J. Phys. Chem. 1996, 100, 9649-9657
9649
Characterization of Homonuclear Diatomic Ions by Semiempirical Morse Potential Energy Curves. 1. The Halogen Anions J. G. Dojahn and E. C. M. Chen* School of Natural and Applied Sciences, UniVersity of Houston, Clear Lake, Houston, Texas 77058
W. E. Wentworth Department of Chemistry, UniVersity of Houston, Houston, Texas 77024-5641 ReceiVed: December 5, 1995; In Final Form: April 5, 1996X
Morse potential energy curves for the homonuclear diatomic halogen anions and their excited states were constructed using experimental data available from the literature. All of the curves are uniquely or overdetermined. The properties of the negative ions have been related to those of the neutral by using three dimensionless parameters, kA, kB, and kR, to modify the Morse curves of the neutral. The magnitudes of the parameters are reasonably consistent and suggest ranges for other homonuclear diatomic ions. A set of Morse potential energy curves is predicted for astatine anions on the basis of the consistency of these parameters. These curves are a significant improvement over those presented 10 years ago because of the existence of additional experimental data. In cases where the curves are overdetermined, these data agree very well with the calculated Morse potentials. Estimates for internuclear distances were made on the basis of the assumption of the additivity of radii. Agreement with available experimental data which were used to define the curves shows this assumption to be valid. The bond dissociation energies of the ground states of the halogen anions agree with those of the corresponding isoelectronic rare gas positive ions within the experimental error. This led to the use of the experimental values for the excited state bond dissociation energies of the rare gas positive ions to estimate those for the corresponding state of the halogen negative ions. Experimental crosssection data have been used to define Morse potentials for the higher spin orbital substates of iodine which were previously only estimated. However, the structure in the cross-section data and a recently published theoretical calculation has led to the conclusion that I2- may consist of more than the currently projected six states. In addition, the spin orbital substates of F2- are now better defined.
Introduction In 1985, the homonuclear diatomic halogen anions were characterized by using three dimensionless parameters, kA which modifies the attractive portion, kR which modifies the repulsive portion, and kB which modifies the frequency, to relate the Morse potentials of the negative ions to those of the neutral molecules.1 The Morse potentials for all but the C 2Πu,1/2 and D 2Σg+ energy states of the iodine anion were defined from experimental data or reasonable assumptions. This set of curves was unique in that it was the only complete set of Morse potential energy curves found in the literature based on diverse experimental data. The ground states of the negative ion were determined from the adiabatic electron affinity which defined the bond dissociation energy, the frequency measured in the solid state, and the activation energy for thermal electron attachment for the two lower halogens or the vertical electron affinity for bromine and iodine. The absorption spectra of the ground state negative ions and the electron attachment cross section were partially or totally used to define the excited states. The three highest states were defined by assuming that the curves are repulsive. The excited states for the iodine anion were determined by the extrapolation of the electron attachment cross sections from the data for the lower halogens. In 1988, these cross sections were measured and can now be used to partially define these higher states.2 The three dimensionless parameters, kA, kB, and kR, were fairly consistent for the halogens, and it was suggested that these * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03601-X CCC: $12.00
values could be used to predict reasonable ranges for other molecules. The values of kB were consistent with predictions from Badger’s rule. The bond orders were generally greater than those predicted by simple qualitative molecular orbital theory. The ionic radii of the halogen anions, calculated by assuming that the internuclear distance is equal to the sum of the covalent and ionic radii, agreed well with ionic crystal radii, showing an average deviation of -0.04 Å.1 The greatest deviation was -0.15 Å for I -. This set of curves has been used or referenced in numerous other studies.3-9 These include the photodissociation and geminate recombination dynamics of I2- in mass-selected and size-selected I2-(CO2)n and Br2-(CO2)n cluster ions,3-6 the solvation of electronically excited I2-,7 and the photodissociation, recombination, and vibrational relaxation of I2- in various solvents with various counterions.8 However, it was noted that, especially for iodine, the curves are only qualitatively correct and do not reflect experimental data on the dissociative electron attachment to higher excited states. The experimental cross sections2 have been used to define all of the spin states of iodine. In addition, high-level theoretical calculations of both I2- and F2- have been carried out and provide guidelines for the dissociation energies and internuclear distances, especially for the ground state.3,7 These results, as well as our earlier findings, suggest that the internuclear distance is equal to the sum of the covalent and ionic radii and can be obtained from independent measurements. This indicated that a better procedure for defining the ground state of the negative ion would be to use this internuclear distance. © 1996 American Chemical Society
