Dynamics of small, floppy molecules studied by high-resolution spectroscopic techniques

dow7d of Moreadar Structure. 126 (1966) 41-66 Elsevier Science Publishers B-V.. Amsterdam - Printed in The Netherlands

41

DYWAWICS OF SMALL, FLOPPYMOLECULES STUDIEDBY HIGH-RESOLUTION SPECTROSCOPIC TECHNIQUES Wanfred Winnewisser Physikalisch-Chemisches Heinrich-Buff-Ring

Institut,

Justus-Liebig-UniversitZt,

58, D-6300 Giessen (F.R.G.)

ABSTRACT In molecuiar soectroscoov one of the coaxson interests is how to transform the information obtained by ‘high-resolution spectroscopic techniques into some reliable aooroximation of the potential energy surface of a particular molecule. Traditionaiiy vibrational spectroscopy has been used. Rotational spectroscopy can only probe, at least at room temperature, molecular tra_yitions arising from excited vibrational states up to approximately 1000 cm . This corresoonds roughly to 1090 of a typical bond dissociation energy. However, floppy molecules which exhibit a 1arge-amp1 i tude, low-lying vibrational mode can be studied to a large exrent by rotational spectroscopy in the microwave, millimeter and submillimeter wave range. Quasilinearity is a special form of large-amp1 itude motion, which complicat& the observed Glecular spectra substantially and which presents a real challenge to theoretical spectroscopists. In this lecture the highlights of quasilinear behavior of the molecules HCNO, OCCCO, HNCS and HNCO will be discussed. Another form of larqe amplitude motion is the inversion exhibited nrimarily by mol ecu1 es derived from NH,. Isocyanamide will be discussed and its ;pec;al spectroscopic features will be shown- Cyanamide and cyanamide has been detected as a isocyanamide are potential prebiotic molecules: constituent in the interstellar medium The analysis of the molecular dynamics of these molecules is shown to be necessary for understanding the frequencies and intensities of the observed spectra in the laboratory and in interstellar space. INTRODUCTION It is a great honor and pleasure for my wife in the Oji International Seminar on Rotational of

work

of their work is see the theme of

Professor Mizushima and Professor Horino and celebrating the extension studies in the many liirections being presented here this week, Our own not directly concerned with rotational isomerism but I think you will relationsship between the large amplitude motions I will discuss and the this seminar.

The Discovery It

seems

experimental current

Brenda and myself to participate Isomerism honoring the original

of Isomerism to

me relevant

proof

sources

of

was put forward

0022~2360/85/.SO3.30

to

structural

review

briefly a

isomerism, by Berzelius

(I)

the history of the ‘irst concept which according to in 1817. Fulminic

6 1986 JIlsevier Science PubUshersB-V.

acid,

HCNO,

42 and its role

isomer

isocyanic

acid,

in

the

deYelopm?nt

CYanates

or

iSOcYanatcS

bonding

schemes

occurrence of representatives Liiwenstem salts

history

of

and strucZura1 these of

in

silver

the of

sfxteenth

that

fulminic

obtained the

formulas.

century

acid

fulminic

acid

the

fulminate

salts

played

were probably

with

familiar

acid

the

(4).

dramatic

with

first

correct must

analysis contain

of

mercury

the

description

silver

oxygen

the

However,

E. Howard (61. This description age of chemistry. In 1824 Liebig

group

an important

The historical pursuit of the first to the age of the alchemists. Two Drebbel and Johann Kunckel von

and isocyanic

begins

various

as a science (Z-51. The fulminates and greatly to the development of chemical

substances leads back this tribe, Cornelius

salt by the English chemist beginning of the classical Paris

HNCO. and their

of chemistry contributed

of

its

fulminate

and recognized The work of

(7,81.

Liebig (91 coincided with that of Wiihler who reported the composition cyanate (10 I. Indeed, a puzzling situation was observed: both salts

course, a controversy fu?minating proportions

mercury

coincided with the and Gay-Lussac in

and cyanogen

the identical chemical composition but they properties. Mercury fulminate exploded violently,

and

scientific

of silver exhibited

had undeniably quite different while the cyanate did not. Of

developed betueer %e two research groups, which reached when each side accused the other of incorrect analytical

in 1826, then at the University of Giessen Ill), took up and nas able to confirm his earlier analytical results. did the same. It was finally established at the University of Giittingen,

research work, Liebig his Paris work again WBhier,

and that

that both analyses were correct, experimentally demonstrated. me

next

involved attempts brilliant

step

students

modem terms: (121, I894

was to

devise

structural After

in this discussion. were made to devise of

fulminic

The first

monomeric

structure

acid

by Wieland

and

challenge Nef’s formula. In one of the exemplary Pauling

and

Hendricks

in

his

the

isomerism salts

where

and the

many

Ke)kuli.

had been

one

acids

unsuccesful of

the

most

in

in

fulminic

acid

was supported

reactions to the divalent carbon atom. anmunt of research uas carried out on fulminic

for

interlude formulae,

of

he thought

of

1857 the first structural fomula as what we would call nitro-acetonitrile

proposed

was written

(131 to be HONC, which

concept

fomulas

a long

structural

Liebig,

acid

the

conceived

by Nef

in

of l,l-addition

In the following years a formidable the formation and polymerization of

associates

contributions 1926 published

uas

by evidence

(14-181. to

a

the

However,

emerging

theoretical

they

quantum

paper

on

did

not

chemistry

compounds

containing only the four atoms H, C, N, and 0 (19). According to their potential energy calculations HNCO should be the most stable isomer, followed by HCKO, while HOCNand HONC, which have yet to be detected in the gaseous phase, should be

the

least

stable.

