theoretical study of the nitrous acid conformers: comparison of theoretical and experimental...

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Theoretical study of thenitrous acid conformers:Comparison of theoreticaland experimental structures,relative energies, barrierto rotation and vibrationalfrequenciesGeorge R. De Mare & Yahia MoussaouiPublished online: 26 Nov 2010.

To cite this article: George R. De Mare & Yahia Moussaoui (1999) Theoreticalstudy of the nitrous acid conformers: Comparison of theoretical andexperimental structures, relative energies, barrier to rotation and vibrationalfrequencies, International Reviews in Physical Chemistry, 18:1, 91-117, DOI:10.1080/014423599230017

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I n t e r n a t i o n a l R e v i e w s i n P h y s i c a l C h e m i s t r y , 1999, V o l . 18, N o . 1, 91± 117

Theoretical study of the nitrous acid conformers : comparison of

theoretical and experimental structures, relative energies, barrier to

rotation and vibrational frequencies

GEORGE R. DE M ARE! ‹Laboratoire de Chimie Physique M ole! culaire, Faculte! des Sciences, CP160 } 09,

Universite! Libre de Bruxelles, 50 avenue F.-D. Roosevelt, B-1050 Brussels,

Belgium

and YAHIA MOUSSAOUI

Laboratoire de Physico-chimie Quantique, Institut de Chimie, Universite! des

Sciences et de la Technologie Houari Boumediene, BP 32, El-Alia,

16111 Bab-Ezzouar, Algiers, Algeria

The experimental and theoretical literature data for the trans and cis conformers

of nitrous acid (HONO) are augmented by additional Hartree± Fock (HF),

M ù ller± Plesset second-order perturbation (MP2), Mù ller± Plesset fourth-orderperturbation (MP4) and density functional (B3LYP) computations. The latter

yield optimized theoretical parameters and vibrational frequencies that are closest

to the best experimental values. Adding diŒuse functions to a given basis set lowersthe energy of the trans conformer relative to the cis at all levels of theory utilized

in this work. There have been no convincing assignments of infrared (IR) spectral

bands to the O E N F O ( m$) and H E O E N ( m

&) bending modes of cis-HONO, both of

which are predicted to have very low intensities. Although IR spectral features

about 40 cm -" below m

$for trans-HONO has been tentatively assigned to m

$of cis-

HONO, calculations with unscaled and scaled quantum-mechanical force ® eldsinvert this order. If these predictions are correct, m

$of cis-HONO would fall in the

spectral region around 1300 cm -" , where a number of other compounds containing

N and O atoms have IR bands (N#O, N

#O

%, etc.) and make it di� cult to observe.

The frequency calculations for cis-HONO, with all the unscaled HF force ® elds,

yield m&

" m’

(the torsional mode). The situation is reversed for all the frequency

calculations with the unscaled B3LYP and MP force ® elds. Transferring the scalefactors obtained for the trans-HONO conformer HF } 6-311G** force ® eld to the

corresponding force ® eld of cis-HONO yields m&

= 590 cm -" and m

’= 673 cm -

" , a

very good indication that m&

is indeed at a lower frequency than m’

for the cis

conformer.

1. Introduction

Nitrous acid reacts with deoxyribonucleic acid (DNA), converting amino

functional groups to carbonyl groups and causing interstrand cross-linking which is

generally believed to be toxic or even lethal to cells (for leading references see [1]).

M elvin and W ulf [2, 3] observed spectral features of nitrous acid in the gas phase in the

early 1930s when they studied the ultraviolet (UV) spectra of mixtures of NO, NO#

and

water. This method of producing nitrous acid proved to be very important in

subsequent studies of its physical properties. Thus, D’ Or and Tarte, [4, 5], Tarte [6]

and Jones et al. [7], in independent seminal studies on the infrared (IR) spectra of

gaseous mixtures of various amounts of NO, NO#

and light or heavy water, showed

‹ Author for correspondence. Email : gdemare ! ulb.ac.be

Internationa l Re v iews in Physical Chemistry ISSN 0144-235 X print } ISSN 1366-591 X online ’ 1999 Taylor & Francis Ltd

http: } } www.tandf.co .uk} JNLS } rpc.htm http:} } www.taylorandf rancis.com } JNLS } rpc.htm

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92 G . R . De M areU and Y . Moussaoui

that there is an equilibrium between s-trans and s-cis conformers of nitrous acid

(hereafter denoted by t-HONO and c-HONO respectively). The isotopic shifts due to

deuteration permitted positive identi® cation of some of the absorption bands arising

from both of the nitrous acid conformers in the complex equilibrium mixtures [4 ± 7].

Nitrous acid is thus one of the smallest molecules showing rotational isomerism. (The

C#

visomer, HNO

#, is higher in energy [8, 9] and probably exists only as a transient

species [9]).

Besides the above-mentioned equilibrium, the formation of nitrous acid is observed

under a wide variety of conditions. The following are given only as examples because

they have been important in studies of the properties of nitrous acid.

(a) In low-temperature matrices it is a product of the photolysis of nitric acid [9,

10], of the photolysis of mixtures of ammonia and oxygen [11], of the

photolysis of mixtures of hydrazoic acid and oxygen [12 ± 15] and of the

reaction of NO#

with hydrogen atoms formed by the vacuum UV photolysis

of CH%, H

#O or HCl [16].

(b) It is formed in solution by the reaction of sodium nitrite with an acid [17± 19],

that is2NaNO

#1 H

#SO

%! Na

#SO

%1 2HONO (1)

(and also by the reaction of NOx

on H#O [20] or H

#SO

%± H

#O [21] surfaces).

The HONO concentrations in the solution and above it (gas phase) depend on

the experimental conditions [17 ± 21].

(c) It is formed by the `thermal decomposition ’ of ammonium nitrite (for

examples see [22 ± 25]) :

NH%NO

#(s) % NH

$(g) 1 HONO(g). (2)

The equilibrium pressure of HONO at 298 K is reported to be about 0.04 mbar

[22 ± 25] and the HONO concentration `remained practically constant on a time

scale of 100 s ’ [22]. However, the reversible surface-catalysed reaction (or

eventually the bimolecular gas phase reaction)

2HONO % H#O 1 NO 1 NO

#(3)

will inevitably occur, leading to the destruction of HONO and contamination

by other nitrogen-containing compounds [26, 27].

(d ) W hat could be the most important recent development for future experimental

studies of the properties of nitrous acid in the gas phase is the observation that

nearly pure initial concentrations of gaseous nitrous acid (greater than 99.5 % ;

absence of other nitrogen-containing compounds) can be obtained by ¯ owing

gaseous HCl over solid sodium nitrite [28, 29] :

HCl(g) 1 NaNO#(s) % NaCl(s) 1 HONO(g). (4)

The experimental conditions again determine the importance of reaction (3).

The experiments performed on HONO in low-temperature matrices using Fourier

transform infrared (FTIR) spectroscopy have revealed interesting features such as

doubling of bands due to occupation of diŒerent sites in the matrices [10, 11, 15, 23,

24] and the formation of 1 : 1 complexes of the HONO conformers with such diverse

molecules as NH$

[22, 23], N#

[24], CO [24], C’H

’[25] and HNO

$[25].

Nitrous acid is reactive in the gas phase, in solutions and on surfaces [30, 31]. It is

an important pollutant in the stratosphere (enhancing production of chlorine atoms

through the conversion of HCl to ClNO on ice crystals or other particulates [32]) and

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Theoretical study of nitrous acid conformers 93

Tab

le1.

Exp

erim

enta

ld

ata

(mo

de

(sym

metr

ysp

ecie

s),

ap

pro

xim

ate

des

cri

pti

on

)fo

rth

efu

nd

am

enta

lvib

rati

on

al

freq

uen

cies

of

c-H

ON

Oin

the

gas

ph

ase

an

din

low

-tem

pera

ture

matr

ices

.(I

nth

isan

dth

efo

llo

win

gta

ble

sth

eq

uo

ted

un

cert

ain

ties

inth

ela

std

igit

so

fth

eex

per

imen

tald

ata

are

giv

en

inp

are

nth

eses.

Th

eyare

on

est

an

dard

dev

iati

on

(1r

)excep

tw

here

the

no

tati

on

(xr

)is

giv

enin

the

corr

esp

on

din

gfo

otn

ote

.)

Met

ho

d,

med

ium

m "(a

´),

OEH

stre

tch

(cm

-")

m #(a

´),

N?

Ost

retc

h

(cm

-")

m $(a

´),

NEO

EHb

end

(cm

-")

m %(a

´),

NEO

stre

tch

(cm

-")

m &(a

´),

O?

NEO

ben

d

(cm

-")

m’(a

§),

NEO

tors

ion

(cm

-")

FT

IR,

gas

ph

ase

3426.1

96

33(1

7)a

,1640.5

18

65(2

2)a

(E1292)b

851.9

43

064(3

1)a

,Ð

638.5

(5)c

,

3426.2

18(6

)c851.9

42

93(5

6)d

639.8

b

Lase

rS

tark

spec

tro

sco

py

1640.5

17(1

)eÐ

ÐÐ

Ð

Tu

nab

led

iod

ela

ser,

gas

ph

ase

ÐÐ

Ð851.9

42

54(1

8)f

ÐÐ

IR,

gas

ph

ase

g3424

1640

(m)

1261

(w)

853

(s)

608

(w)

638

(m)

IR,

Ar

matr

ices,

4k

an

d14

Kh

3412

1633

1265

850

610

637

FT

IR,

NH

$±O

#±A

rm

atr

ix,

4.2

Ki

Ð1632.6

1263.3

±1259.4

849.6

±843.8

608.0

±605.1

639.9

±636.0

FT

IR,

Ar

matr

ix,

20

Kj

3412.4

±3410.7

1634.0

±1632.8

Ð853.1

±850.2

Ð638.4

FT

IR,

N#

matr

ix,

4.2

Kk

3404.0

1629.9

Ð869.4

ÐÐ

IR,

N#

matr

ix,

20

Kl

3410

(3408

m)

1633

Ð865

Ð658

FT

IR,

N#

matr

ix,

12

Kn

3406.3

1632.7

±1630.5

Ð871.0

ÐÐ

IR,

soli

d,

–190

ÊCg

Ð1611

(s)

Ð857

(m)

721

(m)

518

(m)

aF

rom

[41,

50].

bF

rom

[4],

low

reso

luti

on

IR.

cF

rom

[46].

dF

rom

[45];

10r

for

the

ban

do

rigin

s.eF

rom

[51];

3r

.fF

rom

[47];

2r

.gF

rom

[49].

Th

eso

lid

is

deri

ved

by

freez

ing

the

equ

ilib

riu

mgas-

ph

ase

mix

ture

ob

tain

edat

25

ÊC.

hF

rom

[16].

Pro

du

ced

by

ph

oto

lysi

so

fH

#O

±N

O#±A

rm

atr

ices

or

sim

ult

an

eo

us

ph

oto

lysi

so

fH

#an

dd

ep

osi

tio

no

fei

ther

HC

l±N

O#

or

CH

%±N

O#

mix

ture

s.T

he

ban

dass

ign

edto

c-H

ON

Oin

this

pap

erp

rob

ab

lyb

elo

ng

tom

$t-

HO

NO

(see

text)

.iF

rom

[11].

Pro

du

ced

by

irra

dia

tio

no

fth

em

atr

ixw

ith

the

184.9

±253.7

nm

mer

cu

ryli

nes.

