steven miller et al- first principles calculation of rotational and ro-vibrational line strengths:...

8/3/2019 Steven Miller et al- First principles calculation of rotational and ro-vibrational line strengths: Spectra for H2D^+ and

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MOLECULAR PHYSICS,1989, VOL. 66, N o. 2 , 42 9- 45 6

F i r s t p r i n c i p le s c a l c u l a t i on o f r o t a t i on a l an dro-v ibrat ional l ine s trengthsS p e ct ra f or H 2 D + a n d D 2 H +

b y S T E V E N M I L L E R a n d J O N A T H A N T E N N Y S O ND e p a r t m e n t o f P h y s ic s a n d A s t r o n o m y , U n i v e r s i ty C o l le g e L o n d o n ,

G o w e r S tr ee t, L o n d o n W C 1 E 6 B T , E n g l a n da n d B R I A N T . S U T C L I F F E

D e p a r t m e n t o f C h e m i s t r y , U n i v e r si ty o f Y o r k ,Y o r k Y O 1 5 D D , E n g la n d(Received 2 Au gu st 1988; accepted 5 October 1988)

Th eory i s developed for the ca lcula tion o f d ipole t rans i t ion l ine s t rengthsand frequencies for rotat ional and ro-vibrat ional t ransi t ions from wavefunc-t ions expressed in the general ized bod y-f ixed co-ord inates pro po sed by Sutcl iffeand Tennyson (1986 , Molec. Phys., 58, 1053) . Com puta t ions us ing th is theorypro du ce calculated frequencies for the fund am ental ro-vibra t ional t ransi t ions ofH 2D+ and D2 H in very go od ag reem ent with experiment. Th ese fi rs t pr in-ciples calculat ions use the highly accurate ab initio elec tronic potent ia l energyand dipole sur face of Meyer , Botschwina and Bur ton, which has previous lybeen shown by the authors to give ro-vibrat ional t ransi t ion frequencies, rota-t ional cons tants an d vibra t ional fundam enta l s of spect roscopic accuracy. Thre el ine reassignments are pro pos ed o n frequen cy considerat ions. Several t ran-s it ions a re propose d as candidates for observat ion on the groun ds o f com putedrelat ive intensi t ies . Calculated pure rotat ional t ransi t ions in ground state forH2D+ an d D2 H+ are in excellent agreement with limited data available, andthe ful l rotat ion al sp ectra o f these m olecules are predicted.

1 . I n t r o d u c t i o nR e c e n t a d v a n c e s i n e x p e r i m e n t a l t e c h n i q u e s h a v e e n a b l e d t h e i n f r a r e d a n dm i c r o w a v e s p e c t r a o f m a n y n e w s p e ci es t o b e m e a s u r e d . I n p a r t i c u la r , t h e r e isc u r r e n t l y g r e a t i n t e r e s t i n m o l e c u l a r i o n s w h i c h h a v e n o t o n l y l a b o r a t o r y a n di n d u s t r ia l r e l ev a n c e , b u t a r e c o n s i d e r e d t o b e i m p o r t a n t i n u n d e r s t a n d i n g t h e c h e m i -c a l p a t h w a y s i n t h e i n t e rs t e l la r g a s c l o u d s w h i c h o c c u p y v a s t r e g i o n s o f t h e g a l a x y .

O n e s u c h m o l e c u l a r i o n is H , w h o s e i n f r a r e d s p e c t r u m w a s f i r s t m e a s u r e d b yO k a i n 1 9 80 [ 1 ] . S i n ce t h e n t h e r e h a v e b e e n s e v e ra l s p e c t ro s c o p i c s tu d i e s n o t o n l yo f H ~ i ts e lf , b u t o f i ts d e u t e r a t e d i s o t o p o m e r s D ~ -, f i rs t o b s e r v e d a t t h e s a m e t i m e a sH ~ b y S h y et al . [ 2 ], H 2 D + a n d D 2 H + , i n t h e i n fr a r e d r eg i o n [ 3 - 1 0 ] . H ~ h a s a ne q u i l i b r i u m g e o m e t r y w h i c h is a n e q u i l a te r a l t ri a n g le , g iv i n g H ~ a n d D ~ D3h s y m -m e t r y , a n d H 2 D + a n d D 2 H C 2v s y m m e t r y .

F o r t h e Dab t r i a t o m i c s t h e o n l y f u n d a m e n t a l w h i c h i s i n f r a r e d a c t i v e i s t h ed e g e n e r a t e v2 m o d e . T h e a b s e n c e o f a p e r m a n e n t d i p o l e m e a n s t h a t , i n t h e s t a n d a r da p p r o x i m a t i o n , p u r e r o t a t i o n a l t r a n s i ti o n s a r e ' f o r b i d d e n '. T h e p o s s i b il it y o f d e t e c t -i n g t h e s e ' f o r b i d d e n ' r o t a t i o n a l s p e c t r u m h a s b e e n d i s c u ss e d e ls e w h e r e [ 11 , 1 2 ].

A l l th r e e f u n d a m e n t a l v i b r a t io n s , v l , v2 a n d v 3 , a r e i n f ra r e d a c t i v e f o r H 2 D + a n d0026-8976/89 $3.00 9 1989 Taylor & Francis Ltd


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430 S. M il ler e t a l .D2 H +. S ince the re i s a pe rm anen t d ipo le in the g ro und s t a te , due to the no n-co inc idence o f t he cen t re o f cha rge and the cen t re o f mass , t he re i s a l so the poss i -b i l it y o f obse rv ing p ure ro t a t iona l t r ans it i ons . T o da te , h ow ever , on ly th ree l ines o ft h e H2 D sp e c t r u m h a v e b e e n m e a su r e d [ 1 3 -1 6 3 , a n d o n e o f D2 H [ 1 6 ] .As we l l a s t he expe r imenta l i nves t iga t ions , t he re have been seve ra l t heore t i ca ls tud ie s o f t he ro -v ib ra t iona l ene rgy l eve ls o f t hese molecu les spann ing a pe r iod o f 15y e a r s [ 1 7 - 2 4 ] , u s i ng a n u m b e r o f d i ff e re n t a b i n i t i o poten t i a l ene rgy su r faces [17 ,2 5 - 2 7 ] .

I n t h e la s t fe w y e a rs , we h a v e e m p l o y e d a p o t e n t ia l d u e t o M e y e r e t a l . ( M B B )[27] w hich has p ro ved ex t reme ly accura t e fo r ca lcu la t ions o f t he v ib ra t iona l fund a -menta l s . Our s tud ie s showed tha t i t a l so gave exce l l en t r e su l t s fo r t he ro t a t iona lene rgy l eve l s and cons tan t s o f a ll four molecu les in com par i s on wi th expe r imen t[24] . W e have used the M BB po ten t i a l t o p red ic t ro -v ib ra t iona l ene rgy l eve ls i n theove r to ne mani fo lds o f H ~ up to 3v2 [28] , and these have led to the success fu li d e n ti f ic a t io n o f b o t h o v e r t o n e [ 2 9 ] a n d ' h o t b a n d ' [ 3 0 ] t r a ns i ti o n s.

O ne v i t a l p i ece o f i n fo rm a t ion which can be fu rn i shed by theore t i ca l s tud ies , bu twhich i s di f fi cu lt t o ex t rac t f rom the expe r im enta l m easure me nt s m ade so fa r, is a se to f accura t e l ine s t r eng ths fo r t he ro t a t iona l o r ro -v ib ra t iona l t r ans i ti ons o f i n te re s t.I n t h i s p a p e r we g e n e r a l i z e t h e t h e o r y d e v e l o p e d b y B r o o k s e t a l . [31] fo r t hec a l c u la t io n o f l in e s t re n g t h s f r o m t h e wa v e f u n c t i o n g e n e r a te d b y t h e m e t h o d o fSutc l i f fe and Tennyson (ST) [19, 23] .

W e p r e se n t c o m p a r i so n s o f t r a n s it i o n f r eq u e n c ie s fo r t h e i n f ra r e d f u n d a m e n t a l so f H2 D + a n d D2 H + wi t h t h o se m e a su r e d e x p e r i m e n t a ll y a l o n g s id e t h e p r e d i c t e dl ine s t r eng ths . Ca lcu la t ed f requenc ie s and l ine s t r eng ths fo r t he pure ro t a t iona lg ro und s t a t e t r ans i t ions a re a l so g iven .

2. TheoryT h e ST m e t h o d e m p l o y s a g e n e ra li z ed sy s t e m o f i n te r n a l m o l e c u l a r c o - o r d i n a te s

[23] , d i s t ances r l and r 2 , and the ang le b e tw een them, 0 . In sca t t e ring co-ord ina te s ,r l i s t h e b o n d b e t we e n t w o o f t h e a t o m s a n d r2 is t h e li ne j o i n i n g t h e m i d p o i n t o f r~a n d t h e t h i r d a t o m . I n b o n d - l e n g t h / b o n d - a n g l e c o - o r d i n a t e s [ 3 2 ] , t wo b o n d s a n dthe inc luded ang le a re chosen . Othe r cho ices a re a l so poss ib l e [23] . The ro -v i b r a ti o n a l wa v e f u n c t i o n s c o m p u t e d i n th i s m e t h o d a r e e x p a n d e d i n t e rm s o f a b a s isse t which cons i s t s o f p ro du c t s o f angu la r and rad ia l func t ions .

T h e a n g u l a r f u n c t io n s c h o se n a r e t h e C o n d o n a n d Sh o r t l e y O j k ( 0 ) f u n c ti o n s ,coup led w i th the usua l W igner ro t a t ion ma t r i ces D~k(~t, f l, ~ ) [33] . The to t a l angu la rm om entu m i s g iven by J , wi th k i t s p ro jec t ion o n the bo dy- f ixed z -axis . Th e wav e-f u n c t i o n s a r e sy m m e t r i z e d a c c o r d i n g t o t h e u su a l W a n g o p e r a t o r s , u s i n g t h e sy m -m e t r y q u a n t u m n u m b e r p wh i c h c a n t a k e o n t h e v a l u e s s o f 0 o r 1 . W i t h t h issym m etr iza t io n k i s then se t to [ k I, wi th p ~< k ~< J . Th e w ave fun ct ion h as an overa l lp a r i ty g i v e n b y ( - 1 ) s T h e su b sc r i p t M sp a n s t h e m a g n e t i c su b - le v e ls o f t h ewavefunc t ion . The angu la r b as i s se t i f t hen g iven by( 2 J + 1'~ 1/2I J M, k , j , p ) = \ ~ j O~o(0)D~tJo(~t, l, ),), k = 0 , p = 0 ;

- - -k/ '2J q - 1 ' ~ 1 / 2 I 2-- t - 1~ ~ ) (1/2) / {| fl, y)+ ( - - 1)POj_k(O)D~tJk(Ot, f l , ~)}, k > 0, p = 0, 1. (1)


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C a l c u l a t i o n o f r o t a t i o n a l a n d to - v i b r a t i o n a l l in e s t r e n g t h s 43 1T h e r a d i a l p a r t o f t h e w a v e f u n c t i o n i s r e p r e s e n t e d b y ~ m ( r l ) ~ n ( r 2 ) , h i c h c a n b e

M o r s e - o s c i l l a t o r - l i k e f u n c t i o n s o r o t h e r s u i t a b l e r a d i a l f u n c t i o n s [ 1 9 ] . W c d e f i n eI n , m ) = ~ m ( r l) ~ n ( r2 ) . (2)T h e n t h e / t h c i g en f u n c ti o n o f t h e J t h a n g u l a r m o m e n t u m l ev el w i th p a r i t y p isg iven by :

JI J u , P , l > = ~ ~ d ~ ' l J u , k, j , p > Im , n >k = p jamJ= Z Z flJMpl9kjm. x I J~ t, k, j, m, n, p ). (3)k= p jmn

T h e l i n e s t r en g t h S ( f - / ) o f a p a r t i cu l a r t r an s i ti o n f ro m i n it ia l s ta t e i t o a f in a ls t a t e f i s g i v e n b yS ( f - i) = Z ~ -v M '~ ",~ 2i f ] , (4)M'M"r

w h e r eT ~ r u ' * - ' l' " , p " , I " >i f - < J M ' , P ', [ # ~ i J M " ( 5 )

a n d / ~ i s t h e z c o m p o n e n t o f t h e s p a c e - f i x e d d i p o l e m o m e n t .I n t h e S T m e t h o d , t h e m o l e c u l a r z - a x i s i s f i x e d a l o n g e i t h e r r ~ o r r , a n d t h e

x - a x i s p e r p e n d i c u l a r t o z i n t h e p l a n e o f t h e m o l e c u l e . F o r a t r i a t o m i c m o l e c u l e ,t h e r e f o r e , o n l y t h e z a n d x c o m p o n e n t s o f t h e b o d y - f i x e d d i p o l e m o m e n t a r e n o n -zero .F o l l o wi n g B ro ck s e t a l . [3 1 ] we ex p an d t h e m o l ecu l a r b o d y - f i x ed d i p o l e :

/~ zm ( rl, r 2 , 0 ) = ~ B x , 0 ( r l , r 2 ) P ~ 0 ) ( 6 )4 = 0a n d

m# x ( r l , r 2 , 0 ) - --I t i s con ven ien t to de f ine

Z 1 4 , l ( r l , r 2 ) P ~ ( c o s 0 ) . ( 7 )4 = 1

2 '~/2~ , ' ( r l , r 2 , 0 ) = ~ = o~ \ 2 - 2 - ~ } B ~ , o ( rx , r 2 ) O ~ , o ( 0 ), v = 0 ;( 1 ~ ' / "= 2 = ~ 1 ~ 2 - - - ~ - - I / [ ~ ( ~ {- ) ] I / 2 B 2 ' ( r l' 2 ) O A ' ( 0) ' v ~--- I , ( 8 )

w i t h B 4 , _ 1 ( ri , r 2 ) -- B z , + i (r l , r 2 ) f o r a l l v a l u e s o f LT h e r e l a t i o n b e t w e e n 0 4 , v (0 ) a n d t h e ( a s s o c i a t e d ) L e g c n d r e p o l y n o m i a l s u s e d t o

e x p a n d t h e c a r t e s i a n c o m p o n e n t s o f t h e b o d y - f i x e d d i p o l e m a y b e o b t a i n e d v i a t h es p h e r i c a l h a r m o n i c Y , , v (0 , 0 ) a c c o r d i n g t o t h e d e f i n i t i o n u s e d b y B r i n k a n d S a t c h l c r[ 3 3 ] . T h i s l e a d s t o

~ t ~ ( r l , r 2 , 0 ) ---- / Z z m ( rl , r 2 , 0 ) , (9 )a n d

/ ~ ( r l , r 2 , 0 ) - - T ( I / 2 p / 2 ~ r l , r 2 , 0 ) . ( 1 0 )


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432 S . M i l l e r e t a l .T h e b o d y - fi x e d d i p o le m o m e n t , H m ( r , , r 2 , 0 ) , t r a n s f o r m s a s a t e n s o r o f r a n k o n e

i n t o s p a c e - fi x e d c o - o r d i n a t c s [ 3 1 ] a n d w c c a n t h e r e f o r e w r i t e+ 1

m , 11: , = ~ # v( rz , r2 , O)D , ,v(c t , f l , ?) . (11)v = - 1

T h e i n d iv i d u al c o m p o n e n t s T ~ ' u ' ' m a y n o w b e c a lc u l at e d f ro mT ~ " u '" = ( J ' u . , P ', l ' l l ~ l J h . . , p " , 1">

+ l J ' J "= Z r. Z Z Zv = - - 1 k ' = p " j ' m ' n ' k " = p " j " m " n "

x ( J u ' , k ' , j ' , m ' , n ' , I m , n ,p , 0,ran*, t . . . . j , , . . . . p , ,> .~,~ ,-- ,. ~ - M , , , k , ( 1 2 )T h e e x p a n s i o n o f t h e d i p o l e m o m e n t g i ve n in e q u a t i o n ( 8) c o u p l e d w i t h t h ee x p li ci t f o r m o f t h e w a v e f u n c t i o n i n e q u a t i o n (3 ) m e a n s t h a t t h e r a d i a l a n d a n g u l a r

i n t e g r a l s i n e q u a t i o n ( 1 2 ) m a y b e e v a l u a t e d s e p a r a t e l y . T a k i n g t h e r a d i a l i n t e g r a l sf ir s t, w e m a y d e f i n e

m'm"n': (13)~ . ~ = ( m ' , n ' l B ~ . ~ ( r, , r 2 ) l m " , n " > .T u r n i n g t o t h e a n g u l a r i n t e g r a t i o n , it is p o s si b le t o s e p a r a t e t h i s i n t o t h o s e p a r t s

i n v o l v i n g t h e i n t e g r a l a n g l e 0 a n d t h o s e i n v o l v i n g t h e W i g n e r a n g l e s 0 t, f l, ? . U s i n gt h e c o n v e n t i o n s o f B r i n k a n d S a t c h le r [ 3 3 ] a n d a l l o w i n g f o r t h e p h a s e f a c t o rsi n t r o d u c e d b y t h e S T c h o i c e o f ba s is f u n c t i o n s , w e h a v e

l J " J 'Z Z Z Z Z ~k ,j ,m , n, t~k,, j ,,m, , n-v = - - I 2 = I v I k " = p " k ' = p " j ' j "

x ( J M ' , k , g , P ' l * ' . . . .. . . | ,( O)O~ . ~ ( ~ , f l , ? )l J u " , k , j " , p" >(- 1 ) u '- ~ [(2 J' + 1X2J" + 1)] ' /2

1 J " j ,x E Z Z ~. ~, a( v , v + k",A)[(2j ' + 1X2j" + 1 ) 3 ' / 2v = - x A = l vl k " = p " k ' = p " j " j '( , ,x - M ' z k ' v"}

l p ,,+ p , J ' 1 J " ~ O '+ ( - - ) - k ' v k " ] \ O

( - 1 )u '2 [(2 J' + 1)(2J" + 1)] 1/2I J " J '

- k " ] \ O 0 0 ] \ k ' v - k ' ]

0 0 ] \ - k ' v k " J . J rl',, , ',; k":,,,",,"

x Z Z ~ Z Z a ( v , v + k " , 2 ) [ ( 2 j ' + I X 2 j " + l ) ] ~/2v = - - 1 2 = I v I k " = p " k ' = p ' j ' j "

x ( J ' 1 J " ~ ( J ' 1 J " ~ ( j ' 2 j " ~ ( j ' 2 j " ~\ - - M ' z M " l \ - k ' v k " / \ O 0 0 / \ - k ' v k " /, tJ 'M'p'r, ts"M"p"r" [ ( 1 ) J " + l ' + ,x "k 'ym'n" "/"~",."," X -- + (- - 1) (14)

w h e r e th e s e c o n d e x p r e s s io n is o b t a i n e d b y m a n i p u l a t i o n o f t h e 3 - j s y m b o l s a n dr e o r d e r i n g t h e s u m m a t i o n o v e r v . ( N o t e t h a t t h e r e i s n o p h a s e d e p e n d e n c e o n( - 1 )~ ' + ~ + j' s in c e t h is m u s t b e e v e n f o r t h e i n t e g r a l s n o t t o v a n i s h .)


