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Trajectory calculation results on the orientation of a diatomic molecule in collision with an atom
Volume 31, number 1
CHEMICAL PHYSICS LITI-XRS
TIWJEC~~RYCA~CULATI~NHESUL'F~ON ORIENTATION OF A IHATOMIC MOLEdULE
1.5 February
1975
.’ THE IN COLLISION W!TH AN ATOM ..
P.G. KISTEMAKER and AE. DE VRIES F.O.M.-Instituut
voor Atoorn- en Molecuul~yysi&, Amsterdani/Wgm.,
l7’reNetherlands
Received 7 October 1974
Orientational effects in collisions between a diatomic molecule and a noble gas ato.m are studied by.classicaI trajectory calculations A preferable “perpendicular orientation” of the molecule is found nt the moment of closest npproach of the atom. This orientatioml effect is more pronounced in collisions WXI heavy atoms.
1. Introduction
tion that the orientation of the molecule can be regarded as constant during the collision md only the
Relaxation experiments on the bending vibration of CO, in mixtures of CO2 with noble gases in general show an increase in the observed relaxation time with increasing mass of the nob!e gas [ 11. However, the vibrational relaxation in a CO,-Xe mixture did
component of force in the vibrational direction is effective in the translational-vibratIona energy transfer. Recently Huetz [6] calculated specific steric factors for the de-excitation of the bending vibration of CO, in collision with noble gases. Using.these steric factors a remarkable agreement
not follow this general trend. The observed relaxation time for C02-Xe was found to be less th-an the relax-.
ation time for CO,-Kr, contrary to theoretical predictions: According to Iandau and Teller [2] vibrational energy will be transferred if the duration of the coIlision is short compared to the period of oscillation. From their theory based on Ehrenfest’s adiabatic principle [3] it fallows that vibrational energy transfer is favoured by colliding particles having small masses and steep repulsive potentials. These rathei qualitative considerations have been followed by semi-classical and quantum mechanical approaches to the vibrational excitation probabilities (for a review see ref. [4]). The most successful theory was developed by Schwartz, Slawsky and Herzfeld [S], well known as the SSlj theo:T. In this three-dimerisiorial quantum mechanical treatment the most favourablk mutual orientation of the particles, for vibrational energy transfer,istaken into account. To allow for less favourable orientations, steric fat- : : .. tars are introduced at the end of the.calculation: The steric factor approach is based on the assum&
was obtained between theoretical SSH values ad the experimental data for He, Ne, and Ar [l]. However, the relative low relmation times for C02-Kr and could not be explained. Cannemeyer and de Vries El] suggested that the relative high efficiency of Kr and Xe might be due to a pre-orientation of the CO, molecule during the colLision, by which the probability for vibrational energy transfer to the bending mode is increased. This orientational effect should be less prominent in collisions with the light noble gas atcms. The bending vibration of CO, is most likely to be excited by collisionswhich occur perpendicular to the molecular a&s. Th+e perpendicubr collision: on the other hand are highly inefficient fot the excitatibn of $e’stretching vibration of CO,. Consequently, the proposed l%e-orientation in CO,-Kr and CO,-Xe collisions leads to.a decreased efficiency for the excitation of the stretching vibration. Experimental dare on’the relaxation of the asymmetric stretching vibration of CO, by noble .gases,seeti tq confirm the hypothe+ [7]. C02-Xe
: ‘.
17
Volume 31,
number !
CljERIICAi
PI!YSICS IkTER~
& idea of pre-or&nation tit the CO2 molecule in co!!isions witll noble gases, we perfoirned 2 ‘number cifclassicd trajectory ca!culations on a mode! system, representing the C02-nobie gas interaction.
.:,- :.+&t&t
15
February
1975
: :
‘.
Starting from a innform distribution of the moiecular ciientation at the beginning of the trajectories, we : calculated the orientation of the mo!ecule at th’e moment of.closest approach of the atom.
..