Th

eb

an

ds

ass

ign

ed

toc-

HO

NO

inth

isp

ap

er

pro

bab

ly

belo

ng

tom $

t-H

ON

O(s

eete

xt)

.jF

rom

[23,

24].

kF

rom

[9].

Wea

kb

an

ds

corr

esp

on

din

gto

c-

an

dt-

HO

NO

were

ob

serv

ed

aft

erp

ho

toly

sis

of

HN

O$

inA

r

matr

ices

on

lyw

hen

the

matr

ices

wer

ed

op

edw

ith

O#.T

he

ph

oto

lyse

so

fH

NO

$in

N#,A

ran

dO

#±A

rm

atr

ices

all

revea

led

ban

ds

att

rib

ute

dto

the

C#

vH

NO

#is

om

er.

lF

rom

[12].

mF

rom

[15].

nF

rom

[10].

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Tab

le2.

Exp

erim

en

tald

ata

(mo

de

(sym

met

rysp

eci

es),

ap

pro

xim

ate

des

crip

tio

n)

for

the

fun

dam

en

talvib

rati

on

alfr

equ

en

cies

of

t-H

ON

Oin

the

gas

ph

ase

an

din

low

-tem

pera

ture

matr

ices

.

Met

ho

d,

med

ium

m "(a

´),

OEH

stre

tch

(cm

-")

m #(a

´),

N?

Ost

retc

h

(cm

-")

m $(a

´),

NEO

EHb

end

(cm

-")

m %(a

´),

NEO

stre

tch

(cm

-")

m &(a

´),

O?

NEO

ben

d

(cm

-")

m’(a

§),

NEO

tors

ion

(cm

-")

FT

IR,

gas

ph

ase

3590.7

70

35(1

1)a

,1699.7

60

15(1

3)a

,1263.2

07

05(4

)a,

790.1

17

060(3

2)a

,595.6

20

23(1

05)b

543.8

79

80(8

5)b

3590.7

11(8

)c1699.8

00(1

0)c

1263.1

83(5

)c790.1

16

81(5

4)b

Tu

nab

led

iod

ela

ser,

gas

ph

ase

Ð1699.7

58

2(1

1)d

1263.2

06

81(2

5)e

ÐÐ

Ð

IR,

gas

ph

ase

f3588

(m)

1699

(s)

1265

(s)

791

(s)

593

(s)

540

(m)

FT

IR,

Ar

matr

ix,

20

Kg

3572.6

±3568.5

1689.1

±1688.0

1265.8

±1263.9

800.4

±796.6

608.7

549.4

±548.2

FT

IR,

N#

matr

ix,

4.2

Kh

3510.9

1677.6

1293.7

816.4

ÐÐ

IR,

N#

matr

ix,

20

Ki

3558

(3552

j)

1684

1298

815

625

583

FT

IR,

N#

matr

ix,

12

Kk

3517.8

1681.5

±1680.4

1295.7

±1294.9

812.6

ÐÐ

IR,

soli

d,

–190

ÊCf

3512

(m)

1635

(s)

1421

(s)

801

(m)

702

(m)

499

(w)

aF

rom

[41,42].

bF

rom

[45];

5r

for

the

ban

do

rigin

s.cF

rom

[46].

dF

rom

[47];

2r

.eF

rom

[48];

2r

.fF

rom

[49].

Th

eso

lid

isd

eriv

ed

by

free

zin

gth

eeq

uil

ibri

um

mix

ture

ob

tain

ed

at

25

ÊC.

gF

rom

[23,

24];

m$

on

lyu

nd

ergo

esa

very

small

freq

uen

cysh

ift

inth

eA

rm

atr

ix.

hF

rom

[9].

Wea

kb

an

ds

corr

esp

on

din

gto

c-an

d

t-H

ON

Ow

ere

ob

serv

edaft

er

ph

oto

lysi

so

fH

NO

$in

Ar

matr

ices

on

lyw

hen

the

matr

ices

wer

ed

op

ed

wit

hO

#.T

he

ph

oto

lyse

so

fH

NO

$in

N#,A

r,an

dO

#±A

rm

atr

ices

all

revea

led

ban

ds

att

rib

ute

dto

the

C#

vH

NO

#is

om

er.

iF

rom

[12].

jF

rom

[15].

kF

rom

[10].

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Table 3. Experimental bond lengths and bond angles for the nitrous acid conformers.

r(H E O)(A/ )

r(O E N)(A/ )

r(N F O)(A/ )

x (H E O E N)(degrees)

x (O E N F O)(degrees) References

t-HONO

ra

e0.954(5) 1.433(5) 1.163(5) 102.1(3) 110.7(1) [52]

rb

s0.958(5) 1.432(5) 1.170(5) 102.1(5) 110.7(5) [52, 53]

© r ª c 0.959(5) 1.442(5) 1.169(5) 102.1(3) 110.6(1) [52]

rd

z0.9472(28) 1.4413(20) 1.1731(22) 102.07(28) 110.45(22) [54]0.98 1.46 1.20 © 105 ª 118 [7]

c-HONO

rb

s0.982(5) 1.392(5) 1.185(5) 104.0(7) 113.6(7) [52, 53]

© r ª c 0.989(5) 1.399(5) 1.186(5) 103.9(3) 113.6(1) [52]rd

z0.9753(34) 1.3966(61) 1.1901(54) 104.39(44) 113.48(32) [54]

0.98 1.46 1.20 © 103 ª 114 [7]

a Equilibrium structure estimated using model cubic force ® eld. b Substitution structures.c Average structures with shrinkage corrections. d Average structures without shrinkage

corrections.

in the atmosphere (enhancing oxidation processes in the early morning air through

photolytic production of OH radicals [17 ± 21, 28, 33 ± 36]). StaŒelbach and Neftel [36]

stated that their measurements of HONO concentrations in the Po valley air are

puzzling : `If the measurements are right it would mean that about 25 % of the OH

concentration is due to HONO photolysis and that the contribution of HONO to the

odd-H production is about one third.’ It is also interesting to note that M atsumoto [37]

reported recently that nitrous acid concentrations in the air in Nara, Japan, were

higher than those of nitric acid in winter and vice versa in summer (see also [38]). This

inversion is probably a consequence of a higher photolysis rate of nitrous acid in the

summer.

For the above reasons, the properties of the nitrous acid conformers (geometries,

fundamental frequencies, relative stabilities, reactivities, etc.) have been the object of

numerous experimental [4 ± 7, 9± 26, 29, 32 ± 59] and theoretical studies [8, 22 ± 25, 27,

60 ± 77]. In spite of all this attention, there are still unanswered questions concerning the

fundamental vibrational frequencies m$

and m&

of c-HONO (see table 1 and [39± 41] and

references cited therein), the relative stabilities of the two conformers, and the height

of the rotational barrier between them in the gas phase. Note, however, that all the

ground-state fundamental vibrational frequencies of t-HONO in the gas phase have

been measured to ® ve or more signi® cant ® gures (table 2). The lack of reliable

experimental values for all the fundamental frequencies of c-HONO has prevented the

determination of an experimental equilibrium (re) structure for this species (see [52]

and table 3).

An important experimental di� culty for gas-phase work lies in the fact that stable

equilibrium concentrations of the t-HONO and c-HONO conformers can only be

obtained as trace components in a complex mixture with water, NO, NO#, N

#O

$, N

#O

%and a trace of nitric acid [4 ± 7, 30, 31, 39, 41, 55, 56]. (See [55] for an IR spectrum of the

gas-phase mixture from 700 to 3800 cm -" .) W hereas increasing the temperature of the

gaseous mixture increases the concentration of c-HONO relative to that of t-HONO

in the equilibrium mixtures, it also decreases the total nitrous acid concentration [4 ± 7,

56].

Whether the method of preparing nearly pure nitrous acid by reaction (4) can be

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Tab

le4.

t-H

ON

O:

theo

reti

cal

bo

nd

len

gth

s,b

on

dan

gle

s,d

ipo

lem

om

ents

l,

ZP

Es

an

den

ergie

so

fth

eo

pti

miz

edst

ruct

ure

.

Met

ho

d}b

asi

s

r(H

EO)

(A/ )

r(O

EN)

(A/ )

r(N

FO)

(A/ )

x(H

EOEN

)

(deg

rees)

x(O

ENFO

)

(deg

rees

)

l

(D)

ZP

E

(kJ

mo

l-")

DE

(hart

rees

)R

efe

ren

ces

HF}4

-31G

0.9

539

1.3

995

1.1

665

107.9

1111.3

82.8

056.6

–204.3

11

914

[60±63]a

HF}4

-31G

*0.9

514

1.3

479

1.1

513

105.2

4111.3

32.5

8Ð

–204.4

43

577

[62±64]

HF}4

-31G

**

0.9

462

1.3

468

1.1

515

105.5

1111.3

72.5

9Ð

–204.4

50

187

a

HF}6

-31G

0.9

531

1.3

873

1.1

712

108.4

1111.5

92.8

857.3

–204.5

21

940

[63]a

HF}6

-31G

*0.9

508

1.3

465

1.1

532

105.3

7111.3

72.6

2Ð

–204.6

37

676

[63,

65,

66]a

HF}6

-31G

**

0.9

469

1.3

455

1.1

534

105.5

7111.4

02.6

260.8

–204.6

44

011

[62±64]a

HF}6

-31

1G

**

0.9

475

1.3

436

1.1

525

105.8

1111.7

42.6

760.5

–204.6

52

357

[66]a

HF}6

-31

11

G**

0.9

476

1.3

436

1.1

525

105.8

0111.7

42.6

7Ð

–204.6

52

493

a

HF}6

-311G

**

0.9

438

1.3

435

1.1

436

105.3

3111.7

42.5

560.8

–204.7

00

158

[67]

HF}6

-311

1G

**

0.9

450

1.3

421

1.1

438

105.6

4111.9

32.6

0Ð

–204.7

06

851

a

HF}6

-311

11

G**

0.9

449

1.3

421

1.1

437

105.6

3111.9

32.6

060.5

–204.7

06

922

[62]a

HF}6

-31

1G

(3d

f,2p

)0.9

445

1.3

412

1.1

452

105.5

8111.8

32.4

960.6

–204.6

79

991

a

B3L

YP}6

-31G

**

0.9

724

1.4

266

1.1

787

102.3

5110.6

22.1

653.5

–205.7

00

291

a

B3L

YP}6

-311G

**

0.9

678

1.4

331

1.1

663

102.2

9111.0

32.0

653.3

–205.7

61

769

a,

b

B3L

YP}6

-311

11

G**

0.9

694

1.4

326

1.1

655

102.9

4111.1

52.1

352.9

–205.7

71766

a

MP

2-F

U}4

-31G

**

0.9

700

1.4

232

1.1

942

101.6

1110.3

42.4

9Ð

–204.9

91

485

a

MP

2-F

U}6

-31G

**

0.9

710

1.4

232

1.1

964

101.7

1110.3

22.5

253.1

–205.1

84

403

a

MP

2-F

U}6

-31

11

G**

0.9

735

1.4

303

1.1

937

102.1

0110.5

72.5

352.2

–205.2

03

077

a

MP

2-F

C}6

-311G

**

0.9

652

1.4

155

1.1

804

101.2

2110.9

22.4

453.4

–205.2

74

580

[67]b

MP

2-F

U}6

-311G

**

0.9

645

1.4

132

1.1

797

101.2

6110.9

62.4

553.5

–205.3

30

675

a

MP

2-F

U}6

-311

1G

**

0.9

678

1.4

182

1.1

786

101.9

5111.0

42.4

852.7

–205.3

44

259

a

MP

2-F

C}6

-311

11

G**

0.9

682

1.4

204

1.1

792

101.8

7111.0

02.4

852.6

–205.2

87

770

a

MP

2-F

U}6

-311

11

G**

0.9

677

1.4

181

1.1

786

101.9

3111.0

42.4

852.7

–205.3

44

362

a

MP

4S

DT

Q-F

C}6

-31G

**

0.9

717

1.4

492

1.1

988

101.4

7110.3

52.4

352.1

–205.2

07

493

a

MP

4S

DT

Q-F

C}6

-311

1G

**

0.9

698

1.4

522

1.1

817

101.5

2110.9

72.3

851.3

–205.3

23

237

a

aT

his

wo

rk.

bT

he

op

tim

ized

geo

met

ries

rep

ort

edin

[27,

74]

are

alm

ost

wit

hin

rou

nd

ing-o

Œer

rors

of

thes

ere

sult

s.

