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Energy transfer in Br +-Kr collisions
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
22 August 1986
ENERGY TRANSFER IN Br +-Kr COLLISIONS K. BALASUBRAMANIAN
’
Department of Chemistry, Arizona State University, Tempe, AZ 85287, USA
Joyce J. KAUFMAN,
P.C. HARIHARAN
and Walter S. KOSKI
Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA Received 19 May 1986
In the collision of Br + with Kr there is considerable transfer of translational to electronic energy and vice versa. This energy transfer is modelled as a Landau-Zener process at the points where the potential energy curves of the various electronic states of the halogen positive ion complex (KrBr 3 cross. Experimental transitions among the spin-orbit states of Br+ (viz. ‘Dz +“jPo,,) are observed but all attempts to produce ‘Dz+ 3Pr have failed. Relativistic CI calculations of lowlying states of KrBr+ have been carried out to explain the above experimental observations.
1. Introduction The formation and de-excitation of neutral raregas halide molecules have been extensively investigated [l-6]. Similarly, experimental and theoretical studies have been carried out on rare-gas oxides because of the potential application of these systems in lasers [7,8]. However, there has been a very limited number of studies on the rare-gas halide diatomic ions. These rare-gas halogen positive ion systems are isoelectronic with the rare-gas oxides, and as such, may also have potential laser application. In addition, in hot-atom studies of halogen systems, rare gases have been used as moderators and the assump tion is generally made that they are inert. Recently, it has been demonstrated that this assumption is not applicable to the halogen hot-atom systems since collisional studies between Br+ and Kr show that Kr is not inert but participates in an active chemical way in the hot-atom process [9]. In the 1960s with the discovery of stable xenon and krypton fluorides, it‘was,shown by mass spectrometric techniques that XeF+ and KrF+ are stable 1 Alfred P. Sloan fellow; Camille and Henry Dreyfus Teacher-Scholar.
0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ions [lo]. The rare-gas halide ions, KrCl+, KrF+, ArCI+ and ArI+ have also been reported as stable ions [11,12]. Berkowitz, Chupka and co-workers [13,14] have examined the binding energies of KrF+, XeF+, XeI+, etc. and Watkins and Koski [ 151 prepared KrBr+ and estimated its binding energy from threshold measurements of a collision-induced dissociation reaction. In addition, we have observed that in the collision of halogen positive ions with rare-gas atoms there is an efficient transfer of electronic energy to translational energy and vice versa and we report our results on the Br+-Kr collisions here. An energy-level diagram of the Kr-Br+ system at inftite interatomic separation is given in fig. 1. Since the excitation experiments were carried out at relative energies less than 5 eV, no states other than the ones shown are energetically accessible. Our experiments deal mainly with the excitation and de-excitation as represented by the following equation: Br+(3P) t Kr(lS) + Br’(lD) t Kr(lS) , and the observed transitions are indicated in fig. 1. It will be noted that the transitions Br+(3P2) * Br(lD2) were not observed. The energy transfers in the Kr t Br+ collisions 165
5
-
Br+(‘q)+ Kr
2. Experimental results (‘S)
i
OL
Br+(3Po)
+ Kr(%)
Br+(3P,)
+ Kr(fS)
Br+(3P2) + Kr(*S)
Fig. 1. Energy level diagram of the Br+-Kr system at infinite interatomic separation. The observed transitions are indicated.
seem to be governed by a Landau-Zener process, which suggests that efficient energy transfers are observed at the intersections of the potential energy curves of the intermediate complex, which in this case is KrBr+. In this investigation we carry out relativistic configuration interaction calculations on nine low-lying w --0 states of KrBr+ with the intent of explaining the observed energy transfers. Calculations of the lighter analogues of KrBr+ such as KrF+ have been carried out [ 16- 181. Nonrelativistic calculations of the isoelectronic KrO as well as XeO have been carried out by Dunning and Hay [7]. We employ the method of relativistic configuration interaction calculations developed by Christiansen, Balasubramanian and Pitzer [ 191. This method was found to be quite successful for a number of molecules containing very heavy atoms [20271. Section 2 describes the experimental results. Section 3 outlines the method of our theoretical investigation. In section 4, we describe theoretical results and discuss them in the light of experimental results. Section 5 discusses the nature of CI wavefunctions of the various low-lying states of KrBr+.
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Collision of Br+ and Kr were studied using a tandem mass spectrometer which has been described previously [28]. It consists of an ion source, an electrostatic analyzer and a quadrupole mass filter as an input section. The ions were prepared by electron bombardment of CH,Br. The beam composition so produced had approximately equal amounts of Br+(3P) and Br+(lD) as determined by attenuation measurements. The Br+ beam from this section was passed through a shallow reaction chamber containing the target gas (Kr). The ions scattered at 0” to the beam direction were then detected with a second quadrupole mass spectrometer followed by an elettrostatic analyzer and an electron multiplier. The beam width was 0.1 eV (fwhm). The Br+ spectrum obtained in this manner is shown in fig. 2. The central peak is due to the unperturbed primary ion beam. Two unresolved doublets appear on each side of the primary beam and separated from it by about 1 eV energy. We interpret these peaks as arising from the transitions Br+(sP,,,) * Br+(lD,). The “subelastic” peak on the right corresponds to Br+(lD,) + Br+(sPo,,) and the “superelastic” satellite on the left is due to the transitions Br+(3P0 1) + Br’(lD2). The spacing between the double& is 87 meV preventing complete resolution by our instrument. Notably absent are the peaks due to transitions
LAB ENERGY
IeV)
Fig. 2. Energy spectrum of subelastic and superelastic collisions of Br+ with Kr at a relative kinetic energy of 4 eV.