2. Trajectory calculations
Although Our interest for orient~tional effects in molecular collisions was primari!y fccussed on the CO;-noble gas interactions, the actual collision trajectories have been calc&.i~d for an atom-diatomic moIecuIe system: The choice of a three-particle sys‘tern enables the direct application of existing trajectory programs present in our institute [a]. ~The diatomic moIecule was modelled to resemble the CO2 molecule in dimension, moment of inertia and orientationally averaged potential. In fact we ignored the central carbon atom in the CO, molecule ‘and used the remaining “oxygen molecule” as the molecuIar cohision partner. Further, the calculations : were, restricted to the t&odimensional case, -.vhere the molecule rotates in the plane defined by the initia! positions of the particles. The rotational, vibrational and translational energies of the particles had their classical equilibrium values at 303 K. After eliminatjon of.the center of mass motion, the relative position of the atom and. .molecule is described by the standard coordinaies R, ,b, F1z.and T, see fig. i. For the numerical integration of the cohision trajectories the hamiltonian form of the equations of motion was used. The eight equa- 7 tions were reduced to a set of four linear second-order coupled differential equations: Qi = -7~ Y/dQr, i = 1;...;4, where Y represents the potential energy of the system and Qi the generalized coordinates [PI. The potential energy V was constructed by addition of the pair-wise.interactions between the individual atoms, where each atom-atom interaction is descifbed by a Morse-type potential function: v=cv.: .i#j .:!’ ’ ,.. ” ,.js’::.: .
..: ., ,” ;
.,,, r:. ” :
.,..
...,
‘,
,:
”
..,‘.
.-
‘. ;
‘.
:
:,
T.J]
- 2Bjj exp [--c$rij
- Y$] .
The potential parametersAy Bij, ~ij and ?ii for the different ritom-atom interactions were determined as follows. For the interaction between the oxygen atoms in. the molecule we used the Morse potential pararnetersA, B and (Yfor pure oxygen from the book of Her&erg [9], -whereas the equilibrium distance ‘I2 was taken equal to the equilibrium distance of the oxygen at,Jrns in‘the CO2 molecule, ?12 = 2.32 A. The potential parameters for the oxygen-noble gas interactions were calculated according to the method re‘ported in 3 previous paper [lo]. Essentially, the interatomic distances r13 and rZ3 were approximated by R f T12 cosy. Then the interaction between the molecule and atom, which results from the pair-wise addition, was expressed.in R and 7 and reads in the fustorder .approximation IlO] V(f7.r) = ‘U(1 +202~&cos2y) exp[-2ar(R - i)] - 4B(l+ fo2r$cos2r)
where
_. .
exj[La(R
- -31 ,
‘.
’ u’;A*j,.
.&=aU=& -,’
B=B1,=B23, =,_J .- r=
. 23
7
17 .‘. 1323 -
.-’ :
_.
‘2 ._,
., ‘.
Exp[-3c+,-
vii =p,
;-
. -,,
Parameters defining the relative orientation of the molecule alld atom.
.;A=;A ;.
‘.,
..
x FG. 1.
,’
:
1:”
.; ..
.’
: ..,,,
..
-_
..
Volume 3 1.
