The molecular structure of pyridine in the gas phase determined from electron diffraction, microwave and infrared data and ab-initio force-field calculations

Journal of Molecular Structure, 156 (1987) Elsevier Science Publishers B.V., Amsterdam

315-329 - Printed

in The Netherlands

THE MOLECULAR STRUCTURE OF PYRIDINE IN THE GAS PHASE DETERMINED FROM ELECTRON DIFFRACTION, MICROWAVE AND INFRARED DATA AND AB-INITIO FORCE-FIELD CALCULATIONS

W. PYCKHOLJT,

N. HOREMANS,

University of Antwerp Wib-ijk (Belgium)

(UIA),

C. VAN

Department

ALSENOY*

and H. J. GEISE**

of Chemistry,

Universiteitsplein

1, B-2610

D. W. H. RANKIN University of Edinburgh, EH9 355 (Great Britain) (First received

Department

5 June 1986;

of Chemistry,

in final form

West Mains Road,

Edinburgh

16 June 1986)

ABSTRACT The gas-phase molecular structure of pyridine was studied by joint analysis of electron diffraction, microwave and infrared data, augmented by vibrational constraints taken from force-field calculations at the 4-21G ab-initio level. Geometrical constraints arising from 4-21G, 4-31G, 4-21GN* and microwave results were tested. The 4-21GN* constraints were significantly better than the others. The range of models that fit all available experi mental data was then investigated with respect to the difference between the CNC and NCC valence angles. This resulted in the following best-fitting model (rg distances, ril angles): NC = 1.344 A; C,C, = 1.399 A;C,C, = 1.398 A;CH (average) = 1.094 B;CNC = 116.1”; NCC = 124.6”; C,C,C, = 117.8”; C,C,C, = 119.1”; NCH = 115.2”. The data suggest that the perturbation resulting from the N atom is primarily in the CNC part of the ring. INTRODUCTION

Ab-initio calculations by Pang et al. [l] of pyridine, pyrimidine, pyrazine and s-triazine motivated us to investigate these compounds using a consistent combination of experimental data (gas phase electron diffraction, infrared and microwave spectroscopy), thereby aiming at the construction of selfconsistent molecular models. The objective of the series of studies was to verify experimentally the prediction of Pang et al. [l] that the CNC valence angle decreases by roughly 2” for each N atom introduced in the ring. After having reported on s-triazine earlier [ 21, we discuss now the structure of pyridine (see Fig. 1). Apart from the general objective it was hoped that details about the way the ring geometry reacts upon the introduction of one N atom would be obtained. Ab-initio calculations at the 4-21C level [l] *Research Associate of the Belgian National Science Foundation, **Author to whom correspondence should be addressed. 0022-2860/87/$03.50

D 1987

Elsevier Science

Publishers

B.V.

NFWO.

316

PYRIDINE

Fig. 1. Structural

formula

of pyridine

with atomic

numbering

scheme.

and 4-31G level [3] on the one hand, and the 4-ZlGN* level (i.e., the 4-21G basis augmented by polarisation functions on N) [l] on the other hand display small, but important differences in the endocyclic valence angles. Table 1 shows that the 4-21GN* geometry agrees best with the microwave results of Sorensen et al. [4, 51. However, the agreement cannot be taken as conclusive for the correctness of the 4-21GN* result, because we will show that microwave spectroscopy is rather insensitive to this aspect of pyridine geometry. Older electron diffraction studies could not address the question, because of the limited possibilities of their time [ 6, 71. Nowadays the combination of electron diffraction with information from vibrational spectroscopy and theoretical (e.g., ab-initio) calculations provides a means of solving the problem. A harmonic force field provides the link between the results of the experimental techniques, while characteristic corrections to bond distances provide the link with the ab-initio geometries. The approach is not without problems, but has proved useful in a growing number of cases [ 81. EXPERIMENTAL

A commercial sample of pyridine (Aldrich) with purity exceeding 99% was used. Diffraction patterns were recorded photographically (Kodak Electron Image plates) on the Antwerp diffraction unit (Technisch Physische Dienst TPD-TNO, Delft, The Netherlands). The temperature of the nozzle