9650 J. Phys. Chem., Vol. 100, No. 23, 1996 In 1985, there were few definitive values for the dissociation energies of the rare gas positive ion dimers, Rg2+, which are isoelectronic with the homonuclear diatomic halogen negative ions. In the recent past, many values of the bond dissociation energies and frequencies of the Rg2+ ions have been determined experimentally, and some Morse potentials have been calculated from these data.10-18 For example, experimental and theoretical Morse potentials for three states of Ne2+ have been presented.13 Very recently, a complete set of values for the frequencies and bond dissociation energies for all of the states of Xe2+ was published.14 In addition, many values have been reported for the other two homonuclear diatomic rare gas positive ions.15,16 All of these results clearly indicate that where the data are available, the bond dissociation energies of the isoelectronic species are equal within the experimental error, that the internuclear distances for the Rg2+ ions are smaller than those for the corresponding X2- ions, and that the frequencies of the Rg2+ ions are larger than those of the corresponding X2- ions. For example, the “best” values for the ground state bond dissociation energy of Ne2+ is 1.35 ( 0.1 eV, while that of F2is 1.30 ( 0.1 eV. In the same order, the experimental frequencies are 598 and 470 cm-1 and the internuclear distances 1.75 and 1.90 Å respectively. For the excited states, the internuclear distances are better defined for the halogen anions, while the dissociation energies are better defined for the rare gas positive ions. However, by considering the values for the isoelectronic species, a complete set of Morse potentials can now be determined for both. The results of the curves for the rare gas positive ions will be presented in a forthcoming companion paper along with the details of the isoelectronic comparison. In addition to using the cross-section data for iodine to define the excited states of I2-, the spin orbital substates of fluorine can now be better defined.3 This work presents an update on the Morse potentials of the homonuclear diatomic halogen anions, as there are now three or more data points for all of the curves when the dissociation energy is used as an additional point on the curve. This is in lieu of assuming purely repulsive curves for these states as was done previously. The experimental absorption spectra of all of the C 2Πu states for all of the halogens are used to define the curves as was done previously. Data for only one B 2Πg state for I2- have been obtained and are now assigned to the B 2Πg,1/2 state. Although these curves have many useful applications, no attempt will be made to consider these as they relate to other studies. In this paper, the potential energy curves obtained from the best experimental data will be presented. These curves follow the basic concept of using experimental data and reasonable approximations of spectroscopic properties to establish Morse potentials for the halogen negative ions as originally presented by Mulliken,19 Person,20 and Herschbach.21 Where absorption spectra are not available for the halogen anion, the maximum in the absorption spectra will be estimated from theoretical considerations of systematic variations as a function of the row in the periodic table. When necessary, values for bond dissociation energies from the corresponding excited states of the rare gas positive ions will be used. These parameters will then be used to calculate the Morse parameters. In addition, the consistency of the values of the parameters kA, kB, and kR will be examined and the periodic trend for the bond dissociation energies, the internuclear distances, and the vibrational frequencies will be considered. This paper is the first of a series of five papers which will combine data from different types of experiments to characterize Morse potentials. The second will deal with the rare gas positive
Dojahn et al. ions, which are isoelectronic with the halogen negative ions. The third paper will present the Morse potentials for the alkali metal and coinage metal (Cu2-, Ag2-, and Au2-) diatomic anions. We will estimate curves for excited states by analogy to calculated curves for Li2-. The fourth paper in this series will be a survey of the general trend of the Morse potentials of the ground states of the neutral and negative ions for most of the main group elements based on the classifications of Herschbach presented in 1966.21 The fifth paper will focus on the Morse potentials of the simplest ions with odd electron bonds, He2+, He2-, H2+, and H2-. The procedure for combining data from different sources to obtain Morse potential energy curves will be useful for others since they utilize QBASIC and EXCEL which are readily available. This paper will first present the general equations used in the procedure. Next, the specific calculation procedures used for the halogens will be described. The results will be presented in the form of Morse parameters, dimensionless constants, and graphs of the Morse potentials. The data used in these calculations will be discussed and comparisons will be made for selected data not used to define these curves. Examples of these data are activation energies for dissociative electron attachment, vertical electron affinities, and full width at half-maximum for dissociative electron attachment and electronic absorption spectra. Finally, potential energy curves for astatine will be predicted on the basis of the periodic trends. Theoretical Section The Morse potential of the ground state atoms as referenced to zero energy at infinite separation is given by