ilUIllbCr
CHEMICAL PHYSICS LETTERS
1
Table 1 Morse potential
parameters for the atom-htom used. irr tic mje&ry qrlrsak~rions System
A (K)
B (K)
interactions
a (a-‘)
s:(A)
3.78 1.81 1.34
2.32 3.52 4.46
~o-o O-He 0-Xe
6cMi6 8.04 33.94
60486 20.78 71.66
He
Xe b:2
b=Z
6’ The orientationally averaged value of this expression is compared with the spherically symmetric Morse pctential for the C02-noble gas interaction, as derived from the potential functions for the pure gases via the combination rules of Saxena and Gambhir [ 11,121. Separately the attractive and repulsive parts of the orientationally averaged and spherically symmetric potential are equated for a special choice of t!le potential parameters A, B, a and 7 [lo]. Tlze actual values of the potentinl parameters used in the calculations are collected in table 1. Once the interaction potential is defmed, the colhsion trajectories can be calculated for specific initia! conditions. The equations of motion were solved by numerical integration on the ELX 8 computer of the Mathematical Centre, Amsterdam. The initial value of R was 9 r\, a value large enough for the potential energy to be negligibly srnal! relative to the kinetic energy of the system. With the center of mass of the molecule located at the x-axis, the initial relative velocity was taken parallel to the x-axis. The impact parameter b was varied in steps of 1 ,J%in the range of O-8 8. For each impact parameter b a number of trajectories was calculated with fised rotational, vibrational and translational energy, whereas the initial phase of the rotator was varied by 1” in the subsequent calculations. At the moment of closest approach of the atom, the trajectory calculation was stopped and the orientation ym of the molecular axis relative to R, the line from the center ofmass of the molecule to the atom, was calculated.
,I 20
20NWm)
5
.
He b=L
,
I ! I ! pp-!-l~ He b:6
Xe b-6 f
2c-
20. :
,-l!r!lll!l!~l!IIITl I < * I He b.8
Xe b=8 to-
ZO&“‘!““‘\‘!“‘I 0
60
I 7 III!lIl’I!I’I!~
120
160
-Ym
0
60
I
Ii0
I80
-Ym
Fig. 2. Distribution pattcxnsN(7,) for coliisions with He wd Xe at different impact parameters b. ym is the angle berween the molecular axis and the line between the centers of mass of the moiecule and atom at the moment of ciosest approach. .the approach of the atom, the distribution of the orientational angleN(7,) should be unifoorm upon [0,1801.This uniform distribution is found for trajectories with large impact parameters 6 2 8 .jl, where the interaction energy is negligibly small compared to the kinetic energy. For smaller impect parameters deviations from a uniform distribution are observed. In fig. 2, the distribution patternsN(7m) for a number of impact parameters are shown. It can be seen that the orientation of the molecule at the moment of closest approach depends strongly on the atomic collision partner.’ Tn collisions witti He only a slight increase of collisions with 7, = 90” is observed at smah impact parameters. The preference for this“‘perpendicular” orientation vanishes rapidly with increasing impact parameter.
In collisions with Xe, the rotational motion is strongly affected, resu!ting in a highly non-uniform 3. Results and discussion The calculatiorr reported here concernto systems with He and Xe as the atomic collision partners. If the. rotational motion o.f the molecule is not perturbed by. .,
distribution of Trn. Even at b = 5-7 A, the moiecule is lar,position. For these large rotational motion is slightly ated by the atom, reaching
large impact parzrneters drawn inta a perpendicuimpact parameters the accelerated or decelerthe energetically favour-
Yolumc
3.1, uumbcr 1
CHE~!ICAL PtIYSICS LU-TI:RS
.‘&I& perpendicular orientation at the moment of. closest approach. The trajectories show that at small impact param -et&s the co&ions with Xe.arc more violent and “multiple” atorn-atom impacts domm+e the colliGonal proces,s. If the first impact takes place with y> 90”, the rotational motion is highly accelerated during the approach of the atom, After half a rotational period, a second impact ‘takes place with yrn < 90’. The minimum distance between the atom and molecule is reached at the second impact. The distriblltion patterns for Xe at small impact parameters show clearly the enhancement in the number of collisions with r,.,, < 90” and the accompanying fall-off in the number of collisions with 7m > 90’. Multiple impacts are .scarcely observed in collisions with He
The possi3rlity of orientational effects in collisions between a linear molecuIe and a heavy atom was first
15,February
lY75
pointed
out by Dr. .F. Cannemeyer. The’authors’like him for the encouraging’discussions’about ,.this sutject. This work is part qf the research program ofthe. “Stichting Loor Fun,damenteel Onderzoek der hlaterie!‘(Foundatibn of Fundamental Research on Matter) and was made possible by financial support of the “Nederlandse Organisatie voor Zuiver-Wetenschapp,:lijk-b;nderzdek” (Netherlands Organization for the Adj/ancemcnt of Pure Research). to thank
References 111 F. Carmcmeyer.and
A.E. de Vries, Physico 64 (1973) 123. 121 L. Landau and E. Teller, Physik. 2. Sovijetunion 1C (1336) 34. [31P. Ehrenfest, KoninkL Ned. Akad. Wetenschap. Proc. 16 (1914) 591. I++1G..LI. Burnett and E-M. North, eds, Tmnsfer and storage of energy by molecules, Vol. 2 (Wiley, New York,
where $e light He atom is reflected Aready by the molecule at the first impact. The results show clearly th+ the orientational distribution of a highly asymmetric diatomic molecule in collision with noble gas atoms, cannot be regarded as uniform. The asymmetry in the interaction potentialfavours nearly perpendicular orientations. These effects are more dominant in collisions with heavy atoms. Steric factors calculated from a uniform distributionare thtxefore more reliable for collisions with Iight atoms than for collisions with heavy
._
:
1969).
