An SCF-LCAO-MO study of the conformation of cyclopropylamine

93 Jom~~alof Molecular S_pucture, 15 (1973) 93-102 @I Elsevier Scientific Publishing Company, Amsterdam

AN SCF-LCAO-MO PROPYLAMINE

STUDY

OF THE

- Printed iti The Netherlands

CONFORMATION

OF

CYCLO-

ALAN R. MOCHEL AND JAMES E. BOGGS Department of Gfzenzistry,The University of Texas, Austin, Tex. 78722 (U.S.A.) PER NJ& SKANCKE University of Tromso, (Received

POOO

Trotns0 (Norway)

17 July 1972)

ABSTRACT

The conformationaf preference of cyclopropylamine has been investigated using (7,3/3) and (9,5/4) Gaussian basis sets. The experimentally observed symmetric conformation is predicted to be most stable, with another minimum in the potential function found by a rotation of 126” around the C-N bond. Comparison of the orbitals is made with earlier calculations on cyclopropane.

INTRODUCTION

The nature of the chemical bonds in cyclopropane and the substituted derivatives of cyclopropane has long held the interest of many experimental and theoretical chemists. The orbital schemes of Walsh’, Co&on and Mofi5tt2, and others have provided simple models by which many of the physical and chemical properties of these small ring molecules can be rationalized. The electronic distribution in the cyclopropyl ring is of particular importance. The models all imply regions of high electron density outside the ring with the Walsh model predicting a relatively deficient electron density in the center of the ring. This picture provides two mechanisms by which substituent groups may interact with the ring. Electron deficient or electron withdrawing groups are said to “conjugate” with the eiectron affluent edge of the ring. This argument has been used to rationalize the bisected conformation found for the dimethyl cyclopropyl carbonium ion3, eycloprop~ecarboxaIdehyde4,‘, cyclopropyl methyl ketone6, cyclopropanecarboxylic acid chloride6, phenylcyclopropane’, cyclopropylsemidiones’, and cyciopropanecarboxylic acid fluoride’. For cyclopropanecarboxaldehyde5 and cyclopropanecarboxylic acid fluoride’ both cis- and trans-conformers have been studied

94 and the barrier to rotation of the substituent group has been found to be dominated by a very large V, term. A second possibility is the conjugation of an electron affluent substituent with the electron deficient center of the cyclopropyl ring. The symmetrical conformations found for the 9-cyclopropylanthracene” and 1,4dicyclopropylnaphthalene’ ’ anion radicals and the cyclopropylphosphine” and cyclopropyl amineI molecules have been accounted for on this basis. The conformation of every substituted cyclopropane which has been observed can be “explained” using the simple qualitative concepts. Within the past few years several SCF-LCAO-MO calculations on cyclopropane have been published. The earliest ub initio calculation on cyclopropane was that of Preuss and Diercksen13. A small s-p Gaussian type basis set (4,2/2) was used and the carbon-carbon bond distance was optimized. More recent calculations involving rather large s-p bases are those of Buenker and Peyerimhoffi4 (10,5/5) and Kochanski and Lehn” (9,5/4). The incorporation of dtype functions on the carbon atoms with a rather small uncontracted s-p basis (5,2,1/2) was performed by Marsmann, Robert, and Van Wa.zerr6. The last three of these studies are interesting in that all predict the existence of bent bonds in cyclopropane with a maximum charge density located outside the ring triangle. The calculations of Kochanski and Lehn also predict a “central hole” in which a relative electron deficiency of 15 % is found in the center of the ring. Comparing the relatively high quality ab initio SCF calculations on cyclopropane with experimentally observed properties and with the classical qualitative models has provided some insight into the bonding characteristics. Similar ab initio calculations on substituted derivatives of cyclopropane where the conformational preferences and “ring-attached group interactions” might be examined have yet to appear in the literature. For this reason an SCF-LCAO-MO computation on several conformations of cyclopropylamine have been undertaken.