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Cal cu l a t i on o f r o t a t i ona l and t o - v i b r a t i ona l l ine s tr eng t hs 4 3 3I n e q u a t i o n ( 1 4 )

a(0, n, 2) = 1, O


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434 S . M i l l e r e t a l .f r e q u e n c y i n c m - 1, g~ i s t h e s p i n - p l u s - s y m m e t r y d e g e n e r a c y o f t h e i n i t i a l s t a te , E " i st h e e n e r g y o f th e i n i t i a l s t a te , h i s P l a n c k ' s c o n s t a n t , k i s B o l t z m a n n ' s c o n s t a n t , T i st h e t e m p e r a t u r e , a n d t h e p a r t i t i o n f u n c t i o n , Q , i s g i v e n b y

Q = ~ g i ( 2 J , + 1) exp ( - e i / k T ) . (18)i

T h e E i n s t e in A i f c o e f f ic i e n t f o r s p o n t a n e o u s e m i s s i o n is g i v e n b y1 64n2~162S (f - - i). (19)A i f - ( 2 J f + 1) 3h

3 . C o m p u t a t i o n a l d e t a i l sF o r t h is s t u d y o f H 2 D + a n d D 2 H + w e u s e d t h e c o r r e c te d M P - 7 / 8 7 C G T Op o t e n t i a l e n e r g y a n d d i p o l e s u r f a c e s o f M e y e r e t a l . [ 2 7 ] . T h e c o - o r d i n a t e s y s t e m

c h o s e n w a s t h e s c a t t e r in g c o - o r d i n a t e s u s e d i n o u r p r e v i o u s s t u d y [ 2 4 ] o f t h e sem o l e c u l e s , w i t h t h e m o l e c u l a r z - a x is f i xe d a l o n g r 2 f o r H 2 D + a n d a l o n g r 1 f o rD 2 H + .E i g e n v a lu e s a n d w a v e f u n c t i o n s w e r e c a lc u l a t e d u s i n g t h e s u i te o f p r o g r a m sT R I A T O M , S E L E C T a n d R O T L E V D . F u l l d e ta il s o f t h e f ir st t w o p r o g r a m s , a sw e ll a s m o s t o f t h o s e o f R O T L E V D , h a v e b e e n g i v e n e l se w h e r e [ 3 5] . T h e r e h a v eb e e n a n u m b e r o f r e f i n e m e n t s t o t h i s p r o g r a m s u i te i n th e p a s t f ew y e a r s [ 36 ] , a n da n u p d a t e d v e r s i o n w i l l b e p u b l i s h e d s h o r t l y [ 3 7 ] . T h e s e c a l c u l a t i o n s e m p l o y t h et w o - s t e p v a r i a t i o n a l t e c h n i q u e o f T e n n y s o n a n d S u t c li f fe ( se e, fo r e x a m p l e , [ 3 4 ]) .T h e f i r s t s t e p i n t h i s a p p r o a c h i s t o o p e r a t e o n t h e b a s i s f u n c t i o n s g i v e n i ne q u a t i o n s ( 1)-(3 ) w i t h o n l y t h a t p a r t o f t h e r o - v i b r a t i o n a l h a m i l t o n i a n w h i c h d o e sn o t c o u p l e s t a t e s w i t h d i f f e r e n t v a l u e s o f k. T h i s i s e q u i v a l e n t t o i g n o r i n g o f f -d i a g o n a l C o r i o l i s i n t e ra c t i o n s . A n i n t e r m e d i a t e s e t o f b a s i s f u n c t i o n s is o b t a i n e d

l J , k, p, i> = ~ p J k p i .1~,, _, k, j , m, n, p>. (20)jm n

I n t h e s e c o n d s t ep , t h e fu l l h a m i l t o n i a n , i n c l u d i n g C o r i o l i s c o u p l i n g o f st a t e sw i t h k t o k + 1 , o p e r a t e s o n t h i s i n t e r m e d i a t e b a s i s s e t t o p r o d u c e t h e f i n a l r o -v i b r a t i o n a l w a v e f u n c t i o n s a n d e i g e n en e r g ie s . T h i s g i v e s

I J , P , l > = ~ , b ~ r t i J , k , p , i )k i

- - E E i . I J P I ~ J k p i I .- u u ' ~ jm I , ' , k , m , j , n , p > . ( 2 1 )k i jm n

F r o m t h is it c a n b e s ee n t h a tdJp tj ,~ = Y' . ~J~,l~Jk~,i (2 2)C ' k i ~ j r tm 9

i

T h e s i ze o f t h e i n i t ia l a n d i n t e r m e d i a t e b a s i s s e ts u s e d i s c o n t r o l l e d b y i n p u tp a r a m e t e r s t o t h e p r o g r a m s w h i c h s e t t h e u p p e r l i m i t s o f t h e s u m s o v e r j , m a n d n int h e f i rs t s t ep , a n d i i n t h e s e c o n d . N o t a l l t h e p o s s i b l e c o m b i n a t i o n s o f j , m a n d n a r e,i n p r a c t i c e , n e c e s s a r y t o c o n v e r g e t h e f i r s t s te p . I n s t e a d N s e I m a y b e c h o s e n o n t h eb a s is o f t h e i r e n e r g y o r d e r i n g f o r p a r t i c u l a r v a l u e s o f J , k a n d p [ 3 4 ] . U s u a l l y t h eJ = 0 , k = 0 s e t i s used fo r th i s pur pose .

N o r a r e a l l t h e s o l u t i o n s o f t h e f i r s t s t e p n e c e s s a r i ly n e e d e d f u l l y t o c o n v e r g e t h es e c o n d s t ep . T h e s e t o f i n t e r m e d i a t e b a s is f u n c t i o n s m a y b e c u r t a i l e d e i t h e r b y


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Calcu la t ion o f ro ta t iona l and ro -v ib ra tiona l l ine s t reng th s 435se lec t ing th e N k f u n c t i o n s w i t h l o w e s t e n e r g y f o r e a c h k s u b s e t , o r b y s e l e c t in g t h e Nw i t h l o w e s t e n e r g y , i r r e sp e c t iv e o f t h e v a l u e o f k. I n t h e f i r s t c a s e, N k i s t h e s a m e f o re a c h k s u b s e t, b u t t h i s is n o t n e c e s s a r il y so f o r t h e s e c o n d s e l e c ti o n p r o c e d u r e .

I n c o m p u t i n g t h e w a v e f u n c t i o n s a n d e i g e n e n er g ie s f o r H 2 D a n d D 2 H w e s e tt h e m a x i m u m v a l u e s o f m a n d n t o 1 0, a n d o f j t o 2 4 (j ev e n ) o r 2 5 (j o d d ). O f t h es e ,t h e 6 0 0 j , m , n c o m b i n a t i o n s w h i c h g a v e t h e l o w e s t e i g e n e r g ie s fo r J = 0 , k = 0 , je v e n w e r e u s e d t o g e n e r a t e t h e l J , K , j , m , n , p ) u s e d i n t h e f i r st s te p . T h e f i n a lw a v e f u n c t i o n s , l J , p , l ) , w e r e c o m p u t e d f r o m t h e i n t e r m e d i a t e b a s is s e t o b t a i n e d b yt a k i n g t h e 3 0 0 lo w e s t I J , k , p , i ) f o r e a c h k s u b s e t. T h e f i n a l ei g e n e n e r g ie s w e r ec o n v e r g e d t o 0 .1 c m - 1 , o r b e t t e r , f o r t h e e n e r g y l e ve ls c o n s i d e r e d u p t o J = 1 0, w i t hthe J = 0 l eve ls con ve r ged to 0 .001 cm - 1.

T h e t w o d i f f e r e n t u p p e r l i m i t s f o r t h e c a s e s o f j e v e n o r o d d a r i s e b e c a u s e t h e S Tm e t h o d c o m p u t e s t h e e i g e n v al u e s a n d w a v e f u n c t i o n s a r is i n g fr o m t h es e b a si s f u n c-t i o n s i n s e p a r a t e c a l c u l a t i o n s f o r m o l e c u l e s w i t h C 2 o s y m m e t r y o r g r e a t e r . T h e je v e n c a lc u l a t i o n s c o r r e s p o n d t o p a r a -H 2 D + a n d o r t h o -D 2 H + , w i t h t h e n u c l e a r s p i nw e i g h t i n g s , g ns , o f 1 a n d 6 r e s p ec t iv e l y . T h e j o d d c a l c u l a t i o n s g i v e t h e o r th o - H 2 D a n d p a r a -D 2 H w a v e f u n c t i o n s , w i t h g ns = 3 in b o t h c a se s .

T h e t r a n s i t i o n m o m e n t s , l i n e s tr e n g t h s , E i n s t e i n A - c o e ff i ci e n ts a n d i n t e n s it i e sw e re c o m p u t e d u s in g tw o n e w m e m b e r s o f t he T R I A T O M p r o g r a m s uite , D I P O L Ea n d S P E C T R A , w h i c h w i ll b e p u b l is h e d s h o r t l y [ 37 ] . D I P O L E i s d i r e c tl y d r i v e nf ro m i n p u t ge n e ra t ed e it he r b y R O T L E V D o r T R I A T O M a n d s to r e d o n d is k.O u t p u t f r om D I P O L E a n d e ne rg y lev els f ro m R O T L E V D / T R I A T O M d riv eS P E C T R A .D I P O L E h a s m a n y f ea tu r es i n c o m m o n w i th t h a t p a r t o f T R I A T O M w h ic hc o m p u t e s i n t eg r a l s o v e r t h e p o t e n t i a l e n e r g y s u r f ac e , th e m a i n d i ff e r en c e b e i n g d u et o t h e v e c t o r n a t u r e o f t h e d i p o l e s u r f a c e a s a g a i n s t t h e s c a l a r p o t e n t i a l .

A s i s t h e c a s e w i t h t h e i r p o t e n t i a l e n e r g y s u r f a c e , t h e M B B d i p o l e s u r f a c e i se x p r e ss e d i n s y m m e t r y - a d a p t e d , M o r s e - li k e c o - o r d in a t e s . I n o r d e r t o u s e i t toc o m p u t e t r a n s i t i o n m o m e n t s , t h e d i p o l e s u r f a c e h a s f i r s t t o b e t r a n s f o r m e d t o t h es c a t te r i n g c o - o r d i n a te s u s e d t o c a l c u l a te t h e w a v e f u n c t i o n s , a n d t h e n e x p a n d e d a s as u m o f ( a s s o c ia t e d ) L e g e n d r e f u n c t i o n s , t h u s

\(22 2 1'](2-,/(2 V)!v)!I -B~.v(r 1, rz) = l#~( r t , r 2 , u)P~(u) du, (23)w ith v = 0 , Z = z , an d v = 1 , X = x .

I n a n y c o m p u t a t i o n a l p r o c e d u r e , i t i s c l e a r t h a t t h e i n t e g r a n d c a n o n l y b ee v a l u a t e d a t a f i n it e n u m b e r o f p o i n ts . F o r t h e p o t e n t i a l e n e r g y s u r f ac e e x p a n s i o n ,G a u s s - L e g e n d r e i n t e g r a t i o n [ 3 8 ] h a s p r o v e d h i g h l y a c c u r a t e [ 3 5 ]. I n o r d e r t oo b t a i n g o o d c o n v e r g e n c e f o r t h e e x p a n s i o n o f t h e d i p o l e s u r fa c e ( e q u a ti o n s ( 6) a n d( 7)) , h o w e v e r , w e u s e d a G a u s s - J a c o b i q u a d r a t u r e s y s t e m [ 3 8 ] . T h i s re p l a c e s t h ein teg ra l in equ a t io n (23) by a s e r i e s, thu s

(1 -- u)*'(1 + u)#fv(u) du = ~ Avi f,(ui), (24)1 i=1

w h e r e/ . t ~ ( r l , r 2 , u ) P ] ( u )

f ~ ( u ) = ( 1 - - u ) ' ( 1 + u ) # " (25)a n d v a n d X a r e r e l a t e d a s i n e q u a t i o n ( 23 ).


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436 S . M i l l e r e t a l .W e u s e d t h e r o u t i n e s g i v e n b y S t r o u d a n d S e c r e s t [ 3 8 ] t o c o m p u t e t h e i n t e g r a -

t i on p o i n t s , u~ , an d w e i gh t s , A i , w i t h ~t = f l = v . R e p l ac i ng u b y cos 0 t he n g i vesf~(cos 0) = #~( r l ' r2 , cos 0)P,~(cos 0)(sin 0) 2~ (26)

T h i s f o r m o f f ~ ( u ) r e m o v e s a ll o f t h e f a c t o r s o f s in 0 w h i c h o c c u r i n t h e d i p o l ee x p a n s i o n , e n s u r i n g a s e r i e s w h i c h c o n v e r g e s r a p i d l y w i t h i n c r e a s i n g L f o r b o t hc o m p o n e n t s o f t h e d i p o l e s u rf a ce .

I n p r a c t i c e w e u s e d L = 2 2 m ax + 1 , w here 2max = 2 jma~ an d J i nx w as t he l a rges tv a l u e o f j c h o s e n , a s t h is g u a r a n t e e d a c c u r a t e i n t e g r a ls [ 3 9 ] . F o r t h e r a d i a l c o -o r d i n a t e s w e us e d 2 1 - p o in t G a u s s - L a g u e r r e q u a d r a t u r e , w h i c h h a s p r e v io u s l y b e e ns h o w n t o b e m o r e t h a n a d e q u a t e f o r t h e M B B p o t e n t ia l e n e r g y su r fa c e [2 4 ] . U s in gt h e s e i n t e g r a t i o n s c h e m e s , a l l t h e t r a n s i t i o n m o m e n t s w e r e c o n v e r g e d t o a t l e a s tt h r ee s i gn i f i can t f i gu res f o r s t a t e s up t o J = 10.

A l l t h e d a t a p r e s e n t e d i n t h e n e x t s e c t i o n w e r e c o m p u t e d o n t h e C r a y X M P / 4 8a t th e A t l a s C o m p u t i n g C e n t r e a t th e S c i e n c e a n d E n g i n e e r i n g R e s e a r c h C o u n c i l ' sR u t h e r f o r d A p p l e t o n L a b o r a t o r ie s .

4 . R e s u l t sT h e r o t a t i o n a l a n d r o - v i b ra t i o n a l s p e c t ra o f H 2 D a n d D 2 H + a r e e x t r e m e l y

r i c h s in c e t h e p o s s i b i li ty o f o b s e r v i n g t r a n s i t io n s is g o v e r n e d b y p r o p e n s i t y c o n s i d e r -a t i o n s r a t h e r t h a n s t r ic t s e l e c t io n - r u l e s . F o r s t a t e s w i t h J ~< 1 0, w e h a v e c o m p u t e dm o r e t h a n 2 4 0 0 0 l in e s tr e n g t h s f o r e a c h m o l e c u le .