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


Tab

le5.

c-H

ON

O:

theo

reti

cal

bo

nd

len

gth

s,b

on

dan

gle

s,d

ipo

lem

om

ents

l,

ZP

Es

an

den

ergie

so

fth

eo

pti

miz

edst

ruct

ure

.

Met

ho

d}b

asi

s

r(H

EO)

(A/ )

r(O

EN)

(A/ )

r(N

FO)

(A/ )

x(H

EOEN

)

(deg

rees)

x(O

ENFO

)

(deg

rees

)

l

(D)

ZP

E

(kJ

mo

l-")

DE

(hart

rees

)R

efe

ren

ces

HF}4

-31G

0.9

646

1.3

776

1.1

773

111.6

1113.9

41.8

0Ð

12.6

8[6

0±63]

HF}4

-31G

*0.9

604

1.3

280

1.1

591

107.4

1113.7

31.5

7Ð

–6.6

0[6

2±64]

HF}4

-31G

**

0.9

546

1.3

269

1.1

595

107.6

4113.7

21.5

9Ð

–6.2

6a

HF}6

-31G

0.9

639

1.3

678

1.1

818

112.1

5114.0

21.8

557.0

13.4

8[6

3]a

HF}6

-31G

*0.9

596

1.3

274

1.1

612

107.6

2113.7

31.6

0Ð

–5.9

4[6

3,

65,

66]

HF}6

-31G

**

0.9

553

1.3

263

1.1

614

107.7

8113.7

31.6

161.1

–5.6

4[6

2±64]a

HF}6

-31

1G

**

0.9

557

1.3

264

1.1

609

108.4

1113.9

21.6

8Ð

–1.5

7a

HF}6

-31

11

G**

0.9

558

1.3

264

1.1

608

108.4

0113.9

21.6

7Ð

–1.6

5a

HF}6

-311G

**

0.9

527

1.3

244

1.1

521

107.9

3113.9

71.5

760.9

–3.3

8a

HF}6

-311

1G

**

0.9

534

1.3

247

1.1

523

108.4

9114.0

91.6

5Ð

10.6

4a

HF}6

-311

11

G**

0.9

534

1.3

247

1.1

523

108.4

7114.0

91.6

560.5

10.6

1[6

2]a

HF}6

-31

1G

(3d

f,2p

)0.9

530

1.3

243

1.1

536

108.0

5114.1

01.6

060.5

–0.6

1a

B3L

YP}6

-31G

**

0.9

834

1.3

851

1.1

916

105.4

3113.2

21.5

653.6

–3.7

6a

,b

B3L

YP}6

-311G

**

0.9

795

1.3

884

1.1

804

105.8

6113.6

51.5

253.2

–1.0

0a

B3L

YP}6

-311

11

G**

0.9

801

1.3

916

1.1

794

106.8

0113.8

11.6

152.6

14.5

0a

MP

2-F

U}4

-31G

**

0.9

805

1.3

845

1.2

070

104.1

1112.7

61.4

6Ð

–5.6

5a

MP

2-F

U}6

-31G

**

0.9

813

1.3

853

1.2

093

104.3

5112.7

71.4

753.6

–4.7

5a

MP

2-F

U}6

-31

11

G**

0.9

832

1.3

925

1.2

074

105.4

1113.0

71.5

2Ð

11.7

4a

MP

2-F

C}6

-311G

**

0.9

766

1.3

773

1.1

938

104.2

0113.1

81.4

453.7

–1.7

9[6

7]b

MP

2-F

U}6

-311G

**

0.9

761

1.3

753

1.1

930

104.2

3113.2

01.4

4Ð

–1.8

3a

MP

2-F

U}6

-311

1G

**

0.9

780

1.3

811

1.1

921

105.3

6113.4

31.5

1Ð

14.6

3a

MP

2-F

C}6

-311

11

G**

0.9

784

1.3

831

1.1

928

105.3

0113.4

11.5

152.7

14.5

7a

MP

2-F

U}6

-311

11

G**

0.9

780

1.3

809

1.1

921

105.3

4113.4

41.5

152.8

14.5

3a

MP

4S

DT

Q-F

C}6

-31G

**

0.9

814

1.4

064

1.2

139

103.9

8112.7

01.4

252.5

–4.7

0a

MP

4S

DT

Q-F

C}6

-311

1G

**

0.9

793

1.4

081

1.1

976

104.8

6113.3

51.4

5Ð

14.6

3a

aT

his

wo

rk.

bT

he

op

tim

ized

geo

met

ries

rep

ort

edin

[27,

74]

are

alm

ost

wit

hin

rou

nd

ing-o

Œer

rors

of

thes

ere

sult

s.

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


used to obtain more accurate measurements of its physical properties remains to be

seen (the line strength measurements of t-HONO near 1255 cm -" depend on the

accuracy of the calculation of the relative conformer populations and thus on their

relative energies [28]).

The main objectives of the present paper are ® rstly to give a fairly comprehensive

review of the literature on the physical properties of the HONO conformers

(geometries, relative energies, fundamental frequencies, etc.) in their ground electronic

state and secondly to provide some new theoretical results. The extensive literature on

the photolysis and on the UV and visible spectroscopy of nitrous acid is not discussed.

To simplify the presentation further, the data on the deuterated and nitrogen-15

isotopomers will not be considered in detail in this work.

2. M ethod

Complete optimizations of the molecular geometries of both conformers and for

the transition state (TS) between them were carried out using the closed-shell

Hartree± Fock (HF) [78] and second- and fourth-order M ù ller± Plesset [79] per-

turbation (MPX , X = 2 and 4) methods. The eŒect on the predicted properties of the

nitrous acid conformers, of carrying out MPX-FU (full; all electrons included in the

excitations) instead of M PX-FC (frozen core ; no excitations from the 1s orbitals on

the heavy atoms) may or may not be important. It will be discussed in the appropriate

sections. Complete geometry optimizations for both conformers and for the TS

between them were also performed with density functionals (Becke’ s three parameter

non-local exchange functional (B3LYP) [80, 81] with the non-local correlation

functional of Lee et al. [82]) and with several basis sets including diŒuse functions. (In

tables 4± 9 the notation 1 in the basis set description indicates extra s and p functions

on the heavy atoms ; 1 1 indicates the same plus extra s functions on the hydrogen

atoms.) The relative energies of the conformers were determined by Gaussian 2 (G2)

[83] calculations for comparison with the other results.

All computations were performed with the GAUSSIAN 94 program package [84],

using standard basis sets, and the tight option for the optimizations. Some of the

optimized geometrical parameters and the dipole moments l (in debyes) are presented

in tables 4, 5 and 6 (for t-HONO, for c-HONO and for the TS between them

respectively). The rotational constants for the ground states of the rotamers are listed

in table 7.

Harmonic fundamental vibrational frequencies were calculated for both con-

formers and the TS at most levels of theory used. The theoretical vibrational

frequencies for the t-HONO and c-HONO conformers are listed in tables 8 and 9

respectively. The zero-point energies (ZPEs) are given in tables 4± 6.

3. Results and discussion

The t- and c-HONO dipole moments, obtained by laser Stark spectroscopy, are

l = 1.930(17) D and l = 1.428(7) D respectively [51]. An earlier microwave spec-

troscopy study yielded values of l = 1.855(16) D and l = 1.423(5) D for the t- " & N and

c- " & N isotopomers respectively [53]. The diŒerence between the two values for t-

HONO is larger than the combined error limits ; its origin has been discussed in [51].

It can be seen from tables 4 and 5 that both dipole moments are overestimated at

almost all theoretical levels used in this work. The closest theoretical value for t-

HONO is 2.06 D (B3LYP } 6-311G** (table 4)). For c-HONO, the M P4SDTQ-FC } 6-

31G** value is 1.422 D (table 5) which is within experimental error of the above value.

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


Tab

le6.

Pre

dic

ted

pro

pert

ies

of

the

TS

bet

ween

the

t-an

dc-H

ON

Oco

nfo

rmer

s:

bo

nd

len

gth

s,b

on

dan

gle

s,b

arr

ier

po

siti

on

ZP

Eo

fth

eo

pti

miz

ed

stru

ctu

res;

ener

gy

diŒ

eren

ceb

etw

een

the

t-H

ON

Om

inim

um

an

dth

eT

S;

tors

ion

al

barr

ier

corr

ecte

dfo

rth

eZ

PE

s.

Met

ho

d}b

asi

s

r(H

EO)

(A/ )

r(O

EN)

(A/ )

r(N

FO)

(A/ )

x(H

EOEN

)

(deg

rees)

x(O

ENFO

)

(deg

rees)

h

(degre

es)

ZP

E(T

S)

(kJ

mo

l-")

DE

(kJ

mo

l-")

Barr

ier

(kJ

mo

l-")

Refe

ren

ces

HF}4

-31G

0.9

602

1.4

497

1.1

631

110.6

7111.8

685.4

351.3

40.5

35.2

[60,

62,

64]a

HF}6

-31G

0.9

592

1.4

354

1.1

680

111.4

7112.0

685.4

051.7

42.3

36.7

[62,

64]a

HF}6

-311

1G

**

0.9

477

1.3

871

1.1

389

107.3

8112.2

586.8

955.1

47.0

41.6

[62]a

HF}6

-311

11

G**

0.9

477

1.3

871

1.1

389

107.3

7112.2

586.9

055.1

47.1

41.7

[62]a

B3L

YP}6

-311

11

G**

0.9

704

1.5

069

1.1

552

104.9

6111.6

786.4

847.3

53.9

48.3

a

MP

2-F

U}6

-31

11

G**

0.9

749

1.5

257

1.1

805

103.0

4111.0

786.2

946.0

51.8

45.6

a

MP

2-F

U}6

-311G

**

0.9

661

1.4

947

1.1

690

101.5

7111.3

186.7

047.4

52.0

45.9

a

MP

2-F

U}6

-311

1G

**

0.9

690

1.5

119

1.1

652

102.5

7111.4

385.5

046.5

52.1

45.9

a

MP

2-F

C}6

-311

11

G**

0.9

695

1.5

161

1.1

655

102.4

6111.4

085.5

046.4

51.9

45.6

a

MP

2-F

U}6

-311

11

G**

0.9

690

1.5

120

1.1

652

102.5

4111.4

385.5

346.5

52.2

45.9

a

aT

his

wo

rk.

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


Tab

le7.

