JWJKNAL VI.’ YOLECULAK SPECTKOSCOPY 49, 251-267 (1974)

Molecular Structure and Internal Motion

from Microwave Spectrum

of Formamide

ELZI HIROTA AND RYOKA SUGISAKI

Department of Chemistry, Faculty of Science, Kyuskz~ University, Fukuoka, Japan

AND

CLAUS J~RGEN NIELSEN AND GEORG OLE S$RENSEN

Department of Chemical Physics, University of CopenkaEen, Copenhagen, Denmark

The molecular structure of formamide has been redetermined by observing the microwave

spectra of the r3C and I*0 species of NHXHO and ND&HO. The ra structure calculated

assuming the planarity of the molecule is N-H, = 1.0016 f 0.003 A, N-Ht = 1.001~ f 0.003

b, C-N = 1.352 + 0.012 A, C-O = 1.21s & 0.012 b, C-H, = 1.098 f 0.01 ii, LH,NHz

= 121.6’ f 0.3”, lH,NC = 118.5” f O.S’, LH~NC = 120.0’ f OS”, LNCO = 124.7”

f 0.3”, LNCH, = 112.7O f 2”, and LOCH, = 122.5” & 2“.

The strongest satellite of the rotational spectrum is assigned to the first excited state of

the amino inversion. The far-infrared spectra observed by King are assigned to the v = 1 to,

2 t 1, and 3 t 2 transitions of the inversion, and the 2) = 1 +- 0 and 2 + 1 transitions are

detected also for the NDlCHO species. The observed vibrational frequencies are used to

determine the two potential constants V2 = 156 f 34 cm-r/r-ads and VP = 398 f 29

cm-‘/rad4 in the potential function to the inversion of the form, V = Vd + V&, where r

is the inversion angle of the amino group. The molecule is thus essentially planar without

any potential hump at the planar configuration. The changes of the inertia defect by the

excitation of the inversion have been calculated approximately for NH&HO and NDtCHO

in fair agreement with the observed.

1. INTRODUCTION

The molecular structure of formamide has been reported by Kurland and Wilson(I) and also by Costain and Dowling (2). The latter authors concluded that the amino group has a slightly nonplanar configuration and thus executed an inversion-wagging type vibration with a potential barrier of 370 f 50 cm-r at the planar configuration. Apart from the planarity of the molecule the structural parameters reported by the two groups are widely different; the most important differences lie in the N-C and C-O bond lengths. These distances are invaluable in discussing the electronic structure of the molecule (3). It is to be noted that both of the two groups did not include the spectra of the ‘Y and I*0 species in their structure determinations, which would be indispensable to determine the two bond lengths precisely.

The present work was also motivated by our recent result on a related compound, thioformamide (4). Because the sulfur atom is less electronegative than the oxygen atom,

251

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:\I1 rights of reproduction in any form rewrvcd.

TABLE I. Observed Frequencies of the Transitions

of the 13C and l8 0 Species of Formamide (MHz)

Transition NH*l3CHO NH2CHl'O ND213CH0 ND2CHl'O

101 ’ 000 (21 175.4ja 20 144.1 18 869.9 17 959.8

212 + 111 40 777.6 38 685.7 36 231.3 34 568.2

202 f 101 (42 323.1ja 40 267.6 37 705.0 35 887.0

211 + 110 43 920.1 41 698.9

a. Overlapped by other lines.

TABLE II. Rotational Constants (MHz) and

Moments of Inertia (amu i') of NH2CH0 and

its Isotope-Substituted Species a

NH2CHOb 15NH CHOb 2 NH213CH0 NH2CH1'0

A 72 716.12 72 448.61

B 11 373.75 11 054.40 11 373.5 10 774.9

C 9 833.72 9 589.93 9 801.5 9 370.3

I 6.943 986 6.975 648 a (7.117 7)' (7.022 7)'

'b 44.433 54 45.717 18 44.434 5 46.903 1

Ic 51 392 15 52.698 61 51.561 1 53.933 8

A 0.008 62 0.005 78 (0.008 9)= (0.008 O)=

cis-NHllCHOb'dtrans-NHDCHOb'd NH2CDOb

A 61 345.91 71 179.61 54 948.39

B 11 009.91 10 473.30 11 373.07

C 9 334.09 9 132.47 9 419.70

I 8.238 137 7.100 011 9.197 285 a

'b 45.901 92 48.253 75 44.436 20

Ic 54.143 04 55.338 37 53.650 97

A 0.002 98 -0.015 39 0.017 48

a. Conversion factor is 505376 MHz amu i'.

b. Ref.(2_1.

c. Assumed, see text.

d, N-D bond eclipses with C=O in cis and with C-H in trans.

it has been expected that the N-C bond length is longer in thioformamide than in formamide. However, the N-C distance in thioformamide is determined to be 1.358 A,

which is definitely smaller than 1.3i6 f 0.010 A in formamide, as reported by Costain

and Dowling, although the earlier value of Kurland and Wilson is smaller, 1.343 A. In the present work the microwave spectra of the j3C and ‘“0 species were observed

in natural abundance both for the NHzCHO and NDICHO species, and the structural parameters including the h--C and C-O distances are recalculated. It is noteworthy that the spectra of these species might be of some astrophysical importance, in view of a recent observation of the spectrum emitted from the normal formamide molecule in interstellar space (5).