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CHEMICAL PHYSICS LETTERS
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Br+(3P2) P Br+(lD,). Peaks due to these transitions should appear at about 1.4 eV on each side of the peak due to the projectile ions.
Table 2 Dissociation limits of a few low-lying
W-W
states
Dissociation limit
Molecular states
Energy of the separatf atoms
3. Method of investigation
Kr + Br+
A few low-lying electronic configurations of KrBr+ and the corresponding h-s and o--o states arising from them are shown in table 1. Table 2 shows the dissociation relationship of various low-lying o---w states into the corresponding atomic states. As one can see from table 2, the splitting of the 3P states of Br+ into 3Po, 3P 1, and 3P2 is large. Thus spin-orbit effects are important. Further, the 311and 32- states in the absence of spin-orbit interaction dissociate into Kr(lS) + Br+(3P) while the IX+ state dissociates into Kr(lS) t Br’(lD). Thus the crossing of thesehs states is expected. This would imply avoided crossing of the corresponding O+components. ‘l%us,spinorbit interaction would play an important role not only in splitting the A-s states but also in mixing different A-s states which have the same w---w symmetry (spin-orbit contamination). We employ the method of relativistic configuration interaction calculations described in ref. [ 191. In this method the relativistic effective potentials are averaged with respect to spin at the SCF stage so that Table 1 A few low-lying configurations of KrBr+ and the corresponding h-s and w-w states arising from them. (Only the p electrons of Kr and Brf are shown) Electronic configuration
h-s states
w-w
oZ&r4n*3
3rl ‘n
2, 1, o-, o+ 1
*2vr4ir*4
rx+
0+
02ad,4,e2
3z-
o+,
lA
2 0+
lz+ lJ20* 2,$,@
323z+ 3A
rz+ izlA
(cm-
states
1
0+, 1 o-, 1 392, 1 0+ 02
‘so+3P2
2,1,0+(I) l(II),oo+(II) 2(11), l(II1). o+(III)
0.0
Iso + 3P1 lse + 3P. ‘So +‘D2
3139 3840 11409
Kr++ Br 3,2(III), 2(IV), im, 10% l(M), O-W), O-(III), O+(IVh O+(v) 2(v), WII), lWII), o- (IV), 0WI) 20% l(W loo, O_(v), o+orII) lo(I), o+(vIII), O_(W)
2p3,2
17389
+ 2pl,2
21074
+ 2p3,2
22760 27075
2P3,2 + 1
p3/2
2P 112 2P i/2
+,.2p,,2
Kr + Br+ ‘so+‘so
o+(Ix)
[ 291
27867
those potentials can be introduced into any nonrelativistic SCF program. The spin-orbit operator is obtained as the difference of the relativistic potentials with respect to spin. The spin-orbit integrals are introduced at the CI stage thus allowing the possibility of mixing several h-s states which have the same ow symmetry. we mcluded the sLp4 valence shell of Br+ and s2p6 shell of Kr in our SCF calculations. The basis sets used here are Slater-type functions with d polarization functions. The optimized exponents are shown in table 3. Table 4 shows the list of reference configurations Table 3 Slater-type basis sets employed in KrBr* calculations. The numbers in parentheses are the principal quantum numbers Kr
Br
2.8438 (4) 1.4405 (4) 0.8809 (5)
2.7399 (4) 1.2634 (4) 0.8365 (5)
2.7108 (4) 1.53 14 (4)
2.5884 (4) 1.4964 (4)
1.7 (4)
1.0 (4)
167
130
Table 4 The number of reference configurations and the total number of configurations included in the relativistic CI
VII)
120 1
State
RC a)
Total
110
0+
16 10 9 8
7176 2982 3124 3114
100
:2
090 z 080
a) The number of real Cartesian reference configurations.
and the total number of configurations included in the relativistic CI calculations. Since the spin-orbit coupling mixes all A-s states of the same w---o symmetry, we include 126, (&%r*4), 3110+(u2u*r4~* 3), ~E~+(u~u*~~&*~), lZi+ (u2ue27r47r*2) as well as other O+ configurations in table 1. Similarly, the 1, O- ,2 states include all low-lying configurations of the appropriate symmetry. Since our relativistic CI computer code is written for polyatomics, one has to expand the diatomic configurations in Cartesians. Since this corresponds to a unitary transformation the energy is not altered. All relativistic CI calculations are carried out in C,, symmetry. It is thus possible to obtain a 2 state from O+ reference configurations by changing the sign of some of the imaginary coefficients. We restrict our calculations to the first three or two roots of a given symmetry since calculations of higher roots lead to convergence problems in C,, symmetry for the abovementioned reasons.