T h e s e l in e s in c l u d e p u r e r o t a t i o n a l t r a n s i t i o n s i n e x c i te d v i b r a t i o n a l s ta t es , o v e r -t o n e r o - v i b r a t i o n a l b a n d s a n d ' h o t b a n d s ' . I n th i s p a p e r , h o w e v e r , w e p r e s e n to n l y t h e r o - v i b r a t i o n a l t r a n s i t i o n s t o t h e f u n d a m e n t a l v i b r a t i o n a l m a n i f o l d s a n d t h ep u r e r o t a t i o n a l s p e c t r u m i n th e g r o u n d s t a te f o r b o t h m o l e c u l e s.

O n e a d v a n t a g e o f t h e o r e t i c a l c a l c u l a t io n s o v e r e x p e r i m e n t a l l y m e a s u r e d s p e c t r ais th a t f u ll k n o w l e d g e c a n b e o b t a i n e d o f t h e q u a n t u m n u m b e r s a s s o c ia t e d w i th a n yt r a n s it i o n . T h i s c a n b e i m p o r t a n t w h e r e , a s th e r e i s i n t h e c a s e o f b o t h H 2 D a n dD 2 H t h e r e is s o m e d i s p u t e a s t o t h e a s s ig n m e n t o f c e r t a i n o b s e r v e d l in e s [ 1 0 ] .T a b l e 1 s h o w s t h e b a n d o r i g in s f o r t h e t h r e e f u n d a m e n t a l t r a n s i ti o n s f o r H 2 D a n d D 2 H o b t a i n e d i n o u r J = 0 c a lc u l a ti o n s c o m p a r e d w i t h th o s e o b t a i n e d f r o mt h e e x p e r im e n t a l d a ta . T h e M B B p o t e n t i a l w a s o p t i m i z e d t o o b t a i n v e r y g o o da g r e e m e n t w i t h t h e v 2 b a n d o r i g i n o f H ~ , a n d t h is is r e fl e c te d i n t h e e x t r e m e l y g o o da g r e e m e n t b e t w e e n t h e c a l c u l a t e d a n d e x p e r i m e n t a l v a l u e s f o r b o t h m o l e c u l e s . O n l yt h e v3 m o d e o f D 2 H d i ff e rs b y m o r e t h a n 0 .5 c m - 1 f r o m t h e e x p e r i m e n t a l v a l u e .I n o r d e r t o m a k e t h e a m o u n t o f d a t a p r e s e n t e d h e re m a n a g e a b l e , w e h a v ei n c l u d e d t r a n s i t i o n s i n o u r t a b l e s o n t h e b a s i s o f t h e i r i n t e n s i t y r e l a t i v e t o t h em a x i m u m o b s e r v e d i n t h e s p e c t r a l r e g i o n o f i n t e r e s t, Ig ol(tO ), a t a p p r o p r i a t e t e m -p e r a t u r e s .

C a l c u l a t e d r o - v i b r a t i o n a l t r a n s i t i o n s f o r th e v 2 / v 3 a n d v 1 m a n i f o l d s f o r H 2 D a r e g i v e n in t a b l e s 2 a n d 3 r e s p e c ti v e l y . F o s t e r e t a l . [ 9 ] , e s t i m a t e t h e t e m p e r a t u r e a tw h i c h t h e i r v 2 / v 3 d a t a w a s o b t a i n e d a t a b o u t 2 0 0 K .

F o r t h i s m a n i f o l d w e h a v e t h e r e f o r e i n c l u d e d a ll t ra n s i t i o n s w h o s e c a l c u l a t e dr e l a t i v e i n t e n s i ti e s a t 2 0 0 K a r e g r e a t e r t h a n 0 . 01 . I n a d d i t i o n , w e h a v e a l s o i n c l u d e da ll t h o s e w e a k e r l in e s w h i c h h a v e b e e n e x p e r i m e n t a l l y o b s e r v e d . F o r v 1 ( ta b l e 3 ), th e


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Table 1 .C a l c u l a t i o n o f r o t a t i o n a l a n d r o - v i b r a t io n a l l in e s t r e n g t h s 4 3 7

Calcula ted and measured vibra t ional fundamenta l s for H2 D and D2 H (uni tsc m - 1 ).

H 2 D + D 2 H +M ode C a l cu l at ed O bse rved O bs . - - ca l c . C a l cu la t ed O bse rved O bs . -ca lc .

~,~ 2 2 0 6 . 2 4 4 2 2 0 5 . 8 6 9 a - 0 . 3 7 5 1 9 6 7 . 8 2 5 1 9 6 8 . 1 7 0 b 0 . 3 4 5u ~ 2 3 3 4 . 9 8 6 2 3 3 5 . 4 4 9 ~ 0 . 4 6 3 2 0 7 9 . 2 1 2 2 0 7 8 . 4 1 0 b - 0 . 8 0 2~ l 2 9 9 2 . 9 6 2 2 9 9 2 . 5 0 5 c - 0 . 4 5 7 2 7 3 7 . 3 0 2 2 7 3 6 . 9 4 1 c - 0 . 3 6 1

" I ~ e f e r e n c e 6 .h R e f e r e n c e 9 .'~ I { e f e r e n c e t O .

cu t -o f f w as IRes(CO) > 0"1 , an d t he t em pe ra t u r e w as s e t t o 300 K t o i nc l u de m ore ,r a t h e r t h a n f e w e r , t r a n s i t i o n s .

F o r t he v 2 / v 3 t r a n s it i o n s , t h e 7 3 li n es f o r w h i c h c o m p a r i s o n w i t h e x p e r i m e n t w a sp o s s i b l e g a v e a r o o t m e a n s q u a r e ( r . m . s . ) d e v i a t i o n b e t w e e n t h e c a l c u l a t e d a n de x p e r i m e n t a l l in e s o f 0 - 3 8 8 c m - 1 . O n m o r e d e t a i le d e x a m i n a t i o n , t h e d i f fe r e n c ebe t w e en ob se r ve d and c a l cu l a t ed r e su l t s , A mo__r og~y(obse rved) - t o i : (ca l cu l a t ed ) ) , i sa l m o s t u n i f o r m l y n e g a t i v e f o r v 2 a n d p o s i t i v e f o r v 3 , i n li n e w i t h t h e d i f f e r e n c e s i nb a n d o r i g i n s.

S i m i l a r l y , t h e v I c a l c u l a t i o n s - - f o r w h i c h t h e r . m .s , d e v i a t i o n o n 3 7 l in e s is0 .4 2 1 c m - 1 - - - c o n s i s t e n t l y o v e r e s t i m a t e t h e l i n e f re q u e n c ie s . B u t f o r a ll t h r e e m o d e s ,w h e n t h e d i f f e re n c e i n b a n d o r i g in s a r e t a k e n i n t o a c c o u n t , a l m o s t a l l th e c a l c u l a t e dt r a n s i ti o n s l i e w i t h _ 0 .2 c m - 1 o f t h o s e m e a s u r e d e x p e r i m e n t a l l y .

T h e D 2 H m a n i f o l d s ( ta b l e s 4 a n d 5 ) s h o w v e r y s i m i la r b e h a v i o u r . T h e r .m . s.d e v i a t i o n s a r e 0 - 4 0 0 c m - 1 ( 8 6 l in e s) a n d 0 - 2 8 1 c m - 1 ( 3 4 l in e s) f o r v 2 / v 3 a n d v lr e s p e c t i v e ly . R e l a t i v e i n t e n s it i e s f o r t h e f o r m e r m a n i f o l d w e r e c a l c u l a t e d a t 1 50 K ( inl i n e w i t h e x p e r i m e n t a l a s s u m p t i o n s ) , w h i l e v l i n t e n s i t i e s w e r e a g a i n c a l c u l a t e d a t3 0 0 K .

F o r b o t h m o l e cu l es , t h e re a r e a n u m b e r o f e x p e r i m e n t a ll y m e a s u r e d l i n e s - -e s p e c i a l l y a t l o w e r f r e q u e n c i e s i n t h e v 2 / v 3 m a n i f o l d s - -w h i c h o n e w o u l d n o t e x p e c tt o b e o b s e r v a b l e o n t h e b a s i s o f t h e r e l a t i v e i n t e n s it i e s c a l c u l a t e d a t t h e t e m -p e r a t u r e s e s t i m a t e d . A t t h e s a m e t i m e , o u r c a l c u l a t io n s p r e d i c t a n u m b e r o f t r a n -s i ti o n s t o b e m e a s u r e a b l e w h i c h h a v e n o t , s o f a r, b e e n r e p o r t e d .

I t is cl e ar , h o w e v e r , t h a t t h e v a s t m a j o r i t y o f o b s e r v e d l i n es a l s o c o r r e s p o n d t ot h o s e c a l c u l a te d t o b e t h e m o s t i n te n s e . W e t h u s c o n s i d e r t h a t t h e d i s p a r i t y b e t w e e nt h e c a l c u l a t e d i n t e n s it i e s a n d t h e o b s e r v e d l in e s t o b e a p r o d u c t o f t h e d i f f ic u l t y o fo b t a i n i n g u n i f o r m e x p e r i m e n t a l c o n d i t i o n s ( i.e . a B o l t z m a n n d i s t r i b u t i o n o f e n e r g ie sa n d u n i f o r m s e n s i t iv i ty a c r o s s t h e s p e c t r a l r a n g e ) r a t h e r t h a n a f a i lu r e o f e i t h e r th et h e o r y p r e s e n t e d a b o v e o r t h e M B B d i p o le s u rf ac e .

I n r e - e x a m i n i n g t h e d a t a f o r t h e v l m a n i f o l d s , K o z i n e t a l . [ 1 0 ] m a d e a n u m b e ro f l in e r e a s s ig n m e n t s o n t h e b a s is o f f it ti n g th e d a t a t o t h e r e l e v a n t p h e n o m e n o l o g i -c a l h a m i l to n i a n s . O u r r e s u lt s c o n f i r m t h e i r r e a s si g n m e n t s , w i t h t h e e x c e p t i o n o f t h eD 2 H + v 1 l in e a t 2 9 9 0 - 1 5 4 c m - 1 , w h i c h w e h a v e a s s i g n e d b a c k t o i t s o r i g i n a l d e s i g -n a t i o n o f 4 4o - 3 a i o n c o n s i d e r a t i o n o f f r e q u e n c y .

I t i s i n te r e s t in g t o c o n s i d e r t h e H 2 D + v 1 l in e o c c u r r i n g a t 3 1 6 8 . 7 0 2 c m - 1 , w h i c hK o z i n e t a l . r e a s s i g n e d f r o m 5 1 2 - 4 1 4 t o 5 0 5 - 4 0 4 , ( l a b e l l e d e i n t a b l e 3 ) . O u r


10/28

4 3 8 S . M i l l e r e t a l .

T a b l e 2. C a l c u l a t e d a n d o b s e r v e d v2 an d v 3 t ran s i t ion s for H 2D + . R e la t ive in ten s i t i e sc a l c u l a t e d a t 2 0 0 K .

M o d e J'K'aK'c J " K ~ K ~ E " / a ~ i ~ ( c a l c . ) / o ) u ( o b s . ) ~ / Ao)o_ S (f -- i) b / IRe,.(O))"c m - ' c l n - 1 c r n - 1 c r n - 1 D 2u2 6 1 5 7 1 6u2 6 2 5 7 2 6u 2 5 0 5 6 0 6u 2 5 1 5 6 1 6u 2 5 1 4 6 1 5u 2 5 2 4 6 2 5u2 413 514u2 4 0 4 505v 2 4 1 4 5 1 5v 2 3 1 2 4 1 3v 2 3 0 3 4 0 4v 2 313 4 1 4v 2 211 312u 3 3 2 2 4 3 1u~ 2 2 1 3 2 2u 2 2 0 2 3 0 3u2 2 1 2 3 1 3u 3 3 2 1 4 3 2v~ 4 1 4 3 3 1u2 1 1 0 2 1 1

1272.962 1837.821 1837.573 -.248 .151(+0) .0001273.635 1837.938 1837.688u -.250 .153(+0) .000801.430 1892.818 1892.541~ -.277 .164(+0) .004801.484 1892.837 1892.558 -.279 .164(+0) .011990.739 1896.266 1895.995d -.271 .II0(+0) .0029 9 2 . 9 4 5 1 8 9 6 . 62 1 1 8 9 6 . 3 4 5 ~ - . 2 7 6 . 1 1 4 ( + 0 ) . 00 17 3 8 . 4 7 2 1 9 5 2 . 3 2 8 1 9 5 2 . 0 2 4 u - . 3 0 4 . 7 0 3 ( - 1 ) . 0 0 75 8 6 . 0 4 9 1 9 5 4 . 1 8 2 . 1 2 2 ( + 0 ) . 0 135 8 6 . 2 6 6 1 9 5 4 . 2 6 2 . 1 2 2 ( + 0 ) . 0 3 95 1 5 . 9 3 0 2 0 0 4 . 5 1 4 . 3 7 6 ( -1 ) . 0 2 04 0 2 . 7 2 5 2 0 1 2 . 9 3 3 2 0 1 2 . 6 2 1 - . 3 1 2 . 8 1 7 ( - 1 ) . 0 3 34 0 3 . 5 2 9 2 0 1 3 . 3 2 2 2 0 1 3 . 0 1 0 - . 3 1 2 . 8 3 1 ( -1 ) . 1 003 2 6 . 0 1 1 2 0 5 3 . 6 0 6 2 0 5 3 . 2 1 1 - . 3 9 5 . 1 7 9 ( - 1 ) . 0 3 96 5 4 . 3 2 1 2 0 5 5 . 4 4 1 . 5 9 7 ( - 1 ) . 0 1 23 5 4 . 6 7 7 2 0 6 1 . 0 8 2 2 0 6 0 . 6 8 4 - . 3 9 6 . 2 2 2 ( -1 ) . 0 132 5 1 . 3 1 6 2 0 6 7 . 3 0 0 2 0 6 6 . 9 5 8 - . 3 4 2 . 4 5 3 ( - 1 ) . 0 5 62 5 3 . 9 6 9 2 0 6 9 . 0 2 3 2 0 6 8 . 6 8 0 - . 3 4 3 . 4 8 0 ( - 1 ) . 1 7 56 4 5 . 4 1 1 2 0 7 1 . 3 5 5 . 7 6 9 ( - 1 ) . 0 1 74 5 8 . 2 8 3 2 0 8 2 . 2 4 6 2 0 8 1 . 8 5 1 - . 3 9 5 . 6 4 8 ( - 4 ) . 0 0 01 7 5 . 8 5 9 2 1 0 2 . 9 0 6 2 1 0 2 . 4 8 8 - . 4 1 8 . 7 6 2 ( - 2 ) . 0 5 0

v3 2 2 1 3 3 0v a 2 2 0 3 3 1u 3 2 1 2 3 2 1u2 1 0 1 2 0 2u 2 1 1 1 2 1 2u~ 211 322u2 000 I01u~ 1 1 1 2 2 0v 2 1 1 1 1 1 0v3 II0 221u3 404 515

459.763 2108.250 2108.633 .383 .930(-I) .079458.283 2110.820 2111.226 .406 .994(-I) .085376.204 2114.408 .211(-I) .011131.594 2115.424 2115.046 -.378 .186(-I) .056138.815 2120.317 2119.938 -.379 .196(-I) .168354.677 2157.287 2157.701 .414 .557(-1) .03445.678 2160.571 2160.176 -.395 .557(-2) .032223.813 2178.542 .430(-I) .06872.433 2186.699 2186.344 -.355 .157(-2) .022218.620 2190.231 2190.664 .433 .614(-I) .I02586.266 2190.521 .762(-I) .027


11/28

Calculation o f rotational and ro-vibrational line strengthsT a b l e 2 (continued).