Low-frequency motion in the free formamide molecule is still not well understood; one may consider the lowest mode of the molecule is the KH, torsion, while others assign it to the amino wagging, as was done in Ref. (2). In the present paper some analyses are carried out to discriminate the two possible assignments, and lead to con- clude that the lowest mode is the wagging with a mixed quadratic and quartic potential function.

2. ROTATIONAL SPECTRUM AN3 ROTATIONAL COSSTANTS

Four low-J R-branch transitions of the 13C and ‘“0 species were observed using a 110 kHz Stark-modulated spectrometer at Kyushu University and the assignment was based on characteristic Stark effects and intensity changes when the cell was heated

to about 100°C. The b-type transitions have not been detected because the b component of the dipole moment is small. Observed frequencies of the transitions are listed in Table I.

Rotational constants of the isotopic species of formamide are collected in Tables IT and III, where those of the species other than the l”C and I80 species are taken from Ref. (2). The inertia defects of the latter species are assumed to be 0.0089 and 0.0080 amu

TABLE III. Rotational Constants (MHZ) and

Moments of Inertia (amu i') of ND2CH0 and

its Isotope-Substituted Speclesa

ND2CHOb 15

ND2CHOb ND2

13CH0 ND CHl*O 2

A 59 715.99 59 594.17

B 10 193.58 9 964.80 10 189.2 9 655.6

C 8 710.35 8 540.45 8 680.7 8 304.2

Ia 8.462 993 8.480 293 (8.637 l)C (8.536 2)'

Ib 49.577 87 50.716 12 49.599 2 52.340 2

I 58.020 17 59.174 40 c 58.218 3 60.857 9

: -0.020 69 -0.022 01 (-0.018 o)c(-o.018 5)C

a. Conversion factor is 505376 MHz amu i'.

b. Ref. (2). _ C. Assumed, see text.

2.54 HIKOTA E2’ AL.

k for NH&HO and -0.0180 and -0.0185 amu k for ND&HO. These figures are obtained by a normal coordinate analysis. Costain and Dowling pointed out anomalous isotope shifts of the inertia defects and took them as an evidence of the inversion- wagging motion of the amino group. It is, however, found that inertia defects calculated assuming a planar structure with appropriate force constants behave similarly to the observed. Similar isotope shifts of the inertia defect were reported for vinyl fluoride, although the shifts were much less precise (6).

The spectra of the NH&HO and ND&HO species have been reinvestigated more in detail in Copenhagen; the largest J value of the identified transitions was 55 for NHKHO in the ground state. The observed transitions of J up to 12 are listed in Table IV. All the observed frequencies are analyzed taking into account the centrifugal distortion effects including quartic as well as sextic terms. Because the b-type transi-

TABLE IV. Observed Frequencies of the Transitions of

NH2CHO and ND2CHO in the Ground and Excited

Vibrational States (MHZ)

Transition

Ground state Excited state

obs obs-talc obs obs-talc

NH2CHO

1 -000 01 21 207.445

2,,-111 40 874.91afb

2 -10, 02 42 386.07a'b

211-11,

1 -202 11 18 956.078

404-313 26 922.910

4 Is-41, 15 392.005

514-51, 23 081.247

6,,-61, 23 297.296

625-71, 16 961.133

9,e-82, 37 567.485

Bz,-919 37 260.839

927 101,10 27 513.605

lO,,-102, 13 489.347

lOz,-ll,,,, 19 748.120

ll,,-ll,,,, 19 112.397

llu-120,1, 36 332.172

ll*,-121,*2 14 123.779

Il,,-12*,,, 36 608.999

12 Z,l 1 o-122,* 26 135.699

0.008

-0.541

0.000

0.003

-0.002

0.011

0.012

0.011

-0.042

-0.012

0.002

-0.023

-0.008

-0.006

-0.005

0.004

0.002

-0.008

-0.005

21 190.876 0.050

40 869.0b -0.567

42 353.1b -0.316

43 894.5b 0.618

27 752.353 0.002

15 118.558 0.005

22 671.202 -0.005

31 723.582 0.001

14 539.420 0.002

39 742.816 0.002

33 745.097 -0.003

23 803.851 -0.021

13 223.325 0.012

15 807.344 0.000

18 736.740 -0.013

32 343.865 -0.052

25 624,036 -0.017

MICROWAVE SPECTRUM OF FORMAMIDE

TABLE IV. (continued)

