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Ab initio CI study of the electronic structure and spectrum of the dibromide ion
Volume 148, number 2,3
CHEMICAL PHYSICS LETTERS
8 July 1988
AB INITIO CI STUDY OF THE ELECTRONIC STRUCTURE AND SPECTRUM OF THE DIBROMIDE ION A.B. SANNIGRAHI Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
S.D. PEYERIMHOFF Lehrstuhlftir Theoretische Chemie, UniversitiitBonn, Wegelerstrasse 12, D-5300 Bonn 1, Federal Republic of Germany Received 29 February 1988; in final form 4 May 1988
The ground-state spectroscopic constants, vertical excitation energies and associated oscillator strengths or lifetimes have been calculated for the dibromide ion, Brc by the ab initio MRD CI method using a double-zeta Gaussian basis augmented with a set of diffuse p functions, together with an s and a set of p bond functions. For the sake of comparison, the ground-state spectroscopic constants of Brz have also been calculated. The calculated transition energies of Br; are in good agreement with experimental data.
1. Introduction The ground-state electronic structure of Br, has long been known experimentally [ 11. A number of ab initio theoretical calculations [ 2-7 ] have also been reported on this molecule. In contrast, very little is known about the electronic structure of the dibromide ion, Bry . Wadt and Hay [ 5 ] have recently carried out ab initio all-electron (AE) and valenceelectron (VE) effective core potential (ECP ) polarization CI calculations on both Brz and Br,-, and computed their D,,r,and excitation energies. The main objective of this investigation was to assess the performance of VE ECP calculations vis-a-vis those of AE calculations. They found good agreement between the two sets of calculated values which, however, did not compare favorably with the available experimental data. The large discrepancy between theory and experiment might be due to the inadequacy of both the basis set (( 13slOp6d/%6p2d)) and the CI treatment used. In this paper we have studied the electronic structure and spectrum of Br,- by the ab initio MRD CI method [ 8- 131 using a larger basis set.
The present investigation is largely motivated by the optical spectral studies of Andrews [ 141 on matrix-isolated M+Brl (M= alkali metals) species. He observed that the reaction of Br and alkali metals produced a strong band near 360 nm and a weak band near 640 nm depending upon the alkali atom. These bands were assigned to o+o* and n*+o* transitions in Br, . We intend to verify these observations and provide further information about the electronic spectrum of Br; by means of ab initio CI calculations. Due to the lack of experimental data it is not possible to assess the reliability of our calculated electronic structure of BrF . The relevant data are, however, available [ 1] for the neutral species. Therefore, for the sake of comparison, we have also calculated the ground-state spectroscopic constants of Br2.
2. Method of calculation The A0 basis set employed in the present calculations consists of a total of 88 contracted Gaussian functions. The (13s9p5d/9s6p2d) basis [ 15,161 of
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Br is augmented by a set of diffuse p functions (cu=O.O49), and an s (cu=l.O) and a set of p (a=0.7) functions located at the center of the BrBr bond. The configuration interaction calculations are of the MRD CI type with configuration selection and energy extrapolation as described in the literature [ 8- 131. The energy corresponding to a full CI treatment has been estimated via the relation E est.full Cl
which is a generalization of the correction formula suggested by Langhoff and Davidson [ 17 1. For the sake of technical simplicity calculations on molecules as well as component atoms (Br and Br - ) have been performed using the DZhsubgroup. For Br and Br- a core of 14 AOs were kept doubly occupied in all configurations, while the 9 virtual AOs with the highest orbital energy were excluded from the calculation entirely. The numbers of core and neglected virtual MOs in the case of Br, or Br, were 28 and 16 respectively. Thus in all cases only the valence electrons are correlated. A value of T= 10 phartree has been used throughout for the configuration selection threshold. Other details of the CI calculations will be given with the results.
