- Email: [email protected]
Electron-transfer transitions during the collision of O2, N2, NO and CO with their respective ions
Volume
32, number
ELECTRON-TRANSFER
TRANSITIONS
OF O,, N,, NO AND CO WITH THEIR Ying-Nan
Center for
I April 1975
CHEMlCALPHYSlCSLETTERS
1
DURING
THE COLLLSION
RESPECTIVE
IONS
CHIIJ *
hlolccolnrDyrtamics owl
h’nergy Trawler, Deparfnrenr oj Chemistry, The Cathotic Ufrivcrsiry
o~/Imcrico.
IVasAir;gton, D.c. 20064,usrl
and Yuh-Kang
PAN *.*
Received 7 October 1974 Revised manuscript rcceikd
AII improved
or ion-molecule cstimatcd.
Odht~r
theory
4 December
of clcctron
transfer
I974
absorpticn is proposed. for the Oz-05,
pairs is discussed and frequencies strer.gths UC &o estimated
for tllc 02-0$
The possibility of such absorption during the collision NO-NO-, CO-CO+ and NZ-Nt pnirr arc
0,-O?.
pair.
The phenomenon of electron-transfer radiative transition is well known in mixed-valence transition metal complexes’ [l-4]. In the mixed-valence biferrocene picrate, a new absorption band in the near infrared at 1900 nm (E = 550 in acetonitrile) has been attributed to such a transition fiom Fe2+ to Fe3+ [3]. We propose to show that a similar e!ectron-transfer absorption might be observed in the case of an ion-molecule collision complex with a sufficiently long lifetime. We shall illustrate our theory using simple molecules. The existing theory may be summarized as follows. Because of the rapid electron transfer compared with nuclear vibration, vertical Franck-Condon transitions prevail. The loss of an electron from a molecule in a ground vibrational state results in a vibrationally excited ion. Similarly, acceptance of this electron by the neighboring ion in its ground vibrational state results in a vibrationally excited molecule. Therefore,.the electron-transfer transition from the ground vibrational state of the molecule-ion complex is necessarily absorpciw. ?hc frcque=y of tr&itian has been computed [4] from the semiclassicalexpression, ,5 = (l/a)
@‘+I?“ (Qb)
Q;)2
,
(1)
where k’ and k” a&force constants and Qb and Qi are the equilibrium
normal coordinates of the molecule and the ion, respectively. This model is based on the harmonic oscillator approximation for which classically E = A$* = ihu2 with u = amplitude = Q&- Q6. Although the above semichrssical theory of transition.frequencies is well known, the theory of transition intcnwe choose to consider the elecsity has received less attention. As ai improvement over the existing theory [i-4], tron transfer frorri molecule a to ion b as involving a Franck-Condon transition from the ground vibrational state of molecule a (fo) to the appropriate excited vibrational state of ion a (xi+) and a simultaneous Franck-Condon trarisition’from thc.grqtind vibrational state of ion b ($j’ ) to the approptiate excited vibrational state of molecule b (&. If the electronic interaction between a and b is.smaller than the vibrational spacing and there is little mix .. :. * Supported by a Natiorui Sciekc Foundation &ant No.GP-11212 ** Supported by the Office 6f Nnval R&&&under Con&t #N000’.1469-kCI453. ,,, . ;’ ,: I ‘. .’ : .. ;,. .,, : .,, . .’ .- ‘. ” -, _’_ ,_-:; :’ : ..: : .,-,,
-’ .:
67
. . .
‘VoIime.JZ, nutibcr.1 .
\
CHEMICAL PHYSICS LETTERS ‘.
1 ~&ctkn-~ransfci absorption ‘. ‘,
I April 1975
Table
molcculc collision pairs a) Absorption
Ground ionic moiecule
Ground ncutrsl molcculc
Collision ..:phk
..
Frcqucncics for various ion-neutral
._,
frcqucncy
-~
.’