They

proposed

a

charged

structure

for

fulminic

acid

43

H-CON-O

REACTION

corresponding standing

to

of

has

carried

Grilnanger

(4,231

Ab Initio

Studies last

singlet

potential

of the

appeared

Pople

electronic

structures which

and

for

and

road

addition

the

system

systematically

energetic the

CHNO was

its

The 4-316

more

stable

carried

matrix the

(27,281. gas

phase

kinetically interconversion

to

observe

the

infrared

We must conclude spectrum

unstable

of

under

the

spectrum

from the tmo

laboratory

seems to be reprotonization

of

the

reaction

the

reaction

are

upon wall

from

to

HOCN only

The

tne

the

in

attempts

collisions

it

has

a cryogenic

HONC that

dominant

1.

other

relative

HCNO. However,

HOCN and

conditions.

Fig.

shown in

separated

many unsuccessful

isomers

geometries,

with

According

be

the

along

isomers

to

the

cf

Poppinger,

together

than

1 HOCN should

seems

by

energies

isomerization.

possible

and

the CHNO

study

out

examined

relationships

isomers.

of

detailed

be more stable

been

Grundmann

studies

A very

energies

Fig.

under-

of nitrile-N-oxides.

theoretical

(24-26).

authors

HONC, to

in

the

the years,

Much of this

(20-22).

Fulminic acid or formonitrile-N-oxide isomers by rather high barriers to given

for over

reactions.

the chemistry

more stable

of HCNO

1 iterature

The

its

observed

associates

a number of ab initio the

interconvert

carboxime,

Huisgen

4 to

opened the

reactions

as 1,3-dipolar

by

Isomers

in

(24).

structure

chemical

ago surmaarized

surface

Radom and

from

out

few years

have

paths

puzzling

some years

isomers

pathways

of

can be understood

been

the

H - C T N - 0 . This

a plethora

many of which

In

-

4-316 energies along reaction paths from carboxime (Courtesy of Poppinger, Radom and Pople, ref. 24)

isomers-

work

COO?KXNATE

to detect they

mechanism

are of

of HOCN to HNCO

44 and HQNCto HCNO. That means that normal laboratory conditions. Spcectroscopic

Studies

we are

number of very

with

only these two isomers

under

of the Isomers HCNOand HHCO

With the advent of high resolution large

left

detailed

studies

rotational appeared

and vibrational in the

last

spectroscopy

20 years

a

on both HNCO

and HCHO. Recently these studies and others have been reviewed by B. P. Winnewisser (29). Therefore only the references relevant to our present discussion will be listed. Fulninic Acid, HCNO, is the most distinctly quasilinear molecule for which a large amount of rotationally resolved data could be obtained (5,291. Its competitor in this respect is now carbon suboxide, C303. (29) whose quasilinear The concept of quasilinearity properties

features will also be discussed in this lecture. will then be used to explain some of the intrinsic

of the energy levels

of the

molecules

HHCOand HNCS.

EXPERIMENTAL EVIDENCEOF QL’ASILINEARITYIN HCNO The intriguing properties of a quasiiinear molecule are all related to a low1arge amplitude bending mode having a rather anharnonic bending lying. potential. In such a molecule the bending motion and the rotation about the axis of least

moment of inertia,

linear it has two freedom. However. freedom and 3N-6 smooth transition

the a axis,

are strongly

coupled.

If the molecule

rotational degrees of freedom and 3N-6 vibrational if the molecule is bent it assumes three rotational vibrational degrees of freedom. Therefore, there from the linear limiting case to the bent limiting

degrees degrees must

is of of

be

a

case which

involves the transition of a vibrational degree of freedom into a rotational degree of freedom. This means for the structural discussion, that the semirigid structures with which we like to describe molecules must be replaced by a nonrigid molecular model, which is neither linear nor tent in the established sense. are

Very early in the spectroscopic pursuit disturbing deviations from the linear

of HCNOit became clear that there molecular model. Four of the five

normal modes were consistent

with

however,

by Beck and Feldl

could

an irregular

not be located

series

of abscrptions

expectations.

