing the
intermolecular distance and intermolecular angles. The intermolecular coordinates were
varied cyclicly and independently until convergence criteria were met. It was not until
the 1980's that computationally efficient algorithms were developed for obtaining first
and second derivatives of the energy with respect to the nuclear coordinates. The
derivatives where first evaluated numerically, but later analytically.13-20 As a result,
automated full geometry optimizations can now be easily carried out. The availability of
analytical derivatives also permits routine calculation of harmonic infra-red (IR) spectra.
An important experimental method for studying hydrogen-bonded complexes is
IR spectroscopy. The IR spectra of hydrogen-bonded complexes are characterized by a
shift to lower frequency of the A-H proton-stretching band compared to that of the
corresponding monomer, and by a dramatic increase in the intensity of this band.
7
,21-23
Ab initio calculations of vibrational spectra can help experimentalists gain insight into the
properties of hydrogen-bonded complexes. Many ab initio calculations on various
hydrogen-bonded complexes and their IR spectra have been performed.
7
,22,24,25
Previous studies of hydrogen-bonded complexes that are most closely related to
those investigated in this project were carried out by Del Bene, Person, and Szczepaniak
on complexes between 4-substituted pyridines and hydrogen halides.
5
,6 These
complexes are represented as
X-H··
R
3
where R represents the substituents Be+, CN, F, CI, H, CH
3
, NH
2
, Li, Na, S- and 0-, and
X is a halogen atom. The complexes were optimized at the MP2/6-31+G(d,p) level of
theory. In this study computed structures and vibrational spectroscopic properties were
related to acid and base strength and hydrogen bond type.
Figure 1 shows the computed spectra for the CIH:4-R-pyridine complexes. The
spectra are arranged in order of increasing proton affinity of the substituted pyridine. The
complexes of CIH:4-R-pyridines with R=CN, F, CI, H, CH
3
and NH
2
are stabilized by
traditional hydrogen bonds, and a single strong CI-H stretching band appears in the
computed harmonic spectra, with frequencies ranging from 2524 cm-
I
to 2156 em-I. For
these complexes, as the proton affinity of the 4-substituted pyridine increases, the CI-N
distance decreases, the CI-H distance increases, the binding energy ([I.E) increases, and
the frequency (v) ofthe CI-H stretching band decreases.
The complexes of CIH:4-Li-pyridine and CIH:4-Na-pyridine are stabilized by
proton-shared hydrogen bonds. These complexes have very short Cl-N distances.
Several strong bands appear in the computed spectra of these two complexes, with
frequencies ranging from 1700 to 600 em-I. The multiple bands are due to coupling of
the CI-H stretching mode to ring vibrational modes.
As the proton affinity of the base increases further, proton transfer occurs in the
complexes CIH:4-S-- pyridine and CIH:4-0--pyridine. The CI-N distance and the proton 
stretching frequency increase relative to complexes with proton-shared hydrogen bonds,
x= eN
x ::: F
X ::: Cl
x ::: H
X:: CH3
X ::: II
:x =Na
X::: s-
x::: 0-
I
3400
2524
1
1
2434
1
2324
1
2271
1
2636
1
2826
,
2560
OJ •
J700
,
850
4
Cl-H....N
Cl...H...N
} Cl..•.Fi-N
o
WAVENUMBER (em-i)
Figure 1: Computed harmonic vibrational spectra of ClH:4-R-pyridine complexes, from
reference 6.
5
and the N-H distance continues to decrease. The single strong band in the IR spectra
corresponds to an N-H+ stretch, shifted downfield relative to the corresponding
pyridinium ion.
In related studies, Del Bene and Jordan examined hydrogen-bonded complexes
between hydrogen halides as proton donors and NH
3
and N(CH
3
)3 as proton
acceptors.
26
,27 Examples of traditional, proton-shared and ion-pair hydrogen bonds were
found. Systematic studies such as those reported for complexes with hydrogen halides
have not been carried out on complexes with N-H-N hydrogen bonds. Therefore, in this
project hydrogen-bonded complexes of pyrrole and substituted pyrroles with various
nitrogen bases will be investigated. The proton-donating ability and proton-accepting
ability of the hydrogen-bonded pair will be systematically varied by chemical substitution
in an attempt to span the three hydrogen bond types.
Ab initio calculations on isolated pyrrole have been carried out, and optimized
structures and harmonic vibrational spectra were reported.
28
,29 The only study of
hydrogen-bonded complexes with pyrrole was reported by Jiang and Tsai.
3o
These
authors obtained structures and harmonic vibrational frequencies for pyrrole:HF
complexes using second-order M(25ller-Plesset perturbation theory and density functional
theory with various basis sets.
Aims of Study:
The current ab initio study focuses on N-H-N hydrogen bonds. Therefore in
this work complexes with pyrroles and disubstituted pyrroles as proton donors to a series
of nitrogen bases will be investigated. The complexes can be represented as
6
y
z
N-H"'B
a
z
y
where Y may be H, F, or Be+ and Z is H, giving 2,5-disubstituted pyrroles; or Z is H, F,
or Be+ and Y is H, giving 3,4-disubstituted pyrroles. The nitrogen bases Bare HCN and
its derivatives, LiCN, NaCN, SCN-, and OCN-, as well as NH
3
and N(CH
3
h.
The specific aims of this work are
1. to systematically vary the proton-donating and proton-accepting abilities of
the hydrogen-bonded pair in an attempt to span the three hydrogen bond
types;
2. to determine the optimized MP2/6-31+G(d,p) structures of the monomers and
complexes;
3. to calculate the harmonic vibrational spectra of monomers and complexes at
the same level of theory;
4. to examine the effect of hydrogen bonding on the frequency and intensity of
the proton-stretching band;
5. to correlate structural and spectroscopic properties with binding energies and
hydrogen bond type;
7
6. to determine whether proton-shared or ion-pair hydrogen bonds can be formed
in neutral complexes with N-H-N hydrogen bonds.
II. METHODS:
In order to calculate the electronic energy and electron distribution of a molecule,
the wavefunction '¥ must be known. Both the energy E, and the wavefunction '¥, can be
obtained by solving the nonrelativistic time-independent Schr6dinger equation
H'¥ =E '¥
where H is the Hamiltonian operator. The Hamiltonian is defined as
H=T+V
where T is the kinetic energy operator and V the potential energy operator. The
(1)
(2)
Hamiltonian operator in atomic units for n electrons in a field of m fixed nuclei is written
as
31
-
33
1 11. 2
H= --1:: 'V.
2 i 1
11. 11. 1
+1::1:: 
i<:j f
ij
11. In Z. In m Z Z
1:: 1:: _n+ 1:: 1:: _A_B
i A f iA A <: B R
AB
(3)
where the first term is the kinetic energy operator, and the remaining terms are the terms
of the potential energy operator including the repulsion between each pair of electrons,
the nuclear-electron attraction, and the nuclear-nuclear repulsion, respectively. The
8
Schr6dinger equation can be solved exactly only for the hydrogen atom or any one 
electron system. However, the results of this exact solution, namely the hydrogen atomic
orbitals, are useful as a starting point for calculating the electronic distribution of other
atoms and molecules which have more than one electron.
33
,34
In this study, ab initio calculations will be performed to determine 'P and E. Ab
initio means, "from first principles", that is, using only the fundamental constants and the
atomic numbers of the nuclei, with no other adjustable parameters or data from
experiment. However, within the ab initio framework it is necessary to choose a basis set
to describe the atomic orbitals, and a wavefunction model. These will now be discussed
in general, and the wavefunction model and basis set that will be used in this study will
be identified.
Basis sets:
A basis set is a set of mathematical functions that describe orbitals on atoms.
Basis sets are of three general types: minimal, split-valence, and augmented. A minimal
basis set contains one basis function to describe each orbital of an atom in the valence
shell and below. The advantage of using a minimal basis set is that the number of
coefficients to be determined variationally is small, and this reduces the computational
problem. However, the disadvantages are that the number of basis functions is not
proportional to the number of electrons, anisotropic molecular environments are not
correctly represented, and polarization effects are usually not well-described.
3
!
An improvement over a minimal basis set is a double-zeta (DZ) or triple-zeta
(TZ) basis set. In a DZ basis set, each orbital in the valence shell and below is
9
represented by two basis functions, while for a TZ basis set each orbital is replaced by
three basis functions. These basis sets are now twice and three times larger than a
minimal basis set, respectively, and this increases the computational task.
A valence double-split basis set is a DZ basis for orbitals in the valence space, but
only a single basis function for each orbital below the valence shell. Similarly, a valence
triple-split basis set is a TZ basis set for the valence shell, but has only one basis function
per inner shell orbital. The most popular double-split valence basis set used as a starting
point to construct larger basis sets is the 6-31G basis set,31 which contains one set of
inner shell functions for each atomic orbital below the valence shell, and two sets of
valence shell atomic functions. For example, for C, the 6-31G basis set has one function
to describe the inner shell Is orbital, and two sets of sand p functions to describe the
valence shell. The notation 6-31G means 6 gaussian functions are used to describe each
inner shell function, 3 gaussians are used to describe each valence shell orbital in the first
set, and 1 gaussian is used for each function in the second set. However, these basis
functions are still severely limited.
22
,31
In a molecular environment atomic orbitals are distorted and polarized due to the
formation of bonds. To account for this nonuniform displacement of charge away from
the nuclear center, basis functions are added with angular momentum quantum number~
one greater than the maximum value found in the valence shell. For carbon this means
adding a set of d orbitals(~=2),and for hydrogen a set of p orbitals(~=1).The newly
added functions are called polarization functions, and are required to describe anisotropic
environments. Adding polarization functions to the 6-31G basis set gives 6-31G(d,p),
10
where one set of six Cartesian d functions are added to each nonhydrogen atom, and one
set of p functions to each H atom.
Further basis set improvements are made by adding diffuse functions. These are
important for describing negatively charged species, lone pairs ofelectrons, and 11:
electrons
31
. The diffuse basis functions are of sand p type for nonhydrogen atoms, and s
for hydrogen. They have exponents that are considerably smaller than the other valence
basis functions and provide a better description of electron density far removed from the
nuclear centers. The notation for basis sets augmented with diffuse functions is a "+"
symbol for diffuse functions on heavy atoms, and "++" for diffuse functions on
hydrogen as well. Thus, the 6-31+G(d,p) basis set is an augmented valence double-split
basis set with polarization functions on all atoms and diffuse functions on nonhydrogen
atoms.
Wavefunction models:
Before discussing the wavefunction model in detail it is important to note that
1 1
electrons have spin ( + 2or - 2)' and that electron spin must be incorporated into 'P.
The spin angular momentum is represented by a vector s that has the components of sx, Sy
and Sz. Since these components follow the commutation relations of general angular
momentum, only S2, the magnitude of the vector s and one other component (sx, Sy or sz)
can be determined simultaneously. The z-axis component is normally chosen as this
component. Thus, a one-electron wavefunction must describe both space and spin
coordinates. If 1Vj (i) describes the spatial coordinates of electron i, the spin coordinate is
described by31,33
1
Sz a(i) = +"211 a(i)
Sz~(i)= -~11~(i)
11
(4)
(5)
h
where 11-
2n
and Sz is the operator of the spin angular momentum component along the z-
axis. The many-electron wavefunction 'P must also be an eigenfunction ofthe many-
electron spin operators S2 and Sz, whose eigenrelations may be written as
33
S2 'P = S(S+1)'P
where M
s
is the sum of the individual spin eigenvalues (m
s
).
