Structure Analysis Restrained by ab Initio Calculations: The Molecular Structure of 2,5-Dichloropyrimidine in Gaseous and Crystalline Phases

Article abstract of DOI:10.1021/jp960084r

A new method to obtain improved structural parametes by supplementing gas-phase electron diffraction (GED) data with restrains based on the results of ab initio calculations is proposed.The procedure involves the use of ab initio parameters with estimated uncertainties as additional observations; this allows previously fixed parameters to refine, with all geometrical parameters included in the final refinement.The refinement of the molecular structure of 2,5-dichloropyrimidine is used as an example to illustrate the principle of this technique.In this simple case, the effects are not very great, but this new approach allowed refinement of all structural parameters.The nine independent structural parameters (r_α structure) were found to be: r = 139.3(11) pm, r = 133.2(4) pm, r = 132.5(5) pm, r = 172.2(3) pm, r = 172.8(3) pm, r = 109.9(12) pm, <*> = 127.9(4) deg, <*> = 116.3(7) deg, and <*> = 117.2(5) deg.All structural parameters were found to be in good agreement with both ab initio and crystallographic values, which are presented for comparison.

Full text of DOI:10.1021/jp960084r

12280
J. Phys. Chem. 1996, 100, 12280-12287
Structure Analysis Restrained by ab Initio Calculations: The Molecular Structure of
2,5-Dichloropyrimidine in Gaseous and Crystalline Phases
Alexander J. Blake,† Paul T. Brain, Hamish McNab, Jennifer Miller, Carole A. Morrison,
Simon Parsons, David W. H. Rankin,* Heather E. Robertson, and Bruce A. Smart
Department of Chemistry, UniVersity of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, U.K.
ReceiVed: January 5, 1996; In Final Form: April 3, 1996X
A new method to obtain improved structural parameters by supplementing gas-phase electron diffraction
(GED) data with restraints based on the results of ab initio calculations is proposed. The procedure involves
the use of ab initio parameters with estimated uncertainties as additional observations; this allows previously
fixed parameters to refine, with all geometrical parameters included in the final refinement. The refinement
of the molecular structure of 2,5-dichloropyrimidine is used as an example to illustrate the principle of this
technique. In this simple case, the effects are not very great, but this new approach allowed refinement of
all structural parameters. The nine independent structural parameters (rR structure) were found to be: r[C(4)-
C(5)] ) 139.3(11) pm, r[N(1)-C(6)] ) 133.2(4) pm, r[N(1)-C(2)] ) 132.5(5) pm, r[C(5)-Cl(9)] ) 172.2-
(3) pm, r[C(2)-Cl(7)] ) 172.8(3) pm, r[C(6)-H(10)] ) 109.9(12) pm, [N(1)C(2)N(3)] ) 127.9(4)°,
[C(2)N(3)C(4)] ) 116.3(7)°, and [N(3)C(4)H(8)] ) 117.2(5)°. All structural parameters were found to
be in good agreement with both ab initio and crystallographic values, which are presented for comparison.
Introduction
constraints, and choosing to refine all geometrical parameters
as a matter of principle.
The problems associated with refining a molecular structure
using gas-phase electron diffraction (GED) data alone are well-
known.1 In particular, similar interatomic distances may be
strongly correlated, and the positions of light atoms (particularly
hydrogen) are poorly determined due to their low electron
scattering ability. These problems make it necessary to fix some
parameters at assumed values. This is undesirable for two
reasons, which are closely related. First, because this fixed
parameter is tacitly assumed to be absolutely correct, its effect
on other refining parameters cannot be gauged; second, fixing
parameters can result in unrealistically low estimated standard
deviations for correlated parameters.
It has been found that the inadequacies of GED data can, to
some extent, be overcome by combining the data with those
obtained by other structural techniques, particularly rotational
spectroscopy and/or liquid crystal NMR (LCNMR) spectros-
copy. Structures of many small compounds have been deter-
mined successfully using this combined approach. Examples
include an array of chlorobenzenes,2-5 heteroaromatics,1,6-8 silyl
compounds,9,10 perfluorocyclobutene,11 and N-chloroazetidine.12
Bartell also demonstrated13 that estimates of geometrical
parameters, with their uncertainties (so-called predicate observa-
tions), could be used in the same way as extra experimental
observations to supplement GED data. Scha¨fer first supple-
mented GED data with ab initio data by fixing difference
parameters which could not be refined at values calculated ab
initio.14
For example, if two bond distances are correlated, the
difference between the ab initio predictions for these distances
can be added to the GED refinement as an extra observation. It
is necessary to provide an estimate of the uncertainty associated
with this new information. There is, of course, no standard
deviation associated with a parameter calculated ab initio, so
the estimated uncertainty must be subjective to some extent. It
can be obtained by performing a series of ab initio calculations
and observing the size of any changes as the quality of the
calculations is improved, or it can be based on experience of
the known accuracy of calculations at that level. In practice
these restraints are introduced to the electron diffraction analysis
by means of an extra subroutine defining appropriate parts of
the structure, written at the end of the mathematical model which
describes the structure. Extra observations concerning these
parameters (whether from spectroscopic experiments, ab initio
calculations, or, for example, chemical intuition based on
studying a series of closely related structures) can then be
entered in the refinement in the usual way.