The

lowest-lying

normal

mde.

in 1966 (301. Instead they found in the far infrared (311 which were confinned

through our higher resolution measurements (32,331. A sunnary of these measurements is presented in Fig. 2, which shows the unique hot band and overtone system of the quasilinear bending mode ~6. The prominant Q branch at 538 cm-’ belongs to the skeletal bending mode v4 which is not quasilinear but of small amplitude. Its R and P branches are buried under the strong 2~6 band. By assigning the rovibrational spectrum through comparison with pure rotational data and using the Ritz combination principle, the relative spacing

) A50 nz1-0

100

.E n p

f 5

s

50

&I

em

t -1

1=2

I=

anArz2

HCNO +a A _~_~~~~~~~~~~~~~~~~~~ I j I I I I ! n;7-7 L

r-__-___-_~* '13 ------5:10s.---I_-+-------+,, : I +0 I

i

I

22bl

!

!

l{O

I

I 5+7 t I

1

5A7

i I,

Fig. 3. Energy level diagram for the vibrational manifold of v 5 for HCNO and DCNO, The arrows represent the various transitions belonging to the series indicated in Fig. 2, (From ref. 32).

47

of

the

energy

demonstrated Fig.

levels

belonging

and an energy

3. The allowed

to

the

~5

diagram could

transitions

which the transition series decreasing shown in Fig 2.

level

vibrational manifold could be be constructed, which is shown in

can be classified

moments are related, in intensity

as is

into

so that

indicated

groups,

within

each of

each forms a regular,

in the low resolution

smooth spectrum

The classification of the vibrational states is that of a molecular model, using the quantum nuu?ber K = 1 for the axial angular momentum, and the vibrational quantum number n. This quantum number may limiting

linear

be thought of either as the quantum number of the bending mode of a slightly asmtric rotor molecule or as the radial quantum number in the linear limiting case, with ~1 inear= 2n + 1. The strongest transitions are those with r. = 0, An =o, Al = 1. They are indicated in Fig. 2 by the positions of their Q branches with R and P branches clearly visible in the high resolution spectrum shnwn at the top of Fig. 2. Of course these transition would form in the linear limiting case the fundamental band with its hot bands with n = 0, Av = +l and case, however, they must be considered pure Al = +1. In the bent limiting rotational transitions. Their intensity would depend on the component of the electric dipole moment perpendicular to the axis of least mome;it of inertia, which in the linear It

is

molecule

interesting

to note

is the figure that

axis.

the series

of

transitions

in the wavenumber

region from 450 cm-l to SO0 cm-l (see Fig. 2) can be classified as n = 1 - 0, with An = +l and Al = 0. In the bent limiting case these trarsition would correspond

to

the

subbands

of

the parallel component of a hyt rid in-plane In a linear molecule they would correspond to the

bending fundamental vibration. overtone band and its hot bands. From the above discussion it features

and structural

information

should

be clear

that

which were obtained

most

of

the

SPeCtral

by 1974 indicated

that

the molecule HCNOis somewhere between a linear molecule and a bent mleCUleCombining all the available experimental data from far infrared measurements. high resolution measurements (5,2g,mill iwter wave measurements, the latest 34,351 and Laser Stark measurements (361 now available many vibrational levels could be vibrational

determined with high precision. energy level diagram is presented

QUASILINEAR POTENTIALFUNCTION The unambiguous assignments made possible data provided not only accurate energy levels

The

current 4.

state

of

the

HCNO

in Fig.

by the wealth of high resolution for HCNOand DCNObut also precise

spec:roscopic constants (in the sense of effective constants) for both molecules (37-41,33,35 and other references cited in the reviews 5,291. These constants were essential in the development of the understanding of the molecular dynamics and the pozential function for fulminic acid. Al 1 the standard spectroscopic

48

20---!__-‘o

: : : : : : : : :

Fig. 4. Current energy level diagram of HCNO. Solid arrows bands recently analysed or (dotted arrows) for which only the be observed. (From ref. 341. treataents,

series determine

molecular results.

which

fitting

involve

expressions

in

the spectroscopic

structure

and

The power series

the

the rotation

rotational constants,

potential expressions

and

vibration vibrational

and then relating function, clearly are only useful

show vibrational branches could

Q

energy levels to power quantum numbers to thfs

Sfifonuation

to the

brought unsat5sfactor-y for descrfbing energy

49

levels

if

a lack

of convergence

they

molecular energy

converge

model which levels

large

appropriate dimensional

that

potential

the

the

HCNO

earlier

coordinates the CH rule

H atom

bender

to

KH

linear

clarify

and Yij be

force part

(CN

of the

Bunker r ij

with v4

about

linear

by allowing

quasilinear

and 2~6 60

the

The two-

the

a constant

from

HCN reduced

(431,

which

the

violated

molecules

showed

C atom when VS is

required.

been is

is

involves

an extension

v3

(NO

large

(491

to be determined are

The expressions

simple for

rij

functions are

n;olecule.

lowest-lying

bending states

are

(CNO bend).