8 July 1988
3. Results and discussion 3.1. Ground-state electronic structure of Br, and Br,-
The ground-state electronic configuration of Br, (‘El) is la,2...8fs;l10$..7f$ls,4 1s; 1$.4X; 17c;... 4n:. In Br,- the additional electron occupies the 80, MO resulting in a %,’ ground state. The total energies of the molecules at their respective calculated equilibrium bond lengths and that of the component species (Br and Br- ) are given in table 1. In fig. 1 the estimated full CI potential energy (PE) curves are shown for the ground states of Br, and Bry . As can be seen from table 1 and the figure, both the PE curves describe the dissociation process correctly. The calculated spectroscopic constants are listed in table 2. It can be seen from table 2 that the constants w,, ode, r, and B, of Br, are obtained in satisfactory agreement with experiment. It is expected that the corresponding quantities for Br,- are also predicted with comparable accuracy. The MRD CI and estimated full CI D, values of Brz are overestimated by about 0.3 and 0.4 eV, respectively. In the case of Bry the calculated D, is higher by about 0.25 eV than the experimental value (the ZPE correction to D, is roughly 0.01 eV). If spin-orbit interaction is taken
Table 1 Total energies (hartree) ofthe ground states of Br(2P), Br-( ‘S), Br,( ‘Z: ) and Br;; (*Z: ) System
Br BrBr2
Br;
Energy ‘xb) SCF
MRD CI
estimated full CI
-0.14999 - 0.24442 -0.32808 -0.32808 -0.09722 -0.41844 -0.41803 -0.37288
-0.19841 -0.30521 -0.48151 - 0.48 I 54 -0.39543 -0.55225 -0.55277 - 0.50244
-0.19927 -0.30691 - 0.48744 - 0.48746 -0.39906 -0.55824 -0.55884 -0.50745
pMqR ‘)
1ooc; d,
Number of configurations generated/selected
IMlR 1MlR 7M3R 7M3R 7M3R 4M2R 4M2R 4M2R
98.2 97.2 95.6 95.6 96.4 95.3 95.3 95.0
477/303 3071202 3399614584 3399614584 3399614243 9037215489 9037215582 9037214546
aJ The energies of Br/Br- are relative to - 2572.0 hartree and that of BrJBr, are relative to - 5 144.0 hartree. b, The first and second set of values for Br, and Br,- are obtained at their SCF and MRD CI or estimated full CI geometries respectively given in table 2. The third set of values corresponds to r=20 bohr. ‘) pMqR denotes that configuration selection has been made with respect top main configurations and q roots. d, C, is the cceffkient of the leading configuration in the final CI expansion.
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CHEMICAL PHYSICS LETTERS
Volume 148, number 2,3
for the exponent of the p bond functions. Now the CI 0. values of Brz and Br? are reduced to 1.70 and 1.10 eV, respectively. This procedure, however, predicted much longer bond lengths (Bra: SCF, 2.37 A and CI, 2.43 A;Br:: SCF, 2.91 A and CI, 2.92 A) and worsened the agreement between other spectroscopic constants of BrZand experiment. The 80, MO, which is half-filled in Br?, turns out to be an extremely diffuse orbital composed entirely of the p bond function (a = 0.00 1). This limited experiment with the basis sets indicates that one should not use arbitrary exponents for bond functions; these must be optimized separately for Br, and Br? in order to obtain a more realistic description of the electronic structure. Although we were forced to restrict the size of the basis set in order to keep the excited state CI calculations tractable, it is desirable that at least one set of polarization d functions be included ih the basis set.
40
Fig. I. Estimated full CI potential energy curves for the ground state of BrZand Br, .