~~-0;
X3$
02-q; NO-NOc&co+. N;-N;
xbg X%-I,,2 X’Z+ Xli$. b
wc (cm-‘)
re(A)
1580.3b) 1580.3 b) 1904.03 b) 2170,21 b) 2359.6 b)
1.2074 1.2074 1.1508 1.1281 1.094
X%-lg XZl-Ig X3xX2x+ X2X,+
(nm)
f,& (Cm-q
QyLj- ‘:
(cm-‘)
1876.4 b) mod) 1470 r) .’ 2214.24 2207.19
1.1227 I .341 e). 1.258 1.1150 1.116
5.115.5 c) 780‘1.5 736l;l 167.7 524.6
1954.4 128i.8 1358.4 59632 19062
3j Cjiculnkd from, eq. (1). b) Ref. [S]. ” c) Rcs?rlls from potcnti;ll CU~YCS and uncorrected Oscillator strength for 2.8 A separatiqn .c@uplirl~. d) Rcf.:[23].
e). Ret’. [ 241.
: ‘. ing &f.the electronic cask by
.’
q=Jh(ri?
quantum mechanical form111aare !185 cm-l and 1928.6 nm. is estimated to be 1.6 X lOwa for jyeak coupling, 1.2 X lb-‘, for stronp
f) Ref. [ZS].
states of the two m&ties,
$‘(Q,)
then the transition
moment
may be represented
$iQb) pi b,iri> >I’oX~‘CQ~)‘~~idQa dQb = MRop+R,
in this extreme
(2)
3.
:where.@,:‘and &, are the donor and acceptor electronic tirbitals of the molecule and the ion, respectively,‘and the R’s are Franck-Condon integrals. To illustrate tlie magnitude of the transition freque,ncy, we consider the collision of 0; and,02. From Herz&rg’s.book’ [5] we find for the X3Zg state of 02, @, =ri = 1.2074 A, we = 1 MO,3 cm-l and for the X 2iIs St; 7 rz = l.l227A,
.Aitate of pi,
-,;=-I
876.4 cm -l.
Using these pzrameter’s
and eq. (l),
we obtained
the eiectron-
transfer transition frequency-F= 5116.6 cm-l (X = 14 544 8, = 1954.4 n-m), in the near infrared region. From the potential curv‘es [6] of p2 and 6; WCnote that the upward vertical transition frdm 0, (Qb at 1.207 A) most likeIy.yieids C$ in the P(+= 1 vibrational level and that the downward lrertical transition from the 0; ground vibra-tional state (Qi at. 1 :122 a) should produce 0, in the u.= 1 vibrati3nal.state. The-final-state vibraiionalenergy is predicted to.be F=.b’ii) a: + (v,ti) we = 5185.0 cm-l, which ia seen to be close to the frequency calculated from eql (l)..Semiclassical calculations of the abs&iion frequenci:s for this and other i&-molecule pairs are ‘given in table 1. ’ ,: .’ Otir. transition moment formula eq. (2) differs from the existing’treatment in that it contains a product of two Franck-Cotidon factors. This C&Ibe derived by analogy tith t,he exciton model for a molectilay dimer [7-91 and by writing the, appropriate zeroth.order.ground (N) and excited (V) vibronic stat& with corresponding firstorder
energicS
(hicglecting
overlap)
..
as follows:
: +-$&$+&; ,’
-+$=‘k-p+,+f!;+,
.’
., : ,‘. ; 1 :-
.’ (?a) :. _.:__
.I,
-1 _’
. .
(3b)
The energy splittjngwo&d
lead t0.a doublet tith a separation.bf 2&>‘~-$,$. W&n the,$xing of the-two ., ; ,.‘I ,. ; .. siates &e:t? electronic inteiaction’increa!es,. th” electronic [email protected]’becqtie. [2,9]. :
:.
acwell a~,lon-t~~‘vibrjtional ,‘I :,., :. ,- ./ ,:: :. .,y .’
.. ,.__ .:: -. ,-
‘::.
._‘...‘. ;;.;._.” ..’ : : _: ..
/ .’” :_
.
.,.
;, ..