If the refined value for a parameter and its standard deviation
turn out to be exactly the same as those entered as supplementary
data, it is clear that the experimental data contain no information
regarding that parameter. In this case it is particularly important
to take great care to ensure that the value of the additional datum
and its uncertainty represent the most realistic estimates that
can be made. If, however, the refined value is different, or its
standard deviation is lower than the uncertainty of the extra
observation, then information about this parameter is contained
within the experimental data set. But even in the less favorable
case, it is possible to refine all geometric parameters, and the
resulting structure is the best obtainable in light of all relevant
information, experimental and theoretical, and all parameters
have realistic standard deviations. Moreover, estimated standard
deviations of other refining parameters may change. They may
decrease as a consequence of the addition of extra “observa-
tions”, or they may increase, if they are correlated with
parameters which are added to the refinement.
A new approach utilizing data obtained from ab initio
calculations is now proposed to allow the refinement of all
geometric parameters, and it is the natural extension of these
two methodologies. In essence this method, called the SA-
RACEN (Structure Analysis Restrained by Ab initio Calculations
for Electron diffractioN) method, hinges on two points: the use
of calculated parameters as flexible restraints, instead of rigid
† Current address: Department of Chemistry, University of Nottingham,
University Park, Nottingham, NG7 2RD, U.K.
X Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00084-6 CCC: $12.00 © 1996 American Chemical Society

The Molecular Structure of 2,5-Dichloropyrimidine
J. Phys. Chem., Vol. 100, No. 30, 1996 12281
TABLE 1: Ab Initio Molecular Geometries and Energies of 2,5-Dichloropyrimidinea
basis set/level of theory
parameter
3-21G*/SCF
6-31G*/SCF
6-311G**/SCF
6-31G*/MP2
6-31+G*/MP2
6-311G**/MP2
bond lengths
rN(1)C(2)
rN(1)C(6)
rC(5)C(6)
rC(2)Cl(7)
rC(5)Cl(9)
rC(6)H(10)
angles
132.0
133.0
138.0
172.0
172.8
106.8
131.0
131.9
138.1
172.6
172.8
107.4
130.8
131.7
137.9
172.9
173.0
107.5
133.6
134.1
139.4
172.9
172.4
108.8
133.8
134.2
139.5
172.6
172.4
108.8
133.4
133.8
139.5
172.8
172.1
108.7
N(1)C(2)N(3)
124.8
118.0
120.9
117.5
117.6
127.3
116.4
121.6
116.7
117.1
127.4
116.4
121.5
116.8
117.2
127.8
115.8
121.6
117.5
117.0
127.6
115.8
121.7
117.4
116.8
127.9
115.7
121.7
117.3
117.2
C(2)N(3)C(4)
N(3)C(4)C(5)
C(4)C(5)C(6)
N(3)C(4)H(8)
energy, hartree
-1 174.839 342 3
-1 180.486 148
-1 180.587 367 8
-1181.568 795
-1181.585 321
-1181.734 489 1
a All distances are in pm, all angles in degrees.
TABLE 2: Derivation of Parameter Restraintsa
parameter
3-21G*/SCF 6-31G*/SCF 6-311G**/SCF 6-31G*/MP2 6-31+G*/MP2 6-311G**/MP2 value used
p3 rN(1)C(6)-rN(1)C(2)
p5 rC(5)Cl(9)-rC(2)Cl(7)
p6 rCH
1.0
0.1
106.8
117.6
0.8
0.2
107.4
117.1
0.9
0.1
107.5
117.2
0.4
-0.6
108.8
117.0
0.5
-0.2
108.8
116.8
0.4
-0.7
108.7
117.2
0.4(5)
-0.7(5)
108.7(15)
117.2(5)
p9
NCH
a All distances are in pm, all angles in deg.
In this paper we present the molecular structure of 2,5-
are presented in Table 1. Calculated bond distances proved to
be rather insensitive to the details of the basis set; improving
the basis set from 3-21G* to 6-31G* at the SCF level of theory
led to changes in bond distances which never exceeded 1 pm,
while further improvements (to 6-311G**) led to smaller changes.
As is characteristic of bonds which contain significant multiple-
bond character, the inclusion of the effects of electron correlation
at the MP2 level of theory led to a lengthening of ring bonds.26
Bond angles were invariably found to be insensitive to the
adopted theoretical treatment. If the results from the smallest
of the basis sets (3-21G*) are excluded, calculated bond angles
always fell within 1° of each other.
dichloropyrimidine, chosen as a straightforward example to
illustrate this new procedure. The ab initio calculations
performed are given in section I, and in addition a detailed
discussion of the assignment of uncertainties to ab initio
parameters is presented. The limited structural refinement
obtained from just the GED data is presented in section II and
the complete structural analysis based on a combination of GED
data and ab initio restraints in section III. For comparison the
crystal structure data are given in section IV. Finally the
molecular structures obtained by the different techniques are
compared in section V.
The apparent convergence of molecular parameters with
respect to improvements in the theoretical treatment suggests
that predicted parameters which are needed to refine the structure
of 2,5-dichloropyrimidine should be reliable. The values of
restraints were always chosen to be those calculated from the
6-311G**/MP2 level, and uncertainties were estimated by
considering the variations in calculated parameters as the level
of theory was improved, with heavier weighting being placed
on the higher level calculations. At these high levels of theory
it is unlikely that there are significant systematic errors for a
molecule of this kind, but we have been conservative in
estimating the uncertainties to avoid over-weighting the theoreti-
cal restraints. The values of the differences used in the GED
refinement are presented in Table 2.
