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On the effect of chemical radiative collisions
CHEMICAL PH\iSICS-LETTERS
Volume 45, number 2
1.5 January 1977
ON THE EFFECT OF CHEMICAL RADIATIVE COLLKIONS VS. DUBOV, L.I. GUDZENKO, L.V. GURVICH and S.I. lAKOVLENK0 Depatrtnent of Ciremical Thermodynamics, lirsritute for High Temperatures, bfoscow I-412. USSli i27412 Received 16 July 1976 Revised manuscript received 6 September
A new type of chemical optically
1976
induced reaction is descrl%ed during which the colliding molecules absorb (emit) a
photon and simultaneously new molecules are formed. The exchange reaction of a halogen molecule with a noble gas atom and simultaneous photon absorption was analysed. The analysis shows that the absorption coefficient at respective frequencies and atmospheric pressure can reach several reciprocal centimeters.
A new type of chemica1 optically induced reaction, chemical radiative collisions (RC), will be discussed_ The main distinctive feature of RC is that the optical field dire&y participates in the elementary collision process, not merely “preparing” the state of the colliding objects. In these reactions the photon ensures fulfiiment of the energy conservation law and relaxes the adiabatic transition prohibition during the collisional transition. Until now RC of atoms and ions, whose nuclei make a free-free transition have been mainly discussed in the literature [I-.5] _(The first experimental observation of the radiative collisions has been reported in ref. [4] .) The principal distinctive feature of chemical Rc’s is that they not only change the electronic structure, but also the chemical composition of the colliding objects- The simplest example is the photoassociation of atoms A and B during a collision in the photon field with energy tiw A+B+fiwdAB.
(1)
Most interesting is, however, the bimoIecular with rearrangement of molecular structure: x-t-Y-+Wo
=+z+u,
reaction
(2)
where X, Y, Z, U are the colliding and scattering molecules. Below we shall consider in detail the RC reaction of atom replacement in a diatomic molecule 330
A+BC+fiw*AB+C
(3)
as the simplest case to be discussed. When considering chemical RC reactions we can use some general principles of the theory of simple RC’s [l-3,5] , as the atomic collision theory in the theory of ordinary chemical reactions is used. The main point in the RC theory is the confinement of the discussion to those tasks adequate to the ordinary collision theory. This is being done on the basis of transition analysis in the compound system “colliding particles -I-electromagnetic field”. The terms of such a compound system Ui(r) fhw, U&r) are different from the terms of the quasimolecule because they are “brought” closer to each other by a photon fro; in this case the most interesting situation arises when the terms of the compound system cross, whereas the terms of the quasimolecule are far from each other (see fig_ 1). In the crossing point of the compound system terms the RC transition i + f takes place. The matrix element of the RC transition v= d *E. canbe expressed by means of a dipole moment of the quasimolecule d (it is often induced by the interacting particles during the collision) and the amplitude of the electrostatic field density vector &‘. . In chemical RC’s the appropriate terms involve multidimensional potential surfaces, this not only makes the probIem more difficylt, but also includes certain
Volume 45, number 2
CHEMICAL PHYSICS LETZERS
15 January 1977
(atomic
units are used). For alkali metals and halogen molecules usualIy EA = l-3 eV and consequently
Z= 5-15& As a matter of fact, the terms of the ‘0 quasimolecule MX2 are three-dimensional surfaces,
and the result of their crossing - a two-dimensional surface situated in the spherical layer near ro. If, for example, we put the MXX nuclei in one line, there would be not one crossing point, as would happen in the case of photoassociation (see fig. l), but a whole
Fig. 1. Terms of the quasimolecule and compound system (dotted curve) for a photoassociative
reaction.