3.2. Electronic spectrum of Br,-
into account the calculated D, values of Br2 and Br; are reduced by approximately 0.3 [ 7 ] and 0.15 eV, respectively, and a better agreement between theory and experiment is achieved. As can be seen from tables 1 and 2 both MRD CI and estimated full CI calculations are size consistent. However, the overestimation of D, is rather a disturbing feature. It seems to us that this stems from the use of both s and p bond functions in the basis set. In order to verify this conjecture we carried out some calculations using a very small value (0.00 1)
Vertical excitation energies of Br? have been calculated at the CI geometry (r,=2.81 A) using the ground-state molecular orbitals. A similar procedure yielded very good results in the case of CIFz [ 18 ] and Cl: [ 191. The dominant electronic configurations of the excited states of BrF and their weight in the final CI expansion are given in table 3. It can be seen that, barring a few cases, the leading configuration is sufficiently representative of the entire configuration space generated. The vertical excitation
Table 2 Ground-state spectroscopic constants (0, in eV, r, in A,B,,o, and ode in cm-’ ) of Br2 and Br? Constant
Brr
Br2 SCF
MRD CI
estimated full CI
Deb’
-
r, & w @-&
0.76 2.31 0.080 335 0.67
2.34 2.31 2.32 0.079 309 0.96
2.41 2.42 2.32 0.079 312 0.96
exp. a)
SCF
MRD CI
estimated full CI
1.99 2.28 0.082 325 1.077
0.65 2.90 0.05 I 166 0.76
1.37 1.34 2.81 0.054 I78 0.88
I.40 1.43 2.81 0.054 179 0.86
exp. a’
1.15
a) Taken from ref. [ I 1. b’The first set of D, values refers to r=20 bohr and the second set to separated atoms. For Br? the experimental value corresponds to Do-
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Table 3 Dominant electronic configurations in the excited states of Br,- and their weight (Ci) in the final CI expansion State
Excitation
x 2E+ 22% 2z+ ZrI”, *J-J. “Xi 2.z: ‘28’
8b”-t90” 4n,+8o, 4xU+sx. 4x,-+9a, 8q+8a, 4x+l, 4ir-’ 5x, 4x,+80, 4x,+9a, 44+9o. (4x,, 4x, ) -) ( 80°F5x, ) (4x,, 4n,)- (8~ 5x,) 80.+5n[1
2J-Jr *J-J* *JJn *Ha Qs *J%
Electronic configuration a)
PMqR
1004
lo:70;80@r:4x~80u 7~:7o,z8~4~:4~9o, la:7a,Z8~4x,44X:8a”5r, 7a: 70; 84 4x: 80: 4x: lo:7o,’ 8c$47t,44x:80,90U la~80~7~4r:4n~80g 70~7a~8~4x~4x~8aU5s, 7a~7a,Z8c$4n~47tj8a,5xU 7a~8a:7o~8o~4x~4x~ 70~7a~8o~4x~41r~80,90, 7ai 7o,’84 4~: 41~:8a. 9oU ?‘a:8a: 7c1,Sai 4x14x: 5x, 70: 80: 7oi So,’4x: 4~: 5x, 7a~7a~8t$4x~4l@r,
I lM3R
94.6 86.0 80.0 93.0 75.8 91.2 82.5 80.1 93.0 84.8 79.6 90.0 91.0 84.1
I lM3R 1lM3R 9M2R 9M2R 15M3R 15M3R l5M3R 14M6R 14M6R l4M6R l4M6R l4M6R 14M6R
a) Only the valence electronic configurations are given.
energies and associated oscillator strengths or lifetimes of Br,- are summarized in table 4. The calculated excitation energy (3.56 eV) of the ‘2: state corresponding to the 8o,A3o, transition is in good agreement with the experimental [ 141 values (3.37-2.53 eV). The associated oscillator strength is high, and indicates - again in agreement
with experiment - that the pertinent transition is a strong one. The excitation energy of the ‘lTn state arising from the 4x, A&s, transition is predicted to be 1.67 eV, which compares well with the experimental [ 141 value (1.73-1.95 eV). Rather low values of the oscillator strength indicate that this is a weak transition. Spence [ 201 located two Feshback
Table 4 Vertical excitation energies (A& in eV), oscillator strengths cf( r) andf( V) ) and lifetimes (T, in s) of the excited states of Br? State’)
X3+ ” 5: ‘z: 2H” *lX ‘Xl *c: ‘z; % Qr % X *J-Js X
AE
rb)
f(r)
MRD CI
estimated full CI
0.00 c, 5.97 8.73 2.74 7.81 3.60 7.47 7.95 1.66 7.04 7.45 8.60 8.93 7.51
0.00 d) 5.93 8.01 2.70 7.77 3.56 1.43 7.80 1.67 7.01 1.42 8.59 8.95 7.14
0.62 0.59x 0.14x 0.40x 0.96x 0.27x 0.32x 0.53x 0.33x
lo-* 10-l 10-3 IO-’ lo-* 1O-5 10-S 10-l
0.47 0.40x 1o-2 0.19x 10-l 0.20x IO-’ 0.79x 10-l 0.97x 10-3 0.26x lo-’ 0.86x 10-5 0.21 x10-l
‘) These are arranged in the same order as in table 3. b, Calculatedfromf(r). dJ -5144.55889 hartree=O.OO. eJpMqR and Ci are given in table 3.
