the vibrations and the molecular structure of urea and guanidonium

The Vibrations and the Molecular Structure of Urea and GuanidoniumAuthor(s): Lotte KellnerSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 177, No. 971 (Mar. 18, 1941), pp. 456-475Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/97468 .

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456 L. Kellner

Edsall 1936 J. Chem. Phys. 4, 1. Ellis and Bath 1939 Phys. Rev. 55, 1098. Ellis and Bath 1939 J. Chem. Phys. 7, 862. Fox and Martin 1940 Proc. Roy. Soc. A, 175, 208. Howard 1935 J. Chem. Phys. 3, 207. Kahovec and Kohlrausch 1936 S.B. Akad. Wiss. Wien, Ilb, 145, 579. Kellner 1936 Proc. Roy. Soc. A, 157, 100. Kellner 1937 Nature, Lond., 140, 123. Kohlrausch and Pongratz 1934 Z. phys. Chem. B, 27, 176. Sanborn 1932 J. Phys. Chem. 36, 1799. Tisza 1933 Z. Phys. 82, 48. Wright and Lee 1935 Nature, Lond., 136, 300.

The vibrations and the molecular structure of urea and guanidonium

BY LOTTE KELLNER

(Communicated by W. T. Astbury, F.R.S.- Received 25 June 1940-Revised 21 November 1940)

The vibrations of urea and guanidonium have been calculated for a field containing valence and angle forces. The assumption is made that urea has the symmtery C2, and guanidonium C3h.

It is shown that it is possible to assign every observed frequency of these two substances to definite modes of vibration under these assumptions. The force constants have been evaluated and have been found to be

fc-N= 7a1 x 105 dynes/cm. for guanidonium, and fCN - 6-6 x 105 dynes/cm. andfc=o = 9 7 x 105 dynes/cm. for urea. These values are compatible with the hypothesis that quantum mechanical resonance occurs in both molecules, with the result that the C-N bond in urea has approximately 28 % double- bond character and the C=O linkage a corresponding single-bond character. The guanidonium ion shows complete resonance; each C-N bond has f double-bond character. Curves have been drawn to illustrate the relation

between the valence force constants and the bond character.

1. INTRODUCTION

It has been evident for some time, from the study of the chemical behaviour

as well as from the X-ray investigation of the crystalline structure of urea

and guanidonium, that these two molecules show quantum mechanical

resonance between several possible configurations. Pauling (1935) suggests resonance between a homopolar (figure 1, I) and two ionic (figure 1, II, III)



The vibrations of urea and guanidonium 457

structures for urea, CO(NH2)2, and ascribes 28 % double-bond character to the C-N linkages and a corresponding single-bond character to the C=O bond, in agreement with the X-ray measurements of the nuclear distances of dc=o = 125A and dc_N = 1F37A (Wyckoff and Corey I934). In the guanidonium ion, C+(NH2)3, all three structures (figure 2, 1, 11, 111) should have equal probability, which means that resonance is complete and each C-N bond has 3 double-bond character. The nuclear distances in organic

NH2 H2N

:.0, C C-C NH2

NH2 H2N

NH2 H2N

0 C c+ NH2

I NH2 H 1NX -- NH2HN

,, / H2NN

:0-

--------

III NH+2 H2N III

FIcGURE 1. Electronic structure of FIGURE 2. Electronic structure of urea. guanidonium

compounds are known to be very accurately constant for linkages of the same type in different molecules, and these distances have been used up to now as the only criteria for the bond character. The force constants measuring the valence forces remain constant in the same way, and provide further means of determining the occurrence of quantum mechanical resonance between different configurations. It has been found in the case of the C-C bond, which is best known, that ethane, with a typical single bond, furnishes fc = 4.96 x 105 dynes/cm. (Sutherland and Dennison 1935), while the

Vol. 77. A. 29



458 L. Kellner

values fc = 9 79 x 105 (Sutherland and Dennison i935),f c= = 7 56 x 105 (Kohlrausch 1936) and fcc = 15-71 x 105 (Sutherland and Dennison 1935)

are obtained from ethylene, benzene and acetylene, respectively. It will be seen that in a molecule with alternating double bonds (so far, benzene is the only molecule for which this has been worked out) the force constant is nearly (fcfc +fc=c). In the present paper the vibrations of urea and guanidonium have been computed theoretically and the force constants calculated from the observed vibration spectra.