prohibitions, resulting from the Franck-Condon principle. For instance atom A should come so close to atom B that the configuration of the ABC quasimolecule, which in the original i-state corresponded to bonding of BC and repulsion of A, after the transition to “f’ (the finaI state), would correspond to bonding
of AB and repulsion of C. As a rule, at room temperature the repulsion forces do not allow the A-atom to approach the BC molecule close enough even if we take into account vibrationaIIy excited states of AB and BC molecuIes. But there are some important exceptions, e.g. if an A + BC system has an ionic term with a comparatively great well-depth even for large distances between A and BC, when the repulsion due to the-covalent term still is not signit?cant. This case is similar to the so-calIed harpooning reactions [6,7] _ Harpooning reactions take place as a rule during the collision of a metal atom M with a low ionisation potential JM (M is usually an alkali metal) and an X, molecule (usually a halogen) with large enough electron affinity (EA): M+X2+MX*+X.
the initiation of a harpooning reaction by monochromatic radiation energy different from that of the exci-
(4)
The harpooning reactions have correspondingly large cross sections, usually several hundreds a2. Because of the greater distances ‘0 at which these reactions take place. atom M and molecule X2 can be considered as points. In this case the ionic term of the M” + 3 complex is practically the surface of a Coulomb interaction Uf (r) = -e2/r. The crossing of the ionic term with a covalent one occurs at distances of about ‘0 = (JM + EA)-1
set, some point of which relates to the vibrational states of XT, whereas the continuum part relates to dissociative ones (the covalent term crosses with the repuIsive part of the term Xi, se& fig. 2). In the last case the dissociation of X: occurs immediately after the transition from the covalent term to an ionic one and a neutral molecule M+X- might formed, as a rule in a highly excited state. If instead of the metal atom M an atom with a higher ionisation potential (for example atom R of a noble gas in its ground state) collides with a halogen molecule X2, the harpooning reaction naturally is impossible as the exchange forces would cause repulsion of R and X2 before the ionic term would reach the ground state (see fig. 2). However many excited atoms could enter harpooning reactions with halogens. If, for example, the atoms of a noble gas are excited with resonance radiation, active reactions would start in their mixture with halogens. This fact is interesting by itself and reactions of excited noble gas atoms with molecules have been discussed in the literature [8,9]. However, we should like to consider some other possibility -
(5)
Fig. 2. Terms of the quasimolecule and compound system (dotted curve) for a harpooning RC reaction. U,,
is the term
of the halogen molecule, Uxz is the term of its negative ion.
331
Volume45, number2
CHEMICAL. PHYSICSLklTERS
-ted state of the R a&m. Let us discuss the chemical RS reaction oirhe harpooning typeR+Xzclri,+Rf+XZj+RX*+X.
rAo = (JR + EA - a~)-’
= @a-l.
(7)
Jxt us estimate the rate constant of the harpooning RC reaction. We assume that the second stage of reaction (6) starts instantly after the transition to an ionic term with a probability of about 1. This assumption is usually correct in the case of an ordinary reaction (4).
In this case the fuil probability of the transition after passing two crossing points can be expressed similarly to the Landau-Zener fo~uJa 2.i follows: W= (I - e-a’) + edl(l
- e-a*),
= !u cos et,2,a,
(8)
= 2rd2E;luAF Q =
y..g$“do v o is the parameter of non-adiabativity; AF= Am2 the difference in the slopes of the terms at the crossing “‘point”; B 1 theangIe between the vectors d and LEOin the first andzsecond crossing “points” re-
spectively; Q the square of the overlap integral of the radial waveftinctions of X, and q integrated over the crossing area of the covalent term with the repulsive part of the term q (see fig_ 2). After integrating over the impact parameter and averaging according to 2 Maxwell distribution (similar to ref_ [S] ) we get the expression for the rate constant of the RC reaction
K(Ao, T, CK)= KT(Aw) b’(o),
oc= (Eu /ET)2,
69
whereK*(Aw) = 27rfi2&bT is the m~imum possible rate constant of the RC reaction (this expression can be used in the assessment of the ordinary harpooning reaction); VT = (2kT/Er)‘J2;T isihe gas temperature;p the reduced mass of the quasimolecule RX2; i? = - ~~A~2~2~d2(~~~)Q a certain characteristic f&d decsity, starting from which the correlation between the rate constant of the RC reaction and the light intensity becomes non-linear (in the RC theory mch a field is c2lIed critical): W(o) is the average probability of the RC transition after passing two crossing ‘cpoints’*, It is expressed as follows:
332
0
(6)
The second stage of this reaction must go in principle the same way as that of reaction (4). However the transition to the ionic term is caused by the optic4 field, which compensates for the energy defect so that the terms of the compound system cross in the region of
15 January 1977
X Cl - (exp [-(o/x)(cos2S
=+a: for = 1
I f cos20,)] >3
a< 1,
for aal.