200
Number of configurations generated/selected ‘)
0.29x lo-* 0.70x lo-’ 0.26 x lo-’ 0.21 x lo-’ 0.49x 10-8 0.15x10-6 0.97x 1o-4 0.54x 10-4 0.14x lo-’
“-5144.55278
19556117686 195561/7686 19556117686 141124/5375 141124/5375 34219615185 34219615185 342196/5185 284197/l 1023 284197111023 284197/l 1023 284197/11023 284197/l 1023 284197/11023
hartree=O.OO.
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CHEMICAL PHYSICS LETTERS
resonant states in Br, at 6.72 and 7.065 eV. From this the existence of a preionized doubly excited 211s state of Bry has been predicted [ 11 with excitation energiesof 9.26 eV (5=3/2) and 9.61 eV (J= l/2). According to the present calculations this 211rresonant state probably arises from the (4~ 41~~)-&,, 5x,) double excitation. The calculated excitation energy is only in qualitative agreement with experiment. It is not possible to make further comments on this transition due to a lack of convincing experimental data and the inadequacy of the theoretical treatment undertaken for the description of resonant states. In addition to these three bands, a few moderately intense transitions with excitation energies in the range 7-8 eV are predicted by the present calculations. These are the two doublets of the ‘Cl and YIP states ans’ in g from 47cg+5n, and 4~,,+9a, transitions respectively. The *I$ state corresponding to the 8a,-+ 57rgtransition is also predicted to give rise to a fairly intense band.
4. Concluding remarks To the best of our knowledge this is the most extensive CI calculation to date on the electronic structure and spectrum of Br,. The excitation energies and intensities of the low-lying transitions are predicted in good agreement with experiment. In order to gain a better understanding of the electronic spectrum of Bri (in fact, of any dihalide ion) spin-orbit interactions should be taken into account, We plan to undertake such a study in the near future.
Acknowledgement One of us (ABS) is thankful to the Humboldt Foundation for the award of a fellowship during the tenure of which the calculations reported in this paper were performed in Bonn. The time and service
8 July 1988
made available by the Computer Center, Bonn University, were essential to this study and are gratefully acknowledged.