4. Results and discussions Figs. 3 and 4 show the potential energy curves of some of the low-lying w--w states and X-s states of KrBr?, respectively. Table 5 shows the energies of nine low-lying o--w states (arising from 311,3X-, ‘YE’, ill, lA X-s states) of KrBr+. As one can see from fig. 3, KrBr+ has a few low-lying bound states but the ground state (2(I)) is repulsive. In the Landau-Zener model the energy transfer between several states induced by collisions, takes place at the points where the potential energy curves of the appropriate electronic states of the rare-gashalogen ion complex cross. From table 2, it can be 168
22 August 1986
CHEMICAL PHYSICS LETTERS
Volume 129, number 2
e 070
t 6 b
060
2I\(
,\“:+(,I, \
o+(lw
\c(
‘D2+‘Sc
l(lll)
050
*c
0+w
Oi(lll)
o+u1
040 8
2(l)
l(lll
E
c W
I
-
45
50
,
60
70
R +
80
90
(Bohr)
Fig. 3. Potential energy curves of low-lying states of KrBr+ in the presence of spin-orbit interaction. The potential energies of l(I) and l(U) states are shown in table 5.
seen that the 2, 1, and O’(I) states of KrBr+ correspond to Kr(lSo) + Br+(3P2) atoms. Similarly, the l(H) and O- states correlate to Kr(lSo) t Br+(3Pl) and 2(H), l(III) and O+(III) correspond to Kr( 1So) t Br+( 1D2) atoms. In the Landau-Zener model, for example, the transition between Br+(lD,) to Br+(sP, is allowed if one of the curves which dissociate into Kr(lSo) + Br+(lD,) (2(H), 1(X1), O’(M)) crosses with one of the curves which dissociate into Kr(l So) t Br+(3P1) (l(H), O-(I)). There are a few Zestrictions imposed by symmetry. For example, two curves of the same (w-w) symmetry cannot cross. Also, it appears that the selection rule for predissociation should be applicable for this case to determine among the several channels, the one that is allowed by symmetry restrictions. This selection rule for predissociation [30] is Aa = 0, +l, + 4 -. Thus, for example, if O+(III) curve crosses with l(I1) then the transition
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
22 August 1986
lD2 * 3P1 of Br’ is allowed. From table 5, it can be seen that the O+(III) and 101) curves cross at 5.75 bohr which explains the experimental observation of the ID2 + 3P, transition. Although the O’(U) curve does not directly cross with O’(III), I(II1) or 201) curves, however, it crosses with the l(H) curve (between 5.75 and 6.0 bohrs). Since the l(U) curve is a channel for the lD2 -+ 3Pl transition, a complex formed by lD2 (Br+) which goes through this channel could meet the bound O’(H) state. Thus, by this process a Br+ which starts as lD2 could go to O’(H) KrBr+ state which dissociates into Kr&-,) + Br+(3P0) atoms. Thus the transition lD2 + 3P0 also becomes allowed and was observed experimentally. The curves which dissociate into ground state atoms (2,0+, 1) do not cross with the curves which dissociate into Kr(lS,) + Br+(lD,). Further, 2,0+ and 1 curves do not cross with the curves dissociating into Kr(lSO) t Br+ (3Po) or Kr(lS ) t Br+(3P1). Thus there are no channels for the PD2 (Br+) to go into 3P, (Br’). Thus the lD2 ++3P2 transition is not feasible. All experimental attempts to observe tliis transition have failed. Our calculations seem to offer an explanation for this failure. Our earlier calculations of similar systems indicate that the bond distances predicted by our calculations are approximately 0.1-0.15 A larger than the corresponding experimental values [ 19,211. Thus our calculated crossings,distances of the various curves of 4 R +
Fig. 4. Potentialenergycurvesof spin-orbit
(Bohr)
KrBr+ in the absence of
interaction.
Table 5 Potential energy curves of KrBr+ (energies in hartree)
R
2(I)
4.5 0.1599 5.0 0.0684 5.25 0.0431 5.5 0.0289 5.75 0.0213 6.0 0.0169 7.0 -0.0010 9.0 -0.0008 11.0 0.0
10)
o+m
l(II)
0-
o+w
o+(III)
UIW
2m
0.1639 0.0073 0.0478 0.0334 0.0242 0.0146 -0.0001 -0.0007 0.0
0.1044 0.0492 0.0395 0.0289 0.0227 0.0163 0.0021 0.0015 0.00
0.1987 0.0990 0.0725 0.0502 o.cl344 0.0224 0.0119 0.0135 0.0145
0.1705 0.0801 0.0556 0.0419 0.0350 0.0287 0.0129 0.0137 0.0145
0.1720 0.0814 0.0585 0.0454 0.0301 0.0331 0.0205 0.0206 0.0213
0.2016 0.1110 0.0677 0.0468 0.0341 0.0381 0.0497 0.0635 0.0667
0.1999 0.1090 0.1038 0.0771 0.0713 0.0696 0.0662 0.0671 0.0667
0.3186 0.1899 0.1285 0.1036 0.0963 0.0846 O.Oili 0.0690 0.0667
169
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
KrBr+ could be off by this value. Among the O+ states we calculated, the O+(II) and O+(III) states are bound. The O’(H) state could be converted into O+(III) by the l(H) channel which crosses with both these states. The experimentally measured dissociation energy of KrBr+ is around 1.5 eV [ 151. Our calculated separation between the O’(II1) and its dissociation limit is 0.91 eV while the separation of the O’(H) state with respect to K#Su) + Br’(lD2) atoms is 1.OSeV. Since the KrBr+ in the O’(H) state could go to O’(II1) state through the l(H) channel, this possibility should not be ruled out. This would mean a dissociation energy of 1.05 eV. In either case our calculated dissociation energy is not very accurate. This can be attributed to only a small number of configurations included in our CI calculations which are adequate to calculate some of the properties such as T,, w,, crossings of the curves and the general shapes of potential energy curves, but are far from complete. Our earlier calculations on similar systems have yielded only 70% of the experimental De values. Thus the experimental value of 1.5 eV should be regarded as more accurate. The calculated vibrational frequencies of the O+(H) and O’(II1) states are 526 and 446 cm- l, respectively. Their R, values are 3.1 and 3.09 A, respectively. The O+(I)-O- , O+(I)-O+(II), O+(I)-O+(III) splittings at 9.0 bohr correspond to 3P2-3P1, 3P2-3P0, 3P2-lD2 splittings of Br+. The calculated values for these splittings are 3 182,4675, and 14639 cm-l, respectively. These values are in reasonable agreement with the corresponding experimental values reported in‘table 2.