(6)
(7)
(8)
S, the total resultant spin angular momentum, may have any positive half-integral value
(0, Yz, 1,3/2,....), and M
s
is the component of S along the z-axis. For a given resultant
spin S there are 2S+1 possible M
s
values. The quantity (2S+1) is the multiplicity. Thus
for total S=O, the multiplicity is one (singlet, nondegenerate state). For S=1I2, (2S+1) is
2 (doublet, doubly-degenerate state), for S=l, 2S+1 is 3, (triplet, triply-degenerate state),
and so forth.
The total wavefunction 'P must describe both the space and spin coordinates of all
the electrons, and must satisfy two requirements. The first requirement is that 'P must be
~(i)~~(i)~(i)~~(i)
12
antisymmetric. Antisymrnetry means that if two electrons are interchanged, then the
wavefunction must change sign. The second requirement is that the Pauli exclusion
principle must be obeyed. This means that no two electrons can be assigned to identical
spinorbitals. These two conditions are most easily satisfied if the wavefunction is
represented as a determinant, specifically the Slater determinant, which for an n-electron
system with n even and no orbital degeneracies, is
- - -
l.hO) l.hO) *2(1) *20), ···,··, ljIn/2(l) *n/2(1)
* 1(2) *1(2) *2(2) *2(2) ljIn/2(2) *n/2(2)
"PO ,2, ... ,n) =(n !/112
- - -
ljI 1(n) * 1(n) * zCn) * 2(n) ... .. .. .... ljIn/2 (n) *n/2(n)
where '4Ji (a) represents the spinorbital
(9)
(10)
and '4Ji (a) represents the spinorbital
(11)
In the Slater determinant the first row assigns electron one to all the possible spinorbitals,
while the second row assigns electron two to all possible spinorbitals, and so forth. Each
column assigns all electrons to a given spinorbital. Thus, the Slater determinant satisfies
the Pauli-Exclusion Principle, since if two rows or two columns are identical then the
13
determinant is zero. It also maintains antisymmetry, since if rows i and j are
interchanged the sign of the determinant changes.
In order to obtain the best single-determinant wavefunction 'P, the Hartree-Fock
method is used.
31
-
34
The Hartree-Fock method is a variational method used to determine
a set of molecular orbitals (MOs) in terms of a linear combination of atomic orbitals (the
LCAO approximation). The LCAO approximation can be written as
p
llr. = >. c . c.p
'+'1 1l';;)).Il~
(12)
where 1)ri is the molecular orbital,C~iare the expansion coefficients, and 'PI> 'Pz ,..., 'P
p
are
the atomic basis functions. The expansion coefficientsC~iare determined by the
variational method, which minimizes the energy E with respect to the coefficientsC~i.
d<E>
---=0
dC~i
(13)
In carrying out a Hartree-Fock calculation, an initial set of coefficients is chosen
and used to construct the Fock matrix. This matrix is diagonalized, and a new set of
coefficients is obtained. This process is repeated until the coefficients from two
consecutive iterations are identical to within a given tolerance. The Hartree-Fock method
is a self-consistent field (SCF) method, which means that the molecular orbitals are
derived from their own effective potential. The Hartree-Fock energy is the lowest energy
that can be obtained from a single determinant wavefunction with a given nuclear
configuration and basis set.
31
-
34
It is guaranteed to be an upper bound to the exact energy.
C~iC~i
14
Moreover, the Hartree-Fock wavefunction is size-consistent, which means that if a
system of several molecules is infinitely separated, the energy computed at infinite
separation is equal to the sum of these energies computed for the isolated
molecules.22,31 ,32,34
The most severe limitation of the Hartree-Fock method is that it describes an
average (SCF) potential for the electrons.
31
-
34
The model does not properly consider
instantaneous interaction between electrons. This is a particular problem for two
electrons in the same orbital, which on average are too close to each other. As a result,
the Hartree-Fock energy is always too high. The difference between the Hartree-Fock
energy and the true energy of the system is referred to as the electron correlation error.
There has been a great effort in quantum chemistry to improve the Hartree-Fock
wavefunction and energy by explicitly treating the electron correlation problem. The
most rigorous and straightforward way of doing this is through configuration interaction.
In a configuration interaction (CI) treatment, the wavefunction <1> is written as
32
,34
~= Co 'pO +~Cit 'Pt + ,2::, cijab 'P
ij
ab
+ 2:: Cijk abc 'Pijkabc + "',"
l.a lS.J is.j<:k
ts.b as.b<c
where~is the Hartree-Fock reference wavefunction, 'Pia represents all possible
(14)
excitations from orbital i which is doubly occupied in~to unoccupied (virtual) orbital a,
'P
i
/
b
represents all possible two-electron excitations, 'PijkabC all three electron excitations,
and so forth. The expansion coefficients are again determined variationally. If all
possible n-electron excitations are included, the resulting wavefunction <1> is a full CI
wavefunction, which is the exact solution of the Schrbdinger equation with a given basis
~
~
~
~
15
set. Unfortunately, full CI calculations are feasible only for extremely small molecules or
molecular ions?2,31,32,34 Therefore, in practice, it is necessary to approximate the full CI
wavefunction in some way.
The most commonly used methods for obtaining correlated wavefunctions are CI
truncated to singles and doubles (CISD), coupled cluster (CC) theory, and M\Zlller-Plesset
perturbation theory truncated to some order n (MPn).
CISD is a computationally feasible method for moderate size systems, is
variational, but is not size consistent.
22
,31,32,34 For hydrogen-bonded complexes this is a
significant problem since it yields incorrect binding energies. In fact, the computed
binding energy is often positive, which means that the complex is not bound at all.
Therefore, the CISD method is not recommended for hydrogen-bonded systems?2
The second method is the coupled cluster (CC) method in which the Hamiltonian
is written in exponential form.
32
There are various levels of CC theory, including
coupled cluster singles and doubles (CCSD); CCSD(T), which includes non-iterative
triples; CCSDT which includes full triples, and CCSDTQ, which includes triples and
quadruples. Because of the exponential ansatz, CC methods are size consistent, but they
are not variational. CC methods are most reliable, but are computationally demanding
and therefore not feasible for large systems such as those that will be investigated in this
work.
22
,32
In M\Zlller-Plesset (MP) theory, correlation effects are treated as a perturbation
using many-body perturbation theory. M\Zlller-Plesset theory is widely used to investigate
hydrogen-bonded complexes, since it is size consistent.
22
,31,32,34 However, MP
calculations are not variational, and the MP expansion may converge slowly.
16
In M¢ller-Plesset perturbation theory the generalized electronic Hamiltonian is
written as
3
!
1\ 1\
(15)
where Ho is the unperturbed Hamiltonian, and the perturbation AV, is defined by
1V=1(H-Ho)
(16)
H is the correct Hamiltonian and Ais a dimensionless parameter. The unperturbed or
1\
zero Hamiltonian H
o
is taken to be the sum of the one-electron Fock operators. The exact
or full CI wavefunction ('Fl) and energy (E
l
) may be written in powers ofA.
In practical applications the parameter Ais set equal to 1, and the series truncated at
various orders. The method used is referred to by the highest term considered. For
instance, if the series is truncated after the second order correction, it is referred to as
MP2, if it is truncated after third order it is MP3, and so forth. The first terms in the
expansion are
3
!
(17)
(18)
(19)
17
(20)
(21)
where 'Po is the Hartree-Fock wavefunction, E(O) is the Hartree-Fock energy, and Ci are the
one-electron energies of the occupied molecular orbitals (1JrD at Hartree-Fock. Therefore,
the MP energy to first order is the Hartree-Fock energy. The first-order contribution to
the wavefunction is
(22)
where E
s
is the eigenvalue of a particular doubly-substituted determinant 'P
s
, while V
so
1\
are matrix elements of the perturbation operator V, represented by
(23)
The integration is over all space and spin coordinates of the electrons. By Brillouin's
theorem, the first-order energy corrections do not change the Hartree-Fock energy, since
the Hamiltonian matrix elements between the Hartree-Fock wavefunction and singly-
excited determinants are zero.
The second-order M¢ller-Plesset energy can be expressed as
(24)
where (ij I Iab) is a two-electron integral over spin-orbitals defined by
18
and the integration is over all space and spin coordinates of the electrons.
Level of Theory for Studies of Hydrogen-bonded Complexes:
There have been many studies carried out on hydrogen-bonded complexes to
establish what level of theory gives reliable structures and binding energies at minimal
computational expense.
22
,35-40 It has been shown that for hydrogen-bonded complexes,
the MP energy expansion is dominated by the second-order term, while the third and
fourth order contributions are small and may even be of opposite sign. Thus, MP2 with
an appropriate basis set adequately describes the energy of hydrogen-bonded systems
with minimal computational effort. The smallest basis set required is a split-valence basis
set augmented with polarization functions on all atoms and diffuse functions on
nonhydrogen atoms?2,35-38 The MP2/6-31+G(d,p) level of theory has also been found to
produce reliable structures and vibrational frequency shifts of the proton-stretching band
in good agreement with experimental data, provided that anharmonicity corrections are
not large.
7
,22 Binding energies at this level are reasonable, but are usually too high.
Improved energies require a larger basis set, and in some cases a better
wavefunction.22.35-40 In the current study, the MP2/6-31+G(d,p) level of theory will be
used to determine structures, vibrational frequencies and binding energies. Although the
binding energies may be too high, trends in binding energies in a closely related series of
complexes have been shown to be reliable.
5
,6,22
Geometry Optimization:
The geometries of the monomers were fully optimized using the Gaussian 98
41
program at the MP2/6-31+G(d,p) level of theory. The nitrogen bases HCN, LiCN,
19
NaCN, SCN- and OCN- are linear, with C
oov
symmetry, and the bases NH
3
and N(CH
3
)3
have C
3v
symmetry. Pyrrole and the 2,5- and 3,4-disustituted pyrroles have C
2v
symmetry.
The complexes of pyrrole and the 2,5- and 3,4-disubstituted pyrroles with HCN,
LiCN, NaCN, SCN- and OCN- were optimized at the MP2/6-31+G(d,p) level of theory
under the constraint of C
2v
symmetry. The complexes with NH
3
and N(CH
3
)3 have C
s
symmetry, but local C
2v
symmetry was imposed on pyrrole or the disubstituted pyrrole,
and local C
3v
symmetry on NH
3
and N(CH
3
)3. These restrictions maintain the linearity of
the hydrogen bond. Vibrational frequencies were computed to verify that these
optimized structures are equilibrium structures on their respective potential energy
surfaces.
For selected complexes of pyrrole with NH
3
and N(CH
3
h, two rotamers of C
s
symmetry were optimized. In one rotamer, one hydrogen of NH
3
or one carbon of
N(CH
3
)3 was placed in the plane of the pyrrole ring. In the second rotamer, the NH
3
or
N(CH
3
)3 molecule was rotated 90 degrees from the previous conformation, so that one
hydrogen or one carbon lies in the symmetry plane perpendicular to the plane of pyrrole.
The rotational energy barrier for interconversion of the rotamers was found to be less
than .01 kcal/mol, signifying that there is free rotation about the hydrogen bonding N-N
axis.
For all complexes except those with NaCN as the proton acceptor, and all
monomers except NaCN, the standard frozen core approximation was used. This
approximation freezes all Hartree-Fock orbitals below the valence shell, which are then
omitted from the correlation calculation. However, for complexes with NaCN as a base,
20
the standard option for freezing inner shell orbitals split degeneracies, or led to small
energy gaps between frozen and active orbitals. To avoid these problems, only Is
orbitals were frozen in complexes with NaCN. This necessitated freezing only Is orbitals
in the NaCN monomer.