31.7

TABLE 1 Comparison of some pyridine geometries (bond lengths in A, angles in decimal degrees) 4-31Ga

NC, C,C, c3c.l ‘7% W, C,H,

C,NC, NW,

c,w,

c,c,c*

NW, f&W, C,C,%

1.342 1.395 1.396 1.105 1.105 1.107 119.0 122.4 118.6 119.0 116.4 120.3 120.5

4-21Gb

1.339

1.395 1.397 1.106 1.105 1.107 118.4 122.8 118.5 119.0 116.4 120.4 120.5

4-21GN*C

1.341 1.396 1.395 1.109 1.105 1.107 116.7 124.0 118.4 118.5 116.2 120.3 120.8

Microwaved

1.338 1.394 1.392 1.087 1.083 1.082 116.9 123.8 118.5 118.4 116.0 120.1 120.8

Best-fite

Best-fitf

‘a

r&

1.344 1.399 1.398 1.096 1.092 1.094 116.1 124.6 117.8 119.1 115.2 119.3 120.5

1.342 1.397 1.396 1.090 1.086 1.088 116.1 124.6 117.8 119.1 115.2 119.3 120.5

ars geometry calculated from 4-31G data [3] using: rg - r(4-31G) = 0.013 A for CN, rg - r(4-31G) = 0.013 .K for CC and rg - r(4-31G) = 0.035 A for CH. brg geometry calculated from 4-21G data [ 11 using: rg - r(4-21G) = 0.006 a for CN, 0.013 a for CC and 0.035 A for CH. erg geometry calculated from 4-21GN* [l] using: rg - r(4-ZlGN*) = 0.013 .& for CN, 0.013 a for CC and 0.035 a for CH. dMicrowave rs structure from [ 5]. eThis work, best-fit model rg basis for bond lengths, rk basis for angles. fThis work, bestfit model rk basis.

tip was kept at 300 K. An accelerating voltage of 40 kV, stabilized within 0.01% was used. The electron wavelength was calibrated against the known CC bond length of benzene [ 91, resulting in X = 0.060659( 3) .&. Five plates were selected from recordings at the nozzle-to-plate distance of 600.05(2) mm, five plates from the distance of 350.07(2) mm and four from the distance of 200.09(2) mm. Two sets of optical densities were obtained, one measured on a home-built microprocessor-controlled rotating densitometer [lo], the other on the Joyce-Loebl MDM 6 densitometer (S.E.R.C. Microdensitometer Service at Daresbury Laboratory, Warrington, G.B.). All densities were converted to intensities using the one-hit model of Forster [ll]. Coherent scattering functions were taken from Bonham and Schafer [ 121, incoherent scattering functions from Tavard et al. [ 131. The data were further processed by using standard procedures [ 141. Levelled intensities were obtained in the ranges: 60 cm, 3.00 < s < 11.50 8-l; 35 cm, 8.75 < s < 19.50 a-‘; 20 cm, 11.75 < s < 31.00 A-‘; with As = 0.25 8-l (Antwerp set) and As = 0.5 8-l (Daresbury set). The resulting sM(s) curves are shown in Figs. 2 and 3. Numericalvalues are available from B.L.L.D. as Supplementary Publication No. SUP 26320 (3 pages). In anticipation of the results of the subsequent analysis, Fig. 4 shows some residuals obtained from the two sets of densitometer readings. Since no

318 1151

and

B (~1

pyridine

S IA-‘)

Fig. 2. Experimental levelled intensities I(s) between the two sets of densities is small, Antwerp densitometer readings are given.

significant differences occurred, reliable and the Antwerp data-set Strategy

with final backgrounds B(s). The difference hence only I(s) and B(s) obtained from the

we concluded that both sets were equally was used for the rest of this work.