Ro

tati

on

alco

nst

an

tsfo

rth

en

itro

us

aci

dco

nfo

rmer

s.a

t-H

ON

Oc-H

ON

O

AB

CA

BC

Met

ho

d}b

asi

s(c

m-")

(cm

-")

(cm

-")

(cm

-")

(cm

-")

(cm

-")

HF}4

-31G

**

3.4

09

51

0.4

51

54

0.3

98

73

2.9

91

74

0.4

72

94

0.4

08

38

HF}6

-31G

3.2

99

95

0.4

28

21

0.3

79

03

2.8

76

26

0.4

45

88

0.3

86

04

HF}6

-31G

*3.4

01

78

0.4

51

04

0.3

98

24

2.9

82

00

0.4

72

11

0.4

07

58

HF}6

-31G

**

3.4

09

45

0.4

54

55

0.3

98

48

2.9

87

38

0.4

72

41

0.4

07

90

HF}6

-31

11

G**

3.4

44

94

0.4

50

45

0.3

98

36

2.9

98

43

0.4

71

33

0.4

07

30

HF}6

-311G

**

3.4

70

24

0.4

53

65

0.4

01

20

3.0

31

83

0.4

75

00

0.4

10

66

HF}6

-311

11

G**

3.4

89

71

0.4

53

02

0.4

00

97

3.0

35

88

0.4

73

95

0.4

09

95

HF}6

-31

1G

(3d

f,2p

)3.4

78

97

0.4

53

45

0.4

01

17

3.0

35

71

0.4

73

81

0.4

09

84

B3L

YP}6

-31G

**

3.0

85

09

0.4

19

07

0.3

68

95

2.7

79

03

0.4

42

94

0.3

82

05

B3L

YP}6

-311G

**

3.1

37

89

0.4

18

52

0.3

69

27

2.8

28

61

0.4

42

67

0.3

82

77

B3L

YP}6

-311

11

G**

3.1

53

20

0.4

18

06

0.3

69

12

2.8

33

08

0.4

40

55

0.3

81

27

MP

2-F

U}4

-31G

**

3.0

26

70

0.4

17

62

0.3

66

99

2.7

25

88

0.4

41

38

0.3

79

87

MP

2-F

U}6

-31G

*3.0

16

71

0.4

16

92

0.3

66

30

2.7

11

28

0.4

40

00

0.3

78

56

MP

2-F

U}6

-31G

**

3.0

20

09

0.4

17

03

0.3

66

43

2.7

18

83

0.4

40

26

0.3

78

90

MP

2-F

U}6

-31

11

G**

3.0

33

12

0.4

13

99

0.3

64

27

2.7

25

04

0.4

36

23

0.3

76

03

MP

2-F

U}6

-311G

**

3.1

26

58

0.4

22

56

0.3

72

25

2.7

99

85

0.4

46

75

0.3

85

27

MP

2-F

U}6

-311

1G

**

3.1

29

50

0.4

20

37

0.3

70

59

2.8

00

97

0.4

43

24

0.3

82

68

MP

2-F

U}6

-311

11

G**

3.1

29

72

0.4

20

39

0.3

70

61

2.8

01

86

0.4

43

28

0.3

82

73

MP

4S

DT

Q-F

C}6

-31G

**

2.9

68

47

0.4

07

71

0.3

58

47

2.6

78

51

0.4

31

53

0.3

71

65

MP

4S

DT

Q-F

C}6

-311

1G

**

3.0

51

77

0.4

08

50

0.3

60

27

2.7

48

71

0.4

32

03

0.3

73

35

Exp

erim

en

talb

3.0

98

544

08(3

7)

0.4

17

788

089(4

3)

0.3

67

476

383(4

0)

ÐÐ

Ð

Exp

erim

en

talc

ÐÐ

Ð2.8

05

335

84(2

6)

0.4

39

273

149(4

4)

0.3

79

067

802(4

4)

aT

his

wo

rk.

bF

rom

[42](W

ats

on

’sA

red

uced

Ham

ilto

nia

nin

the

Irre

pre

sen

tati

on

).cF

rom

[60](W

ats

on

’sA

red

uce

dH

am

ilto

nia

nin

the

Irre

pre

sen

tati

on

).

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


Tab

le8.

Th

eore

tical

data

(mo

de

(sym

metr

ysp

ecie

s),

ap

pro

xim

ate

des

cri

pti

on

)fo

rth

eh

arm

on

icfu

nd

am

en

tal

vib

rati

on

al

freq

uen

cie

sfo

rt-

HO

NO

ob

tain

edfo

rgeo

met

ries

op

tim

ized

at

the

sam

eth

eore

tica

lle

vel

.aF

or

the

HF

com

pu

tati

on

sth

eIR

inte

nsi

ties

,R

am

an

scatt

eri

ng

acti

vit

ies

A%

an

d

Ram

an

dep

ola

riza

tio

nra

tio

sare

giv

en

inp

are

nth

ese

s.F

or

the

MP

2an

dB

L3Y

Pco

mp

uta

tio

ns

on

lyth

eIR

inte

nsi

ties

are

giv

en

.

Met

ho

d}b

asi

sse

t

m"(a

´)O

EHst

retc

h

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m#(a

´)N

FOst

retc

h

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m $(a

´)N

EOEH

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m%(a

´)N

EOEH

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m&(a

´)O

FNEO

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m’(a

§)N

EOto

rsio

n

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

HF}4

-31

Gb

39

88

18

90.5

14

15.3

90

0.7

72

1.9

55

2.8

HF}6

-31

G40

18

(13

3;

78

;0

33

)19

02

(12

8;

16

;0.3

2)

14

24

(219

;5

;0.7

5)

94

0(2

11

;1

6;

0.2

8)

73

4(3

0;

5;

0.4

3)

56

3(2

06

;3

;0.7

5)

HF}6

-31

G*

40

82

(12

5;

65

;0.3

1)

20

43

(15

2;

26

;0.2

7)

15

14

(263

;4

;0.7

3)

109

8(2

26

;9

;0.2

6)

79

0(2

0;

2;

0.4

3)

59

9(1

37

;2

,0.7

5)

HF}6

-31

G**

41

48

(12

8;

65

;0.3

0)

20

40

(15

5;

14

;0.2

7)

14

96

(264

;4

;0.7

3)

110

1(2

24

;9

;0.2

6)

79

2(1

9;

2;

0.4

4)

59

4(1

36

;2

;0.7

5)

HF}6

-31

1G

**

41

46

(13

5;

53

;0.3

3)

20

40

(17

1;

13

;0.3

2)

14

98

(263

;4

;0.7

5)

108

8(2

35

;9

;0.2

7)

80

0(2

3;

3;

0.4

2)

58

8(1

31

;2

;0.7

5)

HF}6

-31

11

G*

*41

35

(14

6;

59

;0.2

5)

20

28

(19

1;

13

;0.3

6)

14

95

(261

;4

;0.7

0)

107

9(2

55

;1

0;

0.3

3)

80

1(2

3;

3;

0.3

1)

58

3(1

38

;0

;0.7

5)

HF}6

-31

11

1G

**

41

35

(14

6;

59

;0.2

5)

20

28

(19

1;

13

;0.3

6)

14

95

(262

;4

;0.7

0)

107

9(2

55

;1

0;

0.3

3)

80

1(2

4;

3;

0.3

1)

58

3(1

39

;0

;0.7

5)

HF}6

-31

1G

(3d

f,2

p)

41

33

(13

9;

57

;0.2

1)

20

13

(17

2;

12

;0.2

8)

15

00

(254

;2

;0.4

6)

108

5(2

47

;9

;0.3

0)

79

8(2

1;

3;

0.2

3)

59

7(1

22

;0

;0.7

5)

B3L

YP}6

-31G

**

37

55

(57

)17

92

(13

5)

13

06

(188

)86

2(1

44

)63

1(8

3)

59

5(1

06

)

B3L

YP}6

-311

G*

*37

74

(70

)17

94

(16

3)

12

97

(188

)83

4(1

27

)61

9(1

16

)58

9(1

05

)

B3L

YP}6

-311

11

G**

37

62

(83

)17

86

(19

5)

12

91

(187

)81

2(1

35

)61

4(1

53

)58

1(1

16

)

MP

2-F

U}6

-31

G*

*38

14

(74

)16

62

(68

)1

304

(192

)86

5(1

85

)63

0(1

01

)60

1(1

14

)

MP

2-F

U}6

-31

11

G**

37

84

(90

)16

56

(10

4)

12

89

(189

)81

4(1

87

)60

8(1

68

)58

3(1

22

)

MP

2-F

C}6

-31

1G

**

38

41

(87

)16

87

(84

)1

308

(192

)86

3(1

78

)63

7(1

25

)58

8(1

07

)

MP

2-F

U}6

-31

1G

**

38

46

(88

)16

91

(84

)1

310

(192

)86

6(1

79

)64

0(1

24

)59

0(1

08

)

MP

2-F

U}6

-31

11

G*

*38

14

(97

)16

83

(11

1)

12

99

(189

)82

6(1

76

)62

3(1

82

)57

3(1

16

)

MP

2-F

C}6

-31

11

1G

**

38

10

(95

)16

79

(11

1)

12

96

(190

)82

3(1

75

)62

0(1

85

)57

1(1

17

)

MP

2-F

U}6

-31

11

1G

**

38

14

(97

)16

83

(11

1)

12

99

(190

)82

6(1

77

)62

3(1

83

)57

3(1

17

)

MP

4S

DT

Q-F

C}6

-31

G**

37

96

16

40

12

80

81

758

059

4

MP

4S

DT

Q-F

C}6

-31

11

G*

*37

75

16

50

12

66

77

454

855

9

aA

lld

ata

,excep

tfo

rth

eH

F}4

-31G

valu

es,

are

fro

mth

isw

ork

.bF

rom

[60].

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


Tab

le9.

Th

eore

tica

ld

ata

(mo

de

(sym

metr

ysp

eci

es),

ap

pro

xim

ate

des

cri

pti

on

)fo

rth

eh

arm

on

icfu

nd

am

en

tal

vib

rati

on

al

freq

uen

cies

for

c-H

ON

Oo

bta

ined

for

geo

met

ries

op

tim

ized

at

the

sam

eth

eore

tica

lle

vel

.aF

or

the

HF

com

pu

tati

on

sth

eIR

inte

nsi

ties

,R

am

an

scatt

eri

ng

acti

vit

ies

A%

an

d

Ram

an

dep

ola

riza

tio

nra

tio

sare

giv

en

inp

are

nth

ese

s.F

or

the

MP

2an

dB

L3Y

Pco

mp

uta

tio

ns

on

lyth

eIR

inte

nsi

ties

are

giv

en

.