References [ 11K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [2] P.A. Straub and A.D. McLean, Theoret. Chim. Acta 32 (1974) 227. [3] Y. Sakai, H. Takewaki and S. Huzinaga, J. Comput. Chem. 3 (1982) 6. [4] J. Andzelm, M. Klobukowski and E. Radzio-Andzelm, J. Comput. Chem. 5 (1984) 146. [5] W.R. Wadt and P.J. Hay, J. Chem. Phys. 82 (1985) 284. [ 61 J. Urban, V. Klimo and J. Tin& Chem. Phys. Letters 128 ( 1986) 203. [ 71 P. Schwerdtfeger, L. von Szentpaly, K. Vogel, H. Silberbach, H. Stoll and H. Preuss, J. Chem. Phys. 84 (1986) 1606. [ 81 R.J. Buenker and S.D. Peyerimhoff, Theoret. Chim. Acta 35 (1974) 33; 39 (1975) 217. [ 91 R.J. Buenker, S.D. Peyerimhoff and W. Butscher, Mol. Phys. 35 (1978) 771. [lo] R.J. Buenker and S.D. Peyerimhoff, in: New horizons of chemistry, eds. P.O. Liiwdin and B. Pullman (Reidel, Dordrecht, 1983) p. 183. [ 111R.J. Buenker, in: Studies in physical and theoretical chemistry, Vol. 2 I. Current aspects of quantum chemistry, ed. R. Garbo (Elsevier, Amsterdam, 1982) p. 17. [ 121R.J. Buenker, in: Proceedings of Workshop on Quantum Chemistry and Molecular Physics, Wollongong, Australia (February 1980). [ 131 R.J. Buenker and R.A. Phillips, J. Mol. Struct. THEOCHEM 123 (1985) 291. [ 141L. Andrews, J. Am. Chem. Sot. 98 (1976) 2152. [ 151T.H. Dunning Jr., J. Chem. Phys. 69 (1978) 2209. [ 16]B. Engels and SD. Peyerimhoff, J. Mol. Struct. THEOCHEM 138 (1986) 59. [ 171S.R. Langhoff and E.R. Davidson, Intern. J. Quantum Chem. 8 (1974) 61. [ 181A.B. Sannigrahi and S.D. Peyerimhoff, Chem. Phys. Letters 114(1985)6. [ 191A.B. Sannigrahi and S.D. Peyerimhoff, Chem. Phys. Letters 141 (1987) 49. [ 201 D. Spence, Phys. Rev. A 10 (1974) 1045.
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CHEMICAL PHYSICS LETTERS
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AB INITIO CI STUDY OF THE ELECTRONIC STRUCTURE AND SPECTRUM OF THE DIBROMIDE ION A.B. SANNIGRAHI Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, India
S.D. PEYERIMHOFF Lehrstuhlftir Theoretische Chemie, UniversitiitBonn, Wegelerstrasse 12, D-5300 Bonn 1, Federal Republic of Germany Received 29 February 1988; in final form 4 May 1988
The ground-state spectroscopic constants, vertical excitation energies and associated oscillator strengths or lifetimes have been calculated for the dibromide ion, Brc by the ab initio MRD CI method using a double-zeta Gaussian basis augmented with a set of diffuse p functions, together with an s and a set of p bond functions. For the sake of comparison, the ground-state spectroscopic constants of Brz have also been calculated. The calculated transition energies of Br; are in good agreement with experimental data.
1. Introduction The ground-state electronic structure of Br, has long been known experimentally [ 11. A number of ab initio theoretical calculations [ 2-7 ] have also been reported on this molecule. In contrast, very little is known about the electronic structure of the dibromide ion, Bry . Wadt and Hay [ 5 ] have recently carried out ab initio all-electron (AE) and valenceelectron (VE) effective core potential (ECP ) polarization CI calculations on both Brz and Br,-, and computed their D,,r,and excitation energies. The main objective of this investigation was to assess the performance of VE ECP calculations vis-a-vis those of AE calculations. They found good agreement between the two sets of calculated values which, however, did not compare favorably with the available experimental data. The large discrepancy between theory and experiment might be due to the inadequacy of both the basis set (( 13slOp6d/%6p2d)) and the CI treatment used. In this paper we have studied the electronic structure and spectrum of Br,- by the ab initio MRD CI method [ 8- 131 using a larger basis set.
The present investigation is largely motivated by the optical spectral studies of Andrews [ 141 on matrix-isolated M+Brl (M= alkali metals) species. He observed that the reaction of Br and alkali metals produced a strong band near 360 nm and a weak band near 640 nm depending upon the alkali atom. These bands were assigned to o+o* and n*+o* transitions in Br, . We intend to verify these observations and provide further information about the electronic spectrum of Br; by means of ab initio CI calculations. Due to the lack of experimental data it is not possible to assess the reliability of our calculated electronic structure of BrF . The relevant data are, however, available [ 1] for the neutral species. Therefore, for the sake of comparison, we have also calculated the ground-state spectroscopic constants of Br2.