_. .,: ;, .. : .:.. : I,.‘,,,. .:,’ ‘ ‘. ‘,i :’ .,... .. . -;, ‘; .-
Volume 32. number 1
1 April 1975
CHEhiICAL PHYSICS LETTERS
excitations due to electron transfer. The electronic transition moment is.
which is similar to the charge-transfer moment of Mulliken [lo] _The Franck -Condon factors are essentially the same as those obtained from eq. (2), since (4a) and (4b) are predominantly & and &, respectively. Hence eq- (5) reduces to eq. (2) except for a phase factor of -1 when Q = 0. In the limit of very strong electronic coupling, the vibronic wavefunctions are (6)
and the electronic transition moment is
The Franck-Condon
factors are presumably not very different from the previous cases and can be approximated
by the factors in eq. (2) for two independent
oscil!ators.
.The above serve to show that proper interpretation of electron transfer spectra could yield vahabk information on the strength of electronic coupling, the size of splitting for a given geometry of the complex, et=. To illustrate the magnitude of the transition intensity, WC have estimated the intensity for the 0,--O; collision, in the two extreme cases: eqs. (2) nnd (7). Using frequency data from Herzberg [5], we estimated the overlap in tegrals R,,,; =RVstVrfrom tables [ 111 of harmcnic Franck-Condon integrals involving displacements of normai coordinates. The two-center electronic dipoIe transition matrix element M [12-151 was approximated by (2pnblZ,i2pn,) and was estimated by using the Slater 2p orbital of the oxygen atoms assuming co = 4.3 for both the mclecule and the ion. For the average separation of the oxygen atoms, we tried three vdues: (I) the LennardJones [16] u = 3.42 a; (2) the van der Waals diameter [17],2.8 A; and (3) an arbitrarily assumed separation of 1.4 A for dose approach_ Assuming that only the vibrational transitions I * 0 and 0 * I contribute significantly to the oscillator strength, we computed the corresponding oscillator strengthsf= (8~~mc/3f1)P(3~ and Einstein spontaneous transition probabilities_4 = (64flP3/3h) e2 CD2for the threeseparations cited [weak coupling, eq- (Z)] to be (l)f= 3.3 X 10-lo, A = 5.70 X 1O-4 s- l; (2)f= 1.6 X lO-8,,4 = 2.7 X 1O-2 s-l; (3) f= 2.4 X t@, A = 42 s-l. The corresponding oscillator strengths for strong coupling [eq. (7)] are (I)f= 1.8 X IOM2,.4 = 3.2 X 104 s-‘; (2)f= 1.2 X 10d2,d = 2.1 X 104 s-l; (3)f= 3.1 X 10m3,A = 5.3 X lo3 s-l. To estimate the extinction coefficient, we used the Formula [IO] f= 4.32 X 10sg E,, Vllz. To obtain a severe lower limit of crnjx, we took the half-width P’1,2to be equal to Zr.In the weak coupling case [eq. (2)] and for the same distances as above, we obtained (1) E,, = 15 X 10h5, (2) emav = 4.9 X 10d3, (3) E,, = 1.I. For strong coupling [eq. (7)], the values are (1) fmax = 827, (2) fmax 7 551, (3) emn, = 138. The transition frequency, of course, places a minimum requirement on the life-time of the interaction complex. If the molecule and ion are vibrationally excited initially, the’revened process of electron-transfer emission might also be observed if the frequency and interaction time are both large. The emission phenomenon should a1so be of interest in understanding the collisional radiation in hot plasma. Such an electron-tnnsfer trsnsition should ,alsobe of interest in ion-molecule reactiqns invoking unsymmetrid systems [lS---201 2nd some of the spectral
quantities ., ..’
may be related to those
of the ions generated
in matrix
isolation
studies
[21,22].
Thanks are due Dr. William A. Sanders for reading the manuscript wjth suggestions for improving its presentation. Y.N.C. acknowledges helpful djscussiork following a seminar by Dr. F.A. Jumak, which motivated this work. _. ~Wferences
._.
.‘_,
: _.
..: ,,’
,.
: : ,:
.I
[I] D.O.‘Cowan, C. LeVnn&,, J.-Park ani F; K$fn;an’, &counts, Chcm. Rbs. 6 (1973) 11 .’ .: ;_ ._, :” .,,. ‘,. ;’ .‘.. ,. .. .‘‘ /. ..‘.,‘/ -’ ., ,;... .,_ .’ :. : _. ‘. . . ,,.“,’
., ”
69
:. Volume 32, number. 1 _j,.“ , .‘ ‘. I ::. .“ ‘. ;, ,: :.