Met

ho

d}b

asi

sse

t

m"(a

´)O

EHst

retc

h

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m#(a

´)N

FOst

retc

h

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m $(a

´)N

EOEH

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m%(a

´)N

EOEH

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m&(a

´)O

FNEO

ben

d

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

m’(a

§)N

EOto

rsio

n

(cm

-"

(km

mo

l-";

am

u;

Ð)

or

(km

mo

l-"))

HF}4

-31

Gb

38

19

18

26

14

58

95

470

367

0

HF}6

-31

G38

47

(59

;73

;0.3

2)

18

31

(19

0;

17

;0.3

6)

14

67

(3;

7;

0.7

3)

99

8(3

32

;6

;0.2

5)

71

0(1

6;

8;

0.5

0)

67

5(2

31

;4

;0.7

5)

HF}6

-31

G*

39

39

(64

;53

;0.3

0)

19

88

(23

2;

11

;0.3

0)

15

42

(10

;4

;0.7

4)

116

1(3

43

;2

;0.2

0)

78

4(1

6;

5;

0.4

7)

74

6(1

52

;2

;0.7

5)

HF}6

-31

G**

40

09

(64

;52

;0.2

9)

19

86

(23

2;

11

;0.3

0)

15

24

(11

;4

;0.7

4)

116

6(3

46

;2

;0.2

0)

78

4(1

6;

5;

0.4

7)

74

2(1

51

;2

;0.7

5)

HF}6

-31

1G

**

39

98

(61

;51

;0.3

1)

19

84

(24

0;

11

;0.3

8)

15

22

(12

;5

;0.7

3)

115

4(3

65

;2

;0.2

1)

79

1(1

7;

6;

0.4

6)

72

7(1

48

;2

;0.7

5)

HF}6

-31

11

1G

**

39

91

(71

;56

;0.2

3)

19

72

(26

7;

12

;0.3

6)

15

12

(10

;4

;0.7

4)

114

3(3

98

;3

;0.3

1)

78

8(1

5;

5;

0.3

5)

70

4(1

53

;1

;0.7

5)

HF}6

-31

1G

(3d

f,2

p)

39

88

(68

;52

;0.1

8)

19

59

(24

7;

12

;0.2

6)

15

20

(11

;2

;0.7

4)

114

7(3

71

;3

;0.3

0)

78

7(1

1;

5;

0.2

6)

71

2(1

27

;1

;0.7

5)

B3L

YP}6

-31G

**

35

76

(15

)17

26

(17

1)

13

49

(6)

92

1(2

65

)64

8(1

5)

73

6(1

09

)

B3L

YP}6

-311

G*

*35

83

(16

)17

21

(18

7)

13

38

(8)

89

3(2

72

)63

8(2

8)

71

8(1

10

)

B3L

YP}6

-311

11

G**

35

83

(26

)17

14

(22

2)

13

22

(6)

87

1(3

19

)62

6(4

0)

68

4(1

20

)

MP

2-F

U}6

-31

G*

*36

45

(28

)16

22

(11

8)

13

48

(5)

94

8(3

26

)65

5(1

3)

74

6(1

17

)

MP

2-F

C}6

-31

1G

**

36

56

(26

)16

39

(12

3)

13

38

(8)

94

5(3

36

)66

5(2

1)

72

2(1

10

)

MP

2-F

U}6

-31

1G

**

36

59

(26

)16

43

(12

4)

13

41

(8)

94

8(3

36

)66

7(2

1)

72

4(1

11

)

MP

2-F

C}6

-31

11

1G

**

36

40

(36

)16

30

(14

8)

13

19

(7)

90

9(3

90

)64

5(3

5)

67

5(1

20

)

MP

2-F

U}6

-31

11

1G

**

36

42

(36

)16

34

(14

8)

13

21

(7)

91

2(3

90

)64

8(3

3)

67

8(1

20

)

MP

4S

DT

Q-F

C}6

-31

G**

36

40

15

78

13

20

89

161

473

1

MP

4S

DT

Q-F

C}6

-31

11

G*

*36

17

15

79

12

90

85

158

965

7

aA

lld

ata

,excep

tfo

rth

eH

F}4

-31G

valu

es,

are

fro

mth

isw

ork

.bF

rom

[60].

Dow

nloa

ded

by [

Mos

kow

Sta

te U

niv

Bib

liote

] at

04:

11 2

8 D

ecem

ber

2013


3.1. Structural parameters

The structural parameters of t-HONO are signi® cantly diŒerent from those of c-

HONO (see tables 3± 5). This is believed to re¯ ect the competitive interplay in c-

HONO between the repulsive steric hindrance of the terminal atoms and the attractive

hydrogen bonding between these same atoms ; according to the best experimental

determinations of the structure [54], they are separated by only 2.1 A/ which is much

less than the sum of the van der Waals radii for oxygen and hydrogen (2.6 A/ ).

It is interesting to note that, in contrast with the behaviour of the two terminal

bonds, which are longer in c-HONO than in t-HONO, the central formal single O E N

bond is shorter in c-HONO than in t-HONO (table 3).

3.1.1. Experiment

The ® rst experimental determination of the structural parameters of t-HONO and

c-HONO was reported by Jones et al. [7] in 1951. They gave identical values with each

of the corresponding bond lengths in the two conformers. Except for r(O E N) for c-

HONO, these bond lengths are within 0.03 A/ of the best experimental values now

available (see table 3). However, their estimation that the H E O E N and O E N F O bond

angles were smaller by a few degrees in c-HONO than in t-HONO was later proven to

be erroneous.

Substitution structures (rs) for both conformers (table 3) were ® rst reported by Cox

et al. [53] who studied the microwave spectra of eight nitrous acid isotopomers. Small

inertial defects, compatible with planar molecular structures, were determined for

both conformers [53].

Equilibrium structural parameters re

which should be used for comparison with

theoretically optimized parameters, have been determined only for t-HONO (see table

3 and [52]). Using the observed fundamentals, their isotopic shifts and the centrifugal

distortion constants (derived by analysing the centrifugal distortion shifts in the

microwave spectra of t-HONO and c-HONO and their deuterated isotopomers),

Finnigan et al. [52] determined 11 of the 16 force constants for each conformer. Use

of this force ® eld to evaluate the average moments of inertia led to the average

structural parameters © r ª given in table 3. Finnigan et al. [52] pointed out that the © r ªare well de® ned structural parameters, only diŒering from the r

ebecause of the

anharmonicity of the molecular vibrations. They also reported that, allowing for

centrifugal distortion and electronic corrections, the inertial defects vanish for the

average structures, showing conclusively that t-HONO and c-HONO are `planar in the

hypothetical a v erage (ground-vibrational) state ’ [52]. This ® nding has been con® rmed

in [54].

The most recent values for the zero-point-average structures (rz

in table 3) were

calculated using microwave data for ® ve isotopomers of t-HONO and three

isotopomers of c-HONO and explicit isotopic shrinkage corrections [54]. The

diŒerences between these geometrical parameters and those reported earlier in [52] are

attributed mainly to the isotopic shrinkage corrections [54].

3.1.2. Theory

The predicted variations of the optimized ab initio structural parameters on going

from the t- to the c-HONO conformations are in good general agreement with the

experimental data. Both the H E O E N and O E N F O bond angles are predicted to be

larger by a few degrees in c-HONO than in t-HONO at all levels of theory investigated

(see tables 4 and 5). This presumably indicates that the steric hindrance between the

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terminal atoms in c-HONO is more important than the eŒect of intramolecular

hydrogen bonding. However, the diŒerence in the eŒects is not large enough to cause

the conformer to be nonplanar. Indeed, all optimizations started from non-planar

gauche geometries in this work (up to 60Êfrom the c-HONO structure), using tight

optimization criteria, went to completely planar c-HONO structures. Some relaxation

of the c-HONO structure is brought about by a perceptible lengthening of both the

formal single H E O and double N F O bonds, in comparison to the corresponding bonds

in t-HONO (see tables 3± 5). The central formal single O E N bond is predicted to be

shorter in c-HONO, again in agreement with experiment. This structural behaviour is

in sharp contrast with that predicted for 1,3-butadiene where the central C E C bond is

predicted to be longer in the gauche than in the s-trans conformer and the formal

double bond lengths are predicted to remain essentially constant [85]. For 1,3-

butadiene, except for optimizations with a minimal basis set, the planar s-cis structure

is predicted to be a TS between two equivalent gauche minima [85]. This is presumably

because decreased steric hindrance in the gauche conformer is more important than

increased resonance in the planar s-cis structure [85]. Note that, recently, experimental

IR evidence in favour of the gauche conformation of 1,3-butadiene in the gas phase has

been reported [86].

The HF optimized parameters give the largest average deviations from the

experimental data : 2.1± 2.7 % from the re

parameters for t-HONO and 2.7± 3.3 % from

the © r ª parameters for c-HONO. The largest individual diŒerences between the

experimental and theoretical parameters are found again for the HF optimized

parameters, notably for r(O E N) and for the H E O E N bond angle. Comparison with the

experimental parameters in table 3 shows that all the HF optimizations reported in

tables 4 and 5 underestimate the internuclear distances and overestimate the H E O E N

bond angle. In contrast, the experimental values of the O E N F O bond angle are

reproduced satisfactorily for both conformers at all levels of theory reported. Also, all

the MP optimized values of the H E O E N bond angles for both conformers are within

1Êof the latest experimental data. It is interesting to note that, for nitric acid, Lee and

Rice [87] found that M P2 optimizations at the double-zeta plus polarization (DZP)

and triple zeta-plus double-polarization (TZ2P) level also gave very satisfactory values

for the HON bond angle (102.1Êand 102 .0Êrespectively ; experimental value, 102.15Ê[88]). Finally, note that the B3LYP } 6-311 1 1 G** results for nitrous acid are as

satisfactory as those obtained with the more costly M P4SDTQ-FC } 6-311 1 G**

optimizations.

The major diŒerence between the theoretical geometries of the planar conformers

and the TS is the long central O E N bond in the latter. The predicted elongation of this

bond on torsion away from the planar structures has been reported previously [60, 62,

68] and it is probably the result of reduced conjugation in the TS. However, by

comparison with the other M P results in tables 4± 6, it is apparent that the exceptional

elongation of the bond obtained in the MP2-FU } 4-31G optimization performed by

M urto et al. [62] is partly due to the basis set and not to the MP2 method.

3.2. Relativ e energies

3.2.1. Experiment

The experimental determinations of the energy diŒerence between the c- and t-

HONO conformers, denoted by D E = Ecis

–Etrans

, range from 1 1.56 to

1 2.70 kJ mol-" , always in favour of t-HONO as the lowest-energy species [7, 49, 57,

58].

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Jones et al. [7] determined D E = 1 2.12 ‰0.11 kJ mol-" from the dependence,

between 0 and 70 ÊC, of the intensities of the pairs of IR bands, 856 and 794 cm -" ( m

%;

O E N stretch) and 637 and 543 cm -" ( m

’; O E N torsion) [7]. M cGraw et al. [49] studied

the intensities of the same IR bands (which they placed at 853, 791, 638 and 540 cm -"

respectively) between 0 and 46 ÊC and reported that D E = 1 2.22 kJ mol -" , quite close

to the above value. However, they placed a much larger error bar (‰4 kJ mol -" ) on

their determination [49]. This error bar, which seems to be extraordinarily large, would

allow either conformer to be the lowest-energy one. M ore recently, Varma and Curl

[57] determined the relative intensities of rotational transitions at room temperature

and reported that D E = 1 1.56 ‰0.17 kJ mol-" and D E = 1 2.04‰0.15 kJ mol-

" for

the HONO and DONO conformers respectively. They suggested combining these

results to yield an average value : D E = 1 1.69 ‰0.42 kJ mol-" for HONO. Based on

the assumption that the oscillator strength of the p * " n transition of the two rotamers

is the same, Bongartz et al. [58] determined the ratio K = ptrans } p

cis= 3.25 ‰0.30 at

277 K. This ratio corresponds to D E = 1 2.70 ‰0.21 kJ mol -" . They pointed out that

this is probably accidentally nearly identical with `recent theoretical results ’ [63] (and

which, ironically, repeated the earliest theoretical result for complete geometry

optimization of the HONO conformers with the same 4-31G basis set [60]). Compared

with the D E determined by Varma and Curl [57], the value obtained by Bongarts et al.

[58] appears to be rather high, although it could lie within the combined experimental

uncertainties.