4 3 9

. . . . . . . . . e " / o ~ , ~ ( c a l c . ) / ~ o , ~ c ~ b s ; ) ' / a ~ o o _ J s ( f - i ) b / tR . ~ .( o ~ )M o d e J K o K c J K a K c c m - 1 c m - 1 c m - 1 D 2u3 3 2 2 4 1 3u2 3 3 0 3 3 1u3 3 0 3 4 1 4u2 2 2 0 2 2 1

3 1 3 4 0 4u2 1 1 0 1 1 1u3 2 0 2 3 1 3u2 3 2 1 3 2 2u~ 2 1 2 3 0 3

u2 2 1 1 2 1 2uz 2 2 1 3 1 2u3 4 1 4 4 2 3uz 1 0 1 2 1 2u2 1 0 1 0 0 0u 3 4 2 3 4 3 2u3 3 2 2 3 3 1u~ 3 2 1 3 3 0u3 4 2 2 4 3 1u3 4 0 4 4 1 3u3 3 1 3 3 2 2u~ 3 1 2 3 1 3u3 1 1 1 2 0 2u3. 2 1 2 2 2 1u3 0 0 0 1 1 1

4 1 3 4 2 2u2 2 2 1 2 0 2u3 3 0 3 3 1 2u 2 4 : 1 3 4 1 4

3 1 2 3 2 1

u3 2 1 1 2 2 0v2 3 2 2 3 0 3

5 1 5 . 9 3 0 2 1 9 3 . 8 3 2 - . 3 3 8 ( - 1 ) . 0 2 04 5 8 . 2 8 3 2 1 9 8 . 2 8 6 - . 1 7 9 ( - 1 ) . 0 1 64 0 3 . 5 2 9 2 2 0 6 . 6 9 4 . 6 6 7 ( - 1 ) . 0 882 1 8 . 6 2 0 2 2 0 8 . 7 5 0 2 2 0 8 , 4 1 7 - . 3 3 3 . 1 3 8 ( - 1 ) . 0 324 0 2 . 7 2 5 2 2 1 5 . 3 8 6 . 7 0 1 ( - 1 ) . 0 316 0 . 0 2 1 2 2 1 8 . 7 4 4 2 2 1 8 . 3 9 3 - . 3 4 7 . 9 1 2 ( - 2 ) . 1 4 4

2 5 3 . 9 6 9 2 2 2 3 . 3 2 1 2 2 2 3 . 7 0 6 . 3 8 5 . 5 7 6 ( - 1 ) . 2 2 53 5 4 . 6 7 7 2 2 2 5 . 7 5 8 2 2 2 5 . 5 0 1 - . 2 5 7 . 1 9 5 ( - 1 ) . 0 1 22 5 1 . 3 1 6 2 2 3 9 . 2 9 6 2 2 3 9 . 6 3 7 . 3 4 1 . 5 4 4 ( - 1 ) . 0 7 3

1 3 8 . 8 1 5 2 2 4 0 . 8 0 3 2 2 4 0 . 5 1 2 - . 2 9 1 . 1 0 8 ( - 1 ) . 0 973 2 6 . 0 1 1 2 2 4 2 . 0 0 2 2 2 4 2 . 3 0 3 . 3 01 . 1 3 4 ( - 1 ) . 0 325 3 1 . 1 5 8 2 2 4 3 . 9 1 3 . 7 8 9 ( - I ) . 0 1 41 3 8 , 8 1 5 2 2 4 4 . 6 9 8 2 2 4 5 . 1 0 9 . 4 11 . 4 9 0 ( - 1 ) , 4 4 4

0 , 0 0 0 2 2 4 7 . 0 1 8 2 2 4 6 . 6 9 7 - . 3 2 1 . 1 6 0 ( - 2 ) . 0 136 4 5 , 4 1 1 2 2 4 8 . 4 6 1 . 8 1 9 ( - 1 ) . 0 1 94 5 8 . 2 8 3 2 2 5 1 . 4 7 9 . 5 5 1 ( - 1 ) . 0 5 04 5 9 . 7 6 3 2 2 5 7 . 0 0 3 2 2 5 7 . 4 9 5 . 4 9 2 . 7 1 4 ( - 1 ) . 0 6 56 5 4 . 3 2 1 2 2 6 0 . 8 5 4 . 1 4 7 ( + 0 ) . 0 3 35 1 5 . 9 3 0 2 2 6 0 . 8 5 7 2 2 6 1 . 1 7 6 . 3 21 . 8 6 3 ( - 1 ) . 0 5 23 5 4 . 6 7 7 2 2 6 3 . 4 3 4 2 2 6 3 . 8 0 7 . 4 7 7 . 4 9 4 ( - 1 ) . 0 3 22 5 3 . 9 6 9 2 2 6 6 . 4 7 6 . 1 6 7 ( - 1 ) . 0 6 71 3 1 . 5 9 4 2 2 7 0 . 7 6 1 2 2 7 1 . 1 3 5 . 3 7 4 . 2 9 8 ( - 1 ) . 0 9 62 1 8 . 6 2 0 2 2 7 1 . 9 9 1 2 2 7 2 . 3 9 5 . 4 0 4 . 3 7 4 ( - 1 ) . 0 6 46 0 . 0 2 1 2 2 7 4 . 9 6 5 2 2 7 5 . 4 0 3 . 4 3 8 . 3 9 5 ( - 1 ) . 6 3 8

5 8 1 . 2 3 5 2 2 7 8 . 5 3 8 2 2 7 9 . 0 8 5 . 5 47 . 1 7 9 ( + 0 ) . 02 31 3 1 . 5 9 4 2 2 8 4 . 1 6 6 2 2 8 3 . 8 1 0 -. 3 7 6 . 9 0 2 ( - 2 ) . 0 2 93 2 6 . 0 1 1 2 2 8 4 . 2 1 1 2 2 8 4 . 5 6 5 . 3 5 4 . 9 0 7 ( - 1 ) . 2 1 74 0 3 . 5 2 9 2 2 8 7 . 2 7 1 2 2 8 7 . 1 1 8 - . 1 5 3 . 2 4 4 ( - 1 ) . 0 3 33 7 6 . 2 0 4 2 2 8 7 . 4 5 6 . 1 3 8 ( + 0 ) . 07 7

2 2 3 . 8 1 3 2 2 8 8 . 1 5 2 2 2 8 8 . 6 2 3 . 4 71 . 7 4 0 ( - 1 ) . 1 2 32 5 1 . 3 1 6 2 2 8 8 . 3 2 9 . 1 8 9 ( - 1 ) . 0 2 6


12/28

4 4 0 S . M i l l e r e t a l .T a b l e 2 ( c o n t i n u e d ) .

M o d e J ' K ' a K ' c J " K ~ K ' ~ ' E " / c o i f ( c a l c . ) / c o i y ( o b s . ) ~ / A c oo _ f S ( f - i ) b / I R c 1 . ( o 9 )c m - 1 c m - I c m - ~ c m - ~ D 2

v ~ 5 1 5 4 1 4 4 0 3 . 5 2 9 2 2 9 0 . 7 9 1 2 2 9 0 . 6 5 8 e - . 1 3 3 . 4 7 0 ( - 2 ) . 0 0 6v 2 4 2 3 4 0 4 4 0 2 . 7 2 5 2 2 9 5 . 7 3 6 . 2 6 0 ( - 1 ) , 0 1 2v 2 5 1 4 5 1 5 5 8 6 . 2 6 6 2 3 0 0 . 7 3 9 . 3 0 6 ( - 1 ) . 0 1 1u s 2 0 2 2 1 1 1 7 5 . 8 5 9 2 3 0 1 . 4 3 1 2 3 0 1 . 8 3 0 . 3 9 9 . 8 6 6 ( - 1 ) . 6 1 5u 2 2 1 1 1 i 0 7 2 . 4 3 3 2 3 0 7 . 1 8 5 . 3 3 1 ( - 2 ) . 0 5 0u3 1 0 1 1 1 0 7 2 . 4 3 3 2 3 1 1 . 0 8 0 2 3 1 1 . 5 1 2 . 4 2 2 . 6 4 7 ( - 1 ) . 9 7 1u 3 2 2 0 3 1 3 2 5 3 . 9 6 9 2 3 1 5 . 1 3 4 . 3 6 9 ( - 2 ) . 0 1 5u 2 3 3 1 3 1 2 3 2 6 . 0 1 1 2 3 2 5 . 6 9 2 . 5 0 3 ( - 2 ) . 0 1 2u 2 3 1 2 2 1 1 1 7 5 . 8 5 9 2 3 4 4 . 5 8 6 . 2 6 2 ( - 2 ) . 0 1 9u 3 1 1 0 1 0 I 4 5 . 6 7 8 2 3 6 3 . 1 7 3 . 5 7 3 ( - 1 ) . 3 5 5u 3 2 1 1 2 0 2 1 3 1 . 5 9 4 2 3 8 0 . 3 7 0 2 3 8 0 . 8 2 4 . 4 5 4 . 5 8 4 ( - 1 ) . 1 9 7u 2 2 2 0 1 0 1 4 5 . 6 7 8 2 3 8 1 . 6 9 2 2 3 8 1 . 3 6 7 - . 3 3 5 . 3 6 4 ( - 2 ) . 0 2 3u 3 3 2 1 3 1 2 3 2 6 . 0 1 1 2 3 9 0 . 7 5 5 . 7 4 8 ( - 1 ) . 1 8 7u 3 2 2 0 2 1 1 1 7 5 , 8 5 9 2 3 9 3 . 2 4 4 2 3 9 3 . 6 3 3 . 3 8 9 . 4 5 0 ( - 1 ) . 3 3 3u ~ 4 2 2 4 1 3 5 1 5 . 9 3 0 2 3 9 9 . 2 4 5 . 7 9 0 ( - 1 ) . 0 5 1u 3 1 1 1 0 0 0 0 . 0 0 0 2 4 0 2 . 3 5 5 2 4 0 2 . 7 9 5 . 4 4 0 . 4 2 1 ( - 1 ) . 3 6 9u s 3 1 2 3 0 3 2 5 1 . 3 1 6 2 4 1 2 . 3 4 4 . 4 2 2 ( - 1 ) . 0 61u s 2 0 2 1 1 1 6 0 . 0 2 1 2 4 1 7 . 2 6 9 2 4 1 7 . 7 3 4 . 4 6 5 . 3 3 7 ( , 1 ) . 5 7 8

v 3. 2 2 1 2 1 2 1 3 8 . 8 1 5 2 4 2 9 . 1 9 8 2 4 2 9 . 6 4 7 , 4 4 9 . 2 6 2 ( - 1 ) . 2 5 6

v s 3 3 0 3 2 1 3 7 6 . 2 0 4 2 4 4 4 . 1 3 4 - , 3 3 5 ( - 1 ) . 0 2 0v s 2 1 2 1 0 1 4 5 . 6 7 8 2 4 4 4 . 9 3 3 2 4 4 5 . 3 4 8 . 4 1 5 . 6 4 0 ( - 1 ) . 4 1 0u s 3 1 2 2 2 1 2 1 8 . 6 2 0 2 4 4 5 . 0 4 0 2 4 4 5 . 6 0 6 . 5 6 6 . 1 4 9 ( - 1 ) . 0 2 8u ~ 3 2 1 3 0 2 1 3 1 . 5 9 4 2 4 4 8 . 8 4 1 2 4 4 8 . 6 2 7 - . 2 1 4 . 2 8 8 ( - 2 ) . 0 1 0u 3 3 2 2 3 1 3 2 5 3 . 9 6 9 2 4 5 5 . 7 9 3 - . 3 1 3 ( - 1 ) . 1 3 5v s 4 1 3 4 0 4 4 0 2 . 7 2 5 2 4 5 7 . 0 4 8 - . 2 9 6 ( - 1 ) . 0 1 5v 3 3 3 1 3 2 2 3 5 4 . 6 7 7 2 4 6 5 . 6 8 6 2 4 6 6 . 0 4 1 . 3 5 5 . 3 1 4 ( - 1 ) . 0 2 2u 3 3 0 3 2 1 2 1 3 8 . 8 1 5 2 4 7 1 . 4 0 8 2 4 7 1 ~ 6 5 . 4 5 7 . 7 2 5 ( - 1 ) . 7 2 1v 2 3 3 0 2 1 1 1 7 5 . 8 5 9 2 4 8 0 . 7 1 0 . 6 7 5 ( - 2 ) . 0 5 2u3 3 1 3 2 0 2 1 3 1 . 5 9 4 2 4 8 6 . 5 1 8 2 4 8 6 . 9 3 2 . 4 1 4 . 9 7 3 ( - 1 ) . 3 4 2v s 4 2 3 4 1 4 4 0 3 . 5 2 9 2 4 9 0 . 3 4 4 2 4 9 0 . 7 8 2 . 4 3 8 . 2 9 8 ( - 1 ) . 0 4 5v3 2 2 1 1 1 0 7 2 . 4 3 3 2 4 9 5 . 5 8 0 2 4 9 6 . 0 1 4 . 4 3 4 . 6 1 7 ( - 1 ) 1 . 0 0 0v s 4 1 3 3 2 2 3 5 4 . 6 7 7 2 5 0 5 . 0 9 6 2 5 0 5 . 6 9 3 . 5 9 7 . 3 8 0 ( - 1 ) . 0 2 7


13/28

Calculat ion of rotat ion al and ro-vibrational l ine strength s 441

M o d e J ' K ' a K 'c J " K ~ K ~ E " / c o i r o g i : ( o b s . ) a / A o 9 o _ . r S ( f - i )~ / IRel .(og )C l TI I c m - I c m - l c m - 1 9 2

v 3 2 2 0 1 1 1 6 0 . 0 2 1 2 5 0 9 . 0 8 2 2 5 0 9 . 5 4 1 . 4 5 7 . 4 9 0 ( - 1 ) . 8 7 4u 2 3 3 1 2 1 2 1 3 8 . 8 1 5 2 5 1 2 . 8 8 9 2 5 1 2 . 5 9 8 - . 3 9 1 . 9 1 1 ( - 2 ) . 0 9 2u 3 4 0 4 3 1 3 2 5 3 . 9 6 9 2 5 2 2 . 8 1 8 2 5 2 3 . 2 7 1 . 4 5 3 . 1 1 1 ( + 0 ) . 4 91u 3 4 1 4 3 0 3 2 5 1 . 3 1 6 2 5 2 3 . 7 5 5 2 5 2 3 . 9 5 3 . 1 9 8 . 4 5 6 ( - 1 ) . 0 6 9u 2 4 3 1 3 1 2 3 2 6 . 0 1 1 2 5 2 7 . 5 0 5 . 7 1 6 ( - 2 ) . 0 1 9u 3 3 2 2 2 1 1 1 7 5 . 8 5 9 2 5 3 3 . 9 0 3 2 5 3 4 . 3 2 8 . 4 2 5 . 6 9 5 ( - 1 ) . 5 4 3

u 2 4 2 2 3 0 3 2 5 1 . 3 1 6 2 5 3 7 . 0 5 4 2 5 3 7 . 2 0 0 . 1 4 6 . 9 0 0 ( - 1 ) . 1 3 7u 3 5 1 4 4 2 3 5 3 1 . 1 5 8 2 5 6 3 . 0 3 0 . 6 8 4 ( - 1 ) . 0 1 4u 3 4 2 3 3 1 2 3 2 6 . 0 1 1 2 5 6 7 . 8 6 1 2 5 6 8 . 3 0 2 . 4 4 1 . 9 2 3 ( - 1 ) . 2 4 8u 3 5 0 5 4 1 4 4 0 3 . 5 2 9 2 5 7 1 . 1 1 4 2 5 7 1 . 5 8 5 . 4 7 1 . 1 4 6 ( + 0 ) . 2 2 6u 3 5 1 5 4 0 4 4 0 2 . 7 2 5 2 5 7 2 . 3 0 3 2 5 7 2 . 7 5 5 . 4 5 2 . 1 4 1 ( + 0 ) . 0 7 3u s 4 3 2 3 1 3 2 5 3 . 9 6 9 2 5 7 6 . 8 9 9 . 1 7 7 ( - 1 ) . 0 8 0u 3 3 2 1 2 1 2 1 3 8 . 8 1 5 2 5 7 7 . 9 5 1 2 5 7 8 . 4 6 2 . 5 1 1 . 3 1 4 ( - 1 ) . 3 2 6u 3 3 3 1 2 2 0 2 2 3 . 8 1 3 2 5 9 6 . 5 5 0 2 5 9 6 . 9 6 0 . 4 1 0 . 9 2 3 ( - 1 ) . 1 7 5u s . 3 3 0 2 2 1 2 1 8 . 6 2 0 2 6 0 1 . 7 1 8 2 6 0 2 . 1 4 6 . 4 2 8 . 9 1 9 ( - 1 ) . 1 8 0

R . M . S . d e v i a t i o n o f c a l c u l a te d f r o m e x p e r i m e n t a l f r e q u e n c i e s = 0 . 3 8 8 c m - 1 .7 3 l i n e s c o n s i d e r e d .

'~ D a t a f r o m R e f e r e n c e 6 .h P o w e r s o f t e n in b r a c k e t s .

M a x . i n t e g r a t e d a b s o r p t i o n c o e f f i ci e n t = 1 . 1 57 1 0 1 8 (c m . s e c - 1 m o t e - l ) .~ D a t a f r o m S h y J . T . , F a r le y J . W . a n d W i n g W . H . , 1 9 81 , P h y s . R e v . A . , 2 4 , 1 1 4 6 .e R e a s s i g n e d f r o m 5 0 s - 4 04 o n f r e q u e n c y g r o u n d s .

C a l c u l a t e d 5 o s - 4 04 o c c u r s a t 2 2 9 1 . 5 2 2 c m - 1 , w i t h s i m i l a r r e l a t iv e i n t e n s i t y .

calculations puts this transition at 3169.055cm-1, almost exactly at the frequencyobtained from adding the difference in experimental and calculated vl to the experi-mentally measured line, thus confirming their reassignment on frequency grounds.

Nuclear spin considerations, on the other hand, predict that the ortho-51s - 414line ought to be three times as intense as its p a r a -H z D neighbour. So far, this hasnot been reported. Given our error in the 505- 404, we predict the 515- 414transition should occur at 3168.079 cm-1 and ought to be a candidate for observa-tion.In addition, our results indicate that one transition in each of the % / % mani-folds ought also to be reassigned. For H2D +, this is the line at 2290-658 cm-1 whichwe assign to v2 515 --414 (calculated frequency 2290.791 cm -1) rather than v2 505

- 404 (calculated frequency 2291.522cm-1). In this way, we get a value of Acoo_r of


14/28

4 4 2T a b l e 3 .