I. Ab Initio Calculations
Theoretical Methods. Ab initio molecular orbital calcula-
tions were performed to predict geometrical parameters and to
obtain a theoretical harmonic force field using the ASYM40
program,15 from which estimates of vibrational amplitudes could
be obtained. All calculations were carried out on a DEC Alpha
APX 1000 workstation using the Gaussian suite of programs.16,17
Geometry optimizations were performed using standard gradient
techniques at the SCF level of theory using the 3-21G,18-20
6-31G*,21-23 and 6-311G** 24,25 basis sets. Subsequently the
two larger basis sets were used for optimizations at the MP2-
(FC) level of theory. An additional calculation was undertaken
at the 6-31+G* 21-23/MP2 level to gauge the effects of diffuse
functions on molecular parameters.
Vibrational frequency calculations were performed at the
3-21G*/SCF and 6-31G*/SCF levels to verify that 2,5-dichlo-
ropyrimidine has C2V symmetry. The force field used in the
GED refinement was constructed from the 6-31G*/SCF calcula-
tion. Since no fully assigned vibrational spectra were available
for this molecule, an attempt was made to scale the force field
using typical scaling factors of the order 0.9 for bond stretches,
angles, and torsions. Scaling the force field was found to have
little effect on the vibrational amplitude values.
The difference between the two C-N bonds, parameter 3,
was given a value of 0.4 pm and an uncertainty of 0.5 pm; the
uncertainty was chosen so that it encompassed all estimates
using the two largest basis sets. Parameter 5, describing the
difference between the two C-Cl bonds, was given the value
of -0.7 pm and an uncertainty of 0.5 pm, which was derived
from the MP2 level calculations only. Parameter 6 (the C-H
distance) required a different type of restraint. Restraints for
parameters 3 and 5 have involved differences between re bonds
(re signifying the equilibrium bond length as calculated by ab
initio). This value was used directly in the GED rR refinement
(which represents a vibrationally averaged structure). Since the
differences between two bonds are largely independent of the
Results and Discussion. Geometry optimizations were
performed at six levels in order to gauge the effects of improving
theoretical treatment upon the molecular geometry. The results

12282 J. Phys. Chem., Vol. 100, No. 30, 1996
Blake et al.
structure type (i.e., re or rR) they may be equated with some
confidence. However, if the absolute value of a bond distance
computed ab initio is used in the GED refinement without
vibrational correction, a larger uncertainty should be used to
allow for any discrepancies due to the difference in structural
type. Parameter 6 was therefore chosen to be 108.7 pm with
an uncertainty of 1.5 pm. Parameter 9 (the NCH angle) was
taken to have a value of 117.2° with an uncertainty of 0.5°.
This uncertainty is somewhat larger than is needed to encompass
the values obtained using the 6-31G* and 6-311G** basis sets,
but it is chosen to allow for small differences in this parameter
due to vibrational averaging in the GED refinement.
It can be seen that in the case of 2,5-dichloropyrimidine, the
calculated ring bond differences change by only a small amount
even though the absolute values of these bond lengths are altered
by the inclusion of the effects of electron correlation. This result
is not surprising since the electronic environments found in the
C-C and C-N bonds are not dissimilar; both have a bond order
of approximately 1.5. Consequently, it is expected that changes
in bond lengths due to either an incomplete basis set or the
neglect of electron correlation will be very similar for both
bonds. Although there is a significant change in the absolute
value of the bond lengths, the difference remains largely
unchanged; for example, estimates of the difference between
the two C-N ring bonds fall across a range of only 0.6 pm,
while the absolute values of the two bond lengths vary by at
least 2.5 pm. In general, when electronically similar bonds are
correlated in the GED refinement, reliable estimates of the
difference in bond lengths should be obtained, even at modest
levels of theory.
Assigning values for the difference between two bond lengths
and the associated uncertainty becomes much more problematic
when electronically dissimilar bonds are considered. Under
these circumstances, the limitations of the theoretical treatment
may have different effects on the two bonds concerned, and
hence the difference between the bond distances may change
substantially with improvements in the theoretical method. In
particular electron correlation is known to be important for
describing multiple bonds or bonds between atoms which
contain lone pairs. Thus, although a predicted C-N bond
distance is expected to be essentially unaffected by electron
correlation, a CdC double bond or an N-O or N-F bond is
almost certain to become longer when the effects of electron
correlation are included.23
which are electronically dissimilar. However, we urge particular
care if the molecule contains O-F, O-O or N-F bonds, since
it is well established that bonds between electronegative
elements are particularly sensitive to the level of correlation.26
4. In cases where calculations are restricted to the SCF level
of theory, differences will in general be reliable if bonds are
electronically similar, although care is urged when distances
between two electron-rich atoms or two highly electronegative
atoms are involved. We urge extreme caution when the lengths
of electronically dissimilar bonds are correlated in the GED
refinement. In cases such as these it may be that more reliable
estimates of bond length differences can be obtained by
estimating the effects of electron correlation from reported bonds
of the same type in other systems. Clearly the value of both
the restraint and its uncertainty need to be chosen carefully in
this case.
5. Uncertainties in restraints of this type should always be
set too high rather than too low. This method is intended to
allow the maximum information to be extracted from experi-
mental data. Overtight restraints will always guarantee that the
results agree with the theory, regardless of the experimental evi-
dence: this pitfall must be avoided at all costs.
It is worth mentioning at this stage that the use of restraints
need not be solely confined to the independent parameters used
to define the structure. It could be equally well applied to a
specific bond distance, for example, the C-C distance in our
structure, which is not defined as a independent parameter in
our model. In principle, restraints can also be applied to
vibrational amplitudes; however, calculated force constants
obtained ab initio are subject to systematic errors which must
be reduced by application of empirical or refined scale factors.28
For this reason we urge that care be taken. Two methods are
available:
1. A restraint is applied directly to a specific vibrational
amplitude. In such a case we recommend that an uncertainty
of the order of 10% be adopted.