U(X2) ) -2DX2 exp(-β(r - re)) + DX2 exp(-2β(r - re)) (1) where DX2 represents the spectroscopic bond dissociation energy, r is the internuclear or X-X separation, and re ) r at the minimum of U(X2). The constant β is defined by
β ) νe(2π2µ/D)1/2
(2)
with νe representing the fundamental vibrational frequency and µ, the reduced mass. The parametrized Morse potential for the negative ions is given by
U(X2-) ) -2kADX2 exp(-kBβ(r - re)) + kRDX2 exp(-2kBβ(r - re)) - EAX + E*X (3) where kA, kB, and kR are dimensionless constants, E*X is the energy of an excited state of X relative to the ground state, and EAX is the electron affinity of X. Equation 3 does represent a Morse potential, with the relationships between the properties of the neutral and negative ion being derived in the following manner22
DX2- ) DX2(kA2/kR) re,X2- )
ln(kR/kA) + re,X2 kBβX2
(4)
(5)
νe,X2- ) [(kAkB)/kR1/2] νe,X2
(6)
βX2- ) kBβX2
(7)
The two most frequently measured experimental quantities for
Characterization of Homonuclear Diatomic Ions
J. Phys. Chem., Vol. 100, No. 23, 1996 9651
TABLE 1: Parameters for the Homonuclear Diatomic Halogens and Anions molecule state or Anion
state
kA
kR
kB
F2 F2F2F2F2F2F2Cl2 Cl2Cl2Cl2Cl2Cl2Cl2Br2 Br2Br2Br2Br2Br2Br2I2 I2I2I2I2I2I2At2 At2At2At2At2At2At2-
1Σ + g 2Σ + u 2Π g,3/2 2Π g,1/2 2Π u,3/2 2Π u,1/2 2Σ + g 1Σ + g 2Σ + u 2Π g,3/2 2Π g,1/2 2Π u,3/2 2Π u,1/2 2Σ + g 1Σ + g 2Σ + u 2Π g,3/2 2Π g,1/2 2Π u,3/2 2Π u,1/2 2Σ + g 1Σ + g 2Σ + u 2Π g,3/2 2Π g,1/2 2Π u, 3/2 2Π u,1/2 2Σ + g 1Σ + g 2Σ + u 2Π g3/2 2Π g1/2 2Π u 3/2 2Π u1/2 2Σ + g
1.000 1.765 0.363 0.261 0.343 0.418 0.267 1.000 1.203 0.350 0.256 0.324 0.398 0.381 1.000 1.307 0.397 0.292 0.394 0.573 0.545 1.000 1.580 0.589 0.359 0.464 0.624 0.480 1.000 1.700 0.689 0.390 0.504 0.779 0.536
1.000 3.948 2.265 2.061 3.582 3.851 5.238 1.000 2.651 2.144 1.976 3.189 3.528 5.060 1.000 2.852 1.840 2.102 3.393 4.319 5.847 1.000 3.744 2.484 2.526 3.362 3.219 3.261 1.000 3.744 2.718 2.496 3.326 3.200 3.783
1.000 0.553 0.480 0.475 0.425 0.425 0.380 1.000 0.596 0.665 0.695 0.645 0.650 0.575 1.000 0.592 0.540 0.540 0.600 0.650 0.570 1.000 0.655 0.545 0.495 0.550 0.620 0.400 1.000 0.550 0.545 0.550 0.580 0.600 0.400
EAX (eV) 3.40 3.40 3.40 3.40 3.395 3.395 3.61 3.61 3.61 3.61 3.50 3.50 3.36 3.36 3.36 3.36 2.91 2.91 3.06 3.06 3.06 3.06 2.12 2.12 2.80 2.80 2.80 2.80 1.30 1.30
the negative ions are the vertical detachment energy, EV, and the adiabatic electron affinity of the molecule, EA, which leads to a value of DX2-. These values can be related to the dimensionless parameters by eqs 4, 8, and 9. Because there is
EV ) DX2(1 - 2kA + kR) - EAX + E*X - 1/2hνe,X2 (8) EA(X2) ) EAX - E*X + {(kA2/kR) - 1}DX2 /2{(kAkB/kR1/2) - 1}hνe,X2 (9)
1
only a slight dependence of kA and kR on kB, these two equations essentially define kA and kR. The constant kB can be determined from the full width at half-maximum (fwhm) of the dissociative electron attachment cross section by using graphical procedures. The effect of the k values on the fwhm is given in eq 10.23
fwhm ∝ (kR - kA)kB
(10)
Thus, for a fixed value of kR - kA, fwhm is proportional to kB. This value can also be obtained from the activation energy for thermal electron attachment, or as is done for some states in this paper, by iterations from the maximum in the absorption spectra of the anions. Procedures for Calculations A desktop computer equipped with a pentium processor was used to perform the calculations. The software used initially consisted of a QBASIC program called “Morse” which was written so that it could be modified to calculate Morse potentials, given three experimental quantities. Examples of experimental data which were used as determiners in this program include
re (A)
νe (cm-1)
De (eV)
1.411 1.900 2.691 2.870 3.264 3.165 4.041 1.990 2.650 3.349 3.457 3.757 3.662 4.231 2.280 2.960 3.895 4.164 4.130 3.892 4.428 2.670 3.385 4.103 4.626 4.626 4.106 5.413 3.000 3.881 4.546 5.072 4.998 4.445 5.999
916.6 450.0 106.2 79.3 70.6 83.0 40.6 565 249 90 71 66 78 55 323 148 46 35 41 58 41 215 115 44 24 30 46 22 135 65 31 18 22 35 15
1.60 1.31 0.10 0.05 0.05 0.07 0.04 2.52 1.38 0.14 0.08 0.08 0.11 0.07 2.00 1.21 0.17 0.08 0.09 0.15 0.10 1.58 1.055 0.22 0.08 0.10 0.19 0.10 1.320 1.021 0.230 0.080 0.100 0.250 0.080
Ev (eV)
Eabs (eV)
-1.107 0.750 0.750 3.000 3.200 6.000
1.609 1.702 (2.389) (2.388) 3.644
-0.469 2.600 2.650 5.400 6.000 10.00
1.581 1.661 (2.151) (2.244) 3.402
-0.881 0.750 1.700 3.900 5.500 8.700
1.381 1.643 (1.891) (2.244) 3.224
-0.549 0.600 1.400 2.400 2.600 3.700
1.081 1.530 (1.551) 2.118 3.104
-1.023 0.300 0.799 1.600 2.200 3.621
0.939 1.234 1.275 2.405 3.313
