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Reduction of wavenumbers of pure rotational and vibration-rotational transitions of KrH+ X1Σ+ to parameters of radialfunctionsMARCIN MOLSKI aa Department of Theoretical Chemistry, Faculty of Chemistry , Adam Mickiewicz University , ul.Grunwaldzka 6, PL 60-780, Poznań, PolandPublished online: 16 Nov 2009.

To cite this article: MARCIN MOLSKI (2002) Reduction of wavenumbers of pure rotational and vibration-rotational transitions of KrH+

X1Σ+ to parameters of radial functions, Molecular Physics: An International Journal at the Interface Between Chemistry and Physics,100:22, 3545-3552, DOI: 10.1080/00268970210150531

To link to this article: http://dx.doi.org/10.1080/00268970210150531

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MOLECULAR PHYSICS, 2002, VOL. 100, No. 22, 3545-3552 + Taylor & Francis 0 Taylor 6 Francis Group

Reduction of wavenumbers of pure rotational and vibration- rotational transitions of KrH' XIX+ to parameters of radial

functions MARCIN MOLSKI*

Department of Theoretical Chemistry, Faculty of Chemistry, Adam Mickiewicz University, ul. Grunwaldzka 6, PL 60-780 Poznan, Poland

(Received 11 January 2002; revised version accepted 26 April 2002)

From the 352 wavenumbers of the assigned pure rotational and vibration-rotational transi- tion of KrH' X'C' in 11 isotopic variants, 10 coefficients of radial functions defining the Born-Oppeneheimer potential energy, adiabatic and non-adiabatic effects have been deter- mined at C? = 0.982. From the radial coefficients representing non-adiabatic rotational effects the rotational g factor go = 0.576( 12) and electric dipole moment po = 1.967(40) D of 84KrH+ are estimated at polarity [-KrH+]+. The latter conforms acceptably with the ab initio result po = 1.944D, whereas the former differs from the absolute experimental value (gol = 0.5545 by about 3%, and from the relativistic ab initio value go = 0.6082 by about 5%.

1. Introduction The protonated krypton ion KrH+ has twelve stable

isotopic species which consist of a combination of six krypton isotopes 78Kr, 80Kr, 82Kr, 83Kr, 84Kr, 86Kr and two hydrogen isotopes H and D.

The first extensive measurements of the highly resolved Fourier transform infrared spectrum of KrH+ for five krypton isotopes were made by Johns [I]. The spectrum was analysed using the familiar Watson's [2] expression

including mass-independent Dunham's coefficients Uk,, the reduced mass m of the system and the correction factors A:: representing deviations due to the break- down of the Born-Oppenheimer (BO) approximation. Despite the large number of krypton isotopes investi- gated, none of the parameters A i r * H could be deter- mined [I].

Warner et al. [3] observed the J = 0 --+ 1 transitions of KrD+ for all the six krypton isotopes with a millimetre- wave spectrometer and determined the parameters A$ and A y l . The authors resolved also the hyperfine struc- tures of 83KrD+ due to the nuclear spin I = 9/2 of 83Kr and determined both its quadrupole coupling constant

* e-mail: marcin@rovib.amu. edu.pl

eQq = 549.1(5) MHz and its nuclear coupling constant

The KrH+ spectroscopic data obtained by Johns and Warner et al. were used by Peterson et al. [4] to evaluate indirectly (through intermediate quantities Ukl (a i ) ) the BO internuclear potential parameters ai i = 0,. . . , 4 defining the Dunham's potential [5]. Since this potential is valid only for the small region near the minimum. Surkus [6] calculated the potential curve of 84KrH+, numerically fitting the spectral data obtained by Johns [I] to the generalized potential energy functions with correct long range part.

The rotational g factors go = -0.5545 for 84KrH+ and go = -0.2791 for 84KrD+ were determined experi- mentally by Linnartz et al. [7] from the difference in Zeeman splitting for the J = 0 -+ 1 (84KrH+) and J = 1 4 2 (84KrD+) transitions. The negative sign of the rotational g factor was not confirmed by the relati- vistic ab initio calculations by Enevoldsen et al. [9], who obtained the positive value go = 0.6082 for 84KrH+. This supports the earlier suppositions that rotational g factor determined by Linnartz et al. [7] has the anom- alous negative sign.