2. Preferably, a restraint is applied to the ratio of the
amplitudes of vibration for two atom pairs which are electroni-
cally similar and whose interatomic distances lie very close
together. Since ab initio force fields are more accurate at
determining ratios of vibrational amplitudes, rather than their
absolute values, we recommend the use of a lower uncertainty
(of the order of 5%) for such cases. For example, in the case
of 2,5-dichloropyrimidine, this method would be suitable for
restraining vibrational amplitude ratios of C-C and C-N bonds
but less suitable for pairing C-Cl and C-(C, N, or H) bonds
together due to strongly differing electronic environments, which
may be more or less affected by the use of a finite basis set and
an incomplete description of electron correlation.
Unfortunately, there is a necessary degree of subjectivity in
choosing both restraint parameter values and their uncertainties.
For this reason we suggest a series of broad guidelines based
upon different computational resources for estimating bond
differences and uncertainties.
1. Restraints should preferably be applied to differences
between electronically similar bond distances or angles, rather
than to absolute values of structural parameters.
2. Ideally, a graded series of calculations in which both the
size of the basis set and the level of theory are varied should
be performed. A series of calculations of this type should allow
the effects of improving both basis set and level of theory to
be gauged with confidence and hence allow reliable estimates
of structural parameters and their uncertainties to be obtained.
3. When ambitious calculations of the type described in 2
are beyond available resources, one must rely on experience of
calculations at various levels to assess their reliability. Calcula-
tions using basis sets of double-ú plus polarization quality (for
example, 6-31G* or the double-ú basis sets of Dunning27) at
the MP2 level of theory should allow satisfactory estimates of
differences in most instances, even when comparing bonds
In 2,5-dichloropyrimidine several restraints were applied to
vibrational amplitude ratios and values. With reference to Table
6, where a full bond listing is given, bond distances were
grouped together in the following way:
1. Restraints were placed on the three amplitudes of vibration
for the ring-bonded distances. All three amplitudes were
allowed to refine freely but the ratios of u2 [N(1)-C(2)] and
u3[C(5)-C(6)] to u1[N(1)-C(6)] were restrained.
2. The two C-Cl bond distance amplitudes were refined,
with the ratio u5 to u4 restrained.
3. The two-bond ring distances were grouped, such that the
ratios u7/u8 and u12/u8 were restrained. The remaining two-
bond ring distance, C(2)‚‚‚C(6), was treated separately, since it
was shorter than the rest of the group by more than 10 pm.
This amplitude, u11, was therefore restrained directly. All four
amplitudes were refined.

The Molecular Structure of 2,5-Dichloropyrimidine
J. Phys. Chem., Vol. 100, No. 30, 1996 12283
TABLE 3: ED Data Analysis Parameters
camera
dist,
mm
scale
electron
weighting functions, nm-1
correlation factor, wavelength,
∆s smin s1
s2 smax parameter
ka
bpm
95.44
255.56
4
2
80 100 304 356
20 40 140 164
0.1613
0.4762
0.860(27)
0.905(17)
5.707
5.710
a Figures in parentheses are the estimated standard deviations.
b Determined by reference to the scattering patterns of benzene vapor.
4. The two-bond N(C)‚‚‚Cl distances refined freely, with the
ratio u13/u9 restrained.
5. The two three-bond ring distances were refined, with the
ratio u17/u15 restrained. In this case it was found that u15 also
had to be directly restrained to give a meaningful refinement.
6. The three-bond N(C)‚‚‚Cl distances were refined, with
u19/u16 restrained.
7. Finally, the two four-bond C‚‚‚Cl distances were refined,
with u26/u23 restrained.
It will be shown in section III that with the introduction of
these 11 vibrational amplitude restraints the amplitude of each
distance giving rise to a feature larger that 10% of the most
intense component peak of the radial distribution curve could
refine independently, giving values in good agreement with the
ab initio force field.
Figure 1. Molecular framework of 2,5-dichloropyrimidine.
TABLE 4: Structure (rr°) of 2,5-Dichloropyrimidine
resultsa
GED
data alone
GED +
parameter
restraints
independent
II. Gas Electron Diffraction Results
p1 [rN(1)C(2) + rN(1)C(6) + rC(5)C(6)]/3 134.8(2)
p2 rC(5)C(6) - [rN(1)C(2) + rN(1)C(6)]/2
135.0(2)
6.4(15)
0.6(4)
5.4(15)
0.4 (fixed)
172.5(2)
Sample Preparation. 2,5-Dichloropyrimidine was synthe-
sised from 2-hydroxypyrimidine hydrochloride by treatment with
aqueous chlorine solution.29 Reaction of the product with
phosphoryl chloride in the presence of N,N-dimethylaniline30
gave the desired product in 40% yield. The sample was then
purified by sublimation.
p3
p4
p5
p6
p7
p8
p9
rN(1)C(6) - rN(1)C(2)
[rC(5)Cl(9) + rC(2)Cl(7)]/2
rC(5)Cl(9) - rC(2)Cl(7)
rCH
172.5(2)
-0.7 (fixed) -0.6(5)
108.7 (fixed) 109.9(12)
127.9(4)
116.3(7)
117.2 (fixed) 117.2(5)
N(1)C(2)N(3)
C(2)N(3)C(4)
N(3)C(4)H(8)
127.4(4)
116.1(7)
Method. Electron diffraction data were captured on Kodak
Electron Image photographic plates using the Edinburgh ap-
paratus.31 The sample was maintained at a temperature of 404
K while the nozzle was held at 460 K. The four plates (two
from the long camera distance and two from the short distance)
were traced digitally using a computer-controlled Joyce-Loebl
MDM6 microdensitometer at the EPSRC Daresbury labora-
tory.32 Standard programs were used for data reduction32,33 with
the scattering factors of Fink et al.34 The weighting points used
in setting up the off-diagonal weight matrix, s range, scale
factors, correlation parameters, and electron wavelengths are
given in Table 3.