,.l
:...
: : ‘. ., ,,
‘CHEMICAL PH+ICS.LETTERS:
..’ “.
.(.,.
,,
.,
;
: .,
: 7,‘. : .yI.__‘. ‘.; ..’1.,.: ” ‘: :, -,I:‘ :
: 1 A&l
1975
: :_ ‘_1.
:,
: ‘.
:‘.
‘1, : :- . ~.,
..:’ :_s’] G. Henbcrg, ,~oIccular~~ectr~ ‘and moiecuftir struc&, Vol. I. Spectra of &atomic mdlecules (Vari Nostrand, Princtiton, ,:’-y ‘,. ” .:.. ., _.jgsO);-: ‘. ,. ‘. Y’,’[6j’~.R;&lmor6, J;Quant. Spectrj.-Radiative Transfei.5 (1965) 369: ‘, :, ” .. ). [?I D.S:‘McCIure, Can:JI,Chcm. 36 (1958) 59. ‘_ ‘,. .: ” : ‘.. :’ ‘.’ .‘.: _ ‘,- .{6] M.Kasha,Radia~onRes.20(1963)5$. : ,-, and Excjtat& Transfer, E&&tin No. 18; Division of.Biology and Medicine AEC, Insti[91 Th. Fiirstci, Delocalize{ E&a$on ,tut&of Mblecul~ Biophysics, Ftorida State lJniver&y, Tall&&see, Flor’ida, Marc@1965, FSIJ-2090-18; ’ ‘. .( iO] R.S; hiulIik& and !VB. P,&rsoh; Moiecufar complexes (Whey-lnterscienc~, blew Yqrk, 1969). : [ 11 J. J.R. Henderson, R.A. Willctt, ?d. Muramord 3nd.D.C; Richardson, Tables of Harmonic Franck-Condon &erLap fntegils I* :. eluding Displaceme& of Noymal Coordinates, Douglas Rcport’Sh1-45807, D’ouglas Missile rnd Spa&z System Division, Stir@ :’ Moni&, C&for& Jaz.13, 1964. ‘: : C.C.J. Roothazn and W. Jaw$ie&, J,,Chcm, Phys. 24 (19Sri) 201. -. :,:- ,[3ij K. Gutenberg; 1 : 1131 S. khrensoisrid P.E. Philip&?, J. Chem,.Phys, 34 (1961) 1224 .,_, . ...’ ‘. -, I141 G.L. Zarur’and Y:N. Chju,J. Chcm. Phys. 56 (1972) 3278. ‘^ ‘[1.5],,M,‘Kodni, A.‘&ncniya;E. Ishigufq and T. Kimura, Table of rnoler&z intkgdls ihiaruzen, To&o, 195S):A,(p) and B,(rp) .fcnctions.’ :,. ‘. .’ 1 : ” ._:. : I16j.J.O. Hirschfelder,‘C.F. Cur&and R.B. Bird,,M&ular theory df gases a&Ii&ids fi&y, New Y&k, 19j4). ,’ ._ ‘j17] &:@ui&g, The nattire of the chemical b&d (L’orn& U&v. PI& Ithka, 1960).’ .: ‘[iS]‘J.L. Beaccilamp;Ann. Rev. Phys. Chem. 22 (1971)‘527. ,. Harlan, A&i. Rev; Phys. Chem. 25 (1974),48.5; ‘. .:“. ,[19).J.L.‘Frr;r;Minand,P.W. ‘.
: i2Rj’L., Fti~@an and B.C. Reuben, Advan. Chem, Whys. 19 (1971) 33. .‘.; ‘. f21 f .D;E. MiIligan and M.E:J~cox, $. Ch&+ Phys. 51 (1969) 1952, and subsequetit ,,I221 .D.E. ~I~~nand
M.E. Jacox, Advan. High..Temp. chde.
&lotta,
J.L. Hall, M.W:%gel
R.A.:B&ett.
and J:Levi&Phys. Rev. 1.” [zs] M,Vf. Sieie:ef,R.J. Celotta, J.L. Hall, J. Levine nnd.8.A. Bknnet$,Phys-Rev.
3
.:.
__...
‘_
,‘.
,.’
‘.