(JO)
It should be noted that unlike RC the velocity of harpooning RC’s does not diminish in strong fields a % 1 (compare with refs. [l-3,5] ) since the Xi ion decays after passing the second crossing “point”. From (9) and (10) it follows that in the case of a low light intensity (k?Z$ @&$ a @ I) the rate constant of harpooning RC reactions differs from the rather high rate constants of ordinary harpooning reactions by the factor $a< 1. Let us now make an assessment. According to ref.
flO]i the asympto:ic expression for a dipofe transition moment can be expressed as’ d(r) = C(n)Br”-’ emffn, where n = (mJW1j2 is the effective principal quantum number, .!Z_the sum of the vertical electron affinity of the molecule X2 and the potential of the ion interacting in the point of ra, ;B = J-5 the factor describing
the asymptotic behaviour of the wavefunction of the external electron of the negative ion. c = 8 [(2/fz)(2r f- 1)0-r- m)/(Z - m)] t’2(n/2m!)n* X (212.73 njE (~)5(~~-2r(l
: n),
where 2 and M are the angular and magnetic quantum numbers of the electron and i’ is the gamma function. Let us make a numericaJ estimation for the RC reaction of 2 Xe atom with 2 halogen molecule- AssumingI%ti=7_5eVfx* 1400A),EA= l.SeV [ll],B =5au,r(l --)=S,Q=l,u,=5X 104cma-I, rAw = 8 au. We haved2 = 4 X lOa au. For the rate
constant of the RC reaction we obtain KT(hw) = 5 X 10m2 au &+=3x
= 2
10-3 2u=2x
X 1O-1o cm3 s-l, 106vcm-1.
For the absorption coefticient of this mixture in the case of 2 low light intensity (E. WITP) we have WI
Volume 451 number 2
CHEMICAL PHYSICS LETTERS
15 January 1977
References
where +(Ao) = 9 KT(Aw)lc$ is the absorption coefficient relating to a pair of particles, c is the velocity of light, NR and Nx2 the concentrations of R atoms and X2 molecules_ For the parameters shown above we obtain (I-0.1) X 10m3* cm’. Thus at atmospheric pressure, (NRNx,)1’2 = 3 X 101’ cme3, the absdrption coefficient reaches a value of I-10 cm-‘. One more possible way of having an RC exchange reaction should be noted. If the photon energy is not too far from the excitation energy of the R atom (Aw < kT), an RC transition to a covalent term, correlated with an excited state of this atom, is possible. On further motion over this bound or flat term an exchange reaction (3) can take place. If the RC reaction did not take place at the given collision, the excited atom in a dense medium usually enters an ordinary harpooning reaction at the next collision.
[I] L-1. Gudzenko and S.I. Iakovlenko, J. Exp. Theor. Phys. 62 (1972) 1686_ [2] VS. Lisitsa and S.I. Iakovlenko, J. Theor. Phys. 66 (1974) 2032. [3] R.Z. Vitlina, A.V. Chaplic and M.V. Entin, J. Exp. Theor. Phys. 67 (1974) 1667.141 D-B. Lidov, R.W. F&one, T.F. Young and S.E. Harris, Phys. Rev. Letters 36 (1976) 462.
151 S-1. lakovlenko, Radiative Collisions of Atoms, Preprint IAE-2666
(1976).
161 J-L- Magee, J. Chem. Phvs. 8 (1940) 687. 171 J. Maya and P. Daviclovits. J. Chem. Phys. 59 (1973) 3143.
181 M.F. Colde and B.A. Thrush, Chem. Phys. Letters
29
(1974) 486. T91 M.F. Golde, J. Mol. Spectry. 58 (1975) 261. [lOI V.P. Zshdanov and M.I. Chibisov, J. Exp. Theor. Phys. 70 (1976) 2087. [111 W.B. Person, J. Chem. Phys. 32 (1963) 109.