2. METHOD OF COMPUTATION OF VIBRATIONS

The vibrations of urea and guanidonium have been calculated as functions of the force constants in the usual way. A harmonic potential function was chosen, and the molecule assumed to be held together by valence and angle forces only. The resulting secular equation was factorized, by means of group theoretical methods, into determinants of lower orders corresponding to the symmetry type of the molecule under consideration.

3. VIBRATIONS OF UREA

The potential function has the form:

2V = fo gc=o +fc_N(62 N + 6C-N2) +fNH(1H1' +2

+ 2 + gN2-l2') + d'scoscN {(2a,)2 + (z2)2} + d8sN {a (2f)}2

? 6C_N SN_H {(Ayl)2 + (Ay2)2 + (Ay3)2 + (Ll4)2} + 628N-2 {(_6)2 + (Ay7)2}

+ 4Ts2i11 sin2 0{(l 1)2+ (A+2)2}

+ Ksc80 sin/I sin 2/3{(zPiP1)2? (zi2)2 + (3V)2} (1)

The 6i are the elongations of the valence links under the influence of the valence forces; the zai and A y refer to the deviations of the valence angles from the equilibrium position and will be understood by reference to figure 3.

A&j measures the twist of the C-N bonds, and z0j the angle between the planes OCNi and OCNi+?. Aij occurs only when the atoms C, 0 and N move out of the plane originally containing them. 2fl is the angle between the two C-N valencies, and the angle between the N-H bonds has been taken to be the tetrahedral angle 109? 28'. fc-N, fc.0 and fN-H are the valence force constants, and d', d, 81 and 62 the angle force constants. T measures the torsion of the C-N bonds and K the force with which the C, 0 and N atoms are held in one plane. The co-ordinates are simple linear functions of the displacements of the vibrating atoms from their equi-




librium positions. In calculating these functions the procedure of Lechner (1932) has been followed; his method has been extended to include oscillations in which the atoms move out of the molecular plane.

+/IOCN, =a

H2 \ OCN2 = 72

<N1 ~~NICN2 = 2, H' HCN1H' = 76

Ny ~~~~CN,H- = Y2

CN2H' = y4 \ - H1~~N2 2 = Y4

H2'

FIGURE 3. The urea molecule.

It is known from the investigation of the crystalline structure of urea (Wyckoff and Corey 1934) that the molecule has the symmetry C2v and that the carbon, oxygen and nitrogen atoms lie in one plane. The twofold symmetry axis C2 passes through the C O line. It follows from group theoretical considerations that the vibrations of urea split up into four symmetry types. Table 1 shows their behaviour with respect to the symmetry elements of C2,, their activity in the infra-red and Raman spectra and the number of vibrations in each symmetry class.

TABLE 1

Raman spectrum Symmetry propertiesi

Sym- _ Infra-red spectrum Degree of No. ot metry Anti- _ depolar- vibra- class Symmetric symmetric Activity Band type Activity ization tions

A1 C2, o- , o-~ - Active Perpendicular Active p < -6P 6 A2 02 oz, o~ Inactive - ,, p= 7 3 B1 C2,9G Active Perpendicular ,, p= 6 4 B2 oS C2, 9ol Active Parallel ,, p-= 5

C2, o-x and or refer to the symmetry elements of the group C2,* There are 3 x 8-6 = 18 vibrations altogether. The equation connecting the six vibrations of the class A1 is given by the determinant (2), where A = 4,g2j2.

The vibrations of the type A2 are found by solving the equation (3). The symmetry type B1 furnishes the fourth-order determinant (4), and the five vibrations belonging to the class B2 are connected bythesecularequation (5).

29-2



460 L. Kellner

z~~~~~~~~~~~~~ z

z~~~~~~~~ z Z

O < S wz z

cz E C

+ O O e ca+ , + O~~~~CO

z, I i I I X + ZI iZ

Io ZI z z ~~~~ ~~zz coz c~~~~v ~ ~ ~ C Ieq I I

x I z ~~~~~~~~~~z o + 0~~~ ~~~~~~~ ?