S . M i l l e r e t a l .C a l c u l a t e d a n d o b s e r v e d v~ t r a n s i t i o n s f o r H 2 D + . R e l a t i v e i n t e n s it i e s c a l c u l a t e d a t

3 0 0 K .

J ' K 'a K ' J " K " K ~ E " / o g i f ( ca l c . ) / %Y (~ emA~ S ( f - i )a/ IRel . (09 )c m - ~ c m - ~ c m - 1 D 2

3 1 2 4 1 3 5 1 5 . 9 3 0 2 8 0 1 . 4 3 4 . 2 2 9 ( -1 ) . 1 6 54 1 4 5 1 5 5 8 6 . 2 6 6 2 8 0 5 . 0 8 1 . 2 4 8 ( -1 ) . 1 2 73 I 3 4 1 4 4 0 3 . 5 2 9 2 8 3 9 . 8 8 0 2 8 3 9 . 3 8 7 - . 4 9 3 . 2 0 6 ( -1 ) . 2 5 82 1 1 3 1 2 3 2 6 . 0 1 1 2 8 4 1 . 4 8 0 2 8 4 0 , 9 6 2 - . 5 1 8 . 1 7 5 ( -1 ) . 3 1 82 0 2 3 0 3 2 5 1 . 3 1 6 2 8 7 2 . 3 9 3 2 8 7 1 . 8 9 7 - . 4 9 6 . 1 6 7 ( -1 ) . 1 4 62 1 2 3 1 3 2 5 3 . 9 6 9 2 8 7 5 . 3 0 2 2 8 7 4 . 8 1 1 - . 4 9 1 . 1 5 7 ( -1 ) . 4 0 61 1 0 2 1 1 1 7 5 . 8 5 9 2 8 8 7 . 8 7 0 2 8 8 7 . 3 7 0 - , 5 0 0 . 1 0 2 ( -1 ) . 3 8 72 0 2 2 2 1 2 1 8 . 6 2 0 2 9 0 5 . 0 8 9 2 9 0 4 . 6 5 7 - . 5 3 1 . 1 9 6 ( -2 ) . 0 2 01 0 1 2 0 2 1 3 1 . 5 9 4 2 9 0 7 . 0 2 0 2 9 0 6 . 5 2 3 - . 4 9 7 . 1 2 1 ( -1 ) . 1 9 01 1 1 2 1 2 1 3 8 . 8 1 5 2 9 1 2 . 1 1 2 2 9 1 1 . 6 3 5 - . 4 7 7 . 9 3 7 ( -2 ) . 4 2 80 0 0 1 0 1 4 5 . 6 7 8 2 9 4 7 . 2 8 4 2 9 4 6 . 8 0 2 - . 4 8 2 . 6 6 4 ( -2 ) . 1 6 02 1 2 2 1 1 1 7 5 . 8 5 9 2 9 5 3 . 4 1 2 2 9 5 2 , 9 4 0 - . 4 7 2 . 6 2 6 ( -2 ) . 2 4 33 2 2 3 2 1 3 7 6 . 2 0 4 2 9 6 3 . 9 5 8 2 9 6 3 . 5 1 3 - . 4 4 5 . ,136(-1) .0683 3 1 3 3 0 4 5 9 . 7 6 3 2 9 7 5 . 4 2 2 2 9 7 5 . 0 6 4 - . 3 5 8 . 3 3 5 ( -1 ) . 3 3 51 1 I 1 1 0 7 2 . 4 3 3 2 9 7 8 . 4 9 4 2 9 7 8 . 0 4 5 - . 4 4 9 . 1 0 5 ( -1 ) . 6 7 53 3 0 3 3 1 4 5 8 . 2 8 3 2 9 7 8 . 8 4 3 2 9 7 8 . 4 9 2 - . 4 5 1 . 3 2 8 ( -1 ) . 3 3 22 2 1 2 2 0 2 2 3 . 8 1 3 2 9 8 0 . 4 0 3 2 9 7 9 . 9 8 7 - . 4 2 6 . 2 1 3 ( -1 ) . 2 2 12 2 0 2 2 1 2 1 8 . 6 2 0 2 9 9 1 . 5 6 2 2 9 9 1 . 1 6 2 - . 4 0 0 . 2 0 3 ( -1 ) . 2 1 71 I 0 1 1 1 6 0 , 0 2 1 3 0 0 3 . 7 0 8 3 0 0 3 . 2 7 6 - . 4 3 2 . 9 7 4 ( -2 ) . 6 6 93 2.1 3 2 2 3 5 4 . 6 7 7 3 0 0 9 . 5 1 0 3 0 09 ~12 3 - . 3 9 7 . 1 1 4 ( -1 ) . 0 6 4

2 1 l 2 1 2 1 3 8 . 8 1 5 3 0 2 8 . 6 7 7 3 0 2 8 . 2 6 3 - . 4 1 4 . 4 9 7 ( -2 ) . 2 3 6! 0 1 0 0 0 0 , 0 0 0 3 0 3 8 . 6 1 4 3 0 3 8 . 1 7 7 - . 4 3 7 . 6 9 6 ( -2 ) . 2 1 53 1 2 3 1 3 2 5 3 . 9 6 9 3 0 6 3 . 3 9 6 3 0 6 3 . 0 0 6 - . 3 9 0 . 3 3 2 ( -2 ) . 0 9 22 1 2 1 1 1 6 0 . 0 2 1 3 0 6 9 . 2 5 0 3 0 6 8 . 8 4 5 - . 4 0 5 . 1 1 1 ( -1 ) . 7 8 02 2 l 2 0 2 1 3 1 . 5 9 4 3 0 7 2 . 6 2 2 3 0 7 2 . 1 9 0 - . 4 3 2 . 9 5 3 ( -3 ) . 0 1 62 0 2 1 0 1 4 5 . 6 7 8 3 0 7 8 . 0 3 1 3 0 7 7 . 6 1 1 - . 4 2 0 . 1 3 6 ( -1 ) . 3 4 12 1 1 1 1 0 7 2 . 4 3 3 3 0 9 5 . 0 5 9 3 0 9 4 . 7 6 1 - . 2 9 8 . 1 0 4 ( -1 ) . 6 9 43 1 3 2 1 2 1 3 8 . 8 1 5 3 1 0 4 . 5 9 4 3 1 0 4 . 2 0 7 - . 3 8 7 . 2 0 5 ( -1 ) 1 . 0 0 03 0 3 2 0 2 1 3 1 . 5 9 4 3 1 1 0 . 0 4 9 3 1 0 9 . 6 4 5 - . 4 0 4 . 2 1 0 ( -1 ) . 3 5 3


15/28

C a l c u l a t i o n o f r o t a t i o n a l a n d t o - v i b r a t i o n a l l in e st r e n g t h sT a b l e 3 (continued).

4 4 3

J 'K ' , K ' , J" K : K~' E" / co , j (ca lc . ) / oJ , r(obs .W A o , ,_ f f S ( f - i ) b / IR, t . (co)c m - ~ c m - t c m - ~ c ln - 1 D 2

3 2 2 2 2 1 218 .620 3121.541 3121.202 - .339 .123(-1) .1374 I 4 3 1 3 253 .969 3137.378 3137.007 - .371 .303(-1) .8594 0 4 3 0 3 251.3 16 3139.578 3139.197 -.381 .303 (-1) .2903 2 ! 2 2 0 223 .813 3140.374 3140.044 - .330 .121(-1 ) .1323 1 2 2 1 1 175.859 3141 .506 3141.131 -.37 5 .184 (-1) .7604 2 3 3 2 2 354 .677 3161.297 3160.971 - .326 .230(-1) .1354 3 2 3 3 1 458 .283 3164.560 .134(-1) .1435 1 5 4 1 4 403.5 29 3168.432 .411 (-1) .5745 0 5 4 0 4 d 402 .725 3169.055 3168.702 - .353 .407 (-1 ) .1904 3 1 3 3 0 459 .763 3174.389 .130(-1) .1394 1 3 3 1 2 326 .011 3179.336 3178.973 - .363 .257(-1 ) .521

4 2 2 3 2 1 376 .204 3194.284 3193.963 - .321 .225(-1 ) .1206 1 6 5 1 5 586 .266 3198.416 .529(-1) .3106 0 6 5 0 5 586 .049 3198.543 .530(-1 ) .1045 l 4 4 1 3 515 .930 3208.535 3208.187 - .348 .339(-1) .2805 3 3 4 3 2 645 .411 '3208 .582 .256(-1) .113

R . M . S . d e v i a t i o n o f c a l c u l a t e d f ro m e x p e r i m e n t a l f r e q ue n c i es = 0 . 42 1 c m - 1 .3 7 l i n e s c o n s i d e r e d ." D a t a f r o m R e f e r e n c e 1 0.h P o w e r s o f t e n in b r a c k e t s .M a x . i n t e g r a t e d a b s o r p t i o n c oe f f ic i e n t = 2 . 22 0 1 01 7 ( c m . s e c - 1 m o l e - l ) .,l R e a s s i g n e d b y K o z i n et al (Ref . 10 ) ( see t ex t ) .

- 0 . 1 3 3 c m - 1 , in l i n e w i t h o t h e r n e a r b y v2 l in e s . U s i n g t h e o r i g i n a l a s s i g n m e n tw o u l d h a v e g i v e n A o~o_.r = - 0 " 8 6 4 c m - 1 , w h i c h i s m o r e t h a n t w i c e a s l a r g e a s a n yo t h e r v a l u e o f Aa~o__ f o u n d f o r v 2 .

W e a l s o c o n s i d e r t h e D 2 H + v 2 t r a n s i t i o n a t 2 0 4 0 " 7 6 0 c m - 1 o u g h t t o b e r e a s -s i g n e d f r o m 6 o 6 - 5 1 s ( c a l c u l a t e d f r e q u e n c y 2 0 4 1 . 6 4 1 c r n - 1 ) t o 5 1 s - 4 o4 ( c a l c u l a t e df r e q u e n c y 2 0 4 0 - 6 7 8 c m - 1 ) . H e r e a g a i n t h e v a l u e o f Acoo__r = 0 " 0 8 2 c m - 1 i s m o r et y p i c a l o f t h e t r e n d w e s e e t h a n t h e 0 -8 81 c m - 1 t h a t w o u l d b e o b t a i n e d u s i n g t h eo r i g i n a l a s s i g n m e n t . A s f u r t h e r s u p p o r t f o r th i s r e a s s i g n m e n t w e c a n a d d t h a t t h e5 1 s - 4 04 t r a n s i t i o n is c a l c u l a t e d t o b e m o r e t h a n t h r e e t i m e s a s i n t e n s e a s t h e6o6 - 515 l i ne .

P u r e r o t a t i o n a l t r a n s i t i o n s i n th e g r o u n d s t a t e a r e g iv e n fo r H 2 D + a n d D 2 H + i n


16/28

4 4 4 S . M i l l e r e t a l .T a b l e 4 . C a l c u l a t e d a n d o b s e r v e d v 2 a n d v a t r a n s i t i o n s f o r D 2 H + . R e l a t i v e i n t e n s i t ie s

c a l c u l a t e d a t 1 5 0 K .

M o d e J 'K 'a K 'c J " K " K [ E " / o ) i / ( c a l c . ) / m , / . ( o b s . ) ~ A m o _ _ r S ( f " - i ) b / I R e l . ( ~ ) cc m - ~ c m - 1 c m - ~ c m - 1 D ~v 2 3 2 2 4 3 1 5 2 3 . 2 5 9 1 7 1 2 . 8 5 6v 2 5 1 5 6 0 6 6 3 0 . 0 7 4 1 7 2 6 . 2 2 6u 2 4 1 3 5 2 4 5 8 5 . 4 3 1 1 7 5 4 . 1 0 3u 2 2 1 2 3 2 1 2 9 5 . 9 4 7 1 7 6 6 . 7 5 5v 2 2 2 1 3 3 0 3 7 7 . 6 8 7 1 7 6 7 , 6 9 3u 2 2 2 0 3 3 1 3 7 7 . 0 5 8 1 7 7 2 . 2 5 0v 2 4 0 4 5 1 5 4 6 0 . 7 7 1 1 7 7 2 . 4 4 5v ~ 4 1 4 5 0 5 4 6 0 . 2 4 5 1 7 7 3 , 9 7 5v 2 4 2 3 5 1 4 5 7 4 . 5 6 3 1 7 8 2 . 2 3 7v2 3 1 2 4 2 3 4 1 9 . 3 3 3 1 7 8 6 . 0 4 0u 2 6 1 5 6 2 4 8 6 9 . 0 0 8 1 8 0 7 . 2 9 5v 2 3 0 3 4 1 4 3 1 7 , 1 3 5 1 8 1 6 . 1 2 9

v 2 2 1 1 3 2 2 2 8 3 . 2 4 2 1 8 1 6 . 2 9 0u 2 3 1 3 4 0 4 3 1 5 . 6 2 1 1 8 2 0 . 6 7 0u ~ 1 1 1 2 2 0 1 8 2 . 0 3 3 1 8 3 1 . 7 8 6u 2 4 0 4 4 1 3 3 9 8 . 8 8 1 1 8 3 4 . 3 3 5u 2 3 2 2 4 1 3 3 9 8 . 8 8 1 1 8 3 7 . 2 3 3v 2 1 1 0 2 2 1 1 7 9 , 1 3 9 1 8 4 7 . 5 5 8t '2 3 1 3 3 2 2 2 8 3 . 2 4 2 1 8 5 3 . 0 4 9v 2 5 1 4 5 2 3 6 4 3 . 0 7 0 1 8 5 4 . 0 8 2

v 2 2 0 2 3 1 3u 2 3 2 2 3 3 1v 2 2 1 2 3 0 3u 2 3 0 3 3 1 2u2 2 1 2 2 2 1v 2 1 0 1 2 1 2v 2 4 1 3 4 2 2v 2 3 3 1 4 2 2u 2 2 2 1 3 1 2v2 5 2 3 5 3 2v 2 3 1 2 3 2 1

. 4 2 3 ( - 1 ). 1 7 4 ( + 0 ). 8 6 8 ( - 1 ). 1 5 6 ( - 1 ). 5 0 1 ( - 1 ). 4 9 7 ( - 1 )

- . 1 3 8 ( + 0 )- - . 1 3 7 ( + 0 )

1 7 8 2 . 2 8 7 d . 0 5 0 . 7 7 6 ( 2 1 )1 7 8 6 . 3 3 0 d . 2 9 0 . 6 1 2 ( - 1 )1 8 0 7 ~ 3 4 7 d . 0 5 2 . 4 7 4 ( - 1 )1 8 1 6 . 2 4 9 . 1 2 0 . 1 0 2 ( + 0 )

- - . 4 5 0 ( - 1 )- - . 1 0 1 ( + 0 )

1 8 3 2 . 0 4 1 d . 2 5 5 . 2 5 3 ( - 1 ). 2 2 9 ( - 1 )

1 8 3 7 . 3 1 2 d . 0 7 9 . 4 3 1 ( - 1 )1 8 4 7 . 8 8 5 . 3 2 7 .3 6 2 ( - 1 )1 8 5 3 . 1 8 2 J . 1 3 3 . 1 8 9 ( - 1 )1 8 5 4 . 2 3 1 d . 1 4 9 . 5 4 2 ( - 1 )

1 9 9 . 9 6 2 1 8 5 4 . 8 4 1 1 8 5 5 . 0 6 8 . 2 2 73 7 7 , 0 5 8 1 8 5 9 . 0 5 71 9 6 . 0 2 4 1 8 6 6 . 6 7 8 1 8 6 6 . 8 4 1 d . 1 6 32 5 1 . 1 9 4 1 8 8 2 . 0 7 0 1 8 8 2 . 2 0 1 d . 1 311 7 9 . 1 3 9 1 8 8 3 . 5 6 4 1 8 8 3 . 7 7 7 . 2 1 31 1 9 . 2 2 8 1 8 8 7 . 9 8 2 1 8 8 8 . 2 8 0 d . 2 9 84 5 0 . 5 8 4 1 8 8 8 . 9 5 14 5 0 . 5 8 4 1 8 8 9 . 1 7 32 5 1 . 1 9 4 1 8 9 4 . 1 8 6 1 8 9 4 . 3 1 6 . 1 3 07 0 9 . 4 4 7 1 8 9 5 . 4 7 8 1 8 9 5 . 4 3 1 d - . 0 5 72 9 5 . 9 4 7 1 9 0 9 . 4 2 6

. 6 8 3 ( - 1 )

. 1 7 4 ( - 1 )

. 0 3 1 ( - i )

. 2 7 o ( - i ). 1 3 8 ( - 1 ). 4 1 0 ( - 1 ). 5 9 1 ( - 1 ). 2 1 3 ( - 1 ). 171( - 1 ). 4 5 6 ( - 1 ). 5 0 4 ( - 1 )

. 0 1 0

. 0 1 5

. 0 1 2

. 0 1 7

. 0 2 5

. 0 5 1

. 0 6 3

. 0 3 2

. 0 0 6

. 0 2 1

. 0 0 0

. 0 9 5

, 1 1 6. 1 9 1. 1 7 3. 0 2 0. 0 3 7. 1 2 9. 0 5 0. 0 0 2, 3 9 9. 0 1 9. 1 9 3. 0 4 9. 0 5 0. 2 8 9. 0 3 2. 0 1 1. 0 3 1. 0 0 1. 0 6 0


17/28

Calculat ion o f rotat iona l and ro-v ibrat ional l ine s trength sT a b l e 4 (continued).