COMPUTATIONAL

METHOD

AND

GEOMETRY

The conformational preference of cyclopropylamine was studied by computing molecular energies at several dihedral angles of the amino group relative to the cyclopropyl ring. The ab initio SCF-LCAO-MO calculations were performed using the general program IBMOL l7 . Two Gaussian basis sets were employed. The first set consists of 7sand 3p type Gaussian functions centered on the carbon and nitrogen atoms with 3s type functions centered on the hydrogen atoms. The second basis is composed of 9s and 5p type functions centered on the carbon and nitrogen atoms with 4s type functions centered on the hydrogens. For the (7,3/3) basis the s Gaussians on the heavy centers were contracted into two group functions and thep Gaussians on the heavy centers were contracted into one group function. For the (9,5/4) basis the s andp type Gaussians on the heavy centers were con-

95

tracted into four and two group functions, respectively. The s type Gaussians on the hydrogen atoms were contracted into one group in the (7,3/3) basis and into two groups in the (9,5/4) basis. The orbital exponents and contraction coefficients are those optimized by Huzinaga l8 _ The geometry employed in the calculation was essentially that reported by Hendricksen and Harmony”.The Cartesian coordinates of the symmetrical conformation of cyclopropylamine are given in Table 1. TABLE

1

CARTESIAN

Distances

COORDINATES

OF THE SYhlhlETRICAL

given in atomic

Center

x

C(1)

0.0

C(2)

1.436219

C(3) N WI) H(2) H(3) H(4) H(5) H(6) H(7)

-1.436219 0.0 2.370246 2.370246 -2.370246 -2.370246 0.0 1.541101 -1.541101

RESULTS

AND

CONFORMATION

OF CYCLOPROPYLAMINE

units.

Y

Z

0.0

0.0 0.0

-2.487605 -

2.487605 1.385829 3.026864 3.026864 3.026864 3.026864 1.108580 2.508928 2.508928

0.0 2.315544 1.732700 - 1.732700 1.732700 - 1.732700 - 1.713617 2.433588 2.433588

DISCUSSION

Molecular energies at twelve dihedral angles have been calculated using the (7,3/3) basis set. The computed energies are listed in Table 2. A curve of the total TABLE

2

CALCULATED

ENERGIES ATVARIOUS

Angle of One electron rotation energy (degrees) (atomic units)

DIHEDRALANGLES

OF THE AMINO

GROUP

USING

Two electron energy (atomic azzits)

Nuclear potential energy (atomic wits)

Total energy (atomic azzits)

179.002060 179.103 115

125.070449 125.195403

-

171.274199 171.270362 171.268415

0 45

-475.346 -475.568

72

-475.825078

179.207994

125.348 670

-

-475.993379 -476.071146 -476. I43 945 -476.174 743 -476.232899 -476.273 622

179.270675 179.298 677 179.324820 179.335963 179.357262 179.372486

-171.268797

-476.329 473 -476.378024 -476.472541

179.393 927 179.413234 179.453 178

125.453 907 125.503 176 125.549 344 125.568 829 125.605478 125.630968 125.665601 125.695 302 125.751524

- 171.269488 -171.267839

90 99 108 112 120 126 135 144 180

708 880

THE

-171.269293 -171.269781 -171.269951 -171.270159 -171.270169 -

171.269944

(7,3/3)

BASIS

96

45 ANGLE

135

90 OF

ROTATION

I80

fOegreed

I. Total energy versus angle of rotation from the experimentally observed symmetrical formation, using the (7,3/3) basis set.

Fig.

Con-

energy versus angle of rotation is plotted in Fig. 1. The zero degreerotation was chosen to be the experimentally observed symmetrical conformation. It is seen that the absolute minimum is predicted to be the symmetrical cotiormer with another minimum predicted at a dihedral angle of 126”. The difference in energy between the two minima in the potential function is 0.004030 au or 2.53 kcal/mole. This result is consistent with the experimental data in that the symmetrica nonformation is calculated to be the more stable one with the 126” or gatcche conformation so high in energy that its population, even at moderately high temperatures, is too low for detection by standard techniques. To obtain more significant energies for the theoretically predicted conformations, a larger, more appropriate (9,5/4) basis set was empfoyed. Since the (9,5/4) basis requires considerably more computer time, it became necessary to restrict the number of energies calculated to four angles. By assuming that the (7,3/3) basis set calculations provide a qualitatively correct potential function, these four angles were chosen to be the critical values of 0,72, 126 and 180 degrees. The computed energies for the (9,5/4) b asis set are given in Table 3. An assumed potential function for the rotation of the amino group about the C-N bond is shown in Fig. 2. The difference in energy between the symmetrical conformation (0”) and the conformation of 126” is predicted to be 4.4 kcal/mole, a value considerably larger than that predicted by the (7,3/3) basis. The barrier heights relative to the 126” conformation also differ markedly in the two bases. The 72” barrier is calculated to be 1.10 kcai/moIe and the 180” barrier 1.40 kcalfmole using the

97 TABLE ENERGIES

3 FOR CYCLOPROPYLAMINE

Angle of One electron rotation energy (degrees) (atomic zznits) -479.106007 -479.572964 -480.024 186 -480.235677