5. The nature of relativistic CI wavefunctions At 5.5 bohr the u orbital is a slightly bonding MO, with the Br pz orbital making the dominant contribution. The u* orbital is dominantly on Kr but is slightly antibonding. The rr orbital is a non-bonding Kr p orbital while the rr* orbital is predominantly a Br p orbital and is also non-bonding. At short distances the a’(I) state is dominantly ++. At 5.5 bohr, the O’(I) state is 13% (&*4, ::’ ) 2670 ( uu*rr*4, IX’,,), 34%(&*a*3,‘3110+), 17~~&*2~*3,311r-,+)and2%(u~u*~7r*~,32~+). 570
22 August 1986
At 6.0 bohr the O’(I) state is 0.1% (~~rr*~, lx:+), 17% (&7*71*3, “l-lo+), 22% (uu*2r*3,3l-I,+), 1% ( UU*~*~, 1X;+) and 56%(0~u*~rr*~, 3X0+). Thus the O’(I) state exhibits very interesting avoided crossings. At short distances the O’(B) is dominantly 3II0 +. At 5.5 bohr the O’(B) state is 1% (u~,*~, lZ’,+), 2.6%(u~*n*~, I$+), 12%(~~u*n*~, 311,+), 10% (u~*~rr*~, 3110+),and70%(u2u*2n*3, 32;+).At long distances the 3II0 + arising from uu* 2rr*3 and ~~u*tr*~ dominate. At short distances the O’(II1) state is 43% (~~u*~rr*~, 3Z>), 27%(0~u*rr*~, 3n,+),‘l5%(uu*2rr*3,3II,+), 4%(&r*4,lB:;s+), and 6% (uu*~*~, 1CA +). However, at 5.5 bohr, the O+(III) is 14.4% (~~n*~), 26% (uu*R*~), 33% (u2u*rr* 3), 17% (uu* 2rr*3, and 5% (3BC,+). At long distances it is dominantly lZ+ +. The above nature of the Cfwavefunctions of the O+, O+(H) and O+(III) states suggest several avoided crossings in these O+ states. These crossings are the results of the crossings of 3II, 3X- and lZ$ curves in the absence of spin-orbit interaction (see fig. 4).
Acknowledgement
One of us (K(B)would like to thank the National Science Foundation for a partial support of this project through Grant No. CHE8520556.
References [l] L.G. Piper, J.E. Velazco and D.W. Setser, J. Chem. Phys. 59 (1973) 3323. [2] J.E. Velazco, J.H. Kolts and D.W. Setser, J. Chem. Phys. 65 (1976) 3468. [ 31 J. TeUinghuisen, A.K. Hays, J.M. Hoffman and G.C. Tisome, J. Chem. Phys. 65 (1976) 4473. [4] D.L. King, L.G. Piper and D.W. Setser, J. Chem. Sot. Faraday Trans. II 73 (1977) 177. (51 M. Rokni, J.H. Jacobs and J.A. Mangano, Phys. Rev. Al6 (1977) 2216. [6] R.E. Olson and B. Liu, Phys. Rev. Al7 (1978) 1568. [7] T.H. Dunning Jr. and P.J. Hay, J. Chem. Phys. 66 (1977) 3767, and references therein. [8] J.S. Cohen, W. Wadt and P.J. Hay, J. Chem. Phys. 71 (1979) 2955, and references therein. [ 91 H.P. Watkins, N.E. Sondergaard and W.S. Koski, Radiochbn. Acta 29 (1981) 87.
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[IO] J.H. Holloway, Noble gas chemistry (Methuen, London, 1968). [ 111 A. Henglein and G.A. Muccini, Angew. Chem. 72 (1960) 630. [ 121 I. Kuen and F. Howorka, J. Chem. Phys. 70 (1979) 595. [ 131 J. Berkowitz and W.A. Chupka, Chem. Phys. Letters 7 (1970) 447. [ 141 J. Berkowitz, W.A. Chupka, P.W. Guyon, J.H. Holloway and R. Sphor, J. Phys. Chem. 75 (1971) 1461. [ 151 H.P. Watkins and W.S. Koski, Chem. Phys. Letters 77 (1981) 470. [ 16) M.A. Gardner, A.M. Karo and A.C. WahJ, J. Chem. Phys. 65 (1976) 1222. [ 171 D.H. Liskow, H.F. Schaefer Ill, P.S. Bagus and B. Liu, J. Am. Chem. Sot. 95 (1973) 4056. [ 181 B. Liu and H.F. Schaefer Ill, J. Chem. Phys. 55 (1971) 2369.