the bond dissociation energies, internuclear distances, vibrational frequencies, and vertical detachment energies, as well as absorbance, full width at half-maximum for dissociative electron attachment, and E* values. The variation of program Morse used in a particular calculation depended upon the experimental data available from the literature. Where experimental data were not available, extrapolated properties or reasonable estimates based on experimental data for the Rg2+ ions were included. The ground states of the neutrals and negative ions of the homonuclear diatomic halogens are well-defined experimentally.1 The values for the bond dissociation energies, De, are derived from the electron affinities.1 The vibrational frequencies, νe, are measured directly and are the solid state frequencies.24 The internuclear distances at equilibrium, re, are obtained by assuming additivity of the ionic and covalent radii.25,26 By using the experimental values for De, re, and νe as input into program Morse, values for kA, kB, and kR were obtained for the ground states. For the excited states of the negative ions, the experimental values for the electron impact vertical detachment energy2,27-30 were input into program Morse along with an estimate of the bond dissociation energy, which was obtained from the isoelectronic rare gas positive ion, and an assumed value for kB. The values for the bond dissociation energies and kB were then modified through an iterative process so that the experimental or estimated energy of the maximum in the absorption spectra was obtained.8,24-26,31,32 In the case of the D 2Σg+ state of I2-, recent theoretical data7 for the bond dissociation energy was used. The Morse parameters and the experimental quantities such as the full width at half-maximum are then determined. Once the values for kA, kB, and kR were obtained for all of the states of the negative ions, the Morse potential energy curves
9652 J. Phys. Chem., Vol. 100, No. 23, 1996
Dojahn et al.
were plotted using a program in EXCEL called “Morse Curves”. Using estimates of the Morse properties of neutral At2, and estimates of the atomic electron affinity and the excitation energy with the set of values of kA, kB, and kR for diatomic iodine and its anions, Morse potentials for homonuclear diatomic astatine and its anions are predicted. Once the parameters are obtained, then the values of kA, kB, and kR and the experimental Morse parameters for the neutral are used in another program to calculate the distribution for the dissociative electron attachment. These distributions were calculated by projection of the probability distributions of the first two vibrational levels onto the Morse potentials of the negative ions. The values at a fixed energy were divided by the energy and summed to give a value at that energy. A Boltzman distribution was used for calculation of the population of the two levels at different temperatures. In cases where there are large deviations of the distributions, the values of the other input data can be fine tuned within the range of experimental values. This was done specifically in the case of the vibrational frequency for the ground state of the diatomic bromine anion. Results and Discussion Using the calculation procedure described in the previous section, the Morse potential energy curves for the ground states of the neutral and negative ions, as well as for five excited states of the negative ions, were calculated. The ground state neutral curves are designated as 1Σ1/2,g+, the ground state of the negative ions as A 2Σ1/2,u+ [1(1/2u)], and the five excited states as B 2Π 2 2 2 g,3/2 [1(3/2g)], B Πg,1/2 [1(1/2g)], C Πu,3/2 [2(3/2u)], C Πu,1/2 [2(1/2u)], and D 2Σg+ [2(1/2g)] in the order of increasing energy at the re of the neutral. The strength of the spin orbital coupling increases dramatically with the nuclear charge so that the lighter dihalides are best described in Hund’s rule case A (the sigma pi notation), whereas the heavier ones are best described by Hund’s rule case C (the alternate notation given in square brackets).2 For the purposes of a systematic survey, it is convenient to have a uniform set of labels so that we have adopted Hund’s rule case A designations. Table 1 gives a summary of the experimental data and calculated constants for the Morse potentials of the homonuclear diatomic halogens and their anions. In the last three columns of the table are some of the values used to construct the Morse potentials. The Morse potentials for all of the halogens are presented in Figures 1-5, including the extrapolation for astatine. In Figures 6-8, the periodic variation of the data given in the last three columns is examined. The values in parentheses are estimated. In Figures 9 and 10 the calculated and experimental electron impact distributions are given for bromine and iodine. The Morse potential energy curves presented in Figures 1-4 represent a significant improvement over those developed a decade ago by Chen and Wentworth.1 The current curves are more quantitative, not only because they utilize additional experimental and theoretical data but also because the data strengthens conclusions about the internuclear distances of the ground state of the negative ions and the states which contributed to the thermal electron attachment of the halogens. All of the ground state negative ions are defined by at least four experimental data points. In addition, the comparison between the bond dissociation energies of the ground states of the negative ions with those of the diatomic rare gas positive ions led to the conclusion that the bond dissociation energies of the corresponding isoelectronic species were the same within the experimental error. This suggests that experimental values of the bond dissociation energies for the excited states of the diatomic rare gas positive
Figure 1. Morse potential energy curves for the ground state of F2, the ground state of the negative ion F2-, and five excited states of the negative ion F2-.