ND2CHO

101-000

ZLz-lll

202-101

211-110

404-313

514-515

524-615

615-616

621-717

817-721

725-810

826-919

102a-1023

101e-1129

18 903.910 0.008

36 324.750 0.019

37 774.858 0.014

39 290.784 -0.015

29 328.523 0.042

22 231.177 0.012

22 209.466 -0.011

31 102.093 -0.012

25 936.644 0.003

31 290.519 0.008

22 136.838 -0.044

15 193.689 -0.022

27 372.148 -0,029

1129-112,lO 21 392.036 -0.020

ll~a-l2z,ll 33 364.755 0.046

122,10-122,ll 29 045.091 -0.019

18 929.434 0.011

36 402.095 0.004

37 826.527 0.016

39 315.510 -0.017

30 186.256 0.011

21 836.730 0.023

30 550.311 0.017

39 049.738 -0.040

28 166.247 -0.009

28 040.777 -0.016

18 685.200 0.013

23 267.274 0.006

20 988.885 -0.015

28 763.412 -0.012

28 499.459 0.028

255

a. Ref. (2).

b. Not included in the least-squares analysis.

tions are assigned both for the ground and excited vibrational states, the three rotational constants and the inertia defect are determined more precisely, as shown in Table V, where the quartic distortion constants are also listed.] The frequencies calculated using

these constants are compared with the observed in Table IV.

3. MOLECULAR STRUCTURE

In calculating the structural parameters the molecule is assumed to be planar. .4s Costain and Dowling have shown, the molecule might be nonplanar at the equilibrium configuration, but all the out-of-plane coordinates of atoms are not large enough t(J

be determined directly from Kraitchman’s equations. The out-of-plane coordinates, if real, had better be determined by other methods such as the analysis of the vibrational satellites, which might give us detailed information on the potential function and which, in fact, leads to the conclusion that the molecule is planar.

1 When the present work was nearly completed, Kirchhoff, Johnson, and Lovas published two papers,

in which they carried out an extensive analysis of the spectra of NHzCHO in the ground state (f7).

The rotational and the centrifugal distortion constants they determined are in agreement with those iisted_in_Table V.

256 HIKOTA f<T AL.

Using Kraitchman’s equation for a planar molecule the a, and b, coordinates of all atoms are calculated using I, and I* of appropriate species in the axis system of the normal species, NHzCHO. For the 13C and I80 species Ia’s are estimated as described above. The moments of inertia of the NH2CH0 and ND,CHO species reported in Ref.

(2) are used, because these differ only slightly from the more precise ones in Table V and also because the data for the 13C and 180 species are obtained in a way similar to Ref. (2). The coordinates derived are listed in Table VI.

All the b, coordinates are calculated unambiguously, but their accuracy is not high, as indicated by a large (negative) value of the first moment. On the other hand, the a, coordinates of two atoms, carbon and aldehyde hydrogen, are close to zero. Costain and Dowling concluded that the aldehyde hydrogen and nitrogen atoms were located on opposite side of the b axis; in other words, the a, coordinate of the aldehyde hydrogen is

TABLE V. Rotational Constants (MHZI and Inertia

02 Defects (amu A ) of NH2CHO and ND2CHO in the Ground

and Excited States

NH2CHO ND2CHO

Ground state Excited state Ground state Excited state

A

B

C

T aaaa

Tbbbb

?cccc

'1 ,a

T2 ,b

A

72 716.91, 71 738.782 59 716.223 58 903.265

20.019 kO.031 fO.014 kO.011

11 373.509

+0.003

11 351.530

to.005

10 193.511

f0.002

10 193.111

to.002

9 833.958 9 839.326 8 710.415 8 736.336

*0.003 to.005 to.002 fO.002

-5.3623

10 0012

-2.6136

f0.0018

-2.4428

?0.0028

-0.04457

~0.00002

-0.01934

,~0.00002

-0.0820

~0.0002

-0.04481

+0.00008

-0.01971

~0.00.005

-0.0816

?0.0005

-0.03533 -0.03530

+0.00006 +0.00009

-0.01528 -0.01554

~0.00004 ~0.00007

-0.0749 -0.0684

+0.0004 +0.0006

0.000140 0.00007 0.000097 -0.000024

~0.000003 -?-0.000005

0.006 510 -0.202 322

+o.ooo 002 iO.000 006

i0.000006 +0.00002

-0.021 433 -0.312 325

+o.ooo 005 to.000 006

a. T1 ’ = T4 + T6(A-B)/(A-C)

h. T2 '=T 5

t T6,(B-C)/(A-C) (See Ref.(16) for the definitions -

of T4, T5, and T6).