Calculation of Harmonic Vibrational Spectra:
Harmonic vibrational frequencies were calculated at the MP/6-31+G(d,p) level of
theory to confirm equilibrium structures, to simulate IR spectra, and to obtain the zero 
point vibrational energies necessary to evaluate binding enthalpies at 10 K. The
harmonic vibrational calculations were done using the standard algorithms for computing
analytical first and second-derivatives implemented in Gaussian 98.
41
Harmonic vibrational calculations can be used to probe the vicinity of the
minimum on the potential energy surface to determine whether a structure is a true
minimum or a saddle point. If no imaginary frequencies exist, then the structure is a true
minimum. If there are imaginary vibrational frequencies, then the optimized structure is
a saddle point of order 1 if there is only one imaginary frequency, two if there are two
imaginary frequencies, three if there are three imaginary frequencies, and so on.
However, if the imaginary frequencies are small, then for the complexes investigated in
this study, the optimized structures must be transition structures between two equivalent
equilibrium structures, and the optimized structure is the vibrationally averaged structure.
On the other hand, if the imaginary frequency is large, then the optimized structure is not
close to the equilibrium structure, and a full optimization can yield significant geometry
and energy changes.
21
Reaction Energies:
The reaction for the formation of a hydrogen-bonded complex can be written as
A-H(g) + B(g) ---+ A-H:B(g)
Since the vibrational spectra of hydrogen-bonded complexes are usually obtained in low
temperature matrices (-10K), the reaction enthalpy at this temperature can be
approximated as the enthalpy at OK, and~Homay be written as
~HI0~~Eeo+~Ev0
where~Eeois the electronic binding energy and~Ev°is zero-point energy contribution to
~Ho.The electronic binding energy(~Eeo)is the difference between the electronic
energy of the hydrogen-bonded complex [E
e
o (A-H:B)], and the electronic energies of the
two monomers, E
e
o (A-H) and E
e
o (B).
~Eeo=E
e
o (A-H:B) - E
e
o (A) - E
e
o (B) (29)
The zero point energy contribution~Ev°,is evaluated as the difference between the zero 
point energy of the hydrogen-bonded complex a.o (A-H:B) and the zero-point energies of
the isolated monomers, Ev° (A-H) and Ev° (B)
~Ev°=Ev° (A-H:B) - Ev° (A) - Ev° (B) (30)
To determine the basicities of the proton-acceptor molecules, the electronic
proton affinity (PA) was evaluated at OK. The protonation reaction can be written as
The electronic energy of this reaction is
~Eeo(PA) = Eeo(B-W) - Eeo(B)
(31)
(32)
where Eeo(B-W) is the electronic energy ofthe protonated base and Eeo(B) is the
electronic energy ofthe base B.~Eeo(PA) for equation 32 is always negative. However,
~HI0~~Eeo~Ev0
~Ho.
~Eeo=
~Ev°=
~Eeo
~Eeo
~HI0~~Eeo~Ev0
~Ho.
~Eeo=
~Ev°=
~Eeo
~Eeo
22
since the proton affinity at 298K is defined as the negative energy (-i1E
PA
O) for reaction
31, the computed electronic proton affinities will be reported as positive numbers.
III. RESULTS and DISCUSSION:
The MP2/6-31+G(d,p) electronic energy (Beo), zero-point vibrational energy
(Eyo), equilibrium Na-H distance [Re(Na-H)], proton-stretching frequency (v) and intensity
of the proton-stretching band (I) for pyrrole and disubstituted pyrroles are presented in
Table 1. The Na-H distances, frequencies, and intensities are given as reference data so
that changes in these quantities due to hydrogen bonding can be seen. Pyrrole and the
disubstituted pyrroles are listed in order of increasing acidity as determined by their
binding energy to HCN.
Table 2 presents electronic energies (E
e
o), zero-point vibrational energies (By),
and electronic proton affinities (-i1E
pA
0) of the nitrogen bases. The bases, HCN and its
derivatives, are arranged in order of increasing basicity as evaluated from their electronic
proton affinities. The bases NH
3
and N(CH
3
)3 are also listed in Table 2.
Table 3 presents the electronic energies, zero-point vibrational energies and
imaginary frequency data for all of the complexes of pyrrole and disubstituted pyrroles
with HCN and its derivatives that have been investigated in this study. An entry of "0" in
the last column indicates that there are no imaginary frequencies. This means that the
optimized structure is an equilibrium structure on the potential energy surface. There are
some complexes listed in Table 3 that have small imaginary frequencies. The complexes
pyrrole:NCS-, pyrrole:NCO-, 3,4-difluoropyrrole:NCS-, 3,4-difluoropyrrole:NCO-, 2,5 
difluoropyrrole:NCS-and 2,5-difluoropyrrole:NCO- have a small imaginary frequency,
23
Table 1. MP2/6-31+G(d,p) electronic energies (Eeo, amu), zero-point vibrational energies
(Evo, kcal/mol), Na-H distances (R
e
, A), harmonic proton-stretching frequencies
('0, em-I) and band intensities (I, km/mol) for pyrrole and disubstituted pyrroles
Monomer
E
e
o E
v
o
Re(Na-H) '0 I
Pyrrole -209.53768 52.0 1.007 3735 80
3,4-difluoropyrrole -407.55477 41.8 1.006 3745 110
2,5-difluoropyrrole -407.55947 41.6 1.008 3730 149
2,5-diberylliumpyrrole+
2
-236.92122 40.8 1.012 3673 141
3,4-diberylliumpyrrole+2 -236.92778 41.0 1.017 3620 295
24
Table 2. MP2/6-31+G(d,p) electronic energies (E
e
o, amu), zero-point vibrational energies
(Evo, kcal/mol), and electronic proton affinities(~EpAO,kcal/mol) for the nitrogen
bases
Monomer
E
e
o E
v
o
-~EpA
°
HCN - 93.17212 9.9 174.3
LiCN -100.07104 4.3 228.5
NaCN -254.46613 4.0 236.7
SCN-
-490.29666 5.1 326.4
OCN-
-167.69373 6.4 343.7
NH
3
- 56.39205
-173.91095
22.1
77.6
214.7
236.5
-~EpA-~EpA
Table 3. MP2/6-31+G(d,p) electronic energies (E
e
o, amu), zero-point vibrational
energies (E
v
o, kcal/mol), and frequency data for complexes of pyrrole
and substituted pyrroles with HCN and its derivatives
25
Donor
a
Acceptor
E
e
o E
v
o
Imaginary frequencies
b
Py HCN -302.71818 62.7 0
LiCN -309.62486 57.2 0
NaCN -464.02228 57.0 0
SCN-
1
-699.86388 57.6
_ 30
c
,
- 14
d
OCN-
1
-377.26720 58.9
_20
c
3,4-diFPy HCN -500.73713 52.5 0
LiCN -507.64592 47.0 0
NaCN -662.04392 46.8 0
SCN-
1
-897.88985 47.3
_ 31 c _ 14
d
,
OCN-
1
-575.29456 48.6
_21 c
2,5-diFPy HCN -500.74210 52.4 0
LiCN -507.65034 46.8 0
NaCN -662.04836 46.6 0
SCN-
1
-897.89082 46.8
_31 c
OCN-
1
-575.29598 47.7
_24
c
3,4-diBePy+2
HCN -330.13341 51.7 0
LiCN -337.07294 44.7 0
NaCN -491.48087 43.8
_42
e
SCN-
l
-727.48058 43.8 -252
f
-214
g
_105
h
, ,
OCN-
l
-404.89957 45.5 -244
f
, -238
g
, _108
h
2,5-diBePy+2 HCN -330.12815 51.7
_ 31
i
LiCN -337.07249 45.5
_ 83
i
a) Py = pyrrole
b) An entry of 0 means that there are no imaginary frequencies; frequencies in cm,l.
c) Change ofhybridization at the proton acceptor N coupled with pyrrole ring puckering out of the plane of pyrrole
d) Change ofhybridization at the proton acceptor N coupled with an in-plane bending mode of the pyrrole ring
e) Ring puckering of the substituted pyrrole out of the plane
f) Change ofhybridization at the proton acceptor N coupled with pyrrole ring puckering out of the plane of pyrrole
g) Change ofhybridization at the proton acceptor N coupled with an in-plane bending mode of the pyrrole ring.
h) Ring puckering mode out ofthe plane of pyrrole
i) In-plane rotation of the substituted pyrrole due to strong interactions of Be+ with the electron pair on the nitrogen of
the proton acceptor
26
which corresponds to bending the proton acceptor out of the plane of the pyrrole ring,
indicating a hybridization change of the nitrogen of NCO· and NCS·. This bending is
coupled to a slight ring puckering of the pyrrole ring. The imaginary frequencies range
from -31 cm-
1
for 2,5-difluoropyrrole:NCS· and 3,4-difluoropyrrole:NCS-, to -20 cm·
1
for pyrrole:NCO·. The imaginary frequencies of -14 cm-
I
for pyrrole:NCS· and 3,4 
difluoropyrrole:NCS· correspond to an in-plane proton acceptor bend, also signifying a
hybridization change of the NCS· nitrogen. This motion is coupled to in-plane bending
of the pyrrole ring. The imaginary frequency of-42 cm-
1
for 3,4 
diberylliumpyrrole:NCNa+
2
corresponds to an out-of-plane ring puckering of the pyrrole
ring. As noted previously, structures with imaginary frequencies correspond to transition
structures on the surface, but if the imaginary frequency is small, the optimized planar
structure is the vibrationally averaged structure. Thus, complexes that have small
imaginary frequencies « 50 cm·
l
) have been included in this work for comparative
purposes.
The complexes of 3,4-diberylliumpyrrole:NCS+
1
and 3,4 
diberylliumpyrrole:NCO+
1
have large imaginary frequencies, and these complexes have
not been included in this study. The complexes 2,5-diberylliumpyrrole:NCH+
2
and 2,5 
diberylliumpyrrole:NCLi+
2
have imaginary frequencies corresponding to rotations that
break the hydrogen bond and make Be+the electron pair acceptor. Thus, these two
complexes have not been included in this work.
Table 4 reports the electronic energies, zero-point vibrational energies, and
imaginary frequency data for complexes of pyrrole and disubstituted pyrroles with NH
3
and N(CH
3
h. Except for 2,5-diberylliumpyrrole:N(CH
3
)3+2, the single imaginary
Table 4: MP2/6-31+G(d,p) electronic energies (Eeo, amu), zero-point vibrational
energies (E
v
o, kcal/mol), and frequency data for complexes of pyrrole and
disubstituted pyrroles with NH
3
and N(CH
3
)3.