‘. .. : ..’
‘.
4 (1972)X.,
‘- ‘, 123,]-jy. Holz~r;W.F; Mur$hy;-H.J. Bernstein and-J. Rolfe, 3. hlol. Spectry.,26 -. .*’M.J.W:Boncss and G.J. Schulz; Phys. Rev. A2 (1970) 2182. ‘. ’ [24j:R:J.
.”
y+r%;
.’
(1958) 543,.
”
‘;,,
6311 A$ Cl9721 607:
fit?
(19’72)
“’ ..‘.
:
’ ’ _. ‘.
32, number
ELECTRON-TRANSFER
TRANSITIONS
OF O,, N,, NO AND CO WITH THEIR Ying-Nan
Center for
I April 1975
CHEMlCALPHYSlCSLETTERS
1
DURING
THE COLLLSION
RESPECTIVE
IONS
CHIIJ *
hlolccolnrDyrtamics owl
h’nergy Trawler, Deparfnrenr oj Chemistry, The Cathotic Ufrivcrsiry
o~/Imcrico.
IVasAir;gton, D.c. 20064,usrl
and Yuh-Kang
PAN *.*
Received 7 October 1974 Revised manuscript rcceikd
AII improved
or ion-molecule cstimatcd.
Odht~r
theory
4 December
of clcctron
transfer
I974
absorpticn is proposed. for the Oz-05,
pairs is discussed and frequencies strer.gths UC &o estimated
for tllc 02-0$
The possibility of such absorption during the collision NO-NO-, CO-CO+ and NZ-Nt pnirr arc
0,-O?.
pair.
The phenomenon of electron-transfer radiative transition is well known in mixed-valence transition metal complexes’ [l-4]. In the mixed-valence biferrocene picrate, a new absorption band in the near infrared at 1900 nm (E = 550 in acetonitrile) has been attributed to such a transition fiom Fe2+ to Fe3+ [3]. We propose to show that a similar e!ectron-transfer absorption might be observed in the case of an ion-molecule collision complex with a sufficiently long lifetime. We shall illustrate our theory using simple molecules. The existing theory may be summarized as follows. Because of the rapid electron transfer compared with nuclear vibration, vertical Franck-Condon transitions prevail. The loss of an electron from a molecule in a ground vibrational state results in a vibrationally excited ion. Similarly, acceptance of this electron by the neighboring ion in its ground vibrational state results in a vibrationally excited molecule. Therefore,.the electron-transfer transition from the ground vibrational state of the molecule-ion complex is necessarily absorpciw. ?hc frcque=y of tr&itian has been computed [4] from the semiclassicalexpression, ,5 = (l/a)
@‘+I?“ (Qb)
Q;)2
,
(1)
where k’ and k” a&force constants and Qb and Qi are the equilibrium
normal coordinates of the molecule and the ion, respectively. This model is based on the harmonic oscillator approximation for which classically E = A$* = ihu2 with u = amplitude = Q&- Q6. Although the above semichrssical theory of transition.frequencies is well known, the theory of transition intcnwe choose to consider the elecsity has received less attention. As ai improvement over the existing theory [i-4], tron transfer frorri molecule a to ion b as involving a Franck-Condon transition from the ground vibrational state of molecule a (fo) to the appropriate excited vibrational state of ion a (xi+) and a simultaneous Franck-Condon trarisition’from thc.grqtind vibrational state of ion b ($j’ ) to the approptiate excited vibrational state of molecule b (&. If the electronic interaction between a and b is.smaller than the vibrational spacing and there is little mix .. :. * Supported by a Natiorui Sciekc Foundation &ant No.GP-11212 ** Supported by the Office 6f Nnval R&&&under Con&t #N000’.1469-kCI453. ,,, . ;’ ,: I ‘. .’ : .. ;,. .,, : .,, . .’ .- ‘. ” -, _’_ ,_-:; :’ : ..: : .,-,,
-’ .:
67
. . .
‘VoIime.JZ, nutibcr.1 .
\
CHEMICAL PHYSICS LETTERS ‘.
1 ~&ctkn-~ransfci absorption ‘. ‘,
I April 1975
Table
molcculc collision pairs a) Absorption
Ground ionic moiecule
Ground ncutrsl molcculc
Collision ..:phk
..
