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Intermolecular potential parameters of some electronic excited states of atoms and molecules
CHEMlCAL PHYSICS LETTERS
Volume 3, number 6
INTERMOLECULAR
POTENTIAL
EXCITED
STATES
June 1969
PARAMETERS OF
ATOMS
OF
_4ND
SOME
ELECTRONIC
MOLECULES
J. -Y. RONCIN Laeoratoire
des Hautes Pressias,
C.N.R
S.,
92, BeZZeuue, France
Received 26 February 1969 An attempt is maae to derive the Lennard-Jones parameters of some excited states of Xe, Kr, Hg, CO, NO and N20 from the observed sms of electromc transnions m the trapped species.
Previous qualitative discussions of the shifts of electronic transitions of rare gas atoms and small &atomic molecules trapped m a solid matxur had led to some information about the &-
mensions of electronically excited states of atoms and molecules [1,2]. In particular, the matrix isolation technique has str&ingly shown the profound difference 111behavior of trapped molecules accordmg to the nature of the transition: valence transinons are little affected, whereas Rydberg transitions are strongly perturbed. In this paper, we attempt a quantitative estimate of the Lennard-Jones parameters of the excited states involved usmg the shifts of electronic transitions of trapped Xe, Kr, Hg, CO, NO and N20. The mteraction between the active molecule or atom A and the matrix M can be described in ‘de following way. The intermolecukr potential between A and one matrix particle is vA-M
= 4~ [ (:)I2
_ (;)6]
Table 1 Leonard-Jcnes diameters -(A)
A
_
143.
M
Xe
Kr
D2
Ar
Ne
=M
4.06
3.61
2.95
3.42
2.79
3.89
3.50
3.74
3.43
3.27
3.50
3.20
\ ak
Xe
4.06
Iir
3.61
I%
2.90
3.25
3.16
co
3.59
3.60
3.50
3.19
NO
3.47
3.54
3.45
3.13
N20
3.88
3.75
3.65
3.34
408
3.48
Table 2 Lennard-Jones well-deplhs for ground-state mteracactions [4] (k :Boltzmann constant).
nf
Xe
A Xe
229
Kr
190
Hg
851
co
110
Kr
D2
Ar
190
39.3
124
35.7
215
98
174
93
153.5
82
86 455
402
326
145
117
Ne
62
NO
11s
150
121
65
N20
220
205
165
89
_
Table 3 Intermolecular distance d for a substitutIona site of a fee lattice. Data from [5] except a, for D2. which was taken from (61. M
Xe
Kr
D2
Ar
Ne
a0 (-9
6.13
5.64
5.07
5.31
4.46
d(A)
4.33
3.99
3.59
3.75
3.15
Taking into account the spatial &stribution of the matrix particles around a substitutional site of a fee lattice [S], we get
V = 4~ [ 12.13 (:)I” We adopt the classical
aA-M EA_M
- 14.45 ($1
_
(1)
hvpothesis
= $(CTA+UM) = 0 =
dCA’
EM
=E
.
Whenever G and E are known for the ground state of A, it is possible to compute the shift AV
CHEMICAL
Volume 3, number 6
PHYSICS LETTERS
June 1969
Table 4 Experunent (Av) and calculated (AV and AV*) A I
M+ Transition 3P+lS
Xe
Kr Au
AV
4650 (7)
-2073
Ar
Dz Av*
Av
AV
2577
5210
-942
IP-1s
-942
Afl
Ay
4268
3P+%
N20
j_
-X%3+
2000 @)
-949
Hg
lP+1s
Lennard-Jones A Xe
610 (8)
-3563
parameters ground state 1s
-1195
5348
7770 u!
-3814
6575
986
2550 (9)
-1240 (8)
5135
-1195
Xe -2953
Ap
(7)
1051 I
Kr
Ne
AV
6330
(7) Kr
shifts (cm-l).