Figure 2. Morse potential energy curves for the ground state of Cl2 the ground state of the negative ion Cl2-, and five excited states of the negative ion Cl2-.
ions can be used to estimate values for excited states of the halogen diatomic negative ions. The bond dissociation energies as a function of row number in the periodic table are shown in Figure 6. Once the ground state is well-defined, better estimates of the energy of the electronic absorption maximum can then be used
Characterization of Homonuclear Diatomic Ions
Figure 3. Morse potential energy curves for the ground state of Br2, the ground state of the negative ion Br2-, and five excited states of the negative ion Br2-.
J. Phys. Chem., Vol. 100, No. 23, 1996 9653
Figure 5. Morse potential energy curves for the ground state of At2, the ground state of the negative ion At2-, and five excited states of the negative ion At2-.
Figure 6. Periodic trend of bond dissociation energies for the ground and excited states of the homonuclear diatomic halogen anions. The bond dissociation energy is plotted as a function of period number.
Figure 4. Morse potential energy curves for the ground state of I2, the ground state of the negative ion I2-, and five excited states of the negative ion I2-.
to define the excited states. The experimental values used in the construction are shown in Figure 7, along with the estimated values. The estimated values for the C 2Πu,1/2 states are equal to 2.26 eV, the value for iodine, 2.12 eV, increased by 0.14 eV. The values for the C 2Πu,3/2 states were referenced to the above values based on the trend for the B 2Πg,3/2 states. These
Figure 7. Periodic trend of energy of maximum absorbance for the excited states of the homonuclear diatomic halogen anions. The maximum absorbance is plotted as a function of period number.
estimates and the assignment of the experimental value of I2 to the C 2Πu,1/2 state were patterned after the considerations of Herschbach, who calculated potentials for all of the states of the negative ion states of iodine using the absorption data.21
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Figure 8. Periodic trend of vertical attachment energies for the ground and excited states of the homonuclear diatomic halogen anions. The vertical attachment energy is plotted as a function of period number.
Figure 10. Electron impact distribution plots for I2-. From Azria, Abouaf, and Tellet-Billy,2 plot a shows the distribution measured for ions formed from the states having Ω ) 1/2 and Ω ) 3/2 at a temperature of 15 K in the electron impact region. From Tam and Wong,30 plot b shows the distribution measured at a temperature of 298 K. Experimental peaks are the raw data and have not been deconvoluted. The calculated distributions have been scaled to provide a reasonable combined spectrum.
Figure 9. Electron impact distribution plots for Br2- from Kruepa and Belic. Plot a shows the distribution calculated at a temperature of 298 K, while plot b gives the distribution calculated at 50 K.
Earlier, Person constructed Morse potentials of the negative ions of chlorine, bromine, and iodine using vertical electron affinities for the ground states.19 Kruepa and Belic constructed semiempirical curves for chlorine by assuming dissociative curves for the highest three states and using the vertical detachment energies, the cross sections, and the absorption spectra of the negative ions.22 The values for the vertical electron attachment energy were also used to define the excited state curves. The experimental values are shown as a function of the row in the periodic table in Figure 8.2,25-30 Experimental values have been determined and assigned for all of the states of all of the halogens. In the case of the D 2Σg+ state of iodine, the data exist, but the assignments are complicated by the interpretation of the number of states in the Franck-Condon region of the neutral. Although the full width at half-maximum for dissociative electron attachment was not used as a defining point of the curves, in many cases, it is found to be in excellent agreement and serves as a confirming third or fourth point. An example of this can be seen in the distribution curves for bromine, which are given in Figure 9. It should be noted here that the full width at half-maximum as determined from the distribution is sig-
Figure 11. Calculated distribution of vertical electron affinities for the homonuclear diatomic halogens. The vertical lines are the experimental values of the vertical electron affinities obtained from charge transfer spectra (see text for details).