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[ 191 P.A. Christiansen, K. Balasubramanian and K.S. Pitzer, J. Chem. Phys. 76 (1982) 5087. [ 201 K. Balasubramanian, J. Chem. Phys., to be published. [21] K. Balasubramanian, J. Mol. Spectry. 110 (1985) 339. [22] K. Balasubramanian, J. Chem. Phys. 82 (1985) 3741. [23] K. Balasubramanian, J. Phys. Chem. 88 (1984) 5759. [24] K. Balasubramanian,Chem. Phys. Letters 114 (1985) 201. [25] K.S. Piker, Intern. J. Quantum Chem. 25 (1984) 131. [ 261 K. Balasubramanian and K.S. Pitzer, J. Chem. Phys. 78 (1982) 321. [ 271 K. Balasubramanian, Chem. Phys. 95 (1985) 225. [28] K. Wendell, C.A. Jones, J.J. Kaufman and W.S. Koski, J. Chem. Phys. 63 (1975) 750. [ 291 C.E. Moore, private communication. [ 301 G. Herzberg, Spectra of diatomic molecules (Van Nostrand, Princeton, 1950).
171
CHEMICAL PHYSICS LETTERS
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ENERGY TRANSFER IN Br +-Kr COLLISIONS K. BALASUBRAMANIAN
’
Department of Chemistry, Arizona State University, Tempe, AZ 85287, USA
Joyce J. KAUFMAN,
P.C. HARIHARAN
and Walter S. KOSKI
Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA Received 19 May 1986
In the collision of Br + with Kr there is considerable transfer of translational to electronic energy and vice versa. This energy transfer is modelled as a Landau-Zener process at the points where the potential energy curves of the various electronic states of the halogen positive ion complex (KrBr 3 cross. Experimental transitions among the spin-orbit states of Br+ (viz. ‘Dz +“jPo,,) are observed but all attempts to produce ‘Dz+ 3Pr have failed. Relativistic CI calculations of lowlying states of KrBr+ have been carried out to explain the above experimental observations.
1. Introduction The formation and de-excitation of neutral raregas halide molecules have been extensively investigated [l-6]. Similarly, experimental and theoretical studies have been carried out on rare-gas oxides because of the potential application of these systems in lasers [7,8]. However, there has been a very limited number of studies on the rare-gas halide diatomic ions. These rare-gas halogen positive ion systems are isoelectronic with the rare-gas oxides, and as such, may also have potential laser application. In addition, in hot-atom studies of halogen systems, rare gases have been used as moderators and the assump tion is generally made that they are inert. Recently, it has been demonstrated that this assumption is not applicable to the halogen hot-atom systems since collisional studies between Br+ and Kr show that Kr is not inert but participates in an active chemical way in the hot-atom process [9]. In the 1960s with the discovery of stable xenon and krypton fluorides, it‘was,shown by mass spectrometric techniques that XeF+ and KrF+ are stable 1 Alfred P. Sloan fellow; Camille and Henry Dreyfus Teacher-Scholar.
0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
ions [lo]. The rare-gas halide ions, KrCl+, KrF+, ArCI+ and ArI+ have also been reported as stable ions [11,12]. Berkowitz, Chupka and co-workers [13,14] have examined the binding energies of KrF+, XeF+, XeI+, etc. and Watkins and Koski [ 151 prepared KrBr+ and estimated its binding energy from threshold measurements of a collision-induced dissociation reaction. In addition, we have observed that in the collision of halogen positive ions with rare-gas atoms there is an efficient transfer of electronic energy to translational energy and vice versa and we report our results on the Br+-Kr collisions here. An energy-level diagram of the Kr-Br+ system at inftite interatomic separation is given in fig. 1. Since the excitation experiments were carried out at relative energies less than 5 eV, no states other than the ones shown are energetically accessible. Our experiments deal mainly with the excitation and de-excitation as represented by the following equation: Br+(3P) t Kr(lS) + Br’(lD) t Kr(lS) , and the observed transitions are indicated in fig. 1. It will be noted that the transitions Br+(3P2) * Br(lD2) were not observed. The energy transfers in the Kr t Br+ collisions 165
5
-
Br+(‘q)+ Kr
2. Experimental results (‘S)
i
OL
Br+(3Po)
+ Kr(%)
Br+(3P,)
+ Kr(fS)
Br+(3P2) + Kr(*S)
Fig. 1. Energy level diagram of the Br+-Kr system at infinite interatomic separation. The observed transitions are indicated.
seem to be governed by a Landau-Zener process, which suggests that efficient energy transfers are observed at the intersections of the potential energy curves of the intermediate complex, which in this case is KrBr+. In this investigation we carry out relativistic configuration interaction calculations on nine low-lying w --0 states of KrBr+ with the intent of explaining the observed energy transfers. Calculations of the lighter analogues of KrBr+ such as KrF+ have been carried out [ 16- 181. Nonrelativistic calculations of the isoelectronic KrO as well as XeO have been carried out by Dunning and Hay [7]. We employ the method of relativistic configuration interaction calculations developed by Christiansen, Balasubramanian and Pitzer [ 191. This method was found to be quite successful for a number of molecules containing very heavy atoms [20271. Section 2 describes the experimental results. Section 3 outlines the method of our theoretical investigation. In section 4, we describe theoretical results and discuss them in the light of experimental results. Section 5 discusses the nature of CI wavefunctions of the various low-lying states of KrBr+.