3536
Au 5210
Ap
2493
7703
7657
10617
tv
2960 @)
Ar -5055
2055 (8)
-3284
-1229
Table 5 for some excited states of species A, mteractmg wth foreign molecules uA& 4.06
excited state
EA&% 229
3P
4.8
210
1P
LO
185
3P
4.65
225
1s
3.61
190
Hg
1s
2.90
851
1P
4.25
825
co
Xlz;+
3.59
110
AllI
3.75
275
B2l-i
3.70
175
NO
X2l-i
3.47
119
Bf2A
3.70
230
G2Z
3.70
275
N20
zlc+
3.88
220
E
4.75
115
mental shift of spectral
of this state
AV*
v(d)
where d= a,,/fiis the intermolecular &stance and a0 is the lattice parameter. We can completely neglect any interaction betweentrapped spe&esfor+&e dilution considered; inthe "stahsticaI"type theory, the shift of the excited state follows from the experi-
andma
&I_
Q*/keK)
CA* !A)
Kr
Av=
AV
transition
involved
= V(a) + Av = V*(d)
crudeapproximation uA+_M
=
+(OA+MM) =cr*;
EA+_M=~M=E* and 409
Volume 3, number 6
V* = 4~* [12.13
CHEMICAL PRYSICS LETTERS
($”
- 14.45 ($1
.
(2)
In turn, putting r = d and V* = V*(d) we may of E* (or EA*) values around E and compute the corresponding (T* (hence DA*). The best value of E* is chosen to be that for wkch CA* is the closets in the various matrices. The tables 1 and 2 give the known data for CA, CM ,EA and EM and also the deduced values of 0 and E. Table 3 gives d. In table 4 experimental AV and calculated AV and AV* smts are presented. Finally table 5 contains the resulting values of uA* and EAt for Some excited states of the active species A; @A* iS the average among the nearest values Of GA* in three matrices, E * being taken successively equal to twelve values m the range E f 30 cm-l and then five mor values of E* if necessary. It will be noticed that the u* values obtamed for atomic excited states are certainly greater than u while during a valence transition of a diatomlc molecule, the valge of u does not change too much. However, our previous qualitative deduction of a slightly smaller diatomic molecule in its valence excited states needs to be revised somewhat 111light of the present quanbtake results: talzng mto account the spatial distribution of matrur particles leads to a diatomic molecule a little larger in its valence excited states. But it is necessary to remember that excited states of &atomic molecules are not spherically svmmetrlc. Previous calculations using the same potential model started from the very crude approximation that u does not vary appreciably &Jring a transltion [lo]. Apart from the fact that it 1s not true for Rydberg transltlons, these calculations made no attempt to obtain new data on excited states take a Series
but only to fmd a law for the shift in Merent matrices. Here we make the hypothesis that values of u* and E * for the excited state are pract~a.lly the same m various matrices but are U-
410
June 1969
ferent from those of the ground state. While we do not claim that the values computed are the best possible, this is the first time in the case of the matrix isolation method that a quantitative idea of mtermolecular interactions regardmg atoms and molecules in their excited states is obtained. Additional experimental results, for example Hg, CO, NO and N2O in D2, and lmproved computation (with a better composition law for u and E , for instance) would allow us to obtain more realistic data for other excited species 1. We wish to express our sincere thanks to Dr. Chandrasekharan who encouraged us in attempting such a calculation and with whom we had many stimulating discussions. $ Intermolecular potentlal parameters have recently been calculated for the excited states of the doublet of dk& metal atoms, from the shift of the resonance Imes perturbed by a moderate pressure of foreign gas Ill].
REFERENCES [l] J.-Y.Ronc& N.Damany and J. Romsnd, J. Mol. Spectry. 22 (1967) 154. 121J.-Y.Roncm, J. Mol. Spectry. 26 (1968) 105. 131T.fihara and S.Koba, J. Phys. SOC. Japan 7 (1952) 348. [4] J-0 Hirschfelder, C.F.Curt~ss and R.B.Blrd, Molecular theory or‘gases and Llqulds (Wiley, New York, 1964) 1112 [5] G. L. Pollack, Rev. Mod. Phys. 36 (1964) 748. [6] A.E.Curzon and I.J.Mascall. Brit. J Appl. Phys. 16 (1965) 1301. [fl G.Baldmi, Phys. Rev. 137 (1965) A 508. [8] W. W.Duley. Phys. Letters 19 (1965) 361. [S] M.SlbIeyrss, J.-Y.Roncln and N.Damsny, Compt. Rend. Acad. Scl. (Paris) 266 (1968) B 975. 1101M.McCarty Jr. and G. W.Robmson, Mol. Phys. 2 (1950) 415. [ll] R.Gramer. Thesis, Paris (1968).