Results and Discussion. 2,5-Dichloropyrimidine was as-
sumed to be planar with C2V symmetry. Nine independent
geometrical parameters were used to define the structure. With
reference to the molecular frame shown in Figure 1, they are
the average r(C-C)/r(C-N) ring distance, the difference
between r(C-C) and the average r(C-N) distance, the differ-
ence between the two r(C-N) ring distances, the sum of and
difference between the two r(C-Cl) distances, r(C-H), angle
N(1)C(2)N(3), angle C(2)N(3)C(4), and angle NCH.
The rR0 structural parameters determined from the GED data
alone are given in the first column in Table 4. As expected the
three distinct ring bond distances r[N(1)-C(2)], r[N(1)-C(6)],
and r[C(5)-C(6)] could not be refined together because they
were strongly correlated, and so parameter 3 was fixed at the
calculated 6-311G**/MP2 ab initio value. The difference
between the two C-Cl bond lengths could also not be
determined: parameter 5 was therefore fixed at the ab initio
value from the same calculation. Finally, the data set contained
little information regarding the positions of the two hydrogen
atoms, leading to parameters 6 and 9 also being fixed at the
6-311G**/MP2 ab initio values.
dependent
N(3)C(4)C(5)
C(4)C(5)C(6)
rCC
rN(1)C(6)
rN(1)C(2)
rC(5)Cl(9)
rC(2)Cl(7)
121.3(9)
117.9(7)
138.5(12)
133.3(3)
132.8(3)
172.1(2)
172.8(2)
120.6(8)
118.3(6)
139.3(11)
133.2(4)
132.5(5)
172.2(3)
172.8(3)
a All distances are in picometers, all angles in degrees. Estimated
standard deviations, obtained in the least-squares refinement, are given
in parentheses.
The average ring bond distance (parameter 1) was found to
be 134.8(2) pm, and as the small uncertainty suggests, this value
is determined to a high degree of accuracy. However, it is the
individual bond distances, rather than the average, which are
of most interest. To obtain all three of the distances in the ring
separately, it is necessary to include parameters 2 and 3 in the
refinement. Parameter 2, describing the difference between the
C-C and average C-N bond distances, refined to 5.4(15) pm;
the difference between the two C-N bond lengths (defined by
parameter 3) remained fixed at 0.4 pm at this stage. The three
ring distances were thus found to be 138.5(12), 133.3(3), and
132.8(3) pm for the C-C and two C-N bonds, respectively.
The average C-Cl bond distance (parameter 4) refined satis-
factorily to 172.5(2) pm, but the difference between the two
bonds (parameter 5) had to be fixed at -0.7 pm. With this
parameter fixed the quoted uncertainty for each of the individual
bond distances must be identical to that of the average distance.
The individual values and uncertainties for the two bonds were
therefore 172.1(2) pm and 172.8(2) pm. Clearly, uncertainties
of 0.2 pm are too small since there is insufficient information
to allow the refinement of the two parameters which define
them.

12284 J. Phys. Chem., Vol. 100, No. 30, 1996
Blake et al.
TABLE 5: Least-Squares Correlation Matrix for
2,5-Dichloropyrimidinea
It seems that there is no straightforward way to obtain reliable
uncertainties using this method and so invariably those which
are reported are too small. Electron diffraction alone cannot
lead to a set of structural parameters which are both reliable
and have realistic uncertainties. It will be shown in section III
that the introduction of restraints enables more realistic errors
to be obtained and hence more reliable structures to be derived.
parameter
p2 p8 u1
p1 74 65 -60 -63 -53
amplitude
u2
u3 u5 u8 u9 u12 u13 u17 u19 u26 k2
-68
-81
-53
75
74
72
-64
-77
p2
p8
u1
u2
u3
u4
u5
u7
u8
u9
u15
u16
u23
81 -87 -85 -84
-73 -72 -70
93 94
73
72
70
89
III. Structure Analysis Restrained by Ab Initio
Calculationssthe SARACEN Method
78
56
56
The introduction of the four independent parameter restraints
presented in Table 2 allowed all nine independent geometric
parameters to refine. In addition, the 11 vibrational amplitude
restraints described in section I permitted amplitudes to refine
for all distances responsible for features greater than 10% of
the most intense component peak in the radial distribution curve.
The final structural parameters obtained are given in column 2
of Table 4, along with the results based on the GED data alone
for direct comparison. In general, the introduction of restraints
and refinement of additional parameters lead to only modest
changes in the values of the independent parameters which had
already been refined. For example, the average ring bond
distance changed by just 0.2 pm to 135.0(2) pm, while parameter
2 changed by 1 pm to 6.4(15) pm. The two parameters defining
ring angles (parameters 7 and 8) changed by no more than 0.5°
to 127.9(4)° and 116.3(7)°, respectively. In all four cases
standard deviations remained unchanged.
83
69
84
92
86
78
82
a All elements are scaled by a factor of 100, and only off-diagonal
elements with absolute values >50% are included.
zero. Moreover, the effects of uncertainty in this parameter are
now included in standard deviations for other parameters, which
are therefore more reliable.
