Potential constants of nitric acid

Research notes

1658

Bindungsverhiiltnisse aus. Wie bei (1) ist such bei (2) fur die therm&he Tautomerisierung KBr als polare Matrix notwendig. Die Beobachtungen lassen sich so formulieren, da13 sich mit zunehmender Temperatur das Gleichgewicht zwischen (a) und (b) immer m&r nach (b) hin verschiebt.

AT

il

I? p%]-

(a)

(b)

AEG-Telefunken PorscheLngsinstitut 79 Ulm, Donazc Germany

G. ARNOLD D. STAUDACHER D. HENDRIKS C. SCHIELE

Spectrochimica Acta, Vol. 218, pp. 1658 to 1661. Pergamon Press 1968. Printedin Northern Ireland

Potential constants of nitric acid (Received

4 Januaw

1967;

revised 29 April

1968)

Abstract-Based on the published spectra of the fundamental modes of vibration of the four isotopic species H, D, Nl4 and N15 of HNO,, a set of most probable valence force constants has been evaluated by the Wilson F-G matrix method. To f&t order approximation the potential constants “cis” and “trud’ with respect to the OH bond are assumed to be indistinguishable. Thereby, only those interaction constants are retained which are essential for an adequate description of the resonance field of the molecule. THE interest in the vibrational modes and the intermolecular force field of nitric acid dates back many years [l, 21, but due to the complexity of its structure a number of uncertainties have remained. Recently MCGRAW et aE. [ 31, have reported the complete spectra of the four isotopic species, IIN140,, HNr50,, Dw40, and DN150, and the results of a normal coordinate analysis. Although they have obtained good agreement between the observed and calculated frequencies, all but two interaction constants have beenneglected[4]. Therefore, anattempthas been made to determine a more general quadratic force field by retaining those interaction constants which are essential to describe the resonance field of the molecule. Since the published work concerned with HNO, has been thoroughly reviewed [3], only the most relevant data are presented. The fundamental modes of vibration are summarized in Table 1; it contains an unpublished set of spectra which have been obtained with the aid of a double-beam Perkin-Elmer model 21 spectrometer equipped with NaCl and CsBr optics [2]. [l] H. COHN, C. K. INUOLD and H. G. POOLE, J. Chm. Sot. 4272 (1952). [2] A. PALM, UCRL 4811 (1957); Tech. Note No. 8 (1960), Lawrence Radiation Laboratory, University of California, Livermore, California. [3] G. E. MCGRAW, D. L. BERNITT and I. C. HISATSUNE, J. Chem. Whys. 42, 237 (1965). [4] J. A. LADD and W. J. ORVILLE-THOMAS, Spectrochim. Acta 22, 919 (1966).

1659

Research notes Table 1. Observed and calculated fundamentals HN’40, M

Calc

C

DN”0 M

Jcslc

P

HNz60 M *ca1c

P

DN”0, M

of gaseous nitric acid Assignments

c*

P

Calc

366Ot

3669

3660 3677 2627 2621 2611 3665 3660 3577 2610 2621 2611

A’

O-H,

1710

1701

1708 1739 1686 1687 1708 1672 1672 1700 1661 1666 1666

N=O

1336

1338

1331 1314 1014 1014 1032 1334 1327 1297 1010 1012 1029

NOH, NOD

bend

1320

1313

1325 1361 1313 1308 1344 1320 1321 1360 1289 1291 1322

N=O NO,

s-stretch

O-D

stretch s-stretch

886

882

879

893

888

888

869

869

871

893

876

876

868

A' A' A' A'

680

-

647

662

670

641

662

632

647

649

645

641

649

A’

NO’

stretch

583

-

679

671

643

641

666

677

678

670

539

541

663

760

762

764

764

763

764

741

744

744

761

743

744

ONO' O'NO,

465

-

466

467

370

342

368

464

466

467

357

345

368

A' A" A"

bend

i66

OH,OD

torsion

bend

o-pbend

* The deta in columns C, P and M are those given in Ref. [l], [2] and 131, respectively. t The units ere cm-‘.