Volume 3, number 6
INTERMOLECULAR
POTENTIAL
EXCITED
STATES
June 1969
PARAMETERS OF
ATOMS
OF
_4ND
SOME
ELECTRONIC
MOLECULES
J. -Y. RONCIN Laeoratoire
des Hautes Pressias,
C.N.R
S.,
92, BeZZeuue, France
Received 26 February 1969 An attempt is maae to derive the Lennard-Jones parameters of some excited states of Xe, Kr, Hg, CO, NO and N20 from the observed sms of electromc transnions m the trapped species.
Previous qualitative discussions of the shifts of electronic transitions of rare gas atoms and small &atomic molecules trapped m a solid matxur had led to some information about the &-
mensions of electronically excited states of atoms and molecules [1,2]. In particular, the matrix isolation technique has str&ingly shown the profound difference 111behavior of trapped molecules accordmg to the nature of the transition: valence transinons are little affected, whereas Rydberg transitions are strongly perturbed. In this paper, we attempt a quantitative estimate of the Lennard-Jones parameters of the excited states involved usmg the shifts of electronic transitions of trapped Xe, Kr, Hg, CO, NO and N20. The mteraction between the active molecule or atom A and the matrix M can be described in ‘de following way. The intermolecukr potential between A and one matrix particle is vA-M
= 4~ [ (:)I2
_ (;)6]
Table 1 Leonard-Jcnes diameters -(A)
A
_
143.
M
Xe
Kr
D2
Ar
Ne
=M
4.06
3.61
2.95
3.42
2.79
3.89
3.50
3.74
3.43
3.27
3.50
3.20
\ ak
Xe
4.06
Iir
3.61
I%
2.90
3.25
3.16
co
3.59
3.60
3.50
3.19
NO
3.47
3.54
3.45
3.13
N20
3.88
3.75
3.65
3.34
408
3.48
Table 2 Lennard-Jones well-deplhs for ground-state mteracactions [4] (k :Boltzmann constant).
nf
Xe
A Xe
229
Kr
190
Hg
851
co
110
Kr
D2
Ar
190
39.3
124
35.7
215
98
174
93
153.5
82
86 455
402
326
145
117
Ne
62
NO
11s
150
121
65
N20
220
205
165
89
_
Table 3 Intermolecular distance d for a substitutIona site of a fee lattice. Data from [5] except a, for D2. which was taken from (61. M
Xe
Kr
D2
Ar
Ne
a0 (-9
6.13
5.64
5.07
5.31
4.46
d(A)
4.33
3.99
3.59
3.75
3.15
Taking into account the spatial &stribution of the matrix particles around a substitutional site of a fee lattice [S], we get
V = 4~ [ 12.13 (:)I” We adopt the classical
aA-M EA_M
- 14.45 ($1
_
(1)
hvpothesis
= $(CTA+UM) = 0 =
dCA’
EM
=E
.
Whenever G and E are known for the ground state of A, it is possible to compute the shift AV
CHEMICAL
Volume 3, number 6
PHYSICS LETTERS
June 1969
Table 4 Experunent (Av) and calculated (AV and AV*) A I
M+ Transition 3P+lS
Xe
Kr Au
AV
4650 (7)
-2073
Ar
Dz Av*
Av
AV
2577
5210
-942
IP-1s
-942
Afl
Ay
4268
3P+%
N20
j_
-X%3+
2000 @)
-949
Hg
lP+1s
Lennard-Jones A Xe
610 (8)
-3563
parameters ground state 1s
-1195
5348
7770 u!
-3814
6575
986
2550 (9)
-1240 (8)
5135
-1195
Xe -2953
Ap
(7)
1051 I
Kr
Ne
AV
6330
(7) Kr
shifts (cm-l).