of the analysis and theoretical

calculations

Pyridine poses a particularly difficult problem because of the extremely large correlations between its parameters. In the Molecular Orbital Constrained Electron Diffraction (MOCED) approach, correlation between geometrical and thermal parameters is tackled by using calculated vibrational amplitudes and by constraining certain geometrical differences to calculated values. A prerequisite to this is the availability of a harmonic force field to compute the vibrational amplitudes, to convert different geometry types (ra, rg, r-z) to a common basis and to link electron diffraction with microwave data. The vibrational properties of pyridine have been the subject of many investigations. The matter has recently been reviewed by Wiberg et al. [3]

319 PY RIDINE sM(S)

il S(A-‘1

Fig. 3. Experimental (- * - *) and theoretical ( -) densitometer readings.

44(s) curve obtained with the Antwerp

and Pongor et al. [15, 161, who also calculated vibrational force fields. Because in an analysis such as this the basis set, reference geometry and set of internal coordinates are preferably selected in a standardized way, we undertook a new calculation. Starting from the uncorrected 4-21G geometry after complete geometry relaxation [l],we followed the recommendations of Pulay et al. [ 171 and used, as in s-triazine [ 21, local symmetry coordinates, defined in Table 2. Stretching coordinates were distorted over 0.01 a, bendings and waggings over 0.05 radians and torsions over 0.1 radians all in the positive and negative sense. Ab-initio force constants then follow from Hooke’s law from: Fij = (@j (Si - Ai) - @j(qi + Ai)I/2Ai where gi denotes the force acting on coordinate qi, while qi is distorted over Ai. These force constants are known to be too large, due to deficiencies inherent in the contracted 4-21G basis and in the harmonic approximations. Scaling was performed with the linear scaling formula [ 18, 191: Fij (scaled) = (o i aj)1’2 Fij (unscaled)

320

5

10

15

20

25

30

S I A-’ 1

Fig. 4. Residuals for the two sets of densitometer readings. (A) s&f(s) [Antwerp - .&f(s) [Joyce-Loebl] ; (B) sM(s) [Antwerp] -&f(s) [best model] ; (C) sM(s) [Joyce-Loebl J s&f(s) [best model]. All differences are multiplied by a factor of 3. The first approximation to the background, B(s),was used to construct curve A, while refined backgrounds were used in B and C.

with (Yi the diagonal scale factor, obtained by fitting the calculated frequencies to the assigned, experimental frequencies of Wong and Colson [ 201, while keeping the number of groups as small as possible. Table 3 shows the group definitions and the,corresponding scale factors, while Table 4 presents the scaled force constants, with in-plane and out-ofplane vibrations factored out separately. The comparison between experimental and scaled 4-21G frequencies is given in Table 5. The root-meansquare deviation is 10.5 cm-‘, and the largest discrepancy 18.9 cm-‘. This makes our force field equivalent to the most recent force field of Pongor et al. [15, 161, which shows a root-mean-square deviation of 9.1 cm-’ and largest discrepancy of 17 cm-’ for 18 instead of 27 fundamentals of do-pyridine and using 8 instead of 5 scale factors. Our scaled force field was then used to obtain reliable vibrational amplitudes (U), perpendicular vibrational amplitudes at 0 K (K,) and shrinkage corrections (r, - r$). The latter were computed as ra - rz = K,, - u/r,, the assumption of small amplitude motion being justified by the rigidity of the aromatic ring. Table 6 summarizes the results for amplitudes and shrinkages. Rotation B, constants were taken from the microwave data of Mata et al. [ 51, and corrected to B, for harmonic vibration-rotation interactions using the scaled 4-21G force field. Centrifugal distortions and corrections arising

32:l

TABLE

2

Local symmetry coordinates in terms of internal coordinates for pyridine. vibrations; see Fig. 1 for the numbering in-plane, S,, * * .S,, out-of-plane (S,*..S,, atoms.) si

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

of

Specificationa

Assignment

r(l, 2)