Donor
a
Acceptor
E
e
o E
v
o
Imaginary frequencies
b
Py NH
3
c
-265.94341 75.8 0
NH
3
d
-265.94341
3,4-diFPy NH
3
c
-463.96290 65.6 - 18
e
NH
3
d
-463.96290
Py N(CH3h
C
-383.46481 130.4
_ 14
e
N(CH3h
d
-383.46481
2,5-diFPy NH
3
c
-463.96952 65.4 - 7
e
NH
3
d
-463.96951
3,4-diFPy N(CH3)3
C
-581.48445 120.2 0
2,5-diBepy+2 NH
3
c
-293.34999 64.5
_ Be
NH
3
d
-293.34999
2,5-diFPy N(CH3)3
C
-581.49261 119.9 0
3,4-diBepy+2 NH
3
c
-293.36161 64.0 0
NH
3
d
-293.36161
2,5-diBePl
2
N(CH3)3C -410.88485 118.8
_40
f
-12
e
,
N(CH3h
d
-410.88483
3,4-diBePy+2 N(CH3)3
C
-410.91210 119.9 0
N(CH3)3
d
-410.91209
a) Py =pyrrole
b) An entry of0 means that there are no imaginary frequencies; frequencies in em-I.
c) Proton acceptor with one H or one C in the plane of the pyrrole
d) Proton acceptor with one H or one C in the plane perpendicular to the plane of the pyrrole
e) Rotation of proton acceptor
f) Ring puckering of the substituted pyrrole out of the plane of pyrrole ring
27
28
frequency in some of these complexes corresponds to rotation of the proton acceptor
molecule about the hydrogen-bonding axis. However, the energies of the two rotamers,
one with an H of NH
3
or a C of N(CH
3
h in the plane of the pyrrole ring, and the other
with an H of NH
3
or a C of N(CH
3
)3 in the plane perpendicular to the plane of the pyrrole
ring, are identical, as evident from Table 4. This indicates that there is free rotation of the
proton acceptor molecule about the hydrogen bonding N-N axis. The complexes with the
N-H or N-C bonds in the plane of the pyrrole ring will be discussed below. The complex
2,5-diberylliumpyrrole:N(CH
3
)3+
2
has two imaginary frequencies. The frequency of -12
cm-
1
corresponds to rotation of N(CH
3
)3 about the hydrogen-bonding axis. The
frequency of -40 cm-
1
corresponds to a ring puckering vibration. However, since these
frequencies are small, this complex has been included in this study. The energies in
Tables 1-4 are given as raw data from which binding energies and enthalpies can be
computed. The z-matrices for the optimized monomers and complexes are given in
Appendix 1 and 2, respectively. The binding enthalpies for the complexes are reported in
Appendix 3.
Table 5 reports equilibrium Na-N
b
distances [Re(Na-N
b
)], Na-H distances
[Re(Na-H)], electronic binding energies(~Ee),harmonic proton-stretching frequencies (u)
and intensities of the proton-stretching band (I) for complexes of pyrrole and
disubstituted pyrroles with HCN and its derivatives. The complexes are arranged in order
of increasing acidity of pyrrole and disubstituted pyrroles as determined by their binding
energy with HCN. For a given proton donor, the complexes are arranged in order of
increasing base strength as determined by the electronic proton affinity of the proton
acceptor.
Table 5. MP2/6-31+G(d,p) Na-N
b
and Na-H distances (R
e
, A), electronic binding
energies(~Ee,kcal/mol), harmonic proton-stretching frequencies (u, em-I)
and band intensities (I, km/mol) for complexes of pyrrole and substituted
pyrroles with HCN and its derivatives.
Donor
a
Acceptor Re(Na-N
b
) Re(Na-H)b~EeIv
Py HCN 3.164 1.011 - 5.3 3671 466
LiCN 3.010 1.019 -10.1 3527 989
NaCN 2.971 1.021 -11.6 3483 1171
SCN-
I
2.835 1.037 -18.5 3198 2653
OCN-
I
2.762 1.048 -22.5 2993 2761
3,4-diFPy HCN 3.115 1.012 - 6.4 3656 591
LiCN 2.956 1.022 -12.6 3472 1249
NaCN 2.916 1.025 -14.4 3414 1477
SCN-
I
2.770 1.045 -24.1 3034 3388
OCN-
I
2.699 1.061 -28.9 2767 3442
2,5-diFPy HCN 3.068 1.016 - 6.6 3594 777
LiCN 2.906 1.029 -12.4 3343 1662
NaCN 2.863 1.033 -14.3 3260 2023
SCN-
I
2.713 1.065 -21.8 2710 4750
OCN-
I
2.629 1.097 -26.9 2202 6340
3,4-diBePl
2
HCN 2.828 1.043 -21.0 3127 2706
LiCN 2.603 1.119 -46.5 1924 6469
NaCN
c
2.666 1.557 -54.6 1871 2836
2473 4208
a) Py = pyrrole
b) The Na-H distance is measured from the pyrrole nitrogen.
c) There are two strong bands associated with the Na-H stretching mode in this complex.
29
~Ee~Ee
30
The first set of complexes in Table 5 are those with pyrrole as the proton donor.
Table 5 shows that for these complexes as the base strength increases, the binding energy
increases. The binding energies range from -5.3 kcal/mol for the weakest hydrogen 
bonded complex pyrrole:NCH, to -22.5 kcal/mol for the strongest, pyrrole:NCO-. As
evident from Table 5, as the binding energy increases the Na-H distance also increases
from 1.011 Ain pyrrole:NCH to 1.048 Ain pyrro1e:NCO-. These Na-H bond distances
are all greater than the Na-H distance in isolated pyrrole (1.007 A). The lengthening of
the Na-H bond is a consequence of hydrogen bonding. Moreover, the lengthening of the
Na-H distance is also accompanied by a decrease in the Na-N
b
distance, which ranges
from 3.164 Ain pyrrole:NCH to 2.762 Ain pyrrole:NCO-. Figure 2 illustrates the
variation of the Na-H and Na-N
b
distances with binding energy. These data show that as
the binding energy increases, the hydrogen moves away from N
a
towards N
b
. This is the
beginning of proton transfer, which is facilitated by a decrease in the Na-N
b
distance.
The IR properties of the complexes of pyrrole with HCN and its derivatives may
also be related to their structural and energetic properties. As the base strength increases,
the proton-stretching frequency decreases, and the intensity of the proton-stretching band
increases. The proton-stretching frequency and the intensity of the proton-stretching
band for isolated pyrrole are 3735 cm-
1
and 80 km/mol, respectively. The proton 
stretching frequency decreases from 3671 cm-
1
in pyrrole:NCH to 2993 cm-
1
in
pyrrole:NCO-. At the same time, the intensity of the proton-stretching band increases
from 466 km/mol in pyrrole:NCH to 2761 km/mol in pyrrole:NCO-. The frequency
2.85
3.15
3.25
-0- Na-H
-l:r- Na-Nb
-23-21-19-11 -13 -15 -17
LlE
e
0
(kcal/mol)
-9-7
Figure 2: Na-N
b
and Na-H distances versus MP2/6-31+G(d,p) binding
1---- , , , , , , , , - , I 2.75
-25-5
1.02
1.01
1.04
1.05
l3.05~
~j
0«
0«
--
~1.03
.0
z
,
co
2.95 z
energies of complexes with pyrrole as the proton donor to HeN and its
derivatives
w
.....
~--..-------.-----r---_--_--..---r------r--.........--~2.75
3.05 ..-
..-
--
I
1.03
I
I
('(l
('(l
z
derivatives
--~
32
shifts and the increased intensities of the proton-stretching band in the complexes relative
to pyrrole are typical of hydrogen-bonded complexes, and are the IR signature of the
hydrogen bond.
The variation in the frequency and intensity of the proton-stretching band for the
complexes with pyrrole as the proton donor is illustrated in Figure 3. The vibrational
spectra are arranged in order of increasing base strength. The intensity of the proton 
stretching band is much greater compared to the other fundamental bands, which cannot
be seen on the scale shown in Figure 3. For the charged complexes of
pyrrole:NCS- and pyrrole:NCO-, one additional relatively intense band at 2015 cm-
1
and
at 2206 cm-
1
, respectively, can be seen. These correspond to monomer NCO- and NCS 
stretching vibrational modes that are essentially unchanged in the complexes. The
spectra in figure 3 illustrate that as the Na-H distance increases, the Na-H bond becomes
weaker. This implies a decrease of the force constant for the Na-H stretch, which leads to
a decrease in the proton-stretching frequency. In addition, as the proton moves towards
the base, the dipole moment of the complex increases. As a result, the intensity of the
proton-stretching band also increases.
The data in Table 5 indicate that complexes with pyrrole as the proton donor to
HCN and its derivatives are stabilized by traditional hydrogen bonds.
42
In these
complexes the Na-H covalent bond remains intact, and the Na-N
b
distances are typical of
complexes stabilized by traditional hydrogen bonds.
42
The spectra of these hydrogen 
bonded complexes are characterized by a single intense proton-stretching band that is
shifted to lower energy relative to the monomer stretching frequency.
33
pyrrole:NCH
4000
r
3000
2300
0
1600~
900-'"
,--__ff-36_7_
1
r-,-------.-----,-----,-----,-----,-----,-------j 200
3500 3000 2500 2000 1500 1000 500 0
v (cm-1)
pyrrole:NCU
4000
[
3000
2300
0
160012
,-- 1--r,35_4_2 ,--- --,-- -----. ,--- --,- -----. :~
3500 3000 2500 2000 1500 1000 500 0
V (cm-1)
pyrrole: NCNa
50010002000 1500
v (cm-1)
25003500 3000
r
3000
2300-
,-- J_
3483
---.- -----r -,----- -,--- -r,---;-_---.--_,----;--__ :1
o4000
50010002000 1500
v (cm-1)
25003500 3000
1
31
", _,NCS t~i
,-------,----.--,..-.---,------!-------.------.-----r-----Il200
o4000
50010002000 1500
v (cm-1)
250030003500
pyrrole:NCO·
I
~f=-1600~
1
900~
,-------,----- -------r-- -----,--------,-----,----------,-------1 200
o4000
Figure 3: MP2/6-31+G(d,p) vibrational spectra ofpyrrole:NCH, pyrrole:NCLi,
pyrrole:NCNa, pyrrole:NCS· and pyrrole:NCO-. Only bands with intensities greater than
250 km/mol are shown.
1600~
~
~
I
~~
~
1600~
~
~
I
~~
~
34
The next set of complexes in Table 5 are those with 3,4-difluoropyrrole as the
proton donor to HCN and its derivatives. For this set of complexes, it is again seen that
as the base strength increases the binding energy increases. The binding energies range
from -6.4 kcal/mol or 3,4-difluoropyrrole:NCH to -28.9 kcal/mol for 3,4 
difluoropyrrole:NCO-. As the binding energy increases, the Na-H distance increases from
1.012 Ain 3,4-difluoropyrrole:NCH to 1.061 Ain 3,4-difluoropyrrole:NCO-. Moreover,
as the Na-H distance increases the Na-N
b
distance decreases from 3.115 Afor 3,4 
difluoropyrrole:NCH to 2.699 Afor 3,4-difluoropyrrole:NCO-. Thus, the same trends in
binding energies, as well as Na-H and Na-N
b
distances, seen previously in the complexes
with pyrrole, are observed in complexes with 3,4-difluoropyrrole.
The IR properties of the complexes of 3,4-difluoropyrrole with HCN and its
derivatives are also related to the structural and energetic properties. As the base strength
increases, the proton-stretching frequency decreases, and the intensity of the proton 
stretching band increases. The 3,4-difluoropyrrole monomer has an Na-H stretching
frequency of 3745 cm-
l
, and the band intensity is 110 km/mol. In the complexes, the
proton-stretching frequency decreases from 3656 cm-
l
in 3,4-difluoropyrrole:NCH to
2767 cm-
l
in 3,4-difluoropyrrole:NCO-. The intensity of the proton-stretching band
increases from 591 km/mol in 3,4-difluoropyrrole:NCH to 3442 km/mol in 3,4 
difluoropyrrole:NCO-. The frequency shifts and increased intensities of the proton 
stretching band in the complexes relative to the monomer are due to hydrogen bonding.
