Jonathan Tennyson and Brian T. Sutcliffe- Calculated ro-vibrational spectrum of H2D^+

8/3/2019 Jonathan Tennyson and Brian T. Sutcliffe- Calculated ro-vibrational spectrum of H2D^+

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MOLECULARPHYSICS,1985, VOL. 54, No . 1,141 144

C a l c u l a t e d r o - v i b r a t i o n a l s p e c t r u m o f H 2 D +by JO N A T H A N T E N N Y S O N

Science and Engineering Research Council, Daresbury, Warrington WA4 4AD,England

and BRIAN T. SUT CLI FFEDepar tment of Chemistry, University of York, Heslington, York YO1 5DD,

England(Receive d 30 Ju ly 1984 ; accepted 11 Septemb er 1984)

Ab initio data for the rotational levels of the (0, 0, 0), (0, 1, 0) and (0, 0, 1)states of H2 D+ are fitted and assignments suggested for the spectrum of Shy,Farley and Wing (1981, Phys. Rev., A, 24, 1146).

In a recent paper, I, we published an ab initio study on the ro-vibrationallevels of H~ and H2 D+ [1]. For H +, fitted rotational parameters were computedin excellent agreement with those obtained experimentally by Oka [2]. Theresults on H2 D+ are of particular interest because of the spe ctrum recorded byShy, Farley and Win g (S FW) [3] in the region of the v z and v 3 fundame ntalswhich arise when the vE fun dam ent al of H~- is split by deutera tion. As yet neithervibrational nor rotational assignments have been made to this spectrum, but sinceI, Aman o and Wa tson [4] have recorded data for the v I band of HzD + in goodagreement with our predictions.

The interest in this problem led us to re-interpret our previous results for thelowest 3 vibrational states of H2 D+. In do ing so it became appa rent that thestrong mixing and overlap between rotational levels belonging to the v z and v3fundamentals makes vibrational assignments for these levels peculiarly problem-atic. I n particular, some of the v z rotational levels given in I were incorrectlyassigned.

In this note we present fits for levels of the lowest 3 vibrational states ofH2 D+. Com bin ed fits to the v2 and v3 levels were performed without any priorvibrational assignment. This allows us to assign correctly ro-vibrational data forour calculated states with J ~ 4. It also allows us to generate a list of transitionsbetween higher rotational states and hence make tentative assignments to thetransitions observed by SFW. We hope that the parameters will also aid in theassignment of other regions of the spectrum of this highly asymmetric (K-~-0"07) molecule.

Table 1 presents rotational parameters for the ground, v z and v3 vibrationalstates. These were obtained by minimizing the energy mismatch between laddersof levels with a particular J and symmetry. This fit is very satisfactory as itreproduces the ab initio data to well within the accuracy of the calculation.

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142

Table 1 .

J . T e n n y s o n a n d B . T . S u t c l i f f e

Rota t iona l cons t an ts in cm-1 for the lowes t 3 v ib ra t iona l s ta tes o f H2D +Ground s ta te V 2 V 3

ABCA jAjKAK5j5K

[ 4 ] T h i s w o r k T h i s w o r k T h i s w o r k43"362 43'391 42'1 50 46"49929.14 3 29"095 30"450 27"63316'6 10 16"580 14"110 17-418

0.001 0.010 0"004 0-018--0.008 0-0 -0 "0 10 0.007

0.032 0"030 0.048 0.0300.004 0.002 0-051 -0 .0 010.020 00 09 0"073 0.012

Ban d orig ins 2184"0 2309"7scaled+ 2207.9 2335.0C o u p l i n g c o n s t a n t s { G 2 3 = - - 25'615

F23 = --1" 685o b s + t a l c +"~ Ad ju st ed by v e (H 3 ) / v E (H a ), see text.

+ See [-5].

Tab le 2 . Low- ly i ng ro ta t iona l s ta tes o f H2D +I ' 2 Y 3J r k j ? Freq uen cy/c m- 1 j t F r e q u e n c y / c m - 1

+ 1 1 f O 72"5 e 74 '01 - - 1 0 e e 40' 6 o 48 '6

0 1 e o 52"6 e 67"8+1 2 e e 209' 2 o 233'9

0 1 f o 173"3 e 177"02 -- 2 0 e e 111"9 o 142"6

-- 1 1 e o 116"1 e 156"4+ 2 2 e e 221"1 o 234"8+3 3 f o 450'1 e 487 '0

0 2 f e 33 2' 9 o 375"7-- 1 1 f o 314"0 e 328"6

3 --3 0 e e 208-8 o 275.8-- 2 1 ~ o 209"7 e 284"2+ 1 2 e e 374-3 o 382.0+ 2 3 e o 445' 1 e 487-1+ 3 4 f e 758"9 o 826-0+ 2 3 f o 647.3 e 675. 4--1 2 f e 491"8 o 56 01--2 1 f o 484.0 e 524.6