2. Method of calculation The A0 basis set employed in the present calculations consists of a total of 88 contracted Gaussian functions. The (13s9p5d/9s6p2d) basis [ 15,161 of
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Br is augmented by a set of diffuse p functions (cu=O.O49), and an s (cu=l.O) and a set of p (a=0.7) functions located at the center of the BrBr bond. The configuration interaction calculations are of the MRD CI type with configuration selection and energy extrapolation as described in the literature [ 8- 131. The energy corresponding to a full CI treatment has been estimated via the relation E est.full Cl
which is a generalization of the correction formula suggested by Langhoff and Davidson [ 17 1. For the sake of technical simplicity calculations on molecules as well as component atoms (Br and Br - ) have been performed using the DZhsubgroup. For Br and Br- a core of 14 AOs were kept doubly occupied in all configurations, while the 9 virtual AOs with the highest orbital energy were excluded from the calculation entirely. The numbers of core and neglected virtual MOs in the case of Br, or Br, were 28 and 16 respectively. Thus in all cases only the valence electrons are correlated. A value of T= 10 phartree has been used throughout for the configuration selection threshold. Other details of the CI calculations will be given with the results.
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3. Results and discussion 3.1. Ground-state electronic structure of Br, and Br,-
The ground-state electronic configuration of Br, (‘El) is la,2...8fs;l10$..7f$ls,4 1s; 1$.4X; 17c;... 4n:. In Br,- the additional electron occupies the 80, MO resulting in a %,’ ground state. The total energies of the molecules at their respective calculated equilibrium bond lengths and that of the component species (Br and Br- ) are given in table 1. In fig. 1 the estimated full CI potential energy (PE) curves are shown for the ground states of Br, and Bry . As can be seen from table 1 and the figure, both the PE curves describe the dissociation process correctly. The calculated spectroscopic constants are listed in table 2. It can be seen from table 2 that the constants w,, ode, r, and B, of Br, are obtained in satisfactory agreement with experiment. It is expected that the corresponding quantities for Br,- are also predicted with comparable accuracy. The MRD CI and estimated full CI D, values of Brz are overestimated by about 0.3 and 0.4 eV, respectively. In the case of Bry the calculated D, is higher by about 0.25 eV than the experimental value (the ZPE correction to D, is roughly 0.01 eV). If spin-orbit interaction is taken
Table 1 Total energies (hartree) ofthe ground states of Br(2P), Br-( ‘S), Br,( ‘Z: ) and Br;; (*Z: ) System
Br BrBr2
Br;
Energy ‘xb) SCF
MRD CI
estimated full CI
-0.14999 - 0.24442 -0.32808 -0.32808 -0.09722 -0.41844 -0.41803 -0.37288
-0.19841 -0.30521 -0.48151 - 0.48 I 54 -0.39543 -0.55225 -0.55277 - 0.50244
-0.19927 -0.30691 - 0.48744 - 0.48746 -0.39906 -0.55824 -0.55884 -0.50745
pMqR ‘)
1ooc; d,
Number of configurations generated/selected
IMlR 1MlR 7M3R 7M3R 7M3R 4M2R 4M2R 4M2R
98.2 97.2 95.6 95.6 96.4 95.3 95.3 95.0
477/303 3071202 3399614584 3399614584 3399614243 9037215489 9037215582 9037214546
aJ The energies of Br/Br- are relative to - 2572.0 hartree and that of BrJBr, are relative to - 5 144.0 hartree. b, The first and second set of values for Br, and Br,- are obtained at their SCF and MRD CI or estimated full CI geometries respectively given in table 2. The third set of values corresponds to r=20 bohr. ‘) pMqR denotes that configuration selection has been made with respect top main configurations and q roots. d, C, is the cceffkient of the leading configuration in the final CI expansion.
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for the exponent of the p bond functions. Now the CI 0. values of Brz and Br? are reduced to 1.70 and 1.10 eV, respectively. This procedure, however, predicted much longer bond lengths (Bra: SCF, 2.37 A and CI, 2.43 A;Br:: SCF, 2.91 A and CI, 2.92 A) and worsened the agreement between other spectroscopic constants of BrZand experiment. The 80, MO, which is half-filled in Br?, turns out to be an extremely diffuse orbital composed entirely of the p bond function (a = 0.00 1). This limited experiment with the basis sets indicates that one should not use arbitrary exponents for bond functions; these must be optimized separately for Br, and Br? in order to obtain a more realistic description of the electronic structure. Although we were forced to restrict the size of the basis set in order to keep the excited state CI calculations tractable, it is desirable that at least one set of polarization d functions be included ih the basis set.