The complexes with 3,4-difluoropyrrole as the proton donor with HCN and its
derivatives are also stabilized by traditional hydrogen bonds. The Na-H distances in these
complexes are characteristic of a perturbed covalent Na-H bond, and the Na-N
b
distances
35
are typical of traditional hydrogen bonds.
42
Furthermore, the vibrational spectra of these
complexes are characterized by a single proton-stretching band which is shifted to lower
energy relative to 3,4-difluoropyrrole.
Data for complexes of 2,5-difluoropyrrole with HCN and its derivatives are also
reported in Table 5. Once again as the base strength increases, the binding energy
increases, the Na-H distance increases, and the Na-N
b
distance decreases. The binding
energies vary from -6.6 kcal/mol for 2,5-difluoropyrrole:NCH to -26.9 kcal/mol for 2,5 
difluoropyrrole:NCO-. The Na-H distances increases from 1.016 Afor 2,5 
difluoropyrrole:NCH to 1.097 Afor 2,5-difluoropyrrole:NCO-. The Na-N
b
distance
decreases from 3.068 Afor 2,5-difluoropyrrole:NCH to 2.629 Afor 2,5 
difluoropyrrole:NCO-. Thus, the same trends in binding energies and Na-H and Na-N
b
distances for complexes of pyrrole and 3,4-difluoropyrrole are observed for the
complexes with 2,5-difluoropyrrole.
The IR properties of the complexes of 2,5-difuoropyrrole with HCN and its
derivatives are again related to the structural and energetic properties. As the binding
energy increases, the proton-stretching frequency decreases, and the intensity of the
proton-stretching band increases. The proton-stretching frequency and the intensity of
the proton-stretching band for 2,5-difluoropyrrole are 3730 cm-
1
and 149 km/mol,
respectively. The proton-stretching frequency decreases from 3594 cm-
1
for 2,5 
difluoropyrrole:NCH to 2202 cm-
1
for 2,5-difluoropyrrole:NCO-. The intensity of the
proton-stretching band increases from 777 km/mol for 2,5-difluoropyrrole:NCH to 6340
km/mol for 2,5-difluoropyrrole:NCO-.
36
All the complexes of 2,5-difluoropyrrole as the proton donor to HCN and its
derivatives, except 2,5-difluoropyrrole:NCO-, are stabilized by traditional hydrogen
bonds. The Na-H distances and Na-N
b
distances of these complexes are typical of
traditional hydrogen bonds,42 and their vibrational spectra are characterized by a single
intense proton-stretching band that is shifted to lower energy relative to the Na-H stretch
of the 3,4-difluoropyrrole monomer.
The complex 2,5-difluoropyrrole:NCO' has an Na-H distance of 1.097 A, and a
very short Na-N
b
distance of 2.629 A. These distances are approaching distances found
for proton-shared N-H-N hydrogen bonds.
42
The Na-H distance of this complex cannot be
simply described as a perturbed Na-H distance. Furthermore, the proton-stretching band
has dramatically shifted to lower energy by 1528 cm'} relative to the 2,5-difluoropyrrole
monomer. This spectral property also indicates that the hydrogen bond in 2,5 
difluoropyrrole:NCO' has proton-shared character. Thus, a hydrogen bond with proton 
shared character is found in this negatively charged complex.
Only three complexes with 3,4-diberylliumpyrrole+
2
as the proton donor are listed
in Table 5. The first is 3,4-diberylliumpyrrole:NCW
2
, which has a binding energy of
-21.0 kcal/mol. The Na-H and Na-N
b
distances for this complex are 1.043 Aand 2.828 A,
respectively, which are comparable to distance seen in complexes with traditional
hydrogen bonds. Furthermore, the vibrational spectrum of this complex is characterized
by a single intense proton-stretching band at 3127 cm'} with a band intensity of 2706
km/mol. These data are typical for a complex stabilized by a traditional hydrogen bond.
The structural, energetic and spectroscopic properties of the complex 3,4 
diberylliumpyrrole:NCLi+
2
are different. The binding energy for this complex has
37
dramatically increased to -46.5 kcal/mol. Furthermore, the Na-H distance has increased
to 1.119 A, and the Na-N
b
distance has decreased to 2.603 A. Thus, this complex has the
longest Na-H distance and shortest Na-N
b
distance observed so far, and is stabilized by a
proton-shared hydrogen bond. For the complex of 3,4-diberylliumpyrrole:NCLi+
2
the
proton-stretching frequency has decreased to 1924 cm-
I
and the intensity of the proton 
stretching band has increased to 6469 km/mol. This frequency is the lowest thus far, and
corresponds to a shift of 1696 cm-
I
relative to 3,4-diberylliumpyrrole+
2
. Thus, both
structural and spectral data for this cationic complex lead to the characterization of the
hydrogen bond as a proton-shared hydrogen bond.
The last complex in Table 5 is 3,4-diberylliumpyrrole:NCNa+
2
. The binding
energy of this complex is -54.6 kcal/mol, the largest in Table 5. The Na-H distance for
this complex has dramatically increased to 1.557 A, and the Na-N
b
distance has increased
to 2.666 Arelative to 3,4-diberylliumpyrrole:NCLi+
2
. Thus, the Nb-H distance is 1.109
A, indicating a perturbed covalent Nb-W bond. Therefore, the hydrogen bond in this
complex is on the ion-pair side of proton-shared. That is, if 3,4 
diberylliumpyrrole:NCLi+
2
and 2,5-difluoropyrrole:NCO- have proton-shared hydrogen
bonds, then 3,4-diberylliumpyrrole:NCNa+
2
must have a hydrogen bond with ion-pair
character. This is also supported by the spectrum of this complex, which is characterized
by two strong proton-stretching bands appearing at 1871 and 2473 em-I, with intensities
of 2836 and 4208 km/mol, respectively. The strongest band at 2473 cm-
l
is at a higher
frequency compared to 3,4-diberylliumpyrrole:NCLi+
2
, further indicating the ion-pair
character of this complex. The proton-stretching band is due to a perturbed Nb-H stretch,
shifted to lower frequency relative to HNCNa+
I
. The fact that there are two bands in the
38
spectrum is due to coupling of the N
b
-H stretch to the N-C stretch of HCNNa+1. The
local N-C stretching band increases in intensity due to intensity borrowing from the Nb-H
stretch.
Complexes of pyrrole and disubstituted pyrroles with NH
3
and trimethylamine
have C
s
symmetry, and binding energies, Na-N
b
and Na-H distances, proton-stretching
frequencies, and intensities of the proton-stretching bands are reported in Table 6. These
complexes are arranged in order of increasing Na-H distance so that changes in hydrogen
bond type can be observed.
The first seven complexes listed in Table 6, namely, pyrrole:NH
3
, 3,4 
difluoropyrrole:NH
3
, pyrrole:N(CH
3
)3, 2,5-difluoropyrrole:NH
3
, 3,4 
difluoropyrrole:N(CH
3
)3, 2,5-diberylliumpyrrole:NH
3
+2 and 2,5-difluoropyrrole:N(CH
3
)3
are stabilized by traditional hydrogen bonds. The Na-H distances for these complexes
increase from 1.021 Afor pyrrole:NH
3
to 1.053 Afor 2,5-difluoropyrrole:N(CH
3
)3, while
the Na-N
b
distances decrease from 3.034 Afor pyrrole:NH
3
to 2.785 Afor 2,5 
difluoropyrrole:N(CH
3
h. These distances correspond to Na-H and Na-N
b
distances
already seen in Table 5 for complexes with traditional hydrogen bonds. The proton 
stretching frequencies for these complexes decrease from 3484 cm-
1
for pyrrole:NH
3
to
2848 cm-
1
for 2,5-difluoropyrrole:N(CH
3
)3, and the intensities of the proton-stretching
bands increase from 862 km/mol for pyrrole:NH
3
to 3237 km/mol for 2,5 
difluoropyrrole:N(CH
3
)3' The vibrational spectra are characterized by a single strong
proton-stretching band consistent with the spectra of complexes with traditional hydrogen
bonds seen in Table 5. It is expected that the binding energies for these complexes
should increase from pyrrole:NH
3
to 2,5-difluoropyrrole:N(CH
3
h. However, this trend is
39
Table 6. MP2/6-31+G(d,p) Na-N
b
and Na-H distances (R
e
, A), electronic
binding energies(.6.E
e
, kcal/mol), harmonic proton-stretching
frequencies (v, em-I) and band intensities (I, km/mol) for complexes of pyrrole
and substituted pyrroles with NH
3
and N(CH
3
)3
Donora Acceptor
ReCN-N)
Re(Na-H)b .6.E
e
v I
Py NH
3
3.034 1.021 - 8.6 3484 862
3,4-diFPy NH
3
2.992 1.023 -10.1 3429 1086
Py N(CH
3
)3 2.931 1.029 -10.1 3305
1453
2,5-diFPy NH
3
2.924 1.032 -11.3 3272 1560
3,4-diFPy N(CH
3
)3 2.881 1.035 -11.8 3196 1773
2,5-diBep/
2
NH
3
2.870 1.050 -23.0
c
2964 1857
2,5-diFPy N(CH
3
)3 2.785 1.053 -13.9 2848 3237
3,4-diBePy+2
NH
3
2.698 1.107 -26.2 2071 5305
2,5-diBep/
2
N(CH
3
)3 2.837 1.773
-33.1c 2772 1972
3,4-diBePy+2
N(CH
3
)3 2.875 1.822 -46.0 2961 2264
a) Py = pyrrole
b) The Na-H distance is measured from the pyrrole nitrogen.
c) Strong electrostatic interactions of Be+ with the nitrogen of the proton acceptor contribute to the large stabilization
energy ofthis complex
40
only observed if 2,5-diberylliumpyrrole:NH
3
is excluded. The binding energy for the
complex 2,5-diberylliumpyrrole:NH
3
+
2
is -23.0 kcal/mol and is greater than the binding
energy of the complex immediately below it in Table 6. The increased stabilization is
due to strong electrostatic interactions of the Be+ atoms with the nitrogen of the proton
acceptor.
The next complex in Table 6 is 3,4-diberylliumpyrrole:NH
3
+2. This complex is
stabilized by a proton-shared hydrogen bond and has a binding energy of -26.2 kcal/mol.
In this complex, the Na-N
b
distance has decreased to 2.698 A, and the Na-H distance has
increased to 1.107 A. Furthermore, the proton-stretching frequency ofthis complex is
2071 cm-
1
and the intensity of the proton-stretching band is 5305 km/mol. The shift
relative to 3,4-diberylliumpyrrole+
2
is 1549 em-I. The Na-H and Na-N
b
distances and
proton stretching frequency are similar to those observed for complexes with proton 
shared hydrogen bonds in Table 5. Therefore, this cationic complex is stabilized by a
proton-shared hydrogen bond.