ISI R.ti. Schwartz, 2.1. Slswsky
’
and K.F. Herzfeld, J. Chem. Pl1ys. 20 (1951) 1591. I61 M. Huetz and P. Chevalier, Advan Mol. Relaxation Proce:;scs 2 (1970) 101. 171 F. Cannemcyer and A.E. de Vries, Physica 70 (1973) 135. $1 k v;n der Meulen, Computer Phys. Commun. 3 11972) 42. G. Herzberg, Spectra of diatomic molecules (Van Nostrand, Princeton, 19.50). P.G. Kistemaker and A.E. de Vries, to be published. J.O. Hirschfelder, CF. Curtiss and R.B. Bird, h!olecular theory of gases and Liquids (Wiley, New York, 1954). SC. Saxena and R.S. Gambhir, Mol. Phys. 6 (1963) 577.
CHEMICAL PHYSICS LITI-XRS
TIWJEC~~RYCA~CULATI~NHESUL'F~ON ORIENTATION OF A IHATOMIC MOLEdULE
1.5 February
1975
.’ THE IN COLLISION W!TH AN ATOM ..
P.G. KISTEMAKER and AE. DE VRIES F.O.M.-Instituut
voor Atoorn- en Molecuul~yysi&, Amsterdani/Wgm.,
l7’reNetherlands
Received 7 October 1974
Orientational effects in collisions between a diatomic molecule and a noble gas ato.m are studied by.classicaI trajectory calculations A preferable “perpendicular orientation” of the molecule is found nt the moment of closest npproach of the atom. This orientatioml effect is more pronounced in collisions WXI heavy atoms.
1. Introduction
tion that the orientation of the molecule can be regarded as constant during the collision md only the
Relaxation experiments on the bending vibration of CO, in mixtures of CO2 with noble gases in general show an increase in the observed relaxation time with increasing mass of the nob!e gas [ 11. However, the vibrational relaxation in a CO,-Xe mixture did
component of force in the vibrational direction is effective in the translational-vibratIona energy transfer. Recently Huetz [6] calculated specific steric factors for the de-excitation of the bending vibration of CO, in collision with noble gases. Using.these steric factors a remarkable agreement
not follow this general trend. The observed relaxation time for C02-Xe was found to be less th-an the relax-.