Linnartz et al. [7] attempted also to determine experi- mentally the electric dipole moment, employing the Townes et al. [8] method. They failed to evaluate a reli- able value of the dipole moment of 84KrH+ due to a major influence by the zero-point vibrations; different methods of extrapolating the same experimental data produced three values of po = 1.0(3), 1.8(3), 3.0(3) D. Hence, a direct comparison with the ab initio value

C N = -0.022(2) MHz.

Mo/erufur Physics ISSN 00268976 print/lSSN 1362-3028 online 0 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals

DOI: 10.l080/0026897021015053 1

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3 546 M. Molski

po = 1.944 D obtained by Rosmus and Reinsch [lo] was not possible

In subsequent measurements performed by Linnartz et af. [ I I] the pure rotational transitions of 84KrH+ and 86KrH' up to J = 6 4 7 with a tunable far-infrared (TuFIR) spectrometer were observed. Using all avail- able spectral data they determined the improved para- meters Ukl and A:.

In recent work of Odashima et al. [ 121 the pure rota- tional transitions of 82KrD+, 84KrD', '%rD+ and 82KrH+ in the ground vibrational state were measured using a TuFIR spectrometer. The wavenumbers obtained were analysed by combining with the previous data of both pure rotational (61 FIR data) and vibra- tion-rotational transitions (291 IR data) in the total set of 352 lines, yielding the improved mass independent Dunham's parameters Uk[, the BO breakdown para- meters A $ , A t l and the additional higher order para- meter A o 2 .

Besides the Peterson et al. [4] and Surkus [6] calcula- tions, no attempts have been undertaken to evaluate the potential parameters by direct or indirect fitting of the KrH' spectral data. The main objective of this work is to determine the BO potential, adiabatic and non- adiabatic corrections by direct inversion of the highly resolved pure rotational and vibration-rotational spectra of KrH'. To this aim we employ the deforma- tional self-consistent procedure (DS-cP) in an analytical version [ 131, that may be applied both to neutral [ 13, 141 and charged [ 151 molecules.

We shall be concerned also with verification of the experimental value of the rotational g factor obtained by Linnartz et af. [7] and the electric dipole moment calculated by Rosmus and Reinsch [lo]. They are deter- mined here without the application of external electric and magnetic fields, employing the relation between non-adiabatic rotational effects and electric and mag- netic properties of molecules [16]. This method was applied first to neutral molecules by Sauer and Ogilvie [17] and by Ogilvie [16], and then extended to diatomic ions by Molski [15]. Application to ArH' X'C' [15] yielded the dipole moment po = 2.1(6) D, in comparison with the ab initio result 2.1(1)D [I81 and the experi- mental value 3.0(6)D [19].

The result obtained by Molski was criticized by Ogilvie [20], who reduced almost the same set of ArH' spectral data (443 lines versus 431) to a different set of radial parameters generated by the hypervirial perturba- tional approach implemented in the computer program Radiatom [16]. Ogilvie failed to determine a reliable value of the dipole moment of ArH' from his non- adiabatic rotational parameters.

The problem of the reduction of the spectral data by Molski's DS-cP and Ogilvie's Radiatom program to two

H

mutually inconsistent sets of radial parameters is not only the case for ArH'; the same was encountered for GaH [13, 211, LiH [22, 231, and NaCl [24] data. To explain this strange situation a numerical test of the DS-cP and the Radiatom program has been performed by Coxon and Molski [25]. The same set of LiH X 'C+ data as that applied by Ogilvie [22] was analysed using a numerical algorithm implemented in Coxon's computer program SSPOT [25]. In this approach, the experimental line positions are compared with those given by the eigenvalues calculated by numerical integration of the radial wave equation using the Cooley-Cashion-Zare algorithm.