4 -- 4 0 ~ e 333 '4 o 442"6-- 3 1 e o 333.2 e 442 .0

0 2 e e 582 .0 o 579 .9+ 1 3 e o 624. 4 e 67 5'0+4 4 e e 76 03 o 825.9

~" Par ity of j in the ba sis : e = e ven , o = odd .

8/3/2019 Jonathan Tennyson and Brian T. Sutcliffe- Calculated ro-vibrational spectrum of H2D^+

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Ro-vibr ational spectrum of H zD + 1 4 3

e~:Z

r

+a

9

I I I I I 1 + + 1 +

I I I I 1 1 + + 1 +

t ' q c q r , -~

09

e~

e"2

0

r

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1 4 4 J . T e n n y s o n a n d B . T . S u t c li f feT a b l e 2 s h o w s t h e ab in i t io d a t a u s e d i n t h e v2/v a f it w i t h a s s i g n m e n t s t a k e n

f r o m t h e f it . T h i s t a b l e t h u s u p d a t e s t a b l e 8 o f I.U s i n g t h e f it w e h a v e g e n e r a t e d a f u ll s p e c t r u m f o r t h e v 2 a n d v 3 b a n d s

i n v o l v i n g J ~< 8 . T o d o t h i s w e h a v e s c a l e d th e b a n d o r i g i n s b y t h e e r r o r b e t w e e nt h e c a l c u l a t e d a n d o b s e r v e d v a l u e f o r th e v E b a n d i n H f , a b o u t 1 p e r c e n t . A l i sto f t r a n s i t io n s m a y b e o b t a i n e d f r o m t h e a ut ho rs ~ " b u t i n a n y ca s e c a n b e c o m p u t e df r o m t h e p a r a m e t e r s o f t a b le 1 .

T a b l e 3 s h o w s t h e p a r t s o f t h e s p e c t r u m w h i c h l ie n e a r t h e t ra n s i t io n s r e c o r d -e d b y S F W . F o r c o m p a r i s o n w e a ls o g i v e t h e o b s e r v e d i n t e n s i ty r a t io s o f t h ed o u b l e t s a n d o n e s c a l c u l a t e d f r o m a 3 : 1 r a t io b e t w e e n t h e o r t h o a n d p a r a H 2 i nH 2 D + . A l t h o u g h e r r o r s i n t h e c a l c u l a t e d t r a n s i t i o n f r e q u e n c i e s o f a b o u t 3 c m - 1m e a n t h a t o u r a s s i g n m e n t s c a n o n l y b e t e n t a ti v e , t h e a g r e e m e n t b e t w e e n t h ee x p e r i m e n t a l a n d c a l c u l a t e d i n t e n s i ty r a t io s m u s t t e n d t o c o n f i r m t h e a s s i g n -m e n t s .

W e a r e g r a t e f u l t o D r . J . K . G . W a t s o n f o r h i s c r it ic a l c o m m e n t s o n o u rp r e v i o u s r e s u l t s a n d a p r e p r i n t .

REFERENCESF1] TENNYSON,J . , and SVTCLIFFE,B . T . , 1 9 8 4 , Molec. Phys. , 5 1 , 8 8 7 .[2 ] O~:A, T . , 1980 , Phys . Rev . Le t t . , 45, 531.[ 3 ] S I~ v , J . - T . , FA RL EY , J . W . , a n d W I N C , W . H . , 1 9 8 1 , Phy s . Re v . , 24, 1146.[4 ] AMANO , T . , and WATSON, J . K . G . , 1984 , J . chem. Phys. ( in the p re ss ) .[5 ] B ARBE, A . , SECROU N, C. , JOUVE, P. , MO NNA NTEU IL, N . , DEPANNEMAECKER, J . ,DUTERAGE, B., BELLET, J. , an d PINSO N, P., 1977 , J. molec. Spectrosc., 64, 343.

t T h i s r e p l a c e s t a b le 9 i n I , w h i c h b e s i d e s p r o b l e m s w i t h a s s ig n m e n t s , c o n t a i n s s e v e ra lt y p o g r a p h i c a l e r r o r s .