3536
Au 5210
Ap
2493
7703
7657
10617
tv
2960 @)
Ar -5055
2055 (8)
-3284
-1229
Table 5 for some excited states of species A, mteractmg wth foreign molecules uA& 4.06
excited state
EA&% 229
3P
4.8
210
1P
LO
185
3P
4.65
225
1s
3.61
190
Hg
1s
2.90
851
1P
4.25
825
co
Xlz;+
3.59
110
AllI
3.75
275
B2l-i
3.70
175
NO
X2l-i
3.47
119
Bf2A
3.70
230
G2Z
3.70
275
N20
zlc+
3.88
220
E
4.75
115
mental shift of spectral
of this state
AV*
v(d)
where d= a,,/fiis the intermolecular &stance and a0 is the lattice parameter. We can completely neglect any interaction betweentrapped spe&esfor+&e dilution considered; inthe "stahsticaI"type theory, the shift of the excited state follows from the experi-
andma
&I_
Q*/keK)
CA* !A)
Kr
Av=
AV
transition
involved
= V(a) + Av = V*(d)
crudeapproximation uA+_M
=
+(OA+MM) =cr*;
EA+_M=~M=E* and 409
Volume 3, number 6
V* = 4~* [12.13
CHEMICAL PRYSICS LETTERS
($”
- 14.45 ($1
.
(2)
In turn, putting r = d and V* = V*(d) we may of E* (or EA*) values around E and compute the corresponding (T* (hence DA*). The best value of E* is chosen to be that for wkch CA* is the closets in the various matrices. The tables 1 and 2 give the known data for CA, CM ,EA and EM and also the deduced values of 0 and E. Table 3 gives d. In table 4 experimental AV and calculated AV and AV* smts are presented. Finally table 5 contains the resulting values of uA* and EAt for Some excited states of the active species A; @A* iS the average among the nearest values Of GA* in three matrices, E * being taken successively equal to twelve values m the range E f 30 cm-l and then five mor values of E* if necessary. It will be noticed that the u* values obtamed for atomic excited states are certainly greater than u while during a valence transition of a diatomlc molecule, the valge of u does not change too much. However, our previous qualitative deduction of a slightly smaller diatomic molecule in its valence excited states needs to be revised somewhat 111light of the present quanbtake results: talzng mto account the spatial distribution of matrur particles leads to a diatomic molecule a little larger in its valence excited states. But it is necessary to remember that excited states of &atomic molecules are not spherically svmmetrlc. Previous calculations using the same potential model started from the very crude approximation that u does not vary appreciably &Jring a transltion [lo]. Apart from the fact that it 1s not true for Rydberg transltlons, these calculations made no attempt to obtain new data on excited states take a Series
but only to fmd a law for the shift in Merent matrices. Here we make the hypothesis that values of u* and E * for the excited state are pract~a.lly the same m various matrices but are U-
410
June 1969
ferent from those of the ground state. While we do not claim that the values computed are the best possible, this is the first time in the case of the matrix isolation method that a quantitative idea of mtermolecular interactions regardmg atoms and molecules in their excited states is obtained. Additional experimental results, for example Hg, CO, NO and N2O in D2, and lmproved computation (with a better composition law for u and E , for instance) would allow us to obtain more realistic data for other excited species 1. We wish to express our sincere thanks to Dr. Chandrasekharan who encouraged us in attempting such a calculation and with whom we had many stimulating discussions. $ Intermolecular potentlal parameters have recently been calculated for the excited states of the doublet of dk& metal atoms, from the shift of the resonance Imes perturbed by a moderate pressure of foreign gas Ill].
REFERENCES [l] J.-Y.Ronc& N.Damany and J. Romsnd, J. Mol. Spectry. 22 (1967) 154. 121J.-Y.Roncm, J. Mol. Spectry. 26 (1968) 105. 131T.fihara and S.Koba, J. Phys. SOC. Japan 7 (1952) 348. [4] J-0 Hirschfelder, C.F.Curt~ss and R.B.Blrd, Molecular theory or‘gases and Llqulds (Wiley, New York, 1964) 1112 [5] G. L. Pollack, Rev. Mod. Phys. 36 (1964) 748. [6] A.E.Curzon and I.J.Mascall. Brit. J Appl. Phys. 16 (1965) 1301. [fl G.Baldmi, Phys. Rev. 137 (1965) A 508. [8] W. W.Duley. Phys. Letters 19 (1965) 361. [S] M.SlbIeyrss, J.-Y.Roncln and N.Damsny, Compt. Rend. Acad. Scl. (Paris) 266 (1968) B 975. 1101M.McCarty Jr. and G. W.Robmson, Mol. Phys. 2 (1950) 415. [ll] R.Gramer. Thesis, Paris (1968).