333
Volume 45, number 2
1.5 January 1977
ON THE EFFECT OF CHEMICAL RADIATIVE COLLKIONS VS. DUBOV, L.I. GUDZENKO, L.V. GURVICH and S.I. lAKOVLENK0 Depatrtnent of Ciremical Thermodynamics, lirsritute for High Temperatures, bfoscow I-412. USSli i27412 Received 16 July 1976 Revised manuscript received 6 September
A new type of chemical optically
1976
induced reaction is descrl%ed during which the colliding molecules absorb (emit) a
photon and simultaneously new molecules are formed. The exchange reaction of a halogen molecule with a noble gas atom and simultaneous photon absorption was analysed. The analysis shows that the absorption coefficient at respective frequencies and atmospheric pressure can reach several reciprocal centimeters.
A new type of chemica1 optically induced reaction, chemical radiative collisions (RC), will be discussed_ The main distinctive feature of RC is that the optical field dire&y participates in the elementary collision process, not merely “preparing” the state of the colliding objects. In these reactions the photon ensures fulfiiment of the energy conservation law and relaxes the adiabatic transition prohibition during the collisional transition. Until now RC of atoms and ions, whose nuclei make a free-free transition have been mainly discussed in the literature [I-.5] _(The first experimental observation of the radiative collisions has been reported in ref. [4] .) The principal distinctive feature of chemical Rc’s is that they not only change the electronic structure, but also the chemical composition of the colliding objects- The simplest example is the photoassociation of atoms A and B during a collision in the photon field with energy tiw A+B+fiwdAB.
(1)
Most interesting is, however, the bimoIecular with rearrangement of molecular structure: x-t-Y-+Wo
=+z+u,
reaction
(2)
where X, Y, Z, U are the colliding and scattering molecules. Below we shall consider in detail the RC reaction of atom replacement in a diatomic molecule 330
A+BC+fiw*AB+C
(3)
as the simplest case to be discussed. When considering chemical RC reactions we can use some general principles of the theory of simple RC’s [l-3,5] , as the atomic collision theory in the theory of ordinary chemical reactions is used. The main point in the RC theory is the confinement of the discussion to those tasks adequate to the ordinary collision theory. This is being done on the basis of transition analysis in the compound system “colliding particles -I-electromagnetic field”. The terms of such a compound system Ui(r) fhw, U&r) are different from the terms of the quasimolecule because they are “brought” closer to each other by a photon fro; in this case the most interesting situation arises when the terms of the compound system cross, whereas the terms of the quasimolecule are far from each other (see fig_ 1). In the crossing point of the compound system terms the RC transition i + f takes place. The matrix element of the RC transition v= d *E. canbe expressed by means of a dipole moment of the quasimolecule d (it is often induced by the interacting particles during the collision) and the amplitude of the electrostatic field density vector &‘. . In chemical RC’s the appropriate terms involve multidimensional potential surfaces, this not only makes the probIem more difficylt, but also includes certain
Volume 45, number 2
CHEMICAL PHYSICS LETZERS
15 January 1977
(atomic
units are used). For alkali metals and halogen molecules usualIy EA = l-3 eV and consequently
Z= 5-15& As a matter of fact, the terms of the ‘0 quasimolecule MX2 are three-dimensional surfaces,
and the result of their crossing - a two-dimensional surface situated in the spherical layer near ro. If, for example, we put the MXX nuclei in one line, there would be not one crossing point, as would happen in the case of photoassociation (see fig. l), but a whole
Fig. 1. Terms of the quasimolecule and compound system (dotted curve) for a photoassociative
reaction.
prohibitions, resulting from the Franck-Condon principle. For instance atom A should come so close to atom B that the configuration of the ABC quasimolecule, which in the original i-state corresponded to bonding of BC and repulsion of A, after the transition to “f’ (the finaI state), would correspond to bonding
of AB and repulsion of C. As a rule, at room temperature the repulsion forces do not allow the A-atom to approach the BC molecule close enough even if we take into account vibrationaIIy excited states of AB and BC molecuIes. But there are some important exceptions, e.g. if an A + BC system has an ionic term with a comparatively great well-depth even for large distances between A and BC, when the repulsion due to the-covalent term still is not signit?cant. This case is similar to the so-calIed harpooning reactions [6,7] _ Harpooning reactions take place as a rule during the collision of a metal atom M with a low ionisation potential JM (M is usually an alkali metal) and an X, molecule (usually a halogen) with large enough electron affinity (EA): M+X2+MX*+X.