II o z~~~~~~~~~~~ +~~~~~

z~~~~~

z~~~~~~~~~~ z

z -

? I Iz~~~

z I x~~~~~~~~~~~~~ z~~~~~~

o ZI o~~~~~ZC

? I~~~~~~~~~~~~~~~~~~~~~~



The vibrations of uhrea and guanidoniuhm 461

_ z

+ O

CM,0 C- z zl

~~ I $ m S t >; ? ? $ o-

z m N J . a s 8 " '0

Z Z - C S

D ~~~~~~~ S ~~~~~

~~~~~~~~~~~~~~~ + CO C.)

eq z I <

CO CO1

_



462 L. Kellner

co Co

11

II

zo o 7

a: > > * O

61:51~~~~~~~~~~~~~7

CO ~~~0+ +

I I ') 0

+ 14~~~g~ ~

(Nt S - 8 j e E

I (N$ _t , * E ttCE

Q < S , 0




4. INTERPRETATION OF THE CO(NH2)2 AND CO(ND2)2 SPECTRA AND EVALUATION OF FORCE CONSTANTS

The Raman spectrum of CO(NH2)2 and CO(ND2)2 has been investigated by Kohlrausch and Pongratz (i934) and by Otvos and Edsall (I939). Their data are given in table 2, together with the results of the study of the infra- red spectrum (see preceding paper). The letters P and D mean 'Polarized' and 'Depolarized' respectively. It follows from table 1 that the polarized bands belong to the symmetry type Al and that there are six vibrations of this class, three of which are principally valence vibrations and three deformation frequencies. The N-H valence vibration is known to lie in the region 3300-3500 cm.-', so that the 3235 band cannot be interpreted as a fundamental as there is only one N-H valence oscillation of the type A,. All the other strongly polarized bands can be assigned to fundamental vibrations (table 3).

TABLE 2

CO(NH2)2 CO(ND2)2 Infra-red spectrum. Raman spectrum Raman spectrum

Kellner (see A

preceding Kohlrausch paper) and Pongratz Otvos and Edsall Otvos and Edsall

525 (2b) 534 (2) D 458 (1) D 548 (1) P

685 (lb) 601 (2) D - 1000 (8) 1008 (10) P 997 (6) P -- 1157(lb) 1167(4)P 890 (5)P

- 1350 (i) Not observed 1049 (1) ? 1458 (0) 1478 (2b) D Not observed

1201 (lb) ? 1593 (2b) 1604 (4b) P? 1247 (3) P

-- 1665 (0) 1680 (3b) P 1613 (3b) P 3218 3218 (lb) 3235 (5b)P -

3376} 3383 (3vb) 3385 (6vb) P 2421 (5vb) P

3434 2506 (3) P? 3434 --

Not observed 3462 (2vb) 3496 (5b) D 2603 (3) D

TABLE 3. FUNDAMENTAL VIBRATIONS OF UREA OF CLASS Al

V1 P2 V3 V4 V5 V6 Molecule Not observed 1008 1167 1604 1680 3385 CO(NH2)2

548 997 890 1247 1613 2421 CO(ND%ht CO(ND2)2



464 L. Kellner

If the determinant (2) is evaluated under the assumption that the angle

forces can be neglected as compared with the valence forces, the following

third-order equation is obtained:

( { (1 + ) +fCN cs)+fN-H( + 3N)}

+ ?A{co fgN [2 cfN 2C2f (f O )+

1+ 1 2 +fcOf-11 +_ 'I +

+fcN fn[(~N 1 2 oC82 )(I + 2 - 9

fc=ofc-N fN-H{MN (m? ml) mN ? M2H)

+2cos2/?(_1 2 Vi0.(6 mm n= 3mN/ 0. (6)

It is known that the C-N valence vibration, which is not very different

from the C-C vibration, lies between approximately 800 and 1000 cm.-',

while the C zO oscillation in aldehydes, ketones and fatty acids occurs at

1700 cm.-'. The frequency 1008 may therefore be assigned to the C-N

valence vibration, and 1680 to the C-O oscillation. The fact that this

latter value is lower than in ordinary C oO bonds indicates that the C=O

linkage in urea is weakened in accordance with the conception of resonance

in the molecule. As the symmetrical N-H valence vibration in ammonia

is 3336, the band 3385 is assigned to the symmetrical N-H oscillation in

urea. Using these frequencies, and putting 2/? - 114?44' (Wyckoff and

Corey 1934), the following figures for the valence force constants are

obtained: fc=o = 9*7 x 1oi dynes/cm.,i

fc-N = 6-6 x 105 dynes/cm., (7)

fN-H = 6*3 x 105 dynes/cm. J

If MnD is substituted for ml, in equation (6) and the above force constants