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Collision of Br+ and Kr were studied using a tandem mass spectrometer which has been described previously [28]. It consists of an ion source, an electrostatic analyzer and a quadrupole mass filter as an input section. The ions were prepared by electron bombardment of CH,Br. The beam composition so produced had approximately equal amounts of Br+(3P) and Br+(lD) as determined by attenuation measurements. The Br+ beam from this section was passed through a shallow reaction chamber containing the target gas (Kr). The ions scattered at 0” to the beam direction were then detected with a second quadrupole mass spectrometer followed by an elettrostatic analyzer and an electron multiplier. The beam width was 0.1 eV (fwhm). The Br+ spectrum obtained in this manner is shown in fig. 2. The central peak is due to the unperturbed primary ion beam. Two unresolved doublets appear on each side of the primary beam and separated from it by about 1 eV energy. We interpret these peaks as arising from the transitions Br+(sP,,,) * Br+(lD,). The “subelastic” peak on the right corresponds to Br+(lD,) + Br+(sPo,,) and the “superelastic” satellite on the left is due to the transitions Br+(3P0 1) + Br’(lD2). The spacing between the double& is 87 meV preventing complete resolution by our instrument. Notably absent are the peaks due to transitions
LAB ENERGY
IeV)
Fig. 2. Energy spectrum of subelastic and superelastic collisions of Br+ with Kr at a relative kinetic energy of 4 eV.
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Br+(3P2) P Br+(lD,). Peaks due to these transitions should appear at about 1.4 eV on each side of the peak due to the projectile ions.
Table 2 Dissociation limits of a few low-lying
W-W
states
Dissociation limit
Molecular states
Energy of the separatf atoms
3. Method of investigation
Kr + Br+
A few low-lying electronic configurations of KrBr+ and the corresponding h-s and o--o states arising from them are shown in table 1. Table 2 shows the dissociation relationship of various low-lying o---w states into the corresponding atomic states. As one can see from table 2, the splitting of the 3P states of Br+ into 3Po, 3P 1, and 3P2 is large. Thus spin-orbit effects are important. Further, the 311and 32- states in the absence of spin-orbit interaction dissociate into Kr(lS) + Br+(3P) while the IX+ state dissociates into Kr(lS) t Br’(lD). Thus the crossing of thesehs states is expected. This would imply avoided crossing of the corresponding O+components. ‘l%us,spinorbit interaction would play an important role not only in splitting the A-s states but also in mixing different A-s states which have the same w---w symmetry (spin-orbit contamination). We employ the method of relativistic configuration interaction calculations described in ref. [ 191. In this method the relativistic effective potentials are averaged with respect to spin at the SCF stage so that Table 1 A few low-lying configurations of KrBr+ and the corresponding h-s and w-w states arising from them. (Only the p electrons of Kr and Brf are shown) Electronic configuration
h-s states
w-w
oZ&r4n*3
3rl ‘n
2, 1, o-, o+ 1
*2vr4ir*4
rx+
0+
02ad,4,e2
3z-
o+,
lA
2 0+
lz+ lJ20* 2,$,@
323z+ 3A
rz+ izlA
(cm-
states
1
0+, 1 o-, 1 392, 1 0+ 02
‘so+3P2
2,1,0+(I) l(II),oo+(II) 2(11), l(II1). o+(III)
0.0
Iso + 3P1 lse + 3P. ‘So +‘D2
3139 3840 11409
Kr++ Br 3,2(III), 2(IV), im, 10% l(M), O-W), O-(III), O+(IVh O+(v) 2(v), WII), lWII), o- (IV), 0WI) 20% l(W loo, O_(v), o+orII) lo(I), o+(vIII), O_(W)
2p3,2
17389
+ 2pl,2
21074
+ 2p3,2
22760 27075
2P3,2 + 1
p3/2
2P 112 2P i/2
+,.2p,,2
Kr + Br+ ‘so+‘so
o+(Ix)
[ 291
27867
those potentials can be introduced into any nonrelativistic SCF program. The spin-orbit operator is obtained as the difference of the relativistic potentials with respect to spin. The spin-orbit integrals are introduced at the CI stage thus allowing the possibility of mixing several h-s states which have the same ow symmetry. we mcluded the sLp4 valence shell of Br+ and s2p6 shell of Kr in our SCF calculations. The basis sets used here are Slater-type functions with d polarization functions. The optimized exponents are shown in table 3. Table 4 shows the list of reference configurations Table 3 Slater-type basis sets employed in KrBr* calculations. The numbers in parentheses are the principal quantum numbers Kr
Br
2.8438 (4) 1.4405 (4) 0.8809 (5)
2.7399 (4) 1.2634 (4) 0.8365 (5)
2.7108 (4) 1.53 14 (4)
2.5884 (4) 1.4964 (4)
1.7 (4)
1.0 (4)
167
130
Table 4 The number of reference configurations and the total number of configurations included in the relativistic CI
VII)
120 1
State
RC a)
Total
110
0+
16 10 9 8
7176 2982 3124 3114
100
:2
090 z 080
a) The number of real Cartesian reference configurations.
and the total number of configurations included in the relativistic CI calculations. Since the spin-orbit coupling mixes all A-s states of the same w---o symmetry, we include 126, (&%r*4), 3110+(u2u*r4~* 3), ~E~+(u~u*~~&*~), lZi+ (u2ue27r47r*2) as well as other O+ configurations in table 1. Similarly, the 1, O- ,2 states include all low-lying configurations of the appropriate symmetry. Since our relativistic CI computer code is written for polyatomics, one has to expand the diatomic configurations in Cartesians. Since this corresponds to a unitary transformation the energy is not altered. All relativistic CI calculations are carried out in C,, symmetry. It is thus possible to obtain a 2 state from O+ reference configurations by changing the sign of some of the imaginary coefficients. We restrict our calculations to the first three or two roots of a given symmetry since calculations of higher roots lead to convergence problems in C,, symmetry for the abovementioned reasons.