TABLE VI. The as and bs Coordinates of Atoms

in NH2CHO (i)

atom as b s

N -1.1468 0.1650

C (+m032a -o.4134

0 1.1334 0.2010

cis-H -1.2002 1.1662

trans-H -1.9661 -0.409*

aldehyde-H (+)0.050a -1.5111

D

6m.a. = -0.688 amu A ill

Zm.b. = -0.197 amu : ill

Em. a. 2 = 44.324 amu ;;' Em.b.' ill

(44.434Jb ill

= 6.918 amu ;'

(6.9501b 02

1m.a.b. illl

= +0.161 amu A

a. See text for the final value.

b. Observed.

ci(l$ (Al

O.lC

0.0:

0.c

-0.05

j-

)-

1

I

I I I_

0.0 0.05 0.10 G, a I(C)

FIG. 1. The a, coordinate of the carbon atom YS that of the aldehyde hydrogen atom in the NH&HO . . system. The coordmates calculated directly from Kraltchman s equation are indicated by a cross.

‘I’he curve (u) denotes the condition Zinz;a, = 0 and the curve (b) Z;VI;Q,~, = 0. Uncertainties of the two

conditions, f 0.3 amu H and f 0.1 amu ipa, are indicated by broken lines. The final values are shown

by an open circle with estimated uncertainties drawn by dotted lines.

258 HIROTA ET AL.

TABLE VII. The as and bs Coordinates of Atoms

in ND2CHO (i)

atom a?. bs

N -1.0795 o.134g

C 0.146ga -0.4211

0 1.1977 0.2016

cis-H -1.1534 1.1326

trans-H -1.8959 a

-0.4462

aldehyde-H - (-1.519>b

a. See text for the final value.

b. Assumed.

positive. The same is assumed in the present work. The a, coordinate of the carbon atom also seems to be positive, because the first moment would otherwise be much more negative. The two a, coordinates are plotted in Fig. 1 where the two conditions, (a) Ci maai = 0 and (b) Ci m;aibi = 0, are drawn by curves with uncertainties, which

are taken to be f0.3 amu A and f0.1 amu AZ, respectively. The cross point of the two curves gives a negative a, coordinate for the aldehyde hydrogen, and thus discarded. The two a, coordinates are estimated to be

as(C) = f0.076 + 0.03 A

u,(aldehyde H) = +0.06 f 0.05 A

and, combining with other ra coordinates of Table VI, the structural parameters of Table VIII are calculated.

A similar analysis is carried out taking the ND&HO species as a reference. The heavier mass of the deuterium atom moves the b axis to the negative direction of the a coordinate, and the a, coordinate of the carbon atom is actually calculated to be +0.1469 A, as shown in Table VII. It is much larger than that in the NH&HO system, and may thus be considered more accurate. The changes on the deuteration of the a, coordinates of other atoms are +0.067 A (N), +0.064 A (0), +0.047 A (cis H), and +0.070 A (trans H). The a, coordinate of carbon, +0.075 A, estimated in the NH&HO system corresponds to a shift of +0.072 A and is thus acceptable. Unfortunately, the spectrum of the ND&DO species is not available. The b, coordinate of the aldehyde hydrogen atom is estimated in the following way. Because the C-H bond is nearly parallel to the b axis, the difference in the b, coordinates of the carbon atom in the two reference species, NH&HO and ND&HO, which amounts to 0.007, A, is subtracted from the b, coordinate of the aldehyde hydrogen atom in the NHzCHO system, giving the b, coordinate of -1.519 A in NDZCHO. The first moment C; mibi then amounts to -0.087 amu A, which is to be compared with -0.197 amu A in the NHKHO

afHa)

J a(c)

FIG. 2. The IE, coordinate of the carbon atom vs that of the aldehyde hydrogen atom in the NDaCHO

system. The a, coordinate of the carbon atom calculated directly from Rraitchman’s equation is 0.146 ;i,

as indicated by a vertical line. The curve (a) denotes the condition Zimiai = 0 and the curve (ZI) Zgniaibi

= 0. Uncertainties of the two conditions, f0.3 amu _& and f 0.1 amu Aa, are indicated by broken lines.