5. The 11 vibrational amplitude restraints enabled the
amplitudes of the 18 most significant interatomic distances to
refine. Refined amplitudes gave values well within the uncer-
tainties of the applied restraints in all but one case, with u13/u9
just falling outside the 5% uncertainty range.
Several specific points are worth noting about the conse-
quences of introducing restraints:
The final least-squares correlation matrix, presented in Table
5, highlights another important feature relating to the use of
restraints. In addition to obtaining realistic uncertainties, the
introduction of restraints results in greatly reduced correlations
between parameters in the GED refinement. With the restraints
in place 36 incidences of correlation between refining parameters
higher than 50% were found. In contrast, when a refinement
was performed with the same parameters and amplitudes
refining, but with the restraints removed, the number of
incidences rose to fifty-one. This is, of course, expected, since
each restraint will enable a previously unrefinable parameter
(or amplitude) to refine or, in other words, to become less
dependent on other parameters. Since high correlation between
parameters is often the cause of a parameter failing to refine
properly, use of restraints can be a useful technique to relieve
high correlation effects found in some GED mathematical
models.
1. Parameter 3, describing the difference between the two
C-N bond distances, refined to 0.6(4) pm, which is different
from the ab initio restraint of 0.4(5) pm, but lies well within
the uncertainty limit. This demonstrates that the restraint was
indeed flexible. Some information about this parameter must
have been present in the GED data, but it was not sufficient to
allow this parameter to refine unassisted. The introduction of
the restraint permitted this information to be retrieved. With
all three parameters describing the ring distances now refining,
standard deviations for individual distances were expected to
increase. This was found to be the case for the two C-N bonds,
with final values found to be 133.2(4) pm and 132.5(5) pm.
However, the standard deviation for the C-C bond distance
fell by 0.1 pm as this parameter refined to 139.3(11) pm.
2. Similarly, parameter 5 refined to -0.6(5) pm as compared
to its restraint of -0.7(5) pm. With this parameter now refining
it was found that the absolute values of the two C-Cl bond
distances changed by no more than 0.1 pm and standard
deviations rose from 0.2 to 0.3 pm.
3. Parameter 6, the C-H distance, refined to 109.9(12) pm.
This differs from the value used as a restraint (108.7(15) pm)
but lies within its uncertainty limit. As in the cases given above,
this indicates that some information about this parameter was
contained within the experimental data set. However, if this
parameter is not constrained in the way we suggest the bond
distance refines to 120(3) pm, which is obviously an unreliable
value.
The complete list of interatomic distances (ra structure) and
amplitudes of vibration determined in this final refinement is
given in Table 6. In addition, the combined molecular scattering
intensities and final differences are shown in Figure 2, and the
final radial distribution and difference curves can be found in
Figure 3.
IV. Crystal Structure
Crystal Data. C4H2Cl2N2, M ) 148.98 monoclinic, space
group P21/m with a ) 6.077(3), b ) 19.771(8), c ) 7.399(3)
Å, â ) 101.23(6)°, U ) 872 Å3 [from 2θ values of 29
reflections measured at (ω, 25 e 2θ e 38°, λ ) 0.710 73Å, T
4. Parameter 9, the NCH angle, refined to 117.2(5)°, in exact
agreement with its ab initio restraint. Clearly the GED data
contained no information about this parameter. Special care is
needed in choosing such a restraint, since the GED refinement
will always echo the ab initio result, but nevertheless this
situation is still an improvement on the earlier method (i.e., using
fixed constraints) since the uncertainty suggested by the restraint
generates the same realistic uncertainty (i.e. standard deviation)
in the GED refinement, rather than an artificial uncertainty of
) 150.0 K], Dcalc ) 1.702 g cm-3, Z ) 6, µ ) 0.993 mm-1
.
The crystal selected was a colorless lath, 0.66 × 0.23 × 0.08
mm. Diffraction data were collected on a Stoe¨ Stadi-4 four-
circle diffractometer employing graphite-monochromated Mo
KR X-radiation and ω/2θ scans, with the crystal cooled using
an Oxford Cryosystems low-temperature device35 operating at
150.0(2) K. Of 1591 unique reflections collected to 2θmax
50°, 1134 had F g 4σ(F) and 1586 were used in all calculations.