4. Results and discussions Figs. 3 and 4 show the potential energy curves of some of the low-lying w--w states and X-s states of KrBr?, respectively. Table 5 shows the energies of nine low-lying o--w states (arising from 311,3X-, ‘YE’, ill, lA X-s states) of KrBr+. As one can see from fig. 3, KrBr+ has a few low-lying bound states but the ground state (2(I)) is repulsive. In the Landau-Zener model the energy transfer between several states induced by collisions, takes place at the points where the potential energy curves of the appropriate electronic states of the rare-gashalogen ion complex cross. From table 2, it can be 168
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CHEMICAL PHYSICS LETTERS
Volume 129, number 2
e 070
t 6 b
060
2I\(
,\“:+(,I, \
o+(lw
\c(
‘D2+‘Sc
l(lll)
050
*c
0+w
Oi(lll)
o+u1
040 8
2(l)
l(lll
E
c W
I
-
45
50
,
60
70
R +
80
90
(Bohr)
Fig. 3. Potential energy curves of low-lying states of KrBr+ in the presence of spin-orbit interaction. The potential energies of l(I) and l(U) states are shown in table 5.
seen that the 2, 1, and O’(I) states of KrBr+ correspond to Kr(lSo) + Br+(3P2) atoms. Similarly, the l(H) and O- states correlate to Kr(lSo) t Br+(3Pl) and 2(H), l(III) and O+(III) correspond to Kr( 1So) t Br+( 1D2) atoms. In the Landau-Zener model, for example, the transition between Br+(lD,) to Br+(sP, is allowed if one of the curves which dissociate into Kr(lSo) + Br+(lD,) (2(H), 1(X1), O’(M)) crosses with one of the curves which dissociate into Kr(l So) t Br+(3P1) (l(H), O-(I)). There are a few Zestrictions imposed by symmetry. For example, two curves of the same (w-w) symmetry cannot cross. Also, it appears that the selection rule for predissociation should be applicable for this case to determine among the several channels, the one that is allowed by symmetry restrictions. This selection rule for predissociation [30] is Aa = 0, +l, + 4 -. Thus, for example, if O+(III) curve crosses with l(I1) then the transition
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lD2 * 3P1 of Br’ is allowed. From table 5, it can be seen that the O+(III) and 101) curves cross at 5.75 bohr which explains the experimental observation of the ID2 + 3P, transition. Although the O’(U) curve does not directly cross with O’(III), I(II1) or 201) curves, however, it crosses with the l(H) curve (between 5.75 and 6.0 bohrs). Since the l(U) curve is a channel for the lD2 -+ 3Pl transition, a complex formed by lD2 (Br+) which goes through this channel could meet the bound O’(H) state. Thus, by this process a Br+ which starts as lD2 could go to O’(H) KrBr+ state which dissociates into Kr&-,) + Br+(3P0) atoms. Thus the transition lD2 + 3P0 also becomes allowed and was observed experimentally. The curves which dissociate into ground state atoms (2,0+, 1) do not cross with the curves which dissociate into Kr(lS,) + Br+(lD,). Further, 2,0+ and 1 curves do not cross with the curves dissociating into Kr(lSO) t Br+ (3Po) or Kr(lS ) t Br+(3P1). Thus there are no channels for the PD2 (Br+) to go into 3P, (Br’). Thus the lD2 ++3P2 transition is not feasible. All experimental attempts to observe tliis transition have failed. Our calculations seem to offer an explanation for this failure. Our earlier calculations of similar systems indicate that the bond distances predicted by our calculations are approximately 0.1-0.15 A larger than the corresponding experimental values [ 19,211. Thus our calculated crossings,distances of the various curves of 4 R +
Fig. 4. Potentialenergycurvesof spin-orbit
(Bohr)
KrBr+ in the absence of
interaction.
Table 5 Potential energy curves of KrBr+ (energies in hartree)
R
2(I)
4.5 0.1599 5.0 0.0684 5.25 0.0431 5.5 0.0289 5.75 0.0213 6.0 0.0169 7.0 -0.0010 9.0 -0.0008 11.0 0.0
10)
o+m
l(II)
0-
o+w
o+(III)
UIW
2m
0.1639 0.0073 0.0478 0.0334 0.0242 0.0146 -0.0001 -0.0007 0.0
0.1044 0.0492 0.0395 0.0289 0.0227 0.0163 0.0021 0.0015 0.00
0.1987 0.0990 0.0725 0.0502 o.cl344 0.0224 0.0119 0.0135 0.0145
0.1705 0.0801 0.0556 0.0419 0.0350 0.0287 0.0129 0.0137 0.0145
0.1720 0.0814 0.0585 0.0454 0.0301 0.0331 0.0205 0.0206 0.0213
0.2016 0.1110 0.0677 0.0468 0.0341 0.0381 0.0497 0.0635 0.0667
0.1999 0.1090 0.1038 0.0771 0.0713 0.0696 0.0662 0.0671 0.0667
0.3186 0.1899 0.1285 0.1036 0.0963 0.0846 O.Oili 0.0690 0.0667
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KrBr+ could be off by this value. Among the O+ states we calculated, the O+(II) and O+(III) states are bound. The O’(H) state could be converted into O+(III) by the l(H) channel which crosses with both these states. The experimentally measured dissociation energy of KrBr+ is around 1.5 eV [ 151. Our calculated separation between the O’(II1) and its dissociation limit is 0.91 eV while the separation of the O’(H) state with respect to K#Su) + Br’(lD2) atoms is 1.OSeV. Since the KrBr+ in the O’(H) state could go to O’(II1) state through the l(H) channel, this possibility should not be ruled out. This would mean a dissociation energy of 1.05 eV. In either case our calculated dissociation energy is not very accurate. This can be attributed to only a small number of configurations included in our CI calculations which are adequate to calculate some of the properties such as T,, w,, crossings of the curves and the general shapes of potential energy curves, but are far from complete. Our earlier calculations on similar systems have yielded only 70% of the experimental De values. Thus the experimental value of 1.5 eV should be regarded as more accurate. The calculated vibrational frequencies of the O+(H) and O’(II1) states are 526 and 446 cm- l, respectively. Their R, values are 3.1 and 3.09 A, respectively. The O+(I)-O- , O+(I)-O+(II), O+(I)-O+(III) splittings at 9.0 bohr correspond to 3P2-3P1, 3P2-3P0, 3P2-lD2 splittings of Br+. The calculated values for these splittings are 3 182,4675, and 14639 cm-l, respectively. These values are in reasonable agreement with the corresponding experimental values reported in‘table 2.