The relative energy of the conformers obtained in the microwave intensity

measurements by Varma and Curl [57] must be considered to be the best to date.

Nevertheless, considering the recent developments in the measurement of absolute

intensities of IR absorption bands, it would be very interesting to have new

experimental studies, similar to those of Jones et al. [7] and McGraw et al. [49], of

which the latest was performed just over 30 years ago. Alternatively, perhaps use of the

method of preparing nitrous acid at known concentrations from the reaction of

gaseous HCl with solid sodium nitrite [28, 29] could be adapted to the determination

of the relative conformer populations.

3.2.2. Theory

For molecules exhibiting rotational isomerism, it is well known that the theoretical

relative energies of the conformers can depend strongly both on the structural

parameters (bond lengths and angles, dihedral angles) and on the theoretical method

used.

To obtain the heat D H of formation of a conformer, the ZPE must be added to the

energy which is computed for an isolated molecule at 0 K. The theoretical values of the

ZPE varies from 52.1 to 60.8 kJ mol -" for t-HONO (table 4) and from 52.5 to

61.1 kJ mol-" for c-HONO (table 5). However, for a given basis set or method the

diŒerence between the ZPEs for the two conformers is r 0.5 r kJ mol-" or less. Note also

that the experimental ZPEs are equal for the two conformers, although the uncertainty

in the frequencies of m$

and m&

of c-HONO must be taken into account.

The confusion arising from the many contradictory theoretical results on the

relative energies of the nitrous acid conformers is exempli® ed by comparison of the

experimental D E with those obtained from G1 and G2 computations ( 1 3.17 and

1 2.33 kJ mol-" respectively (this work)) and with the diŒerence in their heats

of formation obtained with the bond-additivity-corrected (BAC)-MP4 technique

( D H = – 5.9 kJ mol-" [74]). The BAC-MP4 results are thus in contradiction with

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the experimental data in this case (see above) whereas the method has been shown to

give reliable data for many other compounds with hydrogen, nitrogen and oxygen

atoms [89].

3.2.2.1. Hartree± Fock computations. The most comprehensive early theoretical study

on the eŒect of the basis set and theoretical level on the relative energies of the nitrous

acid conformers is that by Murto et al. [62]. They reported 17 sets of computations, at

diŒerent theoretical levels, with complete geometry optimization of the conformers.

Only eight sets predicted t-HONO to be the lowest-energy conformer ; the nine others

placed c-HONO lower in energy than t-HONO. Using a larger basis set for the HF

optimizations did not ensure better results [62].

The dependence of the calculated relative energies of the nitrous acid conformers

on the molecular geometries used is clearly demonstrated by the literature results

obtained with the minimal Slater-type orbital (STO)-3G basis set. Using the

experimental geometries from [52], BenioŒ et al. [69] obtained D E = – 11.2 and

–11.7 kJ mol-" from HF } STO-3G and optimized valence con ® gurations, con® gur-

ation interaction (OVCCI) } STO-3G computations respectively. Complete geometry

optimization of both conformers (HF } STO-3G } } HF } STO-3G computations) in-

verts the relative energies ( D E = 1 0.38 kJ mol-" [61 ± 63, 65, 70]), bringing them into

closer accord with experiment. Another, less marked example is found with the 4-31G

basis set. In 1971, Radom et al. [71] used the `standard geometries ’ of Pople and

Gordon [72] to calculate the relative energies of the nitrous acid conformers and

obtained fortuitously good agreement with the experimental data available at that

time ( D E = 1 1.88 kJ mol -" ). However, HF } 4-31G } } HF } 4-31G computations yield a

higher value : D E = 1 2.68 kJ mol -" [60 ± 63]. (The same value is obtained from the

total energies given in table II of [65] ; however, the relative energy given there

( D E = 1 9.3 kJ mol -" ) is incorrect.) The `good ’ D E value obtained from the 4-31G

optimizations of the HONO conformers is probably fortuitous. Indeed HF } 3-21G

optimizations yield a very diŒerent result : D E = – 6.53 kJ mol -" [61, 62].

3.2.2.2. EŒect of including polarization and } or diŒuse functions in the basis set. Long-

range interactions, especially intramolecular hydrogen bonding between the terminal

atoms, are probably important in c-HONO [90 ± 92]. Such interactions should be better

accounted for at a theoretical level which includes polarization functions, diŒuse

functions, or both of these. However, note that Nguyen and Hegarty [61] and M urto

et al. [62] found that adding polarization functions to a given basis set resulted in a

lowering of the relative energy of c-HONO, bringing the results into further discord

with experiment. For example, whereas HF } 6-311G optimizations yield D E =

1 3.3 kJ mol-" , HF } 6-311G** optimizations invert the relative energies to D E =

–3.4 kJ mol-" [62].

Adding diŒuse functions to a basis set lowers the relative energy of t-HONO

[62, 65, 73]. From HF } 6-311G ** } } HF } 6-31G* single point computations, without

diŒuse functions, Turner [65] obtained D E = – 3.5 kJ mol -" . In contrast, HF } 6-

311 1 1 G** } } HF } 6-31G* computations yielded D E = 1 0.5 kJ mol -" [65]. At about

the same time, M urto et al. [62] reported that their `best ’ near-HF-limit value, D E =

1 0.6 kJ mol-" (about 1 kJ mol -

" less than the best experimental value, see above)

was obtained from HF } 6-311 1 1 G** optimizations. The HF } 6-311 1 1 G** D E

given above is in partial disagreement with the reported ® ndings of Co� n and Pulay

[73] who state that `addition of diŒuse functions to the basis set (6-311G**) leads to

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a stabilization of the trans form of the molecule, but not enough to lower it below the

cis form ’ . W e have therefore carried out HF } 6-311 1 1 G** } } HF } 6-311 1 1 G**

computations and con ® rmed the results of M urto et al. [62] (see table 5).

3.2.2.3. Mù ller± Plesset perturbation theory. A number of M P computations have

been reported for nitrous acid (for examples see [22± 24, 27, 62, 64 ± 67, 73, 74]).

Although the HF approximation is inadequate for this molecule, owing to strong

electron correlation [73], using the MP method does not ensure better results. Indeed,

the D E values obtained from M P computations only predict t-HONO to be the lowest-

energy conformer when diŒuse functions are included in the basis set (see table 5 and

[62, 65, 73]). For example, M urto et al. [62] obtained D E = – 5.29 kJ mol-" and

D E = 1 7.025 kJ mol-" from M P2-FU optimizations with the 4-31G(N*) and 4-

31 1 1 G(N*) basis sets respectively. (N* signi® es polarization functions added only

on the N atom.) Using HF } 6-31G* optimized geometrical parameters for both

conformers, Turner [65] carried out MPX-FU (X = 2, 3 and 4) } 6-31G*, MPX-FU

(X = 2, 3 and 4) } 6-31G** and MP2-FU } 6-31 1 1 G** } } HF } 6-31G* computations.

He found that only the M P2-FU } 6-311 1 1 G** computations predicted t-HONO to

be the lowest-energy conformer ( D E = 1 3.5 kJ mol-" ). Recently, Co� n and Pulay

[73] obtained D E = – 0.505 kJ mol-" from MP4SDQ-FC } 6-311G** optimizations

and D E = 1 4.791 kJ mol-" from M P4SDQ-FC } 6-311 1 1 G** } } M P4SDQ-FC } 6-

311G** computations, emphasizing again the important eŒect of diŒuse functions in

the basis set on the relative energies of the conformers.

In a recent paper, Hsu et al. [74] reported optimized M P2-FC } 6-311G** geometries

which are identical within rounding oŒ accuracy with the M P2-FC } 6-311G **

geometries that we published in 1995 [67]. Their energy diŒerence for H 1 c-HONO

and H 1 t-HONO is –0.6 kcal mol-" ( –2.5 kJ mol -

" ) which is more negative than our

value for the HONO conformers ( D E = – 1.79 kJ mol-" [67]). The diŒerence may be

due to the presence of the hydrogen-atom in their work. In table 1 of [27] there is an

error in the M P2-FC } 6-311G** energy reported for c-HONO (which should be

–205 .275261 hartree [67]). This erroneous energy was apparently used to obtain

D E = – 0.2 kcal mol-" [27] instead of –1.79 kJ mol-

" (see above).

Inclusion of the 1s orbitals on the heavy atoms in the substitutions (MP2-FU } 6-

311G** optimizations) lowers the total energy of each conformer by 0.055 hartree,

leaving D E almost unchanged ( –1.83 kJ mol-" (this work) compared with the M P2-

FC results.

The M P2-FU } 6-311 1 G**, M P2-FC } 6-311 1 G**, MP2-FU } 6-311 1 G** and

M P4-FC } 6-311 1 G** optimizations all predict t-HONO to be the lowest-energy

conformer, by nearly identical amounts. The results all lead to the conclusion that, to

obtain the correct order for the relative energy of the nitrous oxide conformers from

M P computations, the inclusion of diŒuse functions is necessary. The D E values

obtained are too large, however, being more than twice the most reliable experimental

data.

3.2.2.4. Density functionals. As mentioned above, the best agreement between the

theoretical and experimental geometrical parameters is obtained for the B3LYP

optimized parameters at the three computational levels used in this work. Extending

the basis set and, especially, including diŒuse functions in the basis set have a very

important incidence on the relative energies of the conformers ; one obtains

D E(B3LY P) = – 3.76, –1.00 and 1 4.50 kJ mol -" from the 6-31G**, 6-311G** and

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6-311 1 1 G** optimizations respectively (table 5). (Mebel and co-workers [27, 74]

reported D E(B3LYP } 6-311G**) = – 0.2 kcal mol -" , which is within rounding oŒ

error of our result.) Note that, although the relative energies obtained with the two sets

of B3LYP optimizations without diŒuse functions favour c-HONO as the lowest-

energy conformer, they are closer to the experimental data (t-HONO lower in energy)

than the corresponding M P2-FU results are (see table 5).

Whereas the B3LYP } 6-311 1 1 G** optimizations yield a relative energy which is

approximately twice the best experimental value, they correctly predict t-HONO to be

the lowest-energy conformer.

3.2.2.5. Con® guration interaction ; coupled clusters. The ® rst con ® guration interaction

(CI) computations on both nitrous acid conformers and the TS between them were

carried out by BenioŒet al. [69] in 1976. Using 19 con® gurations, a double-zeta quality

basis set and the optimized geometries reported by Skaarup and Boggs [68] they

obtained D E = 1 10.5 kJ mol-" or about ® ve to six times the experimental values (see

above). From con ® guration interaction with double excitation (CID) } 4-31G

optimizations, including all orbitals in the excitations, Murto et al. [62] obtained a

slightly lower value : D E = 1 7.15 kJ mol -" .

In recent work, [27, 75, 76], the absolute values reported for D E are much smaller

but the results are contradictory ; depending on the method used, either c-HONO or

t-HONO is predicted to be the lowest-energy conformer. For instance, from single

reference con® guration interaction with single and double excitations (CISD) and

coupled-electron-pair-approach (CEPA)-1 computations, Suter and Huber [75]

obtained D E = – 0.72 kJ mol -" and 1 0.36 kJ mol-

" , respectively. Lee and Rendell

[76] used a triple zeta plus double polarization quality basis set to perform coupled

clusters with single and double excitations (CCSD) and coupled clusters with single

and double excitations with perturbative triples (CCSD(T)) optimizations on both

conformers. Even with such a large basis set, the D E obtained are not very satisfactory :

D E(CCSD) = – 0.14 kJ mol -" and D E(CCSD(T)) = 1 0.29 kJ mol -

" [76]. In their

recent paper M ebel et al. [27] reported that CCSD(T) } 6-311G(d, p) and QCISD(T) }6-311G(d, p) optimizations yield D E = – 0.3 and –0.2 kcal mol -

" respectively, again

in discord with experiment.