the initiation of a harpooning reaction by monochromatic radiation energy different from that of the exci-
(4)
The harpooning reactions have correspondingly large cross sections, usually several hundreds a2. Because of the greater distances ‘0 at which these reactions take place. atom M and molecule X2 can be considered as points. In this case the ionic term of the M” + 3 complex is practically the surface of a Coulomb interaction Uf (r) = -e2/r. The crossing of the ionic term with a covalent one occurs at distances of about ‘0 = (JM + EA)-1
set, some point of which relates to the vibrational states of XT, whereas the continuum part relates to dissociative ones (the covalent term crosses with the repuIsive part of the term Xi, se& fig. 2). In the last case the dissociation of X: occurs immediately after the transition from the covalent term to an ionic one and a neutral molecule M+X- might formed, as a rule in a highly excited state. If instead of the metal atom M an atom with a higher ionisation potential (for example atom R of a noble gas in its ground state) collides with a halogen molecule X2, the harpooning reaction naturally is impossible as the exchange forces would cause repulsion of R and X2 before the ionic term would reach the ground state (see fig. 2). However many excited atoms could enter harpooning reactions with halogens. If, for example, the atoms of a noble gas are excited with resonance radiation, active reactions would start in their mixture with halogens. This fact is interesting by itself and reactions of excited noble gas atoms with molecules have been discussed in the literature [8,9]. However, we should like to consider some other possibility -
(5)
Fig. 2. Terms of the quasimolecule and compound system (dotted curve) for a harpooning RC reaction. U,,
is the term
of the halogen molecule, Uxz is the term of its negative ion.
331
Volume45, number2
CHEMICAL. PHYSICSLklTERS
-ted state of the R a&m. Let us discuss the chemical RS reaction oirhe harpooning typeR+Xzclri,+Rf+XZj+RX*+X.
rAo = (JR + EA - a~)-’
= @a-l.
(7)
Jxt us estimate the rate constant of the harpooning RC reaction. We assume that the second stage of reaction (6) starts instantly after the transition to an ionic term with a probability of about 1. This assumption is usually correct in the case of an ordinary reaction (4).
In this case the fuil probability of the transition after passing two crossing points can be expressed similarly to the Landau-Zener fo~uJa 2.i follows: W= (I - e-a’) + edl(l
- e-a*),
= !u cos et,2,a,
(8)
= 2rd2E;luAF Q =
y..g$“do v o is the parameter of non-adiabativity; AF= Am2 the difference in the slopes of the terms at the crossing “‘point”; B 1 theangIe between the vectors d and LEOin the first andzsecond crossing “points” re-
spectively; Q the square of the overlap integral of the radial waveftinctions of X, and q integrated over the crossing area of the covalent term with the repulsive part of the term q (see fig_ 2). After integrating over the impact parameter and averaging according to 2 Maxwell distribution (similar to ref_ [S] ) we get the expression for the rate constant of the RC reaction
K(Ao, T, CK)= KT(Aw) b’(o),
oc= (Eu /ET)2,
69
whereK*(Aw) = 27rfi2&bT is the m~imum possible rate constant of the RC reaction (this expression can be used in the assessment of the ordinary harpooning reaction); VT = (2kT/Er)‘J2;T isihe gas temperature;p the reduced mass of the quasimolecule RX2; i? = - ~~A~2~2~d2(~~~)Q a certain characteristic f&d decsity, starting from which the correlation between the rate constant of the RC reaction and the light intensity becomes non-linear (in the RC theory mch a field is c2lIed critical): W(o) is the average probability of the RC transition after passing two crossing ‘cpoints’*, It is expressed as follows:
332
0
(6)
The second stage of this reaction must go in principle the same way as that of reaction (4). However the transition to the ionic term is caused by the optic4 field, which compensates for the energy defect so that the terms of the compound system cross in the region of
15 January 1977
X Cl - (exp [-(o/x)(cos2S
=+a: for = 1
I f cos20,)] >3
a< 1,
for aal.