The calculations performed revealed [25] that the numerically determined LiH radial parameters are in excellent agreement with those produced by Molski's DS-cP and differ significantly from those generated by Ogilvie's Radiatom program. Since the same result was obtained for NaCl [26], GaH, GeS, BrCI, ArH' [27] one may draw a general conclusion that the radial para- meters produced by Ogilvie's Radiatom program are not reproducible by other fitting procedures, hence Ogil- vie's radial parameters have no meaning beyond his own computer program.

The other test calculations [25-271 indicated that Ogil- vie's analytical approach reproduces the rotational and vibration-rotational energy levels of diatomic molecules with much less accuracy than the Coxon's SSPOT and Molski's DS-cP; hence, the radial parameters generated by Ogilvie's method are not sufficiently accurate for use in external applications.

The test calculations performed by ArH' radial parameters obtained by Ogilvie [20] prove that they fail to reproduce the ArH' spectra reliably when employed in a standard numerical eigenvalue routine [25]. The normalized standard deviation of the fitted ArH' data is 6 = 3576 [27]; for comparison the DS- CP parameters give 6 = 1.88. In such circumstances the results obtained for ArH' by Ogilvie [20] are mean- ingless and should not be employed for comparison with the results produced by DS-cP which, according to the tests [25-271, is a reliable method for direct reduction of spectral data.

2. Theoretical basis To carry out the direction reduction of the KrH+

spectral data we employ the Herman-Ogilvie wave equation [28]

with an effective potential [I31

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Parameters of KrH+X’C’ 3547

BoJ(J + 1)[1 + 4 x ) - P ( x ) l (1 + x ) 2

u , J ( x ) =

f V(x)[l - P ( x ) ] -k v ( x ) ’ f EuJP(x)i (3)

including adiabatic V ( x ) ’, non-adiabatic rotational a ( x ) and vibrational p ( x ) corrections to BO energy levels.

In the above equations, Bo = h2/(2mRt) denotes the rotational parameter for the BO equilibrium inter- nuclear separation Ro and x = (R - Ro)/Ro is the Dun- ham’s variable [5].

All the radial functions in equation (3) are expanded into a series of the Molski’s generalized variable [29]

R - R, ‘ = a R + ( I -a)Ro

(R - Ro)/Ro

{ (R - Ro)/R

a = 0 ,

a = 1, = 2(R - Ro)/(R + Ro) a = 1/2, (4)

being a combination of Dunham (a = 0 ) [5], Ogilvie- Tipping (a = 1/2) [30] and Simon-Parr-Finlan (a = 1) [31] variables. Treating a as an adjustable free fitted parameter, one can determine its values from the spectra; in this way important information on the optimal form of the expansion of the radial functions in expression (3) is obtained.

The radial functions for a diatomic ion take the form [281

(5)

here me is the mass of the electron and rn, and mb are the masses of atoms a and b, respectively.

The term containing K. becomes viewed as simply leading to overall modification of the effective reduced mass in’ of an isotopic species of KrHf through a rela- tion [28]

2 m’ = in - &&me, m = mamb/(m, + mb), (9)

in which [28]

KnO = .A/(.: + a:) - n a / ( n a + n b )

= nb/ (nQ + n b ) - ni/(fl: + n i ) (10)

is defined for the standard isotopic species 84KrH+ (0 = 0) endowed with nuclear masses n,(b) . The nuclear masses of an isotopic variant are denoted by primed quantities.

To solve the wave equation (2) we express all terms in (2) with an effective variable dependent on vibrational and rotational quantum numbers ( u , J ) [13]

= (R - R ~ J ) / R ~ J ~ (11)

to which we apply a linear transformation

= V(l + x ~ J ) + X u J i XuJ = (RvJ - R O ) / R O . (12)

The quantity xUJ in an analytical form is calculated from the criterion for a minimum

using the Maple processor [ 131. The u,J dependence of the dynamic reference confor-

mation R,j is a result of centrifugal deformation and non-adiabatic vibrational effects of higher order (s$,)) responsible for the appearance of the term E , j P ( x ) in the effective potential energy equation (3) and an addi- tional v dependence of R,j. The eigenenergies E,j which appear in equation (3) are calculated numerically using the iterative procedure described in [13].