Frcqucncics for various ion-neutral
._,
frcqucncy
-~
.’
~~-0;
X3$
02-q; NO-NOc&co+. N;-N;
xbg X%-I,,2 X’Z+ Xli$. b
wc (cm-‘)
re(A)
1580.3b) 1580.3 b) 1904.03 b) 2170,21 b) 2359.6 b)
1.2074 1.2074 1.1508 1.1281 1.094
X%-lg XZl-Ig X3xX2x+ X2X,+
(nm)
f,& (Cm-q
QyLj- ‘:
(cm-‘)
1876.4 b) mod) 1470 r) .’ 2214.24 2207.19
1.1227 I .341 e). 1.258 1.1150 1.116
5.115.5 c) 780‘1.5 736l;l 167.7 524.6
1954.4 128i.8 1358.4 59632 19062
3j Cjiculnkd from, eq. (1). b) Ref. [S]. ” c) Rcs?rlls from potcnti;ll CU~YCS and uncorrected Oscillator strength for 2.8 A separatiqn .c@uplirl~. d) Rcf.:[23].
e). Ret’. [ 241.
: ‘. ing &f.the electronic cask by
.’
q=Jh(ri?
quantum mechanical form111aare !185 cm-l and 1928.6 nm. is estimated to be 1.6 X lOwa for jyeak coupling, 1.2 X lb-‘, for stronp
f) Ref. [ZS].
states of the two m&ties,
$‘(Q,)
then the transition
moment
may be represented
$iQb) pi b,iri> >I’o
in this extreme
(2)
3.
:where.@,:‘and &, are the donor and acceptor electronic tirbitals of the molecule and the ion, respectively,‘and the R’s are Franck-Condon integrals. To illustrate tlie magnitude of the transition freque,ncy, we consider the collision of 0; and,02. From Herz&rg’s.book’ [5] we find for the X3Zg state of 02, @, =ri = 1.2074 A, we = 1 MO,3 cm-l and for the X 2iIs St; 7 rz = l.l227A,
.Aitate of pi,
-,;=-I
876.4 cm -l.
Using these pzrameter’s
and eq. (l),
we obtained
the eiectron-
transfer transition frequency-F= 5116.6 cm-l (X = 14 544 8, = 1954.4 n-m), in the near infrared region. From the potential curv‘es [6] of p2 and 6; WCnote that the upward vertical transition frdm 0, (Qb at 1.207 A) most likeIy.yieids C$ in the P(+= 1 vibrational level and that the downward lrertical transition from the 0; ground vibra-tional state (Qi at. 1 :122 a) should produce 0, in the u.= 1 vibrati3nal.state. The-final-state vibraiionalenergy is predicted to.be F=.b’ii) a: + (v,ti) we = 5185.0 cm-l, which ia seen to be close to the frequency calculated from eql (l)..Semiclassical calculations of the abs&iion frequenci:s for this and other i&-molecule pairs are ‘given in table 1. ’ ,: .’ Otir. transition moment formula eq. (2) differs from the existing’treatment in that it contains a product of two Franck-Cotidon factors. This C&Ibe derived by analogy tith t,he exciton model for a molectilay dimer [7-91 and by writing the, appropriate zeroth.order.ground (N) and excited (V) vibronic stat& with corresponding firstorder
energicS
(hicglecting
overlap)
..
as follows:
: +-$&$+&; ,’
-+$=‘k-p+,+f!;+,
.’
., : ,‘. ; 1 :-
.’ (?a) :. _.:__
.I,
-1 _’
. .
(3b)
The energy splittjngwo&d
lead t0.a doublet tith a separation.bf 2&>‘~-$,$. W&n the,$xing of the-two ., ; ,.‘I ,. ; .. siates &e:t? electronic inteiaction’increa!es,. th” electronic [email protected]’becqtie. [2,9]. :
:.
acwell a~,lon-t~~‘vibrjtional ,‘I :,., :. ,- ./ ,:: :. .,y .’
.. ,.__ .:: -. ,-
‘::.
._‘...‘. ;;.;._.” ..’ : : _: ..
/ .’” :_
.
.,.
;, ..