are used, the following frequencies (table 4) are computed for CO(ND,)2

from (6):




TABLE 4. VALENCE VIBRATIONS OF CLASS A1 FOR CO(ND2)2

V2 V5 V6

Observed 997 1613 2421 Calculated 909 1727 2440

The agreement between observed and calculated values is satisfactory, as the contribution of the angle forces to the vibrations has not been taken into account. The frequencies 1167 and 1604 for CO(NH2)2 (if 1604 is polarized, which still seems doubtful) and 548, 890 and 1247 for CO(ND2)2 are to be interpreted as deformation vibrations.

It follows from (3) and (4) that the symmetry classes A2 and B1 contain one N-H valence vibration each, in which the two N-H bonds of each NH2 group perform an asymmetric vibration. The other frequencies of these types are bending frequencies. If the angle forces are again neglected, the asymmetric N-H frequency is found to be v = 3460, takingfN-fl = 6 3 x 105

dynes/cm., so that the observed band v = 3496 may be identified with this oscillation. In the case of the N-D linkage, the corresponding vibration is obtained at v 2550 (V 2603 observed). The infra-red spectrum shows a band at 3434 and no band at 3496. As the bands of the type A2 are forbidden in the infra-red spectrum, v 3496 is therefore to be assigned to the class A2 while v 3434 belongs to the symmetry type B1.

The vibrations of B2 (5) contain one C-N valence frequency in addition to a symmetric N-H oscillation. This C-N frequency represents an asymmetric oscillation of the two C-N bonds. If the angle forces are left out of consideration and the above values (7) used forfC-N and fN_H, the frequency 1456 is obtained for CO(NH2)2 and 1470 for CO(ND2)2. In the latter case no corresponding band has been observed, while the observed v 1478(CO(NH2)2) agrees very well with the calculated value.

Equation (3) shows that a bending frequency and a torsional vibration of the NH2 groups fulfils the symmetry requirements of the class A2. The nitrogen and hydrogen atoms move in such a way in this bending frequency that the valence angles H-N-H remain unchanged while the angles H-N-C are deformed. A comparison with the corresponding frequencies of guanidonium (12) shows that the secular equation has the same form, and the assignment of the vibrations can therefore be taken over with the only alteration that the distance SC-N is slightly different in the case of urea. The band 1164 is correspondingly assigned to the bending frequency of class A2 for CO(ND2)2. The torsional vibration is probably too low for observation. It seems that the analogous oscillation of CO (NH2)2 is obscured by the relatively intense band v 1680. If the same values of 61, r and fN-_



466 L. Kellner

are used as for guanidonium (13), the computation leads to the following results (table 5):

TABLE 5. VIBRATIONS OF UREA OF CLASS A2

CO(NH2)2 CO(ND2)2 CO(NH2)2 CO(ND2)2 CO(NH2)2 CO(ND2)2

N-H valence Bending Torsional vibration vibration vibration

Calculated 3420 2544 1563 1110 113 107

Obscured Not Not Observed 3496 2603 by 1680? 1164 observed observed

As the oscillations of the type B1 (5) are forbidden in the C+(NH2)3 spectrum (10), they are tentatively assigned to CO(NH2)2 frequencies which have no analogues in the guanidonium spectrum. The remaining lines, which occur in both spectra in approximately the same positions, have been placed in class B2.