ation time for CO,-Kr, contrary to theoretical predictions: According to Iandau and Teller [2] vibrational energy will be transferred if the duration of the coIlision is short compared to the period of oscillation. From their theory based on Ehrenfest’s adiabatic principle [3] it fallows that vibrational energy transfer is favoured by colliding particles having small masses and steep repulsive potentials. These rathei qualitative considerations have been followed by semi-classical and quantum mechanical approaches to the vibrational excitation probabilities (for a review see ref. [4]). The most successful theory was developed by Schwartz, Slawsky and Herzfeld [S], well known as the SSlj theo:T. In this three-dimerisiorial quantum mechanical treatment the most favourablk mutual orientation of the particles, for vibrational energy transfer,istaken into account. To allow for less favourable orientations, steric fat- : : .. tars are introduced at the end of the.calculation: The steric factor approach is based on the assum&
was obtained between theoretical SSH values ad the experimental data for He, Ne, and Ar [l]. However, the relative low relmation times for C02-Kr and could not be explained. Cannemeyer and de Vries El] suggested that the relative high efficiency of Kr and Xe might be due to a pre-orientation of the CO, molecule during the colLision, by which the probability for vibrational energy transfer to the bending mode is increased. This orientational effect should be less prominent in collisions with the light noble gas atcms. The bending vibration of CO, is most likely to be excited by collisionswhich occur perpendicular to the molecular a&s. Th+e perpendicubr collision: on the other hand are highly inefficient fot the excitatibn of $e’stretching vibration of CO,. Consequently, the proposed l%e-orientation in CO,-Kr and CO,-Xe collisions leads to.a decreased efficiency for the excitation of the stretching vibration. Experimental dare on’the relaxation of the asymmetric stretching vibration of CO, by noble .gases,seeti tq confirm the hypothe+ [7]. C02-Xe
: ‘.
17
Volume 31,
number !
CljERIICAi
PI!YSICS IkTER~
& idea of pre-or&nation tit the CO2 molecule in co!!isions witll noble gases, we perfoirned 2 ‘number cifclassicd trajectory ca!culations on a mode! system, representing the C02-nobie gas interaction.
.:,- :.+&t&t
15
February
1975
: :
‘.
Starting from a innform distribution of the moiecular ciientation at the beginning of the trajectories, we : calculated the orientation of the mo!ecule at th’e moment of.closest approach of the atom.
..
2. Trajectory calculations
Although Our interest for orient~tional effects in molecular collisions was primari!y fccussed on the CO;-noble gas interactions, the actual collision trajectories have been calc&.i~d for an atom-diatomic moIecuIe system: The choice of a three-particle sys‘tern enables the direct application of existing trajectory programs present in our institute [a]. ~The diatomic moIecule was modelled to resemble the CO2 molecule in dimension, moment of inertia and orientationally averaged potential. In fact we ignored the central carbon atom in the CO, molecule ‘and used the remaining “oxygen molecule” as the molecuIar cohision partner. Further, the calculations : were, restricted to the t&odimensional case, -.vhere the molecule rotates in the plane defined by the initia! positions of the particles. The rotational, vibrational and translational energies of the particles had their classical equilibrium values at 303 K. After eliminatjon of.the center of mass motion, the relative position of the atom and. .molecule is described by the standard coordinaies R, ,b, F1z.and T, see fig. i. For the numerical integration of the cohision trajectories the hamiltonian form of the equations of motion was used. The eight equa- 7 tions were reduced to a set of four linear second-order coupled differential equations: Qi = -7~ Y/dQr, i = 1;...;4, where Y represents the potential energy of the system and Qi the generalized coordinates [PI. The potential energy V was constructed by addition of the pair-wise.interactions between the individual atoms, where each atom-atom interaction is descifbed by a Morse-type potential function: v=cv.: .i#j .:!’ ’ ,.. ” ,.js’::.: .
..: ., ,” ;
.,,, r:. ” :
.,..
...,
‘,
,:
”
..,‘.
.-
‘. ;
‘.
:
:,
T.J]
- 2Bjj exp [--c$rij
- Y$] .