The molecular parameters for a planar configuration with two slightly unequal ONO’ angles, (see Fig. 1) as derived from microwave spectra [5], have been employed in the present computations: O-H = 0.96& N-O = 1.40A, cis N=O = 1.21 A, bane h’=O = 1.19 A, L NOR = 102”9’, L cis ONO’ = 115”53’ and L trans ONO’ = 113”51’. In the normal coordinate analysis [a] of this molecule which has C, symmetry, the nine vibrations are separated into 6a’ + la’ (OH, OD) + 2a” types, and the simplifying assumptions are made that the following sets of potential constants, “cis” and “tram” with respect to the OH are indistinguishable: far, =fatl,; jr,, =f,,,~ far, =fafr;; f.,.;; =forjr,; fs7, =fpr;; With the aid of an IBM-7090 computer an initial set of constants, transferred from structually related molecules [2, 71, has been modi6ed successively until the observed and calculated frequencies agreed to approximately two percent, as shown in Table 1. The finally accepted potential energy constants are listed in Table 2 using the customary notation to distinguish bond, angle, and interaction constants. Two significant results emerged from the bond,

fba = fs,, and f, =fa*.

Fig. 1. Internal coordinates of nitric acid. [5] A. P. COX and J. M. RIVEROS, J. Chem. Phye. 42, 3106 (1965). [6] E. B. WILSON, JR., J. C. DECIUS and P. C. CROSS, Molecular Vibrations. (1955). [ 73 A. PALM, J. Chem. Phys. 26, 855 (1957); in particular see Ref. [3].

McGraw-Hill

1660

Research notes * fi,

= 3.600

fr, = 7.900 fi,, = -0.848 fr3,* = 1.400

fo = 0.950 fba= -0.198 f@, = 0.300 f& = 0.297 fE = 3.575

fax,= far; = far*= far*=

-0.775 -0.635 0.035 0.707

* The constants are expressed in units of mdyn/A for bond stretch, mdynA for angle and angle-angle, and mdyn for anglebond interactions.

calculations: 1. the frequencies depended most sensitively on the magnitude of the F,, offdiagonal element containing the ONO’, NO interaction terms and 2. the original assignments [ 11 for the NO’ stretch and the NO, bending modes had to be interchanged. The importance of including FsB is reflected in the magnitude and sign of farat whose value represents a sizeable fraction of the corresponding diagonal elements as seen m Table 2. A similar observation was made in the normal coordinate analyses of CX,N02 type molecules [S]. Values of the corresponding force oonstants invoIving the ONX, NO interaction range from -0.15 to -0.65 and the interaction constants involving the /?-coordinate have also non-negligible values. Another result of interest because it substantiates the general transferability of force constants, concerns the magnitude and sign of the NO’,NO interaction constant [9]. A value of -0.848 mdyn/A has been found here, compared with -0.90 to -1.60 for HNO, [7]. The most recent study of HNO, [IO] does not shed further light on the force field of HNO, since only a minimum number of constants has been included in the normal coordinate treatment. The descriptions of the fundamental modes of vibration given in Table 1 agree with earlier ones with the exception of the reassignment of the NO’ stretch and NO, bend. This alteration, already reported by MCGRAW et al. [3], has been made reservedly as it stems from purely computational considerations rather than from isotopic shifts or the transfer of force constants. The 640 cm-l and 880 cm-1 bands have heretofore been identified with the NO, bending and NO’ stretching modes, respectively [l], conforming to spectral assignments of structurally related molecules. In the present calculations the 640 cm-1 frequency has been attributed to the NO’ stretching mode because it appeared to be most sensitive to changes inf,.,. By contrast, the isotopic frequency shifts do not help to clarify the assignments. The 640 cm-l band displays the same isotopic displacements as the 580 cm-l band which is ascribed to the ONO’ bending mode, but the analogous behavior is not sufficient to identify the 640 cm-l band with the ONO’ bending mode. The calculated values of the 640 cm-l band for the four isotopic species agree with the observed, whereas the calculated values for the 880 cm-l band reveal an isotopic shift not indicated by the observed frequencies. However, the reassignment was necessary to obtain self-consistent potential constants by means of which the four sets of fundamental frequencies could be reproduced, confirming the conclusions reached by MCGRAW et al. [3]. These assignments are being accepted until additional spectroscopic measurements in the critical spectral region, 640 cm-l to 900 cm-l will reveal new features. The identification of the remaining fundamental modes of vibration is in accord with the previous ones [I]. For the factored-out OH(OD) frequency a value of frl= 7.15 mdyn/& indicative of weak hydrogen bonding has been obtained. The two c(” modes include the out-ofplane bending and the torsional modes. The latter is actually a hindered rotation with a potential barrier of the order of about 8 kcal/mole [3]. Hence, both motions may be treated as genuine,