C-N stretch C-C stretch C-C stretch C-C stretch C-C stretch C-N stretch C-H stretch C-H stretch C-H stretch C-H stretch C-H stretch CH in-plane deform. CH in-plane deform. CH in-plane deform. CH in-plane deform. CH in-plane deform. ring deformation

r(2>3) r(3,4) r(4,5) r(5,6) r(6,1) r(2,7) r(3,8) r(4,9) r(5,lO) r(6,ll) O(l, 2,7)--e(3,2,7) 0(2,3,8) - s(4,3,8) f3(3,4,9) - e(5,4,9) S(6, 5, 10) - e(4, 5,10) e(l,6,11) -0(5,6,11) f3(2, 1, 6) - 0(3, 2, 1) + 0(4, 3, 2) -0(5,4,3)+e(6,5,4)-e(l,6,5) 20(2,1,6)-e(3,2,1)-0(4,3,2) + 20(5, 4, 3) -e(s, 5, 4) -f3(1,6, e(3, 2,l) - e(4,3,2) + e(6,5,4)-e(l,6,5) 7(6,1,2,3)--(1,2,3,4) + 7(2,3,4,5)--(3,4,5,6) + ~(4, 5,6,1) - 7(5,6,1,2) ~(6, 1,2, 3) - ~(2, 3,4,5) + ~(3, 4, 5, 6) - ~(5, 6, 1, 2) - 7(6,1, 2, 3) + 27(1,2, 3, 4) -7(2, 3, 4, 5)-~(3, 4, 5, 6) + 27(4, 5, 6, 1) - ~(5, 6, 1, 2) x(7,1,3,2) x(8,2,4,3) x(9,3,5,4) x(10, 4, 6, 5) x(11, 5, 1, 6)

A, ring deformation 5) h, ring deformation B, ring torsion

B, ring torsion A, ring torsion

CH CH CH CH CH

wagging wagging wagging wagging wagging

“r(i, j) denotes the distance between atoms i and j; e(i, j, k) denotes the valence angle between atoms i, j and k; ~(i, j, k, I) the torsion motion; and x(i, j, k, 1) out-of-plane motion involving atoms i, j, k and 1.

from electronic contributions were ignored. The results are given in Table 7. To combine the diffraction data with the microwave data a proper weighting scheme is needed. Least-squares weights for the electron diffraction intensities were chosen to be proportional to s and scaled down at the ends of each s interval [14]. Rotational B, data were given a weight w = k/e’,

322 TABLE

3

Scale factors for force constants coordinates (see Table 2) Group

derived

Value

for a minimal

number

Affected

of groups

coordinates,

of symmetry

Si

“i

1 2 3 4 5

0.830 0.967 0.785 0.728 0.841

7,8,9,10,11,13,14,15 17 12,16 18, 19, 20, 21, 22, 23, 24, 25, 26, 27 1,2,3,4,

5,6

relative to the diffraction data. The constant k is commonly chosen to be lo-‘, while e (the estimated error of B,) is taken as 30% of the I?, -.B, correction. This leads to weights of 16 000 (A), 9200 (B) 400 000 (C) for the rotational constants relative to a diffraction data point. Constrained

least-squares

refinements

The radial distribution curve (Fig. 5) demonstrates that not all 10 geometrical and 31 thermal parameters can be determined independently. Hence models were constructed using 5 independent thermal parameters and constraining the others as defined in Table 6. Furthermore, 4 geometrical parameters were chosen with constraints on the others as defined in Table 8. The following models were tested, ensuring ring closure and CZVsymmetry. (1) Model (4-21G), with geometrical constraints derived from the 4-21G geometry converted to an rg basis. The required empirical corrections rg - r (4-21G) were taken from benzene [ 9, 171 for CC and CH and from triazine [l, 21 for CN. (2) Model (4-21GN*), with geometrical constraints taken from the 421GN* geometry [l], corrected to an rg basis. The correction rg - r(421GN*) for CN was derived from triazine, while the CC and CH corrections were copied from rg - r(4-21G). This seems justified in this case, because neither CC nor CH distances differ by more than 0.003 A between the 4-21G and 4-21GN* calculations. (3) Model (4-31G), with geometrical constraints derived from the 4-31G geometry [3], converted to an rg basis. The close correspondance between 4-31G and 4-21GN* distances led us to use rg - r(4-31G) = rg - r(4-21GN*). (4) Model (MW), with geometrical constraints taken directly from the microwave r, geometry [ 51. Table 9 summarises the numerical values of the geometrical constraints tested and the resulting geometrical and thermal parameters as well as the final disagreement factors for the four series of least-squares refinements. Tabulated e.s.d.‘s are least-squares e.s.d.‘s multiplied by 3.