445

M o d e J 'K' .K ' J"K~K~ E"/ coi / (calc. ) / COl / (Obs. )"/ Acoo_r S{f--i)b/ IRcL(O0)c r n - i c r n - I c r n - I c m - 1 D 2

u 2 1 1 1 2 0 2 1 0 1 . 6 7 5 1 9 1 2 . 1 4 5 1 9 1 2 . 3 8 7 d . 2 4 2 . 2 6 9 ( - 1 ) . 4 1 6v 3 4 1 4 4 3 1 5 2 3 . 2 5 9 1 9 1 6 . 7 3 6 1 9 1 6 . 4 5 1 d - . 2 8 5 . 1 7 0 ( - 1 ) . 0 0 5u ~ 2 1 1 2 2 0 1 8 2 . 0 3 3 1 9 1 7 . 4 9 9 1 9 1 7 . 8 5 7 d . 3 5 8 . 2 7 3 ( - 1 ) . 1 9 6u 2 2 0 2 2 1 1 1 3 6 . 3 1 1 1 9 1 8 . 4 9 2 1 9 1 8 . 7 3 2 . 2 4 0 . 3 2 3 ( - 1 ) . 3 5 9u 2 0 0 0 1 1 1 4 9 . 2 4 7 1 9 1 8 . 5 7 8 1 9 1 8 . 9 0 8 . 3 3 0 . 2 3 5 ( - 1 ) . 6 0 4u 3 4 1 3 5 1 4 5 7 4 . 5 6 3 1 9 3 4 . 4 0 5 1 9 3 3 . 8 0 1 d - . 6 0 4 . 7 8 5 ( - 2 ) . 0 0 1v 3 1 0 1 2 2 0 1 8 2 . 0 3 3 1 9 3 7 . 2 6 0 . 2 7 8 ( - 2 ) . 0 2 0u 2 1 0 1 1 1 0 5 7 . 9 7 6 1 9 4 0 . 2 3 4 1 9 4 0 . 5 5 1 . 3 1 7 . 2 8 8 ( - 1 ) . 3 4 4u 2 2 2 0 3 1 3 1 9 9 . 9 6 2 1 9 4 9 . 3 4 6 1 9 4 9 . 5 3 3 . 1 8 3 . 3 7 5 ( - 2 ) . 0 2 3

u 3 3 1 2 4 1 3 3 9 8 . 8 8 1 1 9 5 2 . 5 8 4 1 9 5 1 . 9 2 0 d - . 6 6 4 . 1 0 0 ( - I ) . 0 0 9u z 2 2 0 3 2 1 2 9 5 . 9 4 7 1 9 6 2 . 3 4 9 . 1 1 7 ( - 1 ) . 0 1 4v 3 2 2 1 3 2 2 2 8 3 . 2 4 2 1 9 7 2 . 1 3 2 1 9 7 1 . 3 5 5 - . 7 7 7 . 8 7 2 ( - 2 ) . 0 2 4u 3 2 1 1 3 1 2 2 5 1 . 1 9 4 1 9 7 4 . 5 6 6 1 9 7 3 . 8 5 2 - . 7 1 4 . 1 1 6 ( - 1 ) . 0 2 2u 2 1 1 0 1 0 1 3 4 . 9 0 2 1 9 9 1 . 7 9 5 1 9 9 2 . 1 3 0 . 3 3 5 . 3 4 5 ( - 1 ) . 5 2 7u 2 4 2 2 4 1 3 3 9 8 . 8 8 1 1 9 9 5 . 3 4 0 1 9 9 5 . 5 0 8 . 1 6 8 . 1 0 1 ( + 0 ) . 0 9 5v 2 2 1 1 2 0 2 1 0 1 . 6 7 5 1 9 9 7 . 8 5 8 1 9 9 8 . 2 0 3 . 3 4 5 . 4 4 6 ( - 1 ) . 7 2 0u 3 2 0 2 3 0 3 1 9 6 . 0 2 4 1 9 9 8 . 6 3 6 1 9 9 7 . 9 6 2 - . 6 7 4 . 6 5 7 ( - 2 ) . 0 2 2u 3 1 1 0 2 1 1 1 3 6 . 3 1 1 2 0 0 0 . 6 8 9 1 9 9 9 . 8 7 9 - . 7 1 0 . 1 1 6 ( - 1 ) . 1 3 5u 2 3 2 1 3 1 2 2 5 1 . 1 9 4 2 0 0 1 . 5 4 3 2 0 0 1 . 7 4 4 . 2 0 1 . 8 2 6 ( - 1 ) . 1 5 9u 3 2 1 2 3 1 3 1 9 9 . 9 6 2 2 0 0 3 . 3 4 4 2 0 0 2 . 7 5 0 - . 5 9 4 . 4 7 6 ( - 2 ) . 0 3 0u 2 2 0 2 1 1 1 4 9 . 2 4 7 2 0 0 5 . 5 5 6 2 0 0 5 . 8 4 4 . 2 8 8 . 1 2 1 ( - 1 ) . 3 2 4u a 4 0 4 4 2 3 4 1 9 . 3 3 3 2 0 0 6 . 5 7 4 . 3 3 7 ( - 1 ) . 0 1 3u ~ 3 1 2 3 0 3 1 9 6 . 0 2 4 2 0 0 9 . 3 4 9 2 0 0 9 . 6 9 6 . 3 4 7 . 4 4 4 ( - 1 ) . 1 4 6v 2 2 2 0 2 1 1 1 3 6 . 3 1 1 2 0 1 2 . 9 9 7 2 0 1 3 . 1 9 6 . 1 9 9 . 4 6 7 ( - 1 ) . 5 4 5u 2 1 1 1 0 0 0 0 . 0 0 0 2 0 1 3 . 8 1 9 2 0 1 4 . 1 0 6 . 2 8 7 . 1 6 9 ( - 1 ) . 7 2 9u 2 4 3 1 4 2 2 4 5 0 . 5 8 4 2 0 1 4 . 5 0 6 2 0 1 4 . 4 3 3 - . 0 7 3 . 9 0 4 ( - 1 ) . 0 5 2v 3 3 0 3 3 2 2 2 8 3 . 2 4 2 2 0 1 4 . 7 9 5 2 0 1 4 . 2 6 3 - . 5 3 2 . 1 7 9 ( - 1 ) . 0 5 1u 3 2 0 2 2 2 1 1 7 9 . 1 3 9 2 0 1 5 . 5 2 2 . 4 7 6 ( - 2 ) . 0 1 9u 3 1 0 1 2 0 2 1 0 1 . 6 7 5 2 0 1 7 . 6 1 9 . 8 9 7 ( - 2 ) . 1 4 6

u 3 1 1 1 2 1 2 1 1 0 . 2 2 8 2 0 1 9 . 2 0 2 2 0 1 8 . 4 3 7 - . 76 5 . 7 0 5 ( - 2 ) . 0 53


18/28

446 S. Miller e t a l .

Table 4 ( c o n t i n u e d ) .M o d e J ' K ' o K ' c . [ " I C ' - - c crn E" /- i c~ t t ~176 1 ~ - ~ / S ( ' f - 2 I R 'L ( C O ) c

u2 3 0 3 2 1 2 1 1 0 . 2 2 8 2 0 2 3 . 0 3 6 2 0 2 3 . 2 4 3 . 2 0 7 . 2 1 5 ( - 1 ) . 1 6 2u s 4 1 3 4 0 4 3 1 5 . 6 2 1 2 0 2 3 . 9 1 3 2 0 2 4 . 2 3 0 . 3 1 7 . 4 2 3 ( - 1 ) . 0 8 9u s 3 1 2 2 2 1 1 7 9 . 1 3 9 2 0 2 6 . 2 3 4 2 0 2 6 . 6 3 1 . 3 9 7 . 4 9 8 ( - 2 ) . 0 1 9u s 2 1 2 1 0 1 3 4 . 9 0 2 2 0 2 7 . 8 0 0 2 0 2 8 . 0 2 4 . 2 2 4 . 1 9 2 ( - 1 ) . 2 9 9u s 4 0 4 3 1 3 1 9 9 . 9 6 2 2 0 3 3 . 2 5 5 2 0 3 3 . 3 9 3 . 1 3 8 . 2 7 7 ( - 1 ) . 1 7 8u 2 3 1 3 2 0 2 1 0 1 . 6 7 5 2 0 3 4 . 6 1 7 2 0 3 4 . 7 8 0 . 1 6 3 . 2 2 9 ( - 1 ) . 3 7 7u s 2 2 1 2 1 2 1 1 0 . 2 2 8 2 0 3 5 . 1 5 2 2 0 3 5 . 3 5 9 . 2 0 7 . 2 4 5 ( - 1 ) . 1 8 6u s 3 2 2 3 1 3 1 9 9 . 9 6 2 2 0 3 6 . 1 5 3 2 0 3 6 . 3 3 3 . 1 8 0 . 3 3 9 ( - 1 ) . 2 1 8u 2 5 1 4 5 0 5 4 6 0 . 2 4 5 2 0 3 6 . 9 0 8 - . 4 1 9 ( - 1 ) . 0 1 1u ~ 4 1 4 3 0 3 1 9 6 . 0 2 4 2 0 3 8 . 1 9 6 2 0 3 8 . 3 1 0 . 1 1 4 . 2 7 6 ( - 1 ) . 0 9 2u s 3 3 0 3 2 1 2 9 5 , 9 4 7 2 0 3 8 . 8 0 7 2 0 3 8 . 9 3 6 . 1 2 9 . 5 6 5 ( - 1 ) . 0 7 2u s 5 0 5 4 1 4 3 1 7 . 1 3 5 2 0 3 8 . 8 4 8 2 0 3 8 . 6 3 4 - . 2 1 4 . 3 2 4 ( - 1 ) . 0 3 4u s 4 2 3 4 1 4 3 1 7 . 1 3 5 2 0 3 9 . 6 6 5 2 0 3 9 . 8 3 4 . 1 6 9 . 3 8 4 ( - 1 ) . 0 4 0u 2 5 1 5 4 0 4 3 1 5 . 6 2 1 2 0 4 0 . 6 7 8 2 0 4 0 .7 6 r . 0 8 2 . 3 2 2 ( - 1 ) . 0 6 8u ~ 6 0 6 5 1 5 4 6 0 . 7 7 1 2 0 4 1 . 6 4 1 - . 3 6 7 ( - 1 ) . 0 1 9u.~ 0 0 0 1 0 1 3 4 . 9 0 2 2 0 4 4 . 3 1 0 2 0 4 3 . 5 1 5 - . 7 9 5 . 8 1 4 ( - 2 ) . 1 2 8u s 5 2 4 5 1 5 4 6 0 . 7 7 1 2 0 4 4 . 4 5 5 . 4 0 6 ( - 1 ) . 0 2 1u 2 4 4 0 4 3 1 5 2 3 . 2 5 9 2 0 5 1 . 3 2 0 . 6 4 6 ( - 1 ) . 0 1 9v 2 4 3 2 4 2 3 4 1 9 . 3 3 3 2 0 5 2 . 5 3 6 . 3 7 3 ( - 1 ) . 0 1 5

u 2 4 1 3 3 2 2 2 8 3 . 2 4 2 2 0 5 6 . 2 9 2 . I 1 9 ( - 1 ) . 0 3 5u 2 3 3 1 3 2 2 2 8 3 . 2 4 2 2 0 5 6 . 5 1 4 2 0 5 6 . 4 1 6 - . 0 9 8 . 3 5 2 ( - I ) . 1 0 3u 3 2 1 2 2 1 l 1 3 6 . 3 1 1 2 0 6 6 . 9 9 5 2 0 6 6 . 4 1 5 - . 5 8 0 . 4 0 8 ( - 2 ) . 0 4 9u 3 3 3 1 3 3 0 3 7 7 . 6 8 7 2 0 6 9 . 1 6 1 2 0 6 8 . 4 6 1 - . 7 0 0 . 4 6 9 ( - 1 ) . 0 2 8u 3 3 3 0 3 3 1 3 7 7 . 0 5 8 2 0 7 0 . 5 7 0 2 0 6 9 . 8 6 9 - . 7 0 1 . 4 5 6 ( - 1 ) . 0 5 4u.~ I 1 1 1 1 0 5 7 . 9 7 6 2 0 7 1 . 4 5 4 2 0 7 0 . 7 0 8 - . 7 4 6 . 1 8 1 ( - 1 ) . 2 3 0u 3 2 2 1 2 2 0 1 8 2 , 0 3 3 2 0 7 3 . 3 4 1 2 0 7 2 . 6 0 7 - . 7 3 4 . 3 2 1 ( - 1 ) . 2 4 91,'3 2 2 0 2 2 1 179 .139 20 79 .1 57 207 8 .41 9 - .73 2 .284 ( -1 ) . 114u 2 2 2 1 I 1 0 5 7 . 9 7 6 2 0 8 7 . 4 0 4 2 0 8 7 . 6 3 0 . 2 2 6 . 1 9 9 ( - 1 ) . 2 5 51 '3 1 1 0 1 1 1 4 9 . 2 4 7 2 0 8 7 . 7 5 2 2 0 8 6 . 9 9 0 - . 7 6 2 . 1 2 8 ( - 1 ) . 3 5 7u 2 3 2 2 2 1 1 1 3 6 . 3 1 1 2 0 9 9 . 8 0 4 2 0 9 9 . 9 9 8 . 1 9 4 . 1 6 3 ( - 1 ) . 1 9 9


19/28

Calculation o f rotational and ro-vibrational line strengthsTable 4 (continued).

447

M o d e J ' K 'o K ' J " K ~ K " E " / ( D i f ( c a l c . ) / o3 i f(obs. )a / A fD o ._c / S ( f - - ob / IReI.(fD)CITI- I c i n - 1 C I~ - 1 c m - ~ D 2

u 2 2 2 0 I 1 1 4 9 . 2 4 7 2 1 0 0 . 0 6 0 2 1 0 0 , 3 0 7 , 2 4 7 . 1 0 6 ( - 1 ) . 2 9 6u 2 4 2 3 3 1 2 2 5 1 . 1 9 4 2 1 0 5 . 6 0 6 . 1 6 6 ( - 1 ) . 0 3 4u 2 5 2 4 4 1 3 3 9 8 . 8 8 1 2 1 0 6 . 3 4 5 - . 0 4 4 . 1 9 2 ( - 1 ) . 0 1 9u 3 2 1 1 2 1 2 1 1 0 . 2 2 8 2 1 1 5 . 5 3 2 - . 6 3 7 . 1 8 5 ( - 2 ) . 0 1 5~ I 0 1 0 0 0 0 , 0 0 0 2 1 1 9 . 2 9 3 - . 7 0 5 . 1 4 3 ( - 1 ) . 6 5 2u.~ 2 I 2 1 1 1 49 .2 47 215 4 .05 8 - ,533 .347 ( -1 ) 1 .000u 2 3 3 0 2 2 1 1 7 9 . 1 3 9 2 1 5 5 . 6 1 5 . 6 3 8 ( - 2 ) . 0 2 7u 2 3 3 I 2 2 0 1 8 2 . 0 3 3 2 1 5 7 . 7 2 3 - . 0 5 6 . 1 3 5 ( - 1 ) . 1 0 9u:; 2 [ ) 2 1 0 l 3 4 . 9 0 2 2 1 5 9 . 7 5 8 - . 6 1 3 . 3 1 3 ( - 1 ) . 5 1 9

2 1 0 6 . 3 0 12 1 1 4 . 8 9 52 1 1 8 . 5 8 82 1 5 3 . 5 2 5

2 1 5 7 . 6 6 72 1 5 9 . 1 4 5

u3 2 1 1 l l Ou2 4 3 2 3 2 1u~ 4 2 2 3 1 3u3 3 0 3 2 0 2u3 3 1 3 2 1 2

3 2 2 2 2 13 1 2 2 1 13 2 1 2 2 0

4 0 4 3 0 3u2 3 3 I 2 0 2

4 1 4 3 1 3u2 5 2 3 4 1 4

4 1 3 3 1 24 2 3 3 2 25 0 5 4 0 44 2 2 3 2 1

u2 4 3 2 3 0 34 4 0 3 3 1

u2 4 4 1 3 3 0u2 5 2 3 4 1 4

5 7 . 9 7 6 2 1 6 7 . 7 8 5 2 1 6 7 . 1 6 6 - . 6 1 9 . 2 6 9 ( - 1 ) . 3 5 92 9 5 . 9 4 7 2 1 7 5 . 9 2 2 . 1 1 8 ( - I ) . 0 1 61 9 9 . 9 6 2 2 1 9 4 . 2 6 0 . 2 3 3 ( - 2 ) . 0 1 61 0 1 . 6 7 5 2 1 9 6 . 3 6 2 2 1 9 5 . 8 6 1 - . 5 0 1 . 4 6 6 ( - 1 ) . 8 2 91 1 0 . 2 2 8 2 1 9 6 . 8 7 1 2 1 9 6 . 4 7 5 - . 3 9 6 . 5 9 0 ( -1 ) . 4 8 31 7 9 . I 3 9 2 2 1 0 . 5 3 7 2 2 1 0 . 3 3 1 - . 2 0 6 . 6 1 7 ( - 1 ) . 2 6 21 3 6 . 3 1 1 2 2 1 5 . 1 5 4 2 2 1 4 . 6 0 5 - . 5 4 9 .4 4 9 ( - 1 ) . 5 7 71 8 2 . 0 3 3 2 2 1 5 . 7 6 2 2 2 1 5 . 4 3 7 - . 2 3 5 . 5 4 3 ( - 1 ) . 4 5 0