0

72 126 180

1719460-

FROM THE (9,5/g)

BASIS

Two electron energy (atomic zznits)

Nuclear potential etzergy (atonzic units)

Total energy (atonzic units)

182.078 394 182.276465 182.443060 182.535561

125.070449 125.348670 125.630968 125.751524

-171.957164 - 171.947830 -171.950158 - 171.948593

I

I

I

4.4 kcol/mole

I

- 1719580 0

ANGLE

(7,3/3),

basis

1

I 90

45

135

OF

the basis predicts the 72” barrierto barrier to be 0.98 kcal/mole.

studied by means of the molecular

schemes

highest occupied

in the

basis are identical.

orbital containing MO’s containing

180

98

moIecular orbital picture was considered to be rather close to the Walsh model of cyelopropane. The molecular orbitals of the symmetrical conformation of cyclopropylamine using the (9,5/4) basis are not as well defined as those for cyclopropane; however some similarities are present. The low lying sixth MO in cyclopropylamine is of principally 2s character for the equivalent carbon atoms and p,, for the unique carbon atom. The 14th and 15th molecular orbitals in cyc~opropylamine are composed mainly of C(p,> and C(p,,) AO’S. The highest occupied molecular orbital is largely non-bonding and can be attributed in part to the lone pair or nitrogen. The 9th molecular orbital is interesting in that the charge is delocalized over ali of the heavy atoms with the carbon atoms principally 2p= and the nitrogen atom mainly 2~~. The alterations in the nature of the molecular orbitals as the NH2 group is rotated about the C-N bond provide one means by which the conformational preferences may be examined. The orbital energies, total overlap populations and total atomic populations for the four rotational angles are presented in Tables 4, 5, and 6. TABLE

4

CHANGE

IN ORBITAL

ENERGIES FOR VARIOUS

DIHEDRAL

ANGLES

OF CYCLOPROPYLAMINE,

USING

(9,5/4)

BASIS

MO

E&%?fg?Y

0" (symnreirical) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

- 15.523955 -11.272142 - 11.235127 - 11.234502 1.210364 1.093685 - 0.824681 - 0.797633 - 0.691152 - 0.644102 - 0.624681 - 0.556348 - 0.519661 - 0.450442 - 0.416842 - 0.379292

A Em-gy 72” - 0.972 - 5.678 - 2.545 f 4.607 - 5.805 - 0.205 - 2.146 - 7.388 -112_116 - 0.870 +25.397 - 3.533 - 2.609 -40.809 - 11.675 +30.939

(

x’

I 03) I26O - 2.740 - 8.004 - 8.247 1.819 -11.380 - 0.641 - 7.253 - 14.148 - 8_.502 - 3.488 f 10.709 + 5.252 -11.765 -42.162 - 14.196 +23.961

180” f 0.658 - 5.119 - 10.283 - IO.286 -11.926 + 0.227 - 13.256 -13.015 + 5.735 - 1.612 -17.251 i_ 6.551 -13.215 -23.250 - 6.484 + 4.858

The numbering of the carbons and hydrogens is indicated in the figure of symmetrical conformation shown in Fig. 3. Since the changes in energy with rotation for nearly all of the molecular orbitals are larger than the energy differences between the conformations themselves, no one molecular orbital can be

99 TABLE 5 TOTAL

OVERLAP

POPULATIONS

FOR VARIOUS

DIHEDRAL

OF CYCLOPROPYLAMINE,

USING

(9,5/4)

OF CYCLOPROPYLAMINE,

USING

(9,5/d)

ANGLES

BASlS

Cl-N Cl-c2 Cl-C3 C2-C3 Cl-H5 C2-Xl c2-3x2 c3-H3 C3-H4 N-H6 N-H7

TABLE TOTAL

0”

72”

126”

0.2816 0.1871 0.1871 0.1866 0.3762 0.3715 0.3750 0.3715 0.3750 0.3322 0.3322

0.2556 0.1949 0.1885 0.1076 0.3738 0.3697 0.3635 0.3593 0.3642 0.3378 0.3306

0.2698 0.1555 0.2080 0.1147 0.3784 0.3638 0.3574 0.3684 0.3708 0.3441 0.3326

ISO” 0.2787 0.1768 0.1768 0.1629 0.3847 0.3746 0.3692 0.3746 0.3692 0.3444 0.3444

6 ATOMIC

POPULATIONS

FOR VARIOUS

DIHEDRAL

ANGLES

BASIS

Cl C2 C3 N HI H2 H3 H4 H5 H6 H7

0"

72”

126”

180”

6.1384 6.4297 6.4297 7.7252 0.7592 0.7748

6.1004 6.4686 6.4269 7.7297 0.7806 0.7708 0.7632 0.7763 0.7744 0.7039 0.7052

6.0914 6.4722

6.0993 6.4549 6.4549 7.7304 0.7809 0.7650 0.7809 0.7650 0.7628 0.7030 0.7030

0.7592 0.7748 0.7960 0.7064 0.7064

Fig. 3. Numbering is shown.