The last two complexes in Table 6, 2,5-diberylliumpyrrole:N(CH
3
h+
2
and 3,4 
diberylliumpyrrole:N(CH
3
)3+2, are stabilized by ion-pair hydrogen bonds. For these two
complexes the Na-N
b
distances have increased relative to 3,4-diberylliumpyrrole:NH
3
+2 to
2.837 Aand 2.875 A. The Na-H distances are very long at 1.773 Aand 1.822 A,
respectively. Thus, the Nb-W distances are 1.064 Ain 2,5-diberylliumpyrrole:N(CH
3
)3+2
and 1.053 Ain 3,4-diberylliumpyrrole:N(CH
3
)3+2. Thus, the Nb-H+ bond is a perturbed
Nb-H+ bond of protonated trimethylamine. The Nb-H distance in isolated HN(CH
3
)3+1 is
1.024 A. Furthermore, the IR spectra of these complexes are characterized by a single
strong proton-stretching band at 2772 cm-
1
for 2,5-diberylliumpyrrole:N(CH
3
)3+2 and
41
2961 cm-
1
for 3,4-diberylliumpyrrole:N(CH
3
)/2, with band intensities of 1972 kmImol
and 2264 kmImol, respectively. These proton-stretching bands are best described as
arising from perturbed Nb-H+ stretches. These bands are shifted to lower frequency
compared to the proton-stretching frequency of 3501 cm-
1
for HN(CH
3
)3+1. Therefore,
the structural and spectroscopic data for these two complexes indicate that they are
stabilized by ion-pair hydrogen bonds. The binding energies for these complexes are
-33.1 kcal/mol for 2,5-diberylliumpyrrole:N(CH
3
h+
2
and -46.0 kcal/mol for 3,4 
diberylliumpyrrole:N(CH
3
h +2. Thus, ion-pair hydrogen-bonded complexes occur when
the strongest cationic proton donors, 3,4-diberylliumpyrrole+
2
and 2,5 
diberylliumpyrrole+
2
are combined with the strong proton acceptor, N(CH
3
h.
The characteristic changes in the Na-N
b
and Na-H distances and proton-stretching
frequencies that accompany changes in hydrogen bond type are illustrated in Figure 4. In
this figure, the Na-N
b
distance and the proton-stretching frequency are plotted against the
Na-H distance for the series of complexes of pyrrole and disubstituted pyrroles with
ammonia and trimethylamine. At short Na-H distances, traditional hydrogen bonds are
found, and the Na-N
b
distance and the proton-stretching frequency change almost linearly
with the Na-H distance. The points in this region of the graph correspond to the first
seven complexes in Table 6, which are stabilized by traditional hydrogen bonds. Figure 4
suggests that the change from a traditional to a proton-shared hydrogen bond is not a
dramatic one. Nevertheless, the two points which correspond to the shortest Na-N
b
distance and lowest proton-stretching frequency, are found for the complex with a
proton-shared hydrogen bond. Subsequently, there is a rather dramatic change in the
km/mol
km/mol,
3600
3400
3200
3000
...-
..-
'E 2800
()
"'-""
;>
2600
2400
2200
.. .. ... ,..
.. .. .. .. .. .. .. ..
.. .. .. III .. 'Ill
3.10
3.00
2.90 ... 
0«
"'-""
.0
Z
I
ell
2.80 z
2.70
2000 I I I I I I 2.60
1.00 1.20 1.40 1.60 1.80 2.00
Na-H (A)
Figure 4: Na-N
b
distances and proton-stretching frequencies versus Na-H
distances in complexes of pyrrole and disubstituted pyrroles with NH
3
and
N(CH
3
)3
--0-- Na-N
b
-----i:c- v
~
['J
.. 
,
E
.. ..
.. .. ..
.. .. ..
.. .. ..
.. .. ..
.. .. ..
+------_-----__-------.-------r--------+
43
slope of the two lines which signals the formation of ion-pair hydrogen bonds. It would
be interesting to have had at least one more point for a complex in this series in which the
Na-H distance had a value of about 1.2 A. Such a point would indicate whether proton 
shared hydrogen bonds span a relatively narrow range of Na-H distances or not.
Unfortunately, no such point exists for the complexes investigated in this work.
IV. CONCLUSIONS:
Optimized MP2/6-31+G(d,p) structures have been determined for the complexes
of pyrrole and disubstituted pyrroles with the nitrogen bases HCN, LiCN, NaCN, SCN-,
OCN-, NH
3
and N(CH
3
)3. The harmonic vibrational spectra of these complexes have also
been calculated at MP2/6-31+G(d,p). The following statements are supported by these
calculations.
1. By systematically varying the proton-donating ability of pyrrole and
substituted pyrroles and the proton-accepting ability of nitrogen bases,
complexes stabilized by traditional N-H...N, proton-shared N...H...N,
and ion-pair N- ...+H-N hydrogen bonds have been produced.
2. Proton-shared and ion-pair hydrogen bonds are not found in neutral
complexes. They occur only in charged complexes.
3. Most of the complexes investigated in this study are stabilized by
traditional hydrogen bonds as evident from the Na-H distances, Na-N
b
distances, and proton-stretching frequencies. In series of closely
related complexes stabilized by traditional hydrogen bonds, as the base
strength increases, the binding energy increases, the Na-N
b
distance
44
decreases, the Na-H distance increases, the proton-stretching frequency
decreases, and the intensity of the proton-stretching band increases.
4. Among the complexes with HCN and its derivatives as proton
acceptors, two charged complexes are stabilized by proton-shared
hydrogen bonds, and a third is stabilized by a hydrogen bond which is
on the ion-pair side of proton-shared. Proton-shared hydrogen bonds
have short intermolecular Na-N
b
distances, long Na-H and Nb-H
distances, and proton-stretching frequencies that are dramatically
shifted to lower energy compared to traditional and ion-pair hydrogen
bonds.
5. Among complexes with NH
3
as the proton acceptor, only traditional
hydrogen bonds are formed. When the stronger base N(CH
3
h is the
proton acceptor, one charged complex has a proton-shared hydrogen
bond, and two charged complexes have ion-pair hydrogen bonds.
6. This study suggests that proton-shared and ion-pair hydrogen bonds
probably do not exist in neutral complexes stabilized by N-H-N
hydrogen bonds.
45
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Appendix 1
Z-matrices for optimized monomers reported in Tables 1 and 2, taken directly from
Gaussian 98 output
HCN MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
Symbolic Z-matrix:
Charge =0 Multiplicity =1
C
N 1 eN
x 1 1. 2 90.
H 1 CH 3 90. 2 180. 0
Variables:
CH 1.06652
CN 1.17845
Al-l
LICN MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
C
N 1 CN
X 1 1. 2 90.
Li 1 CLI 3 90. 2 180. 0
Variables:
CN 1.19257
CLI 1.94586
AI-2
NCNa MP2/6-31+G(D,P) OPTIMIZED STRUCTURE WITH ONLY THE Is
ORBITALS FROZEN
Symbolic Z-matrix:
Charge =0 Multiplicity =1
X
NIL
C 2 CN 1 90.
X 3 1. 2 90. 1 O. a
Na 3 CNa 4 90. 1 180. 0
Variables:
CN 1.192947
CNa 2.228593
AI-3
NCS' MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
Symbolic Z-matrix:
Charge =-1 Multiplicity = 1
X
NIL
C 2 CN 1 90.
X 3 1. 2 90. 1 O. 0
S 3 CS 4 90. 1 180. 0
Variables:
CN 1.2022
CS 1.66173
AI-4
NCO- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
Symbolic Z-matrix:
Charge =-1 Multiplicity = 1
N
C 1 CN
X 2 1. 1 90.
o 2 CO 3 90. 1 180. 0
Variables:
CN 1.21407
CO 1.24452
AI-5
NH
3
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
X 1 1.
H 1 R 2 A
H 1 R 2 A 3 120. 0
H 1 R 2 A 3 -120. 0
Variables:
R 1.0117
A 110.82744
Al-6
------------------------------------------
N(CH
3
)3 MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
------------------------------------------
Symbolic Z-matrix:
Charge =0 Multiplicity =1
X
N 1 1.
X 1 1. 2 90.
X 1 1. 3 90. 2 O. 0
C 2 CN 1 ANG 3 O. 0
H 5 CH6 2 ANG6 1 180. 0
H 5 CH7 2 ANG7 6 120. 0
H 5 CH7 2 ANG7 6 -120. 0
X 2 1. 1 90. 3 120. 0
C 2 CN 1 ANG 3 120. 0
H 10 CH6 2 ANG6 9 180. 0
H 10 CH7 2 ANG7 11 120. 0
H 10 CH7 2 ANG7 11 -120. 0
X 2 1. 1 90. 3 -120. 0
C 2 CN 1 ANG 3 -120. 0
H 15 CH6 2 ANG6 14 180. 0
H 15 CH7 2 ANG7 16 120. 0
H 15 CH7 2 ANG7 16 -120. 0
Variables:
CN 1.45524
ANG 108.31107
CH6 1.10391
ANG6 112.12778
CH7 1.08927
ANG7 109.58619
Al-7
PYRROLE MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
--------------------------------------
Symbolic Z-matrix:
Charge =0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
Variables:
NH 1.00719
NC3 1.37454
ANG3 124.91284
CC5 1.38571
ANG5 107.39955
CH7 1.07699
ANG7 121.2349
CH9 1.07789
ANG9 125.5103
AI-8
3,4-DIFLUOROPYRROLE MP2/6-31+GCD,P) OPTIMIZED STRUCTURE
-------------------------------
Symbolic Z-matrix:
Charge =0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 o. 0
H 4 CH7 1 ANG7 2 o. 0
F 5 CF9 3 ANG9 7 o. 0
F 6 CF9 4 ANG9 8 o. 0
Variables:
NH 1.00642