3.3. Rotational barrier

3.3.1. Experiment

Using their experimental data and a three-term torsional potential function, Jones

et al. [7] estimated the t- ! c-HONO and c- ! t-HONO barriers in the gas phase to be

50.2 and 48.1 kJ mol-" respectively. They predicted the top of the barrier to be at

about 88Êfrom the trans minimum ( h = 92Êwhere h is the H E O E N F O dihedral angle ;

h = 0Êand 180Êfor c- and t-HONO respectively). McGraw et al. [49] used a three-term

torsional potential and estimated the t- ! c-HONO and c- ! t-HONO barriers in the

gas phase to be 48.4 ‰0.8 and 43.0 ‰0.8 kJ mol-" respectively. Although these values

are close to the results of Jones et al. [7], they yield a higher energy diŒerence between

the rotamers. M cGraw et al. [49] placed the barrier maximum at h = 86Ê, very close to

later theoretical predictions (see below).

Kinetic studies of the in-situ IR photoinduced isomerization of HONO, which was

produced by UV photolysis of HN$

and O#

mixtures in nitrogen or argon matrices, has

permitted the determination of the upper limits to the torsional barriers in those

environments [12 ± 15]. Hall and Pimentel [12] reported that both c- ! t-HONO and

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t- ! c-HONO processes occurred. During un® ltered IR photoinduced isomerization

experiments, the intensities of the IR bands attributed to m%

of t-HONO (or t-DONO)

increased, with a concurrent decrease in the intensities of the m%

bands of c-HONO (or

c-DONO) (see ® gure 3 in [12]). The eŒective range for the IR photoinduced

isomerization was 3200 ± 3650 cm -" , corresponding to 9.7 ‰0.7 kcal mol-

"

(40.6 ‰2.9 kJ mol-" ) for the t- ! c-HONO torsional barrier height in the matrix at

20 K. The c- ! t-HONO barrier in the gas phase was estimated to be lower,

36.4 ‰4 kJ mol-" [12]. Note that the phenomena in¯ uencing the rates of the IR

photoinduced isomerization of nitrous acid in various low-temperature matrices has

been studied theoretically using molecular mechanics. The authors of [77] maintain

that the results of the calculations support a mechanism in which the energy is

absorbed speci® cally into the O E H vibrational mode and then undergoes a vibration

! lattice phonon modes ! rotation ! torsional vibration migration (see [77] and

references cited therein).

From speci® c IR laser excitation into the m"

and 2 m#

modes of each conformer, in

both nitrogen and argon matrices, Shirk and coworkers [14, 15] showed that the

photoisomerization is a single-photon process, even though the photoinduced rate of

the c- ! t-HONO isomerization was always much faster than that of the corresponding

t- ! c-HONO isomerization. This has been attributed to a stronger coupling between

the torsional mode m’

and the m"

and m#

modes in c-HONO than in t-HONO [14, 15,

90]. Shirk and Shirk [15] determined the barrier height for the c- ! t-HONO torsion

in the nitrogen matrix to be about equal to 2 m#

of c-HONO or 3250 ‰100 cm -"

(38.9 ‰1.2 kJ mol-" ). Combining this value with D E = 1 1.69 ‰0.42 kJ mol-

" [57], one

obtains 40.6 ‰1.7 kJ mol -" for the t- ! c-HONO barrier. These values indicate that

the earlier estimates [7, 49] are slightly too high.

3.3.2. Theory

The values of the theoretical barriers to the torsional motion depend on the relative

energies of the potential minima and the TS between them, corrected by the diŒerences

in the ZPE ( D ZPE = ZPE( t-HONO)-ZPE(TS)). (The imaginary frequency obtained

for the torsional mode in the TS is neglected.) D ZPE is expected to be very close to

5 kJ mol-" and accounting for it lowers the barrier by about 10 ± 15 % (see table 6). The

theoretical ZPEs determined for t- and c-HONO, with a given basis set and method,

are nearly identical (see section 3.2.2). The accuracy of the torsional barrier height will

depend on how accurately the theoretical geometry represents that of the TS and on

the validity of the corresponding wavefunction. The results of early work in which the

TS structure was not optimized [69, 71, 77] will not be discussed in detail. Also, the

data in table 6 are restricted to the theoretical methods which predicted the t-HONO

conformer to be the lowest-energy one.

In the ® rst study of the torsional potential in which complete relaxation of the

molecular geometry was allowed, Skaarup and Boggs [68] used a double-zeta quality

basis set and carried out geometry optimizations at the TS and nine ® xed torsional

angles. They found the TS to be at h = 85.47Ê, 36.4 kJ mol-" above the c-HONO

minimum (which, as noted above, was only 0.1 kJ mol -" lower than the trans

minimum in their work). Note that the torsional barrier was not corrected for D ZPE.

In their comprehensive study of HONO at the HF } 4-31G level of theory, Farnell

and Ogilvie [60] reported the energies for optimizations at seven torsional angles.

These included the trans and cis conformations and the TS for which they found h =

1.492 rad (85.48Ê). This is remarkably and no doubt fortuitously close to the TS

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position determined by Skaarup and Boggs [68] with the larger basis set. In HF } 4-31G

optimizations (tight criteria), we obtained h = 85.43Êin excellent agreement with the

work of Farnell and Ogilvie [60] and Murto et al. [62]. Note that the HF } 4-31G

computations yield 40.5 kJ mol-" for the t ! c-HONO barrier, uncorrected for D ZPE

[60, 62, 63, 65], very close to the values deduced from the IR photoinduced

isomerization experiments [12 ± 15]. However, introducing the D ZPE lowers this value

to 35.2 kJ mol-" (this work).

Turner [65] reported 15 values, ranging from 36 to 62 kJ mol-" , for the torsional

barrier in nitrous acid. These values were all uncorrected for D ZPE and most of them

were obtained for geometries optimized at a lower theoretical level.

For completely optimized geometries, M urto et al. [62] also reported the following

values for the t- ! c-HONO barrier (uncorrected for D ZPE) : 44.26 kJ mol -" (HF } 6-

311G), 47.08 kJ mol -" (HF } 6-311 1 1 G**) ( h = 86.9Ê) and 41.2 kJ mol -

" (MP2 } 4-

31G) ( h = 83.6Ê). These computational levels were chosen for optimization of the TS

because they all predict t-HONO to be the lowest-energy conformer [62].

The TS between the conformers is predicted to be closer to the c-HONO minimum,

with its position being remarkably constant ; h only varies from 85.40Êto 86.90Ê(table

6). Comparison of the predicted barrier heights for the t- ! c-HONO torsion ( D E(TS))

with the best experimental determination (38.9 kJ mol -" % D E(TS) % 42.3 kJ mol-

"

[15]) shows that only the HF } 6-311 1 G** and HF } 6-311 1 1 G** values fall within

the experimental error limits. The D E(TS) obtained from all the HF computations

without polarization and diŒuse functions are too low. The value determined from the

B3LYP computations is the highest, 14 % above the upper experimental limit, whereas

all the M P2 values are about 6 % higher than the upper experimental limit.

3.4. Rotational constants

Experimental values for the rotational constants of the nitrous acid conformers

have been determined with high accuracy [41, 42]. In theoretical computations the

rotational constants calculated for the input and optimized geometries are routinely

part of the output listings. W hereas the near coincidence between the experimental and

theoretical rotational constants can be a decisive factor in the assignment of a

fundamental vibrational band to a given rotational conformer [86], the theoretical

constants are not usually reported in the literature. The agreement between the

experimental and theoretical constants is also a measure of the agreement between the

true and the optimized geometries. The rotational constants calculated for the

optimized t- and c-HONO geometries are given in table 7 together with the latest

experimental data for the ground vibrational state [42, 50].

The rotational constants calculated for the ground vibrational state of both nitrous

acid conformers with the HF optimized geometries are all overestimated. This is

especially true for the A constant for t-HONO where, except for the HF } 4-31G and

HF } 6-31G values, the overestimations are from 10 to 13 %.

In contrast, except for the results obtained with the 6-311G** basis set (with and

without diŒuse functions), the M P2 optimized geometries all lead to a small

underestimation of the three rotational constants for t-HONO and of the A constant

for c-HONO. The rotational constants calculated with the M P4 optimized geometries

are also underestimated (from 1.5 to 4.5 %). Nevertheless, more than half of the

rotational constants calculated with the M P optimized geometries lie within 1 % of the

corresponding experimental value. The diŒerence between the HF and M P results

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with the same basis set is attributed mainly to the eŒect of relaxation of the molecular

structure due to electron correlation in the M P computations.

The B3LYP } 6-31G** optimized geometries yield constants that are the closest to

the experimental values : within 0.4 % and 0.8 % for t-HONO and c-HONO

respectively. The maximum deviation of the other B3LYP values is only 1.8 %. This is

in direct accord with the above observation that the B3LYP optimized geometrical

parameters deviate the least from the experimental values (section 3.1.2).

3.5. Vibrational frequencies

3.5.1. Experiment

There are two recent compilations of the fundamental vibrational frequencies of

the t-HONO and the c-HONO conformers [93, 94]. As mentioned in the introduction,

all the fundamental vibrational frequencies of t-HONO in the gas phase are known to

at least ® ve signi® cant ® gures (table 2). They will only be discussed where comparison

with the frequency data for c-HONO makes this necessary. The small energy

diŒerence between the t- and c-HONO conformers makes it possible to observe IR

bands for both of them and, by substitution of the hydrogen atom by deuterium, to

distinguish easily which bands pertain to the m"

mode (O E H stretch) of both conformers

and to the m$

mode (H E O E N bend) of t-HONO. In contrast, the m$

mode of c-HONO

is predicted to have a very low IR intensity. The same is true for m&

(O F N E O bend) of

c-HONO. Thus there have been only tentative assignments of experimentally observed

bands to these two modes [4, 5, 7, 11, 16, 46, 48, 49]. They will be discussed in detail

below.

Although all the fundamental modes of both conformers should be active in the

Raman measurements, there are apparently no data available for the Raman spectra

of nitrous acid [93, 94]. This is presumably due to the complexity of the gaseous

mixtures (see the introduction).

3.5.1.1. c-HONO : m$

(N E O E H bend), gas phase . D’ Or and Tarte [4, 5] assigned a pair

of bands at about 1370 and 1267 cm -" , which seemed to undergo concurrent decreases

to 1086 and 1015 cm -" upon deuteration, to the H E O E N and D E O E N bending modes

of the respective cis and trans conformers. However, it is probable that the band they

observed at about 1370 cm -" was due to another molecular H, N, O species. Indeed,

using a harmonic force ® eld, Deeley and M ills [40] predicted that m$

= 1298 .7 cm -" for

c-HONO. As we shall see below, frequency calculations using scaled quantum-

mechanical force ® elds also predict the frequency of m$(c-HONO) to be less than

1300 cm -" but higher than that of m

$(t-HONO) [67]. Jones et al. [7] observed a weak

maximum centred at about 1292 cm -" which they tentatively assigned to m

$(c-HONO)

because the out-of-plane torsional frequency for c-HONO is higher than that of the

trans conformer. This is a plausible frequency but other N, O-containing species

exhibit absorption bands in this region (N#O, asym -N

#O

$, etc. [41, 93]). Later,

M cGraw et al. [49] observed a weak band in the gas phase IR spectrum at 1261 cm -"

which they assigned to m$(c-HONO). They pointed out that N

#O

%has a PQR

fundamental centred at 1261 cm -" (Q branch at 1261.10 cm -

" [95]) but they ruled it out

on the basis of its intensity, relative to the intensities of other vibrational bands for the

tetraoxide in the spectra. However, the strongest caveat against the assignment of this

weak band to m$(c-HONO) is found in the higher-resolution work where all observed

lines near 1261 cm -" can be assigned to the strong m

$fundamental of t-HONO, centred

at 1263.2 cm -" in the gas phase (table 2) [41, 46].