Taking advantage of expression (12) we obtain the effective radial wave equation [ 131

$ , J ( q ) = Oi (14) a f = b f , a$,, = b,”:2/af;J, (15)

biJ = (W [d”U”J(rl)/d77n1,=01 (16)

B ~ J = h2/(2mR?J)i (17)

E,j = b f + CY,(U + 1/2)k1

amenable to direct solution in the semi-classical Dunham [5] scheme providing the eigenvalues [ 131

(18) k=O

in which Y, are Dunham’s vibrational coefficients, in analytical expressions [5] into which we substitute

Since in the DS-cP approach we substitute a, -, aiJ into Yko, with aiJ defined by the (n + 2)th derivative of the effective potential (3), the number of BO potential parameters cj in the DS-cP energy formula (18) is not restricted by the order k of the applied Dunham’s coeffi- cients Yko. In such circumstances, Ogilvie’s opinion [20, 241 that in the DS-cP spectral analysis additional parameters cj (beyond those that can be evaluated

{ R O i (RoJ i a:J}.

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3548 M. Molski

with spectral data) with zero values in Yk0 have been used, does not hold true.

3. Electric and magnetic properties The eigenenergies (1 8) can be applied to evaluate the

coefficients of radial functions from expressions (5)-(8) by direct fitting of the experimental wavenumbers. Having determined the non-adiabatic rotational para- meters $',', the electric dipole moment of a diatomic cation can be evaluated from the relationship [32, 281

i=O

for the assumed polarity ['AB-I+, whereas for the other isotopic variant, using the formula [28],

p ( R ) ' = p ( R ) - r;eRQ. (20) The rotational g factor and its isotopic variant may be calculated using the formulae [28]

i=O p=u,b

g'(R) = mp tfLmh,-'E' + r;*Qm,/m'. (22) i=O /'=a.b

4. Application to KrH+ The eigenenergies from expression ( 18) are applied to

evaluate the radial parameters for KrH' X IC' by direct fitting of the measured rotational and vibration- rotational transitions using a weighted nonlinear least- squares routine with weights taken as inverse squares of the uncertainties of experimental data.

Table 1 presents the radial parameters of KrH' obtained for the Dunham (DUN), Ogilvie-Tipping (OT), Simon-Parr-Finlan (SPF) and Molski (MOL) expansions of the radial functions. The uncertainties in parentheses are one estimated standard deviation in units of the last quoted digit of values of the parameters fitted. Plots of the BO potential energy function (5) expanded in different variables 5 are presented in figure 1.

From the relations (19), (21) and parameters t r and tp from table 1 we have evaluated the values of the rotational g factor and electric dipole moment po for s4KrH' at the BO equilibrium distance Ro and polarity [-KrH']'. They are reported at the foot of table 1.

As input data we use 61 pure rotational u = 0 and J = 0-14 lines [3-121 and 291 vibration-rotational lines [ I ] for u = O + 1, u = 1 - 2 and J = & 3 1 of "KrH, 82KrH, 83KrH, s4KrH, "KrH, 78KrD, 80KrD, '*KrD, s3KrD, ''KrD, 86KrD, in the total set of 352 transitions.

To obtain the best set of parameters fitted from the spectra, we use as criteria the minimum number of fitted parameters consistent with a minimum value of normal- ized standard deviation 8 = I , a maximum value of the F-statistic, and the optimum values' of the estimated standard error ci of each fitted parameter i and of cor- relation coefficient cc(i,j) between parameters i and j .

5. Results In the preliminary fit of the KrH' data we have dis-

covered that the adiabatic radial parameters U? are indeterminate from the spectra, whereas the non- adiabatic parameters t:' = -0.0146(335) and s p = -0.26(60) are relatively small and statistically mean- ingless. Thus, except the fit reported in the last column of table 1, they were removed from the set of fitted parameters. This situation is surprising as parameter Ak = 0.972(94) determined from the spectra by Odashima et al. [12] indicates that either u p or tp, or both of those parameters should be determinable due to a relation linking Ak with u p and tp, specified by [ 161, equation 4.284.