_. .,: ;, .. : .:.. : I,.‘,,,. .:,’ ‘ ‘. ‘,i :’ .,... .. . -;, ‘; .-
Volume 32. number 1
1 April 1975
CHEhiICAL PHYSICS LETTERS
excitations due to electron transfer. The electronic transition moment is.
which is similar to the charge-transfer moment of Mulliken [lo] _The Franck -Condon factors are essentially the same as those obtained from eq. (2), since (4a) and (4b) are predominantly & and &, respectively. Hence eq- (5) reduces to eq. (2) except for a phase factor of -1 when Q = 0. In the limit of very strong electronic coupling, the vibronic wavefunctions are (6)
and the electronic transition moment is
The Franck-Condon
factors are presumably not very different from the previous cases and can be approximated
by the factors in eq. (2) for two independent
oscil!ators.
.The above serve to show that proper interpretation of electron transfer spectra could yield vahabk information on the strength of electronic coupling, the size of splitting for a given geometry of the complex, et=. To illustrate the magnitude of the transition intensity, WC have estimated the intensity for the 0,--O; collision, in the two extreme cases: eqs. (2) nnd (7). Using frequency data from Herzberg [5], we estimated the overlap in tegrals R,,,; =RVstVrfrom tables [ 111 of harmcnic Franck-Condon integrals involving displacements of normai coordinates. The two-center electronic dipoIe transition matrix element M [12-151 was approximated by (2pnblZ,i2pn,) and was estimated by using the Slater 2p orbital of the oxygen atoms assuming co = 4.3 for both the mclecule and the ion. For the average separation of the oxygen atoms, we tried three vdues: (I) the LennardJones [16] u = 3.42 a; (2) the van der Waals diameter [17],2.8 A; and (3) an arbitrarily assumed separation of 1.4 A for dose approach_ Assuming that only the vibrational transitions I * 0 and 0 * I contribute significantly to the oscillator strength, we computed the corresponding oscillator strengthsf= (8~~mc/3f1)P(3~ and Einstein spontaneous transition probabilities_4 = (64flP3/3h) e2 CD2for the threeseparations cited [weak coupling, eq- (Z)] to be (l)f= 3.3 X 10-lo, A = 5.70 X 1O-4 s- l; (2)f= 1.6 X lO-8,,4 = 2.7 X 1O-2 s-l; (3) f= 2.4 X t@, A = 42 s-l. The corresponding oscillator strengths for strong coupling [eq. (7)] are (I)f= 1.8 X IOM2,.4 = 3.2 X 104 s-‘; (2)f= 1.2 X 10d2,d = 2.1 X 104 s-l; (3)f= 3.1 X 10m3,A = 5.3 X lo3 s-l. To estimate the extinction coefficient, we used the Formula [IO] f= 4.32 X 10sg E,, Vllz. To obtain a severe lower limit of crnjx, we took the half-width P’1,2to be equal to Zr.In the weak coupling case [eq. (2)] and for the same distances as above, we obtained (1) E,, = 15 X 10h5, (2) emav = 4.9 X 10d3, (3) E,, = 1.I. For strong coupling [eq. (7)], the values are (1) fmax = 827, (2) fmax 7 551, (3) emn, = 138. The transition frequency, of course, places a minimum requirement on the life-time of the interaction complex. If the molecule and ion are vibrationally excited initially, the’revened process of electron-transfer emission might also be observed if the frequency and interaction time are both large. The emission phenomenon should a1so be of interest in understanding the collisional radiation in hot plasma. Such an electron-tnnsfer trsnsition should ,alsobe of interest in ion-molecule reactiqns invoking unsymmetrid systems [lS---201 2nd some of the spectral
quantities ., ..’
may be related to those
of the ions generated
in matrix
isolation
studies
[21,22].
Thanks are due Dr. William A. Sanders for reading the manuscript wjth suggestions for improving its presentation. Y.N.C. acknowledges helpful djscussiork following a seminar by Dr. F.A. Jumak, which motivated this work. _. ~Wferences
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., ”
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:. Volume 32, number. 1 _j,.“ , .‘ ‘. I ::. .“ ‘. ;, ,: :.
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‘CHEMICAL PH+ICS.LETTERS:
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