1 9 6 . 0 2 4 2 2 2 9 . 8 8 3 . 5 9 1 ( - 1 ) . 2 1 61 0 1 . 6 7 5 2 2 3 8 . 0 8 2 2 2 3 8 . 0 1 4 - . 0 6 8 . 5 8 2 ( - 2 ) . 1 0 51 9 9 . 9 6 2 2 2 4 0 . 0 3 3 2 2 3 9 . 8 0 9 - . 2 2 4 . 7 7 0 ( - 1 ) . 5 4 43 1 7 . 1 3 5 2 2 4 7 . 9 2 5 2 2 4 8 . 0 3 3 . 1 0 8 . 2 7 1 ( - 1 ) . 0 312 5 1 . 1 9 4 2 2 5 7 . 7 7 4 2 2 5 7 . 2 9 3 - . 4 8 1 . 5 9 4 ( - 1 ) . 1 2 92 8 3 . 2 4 2 2 2 5 8 . 1 6 0 2 2 5 7 . 9 6 8 - . 1 9 2 . 7 8 8 ( - 1 ) . 2 5 23 1 5 . 6 2 1 2 2 6 4 . 1 0 3 2 2 6 3 . 8 2 8 - . 2 7 5 . 7 5 6 ( - 1 ) . 1 7 82 9 5 . 9 4 7 2 2 6 8 . 0 9 6 2 2 6 7 . 7 1 9 - . 3 7 7 . 6 7 0 ( - 1 ) . 0 9 51 9 6 . 0 2 4 2 2 7 5 . 8 4 6 . 1 7 0 ( - 1 ) . 0 6 33 7 7 , 0 5 8 2 2 7 9 . 0 1 1 2 2 7 9 . 0 9 0 . 0 7 9 . 8 9 0 ( - 1 ) . 1 1 73 7 7 . 6 8 7 2 2 7 9 . 4 6 1 2 2 7 9 . 5 2 1 . 0 6 0 . 8 8 2 ( - 1 ) . 0 583 1 7 . 1 3 5 2 2 8 7 . 7 9 0 . 7 3 9 ( - 1 ) . 0 8 7


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448 S . M i l l e r et al .T a b l e 4 (continued).

M o d e J 'K ' ~K ' J " K ' K ~ E " / r r 1 7 6 A o g , _ _ , / S ( f - - i ) b / IReI.(fD)c n - i - 1 c I n - I C1T1-1 c m - 1 D 2

V3 5 1 4 4 1 3 3 9 8 .8 8 1 2 2 9 1 .2 5 9 2 2 9 0 .8 7 3 - . 3 8 6 . 6 5 1 ( - 1 ) . 0 7 0v '3 6 1 6 5 1 5 4 6 0 .7 7 1 2 2 9 3 .8 2 4 . 7 5 1 ( - 1 ) . 0 4 5u.3 6 0 6 5 0 5 460 .245 229 9 .32 2 .964 ( -1) .029

R . M . S . d e v i a t i o n o f c a l c u l a t e d f r o m e x p e r i m e n t a l f r e q u e n ci e s = 0 . 4 0 0 c m - 1 .8 6 l i n e s c o n s i d e r e d .

" D a t a f r o m R e f e r e n c e 9 .I, P o w e r s o f t e n i n b r a c k e t s ." M a x . i n t e g r a t e d a b s o r p t i o n c o e f fi c i e n t = 5 . 2 0 9 1 0 17 ( c m . s e c - 1 m o l e - l ) .'~ D a t a f ro m S h y J . - T . , 1 9 8 2 , Phi). Dissertation, U n i v . o f A r i z o n a .

R e a s s i g n e d f r o m 6 o 6 - 5 1s o n f re q u e n c y c o n s i d e r a t i o n s .

T a b l e 5 . C a l c u l a t e d a n d o b s e r v e d v 1 t r a n s i t i o n s fo r D 2 H + . R e l a t i v e i n t e n s it i e s c a l c u l a t e d a t3 0 0 K .

J 'K ~ K ; J " K ~ K : E " / ~ , A c a l c . F ~ , ~ o b s . ) ~ A ~ / S ~ - i ) b / IR .,.(W )~ - 1 ~ - 1 ~ - 1 ~ - t D 2l 1 1 2 2 0 1 8 2 .0 3 3 2 6 0 3 .6 1 2 . 1 7 3 ( - 1 ) . 3 3 83 0 3 4 1 4 3 1 7 . 1 3 5 2 6 1 3 . 9 2 2 . 4 2 3 ( - 1 ) . 2 1 8l I 0 2 2 1 1 7 9 .1 3 9 2 6 1 5 .1 2 1 . 2 2 3 ( - 1 ) . 2 2 33 2 2 4 1 3 3 9 8 . 8 8 1 2 6 1 7 . 1 4 8 . 1 4 4 ( - 1 ) . 1 0 13 1 3 4 0 4 3 1 5 . 6 2 1 2 6 1 9 . 1 6 5 . 4 0 8 ( - 1 ) . 4 2 42 0 2 3 1 3 1 9 9 . 9 6 2 2 6 3 7 . 8 6 8 2 6 3 7 . 5 2 4 - . 3 4 4 . 3 0 4 ( - 1 ) . 5 5 53 2 2 3 3 1 3 7 7 . 0 5 8 2 6 3 8 . 9 7 2 - . 1 6 7 ( - 1 ) . 1 3 02 1 2 3 0 3 1 9 6 . 0 2 4 2 6 4 9 . 9 7 6 . 2 6 2 ( - 1 ) . 2 4 54 0 4 4 1 3 3 9 8 . 8 8 1 2 6 5 0 . 3 9 6 . 2 4 8 ( - 1 ) . 1 7 53 1 3 3 2 2 2 8 3 . 2 4 2 2 6 5 1 . 5 4 4 . 1 8 9 ( - 1 ) . 2 3 24 2 2 4 3 1 5 2 3 .2 5 9 2 6 5 8 .4 5 3 - . 3 7 6 ( - 1 ) . 1 4 71 0 1 2 1 2 1 1 0 . 2 2 8 2 6 6 1 . 5 9 9 2 6 6 1 . 2 5 8 - . 3 4 1 . 2 1 0 ( - 1 ) . 2 9 62 1 2 2 2 1 1 7 9 . 1 3 9 2 6 6 6 . 8 6 1 ~ - . 1 2 5 ( - 1 ) . 1 2 73 0 3 3 1 2 2 5 1 . 1 9 4 2 6 7 9 . 8 6 3 . 2 6 6 ( - 1 ) . 1 9 34 1 3 4 2 2 4 5 0 . 5 8 4 2 6 8 0 . 5 9 9 - . 5 1 9 ( - 1 ) . 2 8 9I 1 1 2 0 2 1 0 1 . 6 7 5 2 6 8 3 . 9 7 1 2 6 8 3 . 6 1 3 - . 3 5 8 . 1 1 6 ( - 1 ) . 3 4 50 0 0 1 1 1 4 9 .2 4 7 2 6 8 8 .0 5 5 - . 1 4 1 ( - 1 ) . 5 4 2


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C a l c u l a t i o n o f ro t a t i o n a l a n d r o - v i b r a t i o n a l l in e s t r e n g t h sT a b l e 5 (continued).

4 4 9

J'K'o K'~ J" K " K'~ E" / e o o , ( c a l c . ) / o g i y ( o b s . ) ~ Aeoo__ S ( f - i ) ~ / IR rc m - 1 c m - ~ c m - ~ c m - t 0 2

3 1 2 3 2 1 2 9 5 . 9 4 7 2 6 8 9 . 3 4 5 - . 4 0 3 ( - 1 ) . 2 3 72 1 1 2 2 0 1 8 2 . 0 3 3 2 6 8 9 . 7 0 1 - . 2 1 0 ( - 1 ) . 4 2 52 0 2 2 1 1 1 3 6 .3 1 1 2 7 0 1 . 5 1 9 2 7 0 1 . 1 8 9 - . 3 3 0 . 2 7 4 ( - 1 ) . 6 9 4

1 0 1 1 1 0 5 7 . 9 7 6 2 7 1 3 . 8 5 1 - . 2 1 5 ( - 1 ) . 3 9 81 1 0 1 0 1 3 4 . 9 0 2 2 7 5 9 . 3 5 7 2 7 5 9 . 0 3 6 - . 3 2 1 . 2 0 3 ( - 1 ) . 4 2 72 1 1 2 0 2 1 0 1 . 6 7 5 2 7 7 0 . 0 5 9 2 7 6 9 . 7 5 3 - . 3 0 6 . 2 5 3 ( - 1 ) . 7 7 63 2 1 3 1 2 2 5 1 . 1 9 4 2 7 7 7 . 5 0 9 2 7 7 7 . 1 9 6 - . 3 1 3 . 3 6 6 ( - 1 ) . 2 7 52 2 0 2 1 1 1 3 6 . 3 1 1 2 7 7 9 . 5 6 5 2 7 7 9 . 2 3 8 - . 3 2 7 . 1 8 9 ( - 1 ) . 4 9 34 2 2 4 1 3 3 9 8 . 8 8 1 2 7 8 2 . 8 3 1 2 7 8 2 . 5 4 3 - . 2 8 8 . 4 6 6 ( - 1 ) . 3 4 51 1 . 1 0 0 0 0 . 0 0 0 2 7 8 5 . 6 4 6 2 7 8 5 . 3 3 2 - . 3 1 4 . 1 3 8 ( - 1 ) . 6 9 32 0 2 1 1 1 4 9 . 2 4 7 2 7 8 8 . 5 8 2 2 7 8 8 . 3 0 0 - . 2 8 2 . 1 2 4 ( - 1 ) . 4 9 43 1 2 3 0 3 1 9 6 . 0 2 4 2 7 8 9 . 2 6 9 2 7 8 8 . 9 9 0 - . 2 7 9 . 2 3 5 ( - 1 ) . 2 3 14 3 1 4 2 2 4 5 0 . 5 8 4 2 8 0 1 . 2 1 1 - - . 3 2 2 ( - 1 ) . 1 8 82 2 1 2 1 2 1 1 0 . 2 2 8 2 8 0 2 . 7 4 6 2 8 0 2 . 4 3 6 - . 3 1 0 . 1 0 6 ( - 1 ) . 1 5 82 ] 2 1 0 1 3 4 . 9 0 2 2 8 1 1 . 0 9 8 2 8 1 0 . 8 0 0 - . 2 9 8 . 2 1 1 ( - 1 ) . 4 5 34 1 3 4 0 4 3 1 5 . 6 2 1 2 8 1 5 . 5 6 1 2 8 1 5 . 3 1 4 - . 2 4 7 . 2 0 6 ( - 1 ) . 2 3 03 2 2 3 1 3 1 9 9 . 9 6 2 2 8 1 6 . 0 6 8 2 8 1 5 . 7 7 8 - . 2 9 0 . 1 5 5 ( - 1 ) . 3 0 13 0 3 2 1 2 1 1 0 . 2 2 8 2 8 2 0 . 8 2 9 2 8 2 0 . 5 6 4 - . 2 6 5 . 2 8 4 ( - 1 ) . 4 2 63 3 1 3 2 2 2 8 3 . 2 4 2 2 8 2 3 . 5 7 4 - . 1 3 4 ( - 1 ) . 1 7 53 1 3 2 0 2 1 0 1 . 6 7 5 2 8 3 3 . 1 1 2 2 8 3 2 . 8 2 8 - . 2 8 4 . 3 1 9 ( - 1 ) 1 . 0 0 04 1 3 3 2 2 2 8 3 . 2 4 2 2 8 4 7 . 9 4 0 - . 1 6 2 ( - 1 ) . 2 1 44 0 4 3 1 3 1 9 9 . 9 6 2 2 8 4 9 . 3 1 6 2 8 4 9 . 0 6 6 - . 2 5 0 . 4 5 2 ( - 1 ) . 8 8 95 2 4 5 1 5 4 6 0 . 7 7 1 2 8 5 4 . 2 5 4 . 1 7 9 ( - 1 ) . 1 01

4 1 4 3 0 3 1 9 6 . 0 2 4 2 8 5 4 . 6 8 2 2 8 5 4 . 4 2 1 - . 2 6 1 . 4 6 1 ( - 1 ) . 4 6 32 2 1 1 1 0 5 7 . 9 7 6 2 8 5 4 . 9 9 8 2 8 5 4 . 7 0 7 - . 2 9 1 . 2 0 1 ( - 1 ) . 3 9 22 2 0 1 1 1 4 9 . 2 4 7 2 8 6 6 . 6 2 8 2 8 6 6 . 3 5 0 - . 2 7 8 . 1 5 0 ( - 1 ) . 6 1 25 0 5 4 1 4 3 1 7 . 1 3 5 2 8 7 5 . 1 7 7 2 8 7 4 . 9 4 8 - . 2 2 9 . 6 1 8 ( - 1 ) . 3 5 05 1 5 4 0 4 3 1 5 . 6 2 1 2 8 7 7 . 1 8 9 2 8 7 6 . 9 5 4 - . 2 3 5 . 6 2 0 ( - 1 ) . 7 0 83 2 2 2 1 1 1 3 6 . 3 1 1 2 8 7 9 . 7 1 9 2 8 7 9 . 4 4 2 - . 2 7 7 . 2 2 9 ( - 1 ) . 6 2 0


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450 S. Miller e t a l .Table 5 (continued).

J 'K ', , K ' J" K ~ K~ ' E " / co i f(ca lc . )/ O J i f ( o b s . ) a / A ( D o _ c / S ( f - - i ) b / I R e I . ( ( - O ) ccm-~ cm-~ cm-~ cm-t D 2

5 14 4 2 3 419,333 2885.351 - .318(-1) ,1114 2 3 3 1 2 251.194 2899.505 2899.242 -.263 .287(-1) .2256 0 6 5 1 5 460.771 2899.569 2899.362 -.207 .786(-1) .4516 1 6 5 0 5 460.245 2900.267 .787(-1) .2265 2 4 4 1 3 398,881 2916.143 2915.899 -.244 .384(-1) .2986 1 5 5 2 4 585.431 2917.023 .498(-1) .1583 2 1 2 1 2 110.228 2918.476 2918.238 -.238 .937(-2) .1457 0 7 6 1 6 630.248 2923.123 .960(-1) .1237 1 7 6 0 6 630.074 2923.384 .959(-1) .2463 3 1 2 2 0 182.033 2924.783 2924.524 -.249 .307(-1) .6763 3 0 2 2 1 179.139 2928.319 2928,067 -.252 ,297(-1) .3328 0 8 7 1 7 825.162 2946.134 - .114(+0) .1154 3 2 3 2 1 295.947 2951.777 2951.532 -.245 .299(-1) .1934 3 1 3 2 2 283.242 2968.552 2968.334 -.218 .252(-1) .346

5 3 3 4 2 2 450,584 2972.063 - .315(-1) .1944 2 2 3 1 3 199,962 2981.751 - .534(-2) .1104 4 1 3 3 0 377.687 2989.625 - .429(-1) .1894 4 0 3 3 1 377.058 2990.367 2990.154 d -.213 .428(-1) .378

R.M.S. deviat ion of calculated from experimentM frequencies = 0.281cm -1.34 lines considered.a Data from Reference 1O.b Powers of ten in brackets.c Max. integrated absorption coefficient= 2.465 x 1017 (cm. sec -1 m ole- l) .,l Reassigned from 441 - 330.

tables 6 and 7 respectively. We have considered the spectral range from 0 to1500 cm -1 , an d have includ ed all trans itio ns which have relative intensity of 0.1 ormore at 300K. in practice this reduces the range to a ma xi mum ~oiS of ar ou nd400 cm -l for both molecules, an d excludes all states with J " > 7. It is our i nte nti onto perform a systematic study of transiti ons invol ving highly excited J states whichwould be appropriate for spectra recorded at higher temperatures.