4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

642 78 -57 54 -64 7 6 -1 -2 -2 -15 15 1 2 -2 0 -24 -7

2

673 96 -57 72 -64 89 19 -1 -2 -3 -2 30 0 -2 -3 2 24 36 25

1

3

649 79 -57 72 0 7 7 -1 -3 -1 -17 16 0 0 1 12 -26

4

649 78 -57 -3 -1 7 7 0 0 0 -16 -17 -1 1 12 26

5

642 96 -2 -2 -1 6 7 -2 2 -1 15 -15 0 -24 7 6

673 -2 -3 -2 -1 19 2 -3 2 0 30 24 36 -25 7

514 1 0 0 0 -2 0 1 0 0 9 3 -8 8

517 1 0 0 0 0 -1 -1 0 -11 4 8 9

513 1 0 -1 1 0 1 -1 10 -9 0 10

517 1 0 -1 1 0 0 -11 4 -8 11

514 0 0 -7 0 -2 9 3 8 12

55 1 -1 0 1 1 7 0 13

52 1 1 0 0 -7 4

Scaled 4-21G force constants (X 100, in mdyn a-’ or mdyn rad“) based on local triangle refers to in-plane species and the right triangle to out-of-plane species

TABLE

-1 -7 45

-6 43

14

15

16

55 1 7 0

25 0

17

156 -1 0

-7 43

-3

24

coordinates

26

53 -1 52 1 1 0 0 o-7 -8 -4

45

27

symmetry

18

112 0

0 -3 -1 -6 45

23

22

19

128

7 7 0 26

-14

7 7

21

13 -14 13 -14 13 0 -3 32

20

I 27 26 25 24 23 22 21 20

in Table 2. The left

10 -11 0 11 -10 26

defined

324 TABLE

5

Experimental and scaled theoretical ling was taken from [ 31)

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

IR frequencies

Vobs

“them

601 652 991 1032 1072 1079 1143 1218 1227 1362 1442 1483 1580 1584 3030 3042 3073 3087 3094 373 403 700 744 880 937 980 1007

585.4 636.1 988.3 1044.6 1054.7 1071.2 1141.8 1204.0 1225.0 1361.4 1460.9 1485.2 1579.5 1587.1 3048.6 3054.2 3061.8 3076.2 3085.2 383.2 406.7 690.3 732.2 873.9 938.5 994.1 1008.5

(cm-‘)

for pyridine

Au

(symmetry

label-

Symmetry class

-15.6 -15.9 -2.7 +12.6 -17.3 -7.8 -1.2 -14.0 -2.0 -0.6 +18.9 +2.2 -0.5 +3.1 +18.6 +12.2 -11.2 -10.8 -8.8 +10.2 + 3.7 -9.7 -11.8 -6.1 +1.5 + 14.1 +1.5

In the fifth series of refinements we scanned a number of fixed values of A5 (the difference between the N&C3 and &NC6 valence angle) keeping the other constraints equal to those of model (4-21GN*). Figure 6 shows the path of R(ED) as a function of A 5. Table 10 shows the correlation coefficients for the best-fit model. The model corresponding to the minimum in Fig. 6 is entered in Table 9 as the best-fit model. Table 10 shows the correlation coefficients for this model. Correlation coefficients for the other models are omitted, because they are essentially equal to those of the best-fit model. Since we cannot state exactly how possible systematic errors in rg - r, corrections or vibrational parameters propagate in MOCED analyses such as this, a final least-squares run was made in which all A i data were added to the list of refining parameters. If their refined values are insignificantly different from their input values, then their least-squares e.s.d.‘s multiplied by 3 (see Table 9; last column) give a realistic estimate of the accuracy of individual bond lengths and angles. For the heavy atom skeleton of the present molecule