The

from the

three-atomic

(481. interaction

in

a dependance

bending

(461

bending

the

vibrational

Hamiltonian

in a series

of

and u4

introduced

amplitude

the

other

vibration-bending

can be expressed

they

state

stretch)

and

by Bunker

of an effective

that

the

out by Sarka

dominant

are parameters

note

mode while

rotation

and Glimekisser

detail

vibrational

we should

pure

of the Hougen-Bunker-

in

the determination

was carried

on the

to

Landsberg

described

Hougen-Bunker-Johns the

applied

HCNO by Bunker.

small-amplitude

and Landsberg

shown that

constants.

are

Hamiltonian

stretch).

molecule

interaction

may also

the

even well-behaved

a circle

has for

quasiliner

to introduce

where Xij

of

derivation

situation

the

u;!

distances

dynamical

each

the is

v5,

molecule

nuclear

This whose

for

four-atomic

In order

data

The approach

extension

to the

arc

coordinates

Hamiltonian

(44).

stretch).

original

the

level

(45)

function

In order VI

of

at

problem

of

betueen

knowledge

and by Jensen

mode in HCNO,

resonances

(32)

and our

the

rectilinear determined

energy

(47).

treated

allowed

mode.

isotropic

by a barrier

coordinates

were

rovibrational which

broad,

since

flexible

bender

Johns Hamiltonian and Jensen

(32,421

the

HCN bending

a

perturbed

bending

Coriolis

curvilinear

semirigid

potential

by

distance

as a semirigid

(35)

the

that

case

simple

function

the

internuclear moves on

bending-rotation

in

represented

themselves

observed

atom

function,

in

doubt

by a potential

hydrogen was

was not the

The first

showed beyond

calculations

functions

Therefore

The

the

oscillator

However,

excited.

of

(32)

this

quasilinearity.

reproduced

surface

lhe

short very Bernstein’s

be

potential

basis

mode but

only

motion

configuration. anharmonic

For HCNO, -however,

from the

we used

could

amplitude

mass.

rapidly. arises

coordinate

of

o-

a quasi-

the

inter-

The important

expansion,

from the experimental of

inserted

the into

quadratic the

dati.

It

and cubic

kinetic

energy

of the Hamiltonian.

The quantity effective

of

potential

greatest function

importance for

the

is

not

one particular

quasilinear

bending

geometry. mode

in

but a

the qiven

60

vibrational

Veff(P)

state.

Bunker, Landsberg and Winnewisser

4 + >7 i=l

= vo(pI

ivi

di + ---) 2

where VO(p1 can be considered di are the vibrational vibration, matrices W<(P)

Y,(p)

wavenmbers

=

9

lin

function

(2)

the equilibrium

bending potential

quantum number and degeneracy

are functions

potential

wi(P),

and cri_(p) is the P-dependent

The vibrational

used the

of the ith

harmonic vibrational

are p-dependent

because

function,

vi and

small-amplitude

wavenumber in cm-‘.

the elements

in the F and 6

of p. Both terms in Eq, (21 can be expanded,

+ fL;I$

+ f(i) aacLZ4’

(3)

= fLo,‘p? + f;;i$4,

(41

where

Pf f aa = fre,’•t- &hi i=l

+2-“I_)fpJ

(51

and

pff

aaaa

= f(o)

aaaa

2hi i=i +_“‘,f;;;a.

*

(61

2

Using the wealth

of

experimental

data available

for

HCNOBunker, Landsberg

and

Winnewisser (35) could apply the above outlined theory to the rotational energy levels for many states of HCNO and DCNO. Their work resulted in the first acceptable fit, with a small number of physically defined constants, to the rotational structure and subband centers of the bending-rotatiolevels. Recently the high resolution experimental work (34) and the theoretical interpretation

(44)

of HCNOwas extended

The effective potential function be given in cat-l by (441, V&(p)=-

302*277.7(F,+;)+244_9(c2+;) [

for

to the degenerate

a general

vibrational

v4 vibrational state

state.

of HCNOcan now

YCNOWOOd+fl UOO@@l HCNO ~2oociW predacted HCNO

150 -

OCNO tOOOee, 100 HCNO IZOO~)__.__ ____ predicted

-_-_

50 HCNO

IIOOO”l-------.a

HCNO

:OOOO”)

DCNO

1000O”l--

z -.

\_

--.

\ 0

Fig.

5.

This

means that

-

-

,-=A 5

10

-

15

20

25

30

35

pldeg-ees

Effective HCN bending potential curves for various vibrational states v4 4 of HCNOand UCNO. The horizontal lines indicate the position of bending energy level associated with each etfective potential. The are given for the excited state 2000 and the hypothetical vibrationless state. (From ref. 29). excitation

of v I

or

v2

introduces

a quadratic

barrier

to

linearity with actually very little modification of the quartic wall of the twodimensional oscillator function. Fig. 5 displays the various effective HCN potential curves determined from the data, also indicating the prediction for the excited

state

2~~ and the equilibrium

HCNbending potential Y&1

= -30.2

function

potential

function.