To explain this situation qualitatively lets calculate the values of the parameters

(23)

(24)

derived from relations (19) and (21) for the polarity [-KrH']', using the experimental value of [go] = 0.5545 and the ab initio result po = 1.944D. Although tp = -0.0146(335) determined from the spectra is statistically insignificant, it conforms ac- ceptably with t? calculated from equation (23). It is worth noting that despite tt' being poorly evaluated its value fluctuates (during additional iterations) in- significantly at the fourth decimal point. The same was encountered for t t r = -0.180( 178) evaluated from the ArH' spectra [15]. From the experimental values of go = 0.6638(34) and po = 3.0(6) D [19] for 40ArH' and from equation (23) one obtains tir = -0.303( 190); the ab initio value po = 2.1(1) D [18] yields t f = -0.0179(319).

Those results indicate that the non-adiabatic rota- tional effects for the relatively heavy krypton nucleus are very small; their neglect has only a marginal influ- ence on the values of other fitted parameters and electric and magnetic properties deduced from them (compare the last two columns of table 1). We conclude that the breakdown in the BO approximation in KrH+ is gener- ated mainly by the adiabatic and non-adiabatic effects for the light hydrogen nucleus.

The application of the proposed method and general- ized variable (4) enable a reduction of wavenumbers of

tp = m[go/mp - 2po//(eRomH)] = -0.01424,

to = m[go/mp + 2po/(eRomK,)] = 0.55496, H

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Tabl

e 1.

R

adia

l pa

ram

eter

s' of

KrH

' X

'C+.

DU

N

OT

SPFh

M

OL

M

OL

M

OL

a [O

I' ~

.51

11

.Ol

1.20

3 l(4

4)

[ 1.2

03 11

[1.2

031]

co

/cm

-' 18

5 990

.0(2

.8)

186 0

06.4

3(99

) 18

6 01 1

.O( 1

.1)

186 0

13.7

( 1.2

) 18

6 01 3

.62(

96)

186 0

13.6

3(96

) C

l -2

.579

66(

78)

-1.5

80 1

8(12

) -0

.579

52(

14)

-0.1

732(

87)

-0.1

73 1

9(16

) -0

.173

20(1

6)

c2

4.34

2 6(

53)

1.21

380(

12)

-0.4

1 1 2

7(40

) -0

.642

6(2

7)

-0.6

42 5

8( 12

) -0

.642

58(

12)

c3

-5.9

56(

14)

-0.5

86 O

(21)

-0

.01

8 4( 1

4)

-0.4

53(1

2)

-0.4

52 7

7(32

) -0

.452

77(

32)

b

c4 7.

029(

56)

0.21

36(7

5)

0.19

7 5(9

4)

Q CS

-6

.37(

30)

s 2 1 $

P Y

3.12

(46)

0.41

3 2(9

1)

0.44

8 5(8

3)

0.53

1 ( 10

) 0.

576(

12)

0.57

6( 12

) S

F

0.49

5(39

) 0.

5 1 7(

19)

0.61

4(21

) 0.

658(

22)

0.65

8(23

)

b

-0.0

14 6

(335

) ;Ir

0.57

6(12

) 0.

656(

22)

s?

-3.1

(3.

0)

-2.6

3( 6

0)

-5.8

8(66

) -6

.86(

72)

-6.8

6(69

) -6

.84(

69)

u?/1

04 cm

-' -4

.688

8( 1

473)

-5

.419

3(1

296)

-6

.8 1

1 2( 1

666)

-7

.596

l(1

894)

-7

.596

4( 1

877)

-7

.586

8( 1

892)

%

1.

421 2

06 9

6(84

) t.;i

Ro/

1 OK1

' m

1.

421 2

03 8(

36)

1.42

1 202

41(6

5)

1.42

1 205

99(

75)

1.42

1 207

06(8

1)

1.42

1 207

06(

82)

6 0.

970 4

0.

976

1 0.

979 0

0.

982 0

0.

980 5

0.

981 7

F/

lOIO

7.

04

8.38

8.

40

8.38

9.

36

8.28

Po

D

1.41

0(31

) 1.

531(

28)

1.8 1

4( 36

) 1.

968(

40)

90

+

2.02

(12)

1.

967(

40)

0.41

30(9

1)

0.44

8 2(8

3)

0.53

1( 10

) 0.