)

The Molecular Structure of 2,5-Dichloropyrimidine
J. Phys. Chem., Vol. 100, No. 30, 1996 12285
TABLE 6: Interatomic Distances (ra) and Amplitudes of
TABLE 7: Crystal Structure Parameters for
Vibration for 2,5-Dichloropyrimidinea
2,5-Dichloropyrimidinea
i
atoms
distance
amplitude ui
C1 symmetry
Cs symmetry
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
N(1)-C(6)
N(1)-C(2)
C(5)-C(6)
133.4(4)
132.6(4)
139.4(11)
173.3(3)
172.7(3)
110.9(12)
238.1(9)
236.8(6)
260.1(5)
208.4(11)
225.8(6)
239.1(22)
271.5(10)
219.1(22)
273.2(7)
395.2(6)
262.8(6)
325.2(12)
383.3(6)
341(3)
4.2(6)
4.4(6)
4.3(6)
bond lengths
rN(1)-C(2)/rN(3)-C(2) 131.4(5) 132.6(5)
131.0(4)
133.4(5)
137.3(5)
174.6(6)
173.6(6)
rN(1)-C(6)/rN(3)-C(4) 134.0(5) 133.7(5)
C(2)-Cl(7)
C(5)-Cl(9)
C(6)-H(10)
N(1)‚‚‚N(3)
N(1)‚‚‚C(5)
N(1)‚‚‚Cl(7)
N(1)‚‚‚H(10)
C(2)‚‚‚C(6)
C(4)‚‚‚C(6)
C(4)‚‚‚Cl(9)
C(5)‚‚‚H(10)
N(1)‚‚‚C(4)
N(1)‚‚‚Cl(9)
C(2)‚‚‚C(5)
C(2)‚‚‚H(8)
C(4)‚‚‚Cl(7)
C(4)‚‚‚H(10)
Cl(9)‚‚‚H(10)
N(1)‚‚‚H(8)
C(2)‚‚‚Cl(9)
Cl(7)‚‚‚H(8)
H(8)‚‚‚H(10)
C(5)‚‚‚Cl(7)
Cl(7)‚‚‚Cl(9)
4.5(3)
rC(5)-C(6)/rC(4)-C(5)
rC(2)-Cl(7)
137.4(6) 136.2(6)
173.5(4)
4.4(3)
7.7 fixedb
6.1(5)
rC(5)-Cl(9)
172.5(4)
angles
6.4(5)
N(1)-C(2)-N(3)
C(2)-N(3)-C(4)/
C(2)-N(1)-C(6)
N(3)-C(4)-C(5)/
N(1)-C(6)-C(5)
C(4)-C(5)-C(6)
129.2(4)
114.5(3) 114.5(4)
130.8(4)
114.4(4)
8.0(8)
9.3 fixedb
4.9(5)
122.2(4) 121.9(4)
117.8(4)
120.6(4)
119.4(6)
6.4(6)
9.1(10)
9.4 fixedb
6.2(5)
10.1(6)
5.9(6)
a All distances are in picometers; all angles are in degrees.
9.0 fixedb
10.1(7)
9.0 fixedb
13.2 fixedb
8.9 fixedb
10.2(8)
10.3 fixedb
12.1 fixedb
10.2(8)
11.6(7)
292(2)
383.3(15)
434.9(6)
468.0(12)
435(4)
435.5(6)
607.5(5)
a All distances and amplitudes are in picometers. Estimated standard
deviations, obtained in the least-squares refinement, are given in
parentheses. b Amplitudes fixed at values derived from a scaled 6-31G*/
SCF force field.
Figure 4. Crystal packing structure of 2,5-dichloropyrimidine.
correction for secondary extinction37 refined to 0.003(3). The
weighting scheme w-1 ) [σ2(Fo ) + (0.082P)2], where P )
2
1/3[MAX(Fo ,0) + 2Fo ], led to a convergence with R1 [F g
4σ(F)] ) 0.0460, wR2 [all data] ) 0.1305, respectively, and
S[F2] ) 1.014 for 128 refined parameters. In the final cycle
(∆/σ)max was 0.20 and the final ∆F synthesis showed no feature
2
2
Figure 2. Observed and final difference combined molecular scattering
curves for 2,5-dichloropyrmidine.
outside +0.46 to -0.55 e Å-3
.
Results. One and a half molecules were found in the unit
cell, giving two symmetrically different structures (of C1 and
Cs symmetry), for 2,5-dichloropyrimidine in the solid phase.
The individual parameters derived for the two structures are
given in Table 7 and a diagram of the crystal packing
arrangement is shown in Figure 4.
The values of the N-C(2) bond distances ranged from 131.0-
(4) to 132.6(5) pm, the range of 1.6 pm suggesting that bonds
in the two different unit cells are in substantially different
electronic environments. Similarly the C(5)-C(4/6) distances
lay within a range of 1.2 pm, 136.2(6) to 137.4(6) pm. In
contrast, the N(1)-C(6)/N(3)-C(4) distance was more consis-
tent, ranging from 133.4(5) to 134.0(5) pm, a difference of only
0.6 pm. Differences in internal ring angles were also found,
with the values of angles NCN, NCC, and CCC falling within
a range of 1.6°, in contrast to angle CNC whose value only
changes by 0.1°.
Figure 3. Observed and final difference radial distribution curves for
2,5-dichloropyrimidine. Before Fourier inversion the data were mul-
tiplied by s exp(-0.00002s2)/(ZCl fCl)(ZN fN).
-
-
Structure Solution and Refinement. Automatic direct
methods36 identified the positions of all non-H atoms and
iterative cycles of least-squares refinement and difference
Fourier syntheses located the hydrogen atoms.37 At isotropic
convergence corrections for absorption (min 0.822, max 1.161)
were applied empirically using DIFABS.38 All non-H atoms
The two distinct C-Cl distances were both found to be longer
by 1.1 pm in the Cs structure than in the C1 structure. In each
were refined anisotropically and H atoms isotropically.
A

12286 J. Phys. Chem., Vol. 100, No. 30, 1996
Blake et al.
TABLE 8: Comparison of the Molecular Structure of
2,5-Dichloropyrimidine from GED, ab Initio Calculations,
and Crystallographya
(4) pm in the gas (133.6(5) pm in the solid), with the longest
distance, C(5)-C(6), found at 139.3(11) pm (or 137.1(6) pm)
in the gas (or solid) phase. The crystal structure ring angles
were also found to differ from the GED angles. Deviations
ranged from 0.3° for the CCC angle to 2.1° for the NCN angle.