5. The nature of relativistic CI wavefunctions At 5.5 bohr the u orbital is a slightly bonding MO, with the Br pz orbital making the dominant contribution. The u* orbital is dominantly on Kr but is slightly antibonding. The rr orbital is a non-bonding Kr p orbital while the rr* orbital is predominantly a Br p orbital and is also non-bonding. At short distances the a’(I) state is dominantly ++. At 5.5 bohr, the O’(I) state is 13% (&*4, ::’ ) 2670 ( uu*rr*4, IX’,,), 34%(&*a*3,‘3110+), 17~~&*2~*3,311r-,+)and2%(u~u*~7r*~,32~+). 570
22 August 1986
At 6.0 bohr the O’(I) state is 0.1% (~~rr*~, lx:+), 17% (&7*71*3, “l-lo+), 22% (uu*2r*3,3l-I,+), 1% ( UU*~*~, 1X;+) and 56%(0~u*~rr*~, 3X0+). Thus the O’(I) state exhibits very interesting avoided crossings. At short distances the O’(B) is dominantly 3II0 +. At 5.5 bohr the O’(B) state is 1% (u~,*~, lZ’,+), 2.6%(u~*n*~, I$+), 12%(~~u*n*~, 311,+), 10% (u~*~rr*~, 3110+),and70%(u2u*2n*3, 32;+).At long distances the 3II0 + arising from uu* 2rr*3 and ~~u*tr*~ dominate. At short distances the O’(II1) state is 43% (~~u*~rr*~, 3Z>), 27%(0~u*rr*~, 3n,+),‘l5%(uu*2rr*3,3II,+), 4%(&r*4,lB:;s+), and 6% (uu*~*~, 1CA +). However, at 5.5 bohr, the O+(III) is 14.4% (~~n*~), 26% (uu*R*~), 33% (u2u*rr* 3), 17% (uu* 2rr*3, and 5% (3BC,+). At long distances it is dominantly lZ+ +. The above nature of the Cfwavefunctions of the O+, O+(H) and O+(III) states suggest several avoided crossings in these O+ states. These crossings are the results of the crossings of 3II, 3X- and lZ$ curves in the absence of spin-orbit interaction (see fig. 4).
Acknowledgement
One of us (K(B)would like to thank the National Science Foundation for a partial support of this project through Grant No. CHE8520556.
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[IO] J.H. Holloway, Noble gas chemistry (Methuen, London, 1968). [ 111 A. Henglein and G.A. Muccini, Angew. Chem. 72 (1960) 630. [ 121 I. Kuen and F. Howorka, J. Chem. Phys. 70 (1979) 595. [ 131 J. Berkowitz and W.A. Chupka, Chem. Phys. Letters 7 (1970) 447. [ 141 J. Berkowitz, W.A. Chupka, P.W. Guyon, J.H. Holloway and R. Sphor, J. Phys. Chem. 75 (1971) 1461. [ 151 H.P. Watkins and W.S. Koski, Chem. Phys. Letters 77 (1981) 470. [ 16) M.A. Gardner, A.M. Karo and A.C. WahJ, J. Chem. Phys. 65 (1976) 1222. [ 171 D.H. Liskow, H.F. Schaefer Ill, P.S. Bagus and B. Liu, J. Am. Chem. Sot. 95 (1973) 4056. [ 181 B. Liu and H.F. Schaefer Ill, J. Chem. Phys. 55 (1971) 2369.
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[ 191 P.A. Christiansen, K. Balasubramanian and K.S. Pitzer, J. Chem. Phys. 76 (1982) 5087. [ 201 K. Balasubramanian, J. Chem. Phys., to be published. [21] K. Balasubramanian, J. Mol. Spectry. 110 (1985) 339. [22] K. Balasubramanian, J. Chem. Phys. 82 (1985) 3741. [23] K. Balasubramanian, J. Phys. Chem. 88 (1984) 5759. [24] K. Balasubramanian,Chem. Phys. Letters 114 (1985) 201. [25] K.S. Piker, Intern. J. Quantum Chem. 25 (1984) 131. [ 261 K. Balasubramanian and K.S. Pitzer, J. Chem. Phys. 78 (1982) 321. [ 271 K. Balasubramanian, Chem. Phys. 95 (1985) 225. [28] K. Wendell, C.A. Jones, J.J. Kaufman and W.S. Koski, J. Chem. Phys. 63 (1975) 750. [ 291 C.E. Moore, private communication. [ 301 G. Herzberg, Spectra of diatomic molecules (Van Nostrand, Princeton, 1950).
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