576(

12)

0.57

6( 12

) 0.

575(

12)

0.20

6 7(4

5)

0.22

4 3(4

1)

0.26

5 8(5

2)

0.28

8 3(5

9)

0.28

8 3(

40)

0.28

7 8(4

0)

g?

Para

met

ers

are

inde

pend

ent

of m

ass

exce

pt P

o, g

o th

at a

pply

to

84K

rHf a

nd g

h th

at a

pply

to 8

4KrD

+.

Res

ults

pre

sent

ed i

n [3

4].

'Val

ues

of p

aram

eter

s th

at w

ere

held

fix

ed in

the

fit a

re g

iven

in s

quar

e br

acke

ts.

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3550

Junharn potential

M. Molski

-~ Simon-Parr-Finlan potential

Qiivie-Tipping potential Moiskl potential

Figure 1 . Plots of the Born-Oppenheimer potential energy V ( R ) (in eV; R in lo-" m) of KrH' X 'C' over the range 1.2470 < R < 1.8096 defined by available spectral data.

352 pure rotational and vibration-rotational transitions of KrH' in 1 1 isotopic variants to 10 free adjustable parameters (4th column in table 1) defining radial functions (5k(8). Despite a strong correlation between parameters cc(a,c,) = 0.9998, cc(a, c2) = -0.9991, cc(a, c 3 ) = -0.9996 the parameter a = 1.2031(44) is sig- nificantly evaluated and provides vital information: in the case of KrH' X 'C' the variable (4) with a = 1.203 1 ensures the optimal form of the expansion of radial functions (5k(8).

To evaluate the most compact and physically mean- ingful radial parameters for KrH' X 'C', the spectral data were also fitted with a = 1.2031 treated as con- strained parameter. In this fit, only 2 correlation coeffi- cients between the parameters fitted attained magnitudes greater than 0.99 cc(Ro, cl) = 0.9991 and cc(to , u1 ) = -0.9916. The radial parameters evaluated for con-

H H

strained parameter a are reported in the last two col- umns of table 1 .

Table 2 presents the values of the dynamic reference conformation

RoJ = R O ( l + xoJ) (25)

calculated from equation (12). These clearly show that RVJ increases both with J due to the action of centrifugal force and with u due to the non-adiabatic vibrational effects of high order represented by the parameter s r .

From the non-adiabatic rotational parameters tp and to" reported in table 1 we evaluate the electric dipole moment po = 1.968(40) (for tp = 0), po = 2.02(12), and rotational g factor go = 0.576(12) for 84KrH+ employing (19) and (21). Both values of the dipole moment are consistent with the ab initio result po = 1.944D by Rosmus and Reinsch [lo], whereas

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Parameters of KrH'X'C' 355 1

Table 2. Dynamic reference conformation R,,J (in lo-'" m) of 84KrH+ X 'C+ in the u, J state.

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 2 3 4 5 6 7 8 9

10 15 20 25 29

1.421 382 76 1.421 51095 1.42 1 767 39 1.422 152 21 1.422 665 59 1.423 307 76 1.424 079 03 1.424 979 77 1.426 010 41 1.427 171 45 1.428 463 44 1.43691204 1.448 758 87 1.464 158 70 1.479 178 32

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 1 2 3 4 5 6 7 8 9

10 15 20 25 29

1.421 41698 1.421 545 18 1.421 801 62 1.422 186 44 1.422 699 8 1 1.423 341 98 1.424 1 I3 25 1.425 01 3 99 1.426 044 63 1.427 205 66 1.428 497 65 1.436 946 24 1.448 793 04 1.464 192 86 1.479 212 47

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

0 1 2 3 4 5 6 7 8 9

10 15 20 25 29

1.421 51095 1.421 767 39 1.422 15221 1.422 665 59 1.423 307 76 1.424 079 03 1.424 979 77 1.425 046 82 1.426 077 46 1.427 238 49 1.428 530 47 1.436 979 02 1.448 825 79 1.467 682 69 1.483 325 71

go differs from the absolute experimental value lgol = 0.5545 by about 3%. There is no anomaly reported by Linnartz et al. [7], and the evaluated value of the dipole moment of 84KrH+ conforms acceptably with one of the experimental values of po = 1.8(3) D [7].