Differences in angles are not surprising, since in the crystals
the molecules are subjected to intermolecular forces, and it is
energetically less demanding for a structure to distort by
changing its bond angles than by changing bond lengths.38
However, although there are small differences between ring
angles in the two phases, the same sequence of angle magnitudes
was found. The CNC angle was found to the smallest, just
116.3(7)° in the gas or 114.4(4)° in the solid, followed by the
CCC angle at 118.3(6)° (118.6(4)° in the solid). The next
biggest angle was NCC at 120.6(8)° in the gas and 121.3(4)°
in the solid, and finally the largest angle, NCN, was measured
as 127.9(4)° (130.0(4)°) in the gas (or solid) state.
GED +
6-311G**/
MP2
crystal structure
(av values)c
restraintsb
bond lengths
rN(1)C(2)
rN(1)C(6)
rC(5)C(6)
rC(2)Cl(7)
rC(5)Cl(9)
rC(6)H(10)
132.5(5)
133.2(4)
139.3(11)
172.8(3)
172.2(3)
109.9(12)
133.4
133.8
139.5
172.8
172.1
108.7
131.5(5)
133.6(5)
137.1(6)
174.0(5)
173.0(5)
angles
N(1)C(2)N(3)
127.9(4)
116.3(7)
120.6(8)
118.3(6)
117.2(5)
127.9
115.7
121.7
117.3
117.2
130.0(4)
114.4(4)
121.3(4)
118.6(4)
C(2)N(3)C(4)
N(3)C(4)C(5)
C(4)C(5)C(6)
N(3)C(4)H(8)
a All distances are in picometers, all angles in degrees. b GED results
refer to rR0 structure; see Table 6 for ra structure. c Figures in parentheses
represent uncertainties on average structure, quoted to one σ.
Conclusion
In this paper we have demonstrated a new method (SA-
RACEN) to obtain improved geometric parameters by combin-
ing GED data with restraints based on a graded series of ab
initio calculations. We have shown that in doing so, more
reasonable estimates of uncertainties can be derived (and hence
more realistic structures obtained) because previously fixed
parameters can be allowed to refine, the restraints having
relieved the effects of parameter correlation in the GED
mathematical model of the structure. Parameters which cor-
respond directly to restraints have been shown to behave in two
ways; they may refine to give a sensible value different from
the restraint but within the error limit, indicating that some
information is present in the GED data, or they may refine to
give the same value and error as the restraint, indicating that
little or no information was provided by the experimental data.
Even in this case we have demonstrated that the technique is
valuable since parameters affected now have realistic standard
deviations and the refined structures obtained in this way
represent the sum of our knowledge, experimental and theoreti-
cal, and are thus as reliable as possible at present.
case the internal ring angle associated with the C-Cl bond (i.e.,
NCN or CCC) was larger by 1.6° in the Cs structure than in the
C1 structure. Finally, in each structure the C(2)-Cl(7) distance
(C1, 173.5(4) pm; Cs, 174.6(6) pm) was found to be 1 pm longer
than the C(5)-Cl(9) distance (C1, 172.5(4) pm; Cs, 173.6(6)
pm).
V. Comparison of Molecular Structures Obtained by
Different Techniques
The final results for the molecular structure of 2,5-dichloro-
pyrimidine found by gas-phase electron diffraction with flexible
constraints, ab initio calculations, and X-ray crystallography are
summarized in Table 8. Note that the C1 and Cs molecular
structures found in the crystal are of lower symmetry than the
C
2V ab initio and gas ED structures and therefore require more
independent intramolecular geometrical parameters. To allow
for a direct comparison to be made between the two phases an
average solid-phase structure with C2V symmetry was calculated
from the C1 and Cs structures. It is these averaged values that
are given in Table 8.
Supporting Information Available: Tables 1-5 listing
crystal data and structure refinement, atomic coordinates and
displacement parameters, bond lengths and angles, anisotropic
displacement parameters, and hydrogen coordinates and isotropic
displacement parameters (4 pages); Table 6 listing observed and
calculated structure factors (4 pages). Ordering information is
given on any current masthead page.
Ab initio calculations give a discrete molecular structure,
which should therefore complement the results obtained from
the GED experiment. Some differences would be expected,
however, since ab initio calculations give the equilibrium
structure and are not subject to the vibrational averaging effects
which influence the GED dynamic structure. However, these
differences are small and ab initio and GED parameters were
found to be in excellent agreement, with all fitting within one
or two standard deviations. The only substantial difference
concerned the C-H bond length, found to be 109.9(12) pm by
GED compared to 108.7 pm by ab initio. This parameter is
poorly described in the GED experiment but can be refined
satisfactorily when subject to a flexible constraint.
Although the absolute values of parameters from the gas-
phase ED structure and the solid-phase crystal structure were
found to differ substantially, in general the same structural trends
were observed. The average ring distance measured by GED
was 135.0(2) pm, in contrast to 134.1(5) pm from the crystal
structure. This apparent contraction of the aromatic ring was
expected, since X-ray diffraction locates the centers of electron
density, which in the case of an aromatic ring lie just inside the
ring. However, the same order of increasing ring bond distance
found in the gas was also present in the solid: the shortest ring
bond found was N(1)-C(2) at 132.5(5) pm in the gas (131.5-
(5) pm in the solid), followed by N(1)-C(6) measured at 133.2-
Acknowledgment. We thank the EPSRC for financial
support of the Edinburgh Electron Diffraction Service (Grant
GR/K/44411), for the provision of the microdensitometer
facilities at the Daresbury Laboratory, and for the Edinburgh
ab initio facilities (grant GR/K/04194). We also thank Dr. Lise
Hedberg for providing us with a copy of the ASYM40 program,
and Professors Ken Hedberg and Lothar Scha¨fer for helpful
discussions.
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