The equilibrium

can be given by (44)

p2 -I- 1885 p 4 ,

nhere the cuordinate a quartic

bending

linearity

is

0.2

(81

p is given in radians. potential

cm-l,

However. with excitation more bent and shows all

function

which

of

is

with a wide,

within

the stretching

the effects

We may note that this the

flat

bottom.

model and fitting

modes the molecule

of a quasilinear

species.

is essentially The barrier

to

uncertainties.

becomes more and This result

is in

agreement with the most recent ab initio calculation which defines a potential function which should he compared with the equilibrium potential function given above. PARAMETER TO QUANTIFYQUASILINEARITY The first discussion of the energy levels of literature was that of Thorson and Nakagawa (50). diagram for

the energy levels

of a linear

a quasilinear molecule in the Their work gives a correlation

polyatomic

molecule

and that of a bent

52

-08

-07

-0.3 $p G3

-0.6 -05

05

06

07

ion

as%

10

IllcCCll

CCMHUI HCCH HCCF

Fig. 6. Correlation diagram of energy levels of linear and bent molecules. The functions for the four cases dashed curves represent the bending potential illustrated_ (From ref. 52). The quasilinearity parameteryO is given below for a selection of molecules. molecule, Fig.

whicn was actually

6 we show the correlation

molecular

mDde1 of

a

state.

In both limiting

energy

levels

Dclecule oscillator,

the

first

used in another context

between the energy levels

three-atomic

molecular

systw

in

by Mulliken of a linear a

singlet

(511-

In

and a bent electronic

cases we approximate the potential function and thus the In the case of the linear by those of a harmonic oscillator.

potential function As we move from the

is left

that of of Fig.

an isotropic two-dimensional 6 to the right hand side we

53 introduce gradually

a potential increase its

functions

become

cannot

anharmonic

be represented

Winnewisser

hump into the center portion height and width. The effect at

by a simple

(52) calculated

four

1 - q2 + czexp(- Bq21 2 I

v = hcv0

the

bottom.

functional

different

of

the

is

parabolcid,

that

the

and

potential

The corresponding energy levels expression. For Fig. 6 Yarada and

cases

using the potential

function

with ln(2 OrBI = 1.5,

(91

where a and B are parameters which allow a convenient representation of the four cases indicated. q is a dimensionless coordinate which represents the radial component of the two orthogonal coordinates of an isotropic twodimensional oscillator, expressed in polar coordinates. The carrel ation of the energy levels diagram.

is carried

Furthermore

out by connecting

these

levels

must

levels have

momentumquantum number 1 and the same n value

of

the same parity

the Iv,=

across

same vibrational 2n + 1).

the

angular

By inspecting

Fig.

6 in detail we see that the vibrational energy levels at the left hand side of the diagram belonging to a linear molecule separate into vibratioral and K,-rotational

energy levels

of a bent molecule.

Thus, the correlation

transition of a vibrational degree of freedom into the appropriate freedom across the diagram. Of course, quasilinear molecule depends on the electronic structure In order

to study and classify

molecules

E (lowest Yo=l-4

[ Etlowest

state

excited

with K or 1 = II state

This parameter has the value -1 for

quasilinear parameter y0

behaviour to

give

linear

a

1 ‘101

with K or 1 = 0) 1 an ideal

the

a rotational degree of potential function of a of the molecule.

which exhibit

Yamada and Winnewisser (52) introduced a correlation quantitative but empirical Reasure of quasilinearity:

traces

molecule

and +1 for al ideal

bent molecule. It can be considered the correlation parameter which traces the transition of a vibrational degree of freedom into a rotational degree of Fig. 6 have all different freedom. The molecules entered on the bottom of chemical composition and properties but they posses the cotmaon physical property large-amplitude bending vibration which gives rise to the of one low-lying, quasilinear From Fig. quasilinear

behavior of the molecule. 6 it is clear that carbon molecule,

whose low-lying

suboxide,

C302,

is

indeed

bending mode VT was found to lie

the

most

at

18.2

cm-1 and was subsequently observed in the submillimeter wave region by Krupnov The energy levels of the vibrational manifold of this and coworkers (53:.

w

Fig. 7. Energy level manifold of energy levels of C 0 were taken from ref. (571, 3 * extremely infrared

unusual (541

function

data

their

quasilinear puzzling energy

of

properties

C3C2 has

of

manifold

vibrational satellites ‘J 7 vibrational manifold ponding

l-type

consistent_ by a sulphur

C3OR.

As

(57). it

could

can for

relative

resonance

Therefore

which

be

must

the

fine

on the

explain

already

seen

from

7,

the

were

that

the of

by

us

carried of

the

electron

in sharp out

on

from the the corres-

(581,

substitution

a the

corresponding

C3OS, is

and the analysis analysed

assumed

1970 many of

of C3OS arising

spectrum

balance

diffraction

(56)

in

(531,

quasilinear

electron

sulphide,

measurements

wave

the

Morino

Fig.

oxide

also

be concluded

that

and

measurements

interactions,

sub-millimeter

obvious

effect

tricarbon

intensity

atom in C302 changes

is

Kuchitsu

pure rotational These

by

It

a oronounced

determined

in the

detemined (551,

ianimoto,

function

Precision

contrast-

were

interpretation.

potential

level

mode

and Raman spectroscopy

potential and

bending

C OR and C3OS. The t f e C3OS data came

the ~7 bending mode for (53-55) while from refs.

are

of

self-

one oxygen

distribution

fl$J3 f$+=k] \ 0

0.1

Q/rod

2%+%

1

1

0

-w-

Y W

I,(

va %+Y WY

If.