The anomalous negative sign of the rotational g factor obtained by Linnartz et al. is a consequence of the improper use of the Townes et al. [8] formula ([7], equa- tion l )

Here d is the displacement vector of the centre of mass of the primed isotopic species referred to the centre of mass of the non-primed isotopic species, B is the rota- tional constant and Q is the net charge of the ion.

Formula (26) applied by Linnartz el al. is equivalent to [15]

Introducing equations (21) and (22) into (27) and then adapting relation (10) to atomic masses,

Kat = d/ (& f - %/(mu f mb)

= m b / ( m a + - m6/(mi -k d) , (28)

one obtains for K ~ ~ / K ~ ~ M 1 relation (19) for the electric dipole moment of a diatomic cation endowed with polarity ['AB-1'. When we identify A = H or D and B = Kr the parameter = 0.01 1573 5; hence the absolute experimental values of lgol = 0.5545 and IgAl = 0.2791 produce mg(R) - m'g(R)' = 0.003 210 8 and a positive value of po = 0.9801 D at the polarity [-KrH']+ confirmed by the ab initio calculations of

84

Rosmus and Reinsch [lo]. For A = 84Kr and B = H or D, parameter tcn0 changes sign, and consequently po = -0.9801 D has a negative sign, as it should. Appli- cation of the negative experimental values of go and g; yields the negative value of po, suggesting the incorrect polarity ['KrH-1'.

6. Conclusions Radial functions (5)-(8) defining the BO potential,

adiabatic and non-adiabatic effects have been deter- mined from the available spectra of KrH' X'C' for the lowest vibrational transitions u = 0 -+ I , u = I 4 2, so they have physical meaning only in the range 1.2470 < R < 1.8096 x lo-" m. It corresponds to the turning points of potential (3), calculated for the highest analysed rotation-vibrational state u = 2, J = 24 for 84KrH'. It should be noted, however, that BO potential (5) expanded in the variable (4) with a = 1.2031 shows very interesting properties beyond the specified range. (i) For R = 5.4632 x 10-"m the BO potential reaches a small maximum of 4.792eV, which agrees in the range of quoted error with the experimental dissociation energy D, = 4.805(30) eV for 84KrH' [33]. (ii) For R -+ 03, it tends to a value V ( m ) = 2.424eV. (iii) For R = 0.2399 x 10-"m, it takes an infinite value.

For comparison, the Simon-Parr-Finlan potential (a = I ) for R = 7.0165 x 10-"m reaches a small max- imum of 5.087eV, and for R + 00 tends to a value V ( m ) = 4.343 eV. The Ogilvie-Tipping (a = 0.5) and Dunham (a = 0) potentials for R + m tend to V(m) = 131.401 eV and V ( m ) = m, respectively; they are endowed with unphysical long range properties restricting their applicability in the spectral analysis of the KrH' data.

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3552 Parameters of' KrHfX'2?

As follows from properties (ip(iii) above, the BO potential determined for a = 1.2031 from the KrH' spectrum should correctly reproduce the rotation- vibrational transitions over a much greater range of vibration-rotational excitations (corresponding to 0.2399 d R d 5.4632 x m) than the currently available KrH' data. This fact will enable a search for unkown spectral lines over a much greater range of Zxcitations than hitherto studied.

The dipole moment of KrH' X 'C' has been deter- mined here from the highly resolved IR and MW spectra without the application of Stark and Zeeman effects at an accuracy of 0 = 0.04 D and 0 = 0.1 D, respectively; they are better than 0 = 0.3 D achieved in the experi- ment [7]. The estimated rotational g factor 90 = 0.576( 12) of s4KrHf differs from the absolute Zxperimental value go = 0.5545 by about 3%, and from the relativistic ab initio value go = 0.6082 by about 5%. The results obtained for ArH' [15] and KrH' indicate that not only the magnitude but also the sign of the rotational g factor and dipolar moment 3f diatomic ions can be deduced from the spectra; this nformation is difficult to acquire otherwise.