nificantly affected by temperature, with plots made at 298 K showing much broader peaks than those seen at 50 K. This is because the higher vibrational states of the neutral are populated. The lower energy peaks agree better with a temperature of 298 K, while the higher energy curves agree better with a temper-
Characterization of Homonuclear Diatomic Ions
Figure 12. Comparison of the Morse potential energy curves presented in 1985 1 and those presented in this paper.
ature of 50 K. The experimental data points were not measured directly but were obtained by deconvolution of the total ion peaks for the Π states. Thus, the peak widths are less precise for these states. The D 2Σg+ state appeared as a single peak so that the agreement with the lower temperature for this peak could indicate a low temperature in the ion source. For I2-, the electron impact distribution has been measured for ions formed from the states having Ω ) 1/2 and those with Ω ) 3/2 by achieving a temperature of 15 K in the electron impact region.2 These are shown in Figure 10a. In Figure 10b are the distributions reported by Tam and Wong. The calculated distributions are shown in Figure 10 at 298 and at 15 K. The experimental peaks are the raw data and have not been deconvoluted. The calculated distributions have been scaled to provide a reasonable combined spectrum. The general shapes of the two experimental distributions are in qualitative agreement. However, the higher resolution peaks clearly show more structure. On the basis of the angular measurements, these peaks have been assigned to the six spin states with the 2(1/2)g state assigned to the peak at 2.3 eV or below the 2(1/2)u peak which occurs around 3.0 eV. This is in contrast with the situation with the lower halogens. We have altered this assignment and suggest that there may be more than six states due to the effect of the electric field at the internuclear distance of the neutral. There may be four peaks in the Ω ) 1/2 data and possibly seven to eight peaks in the Ω ) 3/2 data, giving a total of 12 peaks corresponding to the six doubly degenerate states.7 All of the Morse potential energy curves for the homonuclear diatomic halogen anions presented herein have been constructed using three data points obtained from experimental data or reasonable approximations. These data points are the vertical detachment energies, energy of maximum absorbance, and bond dissociation energies. These points were selected because they represent data that are widely spaced over the entire curve so that the curve is well-defined for shorter as well as longer internuclear distances. This can be seen in Figures 1-4 where the points are indicated by dotted lines. In Figure 12, a comparison of the previous curves with the present ones for iodine are given. These are the ones that have been changed the greatest and have also been used the most. It is clear that the ground state curves of the anions cross the neutral curves lower on the “back side” in the present curves. Thus, this curve will be responsible for the dissociative thermal electron atttachment. In the previous curves, there was an activation energy for dissociative electron attachment. The curves in the Franck-Condon region of the neutral are more congested in the current curves than in the previous curves. This reflects the experimental data as mentioned above. A State [A 2Σ1/2,u+ or 1(1/2u)]. For the ground or A 2Σ1/2u+ state of the negative ions, five data points agree with the curves.
J. Phys. Chem., Vol. 100, No. 23, 1996 9655 In addition to the defining points, these include the bond dissociation energy of the rare gas positive ions and the activation energy for thermal electron attachment. The curves all cross the neutral in the region of the first three or four vibrational levels. This is in general agreement with a low activation energy. Two theoretical estimates of the internuclear distances for the anions of chlorine33a,b and one for fluorine3 agree with the values used in this paper. The vertical electron affinities calculated from the curves are not the precise values reported in the literature. The literature values were used to construct many of the earlier curves, including those for bromine and iodine presented by Chen and Wentworth.1 These were given by Person20 and were obtained from spectra of charge transfer complexes of the halogens with aromatic compounds. The actual reported values were between values obtained using a geometry with the halogen molecule perpendicular and parallel to the aromatic molecule. In Figure 11, we show the calculated distribution of vertical electron affinities for the various halogens. The reported values and the values obtained for the two different geometries are shown as vertical lines at the lower and higher energies. The calculated distributions encompass the values from charge transfer spectra. The only other data point which is different from literature values is the vibrational frequency for the bromine anion at 148 cm-1 versus 162 cm-1. However the experimental frequency values cover a range of 452-475 cm-1 for the fluorine anion and 225-264 cm-1 for the chlorine anion. The experimental bond orders for all of the compounds are greater than 0.5. Also, the values of kA are all greater than 1, indicating an increase in the attractive portion of the potential. It is noted that the values of kR have a larger range