The final values are shown by an open circle with estimated uncertainties drawn by dotted lines.

system. The a, coordinates of atoms other than the carbon and aldehyde hydrogen atoms are calculated by Kraitchman’s equation and are listed in Table VII. As to the two a, coordinates a figure (Fig. 2) similar to Fig. 1 is drawn, where the two conditions,

TABLE VIII. Molecular Structure of Formamidea

Darameter NH2CHO ND2CHO

final system system

N-HC 1.0027 + 0.005 ;; 0

1.0004 t 0.005 A 1.0016 + 0.003 ;

N-lit 1.0009 +_ 0.005 1.0021 ? 0.005 1.0015 i 0.003

C-N 1.352 t 0.03 1.352 i 0.015 1.352 f 0.012

c-o 1.224 f 0.03 1.216 i 0.015 1.219 f- 0.012

C-H, 1.0g8 i 0.01 l.ogg + 0.02 1.0g8 ? 0.01

LHcNHt 122.00 + 0.5" 121.20 i 0.50 121.60 k 0.30

LHcNC 118.40 -t 0.70 118.5O i 0.7' 118.5O ? 0.5"

LHtNC 119.60 t 0.70 120.3' + 0.7" 120.00 f 0.50

LNCO 124.5' t 0.5O 124.90 t 0.5" 124.7" i 0.3'

LNCHa 114.60 _t 30 111_5* _+ 2" 112.7O t 2O

LOCH a

120.go i 30 123.60 ? 2O 122.5O i Z"

a. IIc, IIt, and II a

mfan the cis, trans, and aIdehyde hydrogen

atoms.

(a) ~irn,ai = 0 and (b) ~:rngtibi =O, its well as the u, coordinate (+0.1469 A) of the carbon atom above mentioned are indicated. The two a, coordinates are then estimated to be

a,(C) = +O.l& f 0.015 A

a,(aldehyde H) = +O.lO f 0.03 A

The structure calculated using these coordinates is given in Table VIII. It is to be noted that the results obtained on the two separate systems are in good agreement with each other, except for the angles associated with the aldehyde hydrogen atom. The average of the two sets of the structure is considered to be the most probable.

4. VIBRATIONAL SATELLITES AND INTERNAL MOTIONS

The spectra in the ground state are accompanied by a set of strong satellites, as Costain and Dowling (2) have reported (referred to as the set I). The three rotational constants of the two species, NH&HO and ND&HO, in the excited state are determined more precisely as shown in Table V, whereas the B and C constants of the two singly deuterated species in the excited state are calculated by the combined use of the J = 2 +- 1 transitions with the J = 1 +- 0 already reported (see Table IX). The changes in the inertia defect A, = AU=1 - A,=, are determined to be -0.208 832 f 0.000 007 amu A” and -0.290 892 f 0.000 008 amu A* for the KH2CH0 and ND&HO species, respectively. A characteristic feature of the satellite is that there are no lines which

may be assigned to the overtone states on the basis of the frequency intervals. It is, therefore, very probable that the vibration giving rise to the satellites is anharmonic,

as argued by Costain and Dowling. Three more sets of the vibrational satellites were also observed for the normal species, and the relative intensity measurement gave the excitation energies as listed in Table X. Two stronger sets of the satellites, II and III,

TABLE IX. Observed Frequencies of Transitions and

Rotational Constants of Formamide-d in the

Excited Vibrational State (MHz)

Transition cis-NHDCHO trans-NHDCHO

lo, f 000 a 20 341.2 19 621.6

212 f 111 39 038.2 37 929.6

202 + lo1 40 642.2 39 222.4

211 f 110 42 326.9 40 558.8

B V=l

10 992.7 10 467.6

C ', 1 5 4 . 0 V=l

9 348.5

a. Ref. (2).

'I'RBJZ X. Vibrational Satellites of the NH2CHO Species

‘61

Excitation energy (cm -1 )

':.,lrllit+~ -- dssiqnmelll

relative intensity (infrared)

I 295 i 10

II 555 + 20

III 607 4 20

IV 626 + 30

(289)

(565)

(603)

(658)

NH2 inversion, vT=l

NC0 bending

NH2 torsion

NH 2 inversion, vT=2

are found to be in resonance, possibly of the Coriolis type.g It is certain that the molecule

has only one vibrational level below 550 cm-‘.

It is evident that the internal motion responsible for the strongest satellites is either

the inversion-wagging, as concluded by Costain and Dowling, or the internal rotation

of the amino group. Assuming the potential function to the internal rotation of the

form P’(a) = (V2/2)(1 - COS~~), where cy denotes the internal-rotation angle, the

torsional frequency is calculated to be 293.1, 260.6, 248.8, and 228.0 cm-’ for the

NH2CH0, cis-NHDCHO, trans-NHDCHO, and NDzCHO species, when Vs is 5

kcal/mole. The frequency of the normal species increases to 349.5 cm-l, when Vz is 7

kcal/mole. If the strongest satellites (set I) were due to the torsional state, the observecl

frequency of 304 cm-l (2) or 29.5 f 10 cm-‘, the present value, corresponds to the

torsional barrier of 5-6 kcal/mole. It may be interesting to note that splittings of the

torsional levels are negligible for the NH&HO and ND*CHO species.