1 0

-I LINEAR

/\

I

02

03

Q/rod -D

y+y

(16

Y0

Ground State Fig. 8. Classification of various the quasilinear bending state v, of Weber, from ref. 541.

Y Y

OJ

1

I

+I

I

BENT

EqulhbrlumPohntrol

combinations of stretching states of C 0 with 72 using the cortelatioF parameter Yv. (*_ourtesy

around the central carbon atom, and thus the potential function of the bending mode. But we should note that even though the potential function is tPat or a two-dimensional harmonic oscillator, the motion which occurs is of raeher large amplitude

reflected in the small bending force constant found for this vibration the Born-Oppenheimer separation of rotation and bending is still valid for C3OS. In a recent contribution to the problem of quasi1 inear molecules Bunker and Howe (60) have extended the definition of the correlation parameter. In their new definition this parameter is given by (59).

However,

(111

between the 3v-th rotation-bending where av is equal to the energy separation level having J = 1 and the v-th rotation-bending level having J = 0, b, corresponds to the energy difference between the (3v-l)-th rotation-bending level having J = I and the v-th rotation-bending level having J = 0, ard cv is equal to the difference between the (v+l)-th and the v-th rotation-bending energy levels having J = 0. This extension of the original parameter Y 0 has three features: a) From the new definition it follows that a series of parameters Y,with v = 1, 2, 3.... can be derived as a function of the degree of

66

bending

excitation.

excitation +I

of

for

a

the

b) Furthermore small-amplitude

linear

redefinition.

and

bent

case of free

vibrations.

cl

will

vary with

The limiting

the

values

degree of

of

-1 and

molecule,

respectively, are unaffected by the a three-atomic molecule with an internal rotor (for

However, for

example the polytopic limiting

the parameteryv

wlecule

LiCN or

LiNC) y,

assumes a value

of

-3 in the

rotation.

For C302 the parameter y,, can be used to display in an effective nay the interaction of the various normal modes in C302 nith the potential function of the quasilinear wde ~7. In Fig. 8 the observed energy levels and the effective potentials of the most extreme linear and bent C3O2 molecules are indicated as given by Weber (54). I will emphasize this unusual variation of the bending potential and thus the variation of the expectation value of observables reflecting

geometry.

by speaking

of “vibrational

isomerism’.

QUASILINEAR ASPECTSOF HNCO,HNCSand HNCSe Among nominally bent molecules acid, P&CO, isothiocyanic acid, particularly

the series hydrazoic acid, HNNN, isocyanic HNCS, and isoselenocyanic acid, HNCSe, is The increasing;: quasilinear behavior of the acids in

interesting.

this series is reflected in the molecular structure of these acids, shown in Fig. g. Of course, the quasilinearity in these molecules is associated with the motion of the hydrogen atom relative to the heavy frame of the molecule. The values of the quasilinearity parameter are indicated in Fig. 6. One feature of quasilinear

wlec;hes

wlecules centrifugal

seen froGl distortion

fits

squares

whfch

to the spectral

adding higher order effective constants.

has

not

yet

the perspective effects (29.64). terns, The

of

been

discussed

is

that

data is Watson’s

S-reduced

Haniltonian

nodes

in

can be enhanced which means that a quasilinear

adapted by

leading in the case of quasilinear molecules to mean that higher-order terms frequency large

predictions outside the J and K, range of the data are not possible. Moreover, dut to quasilinearity accidental Coriolis and Fermi (43,66,671

quasilinear

a bent molecule exhibit extreme The Hamiltonian used fcr the least

molecule

are

the energy levels

seriously

affected.

resonances

of other

bending

One such an example

should be discussed in this paper since it dewnstrates the anomalous effects which can be observed. For a molecule like HMCSthe a-type Coriofis resonance bending modes couples strongly between the skeletal in-plane anQ out-of-plane energy

levels

Thus we find

with K, > 0 with the result that these levels repel each other. the K, = 1 level of the lowest excited state is pushed close

that

to the K, = 0 level. When the wlecule approaches the linear wlecular resulting interaction grows stronger. This situation can be

lim%t the understood

pictorially

diagram of

by looking

the energy levels

at an excerpt

involved

which is

from the linear-bent shown in Fig.

correlation

10a. We should

note that

the

57

rS

SRB 180.

C

H

1.279

k

4

C

1.053

1.198

U

F

180.