than those of kA. The kB values are still consistent with values obtained from Badger’s rule. All of the data for these comparisons can be found in the earlier reference.1 B States [B 2Πg,3/2 and B 2Πg,1/2 or 1(3/2g) and 1(1/2g)]. The B 2Πg,3/2 and B 2Πg,1/2 states were defined by the measured bond dissociation energy of the corresponding state for the isoelectronic rare gas positive ion, the vertical detachment energy, and the maximum in the absorption spectra. It was found that, for these states, the full width at half-maximum values obtained from the distribution plots agreed well with those calculated from the Morse potentials. The absorption distribution could also be used to check the potential energy curves. However, uncertainty about solvent and temperaure effects makes this less valuable. Thus, there are four experimental quantities obtained for these states of the halogen anions. These are the slope (fwhm) and intercept (E-vertical) in the Franck-Condon region of the neutral and the same quantities in the Franck-Condon region of the ground state of the negative ion. When the bond dissociation energies for the corresponding rare gas positive ions are considered, there are actually five data points for comparison. In the case of the B 2Πg,3/2 state of chlorine, there is an experimental estimate of 0.16 eV for the bond dissociation energy.35 Interestingly, with the exception of chlorine, the B 2Π g,3/2 states all contribute to dissociative thermal electron attachment since they cross the neutral at low energies. According to the procedure used in our earlier publication, this would constitute a sixth independent experimental data point. The dimensionless constants for all of these states are consistent. The values of kR average 2.16, while those of kA are around 0.3 and 0.4. Thus, the attractive portion is decreased and the repulsive portion is increased relative to the neutral. The increase for these states is greater than in the lower states. These constants generally tend to increase as the row in the
9656 J. Phys. Chem., Vol. 100, No. 23, 1996 periodic table increases. The kB values average 0.56, and the trends are not consistent. C States [C 2Πu,3/2 and C 2Πu,1/2 or 2(3/2u) and 2(1/2u)]. The Morse potentials for the C 2Πu,3/2, and C 2Πu,1/2 states were calculated using the bond dissociation energy of the corresponding state for the isoelectronic rare gas positive ion, the vertical detachment energy, and the maximum in the absorption spectra. For the majority of the halogens, the energy of the absorption maximum was estimated so that, in contrast with the lower states, there are only two experimental points actually measured for the halogens. These are the electron impact maximum and the corresponding slope. For the one state for iodine, there is an additional point but the position of the electron impact maximum and the distribution is less certain. The estimated values of the absorption maxima are probably accurate to (0.2 eV, while the values of the bond dissociation energy are probably accurate to (0.02 eV since the values range from 0 to 0.22 eV. With these values there are actually four points on the curve. The dimensionless constants for all of these states are relatively consistent. The values of kR average 3.4 and 3.7, while the values of kA are around 0.4 and 0.5. The kA values generally increase with the row in the periodic table, but the kR values are relatively constant. Thus, the attractive portion is decreased and the repulsive portion is increased relative to the neutral. The increase in the repulsive terms for these states is greater than in the lower states. The kB values average 0.58, but the trends are not consistent. D State [D 2Σg+ or 2(1/2g)]. The curves for the highest energy excited state, or the D 2Σg+ state, were determined by the measured bond dissociation energy of the corresponding state for the isoelectronic rare gas positive ion, the vertical detachment energy, and the maximum in the absorption spectra. The values of Delbecq et al.24 were used for consistency. However, solution spectra and photodissociation of the halogen negative ions give higher values of the energy for the absorption maximum. There are four quantities measured for the halogens besides the rare gas positive ion data, and there are five points on the curves for all of the halogens except iodine. In the case of iodine, the interpretation of the electron impact data is uncertain. However, as will be seen in the next paper, the data for Xe2+ supports the present assignments. A theoretical estimate of the bond dissociation energy for I2- is in agreement with the value of 0.1 eV used to define this state,7 which can be combined with the absorption spectra. This also supports the present assignments. The values of kR are the highest for this state and average 4.91, with the value for iodine significantly lower than the others. Thus, the attractive portion is decreased and the repulsive portion is increased relative to the neutral. The increase for these states is greater than in the lower states. The values of kA are around 0.44, close to the average for all of the other near repulsive states. The kB values average 0.48, but the trends are not consistent since iodine and fluorine have the minimum value of 0.4. The most significant criticism of the curves presented here is that they are Morse potentials and do not reflect the actual potential between ions and neutrals at large separations. However, as stated by Mulliken, “if one only knows D, r, and ν, one cannot easily do better in constructing potential energy curves than to use Morse’s function.”36 In addition, if more data are available, then it has been shown that the true potentials can be represented by modifications of the Morse potential.37 In the case of the function expressed in terms of the dimensionless constants, the repulsive or attractive portion can be modified