The barrier height calculated seems, however, to be too low. An ab initio calculation

of Ref. (3) gives the barrier height of approximately 20 kcal/mole. Barrier height has

been determined by NMR technique (7) for formamide and its derivatives. It is nearI>,

the same for a large number of molecules, including dimethyl formamide, for which the

effect of the hydrogen bond would be small, but still the barrier is high, about 20 kcal/

mole. On the other hand the torsional frequency is reported to be 765 cm-’ in the gas

phase (8), although others (9,10) thought it to be lower than 300 cm-’ (II).3 In addition

to these observations the calculated isotope shift, i.e., the difference 65.1 cm? between

the frequencies of NH2CHO (293.1 cm-‘) and ND&YHO (228.0 cm-‘) is much smaller

than the observed; the isotope shift, 131 = 304 - 170 cm-‘, reported in Ref. (2) ma\

be replaced bl- a more accurate one, 80 = 289 - 209 cm-’ (see Table XI), which is

still much larger than the calculated. The internal motion giving rise to the strongest

satellites (set I) is therefore concluded not to be the internal rotation, but to be the

inversion-wagging motion, in accord with the conclusion of Ref. (.?).

Recently, King (12) reported the far-infrared spectrum of the normal formamide in

the region 200~4.50 cm-’ and observed three peaks at 288.7, 368.6, and 401 cm-‘. An

? A more detailed account of the satellite spectra will be given elsewhere (I&‘)).

:I Itoh and Shimanouchi (II) assigned hands at 843 cm-’ and 67.5 cm-1 to the NH, wagging nnd ihc

KHz twisting of NH,CHO in the crystalline state at - 16OT.

262 HIROTA El’ AL.

interferometric measurement on the dideuterated species, carried out at Copenhagen detected two bands at 209 and 257 cm-r, respectively, as listed in Table XI. King assigned the absorption at 368.6 cm-’ to the difference band vg-v12, but it is more reason- able to ascribe it to the ‘u, = 2 +- 1 transition of the amino inversion and the third band at 401 cm-’ to v, = 3 t 2. A band at 660 cm-r reported by King could then be assigned to v, = 2 +- 0 and that at 770 cm-r to v, = 3 t 1 rather than to v, = 2 +- 1 as done in Ref. (12). An attempt was made to assign the 401 cm-r band to v, = 2 +- 1, but then the two bands at 660 cm-r and 770 cm-’ remained unexplained. The calculated inertia defects were also in poorer agreement with the observed. The two bands of the dideuterated species are assigned reasonably to the v, = 1 +- 0 and v, = 2 +- 1 transi- tions, respectively (see Table XI).

The energy levels of the amino inversion are calculated assuming the potential function of the following form (13) :

V(7) = V2T2 + 11474 + I7476

where V, (n = 2,4, 6) are the potential constants. A negative V2 constant might result in a double-minimum potential function such as those discussed in Ref. (13). The inversion coordinate 7 is defined by an angle between the bisector of the HNH angle

and the NC0 plane. The amino group is assumed to be an equilateral triangle and to be bent while keeping the two HNC angles the same and the HNH angle constant. The four atoms, N, C, &, and 0, are assumed to be in a plane. Using the structural param- eters of Table VIII (two N-H distances and two HNC angles are averaged in the calculation) the reduced mass p is calculated to be 0.38493, 0.48970, 0.54159, and

TABLE XI. Transition Frequencies and Potential Constants

for the Amino Inversion of Formamide (cm -+

obs. talc.

NH2CHO

v=l+O 288.7= 289.4

v=2+1 368.6a 360.2

v=3+2 401.a 406.1

ND2CH0

v=l+O 209 210.1

v=2+1 257 258.8

v= 3 (- 2 (288) 290'.9

"2 = 156 * 34 ,

"4 = 398 2 29 cm-I

a. Ref. 112).

MlCROWAVE SPECTRUM 01; FORMAMIDE 103

E” icm~’ 1

IO00

600

600

400

200

0 60 40 20 0' 20' 40' 60' 7:

E’IG. 3. Potential function to the amino inversion of formamide.

0.64526 amu &/rad* for NH&‘HO, c+NHDCHO, ~rarz~-NHDCHO, and ND9CH0.