Structure of four-atomic pseudohalogen hydracids. The internuclear Fig. 9. distances are given in R and are taken from the following references: HN3 (61), HNCO (62), HNCS (63), HNCSe (64), HCNO (35) and HCCF (65). All are substitution structures except that of HCNO (35). K, = 0 levels with

the

of the

1 = 0 levels

the two degenerate

two bent of

the

vibrations

skeletal

bending

combination (v4,v5)l

state

= (l,l$.

vibrational arising If

states from

a molecule

the

are

correlated

excitation

has a small

of value

b)

b-tme transitionsof MC0

59 HNCS

HNCO -f

1-a

Fig. 11, Energy level diagram showing the K -rotational levels in the around and bending vibrational states for HNCO and HNCS. The vibrational states ate labeled according to the refs. (66-69). The resonances responsible for the observed effects are indicated. cf

~0.

will

the

energy

be rather

strong lower

a-type

small

are degenerate levels.

it

and one pair

linear

molecule

levels

for

excited

higher

excited

in HHCS is

that

In the microwave

region

rQO branch with

Q branch was that

for

Fig.

lob,

Q branch,

and

b-type

frequencies,

a c-type

transitions. as is

HNCS it A

the case

spectrum demands that

in

the

for

the positions

of

gces off

are

the

to

bending

for

modes

case a level

HNCO-HNCS. With

For

of

very

the more quasi-

the K, = 1 and K, = 0

left

As indicated

in Fig.

of the crossing

point.

molecule. energy

levels

loner

frequencies,

molecule however, 95

manifests

The puzzling

in

itself

aspect

of

as shown in

can have only a-type would

shown in Fig. state

of the

has K, = 1 levels

reversed-

just

branch,

HNCO and is

lowest

state

R and P branches.

Q

Hence a

than the 1 = 0

the in-between

the K, = 0 levels.

whereas a planar

b-type for

that

quasilinear

inversion

large.

much lower

is indeed observed

state

associated

this

like

is located

of a molecule

a truly

this

be rather

model the two bending

vibrational

than

bending

Thus, HNCS must be considered in a strong

effect

HNCS, with yQ = +0.72,

the lowest

10 the situation

in the linear

qualitatively

lowest

nevertheless

A will

bending vibrations

which pushes the K, = 1 level

of 1 = 1 levels

This beautiful

HNCO in its

to but

constant

results,

down. Since

can be understood

YO = M-84, close

interaction

state

may occur.

between these two skeletal

and the rotational

Coriolis

vibrational

crossing

difference

level

lOc,

go

to

higher

Therefore

the

HNCS, the K, = 1 ievels

are

actually

which

below

shows the

Fusina and #ills HNCO (7D)

the K, = 0 level.

full

bending

demonstrated

that

the

energy

by means of

fundamentais

HNC-bend and NC&bend or vice apd v5 as an in-phase both

contribute

such mixing of

to

v4

situation diagrams.

v4

is summarized in Fig. 11 It should be noted that

an harmonic force

and v5

versa.

combination the

This level

should

behaviour

of

bending coordinates,

this

molecule.

the normal modes has only been determined

and HNCSe. As can be deduced

from Fig.

analysis

for

cannot be considered as either be regarded as an out-of-phase

of the two in-plane

quasilinear

field

9 HYCSe is

which

The extent

qualitatively

of

for HNCS

even more quasilinear

than

H!XS. with y. about 4.46. However. the chemical instability of HNCSe has made it so far impossible to obtain data extensive enough to study quantative?y its enticingly

quasilinear

behaviour

(64,711.

ISOCYAWMDEA SEWIRIGIDII!VERTER Among the five-atomic molecules diazomethane, abundance of known or suspected structural isomers. various

diazomethane

isomers

have been carried

(73) in 1979, Vincent and Dpstra (74) Thomson and Glidenell (76) in 1983.

H2CH2, is Theoretical

unique in its studies of the

out by Hart (72)

in 1973, Moffat

ir 1980, Ichikawa et al. (75) Al 1 theoretical calculations

in 1982 and agree that

differ cyanamide, H2H-Ce. is the most stable isomer. The calculations predicted order of stability of thy other known is?%rs isocyanamide. diazomethane,

H2C=H=N, carbodiinide,

HhPU.

oud the

cyclic

isomer

in the H2N-NC,

diazirine,

H2Ch2. Our present knowledge concerning the structure of the isomorphic isomers cyanamide and isocyanamide from microwave measurements and ab diazocmthane. initio calculations can be found in refs. (74,77,78). It

shculd

be pointed

out

that

diazomethane

is

planar,

with

symmetry C2,,,

while cyanamide and isocyanamide have structures which are actually pyramidal and the wlecule undergoes an inversion of the two about the amino nitrogen, studies by Jones and Sheppard in 1970 (79) an amino hydrogens. From infrared estimated value of Q67 cm-l was reported for the inversion barrier in cyanamide. confirms this value. A recent qicrouave study by Read et al. (80) essentially is energetically less favorable according to i socyanamide, this inversion (75). Both theoretical studies Vincent and Dykstra (74) and Ichikaua et al. predict a high barrier for H2N-!!C in contrast to H2H-CH. The differences are mainly caused by the different orbital overlaps in the two ismers. Vincent and