The intense polarized lines v 3235 and v 2506 have been classified as the first overtones of the fundamentals 1680 and 1247 respectively. These overtones have the symmetry properties of vibrations belonging to the class A1 (this follows from group theoretical considerations) and are therefore polarized. Their high intensities can be explained by resonance with the intense fundamentals 3380 and 2421. The possibility that these frequencies (2506 and 3235) might be due to a weakening of the N-H bonds, by the formation of hydrogen bonds with the oxygen atom of a neighbouring molecule, is ruled out by the fact that v 2506 is of higher frequency than the N-D vibration 2421, while it should be considerably lower in the case of hydrogen bonding.

The proposed interpretation is set out in table 6, but it must be pointed out here that it is by no means definite. Unfortunately, no use could be made of Teller's product theorem (Angus, Bailey, Hale, Ingold, Leckie, Raisin, Thomson and Wilson I936) which would permit a final decision of the assignment to the symmetry classes, as this theorem presupposes the complete knowledge of the spectrum of two isotopic molecules.

5. VIBRATIONS OF GIUANIDONIUM

It is assumed that the C-N double bond oscillates in the guanidonium ion C+(NH2)3 between the three equivalent C-N linkages. In this case the C-N distances will be equal and each bond will have I double-bond character. The molecule has then the symmetry C3M, i.e. a threefold axis 03 through the carbon atom and perpendicular to the plane through the nitrogen and carbon atoms (the resonance forces these atoms into one plane),




and a symmetry plane 0h perpendicular to this axis. The hydrogen atoms of each NH2 group are symmetrically arranged with regard to G-h. As C3h

has a threefold symmetry axis, it gives rise to degenerate vibrations. The vibrations belong to four classes, of which the oscillations of the last two are doubly degenerate. The symmetry properties and numbers of frequencies are shown in table 7.

TABLE 6 Symmetry

type CO(NH2)2 CO(ND2)2 Mode of vibration A1 vt - 548 Bending vibration

V2 1008 997 Symmetrical valence vibration of C-N linkages V3 1167 890 Bending vibration V4 1604 1247 Bending vibration V5 1680 1613 Valence vibration of C-O linkage

2V5 3235 -

2V4 - 2506 V6 f 3385 2421 Symmetrical valence vibration of N-H (N-D)

3410 infra-red linkages A2 V7 Not observed Not observed Torsional vibration of NH2 groups

v8 Obscured by 1164 Bending vibrations of NH2 groups 1680?

v3 3496 2603 Asymmetrical valence vibration of N-H (N-D) linkages

B1 vio Not observed Not observed Bending vibration N

vil Not observed 1201 ? Folding of O -C plane N

V12 1350 1049 Bending vibration v13 3434 infra-red 2603 Asymmetrical valence vibration of N-H

(N-D) linkages B2 V14 Not observed Not observed Bending vibration

V15 534 458 Bending vibration v16 601 Not observed Bending vibration V17 1478 Not observed Asymmetrical valence vibration of C-N

linkages V18 3376 infra-red Obscured by Symmetrical valence vibration of N-H (N-D)

2421 ? linkages

TABLE 7 Symmetry properties Raman spectrum

Sym- Anti- Infra-red spectrum Degree of No. of m-try Sym- sym- Degen- depolar- vibra- class metric metric eracy Activity Band type Activity ization tions

A1 C3, o - Inactive - Active p< 6 4 A2 C3 'h - Inactive Inactive p = 7 4 B' o,h C- 3 Active Perpendicular Active p = 6 5 B" - oh C3 Inactive - Active p=7 3



468 L. Kellner

There are 3 x 10-6 = 24 vibrations altogether, of which only 12 will be observed in the Raman spectrum (the vibrations of the classes B' and B" have to be counted double), and four of these should be polarized and relatively stronger than the others. The infra-red spectrum will show only five bands.

The potential function V of C+(NH2)3 has been chosen in the same way as for urea.