[8] A. CASTELLI, A. PALM and C. ALEXANDER, JR., J. Chem. Phys. 44, 1577 (1966). [9] R. F. BADER, ilfol. Phya. 3, 137 (1960). [lo] G. E. McGraw, D. L. BERNITT and I. C. HISATSUNE, J. Chem. Phys. 45,1392 (1966).

1661

Research notes

slightly interacting vibrations; the corresponding force constants are fr = 0.5206 mdyn A, f, = 0.0947 mdyn A, and fr, = 0.0207 mdyn A. authors thank I. KLUOLERand B. WHEELER for their assistance in modifying computer programs and VALERIETALMADUE for her graciouscooperation. This work was supported in part by NASA Grant NSG-269. Achmowledgmente-!l!b

Southwest Center fo7 Advanced Studies Da&a,

ANN PALM

Texas 75230

ALEX CASTELLI

Code 5350 Advanced Projecte Laboratory Point Mugu, California 93041

CHESTERALEXANDER,JR.

Department of Physics Unive&ty of Alabama Tzcscalooaa,Alabama 35401

Spectrochimica Acta,Vol.24A,pp.1681

to 1682.

Pergamon Press 1968.

Printed

inNorthern Ireland

Vibrational assignments of some phosphonitrilichalides (Received 29 January 1908)

THE fundamental modes of vibration for (NPCI,),, in solution have been assigned[I] on the basis of Dzd symmetry; some loweringto an S4 molecular symmetry appeared to occur in the crystal. The assignmentsfor the D,, configurationwere based on those given for the planar D4, modes by STE~ERand STAHLBERQ [2], which are incorrect [3]. The 6Bn, modes of [2] have been found to divide into 3B1, + 3B,, modes, sincethree of the B,, modes assignedby STEUERand STAEZBERQ [2] to vasPXZ, pPX, and y ring are in fact B,, modes. For the planar D&(NPX&, molecule, taking the C,’ axes and a, planes to pass through the nitrogen atoms and the Cs” axes and o, planes to pass through the phosphorusatoms, the 42 fundamental modes divide as follows: 4A1, + 2Azs f 3Bi, + 4B2,, + 4E, + l-4,, On reductionto Dzd symmetry,

+ 3A,, + 3B,, + 2BzU + 6-Q

involving C,# -+ C, ’ , the fundamentalmodes divide as follows: 6A, + 5A, + 5B, + 6B, + 10E

where class A, is Raman active only, and polarized, class A, is inactive in both Raman and infrared effects, class B, is Raman active only and depolarized and classes B, and E are both Raman and infra-red active, the Raman modes being depolarized. On further reduction to S, symmetry, the fundamental modes of the “skewed tub” (NPX,), molecule become 11A + 11B + 10E where class A is Raman active only and polarized and classes B and E are both Raman and infra-red active, and depolarized. In Table 4(b) of [l] there is an error in the selection rules for the S, point group. The B species, not the A species should have the T, component. A similar error has been found in HERZBERC) [4], Table 55, page 253. From a m-investigation of the infrared spectrum of (NPCI,), in both CC& and CHCl,, and of the crystal a new assignment for (NPCI,), is proposed. This is based on the above modified [l] [2] [3] [4]

T. E. E. G.

R. MANLEY and D. A. WILLIAMS,Spectrochim. Acta %A, 149 (1967). STE~ERand R. STAHLBERU, 2. Nuturforsch. 17b,780 (1962). STEOER,Private communication. H~RZBER~,Molecular Spectra and Molecular Structure II, Infrared and Raman Spectra of Polyatomic Molecules, 11th Edition. Van Nostrand (1964).