For

Dykstra reported an ab initio value of 6.0 kcal per mole or 209C cm-', which is about 4.5 times the experimentally determined barrier of cyanamide. Furthermore, energetically isocyannide cyanamide (74). An ene-gy gives

an inversion

splitting

should be about 53 kcal per mole less level prediction based on the ab initio of 0.8

to 1 cm-1 for t12R_RC(75).

stable than calculations

61 w-

NH2 NC

5 ss- a2

so%W LS-

‘o-

lo,

35

%s30-

25-

h-

IO-

x2,-

15-

sac-

606

%5-

50s

IO-

Fig. 12. pt of the energy level diagran of H2N-NCshowing rotational structure of the 0 and O- inversion levels. vertical arrows connect energy levels where a-type rotational transitions have been observed, while oblique arrows show observed c-type rotation-inversion transitions. (From ref. 82). Due to our interest in molecules of astrophysical importance (cyanamide has been found in the interstellar medium) and our interest in molecules with large amplitude internal motions, we began the study of isocyanamide. H2N-NC (81,821, before

the theoretical

millimeter

studies

wave and submillimeter

of ref.

(74 and 75) were published. The observed wave spectrum allowed us to assemble the lower

62

Fig. 13. Fortrat diagram of the pure rotation tqR) and inversion-rotation transitions of H2N-CN. Measured lines are indicated by filled circles. (From ref. 82). region

of the energy level

Since belonging r;hes

diagram,

a part of which is shown in Fig.

for

tne

allowed

transitions

can be found

following

Papougek and ?ipirko

(83). There are no pure inversion transitions allowed, but there rotation-inversion transition as well as pure a-type rotational pcssible. Both types of transition have been observed and the Fortrat Fig.

13 gives

region.

an impression

The splitting

of how such a spectrum looks

between the two c-type

just twice the inversion splitting detemined to bo 0.369 az-l. In collaboration applied the

ab initio

of

with Jensen (84)

to the isocyanamide potential

Dykstra and ,‘asien extension

12.

H2N-NC, like H2N0, can be considered an asmtric rotor molecule to the synsnetry group Cpv but undergoing H2N-inversion the selection

(85).

the

ground

the semirigid

function

invertor

bender Hamil tonian

centered

invertor

and the HNH angle

values

(82)

in

wave

at 275 CHz is which

has been

Hamiltonian

has been

for

relaxation

Hamiltonian applied

diagram

in the millimeter

state

problem using as starting

The semirigid

of the semirigid

Q-branches

are c-type transitions

the calculation calculated

can te considered HCNOproblem. to the

by an An

effective inversion potential function was obtained for H2h-NC when the experimental data (82) were fitted by a least squares procedure tc the semirigid invertor Hamiltonian veff

=-4313.7p2

+ 2226p4 + 30.9~8

where the variable the

pctential

p describing

coefficients

(12)

,

the inversion are

given

in

motion is expressed in radians and The last two coefficients

an-l.

63 WVERSION SPLITTING IN CM-’

__--___g

I

_

z

:

:

;

_

.

-1.4

.

_

_

_

.

_

00

3623

-135

3690

P/-d

,

I_4

Fig14. Effective potential function of the H2N-inversion isocyanamide as used in the semirigid invertor Hamiltonian.

motion

are constrained

ootential.

to values

describing

Dykstra and Jasien’s

ab initio

in

The potential function and the calculated inversion splittings are illustrated in Fig. 14 nhich also shows the observed inversion splitting for HDN-NC, recently determined from mill imeter wave measurements (861. The inversion splitting in the ground state of HEN-NCturns out to be nearly the same as in H2ND (831. It is therefore substantially different from the inversion splitting in cyanamide (eO1, and requires indeed a much higher barrier to inversion. CONCLUDING REMARKS From the examples presented in this lecture we have expanse cl‘ the millimeter and submillimeter wave region

seen that the full is needed to make

substantial contributions towards the understanding of molecular dynamics and therefore molecular structure of small, floppy molecules. I believe that the interplay between theoretical methods and high resolution spectroscopy in this spectral region and in the terahertz region will be actively pursued in the future,

interest

The study

of

large

to molecular physics

ACKNOWLEDGEMENTS I express my gratitude comments on this laboratory

amplitude

paper

reported

in

and chemistry

to

Dr.

and aid this

motions

in

continue

to

be of

great

in the years to come.

Brenda Pcompleting

contribution

will

ilinnewisser it.

has been

for

discussions

The work from supported

the

by the

and

Giessen Deutsche

Forschungsgemeinschaft, Institute for

the

of Radioastronomy,

making my participation

Fonds

&r

I would in

the Oji

Chemischen al so 1 ike Seminar

to

Industrie

and the

Max

thank

Fui jhara

Foundation

the

Planck

possible.

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