Wit hi n these limits we find 32 tran siti ons for H2D + (table 6) and 42 for D2H +(table 7). In table 6, we have also included the three experimentally observed lines


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C alcu la t i on o f ro ta t i ona l a nd ro -v ibra t i ona l l i ne s t r eng ths 4 5 1T a b l e 6. P u r e r o t a t i o n a l t r a n s i t i o n s f o r H 2 D + i n t h e g r o u n d s t a te . R e l a t i v e i n t e n s it i e s

c a l c u l a t e d a t 3 0 0 K .

J 'K ', r 'c J " K ' . r ~ E ' / E " I ~ o i t/ S O - i ) a / l . . L ( c o ) b A T f /c m - ~ c m - ~ c m ' - ~ D z s - "2 2 0 2 2 11 1 0 1 1 11 0 1 0 0 02 1 2 1 1 12 0 2 1 0 12 1 1 1 1 03 1 3 2 1 23 0 3 2 0 23 2 2 2 2 14 1 4 3 1 33 1 2 2 1 14 0 4 3 0 33 2 1 2 2 04 2 3 3 2 25 1 5 4 1 45 0 5 4 0 44 3 2 3 3 14 1 3 3 1 24 3 1 3 3 04 2 2 3 2 15 2 4 4 2 36 1 6 5 1 56 0 6 5 0 5514 413533 432717 616532 4315 2 3 4 2 26 1 5 5 1 4634 533

2 2 3 . 8 1 3 2 1 8 . 6 2 0 5 . 1 9 3 c7 2 . 4 3 3 6 0 . 0 2 1 1 2 . 4 1 2 ~4 5 . 6 7 8 0 . 0 0 0 4 5 . 6 7 8 e

1 3 8 . 8 1 5 6 0 . 0 2 1 7 8 . 7 9 41 3 1 . 5 9 4 4 5 . 6 7 8 8 5 . 9 1 61 7 5 . 8 5 9 7 2 . 4 3 3 1 0 3 . 4 2 62 5 3 . 9 6 9 1 3 8 . 8 1 5 1 1 5 . 1 5 42 5 1 . 3 1 6 1 3 1 . 5 9 4 1 1 9 . 7 2 23 5 4 , 6 7 7 2 1 8 . 6 2 0 1 3 6 . 0 5 74 0 3 . 5 2 9 2 5 3 . 9 6 9 1 4 9 . 5 603 2 6 . 0 1 1 1 7 5 . 8 5 9 1 5 0 . 1 5 34 0 2 . 7 2 5 2 5 1 . 3 1 6 1 5 1 . 4 1 03 7 6 . 2 0 4 2 2 3 . 8 1 3 1 5 2 . 3 9 15 3 1 , 1 5 8 3 5 4 . 6 7 7 1 7 6 . 4 805 8 6 . 2 6 6 4 0 3 . 5 2 9 1 8 2 . 7 3 75 8 6 . 0 4 9 4 0 2 . 7 2 5 1 8 3 . 3 2 46 4 5 . 4 1 1 4 5 8 . 2 8 3 1 8 7 . 1 2 95 1 5 . 9 3 0 3 2 6 . 0 1 1 1 8 9 . 9 1 96 5 4 3 2 1 4 5 9 .7 6 3 1 9 4 ~ 5 85 8 1 . 2 3 5 3 7 6 . 2 0 4 205.032744.825 531 .158 213.6688 0 1 . 4 8 4 5 8 6 , 2 6 6 215.2178 0 1 . 4 3 0 5 8 6 . 0 4 9 2 1 5 . 3 8 17 3 8 4 7 2 5 1 5 .9 3 0 2 2 2 .5 4 18 7 6 , 2 9 1 6 4 5 . 4 1 1 2 3 0 . 8 7 91 0 4 8 . 7 0 9 8 0 1 . 4 8 4 2 4 7 . 2 2 59 0 3 . 7 5 0 6 5 4 . 3 2 1 2 4 9 . 4 2 9832,870 5 8 1 . 2 3 5 2 5 1 . 6 3 59 9 0 . 7 3 9 7 3 8 . 4 7 2 2 5 2 . 2 6 71 1 4 7 . 5 1 6 8 7 6 . 2 9 1 2 7 1 . 2 2 6

. 1 2 7 ( + 1 ) . 0 0 1 ,1 1 2 (- 4). 606(+0) , 014 . 121( -3 ). 4 0 5 ( + 0 ) . 0 3 5 .1 2 1 (- 1). 6 1 o ( + o ) z 2 8 . 1 8 7 ( - 1 ). 7 6 1 ( + 0 ) . 1 7 1 .3 0 2 (- 1). 6o9(+o) . 503 . 4o2( -1 ). I 0 7 ( + I ) . 7 7 6 . 7 0 2 ( - I ). 1 1 1 ( + i ) .297 . 8 5 1 ( - I ). 688(+0) . 152 , 777( -1 ). 1 4 9 ( + 1 ) . 97 4 . 1 7 3 ( + 0 ). 1 0 4 ( + 1 ) 1 .0 0 0 1 5 9 ( + 0 ). 1 4 9 ( + 1 ) . 3 3 7 . 1 8 1 ( + 0 ). 7 0 7 ( + 0 ) . 1 8 4 . n 2 ( + o ). 1 2 1 ( + 1 ) .215 . 2 3 2 ( + o ). 1 9 0 ( + 1 ) . 8 4 4 3 3 0 ( + 0 ).190(+i) .284 .333(+0).752(+0) .268 .171(+0).139(+1) 9 .331(+0).754(+0) .284 .193(+0)9 2 6 ( + 1 ) . ~ 5 6 . 3 7 8 ( + 0 ). 1 6 6 ( + 1 ) . 1 72 . 4 6 2 ( + 0 ). 2 3 0 ( + 1 ) . 55 5 5 5 4 ( + 0 ). 2 3 0 ( + 1 ) . 1 85 . 5 5 5 ( + 0 )9 7 1 ( + 1 ) . 60 9 5 3 8 ( + o ). 1 3 5 ( + I ) , 27 2 . 4 7 3 ( + 0 ). 2 7 1 ( + 1 ) . 2 88 . 8 6 0 ( + 0 ). 1 3 7 ( + 1 ) . 3 00 . 6 0 7 ( + 0 )9 6 9 ( + i ) . 1 7 7 7 8 9 ( + 0 ). 2 0 8 ( + 1 ) . 3 0 9 . 8 0 8 ( + 0 ). 1 8 5 ( + 1 ) . 15 8 . 8 9 2 ( + 0 )


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4 5 2 S . M i l l e r e t a l .T a b l e 6 ( c o n t i n u e d ) .

J ' K ' a r ' c J " K ' ~ K 7 cm-E/ cm- trot~ S ( f D - i ) ' / I R e l . (O z ) ) A a f /8 ] 8 7 1 7 1 3 2 7 . 5 2 1 1 0 4 8 . 7 0 9 2 7 8 . 8 1 2 . 3 1 2 (+ 1 ) . 1 2 2 . 1 2 5 (+ 1 )7 1 6 6 1 5 1 2 7 2 . 9 6 2 9 9 0 . 7 3 9 2 8 2 . 2 2 4 . 2 4 8 (+ 1 ) . 1 3 0 . 1 1 7 (+ 1 )6 3 3 5 3 2 1 2 0 5 .5 9 9 9 0 3 . 7 5 0 3 0 1 . 8 5 0 . 1 9 1 ( + 1 ) . 1 67 . 1 2 7 ( + 1 )4 3 1 3 1 2 6 5 4 . 3 2 1 3 2 6 . 0 1 1 3 2 8 . 3 1 0 . 9 7 1 ( -1 ) . 1 5 3 . 1 2 0 (+ 0 )5 3 2 4 1 3 9 0 3 . 7 5 0 5 1 5 . 9 3 0 3 8 7 . 8 1 9 . 1 3 1 ( + 0 ) . 1 04 . 2 1 7 ( + 0 )

a P o w e r s o f t e n i n b r a c k e t s .b M a x . i n t e g r a t e d a b s o r p t i o n c o e f f ic i e n t = 2 . 3 4 3 x 1 0 1 7 ( c m . s e c - 1 m o l e - l ) .c O b s e r v e d a t 5 . 2 0 2 c m - l ( R e f . 1 4 ) .


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Calculation o f rotational and ro-vibrational lin e strengthsT a b l e 7 (continued).

4 5 3

j ' t , : : 1,:'c J" i ,: : K : e ' / e" / " , d S ( f - 0~ ~R.,.(o~) A ~ r /c m - ' c m - ' c m " -~ D 2 s - :1

6 1 63 2 15 2 46 I 57 O 73 3 17 1 73 1 26 2 58 0 84 3 27 2 64 3 15 3 34 2 24 4 14 4 05 3 25 4 25 4 16 4 35 5 15 5 06 4 26 3 36 5 2

6 5 16 6 0

5 0 5 6 3 0 . 2 4 8 4 6 0 . 2 4 5 1 7 0 . 00 3 . 1 3 4 ( + 1 )2 1 2 2 9 5 . 9 4 7 1 1 0 . 2 2 8 1 8 5 . 7 1 9 . 1 8 9 (+ 0 )4 1 3 5 8 5 . 4 3 1 3 9 8 . 8 8 1 1 8 6 . 5 5 0 . 6 7 8 (+ 0 )5 2 4 7 7 4 . 6 9 1 5 8 5 . 4 3 1 1 8 9 .2 6 0 . 8 5 8 (+ 0 )6 1 6 8 2 5 . 1 0 5 6 3 0 . 2 4 8 1 9 4 .8 5 8 . 1 6 0 (+ 1 )2 2 0 3 7 7 . 0 5 8 1 8 2 . 0 3 3 1 9 5 . 0 2 5 . 6 3 3 (+ 0 )6 0 6 8 2 5 . 1 6 2 6 3 0 . 0 7 4 1 9 5 . 0 8 8 . 1 6 0 ( + 1 )2 2 1 3 7 7 . 6 8 7 1 7 9 . 1 3 9 1 9 8 . 5 4 8 . 6 1 8 (+ 0 )5 1 4 7 7 9 . 6 1 3 5 7 4 . 5 6 3 2 0 5 . 0 4 9 . 8 9 5 (+ 0 )7 1 7 1 0 4 5 . 1 79 8 2 5 .1 6 2 2 2 0 . 0 1 8 . 1 8 6 ( + 1 )3 2 1 5 1 9 . 2 3 7 2 9 5 . 9 4 7 2 2 3 . 2 9 0 . 5 8 6 ( + 0 )6 1 5 1 0 0 0 . 3 2 0 7 7 4 . 6 9 1 2 2 5 . 6 2 8 . 1 1 5 (+ 1 )3 2 2 5 2 3 . 2 5 9 2 8 3 . 2 4 2 2 4 0 . 0 1 7 . 5 0 7 ( + 0 )4 2 2 6 9 5 . 8 4 1 4 5 0 . 5 8 4 2 4 5 . 2 5 7 . 5 8 0 ( + 0 )3 1 3 4 5 0 . 5 8 4 1 9 9 . 9 62 2 5 0 . 6 2 2 . 1 0 8 ( + 0 )3 3 0 643.244 377.687 265.557 .921(+0)3 3 1 6 4 3 . 3 5 3 3 7 7 . 0 5 8 2 6 6 . 2 9 5 . 9 2 0 ( + 0 )4 2 3 7 0 9 . 4 4 7 4 1 9 . 3 3 3 2 9 0 . 1 1 4 . 3 6 6 ( + 0 )4 3 1 8 2 0 . 2 6 9 5 2 3 . 2 5 9 2 9 7 . 0 1 0 . 8 3 8 ( + 0 )4 3 2 8 2 1 . 1 8 4 5 1 9 . 2 3 7 3 0 1 . 9 4 7 . 8 2 6 ( + 0 )5 3 2 1 0 3 2 . 5 8 4 7 0 9 . 4 4 7 3 2 3 .1 3 7 . 7 6 2 ( + 0 )4 4 0 9 7 6 . 1 7 9 6 4 3 . 3 5 3 3 3 2 . 8 2 6 . 1 2 4 ( + 1 )4 4 1 9 7 6 . 1 9 6 6 4 3 . 2 4 4 3 3 2 . 9 5 2 . 1 2 4 ( + 1 )5 3 3 1 0 3 6 .6 5 8 6 9 5 .8 4 1 3 4 0 . 8 1 7 . 7 0 6 ( + 0 )5 2 4 9 3 6 . 7 7 9 5 8 5 . 4 3 1 3 5 1 . 3 4 8 . 2 3 8 ( + 0 )5 4 1 1 1 8 6 . 1 3 2 8 2 1 . 1 8 4 3 6 4 . 9 4 7 . 1 1 4 (+ 1 )

5 4 2 1 1 8 6 . 30 2 8 2 0 . 2 6 9 3 6 6 .0 3 4 . 1 1 4 ( + 1 )5 5 1 1 3 7 3 . 3 9 0 9 7 6 . 1 7 9 3 9 7 . 2 1 1 . 1 5 8 ( + 1 )

. 2 2 4 . 1 5 9 ( + o )

. 1 9 5 . 5 4 4 ( - 1 )

. 3 5 3 . 1 2 5 ( + o )

. 1 8 7 . 1 4 o ( + o )

. 1 4 8 . 2 4 8 ( + 0 )1 . o o o . 2 1 o ( + o ).296 .249(+0). 5 0 9 . 2 1 7 ( + o ).117 .186(+0). 1 6 3 . 3 6 6 ( + 0 ). 3 3 2 . 2 2 8 ( + 0 ).133 .276(+0). 6 8 3 . 2 4 4 ( + 0 ). 3 6 2 . 2 4 5 ( + 0 ).233 .594(-1).460 .601(+0). 9 2 5 . 6 0 6 ( + 0 ). 1 7 1 . 2 5 5 ( + 0 ). 4 9 1 . 6 2 6 ( + 0 ). 2 5 2 . 6 4 8 ( + 0 ). 1 0 3 . 6 2 1 ( + 0 ).479 .130(+1)2 4 0 1 3 0 ( + 1 ).220 .675(+0). 1 3 1 . 2 4 9 ( + 0 ).I07 . 1 3 3 ( + 1 )

. 2 1 5 . 1 3 5 ( + 1 ).158 .239(+I)

P o w e r s o f t e n i n b r a c k e t s .b M a x . i n t e g r a t e d a b s o r p t i o n c o e f fi c ie n t = 1 .3 9 2 1 01 7 ( c m . s e c - 1 m o l e - l ) .

O b s e r v e d a t 4 5 . 7 0 2 c m - l ( R e f . 1 6) .


26/28

4 5 41 .0

WC

t .t ~

~ 0 . 5m

5 1 3 - 4 o 4

4 o , - 3 131a-2o2

1 0 0

Figure.

S . M i l l e r e t a l .

331-22o4 , o - 3 s l

3 2 2 - 2 ~

0 6 - -

2 0 0 3 0 0F r e q u e n c y / c m -~

R o t a t i o n a l s p e c t r u m o f D 2 H + a t 3 0 0 K .

5 5 1 " d ~ ' 4 0

4 0 0

[ 1 3 - 1 5 ] , e v e n t h o u g h t h e i r r e l a t i v e i n t e n s i t i e s a t t h i s t e m p e r a t u r e f a l l b e l o w t h e 1 0p e r c e n t c u t - o f f . T h e c a l c u l a t e d f r e q u e n c i e s a r e i n v e r y g o o d a g r e e m e n t w i t h e x p e r i -m e n t . W e o b t a i n v a lu e s o f 5" 1 9 3 e m - 1 f o r th e 2 2 o - 2 2 1 l in e m e a s u r e d a t5 . 2 0 2 c m - 1 [ 1 4 ] a n d 1 2 . 4 1 2 e m - 1 f o r t h e 1 1 o - 1 1~ l in e a t 1 2 .4 2 3 c m - ~ [ 1 3 ] .

R e c e n t l y , E v e n s o n [ 1 6 ] , h a s m e a s u r e d t h e l o l - 0 o o l in e a t 4 5 . 7 0 3 c m - ~ , a g a ini n g o o d a g r e e m e n t w i t h o u r c a l c u l a t ed v a l u e o f 4 5 . 6 7 8 e r a - 1 . I n a d d i t i o n , h e w a sa b l e t o i d e n t i f y a l in e a t 4 5 . 7 0 2 c m - 1 a s t h e 2 2 0 - 2 ~1 l i n e o f D 2 H + , i s th e f ir s tm e a s u r e d l i n e f o r t h i s s p e c i e s , u s i n g d a t a p r e p a r e d f o r t h i s p a p e r ( p r e d i c t e d f r e -q u e n c y 4 5 . 7 2 3 e r a - 1 ) .

T h e s e r e s u l t s b e ar o u t t h e t r e n d o f o u r r o - v i b r a t i o n a l d a t a , w h i c h i n d i c a t e d t h a tt h e r o t a t io n a l t e r m v a l u e s w e r e b e i n g c o m p u t e d w i t h a h i g h l e v el o f a c c u r a cy a n dt h a t t h e d e v i a t i o n f r o m e x p e r i m e n t w a s d u e t o e r r o r s i n t h e v i b r a t i o n a l b a n d o r i g i n .

8/3/2019 Steven Miller et al- First principles calculation of rotational and r

steven miller et al- first principles calculation of rotational and ro-vibrational line strengths:...

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