40
Fig. I. Estimated full CI potential energy curves for the ground state of BrZand Br, .
3.2. Electronic spectrum of Br,-
into account the calculated D, values of Br2 and Br; are reduced by approximately 0.3 [ 7 ] and 0.15 eV, respectively, and a better agreement between theory and experiment is achieved. As can be seen from tables 1 and 2 both MRD CI and estimated full CI calculations are size consistent. However, the overestimation of D, is rather a disturbing feature. It seems to us that this stems from the use of both s and p bond functions in the basis set. In order to verify this conjecture we carried out some calculations using a very small value (0.00 1)
Vertical excitation energies of Br? have been calculated at the CI geometry (r,=2.81 A) using the ground-state molecular orbitals. A similar procedure yielded very good results in the case of CIFz [ 18 ] and Cl: [ 191. The dominant electronic configurations of the excited states of BrF and their weight in the final CI expansion are given in table 3. It can be seen that, barring a few cases, the leading configuration is sufficiently representative of the entire configuration space generated. The vertical excitation
Table 2 Ground-state spectroscopic constants (0, in eV, r, in A,B,,o, and ode in cm-’ ) of Br2 and Br? Constant
Brr
Br2 SCF
MRD CI
estimated full CI
Deb’
-
r, & w @-&
0.76 2.31 0.080 335 0.67
2.34 2.31 2.32 0.079 309 0.96
2.41 2.42 2.32 0.079 312 0.96
exp. a)
SCF
MRD CI
estimated full CI
1.99 2.28 0.082 325 1.077
0.65 2.90 0.05 I 166 0.76
1.37 1.34 2.81 0.054 I78 0.88
I.40 1.43 2.81 0.054 179 0.86
exp. a’
1.15
a) Taken from ref. [ I 1. b’The first set of D, values refers to r=20 bohr and the second set to separated atoms. For Br? the experimental value corresponds to Do-
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Table 3 Dominant electronic configurations in the excited states of Br,- and their weight (Ci) in the final CI expansion State
Excitation
x 2E+ 22% 2z+ ZrI”, *J-J. “Xi 2.z: ‘28’
8b”-t90” 4n,+8o, 4xU+sx. 4x,-+9a, 8q+8a, 4x+l, 4ir-’ 5x, 4x,+80, 4x,+9a, 44+9o. (4x,, 4x, ) -) ( 80°F5x, ) (4x,, 4n,)- (8~ 5x,) 80.+5n[1
2J-Jr *J-J* *JJn *Ha Qs *J%
Electronic configuration a)
PMqR
1004
lo:70;80@r:4x~80u 7~:7o,z8~4~:4~9o, la:7a,Z8~4x,44X:8a”5r, 7a: 70; 84 4x: 80: 4x: lo:7o,’ 8c$47t,44x:80,90U la~80~7~4r:4n~80g 70~7a~8~4x~4x~8aU5s, 7a~7a,Z8c$4n~47tj8a,5xU 7a~8a:7o~8o~4x~4x~ 70~7a~8o~4x~41r~80,90, 7ai 7o,’84 4~: 41~:8a. 9oU ?‘a:8a: 7c1,Sai 4x14x: 5x, 70: 80: 7oi So,’4x: 4~: 5x, 7a~7a~8t$4x~4l@r,
I lM3R
94.6 86.0 80.0 93.0 75.8 91.2 82.5 80.1 93.0 84.8 79.6 90.0 91.0 84.1
I lM3R 1lM3R 9M2R 9M2R 15M3R 15M3R l5M3R 14M6R 14M6R l4M6R l4M6R l4M6R 14M6R
a) Only the valence electronic configurations are given.