References [ l ] JOHNS, J. W. C., 1984, J. molec. Spectrosc., 106, 124. [2] WATSON, J. K. G., 1980, J. molec. Spectrosc., 45, 99. [3] WARNER, H. E., CONNER, W. T., and WOODS, R. C.,

[4] PETERSON, K. A., PETRMICHL, R. H., MCCLAIN, R. L.,

IS] DUNHAM, J. L., 1932, Phys. Rev., 41, 721, 713. [6] SURKUS, A., 1994, Spectrochim. Acta A, 50, 2391. [7] LINNARTZ, H., HAVENITH, M., ZWART, E., MEERTS,

W. E., and TER MEULEN, J. J., 1992, J. molec. Spectrosc., 153, 710.

[8] TOWNES, C. H., DOUSMANIS, R. L., WHITE, R. L., and SCHWARZ, R. F., 1955, Discuss. Faraday Soc., 19, 56.

[9] ENEVOLDSEN, T., RASMUSSEN, T., and SAUER, S. P. A., 2001, J. chem. Phys., 114, 84.

1984, J. chem. Phys., 81, 5413.

and WOODS, R. C., 1991, J. chem. Phys., 95, 2352.

[lo] ROSMUS, P., and REINSCH, E. A., 1980, Z. Naturforsch., a35, 1066.

[l I ] LINNARTZ, H., ZINK, L. R., and EVENSON, K. M., 1997, J. molec. Spectrosc., 184, 56.

[I21 ODASHIMA, H., MATSUSHIMA, F., KOZATO, A., TSUNEKAWA, S., TAKAGI, K., and LINNARTZ, H., 1998, J. molec. Spectrosc., 190, 107.

[13] MOLSKI, M., 1999, J. phys. Chem., 103, 5269. [14] MOLSKI, M., 1999, Chem. Phys. Lett., 306, 88. [15] MOLSKI, M., 2001, Chem. Phys. Lefi . , 342, 293. [I61 OGILVIE, J. F., 1998, The Vibrational and Rotational

Spectrometry of Diatomic Molecules (London: Academic Press).

[I71 SAUER, S. P. A,, and OGILVIE, J. F., 1994, J. phys. Chem., 98, 8617.

[18] GEERTSEN, J., and SCUSERIA, G. E., 1989, J. chem. Phys., 90, 6486.

[I91 LAUGHLIN, K. B., BLAKE, G. A., COHEN, R. C., and SAYKALLY, R. J., 1989, J. chem. Phys., 90, 1358.

[20] OGILVIE, J. F., 2001, Chem. Phys. Lett., 348, 447. [21] OGILVIE, J. F., and LIAO, S. C., 1994, Chem. Phys. Lett.,

[22] OGILVIE, J. F., 1996, J . molec. Spectrosc., 180, 193. [23] MOLSKI, M., 1997, J. molec. Spectrosc., 185, 256. [24] OGILVIE, J. F., and MOLSKI, M., 1999, Spectrochim. Acta

[25] COXON, J. A,, and MOLSKI, M., 2001, Phys. Chem.

[26] COXON, J. A., and MOLSKI, M., 2002, Spectrochim. Acta

[27] COXON, J. A., and MOLSKI, M., unpublished. [28] HERMAN, R. M., and OGILVIE, J. F., 1998, Adv. chem.

[29] MOLSKI, M., 1999, J. molec. Specirosc., 193, 244. [30] OGILVIE, J. F., Proc. R . SOC. Lond. A, 378, 287. [31] SIMONS, G., PARR, R. G., and FINLAN, J. M., 1973, J.

[32] MOLSKI, M., 1997, J. molec. Spectrosc., 182, 1. [33] HOTOP, H., ROTH, T. E., RUF, M.-W., and YENCHA,

A. J., 1998, Theoret. Chem. Accounts, 100, 36. [34] MOLSKI, M., 2001, Poster H29 presented at the 17th

Colloquium on High Resolution Molecular Spectroscopy, Nijmegen.

226, 28 1.

A, 55, 1427.

Commun., 20, 1.

A, in press.

Phys., 103, 287.

chem. Phys., 59, 3229.

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