2V- fc-N{6C-N, + 6C-N2 ? gC-NJ}

+fN-H{ N1-H1' + NI-H + 6N2-II2 + N2-H2" + 6N3-H3' + N3-H3 }

? d&N2(J_al)2 + (x2)2 + (A3)2} + 2282N_{(Jyl))2 + (A2)2 + (Ay3)2}

? '1 SC_N8N_H{(j 01)2 (JO12)2 + (A 21)2 + (JO22)2 + (31)2 + (A 32)2}

? K sin2 1200 2 N{(A P1)2 + (zV2)2 + (J0j)2}

+4T sin2 @ N_1 {(JO1)2 + ?(O2)2 + ?( 3)2}. (8)

The symbols have the same meaning as in the case of urea. The arrangement of the angles will be understood by reference to figure 4 which represents a molecule distorted by a vibration. The C-N linkages form a valence angle of 1200 with each other in the equilibrium position.

H3 H

H'NjH' = yi 2 ~ ~ ~ C N1- < H , tNiC -Z02

H H I''N iC = 0t2 H' NICN2 =cal

H3' N2 N2CN3 -2

N3CN1 -3

H/2

FIGURE 4. The guanidonium molecule.

When the symmetry requirements of table 7 are taken into consideration, it is possible to factorize the secular equation of 16 rows and columns into four determinants. The four vibrations of class A1 are represented by the equation (9)

A4-alA3 + a2A2- a3A+ a4 = 0, (9)




where

fC-N fN(mR3m) (n 3 &1(3 2122 8- 3mN mSN I1)N

al = +fNH( -+ ) + 82(2 +(8 + - + ?_ ( +2

3MN vm] 3MN 3miN il 3mN MfN-H (M

CNM

fC-N fN ( 6534N + 3CNi3l + 1 + 38C-N ) 3mN 6 m SN-H 2mN SC-N 3mN mN MN-HI

fCN l 5SC-N + NH + C-N~N 8 2 8-

mN 6mNS8N-H 2mNCmN 8C-N 3mHS mN mN-H E+9m2 s 3m+ +m DN-H

a fN-15 = c-N +fN-N- l ( 7 2 N 8 S 2 + SCN N

mN N-H mN 8N-H mNCN+ + +N SC-N 3M 2 SNH

+ 2fNfN5 ( 12+_+4)

2HmN mNN 3mN M

+ fcN 82t (_6__+ 23SC-N + 95C-N + 64 +648C-N +38N11 3mN vm5mN CN mNsN-H 2mSNN-H m +3N 8N-H + 3smN C-N

+1N-H 812 ( 6s2N + N-H 3SC-N + 6SCN + 28N +H 2 mH Mm11 mN SN-H m11 mN 8N +SC SN-H M2 MN + -N + +N

a = fC-N fN-E1Y52 ( 736mN + m55c-NH + 33NsC + N1 + 2r-N + N

3ME N 6mHmN][MNSN- SNH M 7EN SC-N I N 9MN H N- SN-HZ

& has been taken to be the tetrahedral angle, 1090 28'. The carbon atom does not take part in the totally symmetric vibrations but remains at rest.

The inactive vibrations of the type A2 are represented by the determinant (10). The oscillations of the type B' follow from equation (11). This is the only active type of vibrations in which the carbon atom takes part. The remaining three vibrations of the class B" are obtained from equation (12):

-CA2(fN 1 2 s + NSC + (COSN SC-N-Nf)2 ] +

mH 2M2 3MmH2NH

+AfN-iH1 (820N6sC-N+SN-:-2coss 3NsN

6l)4sin 2SfN-:r (1 +I2cos j

) mH MNH mHN+ 2 cos2Cs-N mN J m11 mN mHMN

+fC-N [coN &c N8 + 6co 2SC-N-N 3SN-1] 4sin2s6f 9CNr =4- (12)

3HLmHm MNHM2cs N M NSN-H M1N-NSC- N 2m SN1] 3M2



470 L. Kellner

o 0

r1 I

o o z:i o

Z--- z z

.=~~~~~~ +

I ! I m mO~

(12 0 Z (1

-c Cot

I z

es2 Z Z ?' j i2

H1N ~ ~ z z




z ~ ~ ~ ~ 1 m

II Z~~~~~~~~~

zz~~~~~~~~~~

. is z t:l w z

CI

z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~z oZ Z ~ ~~~~~~~~ z

CO = N z C z CI + Z .

U Z z X

0z +

z + CI)~~z

+ z~~ e

z ~ ~~ z~~~~~~~~

z

Z



472 L. Kellner

This equation is exactly the same in form as equation (3) of urea, as mentioned above. It would therefore be expected that these three modes of vibration would be alike in both molecules.

Class A1 contains two valence vibrations, of which one is principally a symmetric oscillation of the nitrogen atom towards and away from the static carbon atom (breathing frequency), while the second is a symmetric vibration of the N-H bonds. The remaining two are bending frequencies, in which the valence angles H-N-C and H-N-H are distorted.

