The electronic transitions of the nitrate ion have been a subject of both theoretical

Mean Life Time of Excited State

of n —> TI* Transition of Nitrate Ion in Solution

K A M L A T A N D O N D e p a r t m e n t of C h e m i s t r y

a n d S . P . T A N D O N D e p a r t m e n t of P h y s i c s U n i v e r s i t y of J o d h p u r , J o d h p u r , I n d i a (Z. Naturforsch. 25 a, 452—453 [1970] ; received 15 October 1969)

T h e m e a n l i f e t i m e , T, of t h e e x c i t e d state of t h e n — r r * transition of the nitrate i o n in d i f f e r e n t solvents h a s b e e n e s t i m a t e d f r o m a s p e c t r o p h o t o m e t r i c s t u d y . T h e s e T v a l u e s are b y a f a c t o r of 1 0 ~3 — 1 0- 4 s m a l l e r t h a n c o m p u t e d v a l u e s f o r v i b r a t i o n p e r t u r b a t i o n . T h e v a l u e s d e c r e a s e w i t h i n c r e a s e in the h y d r o g e n b o n d i n g p o w e r of t h e s o l v e n t . H y d r o g e n b o n d i n g p e r t u r b a t i o n h a s b e e n s u g g e s t e d t o b e the c a u s e of the o b s e r v e d l i f e t i m e of t h e e x c i t e d state.

Introduction

The electronic transitions of the nitrate ion have been a subject of both theoretical

and experimen- t a l

investigations. The mean life time, T, of the excited state of the n —>- n* transition should be infinite and its intensity zero

since it is a symmetry forbidden transition. The mechanism due to which it gets ob- servable intensity is a mater of controversy

'

. With a view to investigate the mechanism the present study was undertaken.

In the present paper the mean life times of the ex- cited state of the n —> n* transition of the nitrate ion have been computed from observed spectra in different solvents. The results are discussed in the light of vari- ous possible perturbations of the electronic states.

Mean Life Time of the Excited State

If a molecule is in an excited state, in the absence of an external electromagnetic field, on the average, after a time

T — l/Amn (1) it will emit a photon. T is called the mean life time of

the excited state and A

is Einstein's coefficient given by

f.A

_4 r,3

A

=

Dmn = 7.24 x 10

v

D

(2) where v is the frequenc of the radiation in c m

and e

D

is the square of the dipole moment of the tran- sition.

D

= 3.98 x K T

f e (v) dv . (3) fe(v) dv is the area of the absorption curve, Dmn is also related to the oscillator strength, /, given by

/ = (8 ti

m

c v/S h) D

= 1.085 x 10

v D

,

and / = 4.32x 10~

f e(v) d r . (4)

v and / values have been determined from absorption measurements. Substituting these values in Eqs. (1) to

(4) T values have been computed.

The observed characteristics of the absorption band and the T values of the excited state have been collect- ed in Table 1. The observed T values are much smaller than expected. The intensity (/ value) in the forbidden transitions is usually due to the following three causes

( I . e . 1 3>1 4) :

(1) Vibration perturbation of the electronic state, (2) hydrogen bonding, and

(3) solvent-perturbation.

P o s i t i o n Intensity L i f e T i m e

Salt S o l v e n t ^•max J'max T

x

m/x c m- 1 / X 1 05 sec

T e t r a m e t h y l A m m o n i u m A c e t o n i t r i l e 3 1 3 31 9 4 9 7.7 1.91

nitrate E t h a n o l 3 0 4 3 2 8 9 5 1 3 . 0 1 . 0 6

W a t e r 3 0 3 3 3 0 0 3 13.8 1 . 0 0

T e t r a e t h y l A m m o n i u m A c e t o n i t r i l e 3 1 2 32 0 5 1 8.4 1 . 7 4

nitrate E t h a n o l 3 0 3 3 3 0 0 3 1 3 . 6 1 . 0 2

W a t e r 3 0 2 3 3 1 1 2 1 5 . 4 0 . 8 8

T a b l e 1. C h a r a c t e r i s t i c s of the b a n d . R e p r i n t s r e q u e s t t o D r . S . P . TANDON, R e a d e r in P h y s i c s ,

U n i v e r s i t y of J o d h p u r , Jodhpur ( I n d i e n ) .

1 S . P . M C G L Y N N a n d M . KASHA. J. C h e m . P h y s . 2 4 . 4 8 1 [ 1 9 5 6 ] .

2 K . L . M C E W E N , J. C h e m . P h y s . 3 4 . 5 4 7 [ 1 9 6 1 ] .

3 S . J. STRICKLER a n d M . KASHA, E l e c t r o n i c S t r u c t u r e a n d A b s o r p t i o n S p e c t r a of N i t r a t e I o n in M o l e c u l a r O r b i t a l s in C h e m i s t r y , P h y s i c s a n d B i o l o g y , A c a d e m i c P r e s s , N e w Y o r k 1 9 6 4 .