NC3 1.37537
ANG3 124.35981
CC5 1.38271
ANG5 106.17897
CH7 1.07515
ANG7 122.98626
CF9 1.353
ANG9 126.09995
AI-9
2,5-DIFLUOROPYRROLE MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
------------------------
Symbolic Z-matrix:
Charge =0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CH7 1 ANG7 2 o. 0
F 4 CH7 1 ANG7 2 o. 0
H 5 CF9 3 ANG9 7 O. 0
H 6 CF9 4 ANG9 8 O. 0
Variables:
NH 1.00822
NC3 1.37245
ANG3 126.57082
CC5 1.36933
ANG5 1102977
CH7 1.34964
ANG7 118.43637
CF9 1.07588
ANG9 126.21828
Al-lO
Al-11
2,5-DlBERYLLIUMPYRROLE+
2
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
R 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
Be 3 CB7 1 ANG7 2 O. 0
Be 4 CB7 1 ANG7 2 O. 0
R 5 CR9 3 ANG9 7 O. 0
R 6 CR9 4 ANG9 8 O. 0
Variables:
NH 1.01205
NC3 1.37986
ANG3 124.70633
CC5 1.41761
ANG5 106.80951
CB7 1.63453
ANG7 131.01899
CR9 1.08059
ANG9 126.42836
Al-12
3,4-DIBERYLLIUMPYRROLE+
2
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
Be 5 CB9 3 ANG9 7 O. 0
Be 6 CB9 4 ANG9 8 O. 0
Variables:
NH 1.01704
NC3 1.35921
ANG3 124.71613
CC5 1.40565
ANG5 108.75509
CH7 1.08075
ANG7 120.15547
CB9 1.62595
ANG9 115.79211
Appendix 2
Z-matrices for optimized complexes reported in Tables 5 and 6, taken directly from
Gaussian 98 output
PYRROLE:NCH MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CNC 13 90. 1 180. 0
X 14 1. 12 90. 13 O. 0
H 14 CHC 15 90. 12 180. 0
Variables:
NH 1.01145
NC3 1.37274
ANG3 125.0453
CC5 1.38729
ANG5 107.69096
CH7 1.0773
ANG7 121.10689
CH9 1.07817
ANG9 125.63111
R 3.16425
CNC 1.17684
CHC 1.06718
A2-1
--------------------------------
PYRROLE:NCLi MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
--------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 eH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Li 14 CLi 15 90. 12 180. 0
Variables:
NH 1.01918
NC3 1.37077
ANG3 125.1347
CC5 1.38902
ANG5 107.92298
CH7 1.07748
ANG7 120.94505
CH9 1.0785
ANG9 125.73911
R 3.00996
CN 1.19037
CLi 1.95756
A2-2
A2-3
PYRROLE:NCNa MP2/6-31+G(D,P) OPTIMIZED STRUCTURE WITH ONLY THE
1s ORBITALS FROZEN
-----------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Na 14 CNa 15 90. 12 180. 0
Variables:
NH 1.02136
NC3 1.37017
ANG3 125.15207
CC5 1.38941
ANG5 107.97728
CH7 1.07754
ANG7 120.90459
CH9 1.07859
ANG9 125.76743
R 2.97113
CN 1.19061
CNa 2.2352
PYRROLE:NCS- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
----------------------------------------
Symbolic Z-matrix:
Charge =-1 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
S 14 CS 15 90. 12 180. 0
Variables:
NH 1.03697
NC3 1.36755
ANG3 125.23316
CC5 1.39197
ANG5 108.24055
CH7 1.07777
ANG7 120.65796
CH9 1.07931
ANG9 125.86253
R 2.83533
CN 1.20192
CS 1.64653
A2-4
--------------------------------
PYRROLE:NCO- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
--------------------~-----------
Symbolic Z-matrix:
Charge =-1 Multiplicity =1
N
R 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
R 3 CR7 1 ANG7 2 O. 0
R 4 CR7 1 ANG7 2 O. 0
R 5 CR9 3 ANG9 7 O. 0
R 6 CR9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 90. 0
0 14 CO 15 90. 12 180. 0
Variables:
NH 1.04842
NC3 1.36662
ANG3 125.32201
CC5 1.39319
ANG5 108.43029
CR7 1.078
ANG7 120.5426
CR9 1.07963
ANG9 125.95387
R 2.76188
CN 1.21103
CO 1.23307
A2-5
3,4-DIFLUOROPYRROLE:NCH MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
--------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
H 14 CH 15 90. 12 180. 0
Variables:
NH 1.01197
NC3 1.37354
ANG3 124.47348
CC5 1.38394
ANG5 106.42129
CH7 1.07534
ANG7 122.7922
CF9 1.35565
ANG9 126.22311
R 3.11482
CN 1.17644
CH 1.06735
A2-6
3,4-DIFLUOROPYRROLE:NCLi MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
---------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Li 14 CLi 15 90. 12 180. 0
Variables:
NH 1.02162
NC3 1.37164
ANG3 124.561
CC5 1.38518
ANG5 106.624
CH7 1.07546
ANG7 122.603
CF9 1.35875
ANG9 126.302
R 2.95558
CN 1.18991
CLi 1.96118
A2-7
3,4-DIFLUOROPYRROLE:NCNa MP2/6-31 +G(D,P) OPTIMIZED STRUCTURE
WITH ONLY THE Is ORBITALS FROZEN
---------------------------------------.--_.-
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Na 14 CNa 15 90. 12 180. 0
Variables:
NH 1.02453
NC3 1.37101
ANG3 124.58235
CC5 1.38554
ANG5 106.68114
CH7 1.0755
ANG7 122.54787
CF9 1.35956
ANG9 126.32501
R 2.91624
CN 1.19013
CNa 2.23883
A2-8
3,4-DIFLUOROPYRROLE:NCS- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
---------------------------------------------------
Symbolic Z-matrix:
Charge = -1 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 90. 0
S 14 CS 15 90. 12 180. 0
Variables:
NH 1.04549
NC3 1.36861
ANG3 124.6613
CC5 1.38743
ANG5 106.88917
CH7 1.07576
ANG7 122.24548
CF9 1.36603
ANG9 126.50156
R 2.77007
CN 1.20183
CS 1.64283
A2-9
A2-1O
3,4-DIFLUOROPYRROLE:NCO- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
---------------------------------------------------
Symbolic Z-matrix:
Charge = -1 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
II 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 90. 0
0 14 CO 15 90. 12 180. 0
Variables:
NH 1.06116
NC3 1.36779
ANG3 124.74926
CC5 1.38839
ANG5 107.05874
CH7 1.07595
ANG7 122.11971
CF9 1.36825
ANG9 126.58183
R 2.69898
CN 1.21034
CO 1.2305
2,5-DIFLUOROPYRROLE:NCH MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
-----------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 O. 0
F 4 CF7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
H 14 CH 15 90. 12 180. 0
Variables:
NH 1.01597
NC3 1.36978
ANG3 126.75778
CC5 1.3709
ANG5 110.70464
CF7 1.35217
ANG7 118.57975
CH9 1.07602
ANG9 126.3571
R 3.06836
CN 1.17607
CH 1.06723
A2-11
A2-12
2,5-DIFLUOROPYRROLE:NCLi MP2/6-31+GCD,P) OPTIMIZED STRUCTURE
---------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 O. 0
F 4 CF7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Li 14 CLi 15 90. 12 180. 0
Variables:
NH 1.02908
NC3 1.36752
ANG3 126.896
CC5 1.37259
ANG5 111.015
CF7 1.35387
ANG7 118.831
CH9 1.07619
ANG9 126.437
R 2.90552
CN 1.18942
CLi 1.9598
A2-13
2,5-DIFLUOROPYRROLE:NCNa MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
WITH ONLY THE Is ORBITALS FROZEN
-------------------------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 O. 0
F 4 CF7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Na 14 CNa 15 90. 12 180. 0
Variables:
NH 1.03329
NC3 1.36672
ANG3 126.93282
CC5 1.37298
ANG5 111.10681
CF7 1.35445
ANG7 118.88337
CH9 1.07624
ANG9 126.46172
R 2.86275
CN 1.18956
CNa 2.236
2,5-DIFLUOROPYRROLE:NCS· MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
----------------------------------------------------
Symbolic Z-matrix:
Charge =-1 Multiplicity =1
N
R 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 o. 0
F 4 CF7 1 ANG7 2 o. 0
R 5 CR9 3 ANG9 7 o. 0
R 6 CR9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
S 14 CS 15 90. 12 180. 0
Variables:
NH 1.06469
NC3 1.36385
ANG3 127.16137
CC5 1.37605
ANG5 111.59723
CF7 1.35582
ANG7 119.32725
CR9 1.07672
ANG9 126.49287
R 2.71255
CN 1.20091
CS 1.64206
A2-14
A2-15
2,5-DIFLUOROPYRROLE:NCO- MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
----------------------------------------------------
Symbolic Z-matrix:
Charge =-1 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 O. 0
F 4 CF7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 90. 0
0 14 CO 15 90. 12 180. 0
Variables:
NH 1.09727
NC3 1.36218
ANG3 127.3628
CC5 1.37767
ANG5 111.99689
CF7 1.35866
ANG7 119.41544
CH9 1.07702
ANG9 126.60676
R 2.62714
CN 1.20816
CO 1.22899
A2-16
3,4-DIBERYLLIUMPYRROLE+
2
:NCH MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
----------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
Be 5 CB9 3 ANG9 7 O. 0
Be 6 CB9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 90. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
H 14 CH 15 90. 12 180. 0
Variables:
NH 1.04261
NC3 1.3562
ANG3 124.97802
CC5 1.40873
ANG5 109.27251
CH7 1.08096
ANG7 120.01148
CB9 1.61987
ANG9 115.86886
R 2.82797
CN 1.17367
CH 1.07127
A2-17
3,4-DIBERYLLIUMPYRROLE+
2
:NCLi MP2/6-31+G(D,P) OPTIMIZED
STRUCTURE
o
o
o
o
o
o
o
3 180.
2 180.
2 180.
2 o.
2 o.
7 o.
8 o.
o. 0
o. 0
o. 0
180. 0
o. 0
180. 0
2 ANG3
2 ANG3
1 ANG5
1 ANG5
1 ANG7
1 ANG7
3 ANG9
4 ANG9
2 90. 3
11 90. 2
1 90. 11
13 90. 2
12 90. 13
15 90. 12
1 NH
1 NC3
1 NC3
3 CC5
4 CC5
3 CH7
4 CH7
5 CB9
6 CB9
1 1.
1 R
12 1.
12 CN
14 1.