The potential parametersAy Bij, ~ij and ?ii for the different ritom-atom interactions were determined as follows. For the interaction between the oxygen atoms in. the molecule we used the Morse potential pararnetersA, B and (Yfor pure oxygen from the book of Her&erg [9], -whereas the equilibrium distance ‘I2 was taken equal to the equilibrium distance of the oxygen at,Jrns in‘the CO2 molecule, ?12 = 2.32 A. The potential parameters for the oxygen-noble gas interactions were calculated according to the method re‘ported in 3 previous paper [lo]. Essentially, the interatomic distances r13 and rZ3 were approximated by R f T12 cosy. Then the interaction between the molecule and atom, which results from the pair-wise addition, was expressed.in R and 7 and reads in the fustorder .approximation IlO] V(f7.r) = ‘U(1 +202~&cos2y) exp[-2ar(R - i)] - 4B(l+ fo2r$cos2r)
where
_. .
exj[La(R
- -31 ,
‘.
’ u’;A*j,.
.&=aU=& -,’
B=B1,=B23, =,_J .- r=
. 23
7
17 .‘. 1323 -
.-’ :
_.
‘2 ._,
., ‘.
Exp[-3c+,-
vii =p,
;-
. -,,
Parameters defining the relative orientation of the molecule alld atom.
.;A=;A ;.
‘.,
..
x FG. 1.
,’
:
1:”
.; ..
.’
: ..,,,
..
-_
..
Volume 3 1.
ilUIllbCr
CHEMICAL PHYSICS LETTERS
1
Table 1 Morse potential
parameters for the atom-htom used. irr tic mje&ry qrlrsak~rions System
A (K)
B (K)
interactions
a (a-‘)
s:(A)
3.78 1.81 1.34
2.32 3.52 4.46
~o-o O-He 0-Xe
6cMi6 8.04 33.94
60486 20.78 71.66
He
Xe b:2
b=Z
6’ The orientationally averaged value of this expression is compared with the spherically symmetric Morse pctential for the C02-noble gas interaction, as derived from the potential functions for the pure gases via the combination rules of Saxena and Gambhir [ 11,121. Separately the attractive and repulsive parts of the orientationally averaged and spherically symmetric potential are equated for a special choice of t!le potential parameters A, B, a and 7 [lo]. Tlze actual values of the potentinl parameters used in the calculations are collected in table 1. Once the interaction potential is defmed, the colhsion trajectories can be calculated for specific initia! conditions. The equations of motion were solved by numerical integration on the ELX 8 computer of the Mathematical Centre, Amsterdam. The initial value of R was 9 r\, a value large enough for the potential energy to be negligibly srnal! relative to the kinetic energy of the system. With the center of mass of the molecule located at the x-axis, the initial relative velocity was taken parallel to the x-axis. The impact parameter b was varied in steps of 1 ,J%in the range of O-8 8. For each impact parameter b a number of trajectories was calculated with fised rotational, vibrational and translational energy, whereas the initial phase of the rotator was varied by 1” in the subsequent calculations. At the moment of closest approach of the atom, the trajectory calculation was stopped and the orientation ym of the molecular axis relative to R, the line from the center ofmass of the molecule to the atom, was calculated.
,I 20
20NWm)
5
.
He b=L
,
I ! I ! pp-!-l~ He b:6
Xe b-6 f
2c-
20. :
,-l!r!lll!l!~l!IIITl I < * I He b.8
Xe b=8 to-
ZO&“‘!““‘\‘!“‘I 0
60
I 7 III!lIl’I!I’I!~
120
160
-Ym
0
60
I
Ii0
I80
-Ym
Fig. 2. Distribution pattcxnsN(7,) for coliisions with He wd Xe at different impact parameters b. ym is the angle berween the molecular axis and the line between the centers of mass of the moiecule and atom at the moment of ciosest approach. .the approach of the atom, the distribution of the orientational angleN(7,) should be unifoorm upon [0,1801.This uniform distribution is found for trajectories with large impact parameters 6 2 8 .jl, where the interaction energy is negligibly small compared to the kinetic energy. For smaller impect parameters deviations from a uniform distribution are observed. In fig. 2, the distribution patternsN(7m) for a number of impact parameters are shown. It can be seen that the orientation of the molecule at the moment of closest approach depends strongly on the atomic collision partner.’ Tn collisions witti He only a slight increase of collisions with 7, = 90” is observed at smah impact parameters. The preference for this“‘perpendicular” orientation vanishes rapidly with increasing impact parameter.