4 K . S. KRISHNAN a n d A . C. GUHA, P r o c . I n d . A c a d . S e i . 1 ( 4 ) , 2 4 2 [ 1 9 3 4 ] .

5 P . PRINGSHEIM. J. C h e m . P h y s . 2 3 , 3 6 9 [ 1 9 5 5 ] .

6 E . W . SAYRE, J. C h e m . P h y s . 3 1 , 7 3 [ 1 9 5 9 ] .

7 G . P . SMITH a n d C. R . BOSTON. J. C h e m . P h y s . 3 4 , 1 3 9 6 [ 1 9 6 1 ] ,

8 D . MEYERSTEIN and A . TREININ. T r a n s . F a r a d a y S o c . 5 7 , 2 1 0 4 [ 1 9 6 1 ] .

9 A . MOOKHERJI and S. P . TANDON. I n d i a n J. P h y s . 3 6 , 2 1 1 , 3 4 4 [ 1 9 6 2 ] ,

10 A . MOOKHERJI and S. P . TANDON, I n d i a n J. P h y s . 3 9 , 1 3 7 [ 1 9 6 5 ] .

11 A . MOOKHERJI and S. P . TANDON. I n d i a n J. P h y s . 3 9 . 3 9 6 [ 1 9 6 5 ] .

12 A . MOOKHERJI and S. P . TANDON. I n d i a n J. P h y s . 3 9 . 5 6 9 [ 1 9 6 5 ] .

13 C. SANDORFY, E l e c t r o n i c S p e c t r a a n d Q u a n t u m C h e m i s t r y , P r e n t i c e - H a l l . I n c . . L o n d o n 1 9 6 4 .

14 H . SUZUKI, E l e c t r o n i c A b s o r p t i o n S p e c t r a a n d G e o m e t r y of O r g a n i c M o l e c u l e s , A c a d e m i c P r e s s , N e w Y o r k 1 9 6 7 .

Vibration Perturbation

The vibration perturbation of the nitrate ion has been studied by

and

. The wave function of the nitrate ion, assuming that the Born-Oppenheimer approximation

holds is

Tki{x Q)=6

(x Q) 0

i(Q) (5) where x represents the coordinates of all the electrons

and Q designates the normal coordinates of the nitrate ion. The subscripts k and / enumerate the electronic and vibrational states respectively.

Assuming the nuclei to be fixed in some configura- tion Q the electronic transition moment between the ground state g and the excited state k is given by

-Wgk (Q) = f 0

* (x, Q) M (x) <9

(*, Q) dx (6) where M (x) is the electric dipole operator of the elec- tron.

The oscillator strength for the transition g - > k, as- suming all molecules to be in the ground state is given by

' " (7)

3 h2 e2

where

I M

|

= / <P

(Q) | M

(Q) I« <P

(Q) dQ . (8) Expanding M

K (Q) we have

( 9 )

Since the n —>• TC* transition is forbidden the first term is zero. The second term is also zero since there are no vibrations of proper symmetry which could enable the transitions. Hence

' ^ L l J a B ^ J o

^ - do)

Substituting the estimated value

of jM

k|

; Eqs.

(4) to (10) yield T - 4.5 x 10~

sec. This value is much larger than the observed ones (Table 1). So vibration perturbation alone is not sufficient to explain the observed T values.

Hydrogen Bonding

The hydrogen bonding perturbation is similar to that of the vibration perturbation. But there is no symmetry

restriction

. Since the nitrate ion is symmetrical there is no single vibration which could produce sufficient perturbation. The hydrogen bonding is equivalent to placing a positive charge near the electronic cloud of the nitrate ion and the energy arises due to its inter- action with the electron cloud. In many cases, where the vibration perturbations are strong the amounts of the electronic perturbations due to hydrogen bonding and vibration are expected to be of the same order

. The observed T values of the n — JI* transition may be attributed mainly to hydrogen bonding. The T values also decrease with the increase in hydrogen bonding power of the solvent (Table 1).

Solvent Perturbation

The oriented solvent dipoles in the case of polar solvents are also expected into disturb the symmetry of the ion, which makes the transition forbidden. Aceto- nitrile cannot form hydrogen bonds, but it is strongly polar. The solvent perturbation may be the cause of the observed T value in acetonitrile solvent. The T values in the case of acetonitrile are much larger than in ethanol or water, suggesting that the solvent inter- action is much smaller than the hydrogen bonding per- turbation.

Experimental

The absorption measurements in the region 250 to 360 mf.i have been carried out with a UVISPEK spec- trophotometer at 25 ± 1 °C. To minimize the effect of the cation, which

is proportional zu Z/r, where Z is the charge and r is the radius of the cation, and due to the solubility in organic solvents, tetraalkyl ammonium nitrates for which the values of Z/r are very small, were selected for study. Both tetramethyl ammonium nitrate and tetraethyl ammonium nitrate were prepared start- ing with reagents of A. R. grade. The solvents aceto- nitrile and ethanol used were of A. R. grade. For mak- ing aqueous solution triply distilled water was used.

Acknowledgments

T h e a u t h o r s wish to express heartfelt t h a n k s to P r o f . R . C.

KAPOOR, D . P h i l . , D . Sc., H e a d of the C h e m i s t r y D e p a r t m e n t , f o r h e l p f u l s u g g e s t i o n s and g u i d a n c e . T h a n k s are also d u e to U n i v e r s i t y G r a n t s C o m m i s s i o n , I n d i a , f o r financial assistance to ( K . T . ) .

1 5 M . BORN and R . OPPENHEIMER, A n n . P h y s . 8 4 , 4 5 7 [ 1 9 2 7 ] . 1 7 K . TANDON, S p e c t r a l S t u d y of S o m e I n o r g a n i c A n i o n s , P h .

16 J. N . MURRELL and J. A . POPLE, P r o c . P h y s . S o c . L o n d o n D . T h e s i s , U n i v e r s i t y of J o d h p u r , J o d h p u r , I n d i a 1 9 6 6 . A 6 9 , 2 4 5 [ 1 9 5 6 ] .