It is to be noted that the reduced mass calculated in the present paper is identical to the diagonal element of the G-r matrix corresponding to the inversion coordinate as defined above and is evaluated at the planar configuration. The inversion frequency reported in Ref. (2) is higher for the trays-NHDCHO than for the cis-NHDCHO species, whereas the reverse is true for the calculated frequency, because the reduced mass calculated is larger for the trans than for the cis.

The observed frequencies of the amino inversion with an assignment discussed above are explained by taking into account only two potential constants, I/r2 and 1/d. A least- squares fitting leads to the result: T/z = 156 f 34 cm-l and 114 = 398 f 29 cm-‘.

The calculated frequencies are compared with the observed in Table XI. The potential function is plotted in Fig. 3. The equilibrium configuration of the molecule is thus planar, hut the vibration is of mixed quadratic and quartic.

It is of some interest to compare the observed rotational constants, in particular their changes with the amino inversion, with those calculated using the potential

constants listed in Table XT. The rotational constants are expanded in power series of the inversion coordinate T in the following way:

A(7) = Aof A172f A#+ ...

where .I ,, denotes the rotational constant at the planar configuration. The coefficients, ; 1 0, ill, ‘12, . . .) may he calculated using the structural parameters of Table VIII; the coefficients of the NH,CHO species are A1 = -2649.06, AZ = 1104.17, B1 = 250.27, B2 = -14.73, c’i = 288.14, and C, = -30.45, all in MHz/r-ad2 or in MHz/rad*. inversion wavefunction is then used to calculate an average value of the rotational

constant (.4)v for a particular inversion state v; (J>” = Jo + AI(+), + _42(74), + . . . . The changes in the rotational constants, such as 6B = B,=l - By=o, are not explained by differences in effective constants, (B)l - (B)o; it is seen from Table V that 6B of the

normal species, for example, is negative, whereas the calculated (B)I - (B)o is positive. The discrepancy is due to coupling of the inversion-wagging vibration with the in-plane modes; the anharmonic potential terms should contribute very much to the changes in the rotational constants. These contributions may be eliminated by calculating the inertia defects. The calculated inertia defect is defined by

where the effective moment of inertia is given by

(Ia), = Iz,‘8r2(A),

which is nearly equal to

(I& = IizO - ~aOCAJAo(+” + Az/Ao(74)u - (AI/AoY(7*)vZ + . . .I

where 1,” denotes the moment of inertia at the planar configuration. The Coriolis coupling between an out-of-plane mode and the in-plane modes con-

tributes to A,, the change in the inertia defect by excitation of the out-of-plane mode. Oka and Morino (14) derived a general expression for the inertia defect, and it is divided

conveniently into two parts :

At = ACorioLis + a(A),

where the first term is due to the Coriolis coupling above mentioned and is given by

Acoriolis = “E @’ u2c 8 LlJt* - W,”

{ (rsr(a92 + (l,l(b92}

where s and t denote the in-plane and the out-of-plane vibrations, respectively, and {Sl(a) and l,,(b) the Coriolis coupling constants associated with the two in-plane principal

TABLE XII. Inertia Defects of Formamide

Species NH2CHO ND2CHO

6A = <A'1 - <A'0 (MHz) -440.69 -451.92

6~ = <~>l - <B>~ (MHZ) 57.70 76.32

6C = 01 - e. (MHZ) 64.01 79.84

02 6<A’t (am A ) -0.1490 -0.2222

-2 A (amu A ) Coriolis

-0.0261 -0.0349 0:

At (amu A ) talc. -0.1751 -0.2571

obs. -0.2088 -0.2909

‘6.5

'L'ADLI: x111 . Structural Parameters of lhc\ Mol~~c:~~l~l~

Skeleton of Formamide

Kurland, Wilsona Costain, Dowlingb present

0 C-N 1.343 ? 0.007 ; 1.376 i 0.010 ; 1.35* L 0.012 A

c-o 1.243 i 0.007 ; 1.1P3 i 0.020 ; 1.21P i 0.012 i

LNCO 123.58' / 0.35' 123.8' i 0.7" 124.7' i 0.3"

a. Ref. (1,.

b. Ref. (2). _

axes, a and b, respectively. The second term of A, comes from the expansion of the moments of inertia, and may thus be approximated by the difference in the effective

inertia defects:

s(A), = (A)1 - (A),,

which is given approximately by

s(A), = -I,“GC/c’o + L”&4/Ao + I$%H/B,,.