In collisions with Xe, the rotational motion is strongly affected, resu!ting in a highly non-uniform 3. Results and discussion The calculatiorr reported here concernto systems with He and Xe as the atomic collision partners. If the. rotational motion o.f the molecule is not perturbed by. .,
distribution of Trn. Even at b = 5-7 A, the moiecule is lar,position. For these large rotational motion is slightly ated by the atom, reaching
large impact parzrneters drawn inta a perpendicuimpact parameters the accelerated or decelerthe energetically favour-
Yolumc
3.1, uumbcr 1
CHE~!ICAL PtIYSICS LU-TI:RS
.‘&I& perpendicular orientation at the moment of. closest approach. The trajectories show that at small impact param -et&s the co&ions with Xe.arc more violent and “multiple” atorn-atom impacts domm+e the colliGonal proces,s. If the first impact takes place with y> 90”, the rotational motion is highly accelerated during the approach of the atom, After half a rotational period, a second impact ‘takes place with yrn < 90’. The minimum distance between the atom and molecule is reached at the second impact. The distriblltion patterns for Xe at small impact parameters show clearly the enhancement in the number of collisions with r,.,, < 90” and the accompanying fall-off in the number of collisions with 7m > 90’. Multiple impacts are .scarcely observed in collisions with He
The possi3rlity of orientational effects in collisions between a linear molecuIe and a heavy atom was first
15,February
lY75
pointed
out by Dr. .F. Cannemeyer. The’authors’like him for the encouraging’discussions’about ,.this sutject. This work is part qf the research program ofthe. “Stichting Loor Fun,damenteel Onderzoek der hlaterie!‘(Foundatibn of Fundamental Research on Matter) and was made possible by financial support of the “Nederlandse Organisatie voor Zuiver-Wetenschapp,:lijk-b;nderzdek” (Netherlands Organization for the Adj/ancemcnt of Pure Research). to thank
References 111 F. Carmcmeyer.and
A.E. de Vries, Physico 64 (1973) 123. 121 L. Landau and E. Teller, Physik. 2. Sovijetunion 1C (1336) 34. [31P. Ehrenfest, KoninkL Ned. Akad. Wetenschap. Proc. 16 (1914) 591. I++1G..LI. Burnett and E-M. North, eds, Tmnsfer and storage of energy by molecules, Vol. 2 (Wiley, New York,
where $e light He atom is reflected Aready by the molecule at the first impact. The results show clearly th+ the orientational distribution of a highly asymmetric diatomic molecule in collision with noble gas atoms, cannot be regarded as uniform. The asymmetry in the interaction potentialfavours nearly perpendicular orientations. These effects are more dominant in collisions with heavy atoms. Steric factors calculated from a uniform distributionare thtxefore more reliable for collisions with Iight atoms than for collisions with heavy
._
:
1969).
ISI R.ti. Schwartz, 2.1. Slswsky
’
and K.F. Herzfeld, J. Chem. Pl1ys. 20 (1951) 1591. I61 M. Huetz and P. Chevalier, Advan Mol. Relaxation Proce:;scs 2 (1970) 101. 171 F. Cannemcyer and A.E. de Vries, Physica 70 (1973) 135. $1 k v;n der Meulen, Computer Phys. Commun. 3 11972) 42. G. Herzberg, Spectra of diatomic molecules (Van Nostrand, Princeton, 19.50). P.G. Kistemaker and A.E. de Vries, to be published. J.O. Hirschfelder, CF. Curtiss and R.B. Bird, h!olecular theory of gases and Liquids (Wiley, New York, 1954). SC. Saxena and R.S. Gambhir, Mol. Phys. 6 (1963) 577.