energies and associated oscillator strengths or lifetimes of Br,- are summarized in table 4. The calculated excitation energy (3.56 eV) of the ‘2: state corresponding to the 8o,A3o, transition is in good agreement with the experimental [ 141 values (3.37-2.53 eV). The associated oscillator strength is high, and indicates - again in agreement
with experiment - that the pertinent transition is a strong one. The excitation energy of the ‘lTn state arising from the 4x, A&s, transition is predicted to be 1.67 eV, which compares well with the experimental [ 141 value (1.73-1.95 eV). Rather low values of the oscillator strength indicate that this is a weak transition. Spence [ 201 located two Feshback
Table 4 Vertical excitation energies (A& in eV), oscillator strengths cf( r) andf( V) ) and lifetimes (T, in s) of the excited states of Br? State’)
X3+ ” 5: ‘z: 2H” *lX ‘Xl *c: ‘z; % Qr % X *J-Js X
AE
rb)
f(r)
MRD CI
estimated full CI
0.00 c, 5.97 8.73 2.74 7.81 3.60 7.47 7.95 1.66 7.04 7.45 8.60 8.93 7.51
0.00 d) 5.93 8.01 2.70 7.77 3.56 1.43 7.80 1.67 7.01 1.42 8.59 8.95 7.14
0.62 0.59x 0.14x 0.40x 0.96x 0.27x 0.32x 0.53x 0.33x
lo-* 10-l 10-3 IO-’ lo-* 1O-5 10-S 10-l
0.47 0.40x 1o-2 0.19x 10-l 0.20x IO-’ 0.79x 10-l 0.97x 10-3 0.26x lo-’ 0.86x 10-5 0.21 x10-l
‘) These are arranged in the same order as in table 3. b, Calculatedfromf(r). dJ -5144.55889 hartree=O.OO. eJpMqR and Ci are given in table 3.
200
Number of configurations generated/selected ‘)
0.29x lo-* 0.70x lo-’ 0.26 x lo-’ 0.21 x lo-’ 0.49x 10-8 0.15x10-6 0.97x 1o-4 0.54x 10-4 0.14x lo-’
“-5144.55278
19556117686 195561/7686 19556117686 141124/5375 141124/5375 34219615185 34219615185 342196/5185 284197/l 1023 284197111023 284197/l 1023 284197/11023 284197/l 1023 284197/11023
hartree=O.OO.
Volume 148, number 2,3
CHEMICAL PHYSICS LETTERS
resonant states in Br, at 6.72 and 7.065 eV. From this the existence of a preionized doubly excited 211s state of Bry has been predicted [ 11 with excitation energiesof 9.26 eV (5=3/2) and 9.61 eV (J= l/2). According to the present calculations this 211rresonant state probably arises from the (4~ 41~~)-&,, 5x,) double excitation. The calculated excitation energy is only in qualitative agreement with experiment. It is not possible to make further comments on this transition due to a lack of convincing experimental data and the inadequacy of the theoretical treatment undertaken for the description of resonant states. In addition to these three bands, a few moderately intense transitions with excitation energies in the range 7-8 eV are predicted by the present calculations. These are the two doublets of the ‘Cl and YIP states ans’ in g from 47cg+5n, and 4~,,+9a, transitions respectively. The *I$ state corresponding to the 8a,-+ 57rgtransition is also predicted to give rise to a fairly intense band.
4. Concluding remarks To the best of our knowledge this is the most extensive CI calculation to date on the electronic structure and spectrum of Br,. The excitation energies and intensities of the low-lying transitions are predicted in good agreement with experiment. In order to gain a better understanding of the electronic spectrum of Bri (in fact, of any dihalide ion) spin-orbit interactions should be taken into account, We plan to undertake such a study in the near future.
Acknowledgement One of us (ABS) is thankful to the Humboldt Foundation for the award of a fellowship during the tenure of which the calculations reported in this paper were performed in Bonn. The time and service
8 July 1988
made available by the Computer Center, Bonn University, were essential to this study and are gratefully acknowledged.
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