6.4455 7.7235 0.7849 0.7722 0.7721 0.7638 0.7597 0.7086 0.7062

of the atoms in cyclopropylamine.

The observed

symmetrical

conformation

I

1 0”

126O

72” ANGLE

OF

ISO

ROTATION

Fig. 4. Overlap population aud total energy of the 14th MO as a function of angle.

I

I

-_44

*

X

-

7z” ANGLE OF Fig. 5.

1260 ROTATION

-.46

l&W

OverIap population and total energy of the 15th MO as a function of angle.

singled out as being particularly important in determining the conformationai preferences. The popuiation analysis for the various rotations indicates that most molecular orbitals alter in a rather compiex manner. The 14th and 15th MO’s are illustrative of this behavior. The overlap population for the heavy atoms and the orbital energies at various dihedral angles are plotted in Figs. 4 and 5. Any attempt to “understand” the reason for the

101 rather stable symmetrical conformation or the less stable 126” conformation appears to be very difficult from those results. If the symmetrical conformation can be “understood” in terms of a delocalization of the lone pair of electrons on the nitrogen into the electron deficient center of the cyclopropyl ring it would be expected that the charge on nitrogen would be functionally dependent on the angle of rotation of the amino group about the C-N bond. Should the amino group be rotated away from the symmetrical conformation the nitrogen lone pair would be more localized and the charge on nitrogen should increase. The calculation of the total population on nitrogen using the (9,5/4) basis indicates little dependence of charge on rotation angle. TABLE

7

CALCULATED

ENERGIES

FOR

PROPYLAMINEATVARIOUS

C-N length

Conformer

THE

(C-N)

SYMMETRICAL (0-J AND gauche (126”) CONFORMATIONS BOND DISTANCES [(7,3/3) basis]

~5 (all)

EL (au)

EN

(all)

OF CYCLO-

ET

G-0

1.428

0” 126’

-475.346708 -476.273 622

179.002060 179.372486

125.070449 125.630968

-171.274199 -171.270169

1.451

0” 126”

- 474.409 196 -475.292428

178.551322 178.902964

124.58 1200 125.116286

-171.276674 -171.273 177

1.474

0” 126;

-473.489 -474.353

178.108492 178.451887

124.102 500 124.627 123

-171.278 151 - 171.274801

I.497

0’ 126”

-472.586069 -473.432 676

177.673371 178.008 789

123.633971 124.148371

-171.278727 - 171.275511

1.520

0” 126”

-471.699482 -472.528510

177.245 750 177.573446

123.175241 123.679668

-171.278490 - 171.275396

1.543

0’ 126’

-470.828916 -471.640827

176.82543 1 177.145647

122-725 963 123.220643

-171.277521 -171.274537

143 811

One of the major structural effects attributed to conjugation or state of hybridization in substituted cyclopropane molecules is the alteration of bond lengths between the cyclopropyl carbon atom and the attached group. A distinct shortening of the C-Cl, C-Br, C-P and C-N bonds in cyclopropyl chloriderg, bromide”, phosphine”, and amineI as compared to the corresponding methyl compounds has been observed. Employing the (7,3/3) basis, an optimization of the C-N bond for the symmetrical and 126” or gauche conformations was performed. The calculated energies for the two conformers as a function of C-N bond length are given in Table 7 with the graph of total energy versus C-N bond distance given in Fig. 6. The minimum in energy is determined to be at very nearly the same bond distance of 1.505 A with the symmetrical conformation perhaps slightly shorter.

I02 I

’

0

I

,

\

0 \

l26o

l

\

Conformer

l --l

\

.’ 0-0

* 0” Conformer \

I.4II

1.44

l--

*

1.47

/.A-’

I.50

I.53

56

r(C-N) Fig. 6. Total energy as a function of the C-N

bond length, using the (7,3/3) basis set.

ACKNOWLEDGEMENT

This work foundation.

has been supported

by a grant

from

the Robert

A. Welch

REFERENCES 1 2 3 4 5 6 7 8 9

10 11 12

13 14 15

16 17 I8 19 20

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