In the symmetry type B' the nitrogen and hydrogen atoms execute a two-dimensional motion round their equilibrium positions; there are two valence vibrations, one corresponding roughly to an asymmetric oscillation of the C-N bonds and one to a symmetric stretching of the N-H linkages. Three bending frequencies belong to the same symmetry type, deforming all the valence angles of the molecule.

The class B" is represented by an asymmetric N-H valence vibration, a torsional vibration of the three NH2 groups in phase with each other, and a deformation frequency in which the angles H-N-C are distorted.

6. INTERPRETATION OF THE C+(NH2)3 AND C+(ND2)3 SPECTRA

AND EVALUATION OF FORCE CONSTANTS

The Raman spectra of solutions of C+(NH2)3 in H20 and of C+(ND2)3 in D20 respectively have been observed by Otvos and Edsall (I939). The results of their experiments are shown in table 8 together with the assignment of the bands proposed here. The assignment has been chosen in analogy with the urea spectrum. As it is well known that the breathing frequency is the most intense line in the Raman spectrum, the frequencies 1008 and 921 are interpreted as vl. The choice of the four A1 vibrations is determined by the fact that they have to be strongly polarized. The upper index, in brackets, indicates the twofold degeneracy. It is not possible to include v 2374 in the assignment, as C+(ND2)3 has only one polarized N-D vibration. Otvos and Edsall themselves suggest that the line belongs to the D20 spectrum. On the other hand, if the lines 3360-3471 and 2496-2591 are really caused by the molecules of the solvent, it seems justifiable to conclude that the intense frequencies of C+(NH2)3 and C+(ND2)3, which are to be expected in this region, are overlapped by the strong water bands.

The force constant fc-N of C+(NH2)3 will be very near to the value for urea, and fN-H may be taken to be the same in both cases. It is assumed that the nuclear distances in the isotopic molecules C+(NH2)3 and C+(ND2)3




are alike, namely 8N-H 1L02 A and SC-N= 1-33A. The latter value requires some explanation. The only hitherto observed C-N distance in guanidonium, viz. 1P18A (Theilacker I935), is obviously too small, as the

TABLE 8. CLASSIFICATION OF THE RAMAN SPECTRUM OF C+(NH2)3 AND C+(ND2)3

Sym- Denota- metry

C+(NH2)3 C+(ND2)3 Gtion type Mode of vibration

536 (4b) D 459 (3) D v(2) B' Bending frequency 1015 (8) P 921 (8) P v1 A1 Breathing frequency 1462 (Ovb) - v(2) B' Asymmetric C-N valence

frequency 1565 (2vb) D 1193 (lb) D v(2) B' Bending frequency

- 1278 (1) P V2 A1 Bending frequency 1670 (lvb)? - v(2) B" Bending frequency

- 2127 (0?) 2v(2) B'

Resonance: 3212 (3b) - 2v(2) B'

- 2374 (6) P D2O? -

3290 (3b) 2433 (6) P V3 A1 Symmetric valence frequencies of N-H

3360-3471 H20? Obscured by 2433 v(2) B' N-D linkages 3360-3471 2496-2591 (6) D20? v(2) B" Asymmetric valence frequency

of N-H (N-D) linkages

triple C N bond in HCN has a length of 1 15 A. The above figure for 80-N

was therefore assumed as likely on the ground that in urea 8C-N is 127 A (in urea the C-N bonds have less than -3 double-bond character). Using 3 these values, it is possible to compute all vibrations of C+(NH2)3 and C+(ND2)3 with one set of force constants (13):

ft-N = 7*1 x 10 dynes/cm., fN-1 = 6-3 x 10 dynes/cm., j

81 = 0-80x 105 dynes/cm., 82= 0-14x 105 dynes/cm., (13)

3d = 0 70x 105 dynes/cm., r = 010 x 105 dynes/cm. J

The constants &2 and 3d are suspiciously small, and no great reliance can be placed upon them. Nevertheless, table 9, in which the observed and calculated frequencies are compared, shows that the accuracy of the calculations (roughly ? 10 %) is quite reasonable.

Vol. I77. A. 30