(JO)
It should be noted that unlike RC the velocity of harpooning RC’s does not diminish in strong fields a % 1 (compare with refs. [l-3,5] ) since the Xi ion decays after passing the second crossing “point”. From (9) and (10) it follows that in the case of a low light intensity (k?Z$ @&$ a @ I) the rate constant of harpooning RC reactions differs from the rather high rate constants of ordinary harpooning reactions by the factor $a< 1. Let us now make an assessment. According to ref.
flO]i the asympto:ic expression for a dipofe transition moment can be expressed as’ d(r) = C(n)Br”-’ emffn, where n = (mJW1j2 is the effective principal quantum number, .!Z_the sum of the vertical electron affinity of the molecule X2 and the potential of the ion interacting in the point of ra, ;B = J-5 the factor describing
the asymptotic behaviour of the wavefunction of the external electron of the negative ion. c = 8 [(2/fz)(2r f- 1)0-r- m)/(Z - m)] t’2(n/2m!)n* X (212.73 njE (~)5(~~-2r(l
: n),
where 2 and M are the angular and magnetic quantum numbers of the electron and i’ is the gamma function. Let us make a numericaJ estimation for the RC reaction of 2 Xe atom with 2 halogen molecule- AssumingI%ti=7_5eVfx* 1400A),EA= l.SeV [ll],B =5au,r(l --)=S,Q=l,u,=5X 104cma-I, rAw = 8 au. We haved2 = 4 X lOa au. For the rate
constant of the RC reaction we obtain KT(hw) = 5 X 10m2 au &+=3x
= 2
10-3 2u=2x
X 1O-1o cm3 s-l, 106vcm-1.
For the absorption coefticient of this mixture in the case of 2 low light intensity (E. WITP) we have WI
Volume 451 number 2
CHEMICAL PHYSICS LETTERS
15 January 1977
References
where +(Ao) = 9 KT(Aw)lc$ is the absorption coefficient relating to a pair of particles, c is the velocity of light, NR and Nx2 the concentrations of R atoms and X2 molecules_ For the parameters shown above we obtain (I-0.1) X 10m3* cm’. Thus at atmospheric pressure, (NRNx,)1’2 = 3 X 101’ cme3, the absdrption coefficient reaches a value of I-10 cm-‘. One more possible way of having an RC exchange reaction should be noted. If the photon energy is not too far from the excitation energy of the R atom (Aw < kT), an RC transition to a covalent term, correlated with an excited state of this atom, is possible. On further motion over this bound or flat term an exchange reaction (3) can take place. If the RC reaction did not take place at the given collision, the excited atom in a dense medium usually enters an ordinary harpooning reaction at the next collision.
[I] L-1. Gudzenko and S.I. Iakovlenko, J. Exp. Theor. Phys. 62 (1972) 1686_ [2] VS. Lisitsa and S.I. Iakovlenko, J. Theor. Phys. 66 (1974) 2032. [3] R.Z. Vitlina, A.V. Chaplic and M.V. Entin, J. Exp. Theor. Phys. 67 (1974) 1667.141 D-B. Lidov, R.W. F&one, T.F. Young and S.E. Harris, Phys. Rev. Letters 36 (1976) 462.
151 S-1. lakovlenko, Radiative Collisions of Atoms, Preprint IAE-2666
(1976).
161 J-L- Magee, J. Chem. Phvs. 8 (1940) 687. 171 J. Maya and P. Daviclovits. J. Chem. Phys. 59 (1973) 3143.
181 M.F. Colde and B.A. Thrush, Chem. Phys. Letters
29
(1974) 486. T91 M.F. Golde, J. Mol. Spectry. 58 (1975) 261. [lOI V.P. Zshdanov and M.I. Chibisov, J. Exp. Theor. Phys. 70 (1976) 2087. [111 W.B. Person, J. Chem. Phys. 32 (1963) 109.
333