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In their FTIR study of HONO, Guilmot [41] and Guilmot et al. [42] assigned some

2800 a-type lines and 1000 b-type lines to the m$

band of t-HONO in the spectral region

extending from 1180.9 to 1309 .8 cm -" . They found no evidence for m

$(c-HONO).

However, in a laser Stark spectroscopy study, M aki [48] reported that a number of

transitions observed near 1223 cm -" could not be assigned to the m

$fundamental of

t-HONO. Maki proposed that they are probably due to the m$(c-HONO) and may be

the weak B-type band whose Q branches are barely discernible in ® gure 4 of [55].

3.5.1.2. c-HONO : m$(N E O E H bend ), matrix results. Matrix eŒects are known to

enhance the intensities of certain IR bands. Thus the bands at 1259.4± 1263 .3 cm -" [11]

and the medium-intensity bands at 1265 ± 1267 cm -" [16] observed for samples in

argon matrices were assigned to c-HONO and would therefore correspond to its m$

fundamental mode. (The doubling of the frequencies is attributed to the occupation of

diŒerent matrix sites by the monomer.) However, there are no other bands which can

be assigned to the much stronger m$

fundamental of t-HONO in the spectra (see ® gure

1 of [11] and table 1 of [16]). These bands are thus most probably due to t-HONO and,

as in [23, 24], show that m$(t-HONO) does not undergo an important frequency shift

in an argon matrix. This is in sharp contrast with its behaviour in a nitrogen matrix

where it is shifted by about 1 30 cm -" (i.e. to 1293.7 cm -

" [9] or 1298 cm -" [12]). (Chen

et al. [10] have reported similar behaviour for the H E O E N bending frequency of nitric

acid ( 1 1.6 and 1 43.6 cm -" in argon and nitrogen matrices respectively).) It is

important to note here that theoretical calculations, with both scaled and unscaled

quantum-mechanical force ® elds, place m$(c-HONO) at a frequency higher than that of

m$(t-HONO) (see tables 7 and 8 in [67] and tables 8 and 9 in this work).

3.5.1.3. c-HONO : m&

(O F N E O bend ). McGraw et al. [49] assigned a weak band at

608 cm -" in the gas-phase spectrum to this fundamental. Although Deeley and M ills

[46] made a tentative assignment of a band at 609.0 cm -" to m

&, they placed a caveat on

the assignment ; the poor signal-to-noise ratio of the FTIR spectrum in this region

prevented a rotational analysis of the band. Later, Deeley et al. [45] investigated this

spectral region at higher resolution and concluded that the lines belong to the R

branch of m&(t-HONO). They conclude further that m

&(c-HONO) has probably never

been observed but that it lies close to m’(c-HONO) and is the cause of perturbations to

the latter.

For nitrous acid in argon matrices, bands at 608.0± 605 .1 cm -" [11] and 610 cm -

"

[16] have been attributed to the m&(c-HONO). These values place the O E N E O bend

frequency below that for the torsion about the central N E O bond and disagree with the

value, 721 cm -" , assigned to it for annealed nitrous acid at –190 ÊC [49]. This latter

value seems to be anomalously high and, as we shall see below, disagrees with results

obtained with scaled quantum-mechanical force ® elds.

3.5.2. Theory

There have been a large number of calculations of the theoretical harmonic

frequencies for nitrous acid using quantum-mechanical force ® elds (for examples see

[22, 23, 27, 60, 62, 64, 67, 68, 73, 76]). The unscaled harmonic theoretical fundament-

al frequencies, calculated at the theoretical level used to optimize the geometries, are

listed in tables 8 and 9.

3.5.2.1. t-HONO . Comparison of the data in table 8 with those in table 2 shows that,

as is generally observed, all the frequencies calculated with the unscaled HF force ® elds

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are overestimated. The overestimation is smallest for m’

(2± 10 %) and largest for the m$

and m%

modes (up to 39 %). The B3LYP frequencies present the smallest overall

deviations from the experimental data ; whereas the M P frequencies are closer to the

experimental data than the corresponding HF values, they all underestimate the

frequency for the m#

fundamental. The calculations at the highest level used in this

work, M P4SDTQ-FC } 6-311 1 G**, also underestimate the m%

(2 %) and m&

(8 %)

modes. These underestimations have no physical meaning and indicate inadequacies

in the M P wavefunctions [67].

3.5.2.2. c-HONO. The frequency calculations using the unscaled HF force ® elds all

yield m&

" m’. The situation is reversed for all the frequency calculations using the

B3LYP and M P force ® elds. This is in accord with the observation by M urto et al. [62]

that MP2 and CID calculations gave the m&

and m’

frequencies of c-HONO in the

reversed order, compared with the values obtained at the HF levels.

Note that transferring the scale factors obtained for the HF } 6-311G** force ® eld

for t-HONO to the corresponding force ® eld for c-HONO yields m&

= 590 cm -" and

m’

= 673 cm -" [67]. This is a large diŒerence and it is a good indication that m

&is

indeed at a lower frequency than m’

for c-HONO.

3.5.3. Infrared intensities of the fundamental bands

Experimental values of the absolute intensities I of the vibrational fundamentals of

nitrous acid are apparently only available for m", m

#, m

$and m

%of t-HONO and m

", m

#and

m%

of c-HONO [41, 55]. From the results of Kagann and M aki [55], one obtains I( m",

t) : I( m#, t) : I( m

$, t) : I( m

%, t) : I( m

", c) : I( m

#, c) : I( m

%, c) = 0.24 : 0.60 : 0.70 : 0.79 : 0.13 : 0.82 : 1.0.

The most recent values, obtained from FTIR line intensity measurements of m$

and m%

of t-HONO and m%

of c-HONO [41], are about 40 % lower than the previous values.

However, the ratios of the intensities determined in the two studies are fairly close :

I( m$, t) : I( m

%, t) : I( m

%, c) = 0.66 : 0.70 : 1.0 [41] compared with 0.70 : 0.79 : 1.0 [55]. Also

both studies agree that, at equal conformer concentrations, m%

of c-HONO has the

highest absolute intensity. (Note, however, that this result depends directly on the

calculated conformer concentrations.)

Comparison of the data in tables 8 and 9 shows that the computed intensities

depend on both the theoretical method and the basis set used. For instance the HF } 6-

311 1 1 G** calculations yield I( m", t) : I( m

#, t) : I( m

$, t) : I( m

%, t) : I( m

", c) : I( m

#, c) : I( m

%, c) =

0.37 : 0.48 : 0.66 : 0.64 : 0.18 : 0.67 : 1.0, conserving the relative order of the experimental

intensities for most of these bands.

For c-HONO, the calculated IR intensities of the m$

and m&

bands are indeed low :

3 % or less and 12 % or less respectively of the calculated intensity of m%, computed to

be the strongest band.

There is a marked discord, however, for the relative intensity of m&

for t-HONO,

computed at the HF level on the one hand and computed at the B3LYP and M P levels

on the other hand. Curiously enough, this marked discrepancy is not observed for m&

of c-HONO. For all the computations reported in table 8, one ® nds that I( m$, t) is

somewhat higher than I( m%, t) in apparent contradiction with the above experimental

ratios.

4. Conclusions

All the geometrical parameters for the planar t- and c-HONO conformers have

been determined with accuracies which permit critical comparison with the optimized

theoretical parameters. It is noteworthy that the experimental values of the O E N F O

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bond angle for both conformers are reproduced satisfactorily at all levels of theory.

However, the HF optimizations reported in this work invariably underestimate the

internuclear distances and overestimate the H E O E N bond angle. M oreover, the largest

individual diŒerences (for the central formal single O E N bond length and for the

H E O E N bond angle respectively) and largest average deviations from the experimental

data are observed for the HF optimized parameters. In contrast, the MP optimizations

for both conformers all predict values of the H E O E N bond angles which are within 1Êof the latest experimental data. Density functional theory (B3LYP) yields optimized

geometrical parameters that are the closest to the experimental data.

Experimentally, t-HONO is found to be lower in energy than c-HONO. The best

determination for nitrous acid in the gas phase is D E = 1 1.69 ‰0.42 kJ mol-" [57].

The di� culty encountered in reproducing such a small energy diŒerence in theoretical

computations is exempli® ed by the results presented in this paper. In general, adding

polarization functions to a given basis set, without diŒuse functions, results in a

lowering of the relative energy of c-HONO, bringing the results into further discord

with the experimental data. In contrast, including diŒuse functions in the basis set

results in a lowering of the relative energy of the t-HONO conformer at all levels of

theory studied (HF, B3LYP and M P).

The best experimental estimate for D E(TS) (barrier to the t- ! c-HONO torsion)

is 40.6 ‰1.7 kJ mol-" (see section 3.3.1.). The theoretical optimizations predict the

position of the top of the barrier to be closer to the c-HONO minimum : h =

85.40 ‰0.75Ê(table 6). The D E(TS) obtained from all the HF computations without

polarization and diŒuse functions are too low ; only the HF } 6-311 1 G** and HF } 6-

311 1 1 G** values fall within the experimental error limits. The value determined

from the B3LYP computations is the highest, 14 % above the upper experimental limit

whereas all the M P2 values are acceptable, being about 6 % higher than the upper

experimental limit.

For t-HONO the largest overestimations of the HF frequencies are observed for

the m$

and m%

modes (up to 39 %). The B3LYP frequencies present the smallest overall

deviations from the experimental data ; whereas the M P frequencies are closer to the

experimental data than the corresponding HF values, they all underestimate the

frequency of the m#

fundamental. The M P4SDTQ-FC } 6-311 1 G** also underestimate

the m%

(2 %) and m&

(8 %) modes. These underestimations have no physical meaning

and indicate inadequacies in the M P wavefunctions [67, 88].

All computations indicate that the frequency of m$(c-HONO) is higher than that for

m$(t-HONO). It is thus highly probable that the former has not been observed and that

assignments of bands near 1265 cm -" to c-HONO in argon matrices are incorrect.

For c-HONO the frequencies calculated with the unscaled HF force ® elds all place

m&

" m’

whereas the situation is reversed for all the B3LYP and M P frequencies.

Transferring the scale factors obtained for the t-HONO conformer HF } 6-311G **

force ® eld to the corresponding force ® eld of c-HONO yields m&

= 590 cm -" and m

’=

673 cm -" [67], a very good indication that m

&is indeed at a lower frequency than m

’for

c-HONO.

Acknowledgments

The authors thank Dr Yurii N. Panchenko (M.V. Lomonosov M oscow State

University), Dr Jean Olbregts (Universite! Libre de Bruxelles) and Dr Jean Vander

Auwera (Universite! Libre de Bruxelles) for many helpful discussions.

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theoretical study of the nitrous acid conformers: comparison of theoretical and experimental...

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