14 CLi
Symbolic Z-matrix:
Charge = 2 Multiplicity = 1
N
H
C
C
C
C
H
H
Be
Be
X
N
X
C
X
Li
Variables:
NH
NC3
ANG3
CC5
ANG5
CH7
ANG7
CB9
ANG9
R
CN
CLi
1.119
1.35389
125.36541
1.41281
109.9593
1.08143
119.86253
1.61305
115.84257
2.60336
1.1865
2.03465
3,4-DIBERYLLIUMPYRROLE+
2
:NCNaMP2/6-31+G(D,P) OPTIMIZED
STRUCTURE WITH ONLY THE Is ORBITALS FROZEN
-----------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 o. 0
H 4 CH7 1 ANG7 2 o. 0
Be 5 CB9 3 ANG9 7 O. 0
Be 6 CB9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
X 12 1. 1 90. 11 O. 0
C 12 CN 13 90. 2 180. 0
X 14 1. 12 90. 13 O. 0
Na 14 CNa 15 90. 12 180. 0
Variables:
NH 1.57739
NC3 1.35632
ANG3 126.58773
CC5 1.41964
ANG5 111.81214
CH7 1.08261
ANG7 120.05359
CB9 1.60544
ANG9 116.69726
R 2.66562
CN 1.17928
CNa 2.37425
A2-18
A2-19
PYRROLE:NH
3
MP2/6-31+0(D,P) OPTIMIZED STRUCTURE WITH N-H IN THE
PLANE OF PYRROLE
----------------------------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 AN03
C 1 NC3 2 AN03 3 180. 0
C 3 CC5 1 AN05 2 180. 0
C 4 CC5 1 AN05 2 180. 0
H 3 CH7 1 AN07 2 O. 0
H 4 CH7 1 AN07 2 O. 0
H 5 CH9 3 AN09 7 O. 0
H 6 CH9 4 AN09 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
H 12 NH13 1 AN013 11 O. 0
H 12 NH13 1 AN013 13 120. 0
H 12 NH13 1 AN013 13 -120. 0
Variables:
NH 1.02051
NC3 1.37221
AN03 125.17681
CC5 1.38816
AN05 107.92035
CH7 1.07762
AN07 121.09502
CH9 1.07829
AN09 125.71059
R 3.03747
NH13 1.01419
AN013 111.87013
A2-20
3,4-DIFLUOROPYRRROLE:NH
3
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
WITH N-H IN THE PLANE OF PYRROLE
----------------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
H 12 NH13 1 ANG13 11 O. 0
X 12 1. 1 ANG14 13 180. 0
H 12 NH15 14 HALF 2 90. 0
H 12 NH15 14 HALF 2 -90. 0
Variables:
NH 1.02315
NC3 1.37312
ANG3 124.61556
CC5 1.3846
ANG5 106.65671
CH7 1.0756
ANG7 122.7817
CF9 1.35641
ANG9 126.26573
R 2.99166
NH13 1.01442
ANG13 111.0618
ANG14 129.79508
NH15 1.01426
HALF 53.52968
A2-21
PYRROLE:N(CH
3
)3 MP2/6-31+G(D,P) OPTIMIZED STRUCTURE WITH C-HIN
THE PLANE OF PYRROLE
-----------------------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
C 12 CN13 1 ANG13 11 O. 0
H 13 CH14 12 ANG14 2 180. 0
H 13 CH15 12 ANG15 14 120. 0
H 13 CH15 12 ANG15 14 -120. 0
X 12 1. 1 90. 11 120. 0
C 12 CN13 1 ANG13 11 120. 0
H 18 CH14 12 ANG14 17 180. 0
H 18 CH15 12 ANG15 19 120. 0
H 18 CH15 12 ANG15 19 -120. 0
X 12 1. 1 90. 11 -120. 0
C 12 CN13 1 ANG13 11 -120. 0
H 23 CH14 12 ANG14 22 180. 0
H 23 CH15 12 ANG15 24 120. 0
H 23 CH15 12 ANG15 24 -120. 0
Variables:
NH 1.02932
NC3 1.37262
ANG3 125.23777
CC5 1.38864
ANG5 108.00819
CH7 1.07797
ANG7 121.09147
CH9 1.0784
ANG9 125.74811
R 2.93063
CN13 1.46104
ANG13
CH14
ANG14
CH15
ANG15
108.27578
1.10083
111.72914
1.08932
109.51702
A2-22
A2-23
2,5-DIFLUOROPYRROLE:NH
3
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE WITH
N-H IN THE PLANE OF PYRROLE
--------------------------------------------------
Symbolic Z-matrix:
Charge = aMultiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. a
C 3 CC5 1 ANG5 2 180. a
C 4 CC5 1 ANG5 2 180. a
F 3 CF7 1 ANG7 2 o. a
F 4 CF7 1 ANG7 2 o. a
H 5 CH9 3 ANG9 7 o. a
H 6 CH9 4 ANG9 8 o. a
x 1 1. 2 90. 3 o. a
N 1 R 11 90. 2 o. a
H 12 NH13 1 ANG13 11 o. a
x 12 1. 1 ANG14 13 180. a
H 12 NH15 14 HALF 2 90. a
H 12 NH15 14 HALF 2 -90. a
Variables:
NH 1.03199
NC3 1.36824
ANG3 126.91867
CC5 1.37175
ANG5 111.02601
CF7 1.35493
ANG7 118.46533
CH9 1.07611
ANG9 126.49143
R 2.92369
NH13 1.01461
ANG13 110.77965
ANG14 129.57577
NH15 1.01432
HALF 53.52718
A2-24
3,4-DIFLUOROPYRROLE:N(CH
3
)3 MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
WITH C-H IN THE PLANE OF PYRROLE
-----------------------------------------------~--------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
F 5 CF9 3 ANG9 7 O. 0
F 6 CF9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
C 12 CN13 1 ANG13 11 O. 0
H 13 CH14 12 ANG14 2 180. 0
H 13 CH15 12 ANG15 14 120. 0
H 13 CH15 12 ANG15 14 -120. 0
X 12 1. 1 90. 11 120. 0
C 12 CN13 1 ANG13 11 120. 0
H 18 CH14 12 ANG14 17 180. 0
H 18 CH15 12 ANG15 19 120. 0
H 18 CH15 12 ANG15 19 -120. 0
X 12 1. 1 90. 11 -120. 0
C 12 CN13 1 ANG13 11 -120. 0
H 23 CH14 12 ANG14 22 180. 0
H 23 CH15 12 ANG15 24 120. 0
H 23 CH15 12 ANG15 24 -120. 0
Variables:
NH 1.03483
NC3 1.37355
ANG3 124.68895
CC5 1.38506
ANG5 106.76203
CH7 1.07593
ANG7 122.76846
CF9 1.35665
ANG9 126.31675
R 2.8813
CN13 1.4626
ANG13
CH14
ANG14
CH15
ANG15
108.36704
1.10006
111.64753
1.08929
109.51161
A2-25
A2-26
2,5-DIBERYLLIUMPYRROLE+
2
:NH
3
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
WITH N-H IN THE PLANE OF PYRROLE
----------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
Be 3 CB7 1 ANG7 2 O. 0
Be 4 CB7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
H 12 NH13 1 ANG13 11 O. 0
X 12 1. 1 ANG14 13 180. 0
H 12 NH15 14 HALF 2 90. 0
H 12 NH15 14 HALF 2 -90. 0
Variables:
NH 1.04998
NC3 1.37678
ANG3 125.29748
CC5 1.42237
ANG5 107.8302
CB7 1.62835
ANG7 130.43711
CH9 1.08061
ANG9 126.61663
R 2.86999
NH13 1.0177
ANG13 114.61623
ANG14 131.06211
NH15 1.01801
HALF 52.84008
A2-27
2,5-DIFLUOROPYRROLE:N(CH
3
)3 MP2/6-31+GCD,P) OPTIMIZED STRUCTURE
WITH C-H IN THE PLANE OF PYRROLE
--------------------------------------------------------------
Symbolic Z-matrix:
Charge = 0 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
F 3 CF7 1 ANG7 2 O. 0
F 4 CF7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
C 12 CN13 1 ANG13 11 O. 0
H 13 CH14 12 ANG14 2 180. 0
H 13 CH15 12 ANG15 14 120. 0
H 13 CH15 12 ANG15 14 -120. 0
X 12 1. 1 90. 11 120. 0
C 12 CN13 1 ANG13 11 120. 0
H 18 CH14 12 ANG14 17 180. 0
H 18 CH15 12 ANG15 19 120. 0
H 18 CH15 12 ANG15 19 -120. 0
X 12 1. 1 90. 11 -120. 0
C 12 CN13 1 ANG13 11 -120. 0
H 23 CH14 12 ANG14 22 180. 0
H 23 CH15 12 ANG15 24 120. 0
H 23 CH15 12 ANG15 24 -120. 0
Variables:
NH 1.05382
NC3 1.36713
ANG3 127.03289
CC5 1.37264
ANG5 111.26767
CF7 1.35739
ANG7 118.25659
CH9 1.07629
ANG9 126.63561
R 2.78489
CN13 1.46348
ANG13
CH14
ANG14
CH15
ANG15
108.09165
1.09938
111.45819
1.08913
109.45257
A2-28
A2-29
3,4-DIBERYLLIUMPYRROLE+
2
:NH
3
MP2/6-31+G(D,P) OPTIMIZED STRUCTURE
WITH N-H IN THE PLANE OF PYRROLE
----------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity = 1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
Be 5 CB9 3 ANG9 7 O. 0
Be 6 CB9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
H 12 NH13 1 ANG13 11 O. 0
X 12 1. 1 ANG14 13 180. 0
H 12 NH15 14 HALF 2 90. 0
H 12 NH15 14 HALF 2 -90. 0
Variables:
NH 1.10749
NC3 1.35665
ANG3 125.38834
CC5 1.4108
ANG5 109.89971
CH7 1.08129
ANG7 120.10222
CB9 1.61813
ANG9 116.27728
R 2.69776
NH13 1.01801
ANG13 112.89233
ANG14 130.52483
NH15 1.01797
HALF 53.01118
----------------------------------------------------------------------
2,5-DIBERYLLIUMPYRROLE+
2
:N(CH
3
)3 MP2/6-31+G(D,P) OPTIMIZED
STRUCTURE WITH C-H IN THE PLANE OF PYRROLE
----------------------------------------------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
Be 3 CB7 1 ANG7 2 O. 0
Be 4 CB7 1 ANG7 2 O. 0
H 5 CH9 3 ANG9 7 O. 0
H 6 CH9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
C 12 CN13 1 ANG13 11 O. 0
H 13 CH14 12 ANG14 2 180. 0
H 13 CH15 12 ANG15 14 120. 0
H 13 CH15 12 ANG15 14 -120. 0
X 12 1. 1 90. 11 120. 0
C 12 CN13 1 ANG13 11 120. 0
H 18 CH14 12 ANG14 17 180. 0
H 18 CH15 12 ANG15 19 120. 0
H 18 CH15 12 ANG15 19 -120. 0
X 12 1. 1 90. 11 -120. 0
C 12 CN13 1 ANG13 11 -120. 0
H 23 CH14 12 ANG14 22 180. 0
H 23 CH15 12 ANG15 24 120. 0
H 23 CH15 12 ANG15 24 -120. 0
Variables:
NH 1.7733
NC3 1.3807
ANG3 127.90116
CC5 1.4362
ANG5 111.91469
CB7 1.61848
ANG7 136.72016
CH9 1.08299
ANG9 127.8354
R 2.83734
CN13 1.49175
A2-30
AN013
CH14
AN014
CH15
AN015
107.80266
1.08759
109.19568
1.08662
108.75663
A2-31
3,4-DIBERYLLIUMPYRROLE+
2
:N(CH
3
h MP2/6-31+G(D,P) OPTIMIZED
STRUCTURE WITH C-H IN THE PLANE OF PYRROLE
--------------------------------------~-------------------------------
Symbolic Z-matrix:
Charge = 2 Multiplicity =1
N
H 1 NH
C 1 NC3 2 ANG3
C 1 NC3 2 ANG3 3 180. 0
C 3 CC5 1 ANG5 2 180. 0
C 4 CC5 1 ANG5 2 180. 0
H 3 CH7 1 ANG7 2 O. 0
H 4 CH7 1 ANG7 2 O. 0
Be 5 CB9 3 ANG9 7 O. 0
Be 6 CB9 4 ANG9 8 O. 0
X 1 1. 2 90. 3 O. 0
N 1 R 11 90. 2 O. 0
C 12 CN13 1 ANG13 11 O. 0
H 13 CH14 12 ANG14 2 180. 0
H 13 CH15 12 ANG15 14 120. 0
H 13 CH15 12 ANG15 14 -120. 0
X 12 1. 1 90. 11 120. 0
C 12 CN13 1 ANG13 11 120. 0
H 18 CH14 12 ANG14 17 180. 0
H 18 CH15 12 ANG15 19 120. 0
H 18 CH15 12 ANG15 19 -120. 0
X 12 1. 1 90. 11 -120. 0
C 12 CN13 1 ANG13 11 -120. 0
H 23 CH14 12 ANG14 22 180. 0
H 23 CH15 12 ANG15 24 120. 0
H 23 CH15 12 ANG15 24 -120. 0
Variables:
NH 1.82163
NC3 1.35924
ANG3 126.9271
CC5 1.42016
ANG5 112.26277
CH7 1.08281
ANG7 120.23648
CB9 1.60752
ANG9 117.53224
R 2.87458
CN13 1.49239
A2-32
ANG13
CH14
ANG14
CH15
ANG15
107.51908
1.08738
108.92436
1.0864
108.73134
A2-33
Appendix 3
Binding Enthalpies(~Ho)for complexes in Tables 5 and 6
A3-1
Binding Enthalpies (kcal/mol)
Pl
3,4-diFPy 2,5-diFPy 2,5-diBePy+2 3,4-diBePy+2
NCR -4.5 -5.6 -5.7 -20.2
NCLi -9.3 -11.7 -11.6 -47.2
NCNa -10.7 -13.5 -13.3 -55.8
NCS-
-18.1 -23.7 -21.7
NCO-
-22.0 -28.6 -27.2
NH
3
-7.0 -8.4 -9.6 -21.4 -25.4
N(CR
3
)3 -9.4 -11.0 -13.3 -32.6 -44.8
a) Py=pyrrole