325 TABLE 6 Calculated mean vibrational amplitudes (V) and shrinkage corrections together with definition of thermal parameters and constraints Distance

uca’c

r, -

u, u2 us us

C3-C6 H7 H8 H9 HlO Hll

0.059

0.099 0.077 0.099 0.094 0.093

-0.001 0.005 0.011 0.005 0.002 0.002

U, U, u, u, U, u, u, u, u,

C4-H7 H8 H9

0.094 0.099 0.077

0.002 0.004 0.011

H7-H8 H9 HlO Hll

0.157 0.127 0.117 0.130

0.002 0.003 0.003 0.004

u, - 0.003 u, + 0.002 U, _a _a _a _a

HS-H9 HlO Hll

0.157 0.128 0.117

0.002 0.003 0.003

_a _a _a

v””

Nl-C2 c3 H7 HS H9

0.046 0.053 0.061 0.097 0.094 0.094

0.001 0.000 -0.001 0.004 0.003 0.002

u, -- 0.003 u, - 0.003

C2-C3 c4 c5 C6 H7 H8 H9 HlO Hll

0.046 0.053 0.059 0.052 0.077 0.099 0.094 0.092 0.094

0.001 0.000 -0.001 0.000 0.011 0.004 0.003 0.002 0.003

c3-c4 c5

0.046 0.052

0.001 0.000

c4

r&) in A,

Definition

Distance

r,-rk

(ra -

- 0.002 - 0.001 + -

0.002 0.003 0.005 0.003

U, u, - 0.001

rk

Definition u, u, U, u, u, u,

- 0.002 + 0.002 + 0.002 - 0.003 - 0.004

aFixed at calculated value. TABLE 7 Experimental B, values, corrections required for harmonic vibration-rotation interactions, B, values and Bk values obtained from the joint microwave-electron diffraction analysis (best-fit model). Estimated errors (multiplied by 3) are given in parentheses

A B C

B, (cm-‘)

B, -B,

0.201442 0.193626 0.098706

-0.000083 -0.000109 -0.000017

(cm”) (25) (33) (5)

B, (cm-‘)

Bk (cm”)

0.201359 0.193517 0.098689

0.201369 0.193535 0.098687

(44) (46) (9)

we estimate individual bond lengths and valence angles to be accurate within 0.006 8, and 0.4”, respectively. For distances and angles involving H atoms the estimates are 0.012 kI and 4”, respectively. The last column of Table 9 gives the refined values of Ai and their e.s.d.‘s times 3, together with the parameters of the best-fit model of the fifth series of refinements. DISCUSSION AND CONCLUSIONS

Throughout all series of least-squares refinements it was noted (see Table 9) that the final disagreement factors for the microwave data, R(MW), are equal, and hence do not discriminate between the various models. The electron

326 RDF(r)

PYRIDINE

--7+0.5

VI

1s

30

2.5

35

4.0

4,5

r(A)

EXl?-TH.

Fig. 5. Experimental radial distribution function for pyridine. A damping factor of exp(-0.002s’) was used. Important distances are indicated by vertical bars of arbitrary length. The final difference curve for the best model is given below.

TABLE

8

Model construction and definition of refinable (a), e i valence angles (“) and 4 i constraints NlCl C2C3 c3c4 C2H7 C3H8 C4H9

r, r1 + r1 + r2 r,+ r,+

Al AZ A, A4

geometrical

parameters;

ri bond

lengths

C2NC6 NC2C3

03 0, + As

H7C2N H8C3C2

04 64 f As

diffraction disagreement factors, R(ED), change appreciably (Table 9 and Fig. 6). Hamilton’s R-ratio test [ 211 can be used as a statistical criterion for acceptance or rejection. The test performed at a significance level (Y = 0.01 showed that the 4-31G and 4-21G models can be rejected. At the significance level CY= 0.05 the MW model can also be rejected, but the 4-21GN* model remains acceptable next to the best-fit model. For sake of comparison the complete geometry of the best-fit model is presented in Table 1.