474 L. Kellner

TABLE 9. FREQUENCIES OF C+(NH2)3 AND C+(ND2)3

Symmetry C+(NH2)3 C+(ND2)3 and _ _A _ _

vibration Calculated Observed Calculated Observed

A1 v, 1020 1015 924 921

V2 1410 Not observed 1113 1278 V3 3354 3290 2432 2433

V4 622 Not observed 501 Not observed

B' V(2) 651 536 483 459

6v(2) 1501 1462 1360 Not observed

7v(2) 1534 1565 1320 1193

8V(2) 3370 3360-3471? 2470 2496-2591?

9v(2) 360 Not observed 342 Not observed

B" v(2) 1510 1670 1116 1063= x 2127 v(2) 3445 3360-3471? 2544 2496-2591?

v422) 112 Not observed 108 Not observed

7. FORCE CONSTANTS AND MOLECULAR STRUCTURE

OF UREA AND GUANIDONIUM

The interpretation given above of the guanidonium spectrum agrees very well with the assumption of complete resonance between the three C-N bonds. Urea would belong to the symmetry group C2v even if no resonance occurred in the molecule between the C_O and C-N linkages, but here confirmation of the resonance hypothesis comes from the values of the valence force constants, fc-N and fc=o. It was mentioned in ? 1 of the present paper that the force constants of the C-C valence bond are roughly proportional to the strength of the bond (single, double, triple, partial bond). The C-N single bond furnishes a force constantfC-N of 4-86 x 105 dynes/cm. for methylamine according to Kohlrausch (I 93 I) and of 4 95 x 105 dynes/cm. according to Bailey, Carson and Daly (I939), while Kohlrausch (I93) obtained a value of fc=N = 17-9 x 105 for the C(N triple bond. The study of the formaldehyde spectrum leads Sutherland and Dennison (I935) to a force constant fc=o = 13-45 x 105 for the C-O double bond. The values obtained here for urea (7), fc=o= 97 x 105 and fC-N = 6-6 x 105, are considerably different from the above figures. As is to be expected in the case of resonance, the C-N force constant is greater for urea than for ordinary C-N single bonds (by 35 %), while the C-O force constant in urea is weakened by 39 % as compared with formaldehyde. It can therefore be concluded that in urea the C-N valence bond has partial double-bond




character, while the C=O linkage is weakened by approximately the same amount. The spectrum of guanidonium furnishes fc-N = 7d1 x 105 (13) in agreement with the assumption that each C-N bond has 3 double-bond character. The force constants of the C-C, C-N and C-O valence linkages have been plotted as functions of the bond strengths in figure 5 as far as they are known. While these curves are not very far removed from straight lines for the C-C and C-N linkages, the C-O curve is irregular.

19x105 Cl N

17 c-c 15

~~~ 11 1~~~~~~~-~urea o 9

0 7 ~~~~~guanidoniumn -urea

1 2 3 1 2 3 1 2 3 force constants as functions of bond character

FIGURE 5. Force constants of the C-C, C-N bonds as functions of the bond character.

REFERENCES

Angus, Bailey, Hale, Ingold, Leckie, Raisin, Thomson and Wilson I936 J. Chem. Soc. p. 971.

Bailey, Carson and Daly I939 Proc. Roy. Soc. A, 173, 339. Kohlrausch I93I Der Smeekal-Ranan Effekt. Kohlrausch I936 Phys. Z. 37, 58. Kohlrausch and Pongratz 1934 Z. phys. Chem. B, 27, 176. Lechner I932 S.B. Akad. Wiss. Wien, IIa, 141, 291. Otvos and Edsall I939 J. chem. Phys. 7, 634. Pauling, Brockway and Beach I935 J. Amer. Chem. Soc. 57, 2705. Sutherland and Dennison I935 Proc. Roy. Soc. A, 148, 250. Theilacker I935 Z. Kristallogr. 90, 51 and 256. Wyckoff and Corey I934 Z. Kristallogr. 89, 462.

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the vibrations and the molecular structure of urea and guanidonium

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