Dojahn et al. by expressing the constants kR or kA as a function of the internuclear distance. Variations in the vibrational frequencies can be expressed by making kB a function of the internal vibrational state. The values of the internuclear distances and frequencies for the halogens follow a consistent pattern. For a given state, the frequencies decrease with the row of the periodic table, and the internuclear distances increase with the row of the periodic table. The experimentally established values of kA, kB, and kR shown in Table 1 could be used to define the curves for astatine. However, it is also necessary to extrapolate the properties of the neutral to do this. The experimental quantities used to define the curves as seen in Figures 6-8 could also be used to estimate the properties of astatine. We have used a combination of these procedures to calculate the curves. We first used the dimensionless constants for iodine with an estimate of the bond dissociation energy, atomic electron affinity, and excitation energy to draw curves. These curves were then modified to take into account the trends in the experimental quantities and the “general appearance” of the curves. These are obviously speculative since no experimental data are available. Conclusions The negative ion states for the homonuclear diatomic halogens have been characterized by calculating the Morse potential energy curves from experimental data collected from the literature. The Morse potentials of the anions were obtained by using three dimensionless parameters, kA, kB, and kR, to modify the Morse curves of the neutral molecules. All of the curves are uniquely determined and, in many cases, overdetermined. The experimental data points used to plot the curves were chosen over a range of small and large internuclear distances in order better define the curves. Where additional experimental and theoretical data exist, these also agree well. This set of Morse curves is an improvement over the previous one presented by us in an earlier work. Using the neutral molecules as a reference, the values of the three dimensionless parameters kA, kB, and kR for the ground state of the negative ions are relatively consistent for all of the halogens. As can be seen from Table 1, ranges can be defined for these ground state parameters as follows:
1.796 g kA g 1.203 0.655 g kB g 0.591 4.060 g kR g 2.651 For the excited states of the negative ions, the ranges are defined as
0.624 g kA g 0.256 0.695 g kB g 0.380 5.847 g kR g 1.976 It can be noted that kA, the attractive term, shows an overall weaker attraction between the species in the excited states, as would be expected. In addition, kA shows a greater relative difference than that of kR, which represents the magnitude of the repulsive force. kB, which describes the vibrational frequency, is relatively consistent for both the ground and excited states of the negative ions. These ranges can be used to estimate
Characterization of Homonuclear Diatomic Ions the values of parameters for other molecules for which there is limited or no data, as was done for homonuclear diatomic astatine. The good agreement of all other data for the curves indicates that the assumption of the additivity of the radii, r ) rX_ + rX, appears valid. The bond order for the ground state of the negative ions is predicted to be 0.5 from simple qualitative molecular orbital theory, and the experimental values are all greater than this value. The data also yield bond orders for the excited states which are all greater than would be predicted from simple qualitative molecular orbital theory. Acknowledgment. The authors thank the Robert A. Welch Foundation, Grant E-0095, and the University of Houston at Clear Lake, Grant BC-0022, for support of this work. References and Notes (1) Chen, E. C. M.; Wentworth, W. E. J. Phys. Chem. 1985, 89, 4099. (2) Azria, R.; Abouaf, R.; Teillet-Billy, D. J. Phys. B 1988, 21, L213. (3) Feller, D. J. Chem. Phys. 1990, 93, 579. (4) Papanikolas, J. M.; Gord, J. R.; Levinger, N. E.; Ray, D.; Vorsa, V.; Lineberger, W. C. J. Phys. Chem. 1991, 95, 8028. (5) Papanikolas, J. M.; Vorsa, V.; Nadal, M. E.; Campagnola, P. J.; Gord, J. R.; Lineberger, W. C. J. Chem Phys. 1992, 97, 7002. (6) Papanikolas, J. M.; Maslen, P. E.; Parson, R. J. Chem. Phys. 1995, 102, 2452. (7) Maslen, P. E.; Papanikolas, J. M.; Faeder, J.; Parson, R.; ONeil, S. V. J. Chem. Phys. 1994, 101, 5731. (8) Walhout, P. K.; Alfano, J. C.; Thakur, K. A. M.; Barbara, P. F. J. Phys. Chem. 1995, 99, 7568. (9) Nelson, T. O.; Setser, D. W.; Qin, J. J. Phys. Chem. 1993, 97, 2585. (10) Ma, N. L.; Li, W. K.; Ng, C. Y. J. Chem. Phys. 1993, 99, 3617. (11) Carrington, A.; Pyne, C. H.; Knowles, P. J. J. Chem. Phys. 1995, 102, 5979. (12) Moseley, J. T.; Saxon, R. P.; Huber, B. A.; Cosby, P. C.; Abouaf, R.; Tadjeddine, M. J. Chem. Phys. 1977, 67, 1659.
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