327 TABLE 9 Sets of geometrical constraints tested, together with refined values of r&-type geometrical and thermal parameters (see Tables 6 and 8 for definitions; e.s.d.‘s are discussed in the text) Model 4-31G Constraints AI (a) AZ (a) As (a) A4 (a) A5 (“) As (“) Geometrical r1 (a) r2 (a) 0 3 (“) e 4 (“)

0.053 0.054 0.000 0.002 3.4 3.9 parameters 1.342(l) 1.068(7) 118.7(l) 114.3(3.3)

Model 4-21G

0.056 0.058 -0.001 0.001 4.4 4.0

1.340(l) 1.070(7) 118.3(l) 114.5( 3.3)

Model 4-21GN*

0.055 0.054 -0.004 -0.002 7.3 4.1

Model best fit

Model MW

0.056 0.054 +I.004 -0.005 6.9 4.1

1.341(l) 1.076(6) 116.7(l) 114.9(3.4)

0.056 0.054 -0.004 -0.005 8.4 4.1

1.341(l) 1.076(6) 116.9(l) 115.0(3.3)

0.047(4) 0.059( 5) 0.067(9) 0.086(10) 0.095( 15)

0.049(3)

0.049(

0.056( 4) 0.066(S) 0.085(9) 0.101(15)

0.057(4) 0.067(9) 0.085(9) O.lOO(15)

0.050(2) 0.054(3) 0.066(S) 0.084(5) 0.103(6)

Indices k, (60 k, (35 k, (20

0.57( 1) 0.58(3) 0.93(5)

0.57(l) 0.59(3) 0.95(5)

0.57( 1) 0.59(3) 0.95(5)

0.57( 1) 0.60(3) 0.96(5)

2.004 0.035 0.401

1.805 0.035 0.361

1.821 0.035 0.364

1.776 0.035 0.349

of resolution cm) 0.57(l) cm) 0.58(3) cm) 0.92(6)

Disagreement R( ED)” R(MW) R(total)

factors 2.158 0.035 0.431

aDefined as R = {cw(&,~~ - Zcalc)*/~zuZ&,~~‘~ weight.

x

0.055(5) 0.054(5) -0.004(6) -0.002(7) 8.4(2) 4.1(2)

1.341(l) 1.079(5) 116.2(l) 115.2(3.3)

Thermal parameters 0.047(4) UI (A) 0.060(4) US (A) 0.067(10) u, (A) 0.086(10) u‘l (A) 0.094(18) u, (A)

3)

Final LS cycle

1000, where Z is I (molecular) and w is

We note that there is a linear decrease of the C&NC6 valence angle with increasing A5 which determines the NCC angles. This suggests that the perturbation caused by the introduction of the N atom remains largely localized in the &NC, part of the pyridine ring. Since many MOCED analyses employ information obtained with the 4-21G basis set, it is of importance to have empirical rg - r(4-21G) corrections available. Using our best-fit rg values (Table 1) and the 4-21G values o.f Pang et al. [l] one arrives at: CN = O.Oll(lO) i$, CC = 0.017(10) 8, CH == 0.025(14) 8, CNC = -2.3(4)” and NCC = lS(4)“. The error limits given in parentheses are estimated as twice the e.s.d.‘s on the Ai presented in Table 9.

328 TABLE

10

Correlation r1 r, 03 04 u, u, u, u, US k, k, k,

100 -96 56 -9 -17 -14 -16 20 0 39 -28 -27 rI

(X 100) among

coefficients

100 -42 -13 15 12 17 -20 -15 -38 27 26

100 -68 -12 -13 -4 10 -40 22 -18 -17

r2

03

100 6 8 -8 0 68 -3 6 5

100 45 31 -9 -3 23 68 83

04

U,

parameters

for the best-fit

100 15 -16 20 14 47 56

100 -13 -8 0 36 38

100 0 0 -25 -14

U,

U,

U,

model

-

100 1 -2 -3

100 10 14

100 65

100

U,

k,

k,

k,

R(%o) 1.85 ‘.