A normal coordinate analysis is carried out, assuming a planar structure and the amino wagging frequency of 304 cm-’ for NH$JHO. All Coriolis coupling constants are

evaluated and Acoriolis is estimated to be -0.0261 and -0.0349 amu A* for xH,CHO

and ND,CHO, respectively. The differences in the effective rotational constants such

as 6il = (A)1 - (A) 0 are listed in Table XII, and s(A), is calculated to be -0.1490 amu AZ and -0.2222 amu AZ for the NHzCHO and NDzCHO species, respectively. Adding the Coriolis term Acorioiis the calculated value of A, is -0.1751 amu k and -0.2571 amu A2 for the two species, respectively, which are in fair agreement with the observed as shown in Table XII.

4. DISCUSSION

The structural parameters of the NC0 skeleton are compared with those reported by Costain and Dowling and by Kurland and Wilson in Table XIII. The present result on the bond length lies between those reported by the two groups; the C-N distance being nearer to that of Ref. (1) whereas the C-O distance to that of Ref. (2). On the other hand, the NC0 angle is larger by about 1” than those already reported. It is interesting to note that the effect of replacing the oxygen by a sulfur atom on the bond length is hardly noticeable, because the C-N distance in thioformamide is 1.358 A, in agreement with that of formamide within experimental error. The NCS angle 125.3” is also nearly equal to the NC0 angle of formamide.

(‘ostain and Dowling have not given the exact definition of their inversion coordinate ; if the inversion coordinate is taken to be the distance of the amino hydrogens from the 11, b plane, which is nearly identical to a plane made by NV, C, H,, and 0 atoms,

266 HIROTA El’ AL.

their reduced I~XLSS should be multiplied by a factor of 4/9. They checked the validity

of their formula by applying it to ammonia, for which the inversion coordinate was normally taken to be the distance of the nitrogen atom from a plane made by the three hydrogen atoms. It is apparent for ammonia that the distance of the two hydrogen atoms from a plane, which includes the nitrogen and the third hydrogen and is parallel to a line connecting the two former hydrogens, is about 1.5 times larger than the inver- sion coordinate. It would be more reasonable to take the inversion coordinate in formamide as the distance of the amino hydrogens from the NC0 plane. One may obtain the correct reduced mass by using the general formulas worked out by Kasuya (15). It is, however, to be noted that these formulas may be applied when the aldehyde group is replaced by an “atom” and thus the reduced mass is the same for the cis- and trans-NHDCHO species. The inversion coordinate assumed in the present paper may not necessarily be a coordinate along which the molecule is actually inverted. The wagging and the internal rotation might be mixed to some extent. Unfortunately the experimental data available on different isotopic species do not permit us to examine the inversion path more in detail.

As far as only the observed frequencies of the v, = 1 +- 0 inversion transition as reported in Ref. (Z), in particular the isotope shifts of the frequency, are utilized, it is not possible to determine the potential function uniquely. This fact has also been pointed out by King (IL’), who has solved the inversion motion using Manning’s potential. A unique set of the potential constants may be obtained only by additional use of frequencies of the transitions between higher inversion states as done in the present work.

Analysis of the inertia defect may be of some use to determine the potential function

to inversion. Although the calculated inertia defect does not agree exactly with the

observed, the isotope shift of (A) t is accounted for fairly well. It is admitted that the

discrepancies are partly due to inadequate treatment of the intramolecular vibrations

and also due to possible mixing of the inversion with the internal rotation. A normal

coordinate analysis giving the inversion frequency of 304 cm-l for NHzCHO but 235

cm-r for ND$.ZHO, which is larger than the observed, leads to (absolutely) larger

inertia defects; -0.2491 amu AZ and -0.3223 amu AZ for NH&HO and ND&HO,

respectively. It is because the root mean square amplitude (~~)i is 30.6’ for NH&HO,

which is much larger than 22.2” calculated using a more realistic potential of Table XI.

It is still very difficult to calculate (A) t accurately for such molecules as formamide

with the large-amplitude inversion motion.

In the present paper the formamide molecule is concluded to be planar, primarily

based upon an assignment of the infrared spectra and an analysis of the vibrational

satellites. An additional evidence may be obtained from the centrifugal distortion

constants listed in Table V (16) ; it is seen that r2’ is very small both for NHZCHO and

ND,CHO, not only in the ground state but also in the excited inversion state.

When the planarity condition is assumed, small contributions of the centrifugal

distortion to the inertia defect may be evaluated. The 711 constant is thus equal to

~,,~b and the effective rotational constants listed in Table V are then corrected. This

affects, however, little the change of the inertia defect At.

MICROWAVE SPECTRUM OF FORMAMIDE 267

ACKNOWLEDGMENT

The authors would like to express their sincere thanks to Professor E. Bright Wilson and Dr. C. C.

Costain for helpful advice. Calculation in the present paper was carried out at the Computation (‘enter

at Kyushu University.

RECEIVED: June 18, 1973

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