Electronic Structure and Spectra of Light Alkali Diatomic Molecules

1 Electronic Structure and Spectra of Light Alkali Diatomic Molecules and Their Molecular Cations D. D. KONOWALOW and M. E. ROSENKRANTZ

Downloaded by 80.82.77.83 on May 9, 2017 | http://pubs.acs.org Publication Date: March 8, 1982 | doi: 10.1021/bk-1982-0179.ch001

State University of New York, Binghamton, Department of Chemistry, Binghamton, NY 13901

A l l - e l e c t r o n a b - i n i t i o c a l c u l a t i o n s of the potential curves and wavefunctions f o r the eight lowest- l y i n g e l e c t r o n i c s t a t e s of Li and of Na and the s i x l o w e s t - l y i n g e l e c t r o n i c s t a t e s o f Li + and Na + are used to p r e d i c t the s p e c t r a l features of a v a r i e t y of t r a n s i t i o n s . We s c a l e these r e s u l t s to p r e d i c t q u a l i t a t i v e l y s e v e r a l aspects o f the s t r u c ture and spectra of K , K +, Rb , Rb +, Cs and Cs +. 2

2

2

2

2

2

2

2

2

2

Recently we have reported ab i n i t i o a l l - e l e c t r o n quantummechanical i n v e s t i g a t i o n s of eight low-lying s t a t e s o_f each o f L i and N a (JL-6) and of s i x low-lying s t a t e s of L i (]_>§) • The computation of the p o t e n t i a l energy curves f o r the low-lying s t a t e s of N a at l a r g e separations (15^R^30 bohr) w i l l be reported s h o r t l y (9). Here, we r e p o r t , f o r the f i r s t time, ab i n i t i o computations of the s i x l o w e s t - l y i n g e l e c t r o n i c s t a t e s of Na2 . These comput a t i o n s u t i l i z e the b a s i s set developed to describe the low-lying states of the n e u t r a l N a molecules (6) and u t i l i z e i n t e g r a l s which have been computed p r e v i o u s l y (6,9). The molecular energies computed at the s i n g l e - c o n f i g u r a t i o n s e l f - c o n s i s t e n t f i e l d (SC-SCF) l e v e l are l i s t e d i n Table I. These SC-SCF comput a t i o n s should provide r e l a t i v e l y r e l i a b l e p o t e n t i a l curves f o r what are e f f e c t i v e l y one-electron systems. We do not attempt to describe the e l e c t r o n c o r r e l a t i o n a s s o c i a t e d with the core e l e c t r o n motions nor that a s s o c i a t e d with the p o l a r i z a t i o n of the core e l e c t r o n s by the s i n g l e valence e l e c t r o n . Thus, while d i s persion e f f e c t s are not w e l l described, the f i r s t order i o n induced d i p o l e i n t e r a c t i o n and the major e l e c t r o s t a t i c i n t e r a c t i o n s of the valence e l e c t r o n are probably reasonably w e l l desc r i b e d at the SC-SCF l e v e l . Note i n Table I I , where we l i s t molecular constants f o r Na? , that the 1 E s t a t e i s bound. I t s 1 °E"' counterpart i n the n e u t r a l molecule i s p r e d i c t e d to be s t r i c t l y r e p u l s i v e a t the SC-SCF l e v e l . The -Ci+R ion-induced d i p o l e i n t e r a c t i o n accounts f o r the d i f f e r e n c e . 2

2

2

2

+

2

+

2

+

t

-4

0097-6156/82/0179-0003$05.00/0 ©

1982 A m e r i c a n Chemical Society

Gole and Stwalley,; Metal Bonding and Interactions in High Temperature Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

4

METAL BONDING AND INTERACTIONS

TABLE I

2

2

bohr


a + P o t e n t i a l energy curves f o r Na obtained from e l e c t r o n , ab ini£io computations 1 E+ g

4.00 4.25 4.50 4.75 5.00 5.50 6.00 6.20 6.50 6.80 7.00 7.20 7.50 8.00 8.50 9.00 10.00 11.00 12.00 13.00 15.00 18.00 21.00 24.00 27.00 30.00

.506383 .520333 .531860 .541350 .549070 .560082 .566501 .568090 .569656 .570418 .570568 .570477 .569974 .568396 .566201 .563637 .558144 .552856 .548282 .544730 .539781 .536632 .535612 .535264 .535122 .535053

1

2

Z

+

u

— —

.421169

—

.439966 .455180 .467831

—

.478515

—

.487618

—

.495409 .502080 .507782 .512625 .520194 .525482 .529089 .531489 .534025 .535150 .535265 .535187 .535106 .535049

2

n

2

U

n

2

2 Z+ g

g

.463534

.397796

—

.327497 .344265 .358824 .371545 .382675 .400960 .415139 .419921 .426332

—

.407381

—

.435330

.428153

—

.442172 .451944 .458789

—

.466749

—

.468842 .470112 .470787 .471025 .470718 .469832 .468730 .467600 .465611 .463675 .462796 .462480 .462391 .462380

all-

— — — .356177 .372738 .386396

—

—

—

.415482 .422352 .428196 .433164 .441043 .446786 .450986 .454058 .457954 .460670 .461714 .462113 .462272 .462343

.442688 .448781 .453869 .458115 .464645 .469099 .471975 .473527 .474092 .471013 .467378 .465051 .463872 .463304

2

2 E

— — — — .321218 .337683

—

.352273

—

.365310 .376990 .387441 .396754 .404994 .418660 .429165 .437208 .443377 .451794 .458482 .461434 .462587 .462934 .462966

-1 Energies l i s t e d i n h a r t r e e atomic u n i t s e^/a = 219474.6 cm A l l energies have a p r e f i x of -323. Thus, tRe energy of the 1 E s t a t e at R = 4 bohr i s -323.506383 e / a . 2

+

+

u

2

Q


1.

KONOWALOW AND ROSENKRANTZ

TABLE I I

Light

Alkali

Diatomic

Molecules

5

Molecular constants f o r s e v e r a l e l e c t r o n i c s t a t e s of Na +

2

State

2

1

l+ g

2

1 I

2


Data Source a b c

+

R (bohr) e

7.02 6.69 6.24

D e

(cm

-i

l

«e. cm

a) xe cm

116.0 126

0.43

1 1

)

7796 8230 7905

e

1

u

a c,d

20.3 25

a b,d c

9.14 (9.0) 9.8

1900 (2170) 1860

49.9

0.33

U

a b, d c, d

14.37 (12) (16)

2399 (2850) (3030)

39.1

0.16

n

9.68

48.5 43.9

0.45

l

2 Z+ g

^Present work. Reference (10). ^Reference (11). Values i n p a r e n t h e s i s have been estimated c r u d e l y by us from t a b u l a t e d data i n the r e f e r e n c e c i t e d . +

At present, the l o w - l y i n g s t a t e s of N a are b e t t e r chara c t e r i z e d computationally than e x p e r i m e n t a l l y , although m u l t i photon i o n i z a t i o n experiments may change that p i c t u r e e v e n t u a l l y . We f i n d reasonably c l o s e agreement between the r e s u l t s of our a l l - e l e c t r o n computations, pseudopotential (10), and model potent i a l (11) computations. The l a t t e r two kinds of computations may give more accurate r e s u l t s than our ab i n i t i o computations s i n c e they may account f o r at l e a s t c e r t a i n core p o l a r i z a t i o n e f f e c t s . The a d i a b a t i c p o t e n t i a l energy curves f o r these e l e c t r o n i c s t a t e s c a l c u l a t e d i n the Born-Oppenheimer approximation, are given i n F i g u r e 1. Since we have d i s c u s s e d the choice of b a s i s funct i o n s and the choice of c o n f i g u r a t i o n s f o r these m u l t i c o n f i g u r a t i o n s e l f - c o n s i s t e n t f i e l d (MCSCF) computations (12) p r e v i o u s l y (1-9), we s h a l l not explore these questions i n any d e t a i l here. S u f f i c e i t to say that the b a s i s set f o r L i d e s c r i b e s the lowest S and P s t a t e s of the L i atom at e s s e n t i a l l y the Hartree-Fock l e v e l of accuracy, and i n c l u d e s a set of c r u d e l y optimized d f u n c t i o n s to accommodate molecular p o l a r i z a t i o n e f f e c t s . The b a s i s s e t we employed f o r c a l c u l a t i o n s i n v o l v i n g Na i s somewhat l e s s w e l l optimized than i s the L i b a s i s ; i n p a r t i c u l a r , sa molecular o r b i t a l s are not as w e l l d e s c r i b e d f o r Na (relatively speaking) as they are f o r L i . 2

2

2

2

2




6

R Figure 1.

(BOHR)

R

(BOHR)

Potential curves for low-lying states of Li , Li , Na , and Na from the all-electron calculations reported in Refs. 1-9. 2

+

2

2

+

2

obtained


1.


Light

Alkali

Diatomic

7

Molecules

Since the research which produced the p o t e n t i a l curves i n Figure 1 has been (or w i l l be) reported over a span of some s i x years, i t seems a p p r o p r i a t e now to make some very general observ a t i o n s about them. F i r s t we note that these p o t e n t i a l s are expected to be h i g h l y accurate at l a r g e i n t e r n u c l e a r s e p a r a t i o n s say, f o r R>15 bohr. Because of l i m i t a t i o n s on the kinds of e l e c t r o n i c c o n f i g u r a t i o n s which we could t r e a t , (see Ref. (1) f o r a d i s c u s s i o n ) , the IT s t a t e p o t e n t i a l curves, f o r the n e u t r a l molec u l e s are somewhat l e s s accurate than t h e S s t a t e curves, e s p e c i a l l y at i n t e r n u c l e a r separations of R < 15 bohr. Our best r e s u l t s f o r £ s t a t e s of L i and a l l s t a t e s of L i are probably i n e r r o r by 2% or l e s s . The corresponding e r r o r s f o r Na and N a are probably about three times l a r g e r . We obtained these e r r o r estimates by s c a l i n g our p o t e n t i a l curves so that they reproduced i n the l e a s t squares sense the experimental energy l e v e l spacing of the X Z+ and A !* s t a t e s . Becaule they are i s o v a l e n t molecules, the s i m i l a r i t y of the p o t e n t i a l curves f o r comparable s t a t e s w i t h i n the L i and the Na systems i s , of course, no s u r p r i s e . As expected, the p o t e n t i a l curves f o r the Na system are s h i f t e d to the r i g h t of the c o r r e s ponding curves i n the L i system and each of the Na curves i s " f a t t e r " and shallower than i t s L i counterpart. Consequently, the bound s t a t e s i n the Na system are expected to have more bound v i b r a t i o n a l l e v e l s which are more c l o s e l y spaced than t h e i r L i counterparts. These expectations are borne out f o r s t a t e s such as X Zg, A !* and B T T which are w e l l c h a r a c t e r i z e d experimentall y and f o r these and other s t a t e s which are so f a r best c h a r a c t e r i z e d by computations such as our own. Note that the lowest £ curve crosses the lowest T I curve for both L i and L i but not f o r N a and Na . T h i s can lead to strong p r e d i s s o c i a t i o n of the T I curves i n the L i system but not i n the Na system. The d i f f e r e n c e i n behavior apparently has three main causes: the f i r s t , the 3s-3p l e v e l s e p a r a t i o n i s some 2050 cm l a r g e r i n Na than the 2s-2p s e p a r a t i o n i n L i . I f we were to t r a n s l a t e r i g i d l y upwards the L i 2s + 2p asymptote together with a l l i t s curves, by some 2050 cm" , we would f i n d the s J II curve c r o s s i n g to occur at about 4.1 bohr i n s t e a d of the a c t u a l 4.6 bohr, and the lowest s e v e r a l v i b r a t i o n a l l e v e l s of the T I s t a t e would be r e l a t i v e l y f r e e of p r e d i s s o c i a t i o n . Secondly, the I I s t a t e i s about 30% deeper i n L i than i n Na . Thus, the IT curve comes much c l o s e r to the lowest ns+ns asymptote (and consequently c l o s e r to the E * curve) i n L i 2 than i n Na2. Thirdly, s i n c e Na and N a are s u b s t a n t i a l l y more p o l a r i z a b l e than L i and L i , the r e p u l s i v e E curves i n the Na system are " s o f t e r " (more a t t r a c t i v e ) than i n the L i system. While these q u a l i t a t i v e arguments have concentrated on the presence or absence of the E IT curve c r o s s i n g i n the n e u t r a l systems, the arguments extend i n an obvious manner to the E J - f t p r e d i s s o c i a t i o n (or not) i n L i (and N a ) . +

2

2

+


2

l

x

2

1

1

1

U

U

u

+

+

2

2

2

2

U

-1

1

3

3

3

3

3

U

2

2

U

3

+

+

u

3

U

3

U

2

2

u

+

2

+

2


U

U


8

Scaled P o t e n t i a l Curves f o r K Rb2, C s and t h e i r Molecular Cations Note that a l l the a l k a l i atoms have ns S and np P as t h e i r two l o w e s t - l y i n g atomic terms, ( c l e a r l y n i s the p r i n c i p a l quantum number). T h i s suggests that we should be able t o s c a l e our p o t e n t i a l curves f o r the l i g h t a l k a l i s i n order t o estimate, however c r u d e l y , the p o s i t i o n s and shapes of the corresponding s t a t e s of K , Rb , C s and t h e i r molecular c a t i o n s . Let us o u t l i n e a very simple s c a l i n g scheme. We d e f i n e s c a l e d i n t e r n u c l e a r s e p a r a t i o n ( R ) and energy ( E ) v a r i a b l e s : 2 >

2

2

2

2

2

2

g


R

= R

s

= ( R / JUp R ,

C

X

P

W

=

g

e

°

(

R

C

)

C

=

( D

1

e

D

}

e

e C ( r C )

>

where p and e are s c a l i n g f a c t o r s f o r i n t e r n u c l e a r s e p a r a t i o n and the d i s s o c i a t i o n energy, R and D are the corresponding values of the c a l c u l a t e d b i n d i n g energy curve E ( R ) which i s to be s c a l e d and E ( R ) i s the r e s u l t i n g s c a l e d b i n d i n g energy curve. I t would be t y p i c a l to take R and D* to be experimental values i f t h i s data were a v a i l a b l e . T h i s i s the s o r t of s c a l i n g that i s c a r r i e d out i n a p p l y i n g the Law of Corresponding States (13). We t e s t e d t h i s scheme f i r s t by s c a l i n g our L i and L i pot e n t i a l s so that we estimate the corresponding p o t e n t i a l s f o r Na and N a . Instead of experimental values of R* and we used our values c a l c u l a t e d f o r the X !*" s t a t e o f N a to o b t a i n p and e. Thus we use only the L i and L i curves and the R and D values for the X s t a t e o f N a to estimate the e n t i r e p o t e n t i a l curve f o r each of e i g h t e l e c t r o n i c s t a t e s of N a and s i x e l e c t r o n i c s t a t e s of N a . Except f o r the E g and I I s t a t e s the s c a l i n g worked w e l l as i s evident from F i g u r e 2. Let us now t u r n to the e s t i m a t i o n of the p o t e n t i a l curves f o r l o w - l y i n g n e u t r a l and c a t i o n i c diatomic molecules f o r the heavy a l k a l i s . For each molecule we take R* and t o be the experimental values (14) f o r the corresponding X !^ s t a t e . We a l s o a d j u s t the s e p a r a t i o n of the asymptotes to correspond t o the a p p r o p r i a t e experimental resonance t r a n s i t i o n (ns-np) and ns S i o n i z a t i o n energies. (We have ignored the s p i n - o r b i t s p l i t t i n g (15) of the P s t a t e of the heavy a l k a l i s as we had f o r L i and Na. The s i n g l e S + P asymptote was made to correspond to the degeneracy-weighted energy of the P s t a t e . C l e a r l y t h i s approximat i o n becomes p r o g r e s s i v e l y more s e r i o u s i n K2, Rb2 and CS2 where the comparable s p l i t t i n g s are about 58 cm" , 237 c m and 554 cm" , r e s p e c t i v e l y . ) The s c a l e d p o t e n t i a l curves a r e shown i n F i g u r e s 2, 3 and 4. I t i s c l e a r that the s c a l e d curves which are based on our L i system and those based on our Na system agree reasonably w e l l with each other except f o r the curves f o r the Z g and I I s t a t e s . (This discrepancy was expected i n view of our comparison of the L i and Na systems.) In view of our e a r l i e r remarks, i t appears that the p r e d i c t i o n s based on L i may be the C

c

C

g

C

s

e

+

2

2

+

2

1

2

+

2

2

e

e

2

2

+

3

3

2

U

1

2

2

2

2

1

3

-1

3

U


1



Light

R

Alkali

Diatomic

Molecules

(BOHR)

Figure 2. A comparison of the potential curves for Na and Na * computed ab initio with those obtained by scaling the corresponding curves of Li and Li * Identity of curves is shown in Fig. 1. 2

2

2

.

.

.

i

.

.

.

2

i

15 27 R (BOHR)

3

Figure 3. Estimated potential energy curves for K and K obtained by scaling computed potentials for Li and Na . Identity of curves is shown in Fig. 1. 2

2

2

2




Figure 4. Estimated potential energy curves for Rb and Rb obtained by scaling computed potential for Li and Na>. Identity of curves is shown in Fig. 1. 2

2

2

Figure 5. Estimated potential energy curves for Cs and Cs obtained by scaling computed potentials for Lij and Na,. Identity of curves is shown in Fig. 1. 2

2


1.


Light

Alkali

Diatomic

Molecules

11

more r e l i a b l e . There i s no question that these estimates f o r the p o t e n t i a l s f o r K2 (and Rb2 and CS2) are easy to o b t a i n . The r e a l question i s to assess the r e l i a b i l i t y of p r e d i c t i o n s based on these curves. F i r s t note that the E * s t a t e of K2 i s p r e d i c t e d not to p r e d i s s o c i a t e the IT s t a t e a t a l l s t r o n g l y s i n c e the curves don't cross at low e n e r g i e s . T h i s question i s important, f o r example, i n terms of understanding p o s s i b l e A*X and B-*X l a s e r emission i n K2, and i n terms of understanding the use of K as a working f l u i d i n a s o l a r powered engine (16). C u r i o u s l y enough, these t r i p l e t curves a r e p r e d i c t e d not to cross no matter whether we base our p r e d i c t i o n on L i 2 (where these curves do cross) or on Na (where they don't c r o s s ) . E v i d e n t l y the shrinkage of the two curves toward t h e i r r e s p e c t i v e asymptotes i n the course of s c a l ing the b i n d i n g energy curves i s s u f f i c i e n t to overcome the s h i f t of the ns + ns - ns + np asymptotes c l o s e r together i n the systems f o r the heavy a l k a l i s than they l i e i n e i t h e r the L i or Na s y s tems . Recently, Bhaskar and coworkers (17) have a t t r i b u t e d an IR a b s o r p t i o n band between 1.1 and 1.6 y t o the E * E ^ transit i o n i n K2. C l e a r l y , our s c a l e d curves suggest that such a band system could e x i s t with reasonable Franck-Condon f a c t o r s i n that wavelength r e g i o n . ( I t would, i n f a c t , be p o s s i b l e to o b t a i n s c a l e d t r a n s i t i o n d i p o l e moment f u n c t i o n s , (see below), c a l c u l a t e Franck-Condon f a c t o r s based on them and our s c a l e d p o t e n t i a l curves, and make more d e t a i l e d q u a n t i t a t i v e estimates of the E+ «- E+ band system i n K .) Before t u r n i n g from our crude c o n s i d e r a t i o n s on the heavy a l k a l i s , l e t us make a f i n a l p r e d i c t i o n . That i s that there s h a l l be observed i n K2 vapor an a b s o r p t i o n f e a t u r e which corresponds to the II E+ a b s o r p t i o n which l i e s somewhat to the blue of the atomic resonance l i n e v = 13000 cm" ; we p r e d i c t i t s peak to occur a t 710nm. [We have learned a t t h i s symposium (18) that a f e a t u r e i n the K a b s o r p t i o n spectrum a t 720 nm has been a t t r i b u ted to t h i s t r a n s i t i o n . ] T h i s f e a t u r e corresponds t o the absorpt i o n i d e n t i f i e d by Koch, Stwalley, and C o l l i n s (19) i n L i 2 , and by Woerdman and deGroot (18) i n Na2. The f e a t u r e i n L i was found at 588 nm, w h i l e our c a l c u l a t i o n s p r e d i c t e d i t to be a t around 595 nm. We estimate the TI -«- E"*" a b s o r p t i o n peak to l i e a t 546 nm i n Na2 while In Rb2 such a f e a t u r e w i l l occur a t about 727 nm and i n CS2 the corresponding feature w i l l occur a t about 800 nm, according to rough estimates we've obtained from our s c a l e d p o t e n t i a l curves. 3

3

U

2


2

3

3

3

3

2

3

3

1

s p

2

3

3

e

Spectroscopic Considerations R e c a l l that a spectrum corresponding to a one-photon t r a n s i t i o n i s e s s e n t i a l l y a p l o t of i n t e n s i t y (of emission or absorpt i o n ) as a f u n c t i o n of the d i f f e r e n c e i n energy ( u s u a l l y expressed as wavelength or frequency) between the two s t a t e s i n volved i n the t r a n s i t i o n . The d i f f e r e n c e p o t e n t i a l (the



12

d i f f e r e n c e between two p o t e n t i a l energy curves) provides rough estimates of t r a n s i t i o n energies. For diatomic molecules, i t i s s t r a i g h t f o r w a r d to s o l v e the Schrodinger equation f o r the v i b r a t i o n a l - r o t a t i o n a l energy eigenvalues and corresponding nuclear motion wavefunctions once the e l e c t r o n i c p o t e n t i a l curve i s known and thus obtain r e f i n e d information about t r a n s i t i o n energies. ( C l e a r l y , we invoke the Born-Oppenheimer approximation here.) I t i s a l s o s t r a i g h t f o r w a r d to c a l c u l a t e the e l e c t r o n i c t r a n s i t i o n d i p o l e moment f u n c t i o n


D(R)

= /** u * e,i e,j

i n terms of the e l e c t r o n i c wavefunctions f o r the s t a t e s i and j involved i n the t r a n s i t i o n , and the d i p o l e moment operator u. I n t e n s i t i e s of a s p e c t r a l t r a n s i t i o n a r e p r o p o r t i o n a l to the square of the i n t e g r a l (20)

R

nk

- '* * n

t D ( R ) ]

*k

where $ denotes the v i b r a t i o n a l - r o t a t i o n a l wavefunction f o r the s t a t e n. Frequently, i n v e s t i g a t o r s approximate the f u n c t i o n D(R) by i t s asymptotic value D(°°) which corresponds t o the t r a n s i t i o n d i p o l e moment o f the r e l e v a n t atomic t r a n s i t i o n . C l e a r l y , t h i s approximation,which we term the atomic approximation, i s worthless f o r molecular t r a n s i t i o n s which are allowed but which correspond a s y m p t o t i c a l l y to forbidden atomic t r a n s i t i o n s . I t i s even i n c o r r e c t to assume that such molecular t r a n s i t i o n s w i l l be weak. We have found t r a n s i t i o n s among e x c i t e d s t a t e s of L i 2 (21) which are forbidden a s y m p t o t i c a l l y y e t which have t r a n s i t i o n d i p o l e values as l a r g e as 24 atomic u n i t s (=61 Debeye)! Even where the t r a n s i t i o n i s allowed a s y m p t o t i c a l l y , the atomic approximation can lead to s u b s t a n t i a l e r r o r i n the p r e d i c t e d i n t e n s i t i e s . I t i s not unusual f o r D(R) to deviate by 20-30% from i t s asymptotic value a t i n t e r n u c l e a r separations where the overlap o f the v i b r a t i o n a l wavefunctions $ and i s appreciable. Thus, i n t e n s i t i e s which are c a l c u l a t e d by using the atomic approximation f o r such t r a n s i t i o n s may be i n e r r o r by 40-70%. A paper i s i n p r e p a r a t i o n (22) which w i l l r e p o r t the D(R) values f o r a l l d i p o l e allowed t r a n s i t i o n s among most of the s t a t e s which are depicted i n Figure 1. n

n

In the f o l l o w i n g paragraphs we give s e l e c t e d examples of the use of our wavefunctions and p o t e n t i a l curves t o p r e d i c t or conf i r m various s p e c t r o s c o p i c features o f the a l k a l i s . We know of plans to observe L i 2 s p e c t r a i n a t l e a s t two l a b o r a t o r i e s (23, 24) so some p r e d i c t i o n s regarding the s p e c t r a appear to be i n order. J u l i e n n e (25) has used our wavefunctions f o r L i 2 to c a l c u l a t e the e l e c t r o n i c t r a n s i t i o n d i p o l e moment f u n c t i o n c o r r e s ponding to the A IT - X Z ^ t r a n s i t i o n and to c a l c u l a t e the matrix element < £ ^ | L - i L y | II > needed to determine the r a t e of p r e d i s s o c i a t i o n of the IT s t a t e by the E s t a t e . Since the +

+

2

2

U

2

2

x

U

2

2

U

U


1.


Light Alkali

Diatomic

a n c

13

Molecules

p

s p i n - o r b i t s p l i t t i n g between the Pi/2 * 3/2 s t a t e s of L i i s only 0.34 cm (15), the IT s t a t e i s c h a r a c t e r i z e d by Hund's case b c o u p l i n g . Thus the " z j s t a t e only p r e d i s s o c i a t e s the r o t a t i o n a l l e v e l s which give r i s e to P and R branches; the Q branch i s not p r e d i s s o c i a t e d . J u l i e n n e has used the c a l c u l a t e d t r a n s i t i o n d i p o l e moment f u n c t i o n t o o b t a i n the r a d i a t i v e l i f e t i m e s f o r the I I r t t r a n s i t i o n . He f i n d s , f o r example, that the r a d i a t i v e l i f e t i m e of the v =0 Q branch emission i s about 12 ns and increases f a i r l y r a p i d l y with v i b r a t i o n a l l e v e l . He a l s o f i n d s that r a d i a t i o n and p r e d i s s o c i a t i o n r a t e s f o r the P and R t r a n s i t i o n s are comparable for certain r o t a t i o n a l - v i b r a t i o n a l levels. Our curves f o r the molecular ions N a ? . . . C s 9 show that the and IT p o t e n t i a l s do not cross a t an energy where the I I s t a t e i s bound. Thus, the i n t e r e s t i n g p r e d i s s o c i a t i o n p r e d i c t e d to be present i n L i w i l l not be present i n these heavier a l k a lis. The o r i g i n of the d i f f e r e n c e i n p r e d i s s o c i a t i o n behavior can be understood by a simple extension of the arguments we've put forward i n d i s c u s s i n g the I I - E+ i n t e r a c t i o n i n the n e u t r a l molecules. The spectroscopy of the s i n g l e t manifold i n the l i g h t a l k a l i s i s r e l a t i v e l y well-developed i n part s i n c e the molecular ground s t a t e i s a s i n g l e t . We have obtained t r a n s i t i o n d i p o l e moment f u n c t i o n s f o r t r a n s i t i o n s i n the s i n g l e t manifold which are i n reasonable agreement with the l i m i t e d experimental data which i s a v a i l a b l e (26,27). We have not y e t undertaken a l i n e b y - l i n e comparison of c a l c u l a t e d and experimental Franck-Condon f a c t o r s (which are more r e a d i l y a v a i l a b l e than are the D(R)). Although i t i s a s t r a i g h t f o r w a r d task, i t i s a p a r t i c u l a r l y time consuming one. I t has been noted by Wellegehausen (28,29) that one can o b t a i n good l a s e r emission i n the A ^ J - X ^ and B ^ - X ! ] * systems of L i and Na2, only weak l a s e r a c t i o n i n these systems of K but, so f a r , no l a s e r emission has been observed i n Rb and C s . The r e s u l t s presented here, together with unpublished c a l c u l a t i o n s on e x c i t e d s t a t e s of L i (21) suggest that s e l f absorption of any l a s e r emission should become a more probable event the h e a v i e r the a l k a l i dimer. Thus, i t appears that Wellegehausen's observat i o n s might be explained by such s e l f absorptions. By contrast t o the s i n g l e t manifolds of the a l k a l i s , lowl y i n g members of the t r i p l e t manifolds have probably been much b e t t e r c h a r a c t e r i z e d computationally. T h i s i s understandable s i n c e the ground s t a t e of the t r i p l e t manifold, E , i s very weakly bound ( D = 300 cm" = 420 K f o r L i , and D = 180 cm"" = 250 K f o r Na , f o r example). Thus at the temperatures o r d i n a r i l y used to o b t a i n a l k a l i vapor, one expects to f i n d a very small f r a c t i o n of bound E+ molecules. (Thus, i t i s not uncommon f o r s p e c t r o s c o p i s t s to term the s t a t e "the r e p u l s i v e s t a t e " and question only whether i t e f f e c t i v e l y p r e d i s s o c i a t e s the TI or e l s e immediately dismiss i t from f u r t h e r c o n s i d e r a t i o n . They -1

2

2

2

U

f

+

+

Z

Z


U

U

+

2

3

3

U

1

1

2

2

2

2

2

3

U

1

e

1

2

e

2

3

3

U



14

have missed the opportunity to i n v e s t i g a t e some f a s c i n a t i n g spectroscopy.) There i s apparently a s u f f i c i e n t amount of E * a v a i l able i n L i , Na, K, and Cs vapors f o r at l e a s t two kinds of t r a n s i t i o n s i n v o l v i n g i t to have been observed (17,1^8,19,30). Bhaskar and coworkers (17) have observed i n potassium vapor an IR absorpt i o n band between 1.1 and 1.6y which they a t t r i b u t e to the E+ -«- E+ t r a n s i t i o n . Zouboulis and coworkers (30) i d e n t i f y a 1.25 - 2.5y band with t h i s t r a n s i t i o n i n CS2. Our s c a l e d potent i a l curves f o r K , f o r example, show that a b s o r p t i o n i n t h i s region could indeed be a t t r i b u t a b l e to that t r i p l e t t r a n s i t i o n . One would expect to observe a band with some s t r u c t u r e as expected f o r a t r a n s i t i o n that i s dominated by a b s o r p t i o n from the continuum to bound l e v e l s of the I * s t a t e . Boundbound t r a n s i t i o n s corresponding to t r a n s i t i o n s from very low v" to rather high v > 40 should be d e t e c t a b l e at wavelengths X < 0.9y. We expect the emission c h a r a c t e r i s t i c s of the E ^ - £ * t r a n s i t i o n i n K to be s i m i l a r to those we have p r e d i c t e d (31) f o r L i and Na . Here, we would expect the peak continuous emission i n t e n s i t y to occur near l . l y . I f the E g s t a t e of K could be populated s u f f i c i e n t l y r a p i d l y , the E * E* transition would comprise a tunable near i n f r a r e d excimer l a s e r with i t s peak about midway between that of the corresponding excimer l a s e r s based on L i X^1.3y and on Na X^0.83y. These estimates f o r K are n e c e s s a r i l y very rough s i n c e they are based on our s c a l e d p o t e n t i a l curves. I t does seem u n l i k e l y that we are i n e r r o r by s u b s t a n t i a l l y more than O.ly, however. A s i m i l a r a n a l y s i s of Rb and C s could be made i n terms of our s c a l e d potentials. 3

3

3

2


3

f

3

3

2

2

2

3

2

3

2

3

2

2

2

3

2

3

The TI Z * t r a n s i t i o n i n the t r i p l e t manifold has app a r e n t l y been observed i n L i (19) and i n Na (17,24). Koch and coworkers (19) observed a bound-free-bound t r a n s i t i o n which they a t t r i b u t e d i n part to n +• Z+ a b s o r p t i o n i n L i . They obtained a peak a b s o r p t i o n at around 588 nm with s u b s t a n t i a l s t r u c t u r e to the red. In F i g u r e 6, we show the p h o t o d i s s o c i a t i o n cross s e c t i o n (32) as a f u n c t i o n of the frequency (and wavelength) of r a d i a t i o n e x c i t i n g the bound-free II E^ transition in L i . We p r e d i c t a peak s l i g h t l y to the blue of 595 nm which agrees n i c e l y with the observed peak at 588 nm. Veza and coworkers (17) c l a i m the f i r s t d i r e c t experimental c o n f i r m a t i o n of the II s t a t e i n Na . They a t t r i b u t e the s a t e l l i t e band i n the B T[„ - X E g band system at 551.5 nm to the maximum i n the TTg d i f f e r e n c e p o t e n t i a l and thus to that t r a n s i t i o n . We estimate, extremely c r u d e l y , that the s a t e l l i t e should l i e at around 546 nm. I t i s c l e a r that ab i n i t i o computations, e s p e c i a l l y of the p o t e n t i a l curves and wavefunctions f o r t r i p l e t s t a t e s has proven to be u s e f u l i n the i n t e r p r e t a t i o n of a v a r i e t y of s p e c t r a l f e a tures i n L i and Na . I t appears that our s e m i - e m p i r i c a l t r e a t ment of the h e a v i e r a l k a l i s may prove u s e f u l u n t i l we are able to t r e a t these systems ab i n i t i o . We have launched a more d e t a i l e d g

2

3

2

3

g

2

3

3

2

3

2

l

2

3

2

2


Light Alkali Diatomic

Molecules



Figure 6.

The calculated photodissociation cross section for the U

Electronic Structure and Spectra of Light Alkali Diatomic Molecules

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