1.83 ‘.

1.82" 1.81..

1.80

1.78--

16

7

8

9

10

Fig. 6. Disagreement factor R(ED) (see Table rejection limits cy = 0.05 and 01 = 0.01.

A5(") 9 for definition)

as a function

of A5, with

329

The experimental corrections for pyridine agree well with those in existence for (hetero)aromatics: CN = 0.006 8, CC = 0.013 A, CH = 0.035 a and CNC = -2.2”. We conclude that the introduction of d-functions into the 4-21G basis set (4-21GN*) leads to a significantly better approximation of thle pyridine geometry and that this first example of a self-consistent MOCED analysis of a heteroaromatic system is as successful as previous analyses with non-aromatics [ 81. ACKNOWLEDGEMENTS

The work was partly supported by NATO, Research Grant Number 03141 82. The Belgian authors gratefully acknowledge financial support to their laboratory by the Belgian National Science Foundation NFWO. We thank the U.K. SERC for the use of their microdensitometer service. REFERENCES 1 F. Pang, P. Pulay and J. E. Boggs, J. Mol. Struct. (Theochem), 88 (1982) 79. 2 W. Pyckhout, I. Callaerts, C. Van Alsenoy, H. J. Geise, A. Almeningen and R. Seip, J. Mol. Struct., 147 (1986) 321. 3 K. B. Wiberg, V. A. Waiters, K. N. Wong and S. D. Colson, J. Phys. Chem., 88 (1984) 6067. 4 G. 0. Sorensen, L. Mahler and N. Rastrup-Andersen, J. Mol. Struct., 20 (1974) 119. 5 F. Mata, M. J. Quintana and G. 0. Sorensen, J. Mol. Struct., 42 (1977) 1. 6 V. Schomaker and L. Pauling, J. Am. Chem. Sot., 61(1939) 1709. 7 A. Almenningen, 0. Bastiansen and L. Hansen, Acta Chem. Stand., 9 (1955) 1306. 8 See for example, W. Pyckhout and H. J. Geise, in I. Hargittai (Ed.), Stereochemical Applications of Gas-phase Electron Diffraction, VCH Publishers, Deerfield Beach, in press. 9 K. Tamagawa, T. Iijima and M. Kimura, J. Mol. Struct., 30 (1976) 243. 10 J. F. Van Loock, L. Van den Enden and H. J. Geise, J. Phys. E: Sci. Instrum., 16 (1983) 255. 11 H. R. Forster, J. Appl. Phys., 41 (1970) 5344. 12 R. A. Bonham and L. Schafer in International Tables for X-ray Crystallography, Vol. 4, Kynoch Press, Birmingham, 1974, Chap. 2.5. 13C. Tavard, P. Nicolas and M. Rouault, J. Chim. Phys., Phys. Chim. Biol., 40 (1964) 1686. 14 L. Van den Enden, E. Van Laere, H. J. Geise, F. C. Mijlhoff and A. Spelbos, Bull. Sot. Chim. Belg., 85 (1976) 735. 15 G. Pongor, P. Pulay, G. Fogaraai and J. E. Boggs, J. Am. Chem. Sot., 106 (1984) 2765. 16 G. Pongor, G. Fogarasi, J. E. Boggs and P. Pulay, J. Mol. Spectrosc., 114 (1984) 445 and references therein. 17 P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. 18P. Pulay, G. Fogarasi and J. E. Boggs, J. Chem. Phys., 74 (1981) 3993. 19 S. Van Carlowitz, W. Zeil, P. Pulay and J. E. Boggs, J. Mol. Struct., 30 (1982) 113. 20 K. Wong and S. Colson, J. Mol. Spectrosc., 104 (1984) 129. 21 W. C. Hamilton, in Statistics in Physical Science, Ronald Press, New York, 1